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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 Gravity.hpp | ||
| 10 | /// @brief Different Gravity Models | ||
| 11 | /// @author T. Topp (topp@ins.uni-stuttgart.de) | ||
| 12 | /// @author M. Maier (marcel.maier@ins.uni-stuttgart.de) | ||
| 13 | /// @date 2020-09-15 | ||
| 14 | |||
| 15 | #pragma once | ||
| 16 | |||
| 17 | #include <cstdint> | ||
| 18 | #include <Eigen/Dense> | ||
| 19 | #include <Eigen/Core> | ||
| 20 | |||
| 21 | #include "Navigation/Transformations/CoordinateFrames.hpp" | ||
| 22 | #include "Navigation/Constants.hpp" | ||
| 23 | #include "internal/AssociatedLegendre.hpp" | ||
| 24 | #include "internal/egm96Coeffs.hpp" | ||
| 25 | |||
| 26 | namespace NAV | ||
| 27 | { | ||
| 28 | /// Available Gravitation Models | ||
| 29 | enum class GravitationModel : uint8_t | ||
| 30 | { | ||
| 31 | None, ///< Gravity Model turned off | ||
| 32 | WGS84, ///< World Geodetic System 1984 | ||
| 33 | WGS84_Skydel, ///< World Geodetic System 1984 implemented by the Skydel Simulator // FIXME: Remove after Skydel uses the same as Instinct | ||
| 34 | Somigliana, ///< Somigliana gravity model | ||
| 35 | EGM96, ///< Earth Gravitational Model 1996 | ||
| 36 | COUNT, ///< Amount of items in the enum | ||
| 37 | }; | ||
| 38 | |||
| 39 | /// @brief Converts the enum to a string | ||
| 40 | /// @param[in] gravitationModel Enum value to convert into text | ||
| 41 | /// @return String representation of the enum | ||
| 42 | const char* to_string(GravitationModel gravitationModel); | ||
| 43 | |||
| 44 | /// @brief Shows a ComboBox to select the gravitation model | ||
| 45 | /// @param[in] label Label to show beside the combo box. This has to be a unique id for ImGui. | ||
| 46 | /// @param[in] gravitationModel Reference to the gravitation model to select | ||
| 47 | bool ComboGravitationModel(const char* label, GravitationModel& gravitationModel); | ||
| 48 | |||
| 49 | /// @brief Calculates the gravitation (acceleration due to mass attraction of the Earth) at the WGS84 reference ellipsoid | ||
| 50 | /// using the Somigliana model and makes corrections for altitude | ||
| 51 | /// @param[in] latitude Latitude in [rad] | ||
| 52 | /// @param[in] altitude Altitude in [m] | ||
| 53 | /// @return Gravitation vector in local-navigation frame coordinates in [m/s^2] | ||
| 54 | /// | ||
| 55 | /// @note See S. Gleason (2009) - GNSS Applications and Methods (Chapter 6.2.3.2 - eq. 6.16) | ||
| 56 | template<typename T> | ||
| 57 | 2888924 | [[nodiscard]] Eigen::Vector3<T> n_calcGravitation_SomiglianaAltitude(const T& latitude, const T& altitude) | |
| 58 | { | ||
| 59 | // eq 6.16 has a fault in the denominator, it should be a sin^2(latitude) | ||
| 60 | 2888924 | auto g_0 = 9.7803253359 * (1.0 + 1.931853e-3 * std::pow(std::sin(latitude), 2)) | |
| 61 | 2890171 | / std::sqrt(1.0 - InsConst::WGS84::e_squared * std::pow(std::sin(latitude), 2)); | |
| 62 | |||
| 63 | // Altitude compensation (Matlab example from Chapter 6_GNSS_INS_1 - glocal.m) | ||
| 64 | 2873167 | auto k = 1.0 | |
| 65 | 5758747 | - (2.0 * altitude / InsConst::WGS84::a) | |
| 66 | 2873167 | * (1.0 + InsConst::WGS84::f | |
| 67 | 2885580 | + (std::pow(InsConst::omega_ie * InsConst::WGS84::a, 2)) | |
| 68 | 2873167 | * (InsConst::WGS84::b / InsConst::WGS84::MU)) | |
| 69 | 2873167 | + 3.0 * std::pow(altitude / InsConst::WGS84::a, 2.0); | |
| 70 | |||
| 71 |
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5756700 | return { T(0.0), T(0.0), k * g_0 }; |
| 72 | } | ||
| 73 | |||
| 74 | /// @brief Calculates the gravitation (acceleration due to mass attraction of the Earth) at the WGS84 reference ellipsoid | ||
