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C++ implementation of the EqF to estimate bias.

release/4.3a0
darshan-17 2025-04-15 21:06:25 -07:00 committed by jenniferoum
parent 39a7a5b627
commit cd1782e5d4
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/**
* @file ABC_EQF.h
* @brief Header file for the Attitude-Bias-Calibration Equivariant Filter
*
* This file contains declarations for 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
*/
#ifndef ABC_EQF_H
#define ABC_EQF_H
#pragma once
#include <gtsam/base/Matrix.h>
#include <gtsam/base/Vector.h>
#include <gtsam/geometry/Rot3.h>
#include <gtsam/geometry/Unit3.h>
#include <gtsam/nonlinear/Values.h>
#include <gtsam/inference/Symbol.h>
#include <gtsam/slam/dataset.h>
#include <gtsam/navigation/ImuBias.h>
#include <iostream>
#include <fstream>
#include <string>
#include <vector>
#include <cmath>
#include <functional>
#include <chrono>
#include <numeric> // For std::accumulate
// All implementations are wrapped in this namespace to avoid conflicts
namespace abc_eqf_lib {
using namespace std;
using namespace gtsam;
// Global configuration
// Define coordinate type: "EXPONENTIAL" or "NORMAL"
extern const std::string COORDINATE;
//========================================================================
// Utility Functions
//========================================================================
/**
* Check if a vector is a unit vector
*/
bool checkNorm(const Vector3& x, double tol = 1e-3);
/**
* Check if vector contains NaN values
*/
bool hasNaN(const Vector3& vec);
/**
* Create a block diagonal matrix from two matrices
*/
Matrix blockDiag(const Matrix& A, const Matrix& B);
/**
* Repeat a block matrix n times along the diagonal
*/
Matrix repBlock(const Matrix& A, int n);
/**
* Calculate numerical differential
*/
Matrix numericalDifferential(std::function<Vector(const Vector&)> f, const Vector& x);
//========================================================================
// Core Data Types
//========================================================================
/**
* Direction class as a S2 element
*/
class Direction {
public:
Unit3 d; // Direction (unit vector on S2)
/**
* Initialize direction
* @param d_vec Direction vector (must be unit norm)
*/
Direction(const Vector3& d_vec);
// Accessor methods for vector components
double x() const;
double y() const;
double z() const;
// Check if the direction contains NaN values
bool hasNaN() const;
};
/**
* Input class for the Biased Attitude System
*/
class Input {
public:
Vector3 w; // Angular velocity
Matrix Sigma; // Noise covariance
/**
* Initialize Input
* @param w Angular velocity (3-vector)
* @param Sigma Noise covariance (6x6 matrix)
*/
Input(const Vector3& w, const Matrix& Sigma);
/**
* Return the Input as a skew-symmetric matrix
* @return w as a skew-symmetric matrix
*/
Matrix3 W() const;
/**
* Return a random angular velocity
* @return A random angular velocity as Input element
*/
static Input random();
};
/**
* Measurement class
* cal_idx is an index corresponding to the calibration related to the measurement
* cal_idx = -1 indicates the measurement is from a calibrated sensor
*/
class Measurement {
public:
Direction y; // Measurement direction in sensor frame
Direction d; // Known direction in global frame
Matrix3 Sigma; // Covariance matrix of the measurement
int cal_idx = -1; // Calibration index (-1 for calibrated sensor)
/**
* Initialize measurement
* @param y_vec Direction measurement in sensor frame
* @param d_vec Known direction in global frame
* @param Sigma Measurement noise covariance
* @param i Calibration index (-1 for calibrated sensor)
*/
Measurement(const Vector3& y_vec, const Vector3& d_vec,
const Matrix3& Sigma, int i = -1);
};
/**
* State class representing the state of the Biased Attitude System
*/
class State {
public:
Rot3 R; // Attitude rotation matrix R
Vector3 b; // Gyroscope bias b
std::vector<Rot3> S; // Sensor calibrations S
State(const Rot3& R = Rot3::Identity(),
const Vector3& b = Vector3::Zero(),
const std::vector<Rot3>& S = std::vector<Rot3>());
static State identity(int n);
};
/**
* Data structure for ground-truth, input and output data
*/
struct Data {
State xi; // Ground-truth state
int n_cal; // Number of calibration states
Input u; // Input measurements
std::vector<Measurement> y; // Output measurements
int n_meas; // Number of measurements
double t; // Time
double dt; // Time step
/**
* Initialize Data
* @param xi Ground-truth state
* @param n_cal Number of calibration states
* @param u Input measurements
* @param y Output measurements
* @param n_meas Number of measurements
* @param t Time
* @param dt Time step
*/
Data(const State& xi, int n_cal, const Input& u,
const std::vector<Measurement>& y, int n_meas,
double t, double dt);
};
//========================================================================
// Symmetry Group
//========================================================================
/**
* Symmetry group (SO(3) |x so(3)) x SO(3) x ... x SO(3)
* Each element of the B list is associated with a calibration state
*/
class G {
public:
Rot3 A; // First SO(3) element
Matrix3 a; // so(3) element (skew-symmetric matrix)
std::vector<Rot3> B; // List of SO(3) elements for calibration
/**
* Initialize the symmetry group G
* @param A SO3 element
* @param a so(3) element (skew symmetric matrix)
* @param B list of SO3 elements
*/
G(const Rot3& A = Rot3::Identity(),
const Matrix3& a = Matrix3::Zero(),
const std::vector<Rot3>& B = std::vector<Rot3>());
/**
* Define the group operation (multiplication)
* @param other Another group element
* @return The product of this and other
*/
G operator*(const G& other) const;
/**
* Return the inverse element of the symmetry group
* @return The inverse of this group element
*/
G inv() const;
/**
* Return the identity of the symmetry group
* @param n Number of calibration elements
* @return The identity element with n calibration components
*/
static G identity(int n);
/**
* Return a group element X given by X = exp(x)
* @param x Vector representation of Lie algebra element
* @return Group element given by the exponential of x
*/
static G exp(const Vector& x);
};
//========================================================================
// Helper Functions for EqF
//========================================================================
/**
* Compute the lift of the system (Theorem 3.8, Equation 7)
* @param xi State
* @param u Input
* @return Lift vector
*/
Vector lift(const State& xi, const Input& u);
/**
* Action of the symmetry group on the state space (Equation 4)
* @param X Group element
* @param xi State
* @return New state after group action
*/
State stateAction(const G& X, const State& xi);
/**
* Action of the symmetry group on the input space (Equation 5)
* @param X Group element
* @param u Input
* @return New input after group action
*/
Input velocityAction(const G& X, const Input& u);
/**
* Action of the symmetry group on the output space (Equation 6)
* @param X Group element
* @param y Direction measurement
* @param idx Calibration index
* @return New direction after group action
*/
Vector3 outputAction(const G& X, const Direction& y, int idx);
/**
* Local coordinates assuming xi_0 = identity (Equation 9)
* @param e State representing equivariant error
* @return Local coordinates
*/
Vector local_coords(const State& e);
/**
* Local coordinates inverse assuming xi_0 = identity
* @param eps Local coordinates
* @return Corresponding state
*/
State local_coords_inv(const Vector& eps);
/**
* Differential of the phi action at E = Id in local coordinates
* @param xi State
* @return Differential matrix
*/
Matrix stateActionDiff(const State& xi);
//========================================================================
// Equivariant Filter (EqF)
//========================================================================
/**
* Equivariant Filter (EqF) implementation
*/
class EqF {
private:
int __dof; // Degrees of freedom
int __n_cal; // Number of calibration states
int __n_sensor; // Number of sensors
G __X_hat; // Filter state
Matrix __Sigma; // Error covariance
State __xi_0; // Origin state
Matrix __Dphi0; // Differential of phi at origin
Matrix __InnovationLift; // Innovation lift matrix
/**
* Return the state matrix A0t (Equation 14a)
* @param u Input
* @return State matrix A0t
*/
Matrix __stateMatrixA(const Input& u) const;
/**
* Return the state transition matrix Phi (Equation 17)
* @param u Input
* @param dt Time step
* @return State transition matrix Phi
*/
Matrix __stateTransitionMatrix(const Input& u, double dt) const;
/**
* Return the Input matrix Bt
* @return Input matrix Bt
*/
Matrix __inputMatrixBt() const;
/**
* Return the measurement matrix C0 (Equation 14b)
* @param d Known direction
* @param idx Calibration index
* @return Measurement matrix C0
*/
Matrix __measurementMatrixC(const Direction& d, int idx) const;
/**
* Return the measurement output matrix Dt
* @param idx Calibration index
* @return Measurement output matrix Dt
*/
Matrix __outputMatrixDt(int idx) const;
public:
/**
* Initialize EqF
* @param Sigma Initial covariance
* @param n Number of calibration states
* @param m Number of sensors
*/
EqF(const Matrix& Sigma, int n, int m);
/**
* Return estimated state
* @return Current state estimate
*/
State stateEstimate() const;
/**
* Propagate the filter state
* @param u Angular velocity measurement
* @param dt Time step
*/
void propagation(const Input& u, double dt);
/**
* Update the filter state with a measurement
* @param y Direction measurement
*/
void update(const Measurement& y);
};
//========================================================================
// 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
*
* @param filename Path to the CSV file
* @param startRow First row to load (default: 0)
* @param maxRows Maximum number of rows to load (default: all)
* @param downsample Downsample factor (default: 1, which means no downsampling)
* @return Vector of Data objects
*/
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
* @param filter Initialized EqF filter
* @param data_list Vector of Data objects to process
* @param printInterval Progress indicator interval (used internally)
*/
void processDataWithEqF(EqF& filter, const std::vector<Data>& data_list, int printInterval = 10);
} // namespace abc_eqf_lib
#endif // ABC_EQF_H

