INSTINCT Code Coverage Report

Directory: src/
File: Navigation/INS/LocalNavFrame/Mechanization.hpp
Date: 2025-06-02 15:19:59
Exec Total Coverage
Lines: 38 40 95.0%
Functions: 4 5 80.0%
Branches: 90 196 45.9%
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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 local navigation frame
11 /// @author T. Topp (topp@ins.uni-stuttgart.de)
12 /// @date 2020-09-02
13
14 #pragma once
15
16 #include <Eigen/Core>
17 #include <Eigen/Dense>
18
19 #include "Navigation/Constants.hpp"
20 #include "Navigation/Ellipsoid/Ellipsoid.hpp"
21 #include "Navigation/INS/Functions.hpp"
22 #include "Navigation/INS/Mechanization.hpp"
23 #include "Navigation/Gravity/Gravity.hpp"
24 #include "Navigation/Math/Math.hpp"
25 #include "Navigation/Math/NumericalIntegration.hpp"
26 #include "Navigation/Transformations/CoordinateFrames.hpp"
27 #include "Navigation/Transformations/Units.hpp"
28 #include "util/Logger.hpp"
29
30 #include <cmath>
31
32 namespace NAV
33 {
34 /// @brief Calculates the time derivative of the quaternion n_Quat_b
35 ///
36 /// \anchor eq-INS-Mechanization-n_Quat_b-dot \f{equation}{ \label{eq:eq-INS-Mechanization-n_Quat_b-dot}
37 /// \mathbf{\dot{q}}_b^n
38 /// = \begin{bmatrix} \dot{x} \\ \dot{y} \\ \dot{z} \\ \dot{w} \end{bmatrix}
39 /// = \frac{1}{2} \begin{bmatrix} 0 & \omega_{nb,z}^b & -\omega_{nb,y}^b & \omega_{nb,x}^b \\
40 /// -\omega_{nb,z}^b & 0 & \omega_{nb,x}^b & \omega_{nb,y}^b \\
41 /// \omega_{nb,y}^b & -\omega_{nb,x}^b & 0 & \omega_{nb,z}^b \\
42 /// -\omega_{nb,x}^b & -\omega_{nb,y}^b & -\omega_{nb,z}^b & 0 \end{bmatrix}
43 /// \begin{bmatrix} x \\ y \\ z \\ w \end{bmatrix}
44 /// \f}
45 ///
46 /// @param[in] b_omega_nb ω_nb_b Body rate with respect to the navigation frame, expressed in the body frame
47 /// @param[in] n_Quat_b_coeffs Coefficients of the quaternion n_Quat_b in order x, y, z, w (q = w + ix + jy + kz)
48 /// @return The time derivative of the coefficients of the quaternion n_Quat_b in order x, y, z, w (q = w + ix + jy + kz)
49 ///
50 /// @note See \ref ImuIntegrator-Mechanization-n-Attitude-Quaternion equation \eqref{eq-ImuIntegrator-Mechanization-n-Attitude-Quaternion-matrix-Titterton}
51 template<typename DerivedA, typename DerivedB>
52 111327 Eigen::Vector4<typename DerivedA::Scalar> calcTimeDerivativeFor_n_Quat_b(const Eigen::MatrixBase<DerivedA>& b_omega_nb,
53 const Eigen::MatrixBase<DerivedB>& n_Quat_b_coeffs)
54 {
55 using T = typename DerivedA::Scalar;
56
57 // Angular rates in matrix form (Titterton (2005), eq. (11.35))
58
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 111327 Eigen::Matrix4<T> A;
59
60 // clang-format off
61
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 111327 A << T(0.0) , b_omega_nb(2), -b_omega_nb(1), b_omega_nb(0),
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 111327 -b_omega_nb(2), T(0.0) , b_omega_nb(0), b_omega_nb(1),
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 111327 b_omega_nb(1), -b_omega_nb(0), T(0.0) , b_omega_nb(2),
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 111327 -b_omega_nb(0), -b_omega_nb(1), -b_omega_nb(2), T(0.0) ;
65 // clang-format on
66
67 // Propagation of an attitude Quaternion with time (Titterton, ch. 11.2.5, eq. 11.33-11.35, p. 319)
68
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 222654 return 0.5 * A * n_Quat_b_coeffs; // (x, y, z, w)