| 75 | /// using gravity as derived from the gravity potential. However, the north component of the centrifugal acceleration is neglected in order to match the implementation of Skydel's 'ImuPlugin' | ||
| 76 | /// @param[in] latitude Latitude in [rad] | ||
| 77 | /// @param[in] altitude Altitude in [m] | ||
| 78 | /// @return Gravitation vector in local-navigation frame coordinates in [m/s^2] | ||
| 79 | /// | ||
| 80 | /// @note See Skydel API plug-in 'skydel_plugin/source/library/inertial_math/Sources/source/gravity.cpp' | ||
| 81 | template<typename T> | ||
| 82 | ✗ | [[nodiscard]] Eigen::Vector3<T> n_calcGravitation_WGS84_Skydel(const T& latitude, const T& altitude) | |
| 83 | { | ||
| 84 | // geocentric latitude determination from geographic latitude | ||
| 85 | ✗ | auto latitudeGeocentric = std::atan((std::pow(InsConst::WGS84::b, 2.0) / std::pow(InsConst::WGS84::a, 2.0)) * std::tan(latitude)); | |
| 86 | // effective radius determination, i.e. earth radius on WGS84 spheroid plus local altitude --> possible error!! altitude in lla should be added rather than subtracted! | ||
| 87 | ✗ | auto radiusSpheroid = InsConst::WGS84::a * (1.0 - InsConst::WGS84::f * std::pow(std::sin(latitudeGeocentric), 2.0)) - altitude; | |
| 88 | |||
| 89 | // Derivation of gravity, i.e. gravitational potential derived after effective radius | ||
| 90 | ✗ | auto gravitationMagnitude = InsConst::WGS84::MU * std::pow(radiusSpheroid, -2.0) | |
| 91 | ✗ | - 3.0 * InsConst::WGS84::MU * InsConst::WGS84::J2 * std::pow(InsConst::WGS84::a, 2.0) * 0.5 * std::pow(radiusSpheroid, -4.0) * (3.0 * std::pow(std::sin(latitudeGeocentric), 2.0) - 1.0) | |
| 92 | ✗ | - std::pow(InsConst::omega_ie_Skydel, 2.0) * radiusSpheroid * std::pow(std::cos(latitudeGeocentric), 2.0); | |
| 93 | |||
| 94 | ✗ | return { T(0.0), T(0.0), gravitationMagnitude }; | |
| 95 | } | ||
| 96 | |||
| 97 | /// @brief Calculates the gravitation (acceleration due to mass attraction of the Earth) at the WGS84 reference ellipsoid | ||
| 98 | /// using gravity as derived from the gravity potential. | ||
| 99 | /// @param[in] latitude Latitude in [rad] | ||
| 100 | /// @param[in] altitude Altitude in [m] | ||
| 101 | /// @return Gravitation vector in local-navigation frame coordinates in [m/s^2] | ||
| 102 | /// | ||
| 103 | /// @note See 'INS-Projects/INSTINCT/SpecificLiterature/GravityPotentialWGS84' in NC folder (eq. (3) derived after 'r') | ||
| 104 | template<typename T> | ||
| 105 | ✗ | [[nodiscard]] Eigen::Vector3<T> n_calcGravitation_WGS84(const T& latitude, const T& altitude) | |
| 106 | { | ||
| 107 | // Geocentric latitude determination from geographic latitude | ||
| 108 | ✗ | auto latitudeGeocentric = std::atan((std::pow(InsConst::WGS84::b, 2.0) / std::pow(InsConst::WGS84::a, 2.0)) * std::tan(latitude)); | |
| 109 | // Radius of spheroid determination | ||
| 110 | ✗ | auto radiusSpheroid = InsConst::WGS84::a * (1.0 - InsConst::WGS84::f * std::pow(std::sin(latitudeGeocentric), 2.0)) + altitude; | |
| 111 | |||
| 112 | // Magnitude of the gravity, i.e. without orientation | ||
| 113 | ✗ | auto gravitationMagnitude = InsConst::WGS84::MU * std::pow(radiusSpheroid, -2.0) | |
| 114 | ✗ | - 3.0 * InsConst::WGS84::MU * InsConst::WGS84::J2 * std::pow(InsConst::WGS84::a, 2.0) * 0.5 * std::pow(radiusSpheroid, -4.0) * (3.0 * std::pow(std::sin(latitudeGeocentric), 2.0) - 1.0) | |
| 115 | ✗ | - std::pow(InsConst::omega_ie, 2.0) * radiusSpheroid * std::pow(std::cos(latitudeGeocentric), 2.0); | |
| 116 | |||
| 117 | ✗ | return { T(0.0), T(0.0), gravitationMagnitude }; | |
| 118 | } | ||
| 119 | |||
| 120 | /// @brief Calculates the gravitation (acceleration due to mass attraction of the Earth) at the WGS84 reference ellipsoid | ||
| 121 | /// using the EGM96 spherical harmonic model (up to order 10) | ||
| 122 | /// @param[in] lla_position [ϕ, λ, h] Latitude, Longitude, Altitude in [rad, rad, m] | ||
| 123 | /// @param[in] ndegree Degree of the EGM96 (1 <= ndegree <= 10) | ||
| 124 | /// @return Gravitation vector in local-navigation frame coordinates in [m/s^2] | ||
| 125 | /// | ||
| 126 | /// @note See Groves (2013) Chapter 2.4.3 and 'GUT User Guide' (2018) Chapter 7.4 | ||
| 127 | template<typename Derived> | ||
| 128 | 295054 | [[nodiscard]] Eigen::Vector3<typename Derived::Scalar> n_calcGravitation_EGM96(const Eigen::MatrixBase<Derived>& lla_position, size_t ndegree = 10) | |
| 129 | { | ||
| 130 | using internal::egm96Coeffs; | ||
| 131 | using internal::associatedLegendre; | ||
| 132 | |||
| 133 |
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295054 | auto e_position = trafo::lla2ecef_WGS84(lla_position); |
| 134 | |||
| 135 | // Geocentric latitude determination from Groves (2013) - eq. (2.114) | ||
| 136 |
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295054 | auto latitudeGeocentric = std::atan(e_position(2) / std::sqrt(e_position(0) * e_position(0) + e_position(1) * e_position(1))); |
| 137 | |||
| 138 | // Spherical coordinates | ||
| 139 |
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295054 | auto radius = std::sqrt(e_position(0) * e_position(0) + e_position(1) * e_position(1) + e_position(2) * e_position(2)); |
| 140 | 295054 | auto elevation = M_PI_2 - latitudeGeocentric; // [rad] | |
| 141 |
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295054 | const auto& azimuth = lla_position(1); // [rad] |
| 142 | |||
| 143 | // Gravitation vector in local-navigation frame coordinates in [m/s^2] | ||
| 144 |
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295054 | Eigen::Vector3<typename Derived::Scalar> n_gravitation = Eigen::Vector3<typename Derived::Scalar>::Zero(); |
| 145 | |||
| 146 | 295054 | typename Derived::Scalar Pnm(0.0); | |
| 147 | 295054 | typename Derived::Scalar Pnmd(0.0); | |
| 148 | |||
| 149 | 295054 | auto coeffsRows = egm96Coeffs.size(); | |
| 150 | |||
| 151 | // Associated Legendre Polynomial Coefficients 'P' and their derivatives 'Pd' | ||
| 152 |
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295054 | auto [P, Pd] = associatedLegendre(elevation, ndegree); |
| 153 | |||
| 154 |
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19178510 | for (size_t i = 0; i < coeffsRows; i++) // NOLINT(clang-analyzer-core.UndefinedBinaryOperatorResult) // FIXME: Wrong error message about Eigen (error: The left operand of '*' is a garbage value) |
| 155 | { | ||
| 156 | // Retrieving EGM96 coefficients | ||
| 157 |
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18883456 | auto n = static_cast<int>(egm96Coeffs.at(i).at(0)); // Degree of the Associated Legendre Polynomial |
| 158 |
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18883456 | auto m = static_cast<int>(egm96Coeffs.at(i).at(1)); // Order of the Associated Legendre Polynomial |
| 159 |
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18883456 | auto C = egm96Coeffs.at(i).at(2); |
| 160 |
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18883456 | auto S = egm96Coeffs.at(i).at(3); |
| 161 | |||
| 162 |
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18883456 | if (static_cast<size_t>(n) == ndegree + 1) |
| 163 | { | ||
| 164 | // Ending of the for-loop once the iterated 'n' becomes larger than the user-defined 'ndegree' | ||
| 165 | 295054 | i = coeffsRows; | |
| 166 | } | ||
| 167 | else | ||
| 168 | { | ||
