INSTINCT Code Coverage Report

Directory: src/
File: Navigation/INS/EcefFrame/Mechanization.hpp
Date: 2025-06-02 15:19:59
Exec Total Coverage
Lines: 31 31 100.0%
Functions: 4 4 100.0%
Branches: 75 162 46.3%
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1 // This file is part of INSTINCT, the INS Toolkit for Integrated
2 // Navigation Concepts and Training by the Institute of Navigation of
3 // the University of Stuttgart, Germany.
4 //
5 // This Source Code Form is subject to the terms of the Mozilla Public
6 // License, v. 2.0. If a copy of the MPL was not distributed with this
7 // file, You can obtain one at https://mozilla.org/MPL/2.0/.
8
9 /// @file Mechanization.hpp
10 /// @brief Inertial Navigation Mechanization Functions in ECEF frame
11 /// @author T. Topp (topp@ins.uni-stuttgart.de)
12 /// @date 2022-06-12
13
14 #pragma once
15
16 #include "Navigation/Gravity/Gravity.hpp"
17
18 #include <Eigen/Core>
19 #include <Eigen/Dense>
20
21 #include "Navigation/Constants.hpp"
22 #include "Navigation/Ellipsoid/Ellipsoid.hpp"
23 #include "Navigation/INS/Functions.hpp"
24 #include "Navigation/INS/Mechanization.hpp"
25 #include "Navigation/Math/Math.hpp"
26 #include "Navigation/Transformations/CoordinateFrames.hpp"
27 #include "util/Logger.hpp"
28
29 #include <cmath>
30
31 namespace NAV
32 {
33 /// @brief Calculates the time derivative of the quaternion e_Quat_b
34 ///
35 /// \anchor eq-INS-Mechanization-e_Quat_b-dot \f{equation}{ \label{eq:eq-INS-Mechanization-e_Quat_b-dot}
36 /// \mathbf{\dot{q}}_b^e
37 /// = \begin{bmatrix} \dot{x} \\ \dot{y} \\ \dot{z} \\ \dot{w} \end{bmatrix}
38 /// = \frac{1}{2} \begin{bmatrix} 0 & \omega_{eb,z}^b & -\omega_{eb,y}^b & \omega_{eb,x}^b \\
39 /// -\omega_{eb,z}^b & 0 & \omega_{eb,x}^b & \omega_{eb,y}^b \\
40 /// \omega_{eb,y}^b & -\omega_{eb,x}^b & 0 & \omega_{eb,z}^b \\
41 /// -\omega_{eb,x}^b & -\omega_{eb,y}^b & -\omega_{eb,z}^b & 0 \end{bmatrix}
42 /// \begin{bmatrix} x \\ y \\ z \\ w \end{bmatrix}
43 /// \f}
44 ///
45 /// @param[in] b_omega_eb ω_eb_b Body rate with respect to the ECEF frame, expressed in the body frame
46 /// @param[in] e_Quat_b_coeffs Coefficients of the quaternion e_Quat_b in order x, y, z, w (q = w + ix + jy + kz)
47 /// @return The time derivative of the coefficients of the quaternion e_Quat_b in order x, y, z, w (q = w + ix + jy + kz)
48 ///
49 /// @note See \ref ImuIntegrator-Mechanization-e-Attitude-Quaternion equation \eqref{eq-ImuIntegrator-Mechanization-e-Attitude-Quaternion-matrix}
50 template<typename DerivedA, typename DerivedB>
51 38664 Eigen::Vector4<typename DerivedA::Scalar> calcTimeDerivativeFor_e_Quat_b(const Eigen::MatrixBase<DerivedA>& b_omega_eb,
52 const Eigen::MatrixBase<DerivedB>& e_Quat_b_coeffs)
53 {
54 using T = typename DerivedA::Scalar;
55
56 // Angular rates in matrix form (Titterton (2005), eq. (11.35))
57
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 38664 Eigen::Matrix4<T> A;
58
59 // clang-format off
60
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 38664 A << T(0.0) , b_omega_eb(2), -b_omega_eb(1), b_omega_eb(0),
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 38664 -b_omega_eb(2), T(0.0) , b_omega_eb(0), b_omega_eb(1),
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 38664 b_omega_eb(1), -b_omega_eb(0), T(0.0) , b_omega_eb(2),
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 38664 -b_omega_eb(0), -b_omega_eb(1), -b_omega_eb(2), T(0.0) ;
64 // clang-format on
65
66 // Propagation of an attitude Quaternion with time (Titterton, ch. 11.2.5, eq. 11.33-11.35, p. 319)
67
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 77328 return 0.5 * A * e_Quat_b_coeffs; // (x, y, z, w)
68 }
69
70 /// @brief Calculates the time derivative of the velocity in ECEF frame coordinates