69 }
70
71 /// @brief Calculates the time derivative of the velocity in local-navigation frame coordinates
72 ///
73 /// \anchor eq-INS-Mechanization-v_n-dot \f{equation}{ \label{eq:eq-INS-Mechanization-v_n-dot}
74 /// \boldsymbol{\dot{v}}^n
75 /// = \overbrace{\boldsymbol{f}^n}^{\hidewidth\text{measured}\hidewidth}
76 /// -\ \underbrace{(2 \boldsymbol{\omega}_{ie}^n + \boldsymbol{\omega}_{en}^n) \times \boldsymbol{v}^n}_{\text{coriolis acceleration}}
77 /// +\ \overbrace{\mathbf{g}^n}^{\hidewidth\text{gravitation}\hidewidth}
78 /// -\ \mathbf{C}_e^n \cdot \underbrace{\left(\boldsymbol{\omega}_{ie}^e \times [ \boldsymbol{\omega}_{ie}^e \times \mathbf{x}^e ] \right)}_{\text{centrifugal acceleration}}
79 /// \f}
80 ///
81 /// @param[in] n_measuredForce f_n = [f_N f_E f_D]^T Specific force vector as measured by a triad of accelerometers and resolved into local-navigation frame coordinates
82 /// @param[in] n_coriolisAcceleration Coriolis acceleration in local-navigation coordinates in [m/s^2]
83 /// @param[in] n_gravitation Local gravitation vector (caused by effects of mass attraction) in local-navigation frame coordinates [m/s^2]
84 /// @param[in] n_centrifugalAcceleration Centrifugal acceleration in local-navigation coordinates in [m/s^2]
85 /// @return The time derivative of the velocity in local-navigation frame coordinates
86 ///
87 /// @note See \ref ImuIntegrator-Mechanization-n-Velocity equation \eqref{eq-ImuIntegrator-Mechanization-n-Velocity}
88 template<typename DerivedA, typename DerivedB, typename DerivedC, typename DerivedD>
89 111327 Eigen::Vector3<typename DerivedA::Scalar> n_calcTimeDerivativeForVelocity(const Eigen::MatrixBase<DerivedA>& n_measuredForce,
90 const Eigen::MatrixBase<DerivedB>& n_coriolisAcceleration,
91 const Eigen::MatrixBase<DerivedC>& n_gravitation,
92 const Eigen::MatrixBase<DerivedD>& n_centrifugalAcceleration)
93 {
94 return n_measuredForce
95 - n_coriolisAcceleration
96 + n_gravitation
97
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 111327 - n_centrifugalAcceleration;
98 }
99
100 /// @brief Calculates the time derivative of the curvilinear position
101 ///
102 /// \anchor eq-INS-Mechanization-p_lla-dot \f{equation}{ \label{eq:eq-INS-Mechanization-p_lla-dot}
103 /// \begin{aligned}
104 /// \dot{\phi} &= \frac{v_N}{R_N + h} \\
105 /// \dot{\lambda} &= \frac{v_E}{(R_E + h) \cos{\phi}} \\
106 /// \dot{h} &= -v_D
107 /// \end{aligned}
108 /// \f}
109 ///
110 /// @param[in] n_velocity [v_N v_E v_D]^T Velocity with respect to the Earth in local-navigation frame coordinates [m/s]
111 /// @param[in] phi ϕ Latitude [rad]
112 /// @param[in] h Altitude above the ellipsoid [m]
113 /// @param[in] R_N North/South (meridian) earth radius [m]
114 /// @param[in] R_E East/West (prime vertical) earth radius [m]
115 /// @return The time derivative of the curvilinear position
116 ///
117 /// @note See \ref ImuIntegrator-Mechanization-n-Position equation \eqref{eq-ImuIntegrator-Mechanization-n-Position}
118 template<typename Derived>
119 111327 Eigen::Vector3<typename Derived::Scalar> lla_calcTimeDerivativeForPosition(const Eigen::MatrixBase<Derived>& n_velocity,
120 const auto& phi, const auto& h,
121 const auto& R_N, const auto& R_E)
122 {
123 // Velocity North in [m/s]
124
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 111327 const auto& v_N = n_velocity(0);
125 // Velocity East in [m/s]
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 111327 const auto& v_E = n_velocity(1);
127 // Velocity Down in [m/s]
128
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 111327 const auto& v_D = n_velocity(2);
129
130 ✗ return { v_N / (R_N + h),
131 ✗ v_E / ((R_E + h) * std::cos(phi)),
132
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 111327 -v_D };
133 }
134
135 /// @brief Calculates the derivative of the quaternion, velocity and curvilinear position
136 /// @param[in] y [ 𝜙, λ, h, v_N, v_E, v_D, n_q_bx, n_q_by, n_q_bz, n_q_bw]^T
137 /// @param[in] z [fx, fy, fz, ωx, ωy, ωz]^T
138 /// @param[in] c Constant values needed to calculate the derivatives
139 /// @return The derivative ∂/∂t [ 𝜙, λ, h, v_N, v_E, v_D, n_q_bx, n_q_by, n_q_bz, n_q_bw]^T
140 template<typename T>
141 111327 Eigen::Vector<T, 10> n_calcPosVelAttDerivative(const Eigen::Vector<T, 10>& y, const Eigen::Vector<T, 6>& z, const PosVelAttDerivativeConstants& c, double /* t */ = 0.0)
142 {
143 // 0 1 2 3 4 5 6 7 8 9
144 // ∂/∂t [ 𝜙, λ, h, v_N, v_E, v_D, n_q_bx, n_q_by, n_q_bz, n_q_bw]^T
145
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 111327 Eigen::Vector<T, 10> y_dot = Eigen::Vector<T, 10>::Zero();
146
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 111327 Eigen::Quaternion<T> n_Quat_b{ y.template segment<4>(6) };
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 111327 n_Quat_b.normalize();
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 111327 Eigen::Quaternion<T> n_Quat_e = trafo::n_Quat_e(y(0), y(1));
150
151 LOG_DATA("rollPitchYaw = {} [°]", rad2deg(trafo::quat2eulerZYX(n_Quat_b)).transpose());
152 LOG_DATA("n_velocity = {} [m/s]", y.template segment<3>(3).transpose());
153 LOG_DATA("lla_position = {}°, {}°, {} m", rad2deg(y(0)), rad2deg(y(1)), y(2));
154
155
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 111327 auto R_N = calcEarthRadius_N(y(0));
156 LOG_DATA("R_N = {} [m]", R_N);
157
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 111327 auto R_E = calcEarthRadius_E(y(0));
158 LOG_DATA("R_E = {} [m]", R_E);
159
160 // ω_ie_n Turn rate of the Earth expressed in local-navigation frame coordinates
161
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 111327 Eigen::Vector3<T> n_omega_ie = n_Quat_e * InsConst::e_omega_ie.cast<T>();
162 LOG_DATA("n_omega_ie = {} [rad/s]", n_omega_ie.transpose());
163 // ω_en_n Turn rate of the local frame with respect to the Earth-fixed frame, called the transport rate, expressed in local-navigation frame coordinates
164
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 111327 Eigen::Vector3<T> n_omega_en = n_calcTransportRate(y.template segment<3>(0), y.template segment<3>(3), R_N, R_E);
165 LOG_DATA("n_omega_en = {} [rad/s]", n_omega_en.transpose());
166 // ω_nb_b = ω_ib_b - C_bn * (ω_ie_n + ω_en_n)
167
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 111327 Eigen::Vector3<T> b_omega_nb = z.template segment<3>(3)
168 - n_Quat_b.conjugate()
169
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 111327 * ((c.angularRateEarthRotationCompensationEnabled ? n_omega_ie : Eigen::Vector3<T>::Zero())
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 111327 + (c.angularRateTransportRateCompensationEnabled ? n_omega_en : Eigen::Vector3<T>::Zero()));