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add_executable(ABC_EqF
main.cpp
EqF.cpp
State.cpp
Input.cpp
G.cpp
Direction.cpp
Measurements.cpp
utilities.cpp
runEQF_withcsv.h
)
target_link_libraries(ABC_EqF gtsam)

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//
// Created by darshan on 3/11/25.
//
#ifndef DATA_H
#define DATA_H
//#pragma once
#include "State.h"
#include "Input.h"
#include "Measurements.h"
#include <vector>
/**
* Data structure for ground-truth, input and output data
*/
struct Data {
State xi; // Ground-truth state
int n_cal; // Number of calibration states
Input u; // Input measurements
std::vector<Measurement> y; // Output measurements
int n_meas; // Number of measurements
double t; // Time
double dt; // Time step
/**
* Initialize Data
* @param xi Ground-truth state
* @param n_cal Number of calibration states
* @param u Input measurements
* @param y Output measurements
* @param n_meas Number of measurements
* @param t Time
* @param dt Time step
*/
Data(const State& xi, int n_cal, const Input& u,
const std::vector<Measurement>& y, int n_meas,
double t, double dt)
: xi(xi), n_cal(n_cal), u(u), y(y), n_meas(n_meas), t(t), dt(dt) {}
};
#endif //DATA_H

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//
// Created by darshan on 3/11/25.
//
#include "Direction.h"
#include "utilities.h"
#include <stdexcept>
Direction::Direction(const Vector3& d_vec) : d(d_vec) {
if (!checkNorm(d_vec)) {
throw std::invalid_argument("Direction must be a unit vector");
}
}

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//
// Created by darshan on 3/11/25.
//
#ifndef DIRECTION_H
#define DIRECTION_H
//#pragma once
#include <gtsam/geometry/Unit3.h>
#include <gtsam/base/Vector.h>
using namespace gtsam;
/**
* Direction class as a S2 element
*/
class Direction {
public:
Unit3 d; // Direction (unit vector on S2)
/**
* Initialize direction
* @param d_vec Direction vector (must be unit norm)
*/
Direction(const Vector3& d_vec);
// Accessor methods for vector components
double x() const { return d.unitVector()[0]; }
double y() const { return d.unitVector()[1]; }
double z() const { return d.unitVector()[2]; }
// Check if the direction contains NaN values
bool hasNaN() const {
Vector3 vec = d.unitVector();
return std::isnan(vec[0]) || std::isnan(vec[1]) || std::isnan(vec[2]);
}
};
#endif //DIRECTION_H

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//
// Created by darshan on 3/11/25.
//
#include "EqF.h"
#include "utilities.h"
#include <Eigen/Dense>
#include <stdexcept>
#include <functional>
// Implementation of helper functions
Vector lift(const State& xi, const Input& u) {
int n = xi.S.size();
Vector L = Vector::Zero(6 + 3 * n);
// First 3 elements
L.head<3>() = u.w - xi.b;
// Next 3 elements
L.segment<3>(3) = -u.W() * xi.b;
// Remaining elements
for (int i = 0; i < n; i++) {
L.segment<3>(6 + 3*i) = xi.S[i].inverse().matrix() * L.head<3>();
}
return L;
}
State stateAction(const G& X, const State& xi) {
if (xi.S.size() != X.B.size()) {
throw std::invalid_argument("Number of calibration states and B elements must match");
}
std::vector<Rot3> new_S;
for (size_t i = 0; i < X.B.size(); i++) {
new_S.push_back(X.A.inverse() * xi.S[i] * X.B[i]);
}
return State(xi.R * X.A,
X.A.inverse().matrix() * (xi.b - Rot3::Vee(X.a)),
new_S);
}
Input velocityAction(const G& X, const Input& u) {
return Input(X.A.inverse().matrix() * (u.w - Rot3::Vee(X.a)), u.Sigma);
}
Vector3 outputAction(const G& X, const Direction& y, int idx) {
if (idx == -1) {
return X.A.inverse().matrix() * y.d.unitVector();
} else {
if (idx >= static_cast<int>(X.B.size())) {
throw std::out_of_range("Calibration index out of range");
}
return X.B[idx].inverse().matrix() * y.d.unitVector();
}
}
Vector local_coords(const State& e) {
if (COORDINATE == "EXPONENTIAL") {
Vector eps(6 + 3 * e.S.size());
// First 3 elements
eps.head<3>() = Rot3::Logmap(e.R);
// Next 3 elements
eps.segment<3>(3) = e.b;
// Remaining elements
for (size_t i = 0; i < e.S.size(); i++) {
eps.segment<3>(6 + 3*i) = Rot3::Logmap(e.S[i]);
}
return eps;
} else if (COORDINATE == "NORMAL") {
throw std::runtime_error("Normal coordinate representation is not implemented yet");
} else {
throw std::invalid_argument("Invalid coordinate representation");
}
}
State local_coords_inv(const Vector& eps) {
G X = G::exp(eps);
if (COORDINATE == "EXPONENTIAL") {
std::vector<Rot3> S = X.B;
return State(X.A, eps.segment<3>(3), S);
} else if (COORDINATE == "NORMAL") {
throw std::runtime_error("Normal coordinate representation is not implemented yet");
} else {
throw std::invalid_argument("Invalid coordinate representation");
}
}
Matrix stateActionDiff(const State& xi) {
std::function<Vector(const Vector&)> coordsAction =
[&xi](const Vector& U) {
return local_coords(stateAction(G::exp(U), xi));
};
Vector zeros = Vector::Zero(6 + 3 * xi.S.size());
Matrix differential = numericalDifferential(coordsAction, zeros);
return differential;
}
// EqF class implementation
EqF::EqF(const Matrix& Sigma, int n, int m)
: __dof(6 + 3 * n), __n_cal(n), __n_sensor(m), __X_hat(G::identity(n)),
__Sigma(Sigma), __xi_0(State::identity(n)) {
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();
}
State EqF::stateEstimate() const {
return stateAction(__X_hat, __xi_0);
}
void EqF::propagation(const Input& u, double dt) {
State 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 * Matrix3::Identity(), __n_cal));
Matrix M_DT = (Bt * tempSigma * Bt.transpose()) * dt;
__X_hat = __X_hat * G::exp(L * dt);
__Sigma = Phi_DT * __Sigma * Phi_DT.transpose() + M_DT;
}
bool hasNaN(const Vector3& vec) {
return std::isnan(vec[0]) || std::isnan(vec[1]) || std::isnan(vec[2]);
}
void EqF::update(const Measurement& y) {
if (y.cal_idx > __n_cal) {
throw std::invalid_argument("Calibration index out of range");
}
// Get vector representations for checking
Vector3 y_vec = y.y.d.unitVector();
Vector3 d_vec = y.d.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
}
static int update_count = 0;
if (update_count < 5) {
std::cout << "Update " << update_count << ":\n";
std::cout << "y_vec: " << y_vec.transpose() << "\n";
std::cout << "d_vec: " << d_vec.transpose() << "\n";
update_count++;
}
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.d.unitVector()) * action_result; // Ensure this is the right operation
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::exp(Delta) * __X_hat;
__Sigma = (Matrix::Identity(__dof, __dof) - K * Ct) * __Sigma;
}
Matrix EqF::__stateMatrixA(const Input& u) const {
Matrix3 W0 = velocityAction(__X_hat.inv(), u).W();
Matrix A1 = Matrix::Zero(6, 6);
if (COORDINATE == "EXPONENTIAL") {
A1.block<3, 3>(0, 3) = -Matrix3::Identity();
A1.block<3, 3>(3, 3) = W0;
Matrix A2 = repBlock(W0, __n_cal);
return blockDiag(A1, A2);
} else if (COORDINATE == "NORMAL") {
throw std::runtime_error("Normal coordinate representation is not implemented yet");
} else {
throw std::invalid_argument("Invalid coordinate representation");
}
}
Matrix EqF::__stateTransitionMatrix(const Input& u, double dt) const {
Matrix3 W0 = velocityAction(__X_hat.inv(), u).W();
Matrix Phi1 = Matrix::Zero(6, 6);
Matrix3 Phi12 = -dt * (Matrix3::Identity() + (dt / 2) * W0 + ((dt*dt) / 6) * W0 * W0);
Matrix3 Phi22 = Matrix3::Identity() + dt * W0 + ((dt*dt) / 2) * W0 * W0;
if (COORDINATE == "EXPONENTIAL") {
Phi1.block<3, 3>(0, 0) = Matrix3::Identity();
Phi1.block<3, 3>(0, 3) = Phi12;
Phi1.block<3, 3>(3, 3) = Phi22;
Matrix Phi2 = repBlock(Phi22, __n_cal);
return blockDiag(Phi1, Phi2);
} else if (COORDINATE == "NORMAL") {
throw std::runtime_error("Normal coordinate representation is not implemented yet");
} else {
throw std::invalid_argument("Invalid coordinate representation");
}
}
Matrix EqF::__inputMatrixBt() const {
if (COORDINATE == "EXPONENTIAL") {
Matrix B1 = blockDiag(__X_hat.A.matrix(), __X_hat.A.matrix());
Matrix B2;
for (const auto& B : __X_hat.B) {
if (B2.size() == 0) {
B2 = B.matrix();
} else {
B2 = blockDiag(B2, B.matrix());
}
}
return blockDiag(B1, B2);
} else if (COORDINATE == "NORMAL") {
throw std::runtime_error("Normal coordinate representation is not implemented yet");
} else {
throw std::invalid_argument("Invalid coordinate representation");
}
}
Matrix EqF::__measurementMatrixC(const Direction& d, int idx) const {
Matrix Cc = Matrix::Zero(3, 3 * __n_cal);
// If the measurement is related to a sensor that has a calibration state
if (idx >= 0) {
// Cc.block<3, 3>(0, 3 * idx) = wedge(d.d.unitVector()); // WRONG
// Set the correct 3x3 block in Cc
Cc.block<3, 3>(0, 3 * idx) = Rot3::Hat(d.d.unitVector());
}
Matrix3 wedge_d = Rot3::Hat(d.d.unitVector());
// This Matrix concatenation was different from the Python version
// Create the equivalent of:
// Rot3.Hat(d.d.unitVector()) @ np.hstack((Rot3.Hat(d.d.unitVector()), np.zeros((3, 3)), Cc))
Matrix temp(3, 6 + 3 * __n_cal);
temp.block<3, 3>(0, 0) = wedge_d;
temp.block<3, 3>(0, 3) = Matrix3::Zero();
temp.block(0, 6, 3, 3 * __n_cal) = Cc;
return wedge_d * temp;
}
Matrix EqF::__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>(__X_hat.B.size())) {
throw std::out_of_range("Calibration index out of range");
}
return __X_hat.B[idx].matrix();
} else {
return __X_hat.A.matrix();
}
}

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//
// Created by darshan on 3/11/25.
//
#ifndef EQF_H
#define EQF_H
#pragma once
#include "State.h"
#include "Input.h"
#include "G.h"
#include "Direction.h"
#include "Measurements.h"
#include <gtsam/base/Matrix.h>
using namespace gtsam;
/**
* Equivariant Filter (EqF) implementation
*/
class EqF {
private:
int __dof; // Degrees of freedom
int __n_cal; // Number of calibration states
int __n_sensor; // Number of sensors
G __X_hat; // Filter state
Matrix __Sigma; // Error covariance
State __xi_0; // Origin state
Matrix __Dphi0; // Differential of phi at origin
Matrix __InnovationLift; // Innovation lift matrix
public:
/**
* Initialize EqF
* @param Sigma Initial covariance
* @param n Number of calibration states
* @param m Number of sensors
*/
EqF(const Matrix& Sigma, int n, int m);
/**
* Return estimated state
* @return Current state estimate
*/
State stateEstimate() const;
/**
* Propagate the filter state
* @param u Angular velocity measurement
* @param dt Time step
*/
void propagation(const Input& u, double dt);
/**
* Update the filter state with a measurement
* @param y Direction measurement
*/
void update(const Measurement& y);
private:
/**
* Return the state matrix A0t (Equation 14a)
* @param u Input
* @return State matrix A0t
*/
Matrix __stateMatrixA(const Input& u) const;
/**
* Return the state transition matrix Phi (Equation 17)
* @param u Input
* @param dt Time step
* @return State transition matrix Phi
*/
Matrix __stateTransitionMatrix(const Input& u, double dt) const;
/**
* Return the Input matrix Bt
* @return Input matrix Bt
*/
Matrix __inputMatrixBt() const;
/**
* Return the measurement matrix C0 (Equation 14b)
* @param d Known direction
* @param idx Calibration index
* @return Measurement matrix C0
*/
Matrix __measurementMatrixC(const Direction& d, int idx) const;
/**
* Return the measurement output matrix Dt
* @param idx Calibration index
* @return Measurement output matrix Dt
*/
Matrix __outputMatrixDt(int idx) const;
};
// Function declarations for helper functions used by EqF
/**
* Compute the lift of the system (Theorem 3.8, Equation 7)
* @param xi State
* @param u Input
* @return Lift vector
*/
Vector lift(const State& xi, const Input& u);
/**
* Action of the symmetry group on the state space (Equation 4)
* @param X Group element
* @param xi State
* @return New state after group action
*/
State stateAction(const G& X, const State& xi);
/**
* Action of the symmetry group on the input space (Equation 5)
* @param X Group element
* @param u Input
* @return New input after group action
*/
Input velocityAction(const G& X, const Input& u);
/**
* Action of the symmetry group on the output space (Equation 6)
* @param X Group element
* @param y Direction measurement
* @param idx Calibration index
* @return New direction after group action
*/
Vector3 outputAction(const G& X, const Direction& y, int idx = -1);
/**
* Local coordinates assuming xi_0 = identity (Equation 9)
* @param e State representing equivariant error
* @return Local coordinates
*/
Vector local_coords(const State& e);
/**
* Local coordinates inverse assuming xi_0 = identity
* @param eps Local coordinates
* @return Corresponding state
*/
State local_coords_inv(const Vector& eps);
/**
* Differential of the phi action at E = Id in local coordinates
* @param xi State
* @return Differential matrix
*/
Matrix stateActionDiff(const State& xi);
#endif //EQF_H

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//
// Created by darshan on 3/11/25.
//
#include "G.h"
#include "utilities.h"
#include <stdexcept>
G::G(const Rot3& A, const Matrix3& a, const std::vector<Rot3>& B)
: A(A), a(a), B(B) {}
G G::operator*(const G& other) const {
if (B.size() != other.B.size()) {
throw std::invalid_argument("Group elements must have the same number of calibration elements");
}
std::vector<Rot3> new_B;
for (size_t i = 0; i < B.size(); i++) {
new_B.push_back(B[i] * other.B[i]);
}
return G(A * other.A,
a + Rot3::Hat(A.matrix() * Rot3::Vee(other.a)),
new_B);
}
G G::inv() const {
Matrix3 A_inv = A.inverse().matrix();
std::vector<Rot3> B_inv;
for (const auto& b : B) {
B_inv.push_back(b.inverse());
}
return G(A.inverse(),
-Rot3::Hat(A_inv * Rot3::Vee(a)),
B_inv);
}
G G::identity(int n) {
std::vector<Rot3> B(n, Rot3::Identity());
return G(Rot3::Identity(), Matrix3::Zero(), B);
}
G G::exp(const Vector& x) {
if (x.size() < 6 || x.size() % 3 != 0) {
throw std::invalid_argument("Wrong size, a vector with size multiple of 3 and at least 6 must be provided");
}
int n = (x.size() - 6) / 3;
Rot3 A = Rot3::Expmap(x.head<3>());
Vector3 a_vee = Rot3::ExpmapDerivative(-x.head<3>()) * x.segment<3>(3);
Matrix3 a = Rot3::Hat(a_vee);
std::vector<Rot3> B;
for (int i = 0; i < n; i++) {
B.push_back(Rot3::Expmap(x.segment<3>(6 + 3*i)));
}
return G(A, a, B);
}

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//
// Created by darshan on 3/11/25.
//
#ifndef G_H
#define G_H
#include <gtsam/geometry/Rot3.h>
#include <gtsam/base/Matrix.h>
#include <gtsam/base/Vector.h>
#include <vector>
using namespace gtsam;
/**
* Symmetry group (SO(3) |x so(3)) x SO(3) x ... x SO(3)
* Each element of the B list is associated with a calibration state
*/
class G {
public:
Rot3 A; // First SO(3) element
Matrix3 a; // so(3) element (skew-symmetric matrix)
std::vector<Rot3> B; // List of SO(3) elements for calibration
/**
* Initialize the symmetry group G
* @param A SO3 element
* @param a so(3) element (skew symmetric matrix)
* @param B list of SO3 elements
*/
G(const Rot3& A = Rot3::Identity(),
const Matrix3& a = Matrix3::Zero(),
const std::vector<Rot3>& B = std::vector<Rot3>());
/**
* Define the group operation (multiplication)
* @param other Another group element
* @return The product of this and other
*/
G operator*(const G& other) const;
/**
* Return the inverse element of the symmetry group
* @return The inverse of this group element
*/
G inv() const;
/**
* Return the identity of the symmetry group
* @param n Number of calibration elements
* @return The identity element with n calibration components
*/
static G identity(int n);
/**
* Return a group element X given by X = exp(x)
* @param x Vector representation of Lie algebra element
* @return Group element given by the exponential of x
*/
static G exp(const Vector& x);
};
#endif //G_H

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//
// Created by darshan on 3/11/25.
//
#include "Input.h"
#include "utilities.h"
#include <Eigen/Dense>
#include <stdexcept>
#include "gtsam/geometry/Rot3.h"
Input::Input(const Vector3& w, const Matrix& Sigma)
: w(w), Sigma(Sigma) {
if (Sigma.rows() != 6 || Sigma.cols() != 6) {
throw std::invalid_argument("Input measurement noise covariance must be 6x6");
}
// 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");
}
}
Matrix3 Input::W() const {
return Rot3::Hat(w);
}
Input Input::random() {
Vector3 w = Vector3::Random();
return Input(w, Matrix::Identity(6, 6));
}

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//
// Created by darshan on 3/11/25.
//
#ifndef INPUT_H
#define INPUT_H
#include <gtsam/base/Matrix.h>
#include <gtsam/base/Vector.h>
using namespace gtsam;
/**
* Input class for the Biased Attitude System
*/
class Input {
public:
Vector3 w; // Angular velocity
Matrix Sigma; // Noise covariance
/**
* Initialize Input
* @param w Angular velocity (3-vector)
* @param Sigma Noise covariance (6x6 matrix)
*/
Input(const Vector3& w, const Matrix& Sigma);
/**
* Return the Input as a skew-symmetric matrix
* @return w as a skew-symmetric matrix
*/
Matrix3 W() const;
/**
* Return a random angular velocity
* @return A random angular velocity as Input element
*/
static Input random();
};
#endif //INPUT_H

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examples/ABC_EQF/Measurements.cpp
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//
// Created by darshan on 3/11/25.
//
#include "Measurements.h"
#include <Eigen/Dense>
#include <stdexcept>
Measurement::Measurement(const Vector3& y_vec, const Vector3& d_vec,
const Matrix3& Sigma, int i)
: y(y_vec), d(d_vec), Sigma(Sigma), cal_idx(i) {
// Check positive semi-definite
Eigen::SelfAdjointEigenSolver<Matrix3> eigensolver(Sigma);
if (eigensolver.eigenvalues().minCoeff() < -1e-10) {
throw std::invalid_argument("Covariance matrix must be semi-positive definite");
}
}

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//
// Created by darshan on 3/11/25.
//
#ifndef MEASUREMENTS_H
#define MEASUREMENTS_H
#include "Direction.h"
#include <gtsam/base/Matrix.h>
using namespace gtsam;
/**
* Measurement class
* cal_idx is an index corresponding to the calibration related to the measurement
* cal_idx = -1 indicates the measurement is from a calibrated sensor
*/
class Measurement {
public:
Direction y; // Measurement direction in sensor frame
Direction d; // Known direction in global frame
Matrix3 Sigma; // Covariance matrix of the measurement
int cal_idx = -1; // Calibration index (-1 for calibrated sensor)
/**
* Initialize measurement
* @param y_vec Direction measurement in sensor frame
* @param d_vec Known direction in global frame
* @param Sigma Measurement noise covariance
* @param i Calibration index (-1 for calibrated sensor)
*/
Measurement(const Vector3& y_vec, const Vector3& d_vec,
const Matrix3& Sigma, int i = -1);
};
#endif //MEASUREMENTS_H

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//
// Created by darshan on 3/11/25.
//
#include "State.h"
State::State(const Rot3& R, const Vector3& b, const std::vector<Rot3>& S)
: R(R), b(b), S(S) {}
State State::identity(int n) {
std::vector<Rot3> calibrations(n, Rot3::Identity());
return State(Rot3::Identity(), Vector3::Zero(), calibrations);
}

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//
// Created by darshan on 3/11/25.
//
#ifndef STATE_H
#define STATE_H
#include <gtsam/geometry/Rot3.h>
#include <gtsam/base/Vector.h>
#include <vector>
using namespace gtsam;
/**
* State class representing the state of the Biased Attitude System
*/
class State {
public:
Rot3 R; // Attitude rotation matrix R
Vector3 b; // Gyroscope bias b
std::vector<Rot3> S; // Sensor calibrations S
State(const Rot3& R = Rot3::Identity(),
const Vector3& b = Vector3::Zero(),
const std::vector<Rot3>& S = std::vector<Rot3>());
static State identity(int n);
};
#endif //STATE_H

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//
// Created by darshan on 3/11/25.
//
#include "EqF.h"
#include "State.h"
#include "Input.h"
#include "Direction.h"
#include "Measurements.h"
#include "Data.h"
#include "runEQF_withcsv.h"
#include "utilities.h"
#include <iostream>
#include <fstream>
#include <string>
#include <vector>
#include <chrono>
#include <cmath>
#include <gtsam/slam/dataset.h>
using namespace std;
using namespace gtsam;
// Simplified data loading function - in a real application, implement proper CSV parsing
std::vector<Data> loadSimulatedData() {
std::vector<Data> data_list;
double t = 0.0;
double dt = 0.01;
// Number of data points
int num_points = 100;
// Set up one calibration state
int n_cal = 1;
for (int i = 0; i < num_points; i++) {
t += dt;
// Create a simple sinusoidal trajectory
double angle = 0.1 * sin(t);
Rot3 R = Rot3::Rz(angle);
// Create a bias
Vector3 b(0.01, 0.02, 0.03);
// Create a calibration
std::vector<Rot3> S;
S.push_back(Rot3::Ry(0.05));
// State
State xi(R, b, S);
// Input (angular velocity)
Vector3 w(0.1 * cos(t), 0.05 * sin(t), 0.02);
Matrix Sigma_u = Matrix::Identity(6, 6) * 0.01;
Input u(w, Sigma_u);
// Measurements
std::vector<Measurement> measurements;
// Measurement 1 - from uncalibrated sensor
Vector3 d1_vec = Vector3(1, 0, 0).normalized(); // Known direction in global frame
Vector3 y1_vec = S[0].inverse().matrix() * R.inverse().matrix() * d1_vec; // Direction in sensor frame
Matrix3 Sigma1 = Matrix3::Identity() * 0.01;
measurements.push_back(Measurement(y1_vec, d1_vec, Sigma1, 0)); // cal_idx = 0
// Measurement 2 - from calibrated sensor
Vector3 d2_vec = Vector3(0, 1, 0).normalized(); // Known direction in global frame
Vector3 y2_vec = R.inverse().matrix() * d2_vec; // Direction in sensor frame
Matrix3 Sigma2 = Matrix3::Identity() * 0.01;
measurements.push_back(Measurement(y2_vec, d2_vec, Sigma2, -1)); // cal_idx = -1
// Add to data list
data_list.push_back(Data(xi, n_cal, u, measurements, 2, t, dt));
}
return data_list;
}
void runSimulation(EqF& filter, const std::vector<Data>& data) {
std::cout << "Starting simulation with " << data.size() << " data points..." << std::endl;
// Track time for performance measurement
auto start = std::chrono::high_resolution_clock::now();
// Store results for analysis
std::vector<double> times;
std::vector<Vector3> attitude_errors;
std::vector<Vector3> bias_errors;
std::vector<Vector3> calibration_errors;
for (const auto& d : data) {
// Propagation
try {
filter.propagation(d.u, d.dt);
} catch (const std::exception& e) {
std::cerr << "Propagation error at t=" << d.t << ": " << e.what() << std::endl;
continue;
}
// Update with measurements
for (const auto& y : d.y) {
try {
if (!std::isnan(y.y.d.unitVector().norm()) && !std::isnan(y.d.d.unitVector().norm())) {
filter.update(y);
}
} catch (const std::exception& e) {
std::cerr << "Update error at t=" << d.t << ": " << e.what() << std::endl;
}
}
// Get state estimate
State estimate = filter.stateEstimate();
// Compute errors
Vector3 att_error = Rot3::Logmap(d.xi.R.between(estimate.R));
Vector3 bias_error = estimate.b - d.xi.b;
Vector3 cal_error = Vector3::Zero();
if (!d.xi.S.empty() && !estimate.S.empty()) {
cal_error = Rot3::Logmap(d.xi.S[0].between(estimate.S[0]));
}
// Store results
times.push_back(d.t);
attitude_errors.push_back(att_error);
bias_errors.push_back(bias_error);
calibration_errors.push_back(cal_error);
// Print some info
if (d.t < 0.1 || fmod(d.t, 1.0) < d.dt) {
std::cout << "Time: " << d.t
<< ", Attitude error (deg): " << (att_error.norm() * 180.0/M_PI)
<< ", Bias error: " << bias_error.norm()
<< ", Calibration error (deg): " << (cal_error.norm() * 180.0/M_PI)
<< std::endl;
}
}
auto end = std::chrono::high_resolution_clock::now();
std::chrono::duration<double> elapsed = end - start;
std::cout << "Simulation completed in " << elapsed.count() << " seconds" << std::endl;
// Print summary statistics
double avg_att_error = 0.0;
double avg_bias_error = 0.0;
double avg_cal_error = 0.0;
for (size_t i = 0; i < times.size(); i++) {
avg_att_error += attitude_errors[i].norm();
avg_bias_error += bias_errors[i].norm();
avg_cal_error += calibration_errors[i].norm();
}
avg_att_error /= times.size();
avg_bias_error /= times.size();
avg_cal_error /= times.size();
std::cout << "Average attitude error (deg): " << (avg_att_error * 180.0/M_PI) << std::endl;
std::cout << "Average bias error: " << avg_bias_error << std::endl;
std::cout << "Average calibration error (deg): " << (avg_cal_error * 180.0/M_PI) << std::endl;
}
int main(int argc, char** argv) {
std::cout << "ABC-EqF: Attitude-Bias-Calibration Equivariant Filter" << std::endl;
std::cout << "========================================================" << std::endl;
std::string csvFilePath;
// Try to find the EQFdata file in the GTSAM examples directory
try {
// Look specifically for EQFdata.csv in GTSAM examples
csvFilePath = findExampleDataFile("EqFdata.csv");
std::cout << "Using GTSAM example data file: " << csvFilePath << std::endl;
} catch (const std::exception& e) {
std::cerr << "Error: Could not find EqFdata.csv in GTSAM examples directory" << std::endl;
std::cerr << e.what() << std::endl;
return 1;
}
try {
// Run with CSV data
runEqFWithCSVData(csvFilePath);
} catch (const std::exception& e) {
std::cerr << "Error: " << e.what() << std::endl;
return 1;
}
std::cout << "Done." << std::endl;
return 0;
}

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//
// Created by darshan on 3/17/25.
//
#ifndef RUNEQF_WITHCSV_H
#define RUNEQF_WITHCSV_H
//
// Created by darshan on 3/17/25.
//
#include "Data.h"
#include "State.h"
#include "Input.h"
#include "Direction.h"
#include "Measurements.h"
#include "utilities.h"
#include <gtsam/geometry/Rot3.h>
#include <gtsam/geometry/Quaternion.h>
#include <fstream>
#include <sstream>
#include <string>
#include <vector>
#include <stdexcept>
#include <iostream>
#include <cmath>
#include <chrono>
/**
* 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
*
* @param filename Path to the CSV file
* @param startRow First row to load (default: 0)
* @param maxRows Maximum number of rows to load (default: all)
* @param downsample Downsample factor (default: 1, which means no downsampling)
* @return Vector of Data objects
*/
inline std::vector<Data> loadDataFromCSV(const std::string& filename,
int startRow = 0,
int maxRows = -1,
int downsample = 1) {
std::vector<Data> data_list;
std::ifstream file(filename);
if (!file.is_open()) {
throw std::runtime_error("Failed to open file: " + filename);
}
std::string line;
int lineNumber = 0;
int rowCount = 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) {
std::cerr << "Error parsing value at line " << lineNumber << ": " << token << std::endl;
values.push_back(0.0); // Use default value
}
}
// Check if we have enough values
if (values.size() < 39) {
std::cerr << "Warning: Line " << lineNumber << " has only " << values.size()
<< " values, expected 39. Skipping." << std::endl;
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::vector<Rot3> S = {Rot3(calQuat)};
State 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(y0, 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(y1, d1, covY1, -1));
// Create Data object and add to list
data_list.push_back(Data(xi, 1, u, measurements, 2, t, dt));
rowCount++;
}
std::cout << "Loaded " << data_list.size() << " data points from CSV file." << std::endl;
return data_list;
}
/**
* Process Data objects with the EqF filter
*
* @param filter EqF filter to use
* @param data_list Vector of Data objects
* @param saveResults Whether to save results to a file
* @param resultFilename Filename to save results to
*/
inline void printDataPoint(const Data& data, int index) {
std::cout << "Data[" << index << "] @ t=" << data.t << ", dt=" << data.dt << std::endl;
// Print angular velocity
std::cout << " ω = [" << data.u.w[0] << ", " << data.u.w[1] << ", " << data.u.w[2] << "]" << std::endl;
// Print measurements
for (size_t i = 0; i < data.y.size(); i++) {
const Measurement& meas = data.y[i];
// Use the unitVector() method to get a Vector3 from a Unit3 object
Vector3 y_vec = meas.y.d.unitVector();
Vector3 d_vec = meas.d.d.unitVector();
std::cout << " y" << i << " = [" << y_vec[0] << ", " << y_vec[1] << ", " << y_vec[2] << "]" << std::endl;
std::cout << " d" << i << " = [" << d_vec[0] << ", " << d_vec[1] << ", " << d_vec[2] << "]" << std::endl;
}
std::cout << std::endl;
}
// Function to print sample data points
inline void printDataSamples(const std::vector<Data>& data_list, int count = 3) {
int total = data_list.size();
std::cout << "\n=== First " << count << " Data Points ===" << std::endl;
for (int i = 0; i < std::min(count, total); i++) {
printDataPoint(data_list[i], i);
}
if (total > 2*count) {
std::cout << "\n... (" << (total - 2*count) << " points omitted) ...\n" << std::endl;
std::cout << "=== Last " << count << " Data Points ===" << std::endl;
for (int i = std::max(count, total - count); i < total; i++) {
printDataPoint(data_list[i], i);
}
}
}
// Function to validate data
inline bool validateData(const std::vector<Data>& data_list) {
if (data_list.empty()) {
std::cerr << "ERROR: No data loaded from CSV" << std::endl;
return false;
}
std::cout << "Validating " << data_list.size() << " data points..." << std::endl;
// Track statistics
int invalid_count = 0;
// Open a log file to record detailed issues
std::ofstream logFile("data_validation.log");
logFile << "Data Validation Report" << std::endl;
logFile << "--------------------" << std::endl;
for (size_t i = 0; i < data_list.size(); ++i) {
const Data& data = data_list[i];
bool point_valid = true;
// Check time and dt
if (std::isnan(data.t) || std::isnan(data.dt)) {
logFile << "Point " << i << ": Invalid time values (t=" << data.t
<< ", dt=" << data.dt << ")" << std::endl;
point_valid = false;
}
// Check ground truth state for NaN - using isnan directly on components
const auto& R_matrix = data.xi.R.matrix();
bool R_has_nan = false;
for (int r = 0; r < 3; r++) {
for (int c = 0; c < 3; c++) {
if (std::isnan(R_matrix(r, c))) {
R_has_nan = true;
break;
}
}
}
if (R_has_nan) {
logFile << "Point " << i << ": NaN in ground truth attitude matrix" << std::endl;
point_valid = false;
}
// Check bias vector for NaN
bool b_has_nan = false;
for (int j = 0; j < 3; j++) {
if (std::isnan(data.xi.b[j])) {
b_has_nan = true;
break;
}
}
if (b_has_nan) {
logFile << "Point " << i << ": NaN in ground truth bias vector" << std::endl;
point_valid = false;
}
// Check calibration matrices for NaN
for (size_t j = 0; j < data.xi.S.size(); ++j) {
const auto& S_matrix = data.xi.S[j].matrix();
bool S_has_nan = false;
for (int r = 0; r < 3; r++) {
for (int c = 0; c < 3; c++) {
if (std::isnan(S_matrix(r, c))) {
S_has_nan = true;
break;
}
}
}
if (S_has_nan) {
logFile << "Point " << i << ": NaN in ground truth calibration matrix "
<< j << std::endl;
point_valid = false;
}
}
// Check input for NaN
bool w_has_nan = false;
for (int j = 0; j < 3; j++) {
if (std::isnan(data.u.w[j])) {
w_has_nan = true;
break;
}
}
if (w_has_nan) {
logFile << "Point " << i << ": NaN in angular velocity" << std::endl;
point_valid = false;
}
// Check measurements
for (size_t j = 0; j < data.y.size(); ++j) {
const Measurement& meas = data.y[j];
// Get the Vector3 representations to check them
Vector3 y_vec = meas.y.d.unitVector();
Vector3 d_vec = meas.d.d.unitVector();
// Check measurement vector for NaN
bool y_has_nan = false;
bool d_has_nan = false;
for (int k = 0; k < 3; k++) {
if (std::isnan(y_vec[k])) {
y_has_nan = true;
break;
}
if (std::isnan(d_vec[k])) {
d_has_nan = true;
break;
}
}
if (y_has_nan) {
logFile << "Point " << i << ", Meas " << j << ": NaN in measurement vector" << std::endl;
point_valid = false;
}
if (d_has_nan) {
logFile << "Point " << i << ", Meas " << j << ": NaN in reference direction" << std::endl;
point_valid = false;
}
// Calculate norm using Vector3 norms
double y_norm = y_vec.norm();
double d_norm = d_vec.norm();
if (std::abs(y_norm - 1.0) > 1e-5) {
logFile << "Point " << i << ", Meas " << j
<< ": Measurement vector not normalized. Norm = " << y_norm << std::endl;
point_valid = false;
}
if (std::abs(d_norm - 1.0) > 1e-5) {
logFile << "Point " << i << ", Meas " << j
<< ": Reference direction not normalized. Norm = " << d_norm << std::endl;
point_valid = false;
}
}
if (!point_valid) {
invalid_count++;
// Print first few invalid points to console
if (invalid_count <= 5) {
std::cerr << "Invalid data at point " << i << " (t=" << data.t << ")" << std::endl;
}
}
}
// Close the log
logFile << std::endl << "Summary: " << invalid_count << " invalid data points out of "
<< data_list.size() << std::endl;
logFile.close();
// Print summary
std::cout << "Data validation complete. " << invalid_count << " invalid points found." << std::endl;
if (invalid_count > 0) {
std::cout << "See data_validation.log for details." << std::endl;
}
return (invalid_count == 0);
}
inline void processDataWithEqF(EqF& filter,
const std::vector<Data>& data_list,
bool saveResults = false,
const std::string& resultFilename = "eqf_results.csv") {
std::ofstream resultFile;
if (saveResults) {
resultFile.open(resultFilename);
if (!resultFile.is_open()) {
throw std::runtime_error("Failed to open result file: " + resultFilename);
}
// Write header - now adding roll, pitch, yaw columns for estimated and true values
resultFile << "t,";
// Estimated state quaternion
resultFile << "est_qw,est_qx,est_qy,est_qz,";
// Estimated bias
resultFile << "est_bx,est_by,est_bz,";
// Estimated calibration quaternion
resultFile << "est_cqw,est_cqx,est_cqy,est_cqz,";
// True state quaternion
resultFile << "true_qw,true_qx,true_qy,true_qz,";
// True bias
resultFile << "true_bx,true_by,true_bz,";
// True calibration quaternion
resultFile << "true_cqw,true_cqx,true_cqy,true_cqz,";
// Add Euler angles for estimated state
resultFile << "est_roll,est_pitch,est_yaw,";
// Add Euler angles for true state
resultFile << "true_roll,true_pitch,true_yaw,";
// Add Euler angles for estimated calibration
resultFile << "est_cal_roll,est_cal_pitch,est_cal_yaw,";
// Add Euler angles for true calibration
resultFile << "true_cal_roll,true_cal_pitch,true_cal_yaw";
resultFile << std::endl;
}
std::cout << "Processing data with EqF..." << std::endl;
// Track time for performance measurement
auto start = std::chrono::high_resolution_clock::now();
// Store error metrics
std::vector<double> att_errors;
std::vector<double> bias_errors;
std::vector<double> cal_errors;
int total_measurements = 0;
int valid_measurements = 0;
int invalid_measurements = 0;
for (size_t i = 0; i < data_list.size(); i++) {
const Data& data = data_list[i];
// Propagation
filter.propagation(data.u, data.dt);
// Update with measurements
for (const auto& y : data.y) {
total_measurements++;
// Check for NaN values in measurement vectors
bool has_nan = false;
Vector3 y_vec = y.y.d.unitVector();
Vector3 d_vec = y.d.d.unitVector();
for (int j = 0; j < 3; j++) {
if (std::isnan(y_vec[j]) || std::isnan(d_vec[j])) {
has_nan = true;
break;
}
}
if (!has_nan) {
try {
filter.update(y);
valid_measurements++;
} catch (const std::exception& e) {
std::cerr << "Error updating at t=" << data.t << ": " << e.what() << std::endl;
invalid_measurements++;
}
} else {
invalid_measurements++;
}
}
// Get state estimate
State estimate = filter.stateEstimate();
// Compute 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());
// Save results
if (saveResults) {
// Extract quaternions
Quaternion est_q = estimate.R.toQuaternion();
Quaternion true_q = data.xi.R.toQuaternion();
// Extract Euler angles (roll, pitch, yaw) from estimated rotation
Vector3 est_rpy = estimate.R.rpy();
// Convert to degrees for easier comparison
Vector3 est_rpy_deg = est_rpy * 180.0 / M_PI;
// Extract Euler angles from true rotation
Vector3 true_rpy = data.xi.R.rpy();
// Convert to degrees
Vector3 true_rpy_deg = true_rpy * 180.0 / M_PI;
// Get calibration quaternions and Euler angles
Quaternion est_cal_q, true_cal_q;
Vector3 est_cal_rpy_deg = Vector3::Zero();
Vector3 true_cal_rpy_deg = Vector3::Zero();
if (!estimate.S.empty() && !data.xi.S.empty()) {
est_cal_q = estimate.S[0].toQuaternion();
true_cal_q = data.xi.S[0].toQuaternion();
// Get Euler angles for calibrations
Vector3 est_cal_rpy = estimate.S[0].rpy();
est_cal_rpy_deg = est_cal_rpy * 180.0 / M_PI;
Vector3 true_cal_rpy = data.xi.S[0].rpy();
true_cal_rpy_deg = true_cal_rpy * 180.0 / M_PI;
} else {
est_cal_q = Quaternion(1, 0, 0, 0); // Identity quaternion
true_cal_q = Quaternion(1, 0, 0, 0);
}
// Write to file
resultFile << data.t << ",";
// Estimated quaternion
resultFile << est_q.w() << "," << est_q.x() << "," << est_q.y() << "," << est_q.z() << ",";
// Estimated bias
resultFile << estimate.b[0] << "," << estimate.b[1] << "," << estimate.b[2] << ",";
// Estimated calibration quaternion
resultFile << est_cal_q.w() << "," << est_cal_q.x() << "," << est_cal_q.y() << "," << est_cal_q.z() << ",";
// True quaternion
resultFile << true_q.w() << "," << true_q.x() << "," << true_q.y() << "," << true_q.z() << ",";
// True bias
resultFile << data.xi.b[0] << "," << data.xi.b[1] << "," << data.xi.b[2] << ",";
// True calibration quaternion
resultFile << true_cal_q.w() << "," << true_cal_q.x() << "," << true_cal_q.y() << "," << true_cal_q.z() << ",";
// Add Euler angles (in degrees) for estimated state
resultFile << est_rpy_deg[0] << "," << est_rpy_deg[1] << "," << est_rpy_deg[2] << ",";
// Add Euler angles (in degrees) for true state
resultFile << true_rpy_deg[0] << "," << true_rpy_deg[1] << "," << true_rpy_deg[2] << ",";
// Add Euler angles (in degrees) for estimated calibration
resultFile << est_cal_rpy_deg[0] << "," << est_cal_rpy_deg[1] << "," << est_cal_rpy_deg[2] << ",";
// Add Euler angles (in degrees) for true calibration
resultFile << true_cal_rpy_deg[0] << "," << true_cal_rpy_deg[1] << "," << true_cal_rpy_deg[2];
resultFile << std::endl;
}
// Print progress
if (i % 1000 == 0 || i == data_list.size() - 1) {
std::cout << "Processed " << i+1 << "/" << data_list.size()
<< " (" << (100.0 * (i+1) / data_list.size()) << "%) ";
std::cout << "Attitude error: " << (att_error.norm() * 180.0/M_PI) << " deg, ";
std::cout << "Bias error: " << bias_error.norm() << ", ";
std::cout << "Calibration error: " << (cal_error.norm() * 180.0/M_PI) << " deg" << 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();
}
std::cout << std::endl;
std::cout << "EqF Processing completed in " << elapsed.count() << " seconds" << std::endl;
std::cout << "Average attitude error: " << (avg_att_error * 180.0/M_PI) << " deg" << std::endl;
std::cout << "Average bias error: " << avg_bias_error << std::endl;
std::cout << "Average calibration error: " << (avg_cal_error * 180.0/M_PI) << " deg" << std::endl;
std::cout << "Total measurements: " << total_measurements << std::endl;
std::cout << "Valid measurements processed: " << valid_measurements << std::endl;
std::cout << "Invalid measurements skipped: " << invalid_measurements << std::endl;
if (saveResults) {
resultFile.close();
std::cout << "Results saved to " << resultFilename << std::endl;
}
}
inline void runEqFWithCSVData(const std::string& filename) {
try {
// Load data from CSV file with optional parameters
int startRow = 0;
int maxRows = -1;
int downsample = 1;
std::vector<Data> data = loadDataFromCSV(filename, startRow, maxRows, downsample);
if (data.empty()) {
std::cerr << "No data loaded from CSV file." << std::endl;
return;
}
// Print sample data points to inspect the loaded data
std::cout << "Data loaded, displaying samples..." << std::endl;
printDataSamples(data);
// Validate the data to check for issues
std::cout << "Validating data integrity..." << std::endl;
bool dataValid = validateData(data);
if (!dataValid) {
std::cout << "Warning: Data validation found issues." << std::endl;
std::string proceed;
std::cout << "Do you want to proceed anyway? (y/n): ";
std::cin >> proceed;
if (proceed != "y" && proceed != "Y") {
std::cout << "Operation cancelled by user." << std::endl;
return;
}
}
// Initialize EqF filter
int n_cal = 1; // Number of calibration states (from the data)
int n_sensors = 2; // Number of sensors (from the data)
// Initial covariance
Matrix initialSigma = Matrix::Identity(6 + 3*n_cal, 6 + 3*n_cal);
initialSigma.diagonal().head<3>() = Vector3::Constant(0.1); // Reduced attitude uncertainty
initialSigma.diagonal().segment<3>(3) = Vector3::Constant(0.01); // Reduced bias uncertainty
initialSigma.diagonal().tail<3>() = Vector3::Constant(0.1); // Reduced calibration uncertainty
// Create filter
EqF filter(initialSigma, n_cal, n_sensors);
// Initialize filter state from the first ground truth if possible
if (!data.empty()) {
// You'll need to add a method to your EqF class to set the initial state
// Something like:
// filter.setInitialState(data[0].xi);
// If you don't have such a method, you can print the first ground truth
// to see if it makes sense
std::cout << "First ground truth state:" << std::endl;
std::cout << "Attitude: " << data[0].xi.R.matrix() << std::endl;
std::cout << "Bias: " << data[0].xi.b.transpose() << std::endl;
std::cout << "Calibration: " << data[0].xi.S[0].matrix() << std::endl;
}
// Process data with the filter and save results
processDataWithEqF(filter, data, true, "eqf_results.csv");
} catch (const std::exception& e) {
std::cerr << "Error: " << e.what() << std::endl;
}
}
/**
* Example usage function to demonstrate how to use the data loader with the EqF
*/
#endif //RUNEQF_WITHCSV_H