71 ///
72 /// \anchor eq-INS-Mechanization-v_e-dot \f{equation}{ \label{eq:eq-INS-Mechanization-v_e-dot}
73 /// \boldsymbol{\dot{v}}^e
74 /// = \overbrace{\boldsymbol{f}^e}^{\hidewidth\text{measured}\hidewidth}
75 /// -\ \underbrace{2 \boldsymbol{\omega}_{ie}^e \times \boldsymbol{v}^e}_{\text{coriolis acceleration}}
76 /// +\ \overbrace{\mathbf{g}^e}^{\hidewidth\text{gravitation}\hidewidth}
77 /// -\ \underbrace{\left(\boldsymbol{\omega}_{ie}^e \times [ \boldsymbol{\omega}_{ie}^e \times \mathbf{x}^e ] \right)}_{\text{centrifugal acceleration}}
78 /// \f}
79 ///
80 /// @param[in] e_measuredForce f_e Specific force vector as measured by a triad of accelerometers and resolved into ECEF frame coordinates
81 /// @param[in] e_coriolisAcceleration Coriolis acceleration in ECEF coordinates in [m/s^2]
82 /// @param[in] e_gravitation Local gravitation vector (caused by effects of mass attraction) in ECEF frame coordinates [m/s^2]
83 /// @param[in] e_centrifugalAcceleration Centrifugal acceleration in ECEF coordinates in [m/s^2]
84 /// @return The time derivative of the velocity in ECEF frame coordinates
85 ///
86 /// @note See \ref ImuIntegrator-Mechanization-e-Velocity equation \eqref{eq-ImuIntegrator-Mechanization-e-Velocity}
87 template<typename DerivedA, typename DerivedB, typename DerivedC, typename DerivedD>
88 38664 Eigen::Vector3<typename DerivedA::Scalar> e_calcTimeDerivativeForVelocity(const Eigen::MatrixBase<DerivedA>& e_measuredForce,
89 const Eigen::MatrixBase<DerivedB>& e_coriolisAcceleration,
90 const Eigen::MatrixBase<DerivedC>& e_gravitation,
91 const Eigen::MatrixBase<DerivedD>& e_centrifugalAcceleration)
92 {
93 return e_measuredForce
94 - e_coriolisAcceleration
95 + e_gravitation
96
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 38664 - e_centrifugalAcceleration;
97 }
98
99 /// @brief Calculates the time derivative of the ECEF position
100 ///
101 /// \anchor eq-INS-Mechanization-x_e-dot \f{equation}{ \label{eq:eq-INS-Mechanization-x_e-dot}
102 /// \boldsymbol{\dot{x}}^e = \boldsymbol{v}^e
103 /// \f}
104 ///
105 /// @param[in] e_velocity Velocity with respect to the Earth in ECEF frame coordinates [m/s]
106 /// @return The time derivative of the ECEF position
107 ///
108 /// @note See \ref ImuIntegrator-Mechanization-e-Position equation \eqref{eq-ImuIntegrator-Mechanization-e-Position}
109 template<typename Derived>
110 38664 Eigen::Vector3<typename Derived::Scalar> e_calcTimeDerivativeForPosition(const Eigen::MatrixBase<Derived>& e_velocity)
111 {
112 38664 return e_velocity;
113 }
114
115 /// @brief Calculates the derivative of the quaternion, velocity and position in ECEF coordinates
116 /// @param[in] y [x, y, z, v_x, v_y, v_z, e_q_bx, e_q_by, e_q_bz, e_q_bw]^T
117 /// @param[in] z [fx, fy, fz, ωx, ωy, ωz]^T
118 /// @param[in] c Constant values needed to calculate the derivatives
119 /// @return The derivative ∂/∂t [x, y, z, v_x, v_y, v_z, e_q_bx, e_q_by, e_q_bz, e_q_bw]^T
120 template<typename T>
121 38664 Eigen::Vector<T, 10> e_calcPosVelAttDerivative(const Eigen::Vector<T, 10>& y, const Eigen::Vector<T, 6>& z, const PosVelAttDerivativeConstants& c, double /* t */ = 0.0)
122 {
123 // 0 1 2 3 4 5 6 7 8 9
124 // ∂/∂t [ x, y, z, v_x, v_y, v_z, e_q_bx, e_q_by, e_q_bz, e_q_bw]^T
125
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 38664 Eigen::Vector<T, 10> y_dot = Eigen::Vector<T, 10>::Zero();
126
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 38664 Eigen::Vector3<T> lla_position = trafo::ecef2lla_WGS84(y.template segment<3>(0));
128
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 38664 Eigen::Quaternion<T> e_Quat_b{ y.template segment<4>(6) };
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 38664 e_Quat_b.normalize();
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 38664 Eigen::Quaternion<T> n_Quat_e = trafo::n_Quat_e(lla_position(0), lla_position(1));
132
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 38664 Eigen::Quaternion<T> b_Quat_e = e_Quat_b.conjugate();
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 38664 Eigen::Quaternion<T> e_Quat_n = n_Quat_e.conjugate();
135
136 LOG_DATA("e_velocity = {} [m/s]", y.template segment<3>(3).transpose());
137 LOG_DATA("e_position = {} [m]", y.template segment<3>(0).transpose());
138
139 // ω_eb_b = ω_ib_b - C_be * ω_ie_e
140
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 38664 Eigen::Vector3<T> b_omega_eb = z.template segment<3>(3)
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 38664 - b_Quat_e * (c.angularRateEarthRotationCompensationEnabled ? InsConst::e_omega_ie : Eigen::Vector3d::Zero()).template cast<T>();
142 LOG_DATA("b_omega_eb = {} [rad/s]", b_omega_eb.transpose());
143
144 // Coriolis acceleration in [m/s^2] (acceleration due to motion in rotating reference frame)
145
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 38664 Eigen::Vector3<T> e_coriolisAcceleration = c.coriolisAccelerationCompensationEnabled
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 38664 ? e_calcCoriolisAcceleration(InsConst::e_omega_ie, y.template segment<3>(3))
147 : Eigen::Vector3<T>::Zero();
148 LOG_DATA("e_coriolisAcceleration = {} [m/s^2]", e_coriolisAcceleration.transpose());
149 // Centrifugal acceleration in [m/s^2] (acceleration that makes a body follow a curved path)
150
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 38664 Eigen::Vector3<T> e_centrifugalAcceleration = c.centrifgalAccelerationCompensationEnabled
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 38664 ? e_calcCentrifugalAcceleration(y.template segment<3>(0), InsConst::e_omega_ie)
152 : Eigen::Vector3<T>::Zero();
153 LOG_DATA("e_centrifugalAcceleration = {} [m/s^2]", e_centrifugalAcceleration.transpose());
154
155
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 38664 Eigen::Vector3<T> e_gravitation = e_Quat_n * n_calcGravitation(lla_position, c.gravitationModel);
156 LOG_DATA("e_gravitation = {} [m/s^2] ({})", e_gravitation.transpose(), to_string(c.gravitationModel));
157
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 38664 y_dot.template segment<3>(0) = e_calcTimeDerivativeForPosition(y.template segment<3>(3)); // Velocity with respect to the Earth in ECEF frame coordinates [m/s]
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 38664 y_dot.template segment<3>(3) = e_calcTimeDerivativeForVelocity(e_Quat_b * z.template segment<3>(0), // f_n Specific force vector as measured by a triad of accelerometers and resolved into ECEF frame coordinates
161 e_coriolisAcceleration, // Coriolis acceleration in ECEF coordinates in [m/s^2]
162 e_gravitation, // Local gravitation vector (caused by effects of mass attraction) in ECEF frame coordinates [m/s^2]
163 e_centrifugalAcceleration); // Centrifugal acceleration in ECEF coordinates in [m/s^2]
164
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 38664 y_dot.template segment<4>(6) = calcTimeDerivativeFor_e_Quat_b(b_omega_eb, // ω_eb_b Body rate with respect to the ECEF frame, expressed in the body frame
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 38664 y.template segment<4>(6)); // e_Quat_b_coeffs Coefficients of the quaternion e_Quat_b
167
168 LOG_DATA("e_position_dot = {} [m/s]", y_dot.template segment<3>(0).transpose());
169 LOG_DATA("e_velocity_dot = {} [m/s^2]", y_dot.template segment<3>(3).transpose());
170 LOG_DATA("e_Quat_b_dot = {} ", y_dot.template segment<4>(6).transpose());
171
172 77328 return y_dot;
173 }
174
175 } // namespace NAV
176