171 LOG_DATA("b_omega_nb = {} [rad/s]", b_omega_nb.transpose());
172
173 // Coriolis acceleration in [m/s^2] (acceleration due to motion in rotating reference frame)
174
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 111327 Eigen::Vector3<T> n_coriolisAcceleration = c.coriolisAccelerationCompensationEnabled
175
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 111327 ? n_calcCoriolisAcceleration(n_omega_ie, n_omega_en, y.template segment<3>(3))
176 : Eigen::Vector3<T>::Zero();
177 LOG_DATA("n_coriolisAcceleration = {} [m/s^2]", n_coriolisAcceleration.transpose());
178 // Centrifugal acceleration in [m/s^2] (acceleration that makes a body follow a curved path)
179
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 111327 Eigen::Vector3<T> n_centrifugalAcceleration = c.centrifgalAccelerationCompensationEnabled
180
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 111327 ? n_Quat_e * e_calcCentrifugalAcceleration(trafo::lla2ecef_WGS84(y.template segment<3>(0)), InsConst::e_omega_ie)
181 : Eigen::Vector3<T>::Zero();
182 LOG_DATA("n_centrifugalAcceleration = {} [m/s^2]", n_centrifugalAcceleration.transpose());
183
184
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 111327 Eigen::Vector3<T> n_gravitation = n_calcGravitation(y.template segment<3>(0), c.gravitationModel);
185 LOG_DATA("n_gravitation = {} [m/s^2] ({})", n_gravitation.transpose(), to_string(c.gravitationModel));
186
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 111327 y_dot.template segment<3>(0) = lla_calcTimeDerivativeForPosition(y.template segment<3>(3), // Velocity with respect to the Earth in local-navigation frame coordinates [m/s]
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 111327 y(0), // 𝜙 Latitude in [rad]
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 111327 y(2), // h Altitude in [m]
190 R_N, // North/South (meridian) earth radius [m]
191 R_E); // East/West (prime vertical) earth radius [m]
192
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 111327 y_dot.template segment<3>(3) = n_calcTimeDerivativeForVelocity(n_Quat_b * z.template segment<3>(0), // f_n Specific force vector as measured by a triad of accelerometers and resolved into local-navigation frame coordinates
194 n_coriolisAcceleration, // Coriolis acceleration in local-navigation coordinates in [m/s^2]
195 n_gravitation, // Local gravitation vector (caused by effects of mass attraction) in local-navigation frame coordinates [m/s^2]
196 n_centrifugalAcceleration); // Centrifugal acceleration in local-navigation coordinates in [m/s^2]
197
198
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 111327 y_dot.template segment<4>(6) = calcTimeDerivativeFor_n_Quat_b(b_omega_nb, // ω_nb_b Body rate with respect to the navigation frame, expressed in the body frame
199
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 111327 y.template segment<4>(6)); // n_Quat_b_coeffs Coefficients of the quaternion n_Quat_b
200
201 LOG_DATA("lla_position_dot = {} [rad/s, rad/s, m/s]", y_dot.template segment<3>(0).transpose());
202 LOG_DATA("n_velocity_dot = {} [m/s^2]", y_dot.template segment<3>(3).transpose());
203 LOG_DATA("n_Quat_b_dot = {} ", y_dot.template segment<4>(6).transpose());
204
205 222654 return y_dot;
206 }
207
208 } // namespace NAV
209