| 169 | // Retrieving the parameters of the associated Legendre Polynomials | ||
| 170 |
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18588402 | Pnm = P(n, m); |
| 171 |
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18588402 | Pnmd = Pd(n, m); |
| 172 | |||
| 173 | 18588402 | auto nd = static_cast<double>(n); | |
| 174 | 18588402 | auto md = static_cast<double>(m); | |
| 175 | |||
| 176 | // Gravity vector from differentiation of the gravity potential in spherical coordinates (see 'GUT User Guide' eq. 7.4.2) | ||
| 177 |
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18588402 | n_gravitation(0) += std::pow((InsConst::WGS84::a / radius), nd) * (C * std::cos(md * azimuth) + S * std::sin(md * azimuth)) * Pnmd; |
| 178 |
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18588402 | n_gravitation(1) += std::pow((InsConst::WGS84::a / radius), nd) * md * (C * std::sin(md * azimuth) - S * std::cos(md * azimuth)) * Pnm; |
| 179 |
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18588402 | n_gravitation(2) += (nd + 1.0) * std::pow((InsConst::WGS84::a / radius), nd) * (C * std::cos(md * azimuth) + S * std::sin(md * azimuth)) * Pnm; |
| 180 | } | ||
| 181 | } | ||
| 182 | |||
| 183 |
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295054 | return { -InsConst::WGS84::MU / (radius * radius) * n_gravitation(0), |
| 184 |
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295054 | (1.0 / std::sin(elevation)) * (-InsConst::WGS84::MU / (radius * radius)) * n_gravitation(1), |
| 185 |
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590108 | InsConst::WGS84::MU / (radius * radius) * (1.0 + n_gravitation(2)) }; |
| 186 | 295054 | } | |
| 187 | |||
| 188 | /// @brief Calculates the gravitation (acceleration due to mass attraction of the Earth) | ||
| 189 | /// @param[in] lla_position [ϕ, λ, h] Latitude, Longitude, Altitude in [rad, rad, m] | ||
| 190 | /// @param[in] gravitationModel Gravitation model to use | ||
| 191 | /// @return Gravitation vector in local-navigation frame coordinates in [m/s^2] | ||
| 192 | template<typename Derived> | ||
| 193 | 2979459 | [[nodiscard]] Eigen::Vector3<typename Derived::Scalar> n_calcGravitation(const Eigen::MatrixBase<Derived>& lla_position, | |
| 194 | GravitationModel gravitationModel = GravitationModel::EGM96) | ||
| 195 | { | ||
| 196 | 2979459 | const typename Derived::Scalar& latitude = lla_position(0); | |
| 197 | 2979175 | const typename Derived::Scalar& altitude = lla_position(2); | |
| 198 | |||
| 199 |
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2981665 | if (gravitationModel == GravitationModel::WGS84) |
| 200 | { | ||
| 201 | ✗ | return n_calcGravitation_WGS84(latitude, altitude); | |
| 202 | } | ||
| 203 |
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2981665 | if (gravitationModel == GravitationModel::WGS84_Skydel) // TODO: This function becomes obsolete, once the ImuStream is deactivated due to the 'InstinctDataStream' |
| 204 | { | ||
| 205 | ✗ | return n_calcGravitation_WGS84_Skydel(latitude, altitude); | |
| 206 | } | ||
| 207 |
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2981665 | if (gravitationModel == GravitationModel::Somigliana) |
| 208 | { | ||
| 209 | 2884235 | return n_calcGravitation_SomiglianaAltitude(latitude, altitude); | |
| 210 | } | ||
| 211 |
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97430 | if (gravitationModel == GravitationModel::EGM96) |
| 212 | { | ||
| 213 | 97530 | return n_calcGravitation_EGM96(lla_position); | |
| 214 | } | ||
| 215 | ✗ | return Eigen::Vector3<typename Derived::Scalar>::Zero(); | |
| 216 | } | ||
| 217 | |||
| 218 | } // namespace NAV | ||
| 219 |