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gtsam/examples/ABC_EQF.cpp

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/**
* @file ABC_EQF.cpp
* @brief Implementation of the Attitude-Bias-Calibration Equivariant Filter
*
* This file contains the implementation 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
*/
#include "ABC_EQF.h"
namespace abc_eqf_lib {
// Global configuration
const std::string COORDINATE = "EXPONENTIAL"; // Denotes how the states are mapped to the vector representations
//========================================================================
// Utility Functions
//========================================================================
/**
* @brief Verifies if a vector has unit norm within tolerance
* @param x 3d vector
* @param tol optional tolerance
* @return Bool indicating that the vector norm is approximately 1
* Uses Vector3 norm() method to calculate vector magnitude
*/
bool checkNorm(const Vector3& x, double tol) {
return abs(x.norm() - 1) < tol || std::isnan(x.norm());
}
/**
* @brief Checks if the input vector has any NaNs
* @param vec A 3-D vector
* @return true if present, false otherwise
*/
bool hasNaN(const Vector3& vec) {
return std::isnan(vec[0]) || std::isnan(vec[1]) || std::isnan(vec[2]);
}
/**
* @brief Creates a block diagonal matrix from input matrices
* @param A Matrix A
* @param B Matrix B
* @return A single consolidated matrix with A in the top left and B in the
* bottom right
* Uses Matrix's rows(), cols(), setZero(), and block() methods
*/
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;
}
}
/**
* @brief Creates a block diagonal matrix by repeating a matrix 'n' times
* @param A A matrix
* @param n Number of times to be repeated
* @return Block diag matrix with A repeated 'n' times
* Recursively uses blockDiag() function
*/
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;
}
/**
* @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;
}
//========================================================================
// Direction Class Implementation
//========================================================================
/**
* @brief Initializes a direction object vector from a provided 3D vector input
* @param d_vec A 3-D vector that should have a unit norm(This represents a
* direction in 3D space) Uses Unit3's constructor which normalizes vectors
*/
Direction::Direction(const Vector3& d_vec) : d(d_vec) {
if (!checkNorm(d_vec)) {
throw std::invalid_argument("Direction must be a unit vector");
}
}
/** Access the individual components of the direction vector defined above using this methods below
* Uses the Unit3 object from GTSAM to compute the components
*/
double Direction::x() const {
return d.unitVector()[0];
}
double Direction::y() const {
return d.unitVector()[1];
}
double Direction::z() const {
return d.unitVector()[2];
}
bool Direction::hasNaN() const {
Vector3 vec = d.unitVector();
return std::isnan(vec[0]) || std::isnan(vec[1]) || std::isnan(vec[2]);
}
//========================================================================
// Input Class Implementation
//========================================================================
/**
* @brief Constructs an input object using the Angular velocity vector and the
* covariance matrix
* @param w Angular vector
* @param Sigma 6X6 covariance matrix
* Uses Matrix's rows(), cols() and Eigen's SelfAdjointEigenSolver
*/
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");
}
}
/**
*
* @return 3X3 skey symmetric matrix when called
* Uses Rot3's Hat() to create skew-symmetric matrix
*/
Matrix3 Input::W() const {
return Rot3::Hat(w);
}
//========================================================================
// Measurement Class Implementation
//========================================================================
/**
* @brief Constructs measurement with directions and covariance.
* @param y_vec A 3D vector representing the measured direction in the sensor frame
* @param d_vec A 3D vector representing the known reference direction in the global frame aka ground truth direction
* @param Sigma 3x3 positive definite covariance vector representing the uncertainty in the measurements
* @param i Calibration index - A non-negative integer specifies the element in the calibration vector
* that corresponds to the sensor of interest. A value of -1 indicates that all the sensors have been calibrated
*
* Creates a measurement object that stores the measured direction(y), reference direction(d), measurement noise covariance(Sigma)
* and Calibration Index cal_idx
*
* Uses Eigen's SelfAdjointEigenSolver
*
*/
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");
}
}
//========================================================================
// State Class Implementation
//========================================================================
/**
*
* @param R Rot3 (Attitude)
* @param b Vector (Bias)
* @param S Vector (Rot 3 calibration states)
* Combines the navigation and the calibration states together and provides a
* mechanism to represent the complete system
*
*/
State::State(const Rot3& R, const Vector3& b, const std::vector<Rot3>& S)
: R(R), b(b), S(S) {}
/**
*
* @param n Number of Calibration states
* @return State object intitialized to identity
* Creates a default/ initial state
* Uses GTSAM's Rot3::identity and Vector3 zero function
*/
State State::identity(int n) {
std::vector<Rot3> calibrations(n, Rot3::Identity());
return State(Rot3::Identity(), Vector3::Zero(), calibrations);
}
//========================================================================
// Data Struct Implementation
//========================================================================
/**
*
* @param xi Ground Truth state
* @param n_cal Number of calibration states
* @param u Input measurements
* @param y Vector of y measurements
* @param n_meas number of measurements
* @param t timestamp
* @param dt time step
* Used to organize the state, input and measurement data with timestamps for
* testing Uses Rot3, Vector 3 and Unit3 classes
*/
Data::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) {}
//========================================================================
// Symmetry Group Implementation - Group Elements and actions
//========================================================================
/**
*
* @param A Attitude element of Rot3 type
* @param a Matrix3 bias element
* @param B Rot3 vector containing calibration elements
* Ouptuts a G object using Rot3 for rotation representation
*/
G::G(const Rot3& A, const Matrix3& a, const std::vector<Rot3>& B)
: A(A), a(a), B(B) {}
/**
* Defines the group operation (multiplication)
* @param other Another Group element
* @return G a product of two group elements
* Uses Rot3 Hat, Rot3 Vee for multiplication
*
*/
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);
}
/**
* Used to compute the Group inverse
* @return The inverse of group element
* Uses Rot3 inverse, Rot3 matrix, hat and vee functions
* The left invariant property of the semi-direct product group structure is implemented here by using the -ve sign
*/
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);
}
/**
* Creates the identity element of the group
* @param n Number of calibration elements
* @return the identity element
* Uses Rot3 Identity and Matrix zero
*/
G G::identity(int n) {
std::vector<Rot3> B(n, Rot3::Identity());
return G(Rot3::Identity(), Matrix3::Zero(), B);
}
/**
* Maps the tangent space elements to the group
* @param x Vector in lie algebra
* @return the group element G
* Uses Rot3 expmap and Expmapderivative function
*/
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);
}
//========================================================================
// Helper Functions Implementation
//========================================================================
/**
* Maps system dynamics to the symmetry group
* @param xi State
* @param u Input
* @return Lifted input in Lie Algebra
* Uses Vector zero & Rot3 inverse, matrix 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;
}
/**
* Implements group actions on the states
* @param X A symmetry group element G consisting of the attitude, bias and the
* calibration components X.a -> Rotation matrix containing the attitude X.b ->
* A skew-symmetric matrix representing bias X.B -> A vector of Rotation
* matrices for the calibration components
* @param xi State object
* xi.R -> Attitude (Rot3)
* xi.b -> Gyroscope Bias(Vector 3)
* xi.S -> Vector of calibration matrices(Rot3)
* @return Transformed state
* Uses the Rot3 inverse and Vee functions
*/
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);
}
/**
* Transforms the angular velocity measurements b/w frames
* @param X A symmetry group element X with the components
* @param u Inputs
* @return Transformed inputs
* Uses Rot3 Inverse, matrix and Vee functions and is critical for maintaining
* the input equivariance
*/
Input velocityAction(const G& X, const Input& u) {
return Input(X.A.inverse().matrix() * (u.w - Rot3::Vee(X.a)), u.Sigma);
}
/**
* 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
*/
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();
}
}
/**
* Maps the error states to vector representations through exponential
* coordinates
* @param e error state
* @return Vector with local coordinates
* Uses Rot3 logamo for mapping rotations to the tangent space
*/
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");
}
}
/**
* Used to convert the vectorized errors back to state space
* @param eps Local coordinates in the exponential parameterization
* @return State object corresponding to these coordinates
* Uses Rot3 expmap through the G::exp() function
*/
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");
}
}
/**
* 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
*/
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;
}
//========================================================================
// 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()
*/
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();
}
/**
* Computes the internal group state to a physical state estimate
* @return Current state estimate
*/
State EqF::stateEstimate() const {
return stateAction(__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
*/
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;
}
/**
* 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
*/
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
}
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;
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;
}
/**
* Computes linearized continuous time state matrix
* @param u Angular velocity
* @return Linearized state matrix
* Uses Matrix zero and Identity functions
*/
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");
}
}
/**
* Computes the discrete time state transition matrix
* @param u Angular velocity
* @param dt time step
* @return State transition matrix in discrete time
*/
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");
}
}
/**
* Computes the input uncertainty propagation matrix
* @return
* Uses the blockdiag matrix
*/
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");
}
}
/**
* 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
*/
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) {
// 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());
// Create the combined matrix
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;
}
/**
* Computes the measurement uncertainty propagation matrix
* @param idx Calibration index
* @return Returns B[idx] for calibrated sensors, A for uncalibrated
*/
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();
}
}
//========================================================================
// Data Processing Functions Implementation
//========================================================================
/**
* @brief Loads the test data from the csv file
* @param filename path to the csv file is specified
* @param startRow First row to load based on csv, 0 by default
* @param maxRows maximum rows to load, defaults to all rows
* @param downsample Downsample factor, default 1
* @return 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::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++;
// 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;
}
/**
* @brief Takes in the data and runs an EqF on it and reports the results
* @param filter Initialized EqF filter
* @param data_list std::vector<Data>
* @param printInterval Progress indicator
* Prints the performance statstics like average error etc
* Uses Rot3 between, logmap and rpy functions
*/
void processDataWithEqF(EqF& 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
if (y.y.hasNaN() || y.d.hasNaN()) {
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
State 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();
State 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;
}
}
} // namespace abc_eqf_lib
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