From 1b51f5a027d95a387dfaf3e46ea0c84beb0c2ce9 Mon Sep 17 00:00:00 2001 From: Nikhil Khedekar Date: Fri, 31 Jul 2026 11:58:14 +0000 Subject: [PATCH 1/7] Add Unit3::scaled to reconstruct a vector from direction and magnitude Returns magnitude * unitVector() with analytic Jacobians wrt both the direction (3x2, through the tangent basis) and the magnitude (3x1). This is the shared chain rule needed whenever a physical vector is parametrized as a known or estimated scalar magnitude times a Unit3 direction, e.g. magnetic field (MagFactor3) or gravity factors. --- gtsam/geometry/Unit3.cpp | 10 ++++++++++ gtsam/geometry/Unit3.h | 15 ++++++++++++++- gtsam/geometry/tests/testUnit3.cpp | 20 ++++++++++++++++++++ 3 files changed, 44 insertions(+), 1 deletion(-) diff --git a/gtsam/geometry/Unit3.cpp b/gtsam/geometry/Unit3.cpp index c957f9c76d..02e7fe9e69 100644 --- a/gtsam/geometry/Unit3.cpp +++ b/gtsam/geometry/Unit3.cpp @@ -154,6 +154,16 @@ Vector3 Unit3::unitVector(OptionalJacobian<3, 2> H) const { return p_; } +/* ************************************************************************* */ +Vector3 Unit3::scaled(double magnitude, OptionalJacobian<3, 2> H_this, + OptionalJacobian<3, 1> H_magnitude) const { + if (H_this) + *H_this = magnitude * basis(); + if (H_magnitude) + *H_magnitude = p_; + return magnitude * p_; +} + /* ************************************************************************* */ std::ostream& operator<<(std::ostream& os, const Unit3& pair) { os << pair.p_ << endl; diff --git a/gtsam/geometry/Unit3.h b/gtsam/geometry/Unit3.h index 75ec07ce05..335272f4c7 100644 --- a/gtsam/geometry/Unit3.h +++ b/gtsam/geometry/Unit3.h @@ -136,7 +136,20 @@ class GTSAM_EXPORT Unit3 { /// Return unit-norm Vector Vector3 unitVector(OptionalJacobian<3, 2> H = {}) const; - /// Return scaled direction as Point3 + /** + * Return this direction scaled by a magnitude, i.e. magnitude * unitVector(). + * Useful to reconstruct a physical vector from a direction and a known (or + * separately estimated) magnitude, e.g. a gravity or magnetic field vector. + * @param magnitude scale applied to the unit vector + * @param H_this optional 3x2 Jacobian wrt this direction + * @param H_magnitude optional 3x1 Jacobian wrt the magnitude + * @sa operator*(double, const Unit3&), which returns the same value + * without Jacobians + */ + Vector3 scaled(double magnitude, OptionalJacobian<3, 2> H_this = {}, + OptionalJacobian<3, 1> H_magnitude = {}) const; + + /// Return scaled direction as Point3 (no Jacobians; see scaled()) friend Point3 operator*(double s, const Unit3& d) { return Point3(s * d.p_); } diff --git a/gtsam/geometry/tests/testUnit3.cpp b/gtsam/geometry/tests/testUnit3.cpp index a9f6cf7af5..b872219d92 100644 --- a/gtsam/geometry/tests/testUnit3.cpp +++ b/gtsam/geometry/tests/testUnit3.cpp @@ -56,6 +56,26 @@ TEST(Unit3, point3) { } } +//******************************************************************************* +static Vector3 scaled_(const Unit3& p, const double& magnitude) { + return p.scaled(magnitude); +} + +TEST(Unit3, scaled) { + const Unit3 d(1, 2, 3); + const double magnitude = 9.81; + Matrix32 actualH_d; + Matrix31 actualH_m; + const Vector3 actual = d.scaled(magnitude, actualH_d, actualH_m); + EXPECT(assert_equal(Vector3(magnitude * d.unitVector()), actual, 1e-9)); + const Matrix expectedH_d = + numericalDerivative21(scaled_, d, magnitude); + const Matrix expectedH_m = + numericalDerivative22(scaled_, d, magnitude); + EXPECT(assert_equal(expectedH_d, Matrix(actualH_d), 1e-5)); + EXPECT(assert_equal(expectedH_m, Matrix(actualH_m), 1e-5)); +} + //******************************************************************************* static Unit3 rotate_(const Rot3& R, const Unit3& p) { return R * p; } From b8c97a4e94888077215b7a47ded3c41d3f68c567 Mon Sep 17 00:00:00 2001 From: Nikhil Khedekar Date: Fri, 31 Jul 2026 11:58:14 +0000 Subject: [PATCH 2/7] Use Unit3::scaled in MagFactor3 (no functional change) Replaces the inline scale-times-basis Jacobian assembly with the shared Unit3::scaled helper. Covered by the unchanged testMagFactor assertions. --- gtsam/navigation/MagFactor.h | 18 +++++++++--------- 1 file changed, 9 insertions(+), 9 deletions(-) diff --git a/gtsam/navigation/MagFactor.h b/gtsam/navigation/MagFactor.h index 4f497d503e..eaf5d3cec9 100644 --- a/gtsam/navigation/MagFactor.h +++ b/gtsam/navigation/MagFactor.h @@ -209,16 +209,16 @@ class MagFactor3: public NoiseModelFactorN { const Point3& bias, OptionalMatrixType H1, OptionalMatrixType H2, OptionalMatrixType H3) const override { // measured bM = nRb� * nM + b, where b is unknown bias - Unit3 rotated = bRn_.rotate(direction, OptionalNone, H2); - Point3 hx = scale * rotated.point3() + bias; + Matrix22 D_rotated_direction; + Unit3 rotated = bRn_.rotate(direction, {}, H2 ? &D_rotated_direction : 0); + Matrix32 D_hx_rotated; + Matrix31 D_hx_scale; + Point3 hx = rotated.scaled(scale, H2 ? &D_hx_rotated : 0, + H1 ? &D_hx_scale : 0) + bias; if (H1) - *H1 = rotated.point3(); - if (H2) // H2 is 2*2, but we need 3*2 - { - Matrix H; - rotated.point3(H); - *H2 = scale * H * (*H2); - } + *H1 = D_hx_scale; + if (H2) + *H2 = D_hx_rotated * D_rotated_direction; if (H3) *H3 = I_3x3; return (hx - measured_); From 7ffaa59b37457e33deacf2e59b57467308f7e5e9 Mon Sep 17 00:00:00 2001 From: Nikhil Khedekar Date: Sat, 1 Aug 2026 10:29:54 +0000 Subject: [PATCH 3/7] Add VectorNormFactor constraining the norm of a vector variable Unary factor with error = ||v|| - norm, generalized over the vector dimension. Typical use is a magnitude pseudo-observation on a physical vector whose direction and magnitude are entangled in one variable, eg. an estimated gravity vector [Lupton and Sukkarieh, TRO 2012] or a local magnetic field vector (MagFactor2). The Jacobian is zeroed below a documented threshold around the (non-differentiable) origin, so variables must not be initialized at exactly zero. The N=3 instantiation is exposed in the wrapper as VectorNormFactor3. --- gtsam/nonlinear/VectorNormFactor.h | 151 ++++++++++++++++++ gtsam/nonlinear/nonlinear.i | 13 ++ .../nonlinear/tests/testVectorNormFactor.cpp | 128 +++++++++++++++ 3 files changed, 292 insertions(+) create mode 100644 gtsam/nonlinear/VectorNormFactor.h create mode 100644 gtsam/nonlinear/tests/testVectorNormFactor.cpp diff --git a/gtsam/nonlinear/VectorNormFactor.h b/gtsam/nonlinear/VectorNormFactor.h new file mode 100644 index 0000000000..5c603eeb43 --- /dev/null +++ b/gtsam/nonlinear/VectorNormFactor.h @@ -0,0 +1,151 @@ +/* ---------------------------------------------------------------------------- + + * GTSAM Copyright 2010, Georgia Tech Research Corporation, + * Atlanta, Georgia 30332-0415 + * All Rights Reserved + * Authors: Frank Dellaert, et al. (see THANKS for the full author list) + + * See LICENSE for the license information + + * -------------------------------------------------------------------------- */ + +/** + * @file VectorNormFactor.h + * @brief Factor constraining the norm of a vector-space variable + * @date July 2026 + */ + +#pragma once + +#include + +namespace gtsam { + +/** + * Unary factor constraining the norm of an N-dimensional vector-space variable + * to a given value, with error = ||v|| - norm. + * + * A typical use is a magnitude pseudo-observation on a physical vector whose + * direction and magnitude are entangled in a single variable, e.g. an + * estimated gravity vector (see ImuFactorWithGravityVector and + * [Lupton and Sukkarieh, TRO 2012]) or a local magnetic field vector + * (see MagFactor2). Add it once per variable: adding it per measurement + * factor would count the same prior knowledge multiple times. + * + * @warning The error is not differentiable at ||v|| = 0; below kMinNorm the + * Jacobian is set to zero, so the factor exerts no pull there. In particular, + * an optimizer whose initial estimate for the variable is exactly zero will + * receive no gradient from this factor and the variable will not move. + * Always initialize the variable with a non-zero guess. + * + * This is a hand-written factor rather than an ExpressionFactor over norm3 + * for discoverability and to avoid the expression-tree evaluation overhead at + * every linearization; see gtsam/slam/expressions.h for the expression + * building blocks if composition with other expressions is needed. + * + * With a noiseModel::Constrained model this acts as a hard constraint under + * QR-based elimination (not recommended with Cholesky factorization). If the + * norm is known exactly, prefer a parametrization that fixes it instead, + * e.g. Unit3 and a fixed magnitude (see ImuFactorWithGravityDirection). + * + * @ingroup nonlinear + */ +template +class VectorNormFactor : public NoiseModelFactorN> { + static_assert(N > 0, "VectorNormFactor requires a fixed positive dimension"); + + public: + typedef Eigen::Matrix VectorN; + + private: + typedef VectorNormFactor This; + typedef NoiseModelFactorN Base; + + double norm_; ///< desired norm of the vector + + public: + /// Below this norm the error is treated as non-differentiable and the + /// Jacobian is zero (see class warning). + static constexpr double kMinNorm = 1e-10; + + // Provide access to the Matrix& version of evaluateError: + using Base::evaluateError; + + /** Shorthand for a smart pointer to a factor */ + typedef std::shared_ptr shared_ptr; + + /** Default constructor - only use for serialization */ + VectorNormFactor() : norm_(0.0) {} + + /** + * Constructor + * @param key of the vector-space variable + * @param norm the desired norm of the vector + * @param model of the (1-dimensional) noise on the norm error + */ + VectorNormFactor(Key key, double norm, const SharedNoiseModel& model) + : Base(model, key), norm_(norm) {} + + ~VectorNormFactor() override {} + + /// @return a deep copy of this factor + NonlinearFactor::shared_ptr clone() const override { + return std::make_shared(*this); + } + + /// @name Testable + /// @{ + void print(const std::string& s = "", + const KeyFormatter& keyFormatter = DefaultKeyFormatter) const override { + std::cout << (s.empty() ? s : s + " ") << "VectorNormFactor on " + << keyFormatter(this->template key<1>()) << ", norm = " << norm_ + << std::endl; + this->noiseModel_->print(" noise model: "); + } + + bool equals(const NonlinearFactor& expected, double tol = 1e-9) const override { + const This* e = dynamic_cast(&expected); + return e != nullptr && Base::equals(*e, tol) && + std::abs(norm_ - e->norm_) < tol; + } + /// @} + + /// The desired norm + double norm() const { return norm_; } + + /// vector of errors: ||v|| - norm + Vector evaluateError(const VectorN& v, OptionalMatrixType H) const override { + const double vnorm = v.norm(); + if (H) { + if (vnorm > kMinNorm) { + *H = v.transpose() / vnorm; + } else { + // The norm is not differentiable at the origin. Return a zero + // Jacobian: the factor exerts no pull on a (near-)zero vector. + H->setZero(1, N); + } + } + return Vector1(vnorm - norm_); + } + + private: +#if GTSAM_ENABLE_BOOST_SERIALIZATION + /** Serialization function */ + friend class boost::serialization::access; + template + void serialize(ARCHIVE& ar, const unsigned int /*version*/) { + ar& boost::serialization::make_nvp( + "NoiseModelFactor1", boost::serialization::base_object(*this)); + ar& BOOST_SERIALIZATION_NVP(norm_); + } +#endif +}; + +/// The most common instantiation, eg. for gravity or magnetic field vectors +using VectorNormFactor3 = VectorNormFactor<3>; + +/// traits +template +struct traits> : public Testable> {}; + +} // namespace gtsam diff --git a/gtsam/nonlinear/nonlinear.i b/gtsam/nonlinear/nonlinear.i index 6d24a716f4..ba4549b27c 100644 --- a/gtsam/nonlinear/nonlinear.i +++ b/gtsam/nonlinear/nonlinear.i @@ -876,6 +876,19 @@ virtual class ConcentratedGaussian : gtsam::ExtendedPriorFactor { This operator*(const This& other) const; }; +#include +virtual class VectorNormFactor3 : gtsam::NoiseModelFactor { + VectorNormFactor3(gtsam::Key key, double norm, + const gtsam::noiseModel::Base* noiseModel); + + // Standard Interface + double norm() const; + gtsam::Vector evaluateError(const gtsam::Point3& v); + + // enabling serialization functionality + void serialize() const; +}; + #include template +#include +#include +#include +#include +#include +#include +#include + +#if GTSAM_ENABLE_BOOST_SERIALIZATION +#include +#endif + +using namespace std; +using namespace gtsam; +using symbol_shorthand::G; + +static const SharedNoiseModel kModel = noiseModel::Isotropic::Sigma(1, 0.1); + +/* ************************************************************************* */ +TEST(VectorNormFactor, Error) { + VectorNormFactor<3> factor(G(0), 5.0, kModel); + const Vector3 v(3.0, 0.0, 4.0); // norm 5 + EXPECT(assert_equal(Vector1(0.0), factor.evaluateError(v))); + EXPECT(assert_equal(Vector1(1.0), factor.evaluateError(Vector3(0, 0, 6)))); +} + +/* ************************************************************************* */ +TEST(VectorNormFactor, Jacobian) { + VectorNormFactor<3> factor(G(0), 9.81, kModel); + const Vector3 v(0.3, -0.2, -9.7); + Matrix actualH; + factor.evaluateError(v, actualH); + const Matrix expectedH = numericalDerivative11( + [&factor](const Vector3& x) { return factor.evaluateError(x); }, v); + EXPECT(assert_equal(expectedH, actualH, 1e-5)); +} + +/* ************************************************************************* */ +TEST(VectorNormFactor, JacobianDimension2) { + VectorNormFactor<2> factor(G(0), 2.0, kModel); + const Vector2 v(1.0, -1.5); + Matrix actualH; + factor.evaluateError(v, actualH); + const Matrix expectedH = numericalDerivative11( + [&factor](const Vector2& x) { return factor.evaluateError(x); }, v); + EXPECT(assert_equal(expectedH, actualH, 1e-5)); +} + +/* ************************************************************************* */ +TEST(VectorNormFactor, ZeroVector) { + // The norm is not differentiable at the origin: the error must still be + // finite and the Jacobian zero (no NaNs). + VectorNormFactor<3> factor(G(0), 9.81, kModel); + Matrix actualH; + const Vector error = factor.evaluateError(Vector3::Zero(), actualH); + EXPECT(assert_equal(Vector1(-9.81), error)); + EXPECT(assert_equal(Matrix(Matrix::Zero(1, 3)), actualH)); +} + +/* ************************************************************************* */ +TEST(VectorNormFactor, Optimization) { + // A loose vector prior fixes the direction; the norm factor should pull the + // magnitude to the target along that direction. + NonlinearFactorGraph graph; + const Vector3 direction = Vector3(1.0, 1.0, 1.0).normalized(); + graph.emplace_shared>( + G(0), Vector3(8.0 * direction), noiseModel::Isotropic::Sigma(3, 10.0)); + graph.emplace_shared>( + G(0), 9.81, noiseModel::Isotropic::Sigma(1, 1e-3)); + + Values