Mechanization.hpp

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// This file is part of INSTINCT, the INS Toolkit for Integrated
// Navigation Concepts and Training by the Institute of Navigation of
// the University of Stuttgart, Germany.
//
// This Source Code Form is subject to the terms of the Mozilla Public
// License, v. 2.0. If a copy of the MPL was not distributed with this
// file, You can obtain one at https://mozilla.org/MPL/2.0/.
 
 
#pragma once
 
#include <Eigen/Core>
#include <Eigen/Dense>
 
#include "Navigation/Constants.hpp"
#include "Navigation/Ellipsoid/Ellipsoid.hpp"
#include "Navigation/INS/Functions.hpp"
#include "Navigation/INS/Mechanization.hpp"
#include "Navigation/Gravity/Gravity.hpp"
#include "Navigation/Math/Math.hpp"
#include "Navigation/Math/NumericalIntegration.hpp"
#include "Navigation/Transformations/CoordinateFrames.hpp"
#include "Navigation/Transformations/Units.hpp"
#include "util/Logger.hpp"
 
#include <cmath>
 
namespace NAV
{
template<typename DerivedA, typename DerivedB>
Eigen::Vector4<typename DerivedA::Scalar> calcTimeDerivativeFor_n_Quat_b(const Eigen::MatrixBase<DerivedA>& b_omega_nb,
                                                                         const Eigen::MatrixBase<DerivedB>& n_Quat_b_coeffs)
{
    // Angular rates in matrix form (Titterton (2005), eq. (11.35))
    Eigen::Matrix4<typename DerivedA::Scalar> A;
 
    // clang-format off
    A <<       0.0     , -b_omega_nb(0), -b_omega_nb(1), -b_omega_nb(2),
          b_omega_nb(0),       0.0     ,  b_omega_nb(2), -b_omega_nb(1),
          b_omega_nb(1), -b_omega_nb(2),       0.0     ,  b_omega_nb(0),
          b_omega_nb(2),  b_omega_nb(1), -b_omega_nb(0),       0.0     ;
    // clang-format on
 
    // Propagation of an attitude Quaternion with time (Titterton, ch. 11.2.5, eq. 11.33-11.35, p. 319)
    return 0.5 * A * n_Quat_b_coeffs; // (w, x, y, z)
}
 
template<typename DerivedA, typename DerivedB, typename DerivedC, typename DerivedD>
Eigen::Vector3<typename DerivedA::Scalar> n_calcTimeDerivativeForVelocity(const Eigen::MatrixBase<DerivedA>& n_measuredForce,
                                                                          const Eigen::MatrixBase<DerivedB>& n_coriolisAcceleration,
                                                                          const Eigen::MatrixBase<DerivedC>& n_gravitation,
                                                                          const Eigen::MatrixBase<DerivedD>& n_centrifugalAcceleration)
{
    return n_measuredForce
           - n_coriolisAcceleration
           + n_gravitation
           - n_centrifugalAcceleration;
}
 
template<typename Derived>
Eigen::Vector3<typename Derived::Scalar> lla_calcTimeDerivativeForPosition(const Eigen::MatrixBase<Derived>& n_velocity,
                                                                           const typename Derived::Scalar& phi, const typename Derived::Scalar& h,
                                                                           const typename Derived::Scalar& R_N, const typename Derived::Scalar& R_E)
{
    // Velocity North in [m/s]
    const auto& v_N = n_velocity(0);
    // Velocity East in [m/s]
    const auto& v_E = n_velocity(1);
    // Velocity Down in [m/s]
    const auto& v_D = n_velocity(2);
 
    return { v_N / (R_N + h),
             v_E / ((R_E + h) * std::cos(phi)),
             -v_D };
}
 
template<typename Scalar, typename = std::enable_if_t<std::is_floating_point_v<Scalar>>>
Eigen::Vector<Scalar, 10> n_calcPosVelAttDerivative(const Eigen::Vector<Scalar, 10>& y, const Eigen::Vector<Scalar, 6>& z, const PosVelAttDerivativeConstants<Scalar>& c, Scalar /* t */ = 0.0)
{
    //  0  1  2  3   4    5    6   7  8  9
    // [w, x, y, z, v_N, v_E, v_D, 𝜙, λ, h]^T
    Eigen::Vector<Scalar, 10> y_dot = Eigen::Vector<Scalar, 10>::Zero();
 
    Eigen::Quaternion<Scalar> n_Quat_b{ y(0), y(1), y(2), y(3) };
    n_Quat_b.normalize();
    Eigen::Quaternion<Scalar> n_Quat_e = trafo::n_Quat_e(y(7), y(8));
 
    LOG_DATA("rollPitchYaw = {} [°]", rad2deg(trafo::quat2eulerZYX(n_Quat_b)).transpose());
    LOG_DATA("n_velocity   = {} [m/s]", y.template segment<3>(4).transpose());
    LOG_DATA("lla_position = {}°, {}°, {} m", rad2deg(y(7)), rad2deg(y(8)), y(9));
 
    auto R_N = calcEarthRadius_N(y(7));
    LOG_DATA("R_N = {} [m]", R_N);
    auto R_E = calcEarthRadius_E(y(7));
    LOG_DATA("R_E = {} [m]", R_E);
 
    // ω_ie_n Turn rate of the Earth expressed in local-navigation frame coordinates
    Eigen::Vector3<Scalar> n_omega_ie = n_Quat_e * InsConst<>::e_omega_ie;
    LOG_DATA("n_omega_ie = {} [rad/s]", n_omega_ie.transpose());
    // 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
    Eigen::Vector3<Scalar> n_omega_en = n_calcTransportRate(y.template segment<3>(7), y.template segment<3>(4), R_N, R_E);
    LOG_DATA("n_omega_en = {} [rad/s]", n_omega_en.transpose());
    // ω_nb_b = ω_ib_b - C_bn * (ω_ie_n + ω_en_n)
    Eigen::Vector3<Scalar> b_omega_nb = z.template segment<3>(3)
                                        - n_Quat_b.conjugate()
                                              * ((c.angularRateEarthRotationCompensationEnabled ? n_omega_ie : Eigen::Vector3<Scalar>::Zero())
                                                 + (c.angularRateTransportRateCompensationEnabled ? n_omega_en : Eigen::Vector3<Scalar>::Zero()));
    LOG_DATA("b_omega_nb = {} [rad/s]", b_omega_nb.transpose());
 
    // Coriolis acceleration in [m/s^2] (acceleration due to motion in rotating reference frame)
    Eigen::Vector3<Scalar> n_coriolisAcceleration = c.coriolisAccelerationCompensationEnabled
                                                        ? n_calcCoriolisAcceleration(n_omega_ie, n_omega_en, y.template segment<3>(4))
                                                        : Eigen::Vector3<Scalar>::Zero();
    LOG_DATA("n_coriolisAcceleration = {} [m/s^2]", n_coriolisAcceleration.transpose());
    // Centrifugal acceleration in [m/s^2] (acceleration that makes a body follow a curved path)
    Eigen::Vector3<Scalar> n_centrifugalAcceleration = c.centrifgalAccelerationCompensationEnabled
                                                           ? n_Quat_e * e_calcCentrifugalAcceleration(trafo::lla2ecef_WGS84(y.template segment<3>(7)), InsConst<>::e_omega_ie)
                                                           : Eigen::Vector3<Scalar>::Zero();
    LOG_DATA("n_centrifugalAcceleration = {} [m/s^2]", n_centrifugalAcceleration.transpose());
 
    Eigen::Vector3<Scalar> n_gravitation = n_calcGravitation(y.template segment<3>(7), c.gravitationModel);
    LOG_DATA("n_gravitation = {} [m/s^2] ({})", n_gravitation.transpose(), to_string(c.gravitationModel));
 
    y_dot.template segment<4>(0) = calcTimeDerivativeFor_n_Quat_b(b_omega_nb,                // ω_nb_b Body rate with respect to the navigation frame, expressed in the body frame
                                                                  y.template segment<4>(0)); // n_Quat_b_coeffs Coefficients of the quaternion n_Quat_b in order w, x, y, z (q = w + ix + jy + kz)
 
    y_dot.template segment<3>(4) = 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
                                                                   n_coriolisAcceleration,              // Coriolis acceleration in local-navigation coordinates in [m/s^2]
                                                                   n_gravitation,                       // Local gravitation vector (caused by effects of mass attraction) in local-navigation frame coordinates [m/s^2]
                                                                   n_centrifugalAcceleration);          // Centrifugal acceleration in local-navigation coordinates in [m/s^2]
 
    y_dot.template segment<3>(7) = lla_calcTimeDerivativeForPosition(y.template segment<3>(4), // Velocity with respect to the Earth in local-navigation frame coordinates [m/s]
                                                                     y(7),                     // 𝜙 Latitude in [rad]
                                                                     y(9),                     // h Altitude in [m]
                                                                     R_N,                      // North/South (meridian) earth radius [m]
                                                                     R_E);                     // East/West (prime vertical) earth radius [m]
 
    LOG_DATA("n_Quat_b_dot = {} ", y_dot.template segment<4>(0).transpose());
    LOG_DATA("n_velocity_dot = {} [m/s^2]", y_dot.template segment<3>(4).transpose());
    LOG_DATA("lla_position_dot = {} [rad/s, rad/s, m/s]", y_dot.template segment<3>(7).transpose());
 
    return y_dot;
}
 
} // namespace NAV