57
examples/ABC_EQF/utilities.cpp
View File

@ -1,57 +0,0 @@
//
// Created by darshan on 3/11/25.
//
#include "utilities.h"
#include <cmath>
// Global configuration
const std::string COORDINATE = "EXPONENTIAL"; // Alternative: "NORMAL"
bool checkNorm(const Vector3& x, double tol) {
return abs(x.norm() - 1) < tol || std::isnan(x.norm());
}
Matrix blockDiag(const Matrix& A, const Matrix& B) {
if (A.size() == 0) {
return B;
} else if (B.size() == 0) {
return A;
} else {
Matrix result(A.rows() + B.rows(), A.cols() + B.cols());
result.setZero();
result.block(0, 0, A.rows(), A.cols()) = A;
result.block(A.rows(), A.cols(), B.rows(), B.cols()) = B;
return result;
}
}
Matrix repBlock(const Matrix& A, int n) {
if (n <= 0) return Matrix();
Matrix result = A;
for (int i = 1; i < n; i++) {
result = blockDiag(result, A);
}
return result;
}
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;
}

28
examples/ABC_EQF/utilities.h
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@ -1,28 +0,0 @@
//
// Created by darshan on 3/11/25.
//
#ifndef UTILITIES_H
#define UTILITIES_H
#pragma once
#include <gtsam/base/Matrix.h>
#include <gtsam/base/Vector.h>
#include <Eigen/Dense>
#include <functional>
using namespace gtsam;
// Global configuration
extern const std::string COORDINATE; // "EXPONENTIAL" or "NORMAL"
/**
* Utility functions
*/
Matrix3 wedge(const Vector3& vec);
bool checkNorm(const Vector3& x, double tol = 1e-3);
Matrix blockDiag(const Matrix& A, const Matrix& B);
Matrix repBlock(const Matrix& A, int n);
Matrix numericalDifferential(std::function<Vector(const Vector&)> f, const Vector& x);
#endif //UTILITIES_H

89
examples/ABC_EQF_Demo.cpp Normal file
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@ -0,0 +1,89 @@
/**
* @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 abc_eqf_lib;
using namespace gtsam;
/**
* Main function for the EqF demo
* @param argc Number of arguments
* @param argv Array of arguments
* @return Exit code
*/
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_cal = 1;
int n_sensors = 2;
// Initial covariance - larger values allow faster convergence
Matrix initialSigma = Matrix::Identity(6 + 3*n_cal, 6 + 3*n_cal);
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
EqF filter(initialSigma, n_cal, 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;
}

1
examples/CMakeLists.txt
View File

@ -17,4 +17,3 @@ if (NOT GTSAM_USE_BOOST_FEATURES)
endif() endif()
gtsamAddExamplesGlob("*.cpp" "${excluded_examples}" "gtsam;${Boost_PROGRAM_OPTIONS_LIBRARY}" ${GTSAM_BUILD_EXAMPLES_ALWAYS}) gtsamAddExamplesGlob("*.cpp" "${excluded_examples}" "gtsam;${Boost_PROGRAM_OPTIONS_LIBRARY}" ${GTSAM_BUILD_EXAMPLES_ALWAYS})
add_subdirectory(ABC_EQF)

5
gtsam/CMakeLists.txt
View File

@ -86,7 +86,10 @@ endforeach(subdir)
# To add additional sources to gtsam when building the full library (static or shared) # To add additional sources to gtsam when building the full library (static or shared)
# append the subfolder with _srcs appended to the end to this list # append the subfolder with _srcs appended to the end to this list
set(gtsam_srcs ${3rdparty_srcs}) set(gtsam_srcs ${3rdparty_srcs}
../examples/ABC_EQF_Demo.cpp
../examples/ABC_EQF.cpp
../examples/ABC_EQF.h)
foreach(subdir ${gtsam_subdirs}) foreach(subdir ${gtsam_subdirs})
list(APPEND gtsam_srcs ${${subdir}_srcs}) list(APPEND gtsam_srcs ${${subdir}_srcs})
endforeach(subdir) endforeach(subdir)