initial; + initial.insert(G(0), Vector3(8.0 * direction)); + const Values result = LevenbergMarquardtOptimizer(graph, initial).optimize(); + + const Vector3 optimized = result.at(G(0)); + DOUBLES_EQUAL(9.81, optimized.norm(), 1e-5); + EXPECT(assert_equal(direction, Vector3(optimized.normalized()), 1e-3)); +} + +/* ************************************************************************* */ +TEST(VectorNormFactor, Equals) { + VectorNormFactor<3> factor1(G(0), 9.81, kModel); + VectorNormFactor<3> factor2(G(0), 9.81, kModel); + VectorNormFactor<3> factor3(G(0), 1.0, kModel); + EXPECT(factor1.equals(factor2)); + EXPECT(!factor1.equals(factor3)); + // Comparing against a different factor type must not crash: + PriorFactor prior(G(0), Vector3::Zero(), + noiseModel::Isotropic::Sigma(3, 1.0)); + EXPECT(!factor1.equals(prior)); +} + +/* ************************************************************************* */ +#if GTSAM_ENABLE_BOOST_SERIALIZATION +BOOST_CLASS_EXPORT_GUID(noiseModel::Isotropic, "gtsam_noiseModel_Isotropic") + +TEST(VectorNormFactor, Serialization) { + using namespace gtsam::serializationTestHelpers; + VectorNormFactor<3> factor(G(0), 9.81, kModel); + EXPECT(equalsObj>(factor)); + EXPECT(equalsXML>(factor)); + EXPECT(equalsBinary>(factor)); +} +#endif + +/* ************************************************************************* */ +int main() { + TestResult tr; + return TestRegistry::runAllTests(tr); +} +/* ************************************************************************* */ From 932d3edb9871078642fe0a3724e0aa6eb1c3e8b2 Mon Sep 17 00:00:00 2001 From: Nikhil Khedekar Date: Thu, 30 Jul 2026 16:38:04 +0000 Subject: [PATCH 4/7] Add gravity-vector Jacobians to correctPIM and gravity overloads to PreintegrationBase NavState::correctPIM gains an optional 9x3 Jacobian of the tangent update wrt the nav-frame gravity vector (the rotation rows are zero; the shared unrotate Jacobian is now computed once). PreintegrationBase gains predict/computeError/computeErrorAndJacobians overloads taking an explicit gravity vector with the corresponding 9x3 Jacobians, so that factors can treat gravity as an optimized variable. The existing signatures delegate to them with the gravity vector from params and are unchanged in behavior. --- gtsam/navigation/NavState.cpp | 26 +++++--- gtsam/navigation/NavState.h | 3 +- gtsam/navigation/PreintegrationBase.cpp | 65 +++++++++++++++---- gtsam/navigation/PreintegrationBase.h | 39 +++++++++-- gtsam/navigation/tests/testImuFactor.cpp | 63 +++++++++++++++++- .../tests/testManifoldPreintegration.cpp | 7 +- gtsam/navigation/tests/testNavState.cpp | 23 ++++++- .../tests/testTangentPreintegration.cpp | 7 +- 8 files changed, 200 insertions(+), 33 deletions(-) diff --git a/gtsam/navigation/NavState.cpp b/gtsam/navigation/NavState.cpp index 54ab9e678f..6ee530ed6a 100644 --- a/gtsam/navigation/NavState.cpp +++ b/gtsam/navigation/NavState.cpp @@ -294,36 +294,46 @@ Vector9 NavState::coriolis(double dt, const Vector3& omega, bool secondOrder, Vector9 NavState::correctPIM(const Vector9& pim, double dt, const Vector3& n_gravity, const std::optional& omegaCoriolis, bool use2ndOrderCoriolis, OptionalJacobian<9, 9> H1, - OptionalJacobian<9, 9> H2) const { + OptionalJacobian<9, 9> H2, OptionalJacobian<9, 3> H3) const { const Rot3& nRb = R_; const Velocity3 n_v = t_.col(1); // derivative is Ri ! const double dt22 = 0.5 * dt * dt; Vector9 xi; - Matrix3 D_dP_Ri1, D_dP_Ri2, D_dP_nv, D_dV_Ri; + Matrix3 D_dP_Ri1, D_dP_Ri2, D_dP_nv; + // The gravity contributions to the position and velocity rows share both + // the unrotated vector and the Jacobians wrt rotation and wrt gravity. + Matrix3 D_bGravity_nGravity; + const Vector3 b_gravity = nRb.unrotate(n_gravity, H1 ? &D_dP_Ri2 : 0, + H3 ? &D_bGravity_nGravity : 0); dR(xi) = dR(pim); dP(xi) = dP(pim) + dt * nRb.unrotate(n_v, H1 ? &D_dP_Ri1 : 0, H2 ? &D_dP_nv : 0) - + dt22 * nRb.unrotate(n_gravity, H1 ? &D_dP_Ri2 : 0); - dV(xi) = dV(pim) + dt * nRb.unrotate(n_gravity, H1 ? &D_dV_Ri : 0); + + dt22 * b_gravity; + dV(xi) = dV(pim) + dt * b_gravity; if (omegaCoriolis) { xi += coriolis(dt, *omegaCoriolis, use2ndOrderCoriolis, H1); } - if (H1 || H2) { - Matrix3 Ri = nRb.matrix(); - + if (H1 || H2 || H3) { if (H1) { + const Matrix3 Ri = nRb.matrix(); if (!omegaCoriolis) H1->setZero(); // if coriolis H1 is already initialized D_t_R(H1) += dt * D_dP_Ri1 + dt22 * D_dP_Ri2; D_t_v(H1) += dt * D_dP_nv * Ri; - D_v_R(H1) += dt * D_dV_Ri; + D_v_R(H1) += dt * D_dP_Ri2; } if (H2) { H2->setIdentity(); } + if (H3) { + // The rotation rows do not depend on gravity: + H3->block<3, 3>(0, 0).setZero(); + H3->block<3, 3>(3, 0) = dt22 * D_bGravity_nGravity; + H3->block<3, 3>(6, 0) = dt * D_bGravity_nGravity; + } } return xi; diff --git a/gtsam/navigation/NavState.h b/gtsam/navigation/NavState.h index 62e76bef58..63a7ebe9ce 100644 --- a/gtsam/navigation/NavState.h +++ b/gtsam/navigation/NavState.h @@ -241,7 +241,8 @@ class GTSAM_EXPORT NavState : public ExtendedPose3<2, NavState> { Vector9 correctPIM(const Vector9& pim, double dt, const Vector3& n_gravity, const std::optional& omegaCoriolis, bool use2ndOrderCoriolis = false, OptionalJacobian<9, 9> H1 = {}, - OptionalJacobian<9, 9> H2 = {}) const; + OptionalJacobian<9, 9> H2 = {}, + OptionalJacobian<9, 3> H3 = {}) const; /// @} diff --git a/gtsam/navigation/PreintegrationBase.cpp b/gtsam/navigation/PreintegrationBase.cpp index a4427f8e3c..3fb80c4a7f 100644 --- a/gtsam/navigation/PreintegrationBase.cpp +++ b/gtsam/navigation/PreintegrationBase.cpp @@ -115,62 +115,91 @@ void PreintegrationBase::integrateMeasurement(const Vector3& measuredAcc, //------------------------------------------------------------------------------ NavState PreintegrationBase::predict(const NavState& state_i, - const imuBias::ConstantBias& bias_i, OptionalJacobian<9, 9> H1, - OptionalJacobian<9, 6> H2) const { + const imuBias::ConstantBias& bias_i, const Vector3& n_gravity, + OptionalJacobian<9, 9> H1, OptionalJacobian<9, 6> H2, + OptionalJacobian<9, 3> H3) const { Matrix96 D_biasCorrected_bias; Vector9 biasCorrected = biasCorrectedDelta(bias_i, H2 ? &D_biasCorrected_bias : nullptr); // Correct for initial velocity and gravity Matrix9 D_delta_state, D_delta_biasCorrected; - Vector9 xi = state_i.correctPIM(biasCorrected, deltaTij_, p().n_gravity, + Matrix93 D_delta_gravity; + Vector9 xi = state_i.correctPIM(biasCorrected, deltaTij_, n_gravity, p().omegaCoriolis, p().use2ndOrderCoriolis, H1 ? &D_delta_state : nullptr, - H2 ? &D_delta_biasCorrected : nullptr); + H2 ? &D_delta_biasCorrected : nullptr, + H3 ? &D_delta_gravity : nullptr); // Use retract to get back to NavState manifold Matrix9 D_predict_state, D_predict_delta; NavState state_j = state_i.retract(xi, H1 ? &D_predict_state : nullptr, - H1 || H2 ? &D_predict_delta : nullptr); + H1 || H2 || H3 ? &D_predict_delta : nullptr); if (H1) *H1 = D_predict_state + D_predict_delta * D_delta_state; if (H2) *H2 = D_predict_delta * D_delta_biasCorrected * D_biasCorrected_bias; + if (H3) + *H3 = D_predict_delta * D_delta_gravity; return state_j; } +//------------------------------------------------------------------------------ +NavState PreintegrationBase::predict(const NavState& state_i, + const imuBias::ConstantBias& bias_i, OptionalJacobian<9, 9> H1, + OptionalJacobian<9, 6> H2) const { + return predict(state_i, bias_i, p().n_gravity, H1, H2, nullptr); +} + //------------------------------------------------------------------------------ Vector9 PreintegrationBase::computeError(const NavState& state_i, const NavState& state_j, const imuBias::ConstantBias& bias_i, + const Vector3& n_gravity, OptionalJacobian<9, 9> H1, OptionalJacobian<9, 9> H2, - OptionalJacobian<9, 6> H3) const { + OptionalJacobian<9, 6> H3, + OptionalJacobian<9, 3> H4) const { // Predict state at time j Matrix9 D_predict_state_i; Matrix96 D_predict_bias_i; + Matrix93 D_predict_gravity; NavState predictedState_j = predict( - state_i, bias_i, H1 ? &D_predict_state_i : 0, H3 ? &D_predict_bias_i : 0); + state_i, bias_i, n_gravity, H1 ? &D_predict_state_i : 0, + H3 ? &D_predict_bias_i : 0, H4 ? &D_predict_gravity : 0); // Calculate error Matrix9 D_error_state_j, D_error_predict; Vector9 error = state_j.localCoordinates(predictedState_j, H2 ? &D_error_state_j : 0, - H1 || H3 ? &D_error_predict : 0); + H1 || H3 || H4 ? &D_error_predict : 0); if (H1) *H1 << D_error_predict * D_predict_state_i; if (H2) *H2 << D_error_state_j; if (H3) *H3 << D_error_predict * D_predict_bias_i; + if (H4) *H4 << D_error_predict * D_predict_gravity; return error; } +//------------------------------------------------------------------------------ +Vector9 PreintegrationBase::computeError(const NavState& state_i, + const NavState& state_j, + const imuBias::ConstantBias& bias_i, + OptionalJacobian<9, 9> H1, + OptionalJacobian<9, 9> H2, + OptionalJacobian<9, 6> H3) const { + return computeError(state_i, state_j, bias_i, p().n_gravity, H1, H2, H3, + nullptr); +} + //------------------------------------------------------------------------------ Vector9 PreintegrationBase::computeErrorAndJacobians(const Pose3& pose_i, const Vector3& vel_i, const Pose3& pose_j, const Vector3& vel_j, - const imuBias::ConstantBias& bias_i, OptionalJacobian<9, 6> H1, - OptionalJacobian<9, 3> H2, OptionalJacobian<9, 6> H3, - OptionalJacobian<9, 3> H4, OptionalJacobian<9, 6> H5) const { + const imuBias::ConstantBias& bias_i, const Vector3& n_gravity, + OptionalJacobian<9, 6> H1, OptionalJacobian<9, 3> H2, + OptionalJacobian<9, 6> H3, OptionalJacobian<9, 3> H4, + OptionalJacobian<9, 6> H5, OptionalJacobian<9, 3> H6) const { // Note that derivative of constructors below is not identity for velocity, but // a 9*3 matrix == Z_3x3, Z_3x3, state.R().transpose() @@ -179,8 +208,8 @@ Vector9 PreintegrationBase::computeErrorAndJacobians(const Pose3& pose_i, // Predict state at time j Matrix9 D_error_state_i, D_error_state_j; - Vector9 error = computeError(state_i, state_j, bias_i, - H1 || H2 ? &D_error_state_i : 0, H3 || H4 ? &D_error_state_j : 0, H5); + Vector9 error = computeError(state_i, state_j, bias_i, n_gravity, + H1 || H2 ? &D_error_state_i : 0, H3 || H4 ? &D_error_state_j : 0, H5, H6); // Separate out derivatives in terms of 5 arguments // Note that doing so requires special treatment of velocities, as when treated as @@ -195,6 +224,16 @@ Vector9 PreintegrationBase::computeErrorAndJacobians(const Pose3& pose_i, return error; } +//------------------------------------------------------------------------------ +Vector9 PreintegrationBase::computeErrorAndJacobians(const Pose3& pose_i, + const Vector3& vel_i, const Pose3& pose_j, const Vector3& vel_j, + const imuBias::ConstantBias& bias_i, OptionalJacobian<9, 6> H1, + OptionalJacobian<9, 3> H2, OptionalJacobian<9, 6> H3, + OptionalJacobian<9, 3> H4, OptionalJacobian<9, 6> H5) const { + return computeErrorAndJacobians(pose_i, vel_i, pose_j, vel_j, bias_i, + p().n_gravity, H1, H2, H3, H4, H5, nullptr); +} + //------------------------------------------------------------------------------ } // namespace gtsam diff --git a/gtsam/navigation/PreintegrationBase.h b/gtsam/navigation/PreintegrationBase.h index b902c94210..89b9ae8d6c 100644 --- a/gtsam/navigation/PreintegrationBase.h +++ b/gtsam/navigation/PreintegrationBase.h @@ -150,26 +150,57 @@ class GTSAM_EXPORT PreintegrationBase { virtual Vector9 biasCorrectedDelta(const imuBias::ConstantBias& bias_i, OptionalJacobian<9, 6> H = {}) const = 0; - /// Predict state at time j + /** + * Predict state at time j, for a given gravity vector in the nav frame. + * This overload allows gravity to differ from params (eg. when gravity is + * an optimized variable, see ImuFactorWithGravityDirection and + * ImuFactorWithGravityVector); H3 is the Jacobian wrt that vector. + */ + NavState predict(const NavState& state_i, const imuBias::ConstantBias& bias_i, + const Vector3& n_gravity, + OptionalJacobian<9, 9> H1 = {}, + OptionalJacobian<9, 6> H2 = {}, + OptionalJacobian<9, 3> H3 = {}) const; + + /// Predict state at time j, using the gravity vector from params NavState predict(const NavState& state_i, const imuBias::ConstantBias& bias_i, OptionalJacobian<9, 9> H1 = {}, OptionalJacobian<9, 6> H2 = {}) const; - /// Calculate error given navStates + /// Calculate error given navStates and a gravity vector in the nav frame + Vector9 computeError(const NavState& state_i, const NavState& state_j, + const imuBias::ConstantBias& bias_i, + const Vector3& n_gravity, + OptionalJacobian<9, 9> H1, OptionalJacobian<9, 9> H2, + OptionalJacobian<9, 6> H3, + OptionalJacobian<9, 3> H4) const; + + /// Calculate error given navStates, using the gravity vector from params Vector9 computeError(const NavState& state_i, const NavState& state_j, const imuBias::ConstantBias& bias_i, OptionalJacobian<9, 9> H1, OptionalJacobian<9, 9> H2, OptionalJacobian<9, 6> H3) const; + /** + * Compute errors w.r.t. preintegrated measurements and jacobians + * wrt pose_i, vel_i, bias_i, pose_j, bias_j and the given gravity vector + */ + Vector9 computeErrorAndJacobians(const Pose3& pose_i, const Vector3& vel_i, + const Pose3& pose_j, const Vector3& vel_j, + const imuBias::ConstantBias& bias_i, const Vector3& n_gravity, + OptionalJacobian<9, 6> H1 = {}, OptionalJacobian<9, 3> H2 = {}, + OptionalJacobian<9, 6> H3 = {}, OptionalJacobian<9, 3> H4 = {}, + OptionalJacobian<9, 6> H5 = {}, OptionalJacobian<9, 3> H6 = {}) const; + /** * Compute errors w.r.t. preintegrated measurements and jacobians * wrt pose_i, vel_i, bias_i, pose_j, bias_j */ Vector9 computeErrorAndJacobians(const Pose3& pose_i, const Vector3& vel_i, const Pose3& pose_j, const Vector3& vel_j, - const imuBias::ConstantBias& bias_i, + const imuBias::ConstantBias& bias_i, OptionalJacobian<9, 6> H1 = {}, OptionalJacobian<9, 3> H2 = {}, - OptionalJacobian<9, 6> H3 = {}, OptionalJacobian<9, 3> H4 = {}, + OptionalJacobian<9, 6> H3 = {}, OptionalJacobian<9, 3> H4 = {}, OptionalJacobian<9, 6> H5 = {}) const; private: diff --git a/gtsam/navigation/tests/testImuFactor.cpp b/gtsam/navigation/tests/testImuFactor.cpp index 203d90a270..f4c3b7225a 100644 --- a/gtsam/navigation/tests/testImuFactor.cpp +++ b/gtsam/navigation/tests/testImuFactor.cpp @@ -123,7 +123,12 @@ TEST_PIM(ImuFactor, PreintegratedMeasurements) { Matrix9 aH1, aH2; Matrix96 aH3; actual.computeError(x1, x2, bias, aH1, aH2, aH3); - auto f = std::bind(&PreintegrationBase::computeError, actual, + // Select the overload without the gravity parameter: + using ComputeErrorNoGravity = Vector9 (PreintegrationBase::*)( + const NavState&, const NavState&, const imuBias::ConstantBias&, + OptionalJacobian<9, 9>, OptionalJacobian<9, 9>, + OptionalJacobian<9, 6>) const; + auto f = std::bind(static_cast(&PreintegrationBase::computeError), actual, std::placeholders::_1, std::placeholders::_2, std::placeholders::_3, nullptr, nullptr, nullptr); EXPECT(assert_equal(numericalDerivative31(f, x1, x2, bias), aH1, 1e-9)); @@ -167,6 +172,10 @@ static const NavState state2(x2, v2); /* ************************************************************************* */ TEST_PIM(ImuFactor, PreintegrationBaseMethods) { + // Select the overload without the gravity parameter: + using PredictNoGravity = NavState (PreintegrationBase::*)( + const NavState&, const imuBias::ConstantBias&, OptionalJacobian<9, 9>, + OptionalJacobian<9, 6>) const; using namespace common; auto p = testing::Params(); p->omegaCoriolis = Vector3(0.02, 0.03, 0.04); @@ -188,15 +197,63 @@ TEST_PIM(ImuFactor, PreintegrationBaseMethods) { Matrix96 aH2; NavState predictedState = pim.predict(state1, kZeroBias, aH1, aH2); Matrix eH1 = numericalDerivative11( - std::bind(&PreintegrationBase::predict, pim, std::placeholders::_1, + std::bind(static_cast(&PreintegrationBase::predict), pim, std::placeholders::_1, kZeroBias, nullptr, nullptr), state1); EXPECT(assert_equal(eH1, aH1)); Matrix eH2 = numericalDerivative11( - std::bind(&PreintegrationBase::predict, pim, state1, + std::bind(static_cast(&PreintegrationBase::predict), pim, state1, std::placeholders::_1, nullptr, nullptr), kZeroBias); EXPECT(assert_equal(eH2, aH2)); } +/* ************************************************************************* */ +TEST_PIM(ImuFactor, PredictWithGravityVector) { + using namespace common; + PIM pim(testing::Params(), kZeroBiasHat); + pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); + pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); + + // A gravity vector tilted away from the params' vector, with a different + // magnitude: + const Vector3 tilted_gravity = Vector3(0.5, -0.3, 9.7); + + // The gravity overload with the params' gravity must match the legacy one: + EXPECT(assert_equal(pim.predict(state1, kZeroBias), + pim.predict(state1, kZeroBias, testing::Params()->n_gravity))); + + // Check all three Jacobians of the gravity overload: + Matrix9 aH1; + Matrix96 aH2; + Matrix93 aH3; + pim.predict(state1, kZeroBias, tilted_gravity, aH1, aH2, aH3); + EXPECT(assert_equal( + numericalDerivative11( + [&](const NavState& s) { return pim.predict(s, kZeroBias, tilted_gravity); }, + state1), + Matrix(aH1))); + EXPECT(assert_equal( + numericalDerivative11( + [&](const Bias& b) { return pim.predict(state1, b, tilted_gravity); }, + kZeroBias), + Matrix(aH2))); + EXPECT(assert_equal( + numericalDerivative11( + [&](const Vector3& g) { return pim.predict(state1, kZeroBias, g); }, + tilted_gravity), + Matrix(aH3))); + + // And the gravity Jacobian of computeError: + Matrix93 aH4; + pim.computeError(state1, state2, kZeroBias, tilted_gravity, {}, {}, {}, aH4); + EXPECT(assert_equal( + numericalDerivative11( + [&](const Vector3& g) { + return pim.computeError(state1, state2, kZeroBias, g, {}, {}, {}, {}); + }, + tilted_gravity), + Matrix(aH4))); +} + /* ************************************************************************* */ TEST_PIM(ImuFactor, MultipleMeasurements) { using namespace common; diff --git a/gtsam/navigation/tests/testManifoldPreintegration.cpp b/gtsam/navigation/tests/testManifoldPreintegration.cpp index 797bcae219..b67704ef32 100644 --- a/gtsam/navigation/tests/testManifoldPreintegration.cpp +++ b/gtsam/navigation/tests/testManifoldPreintegration.cpp @@ -84,7 +84,12 @@ TEST(ManifoldPreintegration, computeError) { Matrix9 aH1, aH2; Matrix96 aH3; pim.computeError(x1, x2, bias, aH1, aH2, aH3); - auto f = std::bind(&ManifoldPreintegration::computeError, pim, + // Select the overload without the gravity parameter: + using ComputeErrorNoGravity = Vector9 (PreintegrationBase::*)( + const NavState&, const NavState&, const imuBias::ConstantBias&, + OptionalJacobian<9, 9>, OptionalJacobian<9, 9>, + OptionalJacobian<9, 6>) const; + auto f = std::bind(static_cast(&ManifoldPreintegration::computeError), pim, std::placeholders::_1, std::placeholders::_2, std::placeholders::_3, nullptr, nullptr, nullptr); diff --git a/gtsam/navigation/tests/testNavState.cpp b/gtsam/navigation/tests/testNavState.cpp index 0312a18f30..0cb93563cd 100644 --- a/gtsam/navigation/tests/testNavState.cpp +++ b/gtsam/navigation/tests/testNavState.cpp @@ -446,12 +446,31 @@ TEST(NavState, CorrectPIM) { xi << 0.1, 0.1, 0.1, 0.2, 0.3, 0.4, -0.1, -0.2, -0.3; double dt = 0.5; Matrix9 aH1, aH2; + Matrix93 aH3; auto correctPIM = std::bind(&NavState::correctPIM, std::placeholders::_1, std::placeholders::_2, dt, kGravity, kOmegaCoriolis, false, - nullptr, nullptr); - kState1.correctPIM(xi, dt, kGravity, kOmegaCoriolis, false, aH1, aH2); + nullptr, nullptr, nullptr); + kState1.correctPIM(xi, dt, kGravity, kOmegaCoriolis, false, aH1, aH2, aH3); EXPECT(assert_equal(numericalDerivative21(correctPIM, kState1, xi), aH1)); EXPECT(assert_equal(numericalDerivative22(correctPIM, kState1, xi), aH2)); + + // Check the Jacobian wrt the gravity vector: + auto correctPIMGravity = [&](const Vector3& gravity) { + return kState1.correctPIM(xi, dt, gravity, kOmegaCoriolis, false); + }; + EXPECT(assert_equal( + numericalDerivative11(correctPIMGravity, kGravity), + Matrix(aH3))); + + // The gravity Jacobian must also be correct with coriolis disabled: + Matrix93 aH3NoCoriolis; + kState1.correctPIM(xi, dt, kGravity, {}, false, {}, {}, aH3NoCoriolis); + auto correctPIMNoCoriolis = [&](const Vector3& gravity) { + return kState1.correctPIM(xi, dt, gravity, {}, false); + }; + EXPECT(assert_equal( + numericalDerivative11(correctPIMNoCoriolis, kGravity), + Matrix(aH3NoCoriolis))); } /* ************************************************************************* */ diff --git a/gtsam/navigation/tests/testTangentPreintegration.cpp b/gtsam/navigation/tests/testTangentPreintegration.cpp index 2b7369d772..de260bc9d2 100644 --- a/gtsam/navigation/tests/testTangentPreintegration.cpp +++ b/gtsam/navigation/tests/testTangentPreintegration.cpp @@ -92,7 +92,12 @@ TEST(TangentPreintegration, computeError) { Matrix9 aH1, aH2; Matrix96 aH3; pim.computeError(x1, x2, bias, aH1, aH2, aH3); - auto f = std::bind(&TangentPreintegration::computeError, pim, + // Select the overload without the gravity parameter: + using ComputeErrorNoGravity = Vector9 (PreintegrationBase::*)( + const NavState&, const NavState&, const imuBias::ConstantBias&, + OptionalJacobian<9, 9>, OptionalJacobian<9, 9>, + OptionalJacobian<9, 6>) const; + auto f = std::bind(static_cast(&TangentPreintegration::computeError), pim, std::placeholders::_1, std::placeholders::_2, std::placeholders::_3, nullptr, nullptr, nullptr); From 66291e73ac84a211e27a2ba3ee56d70525d97daa Mon Sep 17 00:00:00 2001 From: Nikhil Khedekar Date: Sat, 1 Aug 2026 10:29:54 +0000 Subject: [PATCH 5/7] Add ImuFactorWithGravityDirection and ImuFactorWithGravityVector Two parametrizations of an ImuFactor with gravity as a 6th optimized variable, sharing one template and the internal::GravityParametrization adapter: - ImuFactorWithGravityDirection: Unit3 direction with a fixed, known magnitude (explicit constructor parameter, defaulting to the norm of the params' gravity vector), following the scale*direction decomposition used by MagFactor3 and Unit3::scaled. - ImuFactorWithGravityVector: free Point3 vector entangling direction and magnitude, following Lupton and Sukkarieh (TRO 2012); pair with a single VectorNormFactor<3> on the gravity variable when the magnitude is approximately known. Both factors are exposed in the wrapper with a python smoke test. Tests cover analytic-vs-numerical Jacobians for both parametrizations and both preintegration types, equality against mismatched factor types, Merge (including rejection of mismatched gravity keys and magnitudes), and recovery of a tilted gravity from stationary IMU data with both factors. --- gtsam/navigation/ImuFactor.cpp | 69 +++++++ gtsam/navigation/ImuFactor.h | 195 ++++++++++++++++++ gtsam/navigation/PreintegrationBase.h | 37 ++++ gtsam/navigation/navigation.i | 35 ++++ gtsam/navigation/tests/testImuFactor.cpp | 184 +++++++++++++++++ .../tests/testSerializationNavigation.cpp | 15 ++ .../gtsam/tests/test_ImuFactorWithGravity.py | 77 +++++++ 7 files changed, 612 insertions(+) create mode 100644 python/gtsam/tests/test_ImuFactorWithGravity.py diff --git a/gtsam/navigation/ImuFactor.cpp b/gtsam/navigation/ImuFactor.cpp index cee2f5cb3d..bedea0c3c1 100644 --- a/gtsam/navigation/ImuFactor.cpp +++ b/gtsam/navigation/ImuFactor.cpp @@ -210,5 +210,74 @@ template GTSAM_EXPORT std::ostream& operator<<>( std::ostream& os, const ImuFactor2T>& f); +//------------------------------------------------------------------------------ +// ImuFactorWithGravityT methods +//------------------------------------------------------------------------------ +template +std::ostream& operator<<(std::ostream& os, const ImuFactorWithGravityT& f) { + f.preintegratedMeasurements().print("preintegrated measurements:\n"); + if (internal::GravityParametrization::usesMagnitude) + os << " gravity magnitude: " << f.gravityMagnitude() << "\n"; + os << " noise model sigmas: " << f.noiseModel()->sigmas().transpose(); + return os; +} + +//------------------------------------------------------------------------------ +template +void ImuFactorWithGravityT::print(const string& s, + const KeyFormatter& keyFormatter) const { + cout << (s.empty() ? s : s + "\n") << "ImuFactorWithGravity(" + << keyFormatter(this->template key<1>()) << "," << keyFormatter(this->template key<2>()) + << "," << keyFormatter(this->template key<3>()) << "," << keyFormatter(this->template key<4>()) + << "," << keyFormatter(this->template key<5>()) << "," << keyFormatter(this->template key<6>()) + << ")\n"; + cout << *this << endl; +} + +//------------------------------------------------------------------------------ +template +bool ImuFactorWithGravityT::equals(const NonlinearFactor& other, + double tol) const { + const This *e = dynamic_cast(&other); + return e != nullptr && Base::equals(*e, tol) && pim_.equals(e->pim_, tol) && + (!internal::GravityParametrization::usesMagnitude || + std::abs(gravityMagnitude_ - e->gravityMagnitude_) < tol); +} + +//------------------------------------------------------------------------------ +template +Vector ImuFactorWithGravityT::evaluateError(const Pose3& pose_i, + const Vector3& vel_i, const Pose3& pose_j, const Vector3& vel_j, + const imuBias::ConstantBias& bias_i, const GRAVITY& gravity, + OptionalMatrixType H1, OptionalMatrixType H2, OptionalMatrixType H3, + OptionalMatrixType H4, OptionalMatrixType H5, OptionalMatrixType H6) const { + typedef internal::GravityParametrization Parametrization; + Eigen::Matrix D_gvec_gravity; + const Vector3 n_gravity = Parametrization::vector( + gravity, gravityMagnitude_, H6 ? &D_gvec_gravity : nullptr); + Matrix93 D_r_gvec; + const Vector r = pim_.computeErrorAndJacobians( + pose_i, vel_i, pose_j, vel_j, bias_i, n_gravity, H1, H2, H3, H4, H5, + H6 ? &D_r_gvec : nullptr); + if (H6) *H6 = D_r_gvec * D_gvec_gravity; + return r; +} + +//------------------------------------------------------------------------------ +// ImuFactorWithGravityT instantiations +template class GTSAM_EXPORT ImuFactorWithGravityT, Unit3>; +template class GTSAM_EXPORT ImuFactorWithGravityT, Unit3>; +template class GTSAM_EXPORT ImuFactorWithGravityT, Point3>; +template class GTSAM_EXPORT ImuFactorWithGravityT, Point3>; + +template GTSAM_EXPORT std::ostream& operator<<( + std::ostream& os, const ImuFactorWithGravityT, Unit3>& f); +template GTSAM_EXPORT std::ostream& operator<<( + std::ostream& os, const ImuFactorWithGravityT, Unit3>& f); +template GTSAM_EXPORT std::ostream& operator<<( + std::ostream& os, const ImuFactorWithGravityT, Point3>& f); +template GTSAM_EXPORT std::ostream& operator<<( + std::ostream& os, const ImuFactorWithGravityT, Point3>& f); + } // namespace gtsam diff --git a/gtsam/navigation/ImuFactor.h b/gtsam/navigation/ImuFactor.h index eb90b477b5..f6c89fac39 100644 --- a/gtsam/navigation/ImuFactor.h +++ b/gtsam/navigation/ImuFactor.h @@ -436,6 +436,197 @@ using ImuFactor2 = ImuFactor2T<>; template GTSAM_EXPORT std::ostream& operator<<(std::ostream& os, const ImuFactor2T& f); +/** + * ImuFactorWithGravityT is a 6-ways factor: in addition to the previous and + * current states (pose and velocity) and the bias estimate of ImuFactorT, it + * involves a GRAVITY variable so that gravity can be optimized instead of + * being fixed by the preintegration parameters. Two parametrizations are + * provided, see ImuFactorWithGravityDirection and ImuFactorWithGravityVector. + * + * As gravity in the nav frame is entangled with the initial attitude (only + * their combination is observed by the accelerometer), a graph should anchor + * one of the two: either prior knowledge of attitude (roll/pitch), or a prior + * on the gravity variable - not both tightly. + * + * Like ImuFactorT, this factor does not model temporal consistency of the + * biases, which is up to the caller; see CombinedImuFactorWithGravityT for a + * variant that does. + * + * @ingroup navigation + */ +template +class GTSAM_EXPORT ImuFactorWithGravityT + : public NoiseModelFactorN { +private: + + typedef ImuFactorWithGravityT This; + typedef NoiseModelFactorN Base; + + PIM pim_; + double gravityMagnitude_; ///< used by the Unit3 parametrization only + +public: + + // Provide access to the Matrix& version of evaluateError: + using Base::evaluateError; + + /** Shorthand for a smart pointer to a factor */ + typedef std::shared_ptr shared_ptr; + + /** Default constructor - only use for serialization */ + ImuFactorWithGravityT() : gravityMagnitude_(0.0) {} + + /** + * Constructor + * @param pose_i Previous pose key + * @param vel_i Previous velocity key + * @param pose_j Current pose key + * @param vel_j Current velocity key + * @param bias Previous bias key + * @param gravity Gravity key + * @param preintegratedMeasurements The preintegrated measurements since the + * last pose + * @param gravityMagnitude The known gravity magnitude for the Unit3 + * parametrization; defaults to the norm of the gravity vector in the + * preintegration params. Unused by the Point3 parametrization. + */ + ImuFactorWithGravityT(Key pose_i, Key vel_i, Key pose_j, Key vel_j, Key bias, + Key gravity, const PIM& preintegratedMeasurements, + std::optional gravityMagnitude = {}) + : Base(noiseModel::Gaussian::Covariance(preintegratedMeasurements.preintMeasCov()), + pose_i, vel_i, pose_j, vel_j, bias, gravity), + pim_(preintegratedMeasurements), + gravityMagnitude_(gravityMagnitude + ? *gravityMagnitude + : preintegratedMeasurements.params()->n_gravity.norm()) { + if (internal::GravityParametrization::usesMagnitude && + !(gravityMagnitude_ > 0.0)) + throw std::invalid_argument( + "ImuFactorWithGravityT: gravityMagnitude must be positive"); + } + + ~ImuFactorWithGravityT() override { + } + + /// @return a deep copy of this factor + gtsam::NonlinearFactor::shared_ptr clone() const override { + return std::make_shared(*this); + } + + /// @name Testable + /// @{ + void print(const std::string& s = "", const KeyFormatter& keyFormatter = + DefaultKeyFormatter) const override; + bool equals(const NonlinearFactor& expected, double tol = 1e-9) const override; + /// @} + + /** Access the preintegrated measurements. */ + const PIM& preintegratedMeasurements() const { + return pim_; + } + + /** The gravity magnitude used by the Unit3 parametrization. */ + double gravityMagnitude() const { + return gravityMagnitude_; + } + + /** implement functions needed to derive from Factor */ + + /// vector of errors + Vector evaluateError(const Pose3& pose_i, const Vector3& vel_i, + const Pose3& pose_j, const Vector3& vel_j, + const imuBias::ConstantBias& bias_i, + const GRAVITY& gravity, OptionalMatrixType H1, + OptionalMatrixType H2, OptionalMatrixType H3, + OptionalMatrixType H4, OptionalMatrixType H5, + OptionalMatrixType H6) const override; + + /// Merge two factors sharing bias and gravity keys, with consecutive states + template >::value + >::type + > + static typename ImuFactorWithGravityT::shared_ptr Merge( + const typename ImuFactorWithGravityT::shared_ptr& f01, + const typename ImuFactorWithGravityT::shared_ptr& f12 + ) { + if (f01->template key<5>() != f12->template key<5>()) + throw std::domain_error("ImuFactorWithGravityT::Merge: IMU bias keys must be the same"); + + if (f01->template key<6>() != f12->template key<6>()) + throw std::domain_error("ImuFactorWithGravityT::Merge: gravity keys must be the same"); + + if (internal::GravityParametrization::usesMagnitude && + std::abs(f01->gravityMagnitude() - f12->gravityMagnitude()) > 1e-9) + throw std::domain_error( + "ImuFactorWithGravityT::Merge: gravity magnitudes must be the same"); + + if (f01->template key<3>() != f12->template key<1>() || f01->template key<4>() != f12->template key<2>()) + throw std::domain_error( + "ImuFactorWithGravityT::Merge: intermediate pose, velocity keys need to match up"); + + auto pim02 = ImuFactorT::Merge(f01->preintegratedMeasurements(), + f12->preintegratedMeasurements()); + + return std::make_shared( + f01->template key<1>(), // P0 + f01->template key<2>(), // V0 + f12->template key<3>(), // P2 + f12->template key<4>(), // V2 + f01->template key<5>(), // B + f01->template key<6>(), // G + pim02, f01->gravityMagnitude()); + } + + private: +#if GTSAM_ENABLE_BOOST_SERIALIZATION + /** Serialization function */ + friend class boost::serialization::access; + template + void serialize(ARCHIVE & ar, const unsigned int /*version*/) { + // Archive name for the base follows the sibling factors' convention: + ar & boost::serialization::make_nvp("NoiseModelFactor6", + boost::serialization::base_object(*this)); + ar & BOOST_SERIALIZATION_NVP(pim_); + ar & BOOST_SERIALIZATION_NVP(gravityMagnitude_); + } +#endif +}; +// class ImuFactorWithGravityT + +/** + * ImuFactor variant with the gravity direction as an optimized Unit3 variable + * and a fixed, known magnitude (given at construction, defaulting to the norm + * of the gravity vector in the preintegration params). This is the preferred + * parametrization when the magnitude is known, eg. on Earth where standard + * gravity is accurate to ~0.3% everywhere; it removes the magnitude degree of + * freedom by construction. See eg. Nemiroff, Chen and Lopez, "Joint + * On-Manifold Gravity and Accelerometer Intrinsics Estimation for Inertially + * Aligned Mapping", 2023. + */ +using ImuFactorWithGravityDirection = + ImuFactorWithGravityT; + +/** + * ImuFactor variant with the gravity vector as a free Point3 variable, ie. + * direction and magnitude both optimized, following Lupton and Sukkarieh, + * "Visual-Inertial-Aided Navigation for High-Dynamic Motion in Built + * Environments Without Initial Conditions", TRO 2012. If the magnitude is + * approximately known, add a VectorNormFactor<3> on the gravity variable once + * (Lupton's magnitude pseudo-observation); if it is known exactly, prefer + * ImuFactorWithGravityDirection. + */ +using ImuFactorWithGravityVector = + ImuFactorWithGravityT; + +// operator<< for ImuFactorWithGravityT +template +GTSAM_EXPORT std::ostream& operator<<(std::ostream& os, + const ImuFactorWithGravityT& f); + template struct traits> : public Testable> {}; @@ -445,4 +636,8 @@ struct traits> : public Testable> {}; template struct traits> : public Testable> {}; +template +struct traits> + : public Testable> {}; + } /// namespace gtsam diff --git a/gtsam/navigation/PreintegrationBase.h b/gtsam/navigation/PreintegrationBase.h index 89b9ae8d6c..79c5fcf193 100644 --- a/gtsam/navigation/PreintegrationBase.h +++ b/gtsam/navigation/PreintegrationBase.h @@ -24,6 +24,7 @@ #include #include #include +#include #include #include @@ -216,4 +217,40 @@ class GTSAM_EXPORT PreintegrationBase { #endif }; +namespace internal { + +/** + * Adapter mapping a gravity parametrization GRAVITY to the nav-frame gravity + * vector expected by PreintegrationBase, with the chain-rule Jacobian block. + * Two parametrizations are provided: + * - Unit3: an optimized direction scaled by a fixed, known magnitude + * - Point3: a free vector entangling direction and magnitude + * See ImuFactorWithGravityDirection and ImuFactorWithGravityVector. + */ +template +struct GravityParametrization; + +template <> +struct GravityParametrization { + constexpr static int dimension = 2; + constexpr static bool usesMagnitude = true; + static Vector3 vector(const Unit3& gravity, double magnitude, + OptionalJacobian<3, 2> H = {}) { + return gravity.scaled(magnitude, H); + } +}; + +template <> +struct GravityParametrization { + constexpr static int dimension = 3; + constexpr static bool usesMagnitude = false; + static Vector3 vector(const Point3& gravity, double /*magnitude*/, + OptionalJacobian<3, 3> H = {}) { + if (H) H->setIdentity(); + return gravity; + } +}; + +} // namespace internal + } /// namespace gtsam diff --git a/gtsam/navigation/navigation.i b/gtsam/navigation/navigation.i index 248905c8f3..705b29b48a 100644 --- a/gtsam/navigation/navigation.i +++ b/gtsam/navigation/navigation.i @@ -241,6 +241,41 @@ virtual class ImuFactor2: gtsam::NonlinearFactor { void serialize() const; }; +virtual class ImuFactorWithGravityDirection: gtsam::NonlinearFactor { + ImuFactorWithGravityDirection(gtsam::Key pose_i, gtsam::Key vel_i, + gtsam::Key pose_j, gtsam::Key vel_j, gtsam::Key bias, gtsam::Key gravity, + const gtsam::PreintegratedImuMeasurements& preintegratedMeasurements); + ImuFactorWithGravityDirection(gtsam::Key pose_i, gtsam::Key vel_i, + gtsam::Key pose_j, gtsam::Key vel_j, gtsam::Key bias, gtsam::Key gravity, + const gtsam::PreintegratedImuMeasurements& preintegratedMeasurements, + double gravityMagnitude); + + // Standard Interface + gtsam::PreintegratedImuMeasurements preintegratedMeasurements() const; + double gravityMagnitude() const; + gtsam::Vector evaluateError(const gtsam::Pose3& pose_i, gtsam::Vector vel_i, + const gtsam::Pose3& pose_j, gtsam::Vector vel_j, + const gtsam::imuBias::ConstantBias& bias_i, const gtsam::Unit3& gravity); + + // enable serialization functionality + void serialize() const; +}; + +virtual class ImuFactorWithGravityVector: gtsam::NonlinearFactor { + ImuFactorWithGravityVector(gtsam::Key pose_i, gtsam::Key vel_i, + gtsam::Key pose_j, gtsam::Key vel_j, gtsam::Key bias, gtsam::Key gravity, + const gtsam::PreintegratedImuMeasurements& preintegratedMeasurements); + + // Standard Interface + gtsam::PreintegratedImuMeasurements preintegratedMeasurements() const; + gtsam::Vector evaluateError(const gtsam::Pose3& pose_i, gtsam::Vector vel_i, + const gtsam::Pose3& pose_j, gtsam::Vector vel_j, + const gtsam::imuBias::ConstantBias& bias_i, const gtsam::Point3& gravity); + + // enable serialization functionality + void serialize() const; +}; + #include virtual class PreintegrationCombinedParams : gtsam::PreintegrationParams { PreintegrationCombinedParams(gtsam::Vector n_gravity); diff --git a/gtsam/navigation/tests/testImuFactor.cpp b/gtsam/navigation/tests/testImuFactor.cpp index f4c3b7225a..1745b10e70 100644 --- a/gtsam/navigation/tests/testImuFactor.cpp +++ b/gtsam/navigation/tests/testImuFactor.cpp @@ -29,7 +29,10 @@ #include #include #include +#include +#include #include +#include #include #include @@ -935,6 +938,187 @@ TEST_PIM(ImuFactor, CheckCovariance) { EXPECT(assert_equal(expected, actual.preintMeasCov())); } +/* ************************************************************************* */ +/* ************************************************************************* */ +TEST_PIM(ImuFactorWithGravity, DirectionJacobians) { + using namespace common; + using symbol_shorthand::G; + PIM pim(testing::Params()); + pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); + + ImuFactorWithGravityT factor(X(1), V(1), X(2), V(2), B(1), G(0), + pim); + // The default magnitude comes from the params' gravity vector: + DOUBLES_EQUAL(testing::Params()->n_gravity.norm(), factor.gravityMagnitude(), + 1e-9); + + // With the params' gravity direction, the error must match plain ImuFactor: + ImuFactorT plain(X(1), V(1), X(2), V(2), B(1), pim); + EXPECT(assert_equal( + plain.evaluateError(x1, v1, x2, v2, kZeroBias), + factor.evaluateError(x1, v1, x2, v2, kZeroBias, + Unit3(testing::Params()->n_gravity)))); + + Values values; + values.insert(X(1), x1); + values.insert(V(1), v1); + values.insert(X(2), x2); + values.insert(V(2), v2); + values.insert(B(1), kZeroBias); + values.insert(G(0), Unit3(0.1, -0.2, -1.0)); // tilted away from params + EXPECT_CORRECT_FACTOR_JACOBIANS(factor, values, 1e-7, 1e-3); + + // The magnitude scales the gravity Jacobian block; check it at a + // deliberately non-default value: + ImuFactorWithGravityT lunar(X(1), V(1), X(2), V(2), B(1), G(0), + pim, 1.62); + EXPECT_CORRECT_FACTOR_JACOBIANS(lunar, values, 1e-7, 1e-3); +} + +/* ************************************************************************* */ +TEST_PIM(ImuFactorWithGravity, VectorJacobians) { + using namespace common; + using symbol_shorthand::G; + PIM pim(testing::Params()); + pim.integrateMeasurement(measuredAcc, measuredOmega, deltaT); + + ImuFactorWithGravityT factor(X(1), V(1), X(2), V(2), B(1), G(0), + pim); + + Values values; + values.insert(X(1), x1); + values.insert(V(1), v1); + values.insert(X(2), x2); + values.insert(V(2), v2); + values.insert(B(1), kZeroBias); + // Tilted direction and non-standard magnitude: + values.insert(G(0), Point3(0.4, -0.6, -9.5)); + EXPECT_CORRECT_FACTOR_JACOBIANS(factor, values, 1e-7, 1e-3); +} + +/* ************************************************************************* */ +TEST(ImuFactorWithGravity, Equals) { + using symbol_shorthand::G; + auto pim = PreintegratedImuMeasurements(testing::Params()); + ImuFactorWithGravityDirection factor1(X(1), V(1), X(2), V(2), B(1), G(0), pim); + ImuFactorWithGravityDirection factor2(X(1), V(1), X(2), V(2), B(1), G(0), pim); + ImuFactorWithGravityDirection factor3(X(1), V(1), X(2), V(2), B(1), G(0), pim, + 1.62); // lunar gravity + EXPECT(factor1.equals(factor2)); + EXPECT(!factor1.equals(factor3)); + // Comparing against a different factor type must not crash: + ImuFactorWithGravityVector vectorFactor(X(1), V(1), X(2), V(2), B(1), G(0), pim); + EXPECT(!factor1.equals(vectorFactor)); + EXPECT(!vectorFactor.equals(factor1)); +} + +/* ************************************************************************* */ +// A stationary IMU in a nav frame whose gravity is tilted away from the +// params' -z direction: the accelerometer measures -g in the body frame, so +// optimizing the gravity variable must recover the true tilted gravity. +namespace tilted { +static const Vector3 trueGravity = + Rot3::Rodrigues(0.05, -0.03, 0.0) * Vector3(0, 0, -9.81); +static PreintegratedImuMeasurements integrateStationary() { + auto p = testing::Params(); // note: n_gravity = (0, 0, kGravity) = (0, 0, 10) + PreintegratedImuMeasurements pim(p); + for (int i = 0; i < 10; ++i) + pim.integrateMeasurement(-trueGravity, Vector3::Zero(), 0.1); + return pim; +} +static void addStationaryPriors(NonlinearFactorGraph* graph) { + using symbol_shorthand::G; + auto tightPose = noiseModel::Isotropic::Sigma(6, 1e-6); + auto tightVector = noiseModel::Isotropic::Sigma(3, 1e-6); + auto tightBias = noiseModel::Isotropic::Sigma(6, 1e-6); + graph->addPrior(X(1), Pose3::Identity(), tightPose); + graph->addPrior(X(2), Pose3::Identity(), tightPose); + graph->addPrior(V(1), Vector3(Vector3::Zero()), tightVector); + graph->addPrior(V(2), Vector3(Vector3::Zero()), tightVector); + graph->addPrior(B(1), kZeroBias, tightBias); +} +static Values stationaryInitial() { + Values initial; + initial.insert(X(1), Pose3::Identity()); + initial.insert(X(2), Pose3::Identity()); + initial.insert(V(1), Vector3(Vector3::Zero())); + initial.insert(V(2), Vector3(Vector3::Zero())); + initial.insert(B(1), kZeroBias); + return initial; +} +} // namespace tilted + +TEST(ImuFactorWithGravity, RecoverGravityDirection) { + using symbol_shorthand::G; + NonlinearFactorGraph graph; + // The magnitude is given explicitly since the params' norm is kGravity = 10, + // while the data was generated with |g| = 9.81: + graph.emplace_shared( + X(1), V(1), X(2), V(2), B(1), G(0), tilted::integrateStationary(), 9.81); + tilted::addStationaryPriors(&graph); + + Values initial = tilted::stationaryInitial(); + initial.insert(G(0), Unit3(0, 0, -1)); + + const Values result = LevenbergMarquardtOptimizer(graph, initial).optimize(); + EXPECT(assert_equal(Unit3(tilted::trueGravity), result.at(G(0)), 1e-5)); +} + +/* ************************************************************************* */ +TEST(ImuFactorWithGravity, RecoverGravityVector) { + using symbol_shorthand::G; + NonlinearFactorGraph graph; + graph.emplace_shared( + X(1), V(1), X(2), V(2), B(1), G(0), tilted::integrateStationary()); + // Lupton-style magnitude pseudo-observation (consistent with trueGravity): + graph.emplace_shared>( + G(0), 9.81, noiseModel::Isotropic::Sigma(1, 0.03)); + tilted::addStationaryPriors(&graph); + + Values initial = tilted::stationaryInitial(); + initial.insert(G(0), Point3(0, 0, -9.0)); + + const Values result = LevenbergMarquardtOptimizer(graph, initial).optimize(); + EXPECT(assert_equal(Point3(tilted::trueGravity), result.at(G(0)), 1e-4)); +} + +/* ************************************************************************* */ +#ifdef GTSAM_TANGENT_PREINTEGRATION +TEST(ImuFactorWithGravity, Merge) { + using symbol_shorthand::G; + auto p = testing::Params(); + PreintegratedImuMeasurements pim01(p), pim12(p); + const Vector3 acc(0.1, 0.2, -9.81), omega(0.1, 0.02, 0.03); + for (int i = 0; i < 10; ++i) { + pim01.integrateMeasurement(acc, omega, 0.1); + pim12.integrateMeasurement(acc, omega, 0.1); + } + auto f01 = std::make_shared( + X(1), V(1), X(2), V(2), B(1), G(0), pim01); + auto f12 = std::make_shared( + X(2), V(2), X(3), V(3), B(1), G(0), pim12); + + auto f02 = ImuFactorWithGravityDirection::Merge(f01, f12); + DOUBLES_EQUAL(2.0, f02->preintegratedMeasurements().deltaTij(), 1e-9); + DOUBLES_EQUAL(f01->gravityMagnitude(), f02->gravityMagnitude(), 1e-9); + EXPECT(f02->key<1>() == X(1)); + EXPECT(f02->key<3>() == X(3)); + EXPECT(f02->key<6>() == G(0)); + + // Mismatched gravity magnitudes must be rejected: + auto f12_moon = std::make_shared( + X(2), V(2), X(3), V(3), B(1), G(0), pim12, 1.62); + CHECK_EXCEPTION(ImuFactorWithGravityDirection::Merge(f01, f12_moon), + std::domain_error); + + // Mismatched gravity keys must be rejected: + auto f12_key = std::make_shared( + X(2), V(2), X(3), V(3), B(1), G(1), pim12); + CHECK_EXCEPTION(ImuFactorWithGravityDirection::Merge(f01, f12_key), + std::domain_error); +} +#endif + /* ************************************************************************* */ int main() { TestResult tr; diff --git a/gtsam/navigation/tests/testSerializationNavigation.cpp b/gtsam/navigation/tests/testSerializationNavigation.cpp index bd2928c471..f0c897675f 100644 --- a/gtsam/navigation/tests/testSerializationNavigation.cpp +++ b/gtsam/navigation/tests/testSerializationNavigation.cpp @@ -103,6 +103,21 @@ TEST(ImuFactor2, serialization) { EXPECT(equalsBinary(factor)); } +/* ************************************************************************* */ +TEST(ImuFactorWithGravity, serialization) { + auto pim = getPreintegratedMeasurements(); + + ImuFactorWithGravityDirection direction(1, 2, 3, 4, 5, 6, pim, 9.81); + EXPECT(equalsObj(direction)); + EXPECT(equalsXML(direction)); + EXPECT(equalsBinary(direction)); + + ImuFactorWithGravityVector vector(1, 2, 3, 4, 5, 6, pim); + EXPECT(equalsObj(vector)); + EXPECT(equalsXML(vector)); + EXPECT(equalsBinary(vector)); +} + /* ************************************************************************* */ TEST(CombinedImuFactor, Serialization) { auto pim = getPreintegratedMeasurements(); diff --git a/python/gtsam/tests/test_ImuFactorWithGravity.py b/python/gtsam/tests/test_ImuFactorWithGravity.py new file mode 100644 index 0000000000..8dc20929e3 --- /dev/null +++ b/python/gtsam/tests/test_ImuFactorWithGravity.py @@ -0,0 +1,77 @@ +""" +GTSAM Copyright 2010-2019, Georgia Tech Research Corporation, +Atlanta, Georgia 30332-0415 +All Rights Reserved + +See LICENSE for the license information + +Wrapper unit tests for the IMU factors with an optimized gravity variable. +""" + +import unittest + +import numpy as np + +import gtsam +from gtsam import ImuFactorWithGravityDirection, ImuFactorWithGravityVector +from gtsam.symbol_shorthand import B, G, V, X +from gtsam.utils.test_case import GtsamTestCase + + +def stationary_pim(gravity=np.array([0.0, 0.0, -9.81])): + """Integrate a stationary IMU: the accelerometer measures -gravity. + + Note: the params' own gravity (MakeSharedD: z-DOWN, (0, 0, +9.81)) points + opposite to the gravity used to generate the data. Only the params' NORM is + used by the factors (as the default magnitude), so this deliberately + catches any leakage of the params' gravity direction into the error. + """ + params = gtsam.PreintegrationParams.MakeSharedD(9.81) + params.setAccelerometerCovariance(1e-4 * np.eye(3)) + params.setGyroscopeCovariance(1e-4 * np.eye(3)) + params.setIntegrationCovariance(1e-7 * np.eye(3)) + pim = gtsam.PreintegratedImuMeasurements(params) + for _ in range(10): + pim.integrateMeasurement(-gravity, np.zeros(3), 0.1) + return pim + + +class TestImuFactorWithGravity(GtsamTestCase): + """Smoke tests: construction and error evaluation through the wrapper.""" + + def test_direction_factor(self): + pim = stationary_pim() + factor = ImuFactorWithGravityDirection( + X(1), V(1), X(2), V(2), B(1), G(0), pim) + self.assertAlmostEqual(factor.gravityMagnitude(), 9.81) + + error = factor.evaluateError( + gtsam.Pose3(), np.zeros(3), gtsam.Pose3(), np.zeros(3), + gtsam.imuBias.ConstantBias(), gtsam.Unit3(np.array([0.0, 0.0, -1.0]))) + np.testing.assert_allclose(error, np.zeros(9), atol=1e-9) + + def test_direction_factor_explicit_magnitude(self): + pim = stationary_pim() + factor = ImuFactorWithGravityDirection( + X(1), V(1), X(2), V(2), B(1), G(0), pim, 1.62) + self.assertAlmostEqual(factor.gravityMagnitude(), 1.62) + + def test_vector_factor(self): + pim = stationary_pim() + factor = ImuFactorWithGravityVector( + X(1), V(1), X(2), V(2), B(1), G(0), pim) + error = factor.evaluateError( + gtsam.Pose3(), np.zeros(3), gtsam.Pose3(), np.zeros(3), + gtsam.imuBias.ConstantBias(), np.array([0.0, 0.0, -9.81])) + np.testing.assert_allclose(error, np.zeros(9), atol=1e-9) + + def test_vector_norm_factor(self): + model = gtsam.noiseModel.Isotropic.Sigma(1, 0.03) + factor = gtsam.VectorNormFactor3(G(0), 9.81, model) + self.assertAlmostEqual(factor.norm(), 9.81) + error = factor.evaluateError(np.array([0.0, 0.0, -9.81])) + np.testing.assert_allclose(error, np.zeros(1), atol=1e-9) + + +if __name__ == "__main__": + unittest.main() From 5d684773d501cbdf844f5089fb7f7ac11305bfeb Mon Sep 17 00:00:00 2001 From: Nikhil Khedekar Date: Sat, 1 Aug 2026 10:29:54 +0000 Subject: [PATCH 6/7] Add CombinedImuFactorWithGravityDirection and CombinedImuFactorWithGravityVector CombinedImuFactor variants with gravity as a 7th optimized variable, using the same GravityParametrization adapter as the ImuFactor variants. The 15-dof error and block-Jacobian assembly is factored into a helper shared with the plain CombinedImuFactorT (no functional change there); only the 9 preintegration rows depend on gravity, and the bias random walk rows have a zero gravity Jacobian. Jointly estimating gravity and the evolving accelerometer bias requires sufficient rotation excitation (Nemiroff, Chen and Lopez, 2023). Both factors are exposed in the wrapper. --- gtsam/navigation/CombinedImuFactor.cpp | 121 ++++++++++++++-- gtsam/navigation/CombinedImuFactor.h | 137 ++++++++++++++++++ gtsam/navigation/navigation.i | 40 +++++ .../tests/testCombinedImuFactor.cpp | 95 ++++++++++++ .../tests/testSerializationNavigation.cpp | 15 ++ .../gtsam/tests/test_ImuFactorWithGravity.py | 31 ++++ 6 files changed, 429 insertions(+), 10 deletions(-) diff --git a/gtsam/navigation/CombinedImuFactor.cpp b/gtsam/navigation/CombinedImuFactor.cpp index 8061c81cce..c04bf44623 100644 --- a/gtsam/navigation/CombinedImuFactor.cpp +++ b/gtsam/navigation/CombinedImuFactor.cpp @@ -184,14 +184,19 @@ bool CombinedImuFactorT::equals(const NonlinearFactor& other, double tol) c } //------------------------------------------------------------------------------ +namespace internal { +/// Shared 15-dof error and block-Jacobian assembly for CombinedImuFactorT and +/// CombinedImuFactorWithGravityT: rows 0-8 are the preintegration error for +/// the given gravity vector, rows 9-14 the bias random walk. If D_r_gvec is +/// given, it receives the 9x3 Jacobian of the preintegration rows wrt the +/// gravity vector (the bias rows have a zero gravity Jacobian). template -Vector CombinedImuFactorT::evaluateError(const Pose3& pose_i, +static Vector combinedImuError(const PIM& pim, const Pose3& pose_i, const Vector3& vel_i, const Pose3& pose_j, const Vector3& vel_j, const imuBias::ConstantBias& bias_i, const imuBias::ConstantBias& bias_j, - OptionalMatrixType H1, OptionalMatrixType H2, - OptionalMatrixType H3, OptionalMatrixType H4, - OptionalMatrixType H5, OptionalMatrixType H6) const { - + const Vector3& n_gravity, OptionalMatrixType H1, OptionalMatrixType H2, + OptionalMatrixType H3, OptionalMatrixType H4, OptionalMatrixType H5, + OptionalMatrixType H6, Matrix93* D_r_gvec) { // error wrt bias evolution model (random walk) Matrix6 Hbias_i, Hbias_j; Vector6 fbias = traits::Between(bias_j, bias_i, @@ -201,9 +206,10 @@ Vector CombinedImuFactorT::evaluateError(const Pose3& pose_i, Matrix93 D_r_vel_i, D_r_vel_j; // error wrt preintegrated measurements - Vector9 r_Rpv = pim_.computeErrorAndJacobians(pose_i, vel_i, pose_j, vel_j, - bias_i, H1 ? &D_r_pose_i : 0, H2 ? &D_r_vel_i : 0, H3 ? &D_r_pose_j : 0, - H4 ? &D_r_vel_j : 0, H5 ? &D_r_bias_i : 0); + Vector9 r_Rpv = pim.computeErrorAndJacobians(pose_i, vel_i, pose_j, vel_j, + bias_i, n_gravity, H1 ? &D_r_pose_i : 0, H2 ? &D_r_vel_i : 0, + H3 ? &D_r_pose_j : 0, H4 ? &D_r_vel_j : 0, H5 ? &D_r_bias_i : 0, + D_r_gvec); // if we need the jacobians if (H1) { @@ -245,9 +251,23 @@ Vector CombinedImuFactorT::evaluateError(const Pose3& pose_i, // overall error Vector r(15); - r << r_Rpv, fbias; // vector of size 15 + r << r_Rpv, fbias; // vector of size 15 return r; } +} // namespace internal + +//------------------------------------------------------------------------------ +template +Vector CombinedImuFactorT::evaluateError(const Pose3& pose_i, + const Vector3& vel_i, const Pose3& pose_j, const Vector3& vel_j, + const imuBias::ConstantBias& bias_i, const imuBias::ConstantBias& bias_j, + OptionalMatrixType H1, OptionalMatrixType H2, + OptionalMatrixType H3, OptionalMatrixType H4, + OptionalMatrixType H5, OptionalMatrixType H6) const { + return internal::combinedImuError(pim_, pose_i, vel_i, pose_j, vel_j, + bias_i, bias_j, pim_.params()->n_gravity, + H1, H2, H3, H4, H5, H6, nullptr); +} //------------------------------------------------------------------------------ template @@ -272,5 +292,86 @@ template GTSAM_EXPORT std::ostream& operator<<>( std::ostream& os, const CombinedImuFactorT>& f); +//------------------------------------------------------------------------------ +// CombinedImuFactorWithGravityT methods +//------------------------------------------------------------------------------ +template +std::ostream& operator<<(std::ostream& os, + const CombinedImuFactorWithGravityT& f) { + f.preintegratedMeasurements().print("combined preintegrated measurements:\n"); + if (internal::GravityParametrization::usesMagnitude) + os << " gravity magnitude: " << f.gravityMagnitude() << "\n"; + os << " noise model sigmas: " << f.noiseModel()->sigmas().transpose(); + return os; +} + +//------------------------------------------------------------------------------ +template +void CombinedImuFactorWithGravityT::print( + const std::string& s, const KeyFormatter& keyFormatter) const { + std::cout << (s.empty() ? s : s + "\n") << "CombinedImuFactorWithGravity(" + << keyFormatter(this->template key<1>()) << "," << keyFormatter(this->template key<2>()) + << "," << keyFormatter(this->template key<3>()) << "," << keyFormatter(this->template key<4>()) + << "," << keyFormatter(this->template key<5>()) << "," << keyFormatter(this->template key<6>()) + << "," << keyFormatter(this->template key<7>()) << ")\n"; + std::cout << *this << std::endl; +} -} // namespace gtsam \ No newline at end of file +//------------------------------------------------------------------------------ +template +bool CombinedImuFactorWithGravityT::equals( + const NonlinearFactor& other, double tol) const { + const This* e = dynamic_cast(&other); + return e != nullptr && Base::equals(*e, tol) && pim_.equals(e->pim_, tol) && + (!internal::GravityParametrization::usesMagnitude || + std::abs(gravityMagnitude_ - e->gravityMagnitude_) < tol); +} + +//------------------------------------------------------------------------------ +template +Vector CombinedImuFactorWithGravityT::evaluateError( + const Pose3& pose_i, const Vector3& vel_i, const Pose3& pose_j, + const Vector3& vel_j, const imuBias::ConstantBias& bias_i, + const imuBias::ConstantBias& bias_j, const GRAVITY& gravity, + OptionalMatrixType H1, OptionalMatrixType H2, OptionalMatrixType H3, + OptionalMatrixType H4, OptionalMatrixType H5, OptionalMatrixType H6, + OptionalMatrixType H7) const { + typedef internal::GravityParametrization Parametrization; + + Eigen::Matrix D_gvec_gravity; + const Vector3 n_gravity = Parametrization::vector( + gravity, gravityMagnitude_, H7 ? &D_gvec_gravity : nullptr); + + Matrix93 D_r_gvec; + const Vector r = internal::combinedImuError( + pim_, pose_i, vel_i, pose_j, vel_j, bias_i, bias_j, n_gravity, + H1, H2, H3, H4, H5, H6, H7 ? &D_r_gvec : nullptr); + + if (H7) { + // Only the preintegration rows depend on gravity: + H7->resize(15, Parametrization::dimension); + H7->template block<9, Parametrization::dimension>(0, 0) = + D_r_gvec * D_gvec_gravity; + H7->template block<6, Parametrization::dimension>(9, 0).setZero(); + } + return r; +} + +//------------------------------------------------------------------------------ +// CombinedImuFactorWithGravityT instantiations +template class GTSAM_EXPORT CombinedImuFactorWithGravityT, Unit3>; +template class GTSAM_EXPORT CombinedImuFactorWithGravityT, Unit3>; +template class GTSAM_EXPORT CombinedImuFactorWithGravityT, Point3>; +template class GTSAM_EXPORT CombinedImuFactorWithGravityT, Point3>; + +template GTSAM_EXPORT std::ostream& operator<<( + std::ostream& os, const CombinedImuFactorWithGravityT, Unit3>& f); +template GTSAM_EXPORT std::ostream& operator<<( + std::ostream& os, const CombinedImuFactorWithGravityT, Unit3>& f); +template GTSAM_EXPORT std::ostream& operator<<( + std::ostream& os, const CombinedImuFactorWithGravityT, Point3>& f); +template GTSAM_EXPORT std::ostream& operator<<( + std::ostream& os, const CombinedImuFactorWithGravityT, Point3>& f); + + +} // namespace gtsam diff --git a/gtsam/navigation/CombinedImuFactor.h b/gtsam/navigation/CombinedImuFactor.h index 5764d87131..eb1e607b92 100644 --- a/gtsam/navigation/CombinedImuFactor.h +++ b/gtsam/navigation/CombinedImuFactor.h @@ -308,6 +308,139 @@ using CombinedImuFactor = CombinedImuFactorT<>; template GTSAM_EXPORT std::ostream& operator<<(std::ostream& os, const CombinedImuFactorT& f); +/** + * CombinedImuFactorWithGravityT is CombinedImuFactorT with an additional + * GRAVITY variable, so that gravity can be optimized instead of being fixed + * by the preintegration parameters. The 15-dimensional residual is identical + * to CombinedImuFactorT (9 preintegration rows and 6 bias random walk rows); + * only the preintegration rows depend on gravity. Jointly estimating gravity + * and the (evolving) accelerometer bias requires sufficient rotation + * excitation, see Nemiroff, Chen and Lopez, "Joint On-Manifold Gravity and + * Accelerometer Intrinsics Estimation for Inertially Aligned Mapping", 2023. + * + * See ImuFactorWithGravityDirection / ImuFactorWithGravityVector for the two + * gravity parametrizations and their usage guidance. + * + * @ingroup navigation + */ +template +class GTSAM_EXPORT CombinedImuFactorWithGravityT + : public NoiseModelFactorN { + private: + typedef CombinedImuFactorWithGravityT This; + typedef NoiseModelFactorN + Base; + + PIM pim_; + double gravityMagnitude_; ///< used by the Unit3 parametrization only + + public: + // Provide access to the Matrix& version of evaluateError: + using Base::evaluateError; + + /** Shorthand for a smart pointer to a factor */ + typedef std::shared_ptr shared_ptr; + + /** Default constructor - only use for serialization */ + CombinedImuFactorWithGravityT() : gravityMagnitude_(0.0) {} + + /** + * Constructor + * @param pose_i Previous pose key + * @param vel_i Previous velocity key + * @param pose_j Current pose key + * @param vel_j Current velocity key + * @param bias_i Previous bias key + * @param bias_j Current bias key + * @param gravity Gravity key + * @param preintegratedMeasurements Combined IMU measurements + * @param gravityMagnitude The known gravity magnitude for the Unit3 + * parametrization; defaults to the norm of the gravity vector in the + * preintegration params. Unused by the Point3 parametrization. + */ + CombinedImuFactorWithGravityT( + Key pose_i, Key vel_i, Key pose_j, Key vel_j, Key bias_i, Key bias_j, + Key gravity, const PIM& preintegratedMeasurements, + std::optional gravityMagnitude = {}) + : Base(noiseModel::Gaussian::Covariance(preintegratedMeasurements.preintMeasCov()), + pose_i, vel_i, pose_j, vel_j, bias_i, bias_j, gravity), + pim_(preintegratedMeasurements), + gravityMagnitude_(gravityMagnitude + ? *gravityMagnitude + : preintegratedMeasurements.params()->n_gravity.norm()) { + if (internal::GravityParametrization::usesMagnitude && + !(gravityMagnitude_ > 0.0)) + throw std::invalid_argument( + "CombinedImuFactorWithGravityT: gravityMagnitude must be positive"); + } + + ~CombinedImuFactorWithGravityT() override {} + + /// @return a deep copy of this factor + gtsam::NonlinearFactor::shared_ptr clone() const override { + return std::make_shared(*this); + } + + /// @name Testable + /// @{ + void print(const std::string& s = "", const KeyFormatter& keyFormatter = + DefaultKeyFormatter) const override; + bool equals(const NonlinearFactor& expected, double tol = 1e-9) const override; + /// @} + + /** Access the preintegrated measurements. */ + const PIM& preintegratedMeasurements() const { return pim_; } + + /** The gravity magnitude used by the Unit3 parametrization. */ + double gravityMagnitude() const { return gravityMagnitude_; } + + /** implement functions needed to derive from Factor */ + + /// vector of errors + Vector evaluateError(const Pose3& pose_i, const Vector3& vel_i, + const Pose3& pose_j, const Vector3& vel_j, + const imuBias::ConstantBias& bias_i, + const imuBias::ConstantBias& bias_j, + const GRAVITY& gravity, OptionalMatrixType H1, + OptionalMatrixType H2, OptionalMatrixType H3, + OptionalMatrixType H4, OptionalMatrixType H5, + OptionalMatrixType H6, OptionalMatrixType H7) const override; + + private: +#if GTSAM_ENABLE_BOOST_SERIALIZATION + /** Serialization function */ + friend class boost::serialization::access; + template + void serialize(ARCHIVE& ar, const unsigned int /*version*/) { + // Archive name for the base follows the sibling factors' convention: + ar& boost::serialization::make_nvp( + "NoiseModelFactor7", boost::serialization::base_object(*this)); + ar& BOOST_SERIALIZATION_NVP(pim_); + ar& BOOST_SERIALIZATION_NVP(gravityMagnitude_); + } +#endif +}; +// class CombinedImuFactorWithGravityT + +/// CombinedImuFactor variant optimizing the gravity direction (Unit3) with a +/// fixed, known magnitude; see ImuFactorWithGravityDirection. +using CombinedImuFactorWithGravityDirection = + CombinedImuFactorWithGravityT; + +/// CombinedImuFactor variant optimizing the free gravity vector (Point3); +/// see ImuFactorWithGravityVector. +using CombinedImuFactorWithGravityVector = + CombinedImuFactorWithGravityT; + +// operator<< for CombinedImuFactorWithGravityT +template +GTSAM_EXPORT std::ostream& operator<<( + std::ostream& os, const CombinedImuFactorWithGravityT& f); + template <> struct traits : public Testable {}; @@ -319,4 +452,8 @@ struct traits> template struct traits> : public Testable> {}; +template +struct traits> + : public Testable> {}; + } // namespace gtsam diff --git a/gtsam/navigation/navigation.i b/gtsam/navigation/navigation.i index 705b29b48a..72194292eb 100644 --- a/gtsam/navigation/navigation.i +++ b/gtsam/navigation/navigation.i @@ -347,6 +347,46 @@ virtual class CombinedImuFactor: gtsam::NoiseModelFactor { void serialize() const; }; +virtual class CombinedImuFactorWithGravityDirection: gtsam::NoiseModelFactor { + CombinedImuFactorWithGravityDirection(gtsam::Key pose_i, gtsam::Key vel_i, + gtsam::Key pose_j, gtsam::Key vel_j, gtsam::Key bias_i, gtsam::Key bias_j, + gtsam::Key gravity, + const gtsam::PreintegratedCombinedMeasurements& CombinedPreintegratedMeasurements); + CombinedImuFactorWithGravityDirection(gtsam::Key pose_i, gtsam::Key vel_i, + gtsam::Key pose_j, gtsam::Key vel_j, gtsam::Key bias_i, gtsam::Key bias_j, + gtsam::Key gravity, + const gtsam::PreintegratedCombinedMeasurements& CombinedPreintegratedMeasurements, + double gravityMagnitude); + + // Standard Interface + gtsam::PreintegratedCombinedMeasurements preintegratedMeasurements() const; + double gravityMagnitude() const; + gtsam::Vector evaluateError(const gtsam::Pose3& pose_i, gtsam::Vector vel_i, + const gtsam::Pose3& pose_j, gtsam::Vector vel_j, + const gtsam::imuBias::ConstantBias& bias_i, + const gtsam::imuBias::ConstantBias& bias_j, const gtsam::Unit3& gravity); + + // enable serialization functionality + void serialize() const; +}; + +virtual class CombinedImuFactorWithGravityVector: gtsam::NoiseModelFactor { + CombinedImuFactorWithGravityVector(gtsam::Key pose_i, gtsam::Key vel_i, + gtsam::Key pose_j, gtsam::Key vel_j, gtsam::Key bias_i, gtsam::Key bias_j, + gtsam::Key gravity, + const gtsam::PreintegratedCombinedMeasurements& CombinedPreintegratedMeasurements); + + // Standard Interface + gtsam::PreintegratedCombinedMeasurements preintegratedMeasurements() const; + gtsam::Vector evaluateError(const gtsam::Pose3& pose_i, gtsam::Vector vel_i, + const gtsam::Pose3& pose_j, gtsam::Vector vel_j, + const gtsam::imuBias::ConstantBias& bias_i, + const gtsam::imuBias::ConstantBias& bias_j, const gtsam::Point3& gravity); + + // enable serialization functionality + void serialize() const; +}; + #include class PreintegratedAhrsMeasurements { // Standard Constructor diff --git a/gtsam/navigation/tests/testCombinedImuFactor.cpp b/gtsam/navigation/tests/testCombinedImuFactor.cpp index f5e46660c3..2a3966293e 100644 --- a/gtsam/navigation/tests/testCombinedImuFactor.cpp +++ b/gtsam/navigation/tests/testCombinedImuFactor.cpp @@ -31,6 +31,7 @@ #include #include #include +#include #include @@ -315,6 +316,100 @@ TEST(CombinedImuFactor, Accelerating) { EXPECT(assert_equal(estimatedCov, expected, 0.1)); } +/* ************************************************************************* */ +/* ************************************************************************* */ +TEST_PIM(CombinedImuFactorWithGravity, Jacobians) { + using symbol_shorthand::G; + Bias bias(Vector3(0.2, 0, 0), Vector3(0, 0, 0.3)); + Bias bias2(Vector3(0.2, 0.2, 0), Vector3(1, 0, 0.3)); + Pose3 x1(Rot3::Expmap(Vector3(0, 0, M_PI / 4.0)), Point3(5.0, 1.0, -50.0)); + Vector3 v1(0.5, 0.0, 0.0); + Pose3 x2(Rot3::Expmap(Vector3(0, 0, M_PI / 4.0 + M_PI / 10.0)), + Point3(5.5, 1.0, -50.0)); + Vector3 v2(0.5, 0.0, 0.0); + + auto p = combined::Params(); + CombinedPIM pim(p, Bias(Vector3(0.2, 0.0, 0.0), Vector3(0.0, 0.0, 0.0))); + const Vector3 measuredAcc = + x1.rotation().unrotate(-p->n_gravity) + Vector3(0.2, 0.0, 0.0); + const Vector3 measuredOmega(0, 0, M_PI / 10.0 + 0.3); + pim.integrateMeasurement(measuredAcc, measuredOmega, 1.0); + + Values values; + values.insert(X(1), x1); + values.insert(V(1), v1); + values.insert(X(2), x2); + values.insert(V(2), v2); + values.insert(B(1), bias); + values.insert(B(2), bias2); + + { + CombinedImuFactorWithGravityT factor( + X(1), V(1), X(2), V(2), B(1), B(2), G(0), pim); + Values v = values; + v.insert(G(0), Unit3(0.1, -0.2, -1.0)); + EXPECT_CORRECT_FACTOR_JACOBIANS(factor, v, 1e-7, 1e-3); + } + { + CombinedImuFactorWithGravityT factor( + X(1), V(1), X(2), V(2), B(1), B(2), G(0), pim); + Values v = values; + v.insert(G(0), Point3(0.4, -0.6, -9.5)); + EXPECT_CORRECT_FACTOR_JACOBIANS(factor, v, 1e-7, 1e-3); + } +} + +/* ************************************************************************* */ +TEST(CombinedImuFactorWithGravity, Equals) { + using symbol_shorthand::G; + auto p = combined::Params(); + PreintegratedCombinedMeasurements pim(p); + + CombinedImuFactorWithGravityDirection d1(X(1), V(1), X(2), V(2), B(1), B(2), + G(0), pim); + CombinedImuFactorWithGravityDirection d2(X(1), V(1), X(2), V(2), B(1), B(2), + G(0), pim); + CombinedImuFactorWithGravityDirection d3(X(1), V(1), X(2), V(2), B(1), B(2), + G(0), pim, 1.62); + EXPECT(d1.equals(d2)); + EXPECT(!d1.equals(d3)); + + // The Point3 parametrization does not use the magnitude, so factors that + // differ only in the (inert) stored magnitude must compare equal: + CombinedImuFactorWithGravityVector v1(X(1), V(1), X(2), V(2), B(1), B(2), + G(0), pim); + CombinedImuFactorWithGravityVector v2(X(1), V(1), X(2), V(2), B(1), B(2), + G(0), pim); + EXPECT(v1.equals(v2)); + + // Comparing against a different factor type must not crash: + EXPECT(!d1.equals(v1)); + EXPECT(!v1.equals(d1)); +} + +/* ************************************************************************* */ +TEST_PIM(CombinedImuFactorWithGravity, ConsistentWithCombinedImuFactor) { + using symbol_shorthand::G; + auto p = combined::Params(); + CombinedPIM pim(p); + pim.integrateMeasurement(Vector3(0.1, 0.2, -9.81), Vector3(0.1, 0, 0), 0.5); + + const Pose3 x1; + const Vector3 v1(0.1, 0, 0); + const Pose3 x2; + const Vector3 v2(0.1, 0, 0); + const Bias bias1, bias2; + + CombinedImuFactorT plain(X(1), V(1), X(2), V(2), B(1), B(2), pim); + CombinedImuFactorWithGravityT withGravity( + X(1), V(1), X(2), V(2), B(1), B(2), G(0), pim); + // With the params' gravity direction, the errors must agree: + EXPECT(assert_equal( + plain.evaluateError(x1, v1, x2, v2, bias1, bias2), + withGravity.evaluateError(x1, v1, x2, v2, bias1, bias2, + Unit3(p->n_gravity)))); +} + /* ************************************************************************* */ int main() { TestResult tr; diff --git a/gtsam/navigation/tests/testSerializationNavigation.cpp b/gtsam/navigation/tests/testSerializationNavigation.cpp index f0c897675f..eb418beda9 100644 --- a/gtsam/navigation/tests/testSerializationNavigation.cpp +++ b/gtsam/navigation/tests/testSerializationNavigation.cpp @@ -133,6 +133,21 @@ TEST(CombinedImuFactor, Serialization) { EXPECT(equalsBinary(factor)); } +/* ************************************************************************* */ +TEST(CombinedImuFactorWithGravity, Serialization) { + auto pim = getPreintegratedMeasurements(); + + CombinedImuFactorWithGravityDirection direction(1, 2, 3, 4, 5, 6, 7, pim, 9.81); + EXPECT(equalsObj(direction)); + EXPECT(equalsXML(direction)); + EXPECT(equalsBinary(direction)); + + CombinedImuFactorWithGravityVector vector(1, 2, 3, 4, 5, 6, 7, pim); + EXPECT(equalsObj(vector)); + EXPECT(equalsXML(vector)); + EXPECT(equalsBinary(vector)); +} + /* ************************************************************************* */ TEST(AttitudeFactorRot3, Serialization) { Unit3 nDown(0, 0, -1); diff --git a/python/gtsam/tests/test_ImuFactorWithGravity.py b/python/gtsam/tests/test_ImuFactorWithGravity.py index 8dc20929e3..9551f93722 100644 --- a/python/gtsam/tests/test_ImuFactorWithGravity.py +++ b/python/gtsam/tests/test_ImuFactorWithGravity.py @@ -65,6 +65,37 @@ def test_vector_factor(self): gtsam.imuBias.ConstantBias(), np.array([0.0, 0.0, -9.81])) np.testing.assert_allclose(error, np.zeros(9), atol=1e-9) + def test_combined_direction_factor(self): + params = gtsam.PreintegrationCombinedParams.MakeSharedD(9.81) + params.setAccelerometerCovariance(1e-4 * np.eye(3)) + params.setGyroscopeCovariance(1e-6 * np.eye(3)) + params.setIntegrationCovariance(1e-8 * np.eye(3)) + params.setBiasAccCovariance(1e-6 * np.eye(3)) + params.setBiasOmegaCovariance(1e-8 * np.eye(3)) + pim = gtsam.PreintegratedCombinedMeasurements(params) + for _ in range(10): + pim.integrateMeasurement(np.array([0.0, 0.0, 9.81]), np.zeros(3), 0.1) + + zb = gtsam.imuBias.ConstantBias() + factor = gtsam.CombinedImuFactorWithGravityDirection( + X(1), V(1), X(2), V(2), B(1), B(2), G(0), pim) + self.assertAlmostEqual(factor.gravityMagnitude(), 9.81) + error = factor.evaluateError( + gtsam.Pose3(), np.zeros(3), gtsam.Pose3(), np.zeros(3), zb, zb, + gtsam.Unit3(np.array([0.0, 0.0, -1.0]))) + np.testing.assert_allclose(error, np.zeros(15), atol=1e-9) + + explicit = gtsam.CombinedImuFactorWithGravityDirection( + X(1), V(1), X(2), V(2), B(1), B(2), G(0), pim, 1.62) + self.assertAlmostEqual(explicit.gravityMagnitude(), 1.62) + + vector_factor = gtsam.CombinedImuFactorWithGravityVector( + X(1), V(1), X(2), V(2), B(1), B(2), G(0), pim) + error = vector_factor.evaluateError( + gtsam.Pose3(), np.zeros(3), gtsam.Pose3(), np.zeros(3), zb, zb, + np.array([0.0, 0.0, -9.81])) + np.testing.assert_allclose(error, np.zeros(15), atol=1e-9) + def test_vector_norm_factor(self): model = gtsam.noiseModel.Isotropic.Sigma(1, 0.03) factor = gtsam.VectorNormFactor3(G(0), 9.81, model) From 8549976428df69b5ccab247968896ab76dbfe55a Mon Sep 17 00:00:00 2001 From: Nikhil Khedekar Date: Sat, 1 Aug 2026 10:29:54 +0000 Subject: [PATCH 7/7] Add documentation and examples for the gravity-aware IMU factors - doc/ImuFactor.lyx (+ regenerated ImuFactor.pdf, refs.bib entry): new "Gravity as an Optimized Variable" section with the correction-time gravity Jacobian, both parametrizations and their chain rules, the norm pseudo-observation, and the observability caveats, citing Lupton and Sukkarieh (2012) and Nemiroff, Chen and Lopez (2023). - gtsam/navigation/doc/ImuFactorWithGravity.ipynb: family notebook (overview with the three-mode decision rule, summary math, executed usage example recovering a tilted gravity with both parametrizations) following the per-class notebook conventions. - gtsam/nonlinear/doc/VectorNormFactor.ipynb: overview, the once-per-variable rule, the zero-initialization warning, and an executed usage example. - Cross-links from the ImuFactor, CombinedImuFactor and MagFactor notebooks (the latter documenting the new MagFactor2 + VectorNormFactor magnitude-prior capability). - python/gtsam/examples/ImuFactorWithGravityExample.py: runnable demonstration of both gravity parametrizations. --- doc/ImuFactor.lyx | 194 ++++++++++ doc/ImuFactor.pdf | Bin 465405 -> 199305 bytes doc/refs.bib | 6 + gtsam/navigation/doc/CombinedImuFactor.ipynb | 4 +- gtsam/navigation/doc/ImuFactor.ipynb | 4 +- .../navigation/doc/ImuFactorWithGravity.ipynb | 334 ++++++++++++++++++ gtsam/navigation/doc/MagFactor.ipynb | 4 +- gtsam/nonlinear/doc/VectorNormFactor.ipynb | 171 +++++++++ .../examples/ImuFactorWithGravityExample.py | 103 ++++++ 9 files changed, 817 insertions(+), 3 deletions(-) create mode 100644 gtsam/navigation/doc/ImuFactorWithGravity.ipynb create mode 100644 gtsam/nonlinear/doc/VectorNormFactor.ipynb create mode 100644 python/gtsam/examples/ImuFactorWithGravityExample.py diff --git a/doc/ImuFactor.lyx b/doc/ImuFactor.lyx index a286295d40..5c0b7ce197 100644 --- a/doc/ImuFactor.lyx +++ b/doc/ImuFactor.lyx @@ -324,6 +324,200 @@ Since the Combined IMU Factor has a larger state variable due to the inclusion , similarly defined on the tangent space of the NavState manifold. \end_layout +\begin_layout Subsubsection* +Gravity as an Optimized Variable +\end_layout + +\begin_layout Standard +Both factors above treat the gravity vector +\begin_inset Formula $g\in\Rthree$ +\end_inset + +, expressed in the navigation frame, as a known constant taken from the + preintegration parameters. + Because both preintegration variants accumulate the IMU measurements +\emph on +without +\emph default + gravity +\begin_inset space ~ +\end_inset + +\begin_inset CommandInset citation +LatexCommand cite +key "Lupton12tro" +literal "false" + +\end_inset + +, gravity enters only when the preintegrated measurements are corrected + to predict +\begin_inset Formula $\widehat{X_{j}}$ +\end_inset + +, and can therefore be changed, or estimated, at correction time without + re-integrating. + The ImuFactorWithGravity and CombinedImuFactorWithGravity families exploit + this to make gravity an additional optimized variable, for navigation frames + that are not gravity-aligned (e.g. + LiDAR-odometry map frames), for initialization-free operation, or for online + gravity refinement. +\end_layout + +\begin_layout Standard +With +\begin_inset Formula $R_{i}$ +\end_inset + + the attitude at +\begin_inset Formula $t_{i}$ +\end_inset + + and +\begin_inset Formula $\Delta t_{ij}$ +\end_inset + + the preintegration interval, the gravity-dependent part of the correction + adds +\begin_inset Formula $\frac{1}{2}\Delta t_{ij}^{2}R_{i}^{T}g$ +\end_inset + + to the position rows and +\begin_inset Formula $\Delta t_{ij}R_{i}^{T}g$ +\end_inset + + to the velocity rows of the corrected tangent vector +\begin_inset Formula $\xi\in\Rnine$ +\end_inset + +, so the Jacobian of +\begin_inset Formula $\xi$ +\end_inset + + with respect to the gravity vector is simply +\begin_inset Formula +\begin{equation} +\frac{\partial\xi}{\partial g}=\begin{bmatrix}0_{3\times3}\\ +\frac{1}{2}\Delta t_{ij}^{2}R_{i}^{T}\\ +\Delta t_{ij}R_{i}^{T} +\end{bmatrix}\in\Rninethree\label{eq:gravity-jacobian} +\end{equation} + +\end_inset + +where the three block rows correspond to the rotation, position, and velocity + components of the tangent vector. + Two parametrizations of the gravity variable chain onto this matrix: +\end_layout + +\begin_layout Enumerate +ImuFactorWithGravityDirection optimizes a direction +\begin_inset Formula $d\in S^{2}$ +\end_inset + + (a Unit3, 2 +\begin_inset space ~ +\end_inset + +DOF) with a fixed magnitude +\begin_inset Formula $m$ +\end_inset + + given at construction, i.e. + +\begin_inset Formula $g=m\,d$ +\end_inset + + and +\begin_inset Formula $\partial g/\partial\delta d=m\,B$ +\end_inset + + with +\begin_inset Formula $B\in\mathbb{R}^{3\times2}$ +\end_inset + + the tangent basis of +\begin_inset Formula $d$ +\end_inset + +. + On Earth, standard gravity is accurate to about +\begin_inset Formula $0.3\%$ +\end_inset + + everywhere +\begin_inset space ~ +\end_inset + +\begin_inset CommandInset citation +LatexCommand cite +key "Nemiroff23arxiv" +literal "false" + +\end_inset + +, so fixing the magnitude removes a weakly observable degree of freedom + by construction. +\end_layout + +\begin_layout Enumerate +ImuFactorWithGravityVector optimizes the free vector +\begin_inset Formula $g\in\Rthree$ +\end_inset + +, following +\begin_inset CommandInset citation +LatexCommand cite +key "Lupton12tro" +literal "false" + +\end_inset + +. + When the magnitude is approximately known it should be paired with a norm + pseudo-observation +\begin_inset Formula $e=\left\Vert g\right\Vert -g_{0}$ +\end_inset + +, +\begin_inset Formula $\partial e/\partial g=g^{T}/\left\Vert g\right\Vert $ +\end_inset + + (a VectorNormFactor), added +\emph on +once +\emph default + per gravity variable (never per IMU factor, which would count the same + prior information multiple times). +\end_layout + +\begin_layout Standard +Since only the combination +\begin_inset Formula $R_{i}^{T}g$ +\end_inset + + is observed by the accelerometer, gravity and initial attitude are entangled: + a graph should anchor exactly one of the two, either prior knowledge of + roll and pitch or a prior on the gravity variable, but not both tightly. + Gravity magnitude and the accelerometer bias component along gravity are + only jointly observable under rotation excitation whose axis changes over + time +\begin_inset space ~ +\end_inset + +\begin_inset CommandInset citation +LatexCommand cite +key "Nemiroff23arxiv" +literal "false" + +\end_inset + +. + In the CombinedImuFactorWithGravity variants only the nine preintegration + rows of the error depend on gravity; the bias random-walk rows have a zero + gravity Jacobian. +\end_layout + \begin_layout Subsubsection* Covariance Matrices \end_layout diff --git a/doc/ImuFactor.pdf b/doc/ImuFactor.pdf index cf5d109224ea33d179ae744fb5eefb10bd0adeb7..6494d4b02b3da4f96b03611d23f62a964e459382 100644 GIT binary patch literal 199305 zcma%>GqfH2mRse*_YEh8N( z6zRgs=mr!s0Rw@(krfmV4-~zOshzot1pyNS6T$yGQ1oJ!HZG=41oUDyhAyTerpERr zrciu*P|hw+riQjq9$U0?veLke2w(?azfqi$KxR9cKKRtGf`amk(H;;tT7#uRTc!T{ zA=jpS1|Da=GQ-0ocoW3QtOL==6l^Os6l4DdO^ADR|ZWhRHBAQha}E0lgdZ(@Ez}w%N$;y}lCyMCmU(>${aE zn)dd!C#AkX#)}sKQL?cYT)o=zSEkAT`o4IYwu?9m5RWk`MVHZn4HecHxY%$D+&Fnk 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z7U(m`&j6DQ2giCqEDs0AT)6liI3{;yUT_%L#{(GdxE+`dcUJ8z1_uHOkc{K@3*dMX zhk@4@z_1w58UYvzY@2{nhA^;w0b+jCxo3fW0NBUl_6FcR7=WE02jCmQu>~#`1^Z+i z2DV{13~a*y47Xc9J6FJq0W?Ur0JDJs`(GRej!SSD*tX-afA6iF9Stq4O&$L!tF3O~ zX^MM+z$u_+XXgyOI{@CV0A-WqY@gTxFrbkCe3Jxj;uXT6Ot2_JEZ`\"Open\n", + "\n", + "## Overview\n", + "\n", + "The standard [ImuFactor](ImuFactor.ipynb) treats the nav-frame gravity vector as a known\n", + "constant from `PreintegrationParams`. The `ImuFactorWithGravity` family instead makes\n", + "gravity an **optimized variable**, for workflows where the navigation frame is not\n", + "gravity-aligned (eg. LiDAR-odometry map frames), for initialization-free operation, or\n", + "for online gravity refinement.\n", + "\n", + "Gravity knowledge falls on a spectrum, handled by three factor choices:\n", + "\n", + "1. **Known exactly**: use plain `ImuFactor` (gravity from params). Zero cost.\n", + "2. **Known magnitude, unknown direction**: `ImuFactorWithGravityDirection` optimizes a\n", + " `Unit3` direction (2 DOF on $S^2$) scaled by a fixed magnitude given at construction.\n", + " On Earth, standard gravity is accurate to ~0.3% everywhere, so this is usually the\n", + " right choice; it removes the magnitude degree of freedom by construction.\n", + "3. **Unknown magnitude and direction**: `ImuFactorWithGravityVector` optimizes the free\n", + " vector $g \\in \\mathbb{R}^3$ (as a `Point3`), following Lupton and Sukkarieh (2012).\n", + " When the magnitude is *approximately* known, pair it with a single\n", + " [VectorNormFactor](../../nonlinear/doc/VectorNormFactor.ipynb) on the gravity variable.\n", + "\n", + "`CombinedImuFactorWithGravityDirection` / `...Vector` are the corresponding variants of\n", + "[CombinedImuFactor](CombinedImuFactor.ipynb), adding gravity as a 7th variable while\n", + "keeping the bias random walk rows (which have a zero gravity Jacobian).\n", + "\n", + "**Observability**: only the combination $R_i^T g$ is observed by the accelerometer, so\n", + "nav-frame gravity and initial attitude are entangled: anchor exactly one of them (a\n", + "roll/pitch prior *or* a gravity prior, not both tightly). Gravity magnitude and the\n", + "accelerometer bias along gravity are only jointly observable under rotation excitation\n", + "whose axis changes over time (Nemiroff, Chen and Lopez, 2023)." + ] + }, + { + "cell_type": "markdown", + "id": "9efc39bf", + "metadata": {}, + "source": [ + "GTSAM Copyright 2010-2022, Georgia Tech Research Corporation,\n", + "Atlanta, Georgia 30332-0415\n", + "All Rights Reserved\n", + "\n", + "Authors: Frank Dellaert, et al. (see THANKS for the full author list)\n", + "\n", + "See LICENSE for the license information" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "b9b26d2f", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-01T10:20:52.382090Z", + "iopub.status.busy": "2026-08-01T10:20:52.381908Z", + "iopub.status.idle": "2026-08-01T10:20:52.944753Z", + "shell.execute_reply": "2026-08-01T10:20:52.944192Z" + } + }, + "outputs": [], + "source": [ + "# Install gtsam-develop if not installed\n", + "try:\n", + " import gtsam\n", + "except ImportError:\n", + " %pip install --quiet gtsam-develop" + ] + }, + { + "cell_type": "markdown", + "id": "3a646b2d", + "metadata": {}, + "source": [ + "## Mathematical Formulation\n", + "\n", + "Both tangent- and manifold-preintegration accumulate the IMU measurements *without*\n", + "gravity; gravity enters only in the correction step `NavState::correctPIM` (the key\n", + "insight of Lupton and Sukkarieh: gravity can be changed, or estimated, at correction\n", + "time without re-integrating). With $R_i$ the attitude of state $i$ and $\\Delta t$ the\n", + "preintegration interval, the corrected tangent vector is\n", + "\n", + "$$\n", + "\\begin{aligned}\n", + "\\xi_{\\Delta R} &= \\tilde\\xi_{\\Delta R} \\\\\n", + "\\xi_{\\Delta p} &= \\tilde\\xi_{\\Delta p} + \\Delta t\\, R_i^T v_i + \\tfrac{1}{2}\\Delta t^2\\, R_i^T g \\\\\n", + "\\xi_{\\Delta v} &= \\tilde\\xi_{\\Delta v} + \\Delta t\\, R_i^T g\n", + "\\end{aligned}\n", + "$$\n", + "\n", + "so the Jacobian with respect to the gravity *vector* is simply\n", + "\n", + "$$\n", + "\\frac{\\partial \\xi}{\\partial g} =\n", + "\\begin{bmatrix} 0_{3\\times3} \\\\ \\tfrac{1}{2}\\Delta t^2 R_i^T \\\\ \\Delta t\\, R_i^T \\end{bmatrix}\n", + "\\in \\mathbb{R}^{9\\times3}.\n", + "$$\n", + "\n", + "The two parametrizations chain onto this block:\n", + "- **Direction**: $g = m\\,d$ with $d \\in S^2$ a `Unit3` and $m$ fixed, so\n", + " $\\partial g / \\partial \\delta d = m B$ where $B \\in \\mathbb{R}^{3\\times2}$ is the\n", + " tangent basis of $d$ (`Unit3::scaled`) — the same scale-times-direction\n", + " decomposition as [MagFactor3](MagFactor.ipynb).\n", + "- **Vector**: $g$ free, $\\partial g / \\partial g = I_3$; the optional norm\n", + " pseudo-observation is $e = \\lVert g \\rVert - 9.81$ with\n", + " $\\partial e/\\partial g = g^T/\\lVert g \\rVert$, added **once per gravity variable**\n", + " (never per IMU factor, or the same prior information is counted multiple times).\n", + "\n", + "See the \"Gravity as an Optimized Variable\" section of [doc/ImuFactor.pdf](https://github.com/borglab/gtsam/blob/develop/doc/ImuFactor.pdf) for the full derivation." + ] + }, + { + "cell_type": "markdown", + "id": "395d84cc", + "metadata": {}, + "source": [ + "## Usage Example\n", + "\n", + "A stationary IMU in a nav frame whose true gravity is tilted away from the params'\n", + "$-z$ direction: the accelerometer measures $-R^T g_{true}$, so optimizing the gravity\n", + "variable must recover the true tilted gravity." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "ec87c70f", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-01T10:20:52.949842Z", + "iopub.status.busy": "2026-08-01T10:20:52.947469Z", + "iopub.status.idle": "2026-08-01T10:20:52.963619Z", + "shell.execute_reply": "2026-08-01T10:20:52.962902Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "true gravity: [ 0.2941 0.4902 -9.7933]\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "\n", + "import gtsam\n", + "from gtsam.symbol_shorthand import B, G, V, X\n", + "\n", + "# True gravity: tilted ~3.3 degrees away from straight down\n", + "true_gravity = gtsam.Rot3.Rodrigues(0.05, -0.03, 0.0).rotate(\n", + " gtsam.Point3(0, 0, -9.81))\n", + "print(f\"true gravity: {np.round(true_gravity, 4)}\")\n", + "\n", + "# Nominal params believe gravity is straight down (MakeSharedU: z-up nav frame)\n", + "params = gtsam.PreintegrationParams.MakeSharedU(9.81)\n", + "params.setAccelerometerCovariance(1e-4 * np.eye(3))\n", + "params.setGyroscopeCovariance(1e-6 * np.eye(3))\n", + "params.setIntegrationCovariance(1e-8 * np.eye(3))\n", + "\n", + "# Stationary body at identity: the accelerometer measures -g_true\n", + "pim = gtsam.PreintegratedImuMeasurements(params)\n", + "for _ in range(10):\n", + " pim.integrateMeasurement(-true_gravity, np.zeros(3), 0.1)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "c64ee81a", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-01T10:20:52.969144Z", + "iopub.status.busy": "2026-08-01T10:20:52.968927Z", + "iopub.status.idle": "2026-08-01T10:20:52.978487Z", + "shell.execute_reply": "2026-08-01T10:20:52.977203Z" + } + }, + "outputs": [], + "source": [ + "# Common graph: tight priors anchor states and bias, gravity is free\n", + "def make_graph_and_values():\n", + " graph = gtsam.NonlinearFactorGraph()\n", + " tight_pose = gtsam.noiseModel.Isotropic.Sigma(6, 1e-6)\n", + " tight_vec = gtsam.noiseModel.Isotropic.Sigma(3, 1e-6)\n", + " tight_bias = gtsam.noiseModel.Isotropic.Sigma(6, 1e-6)\n", + " graph.addPriorPose3(X(1), gtsam.Pose3(), tight_pose)\n", + " graph.addPriorPose3(X(2), gtsam.Pose3(), tight_pose)\n", + " graph.addPriorVector(V(1), np.zeros(3), tight_vec)\n", + " graph.addPriorVector(V(2), np.zeros(3), tight_vec)\n", + " graph.addPriorConstantBias(B(1), gtsam.imuBias.ConstantBias(), tight_bias)\n", + " values = gtsam.Values()\n", + " values.insert(X(1), gtsam.Pose3())\n", + " values.insert(X(2), gtsam.Pose3())\n", + " values.insert(V(1), np.zeros(3))\n", + " values.insert(V(2), np.zeros(3))\n", + " values.insert(B(1), gtsam.imuBias.ConstantBias())\n", + " return graph, values" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "3aec4ecb", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-01T10:20:52.980345Z", + "iopub.status.busy": "2026-08-01T10:20:52.980152Z", + "iopub.status.idle": "2026-08-01T10:20:52.999390Z", + "shell.execute_reply": "2026-08-01T10:20:52.998560Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "recovered gravity (direction mode): [ 0.2941 0.4902 -9.7933]\n", + "direction error: 1.78e-15\n" + ] + } + ], + "source": [ + "# Mode 2: direction on the sphere, magnitude fixed to 9.81 (from params)\n", + "graph, values = make_graph_and_values()\n", + "graph.add(gtsam.ImuFactorWithGravityDirection(\n", + " X(1), V(1), X(2), V(2), B(1), G(0), pim))\n", + "values.insert(G(0), gtsam.Unit3(np.array([0.0, 0.0, -1.0]))) # initial guess: down\n", + "\n", + "result = gtsam.LevenbergMarquardtOptimizer(graph, values).optimize()\n", + "recovered = result.atUnit3(G(0)).unitVector() * 9.81\n", + "print(f\"recovered gravity (direction mode): {np.round(recovered, 4)}\")\n", + "print(f\"direction error: {np.linalg.norm(recovered - true_gravity):.2e}\")" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "923871a3", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-01T10:20:53.005787Z", + "iopub.status.busy": "2026-08-01T10:20:53.003620Z", + "iopub.status.idle": "2026-08-01T10:20:53.016775Z", + "shell.execute_reply": "2026-08-01T10:20:53.015619Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "recovered gravity (vector mode): [ 0.2941 0.4902 -9.7933]\n", + "vector error: 7.85e-17\n" + ] + } + ], + "source": [ + "# Mode 3: free vector, with Lupton's magnitude pseudo-observation\n", + "graph, values = make_graph_and_values()\n", + "graph.add(gtsam.ImuFactorWithGravityVector(\n", + " X(1), V(1), X(2), V(2), B(1), G(0), pim))\n", + "graph.add(gtsam.VectorNormFactor3(\n", + " G(0), 9.81, gtsam.noiseModel.Isotropic.Sigma(1, 0.03)))\n", + "values.insert(G(0), gtsam.Point3(0, 0, -9.0)) # never initialize at zero!\n", + "\n", + "result = gtsam.LevenbergMarquardtOptimizer(graph, values).optimize()\n", + "recovered = result.atPoint3(G(0))\n", + "print(f\"recovered gravity (vector mode): {np.round(recovered, 4)}\")\n", + "print(f\"vector error: {np.linalg.norm(recovered - true_gravity):.2e}\")" + ] + }, + { + "cell_type": "markdown", + "id": "f165b393", + "metadata": {}, + "source": [ + "## Key Functionality / API\n", + "\n", + "- **Constructors**: same keys as `ImuFactor` plus a gravity key; the Direction variants\n", + " accept an optional `gravityMagnitude` (defaulting to the norm of the params' gravity\n", + " vector). `gravityMagnitude()` returns it.\n", + "- **`evaluateError(pose_i, vel_i, pose_j, vel_j, bias, gravity)`** with `gravity` a\n", + " `Unit3` (Direction) or `Point3` (Vector); optional Jacobians follow the usual\n", + " convention (9×2 or 9×3 for the gravity argument).\n", + "- **`Merge`** (tangent preintegration only) merges consecutive factors sharing bias and\n", + " gravity keys, and rejects mismatched gravity keys or magnitudes.\n", + "- The Combined variants add the second bias key: `CombinedImuFactorWithGravity*` with\n", + " keys `(pose_i, vel_i, pose_j, vel_j, bias_i, bias_j, gravity)` and a 15-dimensional\n", + " error whose bias rows have a zero gravity Jacobian.\n", + "\n", + "## Source\n", + "\n", + "- [ImuFactor.h](https://github.com/borglab/gtsam/blob/develop/gtsam/navigation/ImuFactor.h),\n", + " [CombinedImuFactor.h](https://github.com/borglab/gtsam/blob/develop/gtsam/navigation/CombinedImuFactor.h)\n", + "- Derivation: `doc/ImuFactor.pdf`, section \"Gravity as an Optimized Variable\"\n", + "- T. Lupton and S. Sukkarieh, \"Visual-Inertial-Aided Navigation for High-Dynamic Motion\n", + " in Built Environments Without Initial Conditions\", IEEE T-RO 28(1), 2012.\n", + "- R. Nemiroff, K. Chen and B. T. Lopez, \"Joint On-Manifold Gravity and Accelerometer\n", + " Intrinsics Estimation for Inertially Aligned Mapping\", arXiv:2303.03505, 2023." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "py311", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.15" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/gtsam/navigation/doc/MagFactor.ipynb b/gtsam/navigation/doc/MagFactor.ipynb index 70bdd80e56..1256f95a4a 100644 --- a/gtsam/navigation/doc/MagFactor.ipynb +++ b/gtsam/navigation/doc/MagFactor.ipynb @@ -202,7 +202,9 @@ "## Important Notes\n", "- **Coordinate Frames**: Be very careful with navigation frame (NED vs ENU) and body frame conventions. Ensure the `direction` vector and the `Rot3`/`Pose3` variables use the same navigation frame. The `measured` and `bias` are typically in the body frame.\n", "- **Units**: Ensure consistency between the `scale`, `bias`, `measured` values and the noise model sigma (e.g., all in nanoTesla (nT)).\n", - "- **Calibration**: Accurate knowledge of `scale`, `direction`, and `bias` is crucial for `MagFactor1` and `MagPoseFactor`. If these are unknown, consider using `MagFactor2`/`MagFactor3` or online calibration techniques." + "- **Calibration**: Accurate knowledge of `scale`, `direction`, and `bias` is crucial for `MagFactor1` and `MagPoseFactor`. If these are unknown, consider using `MagFactor2`/`MagFactor3` or online calibration techniques.\n", + "\n", + "When using `MagFactor2` (unknown field vector), the field *magnitude* is often known from the [NOAA tables](http://www.ngdc.noaa.gov/geomag-web/#igrfwmm) even when its direction in the nav frame is not: add a single [VectorNormFactor](../../nonlinear/doc/VectorNormFactor.ipynb) on the field variable as a magnitude pseudo-observation." ] }, { diff --git a/gtsam/nonlinear/doc/VectorNormFactor.ipynb b/gtsam/nonlinear/doc/VectorNormFactor.ipynb new file mode 100644 index 0000000000..fe7e246dae --- /dev/null +++ b/gtsam/nonlinear/doc/VectorNormFactor.ipynb @@ -0,0 +1,171 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "ed487bc4", + "metadata": {}, + "source": [ + "# VectorNormFactor\n", + "\n", + "\"Open\n", + "\n", + "## Overview\n", + "\n", + "`VectorNormFactor` is a unary factor constraining the norm of an N-dimensional\n", + "vector-space variable to a given value, with error\n", + "\n", + "$$ e = \\lVert v \\rVert - \\text{norm}, \\qquad\n", + "\\frac{\\partial e}{\\partial v} = \\frac{v^T}{\\lVert v \\rVert}. $$\n", + "\n", + "The typical use is a **magnitude pseudo-observation** on a physical vector whose\n", + "direction and magnitude are entangled in a single variable:\n", + "\n", + "- an estimated gravity vector, paired with\n", + " [ImuFactorWithGravityVector](../../navigation/doc/ImuFactorWithGravity.ipynb)\n", + " (Lupton and Sukkarieh, 2012), or\n", + "- a local magnetic field vector estimated with\n", + " [MagFactor2](../../navigation/doc/MagFactor.ipynb), whose magnitude is often known\n", + " from the [NOAA tables](http://www.ngdc.noaa.gov/geomag-web/#igrfwmm) even when its\n", + " direction in the nav frame is not.\n", + "\n", + "Add it **once per variable**: adding it per measurement factor would count the same\n", + "prior knowledge multiple times. The N=3 instantiation is available in Python as\n", + "`VectorNormFactor3`.\n", + "\n", + "**Warning**: the error is not differentiable at $\\lVert v \\rVert = 0$; the Jacobian\n", + "is zero there, so a variable initialized at exactly zero receives no gradient from this\n", + "factor and will not move. Always initialize with a non-zero guess." + ] + }, + { + "cell_type": "markdown", + "id": "4fa7ea59", + "metadata": {}, + "source": [ + "GTSAM Copyright 2010-2022, Georgia Tech Research Corporation,\n", + "Atlanta, Georgia 30332-0415\n", + "All Rights Reserved\n", + "\n", + "Authors: Frank Dellaert, et al. (see THANKS for the full author list)\n", + "\n", + "See LICENSE for the license information" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "d796072b", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-01T10:20:56.326366Z", + "iopub.status.busy": "2026-08-01T10:20:56.326254Z", + "iopub.status.idle": "2026-08-01T10:20:56.526270Z", + "shell.execute_reply": "2026-08-01T10:20:56.525643Z" + } + }, + "outputs": [], + "source": [ + "# Install gtsam-develop if not installed\n", + "try:\n", + " import gtsam\n", + "except ImportError:\n", + " %pip install --quiet gtsam-develop" + ] + }, + { + "cell_type": "markdown", + "id": "f355f1ac", + "metadata": {}, + "source": [ + "## Usage Example\n", + "\n", + "A loose vector prior fixes the direction; the norm factor pulls the magnitude to the\n", + "target along that direction." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "39d3bf51", + "metadata": { + "execution": { + "iopub.execute_input": "2026-08-01T10:20:56.538172Z", + "iopub.status.busy": "2026-08-01T10:20:56.537704Z", + "iopub.status.idle": "2026-08-01T10:20:56.542997Z", + "shell.execute_reply": "2026-08-01T10:20:56.542570Z" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "optimized vector: [5.6638 5.6638 5.6638]\n", + "norm: 9.81000 (target 9.81)\n" + ] + } + ], + "source": [ + "import numpy as np\n", + "\n", + "import gtsam\n", + "from gtsam.symbol_shorthand import G\n", + "\n", + "graph = gtsam.NonlinearFactorGraph()\n", + "direction = np.array([1.0, 1.0, 1.0]) / np.sqrt(3.0)\n", + "graph.addPriorPoint3(G(0), gtsam.Point3(8.0 * direction),\n", + " gtsam.noiseModel.Isotropic.Sigma(3, 10.0))\n", + "graph.add(gtsam.VectorNormFactor3(\n", + " G(0), 9.81, gtsam.noiseModel.Isotropic.Sigma(1, 1e-3)))\n", + "\n", + "values = gtsam.Values()\n", + "values.insert(G(0), gtsam.Point3(8.0 * direction)) # non-zero initial guess\n", + "\n", + "result = gtsam.LevenbergMarquardtOptimizer(graph, values).optimize()\n", + "optimized = result.atPoint3(G(0))\n", + "print(f\"optimized vector: {np.round(optimized, 4)}\")\n", + "print(f\"norm: {np.linalg.norm(optimized):.5f} (target 9.81)\")" + ] + }, + { + "cell_type": "markdown", + "id": "574a4abb", + "metadata": {}, + "source": [ + "## Key Functionality / API\n", + "\n", + "- `VectorNormFactor3(key, norm, noiseModel)`: constrain a `Point3`/`Vector3` variable.\n", + "- `norm()`: the target norm.\n", + "- With a `noiseModel::Constrained` model it acts as a hard constraint under QR-based\n", + " elimination (not recommended with Cholesky). If the norm is known *exactly*, prefer a\n", + " parametrization that fixes it instead, eg. `Unit3` with a fixed magnitude\n", + " ([ImuFactorWithGravityDirection](../../navigation/doc/ImuFactorWithGravity.ipynb)).\n", + "\n", + "## Source\n", + "\n", + "- [VectorNormFactor.h](https://github.com/borglab/gtsam/blob/develop/gtsam/nonlinear/VectorNormFactor.h)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "py311", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.11.15" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/python/gtsam/examples/ImuFactorWithGravityExample.py b/python/gtsam/examples/ImuFactorWithGravityExample.py new file mode 100644 index 0000000000..63c4ef9575 --- /dev/null +++ b/python/gtsam/examples/ImuFactorWithGravityExample.py @@ -0,0 +1,103 @@ +""" +GTSAM Copyright 2010-2019, Georgia Tech Research Corporation, +Atlanta, Georgia 30332-0415 +All Rights Reserved + +See LICENSE for the license information + +A script demonstrating gravity estimation with the ImuFactorWithGravity family: +a stationary IMU in a navigation frame whose true gravity is tilted away from +the direction assumed by the preintegration parameters. The accelerometer +measures -R^T g_true, so optimizing the gravity variable recovers the tilt. + +Two parametrizations are demonstrated: +- ImuFactorWithGravityDirection: Unit3 direction with a fixed, known magnitude. +- ImuFactorWithGravityVector: free Point3 vector, paired with a single + VectorNormFactor3 as the magnitude pseudo-observation of + [Lupton and Sukkarieh, TRO 2012]. + +Author: Nikhil Khedekar +""" + +# pylint: disable=no-name-in-module,import-error + +import numpy as np + +import gtsam +from gtsam.symbol_shorthand import B, G, V, X + + +def stationary_pim(true_gravity: np.ndarray) -> gtsam.PreintegratedImuMeasurements: + """Integrate one second of stationary IMU data under the given gravity.""" + # Nominal params believe gravity is straight down (z-up navigation frame); + # they also provide the default magnitude for the Direction factor. + params = gtsam.PreintegrationParams.MakeSharedU(9.81) + params.setAccelerometerCovariance(1e-4 * np.eye(3)) + params.setGyroscopeCovariance(1e-6 * np.eye(3)) + params.setIntegrationCovariance(1e-8 * np.eye(3)) + + pim = gtsam.PreintegratedImuMeasurements(params) + for _ in range(10): + # A stationary accelerometer measures the specific force -R^T g_true: + pim.integrateMeasurement(-true_gravity, np.zeros(3), 0.1) + return pim + + +def make_graph_and_values(): + """Tight priors anchor both states and the bias; gravity is left free.""" + graph = gtsam.NonlinearFactorGraph() + tight_pose = gtsam.noiseModel.Isotropic.Sigma(6, 1e-6) + tight_vec = gtsam.noiseModel.Isotropic.Sigma(3, 1e-6) + tight_bias = gtsam.noiseModel.Isotropic.Sigma(6, 1e-6) + graph.addPriorPose3(X(1), gtsam.Pose3(), tight_pose) + graph.addPriorPose3(X(2), gtsam.Pose3(), tight_pose) + graph.addPriorVector(V(1), np.zeros(3), tight_vec) + graph.addPriorVector(V(2), np.zeros(3), tight_vec) + graph.addPriorConstantBias(B(1), gtsam.imuBias.ConstantBias(), tight_bias) + + values = gtsam.Values() + values.insert(X(1), gtsam.Pose3()) + values.insert(X(2), gtsam.Pose3()) + values.insert(V(1), np.zeros(3)) + values.insert(V(2), np.zeros(3)) + values.insert(B(1), gtsam.imuBias.ConstantBias()) + return graph, values + + +def main(): + # True gravity: tilted ~3.3 degrees away from straight down. + true_gravity = gtsam.Rot3.Rodrigues(0.05, -0.03, 0.0).rotate( + gtsam.Point3(0, 0, -9.81)) + print(f"true gravity: {np.round(true_gravity, 4)}") + + pim = stationary_pim(true_gravity) + + # Mode 1 (for reference): plain ImuFactor with gravity fixed by the params + # would leave a large residual here, since the params assume (0, 0, -9.81). + + # Mode 2: direction on the sphere, magnitude fixed to 9.81 (from params). + graph, values = make_graph_and_values() + graph.add(gtsam.ImuFactorWithGravityDirection( + X(1), V(1), X(2), V(2), B(1), G(0), pim)) + values.insert(G(0), gtsam.Unit3(np.array([0.0, 0.0, -1.0]))) + result = gtsam.LevenbergMarquardtOptimizer(graph, values).optimize() + recovered = result.atUnit3(G(0)).unitVector() * 9.81 + print(f"recovered (direction, |g| fixed): {np.round(recovered, 4)}" + f" error {np.linalg.norm(recovered - true_gravity):.2e}") + + # Mode 3: free vector with Lupton's magnitude pseudo-observation, added + # once on the gravity variable (never per IMU factor). + graph, values = make_graph_and_values() + graph.add(gtsam.ImuFactorWithGravityVector( + X(1), V(1), X(2), V(2), B(1), G(0), pim)) + graph.add(gtsam.VectorNormFactor3( + G(0), 9.81, gtsam.noiseModel.Isotropic.Sigma(1, 0.03))) + values.insert(G(0), gtsam.Point3(0, 0, -9.0)) # never initialize at zero! + result = gtsam.LevenbergMarquardtOptimizer(graph, values).optimize() + recovered = result.atPoint3(G(0)) + print(f"recovered (free vector + norm): {np.round(recovered, 4)}" + f" error {np.linalg.norm(recovered - true_gravity):.2e}") + + +if __name__ == "__main__": + main()