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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 | Const, ///< Constant gravitation | ||
| 33 | WGS84, ///< World Geodetic System 1984 | ||
| 34 | WGS84_Skydel, ///< World Geodetic System 1984 implemented by the Skydel Simulator // FIXME: Remove after Skydel uses the same as Instinct | ||
| 35 | Somigliana, ///< Somigliana gravity model | ||
| 36 | EGM96, ///< Earth Gravitational Model 1996 | ||
| 37 | COUNT, ///< Amount of items in the enum | ||
| 38 | }; | ||
| 39 | |||
| 40 | /// @brief Converts the enum to a string | ||
| 41 | /// @param[in] gravitationModel Enum value to convert into text | ||
| 42 | /// @return String representation of the enum | ||
| 43 | const char* to_string(GravitationModel gravitationModel); | ||
| 44 | |||
| 45 | /// @brief Shows a ComboBox to select the gravitation model | ||
| 46 | /// @param[in] label Label to show beside the combo box. This has to be a unique id for ImGui. | ||
| 47 | /// @param[in] gravitationModel Reference to the gravitation model to select | