Merge pull request #2103 from jenniferoum/feature/equivariant-filter
C++ example of an Equivariant filterrelease/4.3a0
Frank Dellaert
GitHub
commit
deb4045aa6
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/**
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* @file ABC.h
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* @brief Core components for Attitude-Bias-Calibration systems
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*
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* This file contains fundamental components and utilities for the ABC system
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* based on the paper "Overcoming Bias: Equivariant Filter Design for Biased
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* Attitude Estimation with Online Calibration" by Fornasier et al.
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* Authors: Darshan Rajasekaran & Jennifer Oum
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*/
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#ifndef ABC_H
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#define ABC_H
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#include <gtsam/base/Matrix.h>
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#include <gtsam/base/Vector.h>
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#include <gtsam/geometry/Rot3.h>
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#include <gtsam/geometry/Unit3.h>
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namespace gtsam {
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namespace abc_eqf_lib {
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using namespace std;
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using namespace gtsam;
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//========================================================================
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// Utility Functions
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//========================================================================
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//========================================================================
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// Utility Functions
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//========================================================================
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/// Check if a vector is a unit vector
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bool checkNorm(const Vector3& x, double tol = 1e-3);
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/// Check if vector contains NaN values
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bool hasNaN(const Vector3& vec);
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/// Create a block diagonal matrix from two matrices
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Matrix blockDiag(const Matrix& A, const Matrix& B);
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/// Repeat a block matrix n times along the diagonal
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Matrix repBlock(const Matrix& A, int n);
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// Utility Functions Implementation
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/**
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* @brief Verifies if a vector has unit norm within tolerance
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* @param x 3d vector
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* @param tol optional tolerance
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* @return Bool indicating that the vector norm is approximately 1
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*/
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bool checkNorm(const Vector3& x, double tol) {
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return abs(x.norm() - 1) < tol || std::isnan(x.norm());
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}
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/**
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* @brief Checks if the input vector has any NaNs
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* @param vec A 3-D vector
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* @return true if present, false otherwise
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*/
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bool hasNaN(const Vector3& vec) {
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return std::isnan(vec[0]) || std::isnan(vec[1]) || std::isnan(vec[2]);
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}
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/**
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* @brief Creates a block diagonal matrix from input matrices
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* @param A Matrix A
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* @param B Matrix B
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* @return A single consolidated matrix with A in the top left and B in the
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* bottom right
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*/
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Matrix blockDiag(const Matrix& A, const Matrix& B) {
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if (A.size() == 0) {
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return B;
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} else if (B.size() == 0) {
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return A;
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} else {
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Matrix result(A.rows() + B.rows(), A.cols() + B.cols());
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result.setZero();
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result.block(0, 0, A.rows(), A.cols()) = A;
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result.block(A.rows(), A.cols(), B.rows(), B.cols()) = B;
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return result;
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}
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}
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/**
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* @brief Creates a block diagonal matrix by repeating a matrix 'n' times
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* @param A A matrix
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* @param n Number of times to be repeated
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* @return Block diag matrix with A repeated 'n' times
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*/
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Matrix repBlock(const Matrix& A, int n) {
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if (n <= 0) return Matrix();
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Matrix result = A;
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for (int i = 1; i < n; i++) {
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result = blockDiag(result, A);
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}
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return result;
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}
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//========================================================================
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// Core Data Types
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//========================================================================
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/// Input struct for the Biased Attitude System
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struct Input {
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Vector3 w; /// Angular velocity (3-vector)
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Matrix Sigma; /// Noise covariance (6x6 matrix)
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static Input random(); /// Random input
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Matrix3 W() const { /// Return w as a skew symmetric matrix
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return Rot3::Hat(w);
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}
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};
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/// Measurement struct
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struct Measurement {
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Unit3 y; /// Measurement direction in sensor frame
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Unit3 d; /// Known direction in global frame
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Matrix3 Sigma; /// Covariance matrix of the measurement
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int cal_idx = -1; /// Calibration index (-1 for calibrated sensor)
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};
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/// State class representing the state of the Biased Attitude System
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template <size_t N>
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class State {
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public:
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Rot3 R; // Attitude rotation matrix R
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Vector3 b; // Gyroscope bias b
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std::array<Rot3, N> S; // Sensor calibrations S
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/// Constructor
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State(const Rot3& R = Rot3::Identity(), const Vector3& b = Vector3::Zero(),
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const std::array<Rot3, N>& S = std::array<Rot3, N>{})
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: R(R), b(b), S(S) {}
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/// Identity function
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static State identity() {
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std::array<Rot3, N> S_id{};
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S_id.fill(Rot3::Identity());
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return State(Rot3::Identity(), Vector3::Zero(), S_id);
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}
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/**
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* Compute Local coordinates in the state relative to another state.
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* @param other The other state
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* @return Local coordinates in the tangent space
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*/
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Vector localCoordinates(const State<N>& other) const {
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Vector eps(6 + 3 * N);
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// First 3 elements - attitude
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eps.head<3>() = Rot3::Logmap(R.between(other.R));
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// Next 3 elements - bias
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// Next 3 elements - bias
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eps.segment<3>(3) = other.b - b;
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// Remaining elements - calibrations
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for (size_t i = 0; i < N; i++) {
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eps.segment<3>(6 + 3 * i) = Rot3::Logmap(S[i].between(other.S[i]));
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}
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return eps;
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}
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/**
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* Retract from tangent space back to the manifold
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* @param v Vector in the tangent space
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* @return New state
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*/
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State retract(const Vector& v) const {
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if (v.size() != static_cast<Eigen::Index>(6 + 3 * N)) {
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throw std::invalid_argument(
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"Vector size does not match state dimensions");
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}
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Rot3 newR = R * Rot3::Expmap(v.head<3>());
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Vector3 newB = b + v.segment<3>(3);
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std::array<Rot3, N> newS;
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for (size_t i = 0; i < N; i++) {
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newS[i] = S[i] * Rot3::Expmap(v.segment<3>(6 + 3 * i));
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}
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return State(newR, newB, newS);
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}
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};
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//========================================================================
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// Symmetry Group
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//========================================================================
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/**
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* Symmetry group (SO(3) |x so(3)) x SO(3) x ... x SO(3)
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* Each element of the B list is associated with a calibration state
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*/
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template <size_t N>
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struct G {
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Rot3 A; /// First SO(3) element
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Matrix3 a; /// so(3) element (skew-symmetric matrix)
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std::array<Rot3, N> B; /// List of SO(3) elements for calibration
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/// Initialize the symmetry group G
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G(const Rot3& A = Rot3::Identity(), const Matrix3& a = Matrix3::Zero(),
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const std::array<Rot3, N>& B = std::array<Rot3, N>{})
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: A(A), a(a), B(B) {}
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/// Group multiplication
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G operator*(const G<N>& other) const {
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std::array<Rot3, N> newB;
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for (size_t i = 0; i < N; i++) {
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newB[i] = B[i] * other.B[i];
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}
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return G(A * other.A, a + Rot3::Hat(A.matrix() * Rot3::Vee(other.a)), newB);
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}
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/// Group inverse
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G inv() const {
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Matrix3 Ainv = A.inverse().matrix();
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std::array<Rot3, N> Binv;
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for (size_t i = 0; i < N; i++) {
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Binv[i] = B[i].inverse();
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}
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return G(A.inverse(), -Rot3::Hat(Ainv * Rot3::Vee(a)), Binv);
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}
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/// Identity element
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static G identity(int n) {
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std::array<Rot3, N> B;
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B.fill(Rot3::Identity());
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return G(Rot3::Identity(), Matrix3::Zero(), B);
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}
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/// Exponential map of the tangent space elements to the group
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static G exp(const Vector& x) {
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if (x.size() != static_cast<Eigen::Index>(6 + 3 * N)) {
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throw std::invalid_argument("Vector size mismatch for group exponential");
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}
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Rot3 A = Rot3::Expmap(x.head<3>());
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Vector3 a_vee = Rot3::ExpmapDerivative(-x.head<3>()) * x.segment<3>(3);
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Matrix3 a = Rot3::Hat(a_vee);
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std::array<Rot3, N> B;
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for (size_t i = 0; i < N; i++) {
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B[i] = Rot3::Expmap(x.segment<3>(6 + 3 * i));
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}
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return G(A, a, B);
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}
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};
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} // namespace abc_eqf_lib
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template <size_t N>
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struct traits<abc_eqf_lib::State<N>>
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: internal::LieGroupTraits<abc_eqf_lib::State<N>> {};
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template <size_t N>
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struct traits<abc_eqf_lib::G<N>> : internal::LieGroupTraits<abc_eqf_lib::G<N>> {
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};
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} // namespace gtsam
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#endif // ABC_H
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/**
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* @file ABC_EQF.h
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* @brief Header file for the Attitude-Bias-Calibration Equivariant Filter
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*
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* This file contains declarations for the Equivariant Filter (EqF) for attitude
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* estimation with both gyroscope bias and sensor extrinsic calibration, based
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* on the paper: "Overcoming Bias: Equivariant Filter Design for Biased Attitude
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* Estimation with Online Calibration" by Fornasier et al. Authors: Darshan
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* Rajasekaran & Jennifer Oum
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*/
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#ifndef ABC_EQF_H
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#define ABC_EQF_H
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#pragma once
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#include <gtsam/base/Matrix.h>
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#include <gtsam/base/Vector.h>
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#include <gtsam/geometry/Rot3.h>
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#include <gtsam/geometry/Unit3.h>
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#include <gtsam/inference/Symbol.h>
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#include <gtsam/navigation/ImuBias.h>
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#include <gtsam/nonlinear/Values.h>
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#include <gtsam/slam/dataset.h>
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#include <chrono>
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#include <cmath>
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#include <fstream>
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#include <functional>
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#include <iostream>
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#include <numeric> // For std::accumulate
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#include <string>
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#include <vector>
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#include "ABC.h"
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// All implementations are wrapped in this namespace to avoid conflicts
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namespace gtsam {
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namespace abc_eqf_lib {
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using namespace std;
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using namespace gtsam;
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//========================================================================
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// Helper Functions for EqF
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//========================================================================
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/// Calculate numerical differential
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Matrix numericalDifferential(std::function<Vector(const Vector&)> f,
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const Vector& x);
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/**
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* Compute the lift of the system (Theorem 3.8, Equation 7)
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* @param xi State
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* @param u Input
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* @return Lift vector
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*/
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template <size_t N>
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Vector lift(const State<N>& xi, const Input& u);
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/**
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* Action of the symmetry group on the state space (Equation 4)
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* @param X Group element
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* @param xi State
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* @return New state after group action
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*/
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template <size_t N>
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State<N> operator*(const G<N>& X, const State<N>& xi);
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/**
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* Action of the symmetry group on the input space (Equation 5)
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* @param X Group element
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* @param u Input
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* @return New input after group action
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*/
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template <size_t N>
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Input velocityAction(const G<N>& X, const Input& u);
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/**
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* Action of the symmetry group on the output space (Equation 6)
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* @param X Group element
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* @param y Direction measurement
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* @param idx Calibration index
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* @return New direction after group action
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*/
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template <size_t N>
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Vector3 outputAction(const G<N>& X, const Unit3& y, int idx);
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/**
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* Differential of the phi action at E = Id in local coordinates
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* @param xi State
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* @return Differential matrix
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*/
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template <size_t N>
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Matrix stateActionDiff(const State<N>& xi);
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//========================================================================
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// Equivariant Filter (EqF)
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//========================================================================
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/// Equivariant Filter (EqF) implementation
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template <size_t N>
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class EqF {
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private:
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int dof; // Degrees of freedom
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G<N> X_hat; // Filter state
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Matrix Sigma; // Error covariance
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State<N> xi_0; // Origin state
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Matrix Dphi0; // Differential of phi at origin
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Matrix InnovationLift; // Innovation lift matrix
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/**
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* Return the state matrix A0t (Equation 14a)
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* @param u Input
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* @return State matrix A0t
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*/
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Matrix stateMatrixA(const Input& u) const;
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/**
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* Return the state transition matrix Phi (Equation 17)
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* @param u Input
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* @param dt Time step
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* @return State transition matrix Phi
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*/
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Matrix stateTransitionMatrix(const Input& u, double dt) const;
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/**
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* Return the Input matrix Bt
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* @return Input matrix Bt
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*/
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Matrix inputMatrixBt() const;
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/**
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* Return the measurement matrix C0 (Equation 14b)
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* @param d Known direction
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* @param idx Calibration index
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* @return Measurement matrix C0
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*/
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Matrix measurementMatrixC(const Unit3& d, int idx) const;
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/**
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* Return the measurement output matrix Dt
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* @param idx Calibration index
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* @return Measurement output matrix Dt
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*/
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Matrix outputMatrixDt(int idx) const;
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public:
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/**
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* Initialize EqF
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* @param Sigma Initial covariance
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* @param m Number of sensors
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*/
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EqF(const Matrix& Sigma, int m);
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/**
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* Return estimated state
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* @return Current state estimate
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*/
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State<N> stateEstimate() const;
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/**
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* Propagate the filter state
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* @param u Angular velocity measurement
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* @param dt Time step
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*/
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void propagation(const Input& u, double dt);
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/**
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* Update the filter state with a measurement
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* @param y Direction measurement
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*/
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void update(const Measurement& y);
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};
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//========================================================================
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// Helper Functions Implementation
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//========================================================================
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/**
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* Maps system dynamics to the symmetry group
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* @param xi State
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* @param u Input
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* @return Lifted input in Lie Algebra
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* Uses Vector zero & Rot3 inverse, matrix functions
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*/
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template <size_t N>
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Vector lift(const State<N>& xi, const Input& u) {
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Vector L = Vector::Zero(6 + 3 * N);
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// First 3 elements
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L.head<3>() = u.w - xi.b;
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// Next 3 elements
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L.segment<3>(3) = -u.W() * xi.b;
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// Remaining elements
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for (size_t i = 0; i < N; i++) {
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L.segment<3>(6 + 3 * i) = xi.S[i].inverse().matrix() * L.head<3>();
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}
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return L;
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}
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/**
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* Implements group actions on the states
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* @param X A symmetry group element G consisting of the attitude, bias and the
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* calibration components X.a -> Rotation matrix containing the attitude X.b ->
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* A skew-symmetric matrix representing bias X.B -> A vector of Rotation
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* matrices for the calibration components
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* @param xi State object
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* xi.R -> Attitude (Rot3)
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* xi.b -> Gyroscope Bias(Vector 3)
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* xi.S -> Vector of calibration matrices(Rot3)
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* @return Transformed state
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* Uses the Rot3 inverse and Vee functions
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*/
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template <size_t N>
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State<N> operator*(const G<N>& X, const State<N>& xi) {
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std::array<Rot3, N> new_S;
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for (size_t i = 0; i < N; i++) {
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new_S[i] = X.A.inverse() * xi.S[i] * X.B[i];
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}
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return State<N>(xi.R * X.A, X.A.inverse().matrix() * (xi.b - Rot3::Vee(X.a)),
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new_S);
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}
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/**
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* Transforms the angular velocity measurements b/w frames
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* @param X A symmetry group element X with the components
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* @param u Inputs
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* @return Transformed inputs
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* Uses Rot3 Inverse, matrix and Vee functions and is critical for maintaining
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* the input equivariance
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*/
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template <size_t N>
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Input velocityAction(const G<N>& X, const Input& u) {
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return Input{X.A.inverse().matrix() * (u.w - Rot3::Vee(X.a)), u.Sigma};
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}
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/**
|
||||
* Transforms the Direction measurements based on the calibration type ( Eqn 6)
|
||||
* @param X Group element X
|
||||
* @param y Direction measurement y
|
||||
* @param idx Calibration index
|
||||
* @return Transformed direction
|
||||
* Uses Rot3 inverse, matric and Unit3 unitvector functions
|
||||
*/
|
||||
template <size_t N>
|
||||
Vector3 outputAction(const G<N>& X, const Unit3& y, int idx) {
|
||||
if (idx == -1) {
|
||||
return X.A.inverse().matrix() * y.unitVector();
|
||||
} else {
|
||||
if (idx >= static_cast<int>(N)) {
|
||||
throw std::out_of_range("Calibration index out of range");
|
||||
}
|
||||
return X.B[idx].inverse().matrix() * y.unitVector();
|
||||
}
|
||||
}
|
||||
|
||||
/**
|
||||
* @brief Calculates the Jacobian matrix using central difference approximation
|
||||
* @param f Vector function f
|
||||
* @param x The point at which Jacobian is evaluated
|
||||
* @return Matrix containing numerical partial derivatives of f at x
|
||||
* Uses Vector's size() and Zero(), Matrix's Zero() and col() methods
|
||||
*/
|
||||
Matrix numericalDifferential(std::function<Vector(const Vector&)> f,
|
||||
const Vector& x) {
|
||||
double h = 1e-6;
|
||||
Vector fx = f(x);
|
||||
int n = fx.size();
|
||||
int m = x.size();
|
||||
Matrix Df = Matrix::Zero(n, m);
|
||||
|
||||
for (int j = 0; j < m; j++) {
|
||||
Vector ej = Vector::Zero(m);
|
||||
ej(j) = 1.0;
|
||||
|
||||
Vector fplus = f(x + h * ej);
|
||||
Vector fminus = f(x - h * ej);
|
||||
|
||||
Df.col(j) = (fplus - fminus) / (2 * h);
|
||||
}
|
||||
|
||||
return Df;
|
||||
}
|
||||
|
||||
/**
|
||||
* Computes the differential of a state action at the identity of the symmetry
|
||||
* group
|
||||
* @param xi State object Xi representing the point at which to evaluate the
|
||||
* differential
|
||||
* @return A matrix representing the jacobian of the state action
|
||||
* Uses numericalDifferential, and Rot3 expmap, logmap
|
||||
*/
|
||||
template <size_t N>
|
||||
Matrix stateActionDiff(const State<N>& xi) {
|
||||
std::function<Vector(const Vector&)> coordsAction = [&xi](const Vector& U) {
|
||||
G<N> groupElement = G<N>::exp(U);
|
||||
State<N> transformed = groupElement * xi;
|
||||
return xi.localCoordinates(transformed);
|
||||
};
|
||||
|
||||
Vector zeros = Vector::Zero(6 + 3 * N);
|
||||
Matrix differential = numericalDifferential(coordsAction, zeros);
|
||||
return differential;
|
||||
}
|
||||
|
||||
//========================================================================
|
||||
// Equivariant Filter (EqF) Implementation
|
||||
//========================================================================
|
||||
/**
|
||||
* Initializes the EqF with state dimension validation and computes lifted
|
||||
* innovation mapping
|
||||
* @param Sigma Initial covariance
|
||||
* @param n Number of calibration states
|
||||
* @param m Number of sensors
|
||||
* Uses SelfAdjointSolver, completeOrthoganalDecomposition().pseudoInverse()
|
||||
*/
|
||||
template <size_t N>
|
||||
EqF<N>::EqF(const Matrix& Sigma, int m)
|
||||
: dof(6 + 3 * N),
|
||||
X_hat(G<N>::identity(N)),
|
||||
Sigma(Sigma),
|
||||
xi_0(State<N>::identity()) {
|
||||
if (Sigma.rows() != dof || Sigma.cols() != dof) {
|
||||
throw std::invalid_argument(
|
||||
"Initial covariance dimensions must match the degrees of freedom");
|
||||
}
|
||||
|
||||
// Check positive semi-definite
|
||||
Eigen::SelfAdjointEigenSolver<Matrix> eigensolver(Sigma);
|
||||
if (eigensolver.eigenvalues().minCoeff() < -1e-10) {
|
||||
throw std::invalid_argument(
|
||||
"Covariance matrix must be semi-positive definite");
|
||||
}
|
||||
|
||||
if (N < 0) {
|
||||
throw std::invalid_argument(
|
||||
"Number of calibration states must be non-negative");
|
||||
}
|
||||
|
||||
if (m <= 1) {
|
||||
throw std::invalid_argument(
|
||||
"Number of direction sensors must be at least 2");
|
||||
}
|
||||
|
||||
// Compute differential of phi
|
||||
Dphi0 = stateActionDiff(xi_0);
|
||||
InnovationLift = Dphi0.completeOrthogonalDecomposition().pseudoInverse();
|
||||
}
|
||||
/**
|
||||
* Computes the internal group state to a physical state estimate
|
||||
* @return Current state estimate
|
||||
*/
|
||||
template <size_t N>
|
||||
State<N> EqF<N>::stateEstimate() const {
|
||||
return X_hat * xi_0;
|
||||
}
|
||||
/**
|
||||
* Implements the prediction step of the EqF using system dynamics and
|
||||
* covariance propagation and advances the filter state by symmtery-preserving
|
||||
* dynamics.Uses a Lie group integrator scheme for discrete time propagation
|
||||
* @param u Angular velocity measurements
|
||||
* @param dt time steps
|
||||
* Updated internal state and covariance
|
||||
*/
|
||||
template <size_t N>
|
||||
void EqF<N>::propagation(const Input& u, double dt) {
|
||||
State<N> state_est = stateEstimate();
|
||||
Vector L = lift(state_est, u);
|
||||
|
||||
Matrix Phi_DT = stateTransitionMatrix(u, dt);
|
||||
Matrix Bt = inputMatrixBt();
|
||||
|
||||
Matrix tempSigma = blockDiag(u.Sigma, repBlock(1e-9 * I_3x3, N));
|
||||
Matrix M_DT = (Bt * tempSigma * Bt.transpose()) * dt;
|
||||
|
||||
X_hat = X_hat * G<N>::exp(L * dt);
|
||||
Sigma = Phi_DT * Sigma * Phi_DT.transpose() + M_DT;
|
||||
}
|
||||
/**
|
||||
* Implements the correction step of the filter using discrete measurements
|
||||
* Computes the measurement residual, Kalman gain and the updates both the state
|
||||
* and covariance
|
||||
*
|
||||
* @param y Measurements
|
||||
*/
|
||||
template <size_t N>
|
||||
void EqF<N>::update(const Measurement& y) {
|
||||
if (y.cal_idx > static_cast<int>(N)) {
|
||||
throw std::invalid_argument("Calibration index out of range");
|
||||
}
|
||||
|
||||
// Get vector representations for checking
|
||||
Vector3 y_vec = y.y.unitVector();
|
||||
Vector3 d_vec = y.d.unitVector();
|
||||
|
||||
// Skip update if any NaN values are present
|
||||
if (std::isnan(y_vec[0]) || std::isnan(y_vec[1]) || std::isnan(y_vec[2]) ||
|
||||
std::isnan(d_vec[0]) || std::isnan(d_vec[1]) || std::isnan(d_vec[2])) {
|
||||
return; // Skip this measurement
|
||||
}
|
||||
|
||||
Matrix Ct = measurementMatrixC(y.d, y.cal_idx);
|
||||
Vector3 action_result = outputAction(X_hat.inv(), y.y, y.cal_idx);
|
||||
Vector3 delta_vec = Rot3::Hat(y.d.unitVector()) * action_result;
|
||||
Matrix Dt = outputMatrixDt(y.cal_idx);
|
||||
Matrix S = Ct * Sigma * Ct.transpose() + Dt * y.Sigma * Dt.transpose();
|
||||
Matrix K = Sigma * Ct.transpose() * S.inverse();
|
||||
Vector Delta = InnovationLift * K * delta_vec;
|
||||
X_hat = G<N>::exp(Delta) * X_hat;
|
||||
Sigma = (Matrix::Identity(dof, dof) - K * Ct) * Sigma;
|
||||
}
|
||||
/**
|
||||
* Computes linearized continuous time state matrix
|
||||
* @param u Angular velocity
|
||||
* @return Linearized state matrix
|
||||
* Uses Matrix zero and Identity functions
|
||||
*/
|
||||
template <size_t N>
|
||||
Matrix EqF<N>::stateMatrixA(const Input& u) const {
|
||||
Matrix3 W0 = velocityAction(X_hat.inv(), u).W();
|
||||
Matrix A1 = Matrix::Zero(6, 6);
|
||||
A1.block<3, 3>(0, 3) = -I_3x3;
|
||||
A1.block<3, 3>(3, 3) = W0;
|
||||
Matrix A2 = repBlock(W0, N);
|
||||
return blockDiag(A1, A2);
|
||||
}
|
||||
|
||||
/**
|
||||
* Computes the discrete time state transition matrix
|
||||
* @param u Angular velocity
|
||||
* @param dt time step
|
||||
* @return State transition matrix in discrete time
|
||||
*/
|
||||
template <size_t N>
|
||||
Matrix EqF<N>::stateTransitionMatrix(const Input& u, double dt) const {
|
||||
Matrix3 W0 = velocityAction(X_hat.inv(), u).W();
|
||||
Matrix Phi1 = Matrix::Zero(6, 6);
|
||||
|
||||
Matrix3 Phi12 = -dt * (I_3x3 + (dt / 2) * W0 + ((dt * dt) / 6) * W0 * W0);
|
||||
Matrix3 Phi22 = I_3x3 + dt * W0 + ((dt * dt) / 2) * W0 * W0;
|
||||
|
||||
Phi1.block<3, 3>(0, 0) = I_3x3;
|
||||
Phi1.block<3, 3>(0, 3) = Phi12;
|
||||
Phi1.block<3, 3>(3, 3) = Phi22;
|
||||
Matrix Phi2 = repBlock(Phi22, N);
|
||||
return blockDiag(Phi1, Phi2);
|
||||
}
|
||||
/**
|
||||
* Computes the input uncertainty propagation matrix
|
||||
* @return
|
||||
* Uses the blockdiag matrix
|
||||
*/
|
||||
template <size_t N>
|
||||
Matrix EqF<N>::inputMatrixBt() const {
|
||||
Matrix B1 = blockDiag(X_hat.A.matrix(), X_hat.A.matrix());
|
||||
Matrix B2(3 * N, 3 * N);
|
||||
|
||||
for (size_t i = 0; i < N; ++i) {
|
||||
B2.block<3, 3>(3 * i, 3 * i) = X_hat.B[i].matrix();
|
||||
}
|
||||
|
||||
return blockDiag(B1, B2);
|
||||
}
|
||||
/**
|
||||
* Computes the linearized measurement matrix. The structure depends on whether
|
||||
* the sensor has a calibration state
|
||||
* @param d reference direction
|
||||
* @param idx Calibration index
|
||||
* @return Measurement matrix
|
||||
* Uses the matrix zero, Rot3 hat and the Unitvector functions
|
||||
*/
|
||||
template <size_t N>
|
||||
Matrix EqF<N>::measurementMatrixC(const Unit3& d, int idx) const {
|
||||
Matrix Cc = Matrix::Zero(3, 3 * N);
|
||||
|
||||
// If the measurement is related to a sensor that has a calibration state
|
||||
if (idx >= 0) {
|
||||
// Set the correct 3x3 block in Cc
|
||||
Cc.block<3, 3>(0, 3 * idx) = Rot3::Hat(d.unitVector());
|
||||
}
|
||||
|
||||
Matrix3 wedge_d = Rot3::Hat(d.unitVector());
|
||||
|
||||
// Create the combined matrix
|
||||
Matrix temp(3, 6 + 3 * N);
|
||||
temp.block<3, 3>(0, 0) = wedge_d;
|
||||
temp.block<3, 3>(0, 3) = Matrix3::Zero();
|
||||
temp.block(0, 6, 3, 3 * N) = Cc;
|
||||
|
||||
return wedge_d * temp;
|
||||
}
|
||||
/**
|
||||
* Computes the measurement uncertainty propagation matrix
|
||||
* @param idx Calibration index
|
||||
* @return Returns B[idx] for calibrated sensors, A for uncalibrated
|
||||
*/
|
||||
template <size_t N>
|
||||
Matrix EqF<N>::outputMatrixDt(int idx) const {
|
||||
// If the measurement is related to a sensor that has a calibration state
|
||||
if (idx >= 0) {
|
||||
if (idx >= static_cast<int>(N)) {
|
||||
throw std::out_of_range("Calibration index out of range");
|
||||
}
|
||||
return X_hat.B[idx].matrix();
|
||||
} else {
|
||||
return X_hat.A.matrix();
|
||||
}
|
||||
}
|
||||
|
||||
} // namespace abc_eqf_lib
|
||||
|
||||
template <size_t N>
|
||||
struct traits<abc_eqf_lib::EqF<N>>
|
||||
: internal::LieGroupTraits<abc_eqf_lib::EqF<N>> {};
|
||||
} // namespace gtsam
|
||||
|
||||
#endif // ABC_EQF_H
|
||||
|
|
@ -0,0 +1,444 @@
|
|||
/**
|
||||
* @file ABC_EQF_Demo.cpp
|
||||
* @brief Demonstration of the full Attitude-Bias-Calibration Equivariant Filter
|
||||
*
|
||||
* This demo shows the Equivariant Filter (EqF) for attitude estimation
|
||||
* with both gyroscope bias and sensor extrinsic calibration, based on the
|
||||
* paper: "Overcoming Bias: Equivariant Filter Design for Biased Attitude
|
||||
* Estimation with Online Calibration" by Fornasier et al. Authors: Darshan
|
||||
* Rajasekaran & Jennifer Oum
|
||||
*/
|
||||
|
||||
#include "ABC_EQF.h"
|
||||
|
||||
// Use namespace for convenience
|
||||
using namespace gtsam;
|
||||
constexpr size_t N = 1; // Number of calibration states
|
||||
using M = abc_eqf_lib::State<N>;
|
||||
using Group = abc_eqf_lib::G<N>;
|
||||
using EqFilter = abc_eqf_lib::EqF<N>;
|
||||
using gtsam::abc_eqf_lib::EqF;
|
||||
using gtsam::abc_eqf_lib::Input;
|
||||
using gtsam::abc_eqf_lib::Measurement;
|
||||
|
||||
/// Data structure for ground-truth, input and output data
|
||||
struct Data {
|
||||
M xi; /// Ground-truth state
|
||||
Input u; /// Input measurements
|
||||
std::vector<Measurement> y; /// Output measurements
|
||||
int n_meas; /// Number of measurements
|
||||
double t; /// Time
|
||||
double dt; /// Time step
|
||||
};
|
||||
|
||||
//========================================================================
|
||||
// Data Processing Functions
|
||||
//========================================================================
|
||||
|
||||
/**
|
||||
* Load data from CSV file into a vector of Data objects for the EqF
|
||||
*
|
||||
* CSV format:
|
||||
* - t: Time
|
||||
* - q_w, q_x, q_y, q_z: True attitude quaternion
|
||||
* - b_x, b_y, b_z: True bias
|
||||
* - cq_w_0, cq_x_0, cq_y_0, cq_z_0: True calibration quaternion
|
||||
* - w_x, w_y, w_z: Angular velocity measurements
|
||||
* - std_w_x, std_w_y, std_w_z: Angular velocity measurement standard deviations
|
||||
* - std_b_x, std_b_y, std_b_z: Bias process noise standard deviations
|
||||
* - y_x_0, y_y_0, y_z_0, y_x_1, y_y_1, y_z_1: Direction measurements
|
||||
* - std_y_x_0, std_y_y_0, std_y_z_0, std_y_x_1, std_y_y_1, std_y_z_1: Direction
|
||||
* measurement standard deviations
|
||||
* - d_x_0, d_y_0, d_z_0, d_x_1, d_y_1, d_z_1: Reference directions
|
||||
*
|
||||
*/
|
||||
std::vector<Data> loadDataFromCSV(const std::string& filename, int startRow = 0,
|
||||
int maxRows = -1, int downsample = 1);
|
||||
|
||||
/// Process data with EqF and print summary results
|
||||
void processDataWithEqF(EqFilter& filter, const std::vector<Data>& data_list,
|
||||
int printInterval = 10);
|
||||
|
||||
//========================================================================
|
||||
// Data Processing Functions Implementation
|
||||
//========================================================================
|
||||
|
||||
/*
|
||||
* Loads the test data from the csv file
|
||||
* startRow First row to load based on csv, 0 by default
|
||||
* maxRows maximum rows to load, defaults to all rows
|
||||
* downsample Downsample factor, default 1
|
||||
* A list of data objects
|
||||
*/
|
||||
|
||||
std::vector<Data> loadDataFromCSV(const std::string& filename, int startRow,
|
||||
int maxRows, int downsample) {
|
||||
std::vector<Data> data_list;
|
||||
std::ifstream file(filename);
|
||||
|
||||
if (!file.is_open()) {
|
||||
throw std::runtime_error("Failed to open file: " + filename);
|
||||
}
|
||||
|
||||
std::cout << "Loading data from " << filename << "..." << std::flush;
|
||||
|
||||
std::string line;
|
||||
int lineNumber = 0;
|
||||
int rowCount = 0;
|
||||
int errorCount = 0;
|
||||
double prevTime = 0.0;
|
||||
|
||||
// Skip header
|
||||
std::getline(file, line);
|
||||
lineNumber++;
|
||||
|
||||
// Skip to startRow
|
||||
while (lineNumber < startRow && std::getline(file, line)) {
|
||||
lineNumber++;
|
||||
}
|
||||
|
||||
// Read data
|
||||
while (std::getline(file, line) && (maxRows == -1 || rowCount < maxRows)) {
|
||||
lineNumber++;
|
||||
|
||||
// Apply downsampling
|
||||
if ((lineNumber - startRow - 1) % downsample != 0) {
|
||||
continue;
|
||||
}
|
||||
|
||||
std::istringstream ss(line);
|
||||
std::string token;
|
||||
std::vector<double> values;
|
||||
|
||||
// Parse line into values
|
||||
while (std::getline(ss, token, ',')) {
|
||||
try {
|
||||
values.push_back(std::stod(token));
|
||||
} catch (const std::exception& e) {
|
||||
errorCount++;
|
||||
values.push_back(0.0); // Use default value
|
||||
}
|
||||
}
|
||||
|
||||
// Check if we have enough values
|
||||
if (values.size() < 39) {
|
||||
errorCount++;
|
||||
continue;
|
||||
}
|
||||
|
||||
// Extract values
|
||||
double t = values[0];
|
||||
double dt = (rowCount == 0) ? 0.0 : t - prevTime;
|
||||
prevTime = t;
|
||||
|
||||
// Create ground truth state
|
||||
Quaternion quat(values[1], values[2], values[3], values[4]); // w, x, y, z
|
||||
Rot3 R = Rot3(quat);
|
||||
|
||||
Vector3 b(values[5], values[6], values[7]);
|
||||
|
||||
Quaternion calQuat(values[8], values[9], values[10],
|
||||
values[11]); // w, x, y, z
|
||||
std::array<Rot3, N> S = {Rot3(calQuat)};
|
||||
|
||||
M xi(R, b, S);
|
||||
|
||||
// Create input
|
||||
Vector3 w(values[12], values[13], values[14]);
|
||||
|
||||
// Create input covariance matrix (6x6)
|
||||
// First 3x3 block for angular velocity, second 3x3 block for bias process
|
||||
// noise
|
||||
Matrix inputCov = Matrix::Zero(6, 6);
|
||||
inputCov(0, 0) = values[15] * values[15]; // std_w_x^2
|
||||
inputCov(1, 1) = values[16] * values[16]; // std_w_y^2
|
||||
inputCov(2, 2) = values[17] * values[17]; // std_w_z^2
|
||||
inputCov(3, 3) = values[18] * values[18]; // std_b_x^2
|
||||
inputCov(4, 4) = values[19] * values[19]; // std_b_y^2
|
||||
inputCov(5, 5) = values[20] * values[20]; // std_b_z^2
|
||||
|
||||
Input u{w, inputCov};
|
||||
|
||||
// Create measurements
|
||||
std::vector<Measurement> measurements;
|
||||
|
||||
// First measurement (calibrated sensor, cal_idx = 0)
|
||||
Vector3 y0(values[21], values[22], values[23]);
|
||||
Vector3 d0(values[33], values[34], values[35]);
|
||||
|
||||
// Normalize vectors if needed
|
||||
if (abs(y0.norm() - 1.0) > 1e-5) y0.normalize();
|
||||
if (abs(d0.norm() - 1.0) > 1e-5) d0.normalize();
|
||||
|
||||
// Measurement covariance
|
||||
Matrix3 covY0 = Matrix3::Zero();
|
||||
covY0(0, 0) = values[27] * values[27]; // std_y_x_0^2
|
||||
covY0(1, 1) = values[28] * values[28]; // std_y_y_0^2
|
||||
covY0(2, 2) = values[29] * values[29]; // std_y_z_0^2
|
||||
|
||||
// Create measurement
|
||||
measurements.push_back(Measurement{Unit3(y0), Unit3(d0), covY0, 0});
|
||||
|
||||
// Second measurement (calibrated sensor, cal_idx = -1)
|
||||
Vector3 y1(values[24], values[25], values[26]);
|
||||
Vector3 d1(values[36], values[37], values[38]);
|
||||
|
||||
// Normalize vectors if needed
|
||||
if (abs(y1.norm() - 1.0) > 1e-5) y1.normalize();
|
||||
if (abs(d1.norm() - 1.0) > 1e-5) d1.normalize();
|
||||
|
||||
// Measurement covariance
|
||||
Matrix3 covY1 = Matrix3::Zero();
|
||||
covY1(0, 0) = values[30] * values[30]; // std_y_x_1^2
|
||||
covY1(1, 1) = values[31] * values[31]; // std_y_y_1^2
|
||||
covY1(2, 2) = values[32] * values[32]; // std_y_z_1^2
|
||||
|
||||
// Create measurement
|
||||
measurements.push_back(Measurement{Unit3(y1), Unit3(d1), covY1, -1});
|
||||
|
||||
// Create Data object and add to list
|
||||
data_list.push_back(Data{xi, u, measurements, 2, t, dt});
|
||||
|
||||
rowCount++;
|
||||
|
||||
// Show loading progress every 1000 rows
|
||||
if (rowCount % 1000 == 0) {
|
||||
std::cout << "." << std::flush;
|
||||
}
|
||||
}
|
||||
|
||||
std::cout << " Done!" << std::endl;
|
||||
std::cout << "Loaded " << data_list.size() << " data points";
|
||||
|
||||
if (errorCount > 0) {
|
||||
std::cout << " (" << errorCount << " errors encountered)";
|
||||
}
|
||||
|
||||
std::cout << std::endl;
|
||||
|
||||
return data_list;
|
||||
}
|
||||
|
||||
/// Takes in the data and runs an EqF on it and reports the results
|
||||
void processDataWithEqF(EqFilter& filter, const std::vector<Data>& data_list,
|
||||
int printInterval) {
|
||||
if (data_list.empty()) {
|
||||
std::cerr << "No data to process" << std::endl;
|
||||
return;
|
||||
}
|
||||
|
||||
std::cout << "Processing " << data_list.size() << " data points with EqF..."
|
||||
<< std::endl;
|
||||
|
||||
// Track performance metrics
|
||||
std::vector<double> att_errors;
|
||||
std::vector<double> bias_errors;
|
||||
std::vector<double> cal_errors;
|
||||
|
||||
// Track time for performance measurement
|
||||
auto start = std::chrono::high_resolution_clock::now();
|
||||
|
||||
int totalMeasurements = 0;
|
||||
int validMeasurements = 0;
|
||||
|
||||
// Define constant for converting radians to degrees
|
||||
const double RAD_TO_DEG = 180.0 / M_PI;
|
||||
|
||||
// Print a progress indicator
|
||||
int progressStep = data_list.size() / 10; // 10 progress updates
|
||||
if (progressStep < 1) progressStep = 1;
|
||||
|
||||
std::cout << "Progress: ";
|
||||
|
||||
for (size_t i = 0; i < data_list.size(); i++) {
|
||||
const Data& data = data_list[i];
|
||||
|
||||
// Propagate filter with current input and time step
|
||||
filter.propagation(data.u, data.dt);
|
||||
|
||||
// Process all measurements
|
||||
for (const auto& y : data.y) {
|
||||
totalMeasurements++;
|
||||
|
||||
// Skip invalid measurements
|
||||
Vector3 y_vec = y.y.unitVector();
|
||||
Vector3 d_vec = y.d.unitVector();
|
||||
if (std::isnan(y_vec[0]) || std::isnan(y_vec[1]) ||
|
||||
std::isnan(y_vec[2]) || std::isnan(d_vec[0]) ||
|
||||
std::isnan(d_vec[1]) || std::isnan(d_vec[2])) {
|
||||
continue;
|
||||
}
|
||||
|
||||
try {
|
||||
filter.update(y);
|
||||
validMeasurements++;
|
||||
} catch (const std::exception& e) {
|
||||
std::cerr << "Error updating at t=" << data.t << ": " << e.what()
|
||||
<< std::endl;
|
||||
}
|
||||
}
|
||||
|
||||
// Get current state estimate
|
||||
M estimate = filter.stateEstimate();
|
||||
|
||||
// Calculate errors
|
||||
Vector3 att_error = Rot3::Logmap(data.xi.R.between(estimate.R));
|
||||
Vector3 bias_error = estimate.b - data.xi.b;
|
||||
Vector3 cal_error = Vector3::Zero();
|
||||
if (!data.xi.S.empty() && !estimate.S.empty()) {
|
||||
cal_error = Rot3::Logmap(data.xi.S[0].between(estimate.S[0]));
|
||||
}
|
||||
|
||||
// Store errors
|
||||
att_errors.push_back(att_error.norm());
|
||||
bias_errors.push_back(bias_error.norm());
|
||||
cal_errors.push_back(cal_error.norm());
|
||||
|
||||
// Show progress dots
|
||||
if (i % progressStep == 0) {
|
||||
std::cout << "." << std::flush;
|
||||
}
|
||||
}
|
||||
|
||||
std::cout << " Done!" << std::endl;
|
||||
|
||||
auto end = std::chrono::high_resolution_clock::now();
|
||||
std::chrono::duration<double> elapsed = end - start;
|
||||
|
||||
// Calculate average errors
|
||||
double avg_att_error = 0.0;
|
||||
double avg_bias_error = 0.0;
|
||||
double avg_cal_error = 0.0;
|
||||
|
||||
if (!att_errors.empty()) {
|
||||
avg_att_error = std::accumulate(att_errors.begin(), att_errors.end(), 0.0) /
|
||||
att_errors.size();
|
||||
avg_bias_error =
|
||||
std::accumulate(bias_errors.begin(), bias_errors.end(), 0.0) /
|
||||
bias_errors.size();
|
||||
avg_cal_error = std::accumulate(cal_errors.begin(), cal_errors.end(), 0.0) /
|
||||
cal_errors.size();
|
||||
}
|
||||
|
||||
// Calculate final errors from last data point
|
||||
const Data& final_data = data_list.back();
|
||||
M final_estimate = filter.stateEstimate();
|
||||
Vector3 final_att_error =
|
||||
Rot3::Logmap(final_data.xi.R.between(final_estimate.R));
|
||||
Vector3 final_bias_error = final_estimate.b - final_data.xi.b;
|
||||
Vector3 final_cal_error = Vector3::Zero();
|
||||
if (!final_data.xi.S.empty() && !final_estimate.S.empty()) {
|
||||
final_cal_error =
|
||||
Rot3::Logmap(final_data.xi.S[0].between(final_estimate.S[0]));
|
||||
}
|
||||
|
||||
// Print summary statistics
|
||||
std::cout << "\n=== Filter Performance Summary ===" << std::endl;
|
||||
std::cout << "Processing time: " << elapsed.count() << " seconds"
|
||||
<< std::endl;
|
||||
std::cout << "Processed measurements: " << totalMeasurements
|
||||
<< " (valid: " << validMeasurements << ")" << std::endl;
|
||||
|
||||
// Average errors
|
||||
std::cout << "\n-- Average Errors --" << std::endl;
|
||||
std::cout << "Attitude: " << (avg_att_error * RAD_TO_DEG) << "°" << std::endl;
|
||||
std::cout << "Bias: " << avg_bias_error << std::endl;
|
||||
std::cout << "Calibration: " << (avg_cal_error * RAD_TO_DEG) << "°"
|
||||
<< std::endl;
|
||||
|
||||
// Final errors
|
||||
std::cout << "\n-- Final Errors --" << std::endl;
|
||||
std::cout << "Attitude: " << (final_att_error.norm() * RAD_TO_DEG) << "°"
|
||||
<< std::endl;
|
||||
std::cout << "Bias: " << final_bias_error.norm() << std::endl;
|
||||
std::cout << "Calibration: " << (final_cal_error.norm() * RAD_TO_DEG) << "°"
|
||||
<< std::endl;
|
||||
|
||||
// Print a brief comparison of final estimate vs ground truth
|
||||
std::cout << "\n-- Final State vs Ground Truth --" << std::endl;
|
||||
std::cout << "Attitude (RPY) - Estimate: "
|
||||
<< (final_estimate.R.rpy() * RAD_TO_DEG).transpose()
|
||||
<< "° | Truth: " << (final_data.xi.R.rpy() * RAD_TO_DEG).transpose()
|
||||
<< "°" << std::endl;
|
||||
std::cout << "Bias - Estimate: " << final_estimate.b.transpose()
|
||||
<< " | Truth: " << final_data.xi.b.transpose() << std::endl;
|
||||
|
||||
if (!final_estimate.S.empty() && !final_data.xi.S.empty()) {
|
||||
std::cout << "Calibration (RPY) - Estimate: "
|
||||
<< (final_estimate.S[0].rpy() * RAD_TO_DEG).transpose()
|
||||
<< "° | Truth: "
|
||||
<< (final_data.xi.S[0].rpy() * RAD_TO_DEG).transpose() << "°"
|
||||
<< std::endl;
|
||||
}
|
||||
}
|
||||
|
||||
int main(int argc, char* argv[]) {
|
||||
std::cout << "ABC-EqF: Attitude-Bias-Calibration Equivariant Filter Demo"
|
||||
<< std::endl;
|
||||
std::cout << "=============================================================="
|
||||
<< std::endl;
|
||||
|
||||
try {
|
||||
// Parse command line options
|
||||
std::string csvFilePath;
|
||||
int maxRows = -1; // Process all rows by default
|
||||
int downsample = 1; // No downsampling by default
|
||||
|
||||
if (argc > 1) {
|
||||
csvFilePath = argv[1];
|
||||
} else {
|
||||
// Try to find the EQFdata file in the GTSAM examples directory
|
||||
try {
|
||||
csvFilePath = findExampleDataFile("EqFdata.csv");
|
||||
} catch (const std::exception& e) {
|
||||
std::cerr << "Error: Could not find EqFdata.csv" << std::endl;
|
||||
std::cerr << "Usage: " << argv[0]
|
||||
<< " [csv_file_path] [max_rows] [downsample]" << std::endl;
|
||||
return 1;
|
||||
}
|
||||
}
|
||||
|
||||
// Optional command line parameters
|
||||
if (argc > 2) {
|
||||
maxRows = std::stoi(argv[2]);
|
||||
}
|
||||
|
||||
if (argc > 3) {
|
||||
downsample = std::stoi(argv[3]);
|
||||
}
|
||||
|
||||
// Load data from CSV file
|
||||
std::vector<Data> data =
|
||||
loadDataFromCSV(csvFilePath, 0, maxRows, downsample);
|
||||
|
||||
if (data.empty()) {
|
||||
std::cerr << "No data available to process. Exiting." << std::endl;
|
||||
return 1;
|
||||
}
|
||||
|
||||
// Initialize the EqF filter with one calibration state
|
||||
int n_sensors = 2;
|
||||
|
||||
// Initial covariance - larger values allow faster convergence
|
||||
Matrix initialSigma = Matrix::Identity(6 + 3 * N, 6 + 3 * N);
|
||||
initialSigma.diagonal().head<3>() =
|
||||
Vector3::Constant(0.1); // Attitude uncertainty
|
||||
initialSigma.diagonal().segment<3>(3) =
|
||||
Vector3::Constant(0.01); // Bias uncertainty
|
||||
initialSigma.diagonal().tail<3>() =
|
||||
Vector3::Constant(0.1); // Calibration uncertainty
|
||||
|
||||
// Create filter
|
||||
EqFilter filter(initialSigma, n_sensors);
|
||||
|
||||
// Process data
|
||||
processDataWithEqF(filter, data);
|
||||
|
||||
} catch (const std::exception& e) {
|
||||
std::cerr << "Error: " << e.what() << std::endl;
|
||||
return 1;
|
||||
}
|
||||
|
||||
std::cout << "\nEqF demonstration completed successfully." << std::endl;
|
||||
return 0;
|
||||
}
|
||||
|
|
@ -65,4 +65,4 @@ if (TARGET metis AND GKlib_COPTIONS)
|
|||
separate_arguments(GKlib_COPTIONS)
|
||||
# Declare those flags as to-be-imported in "client libraries", i.e. "gtsam"
|
||||
target_compile_options(metis INTERFACE ${GKlib_COPTIONS})
|
||||
endif()
|
||||
endif()
|
||||
Loading…
Reference in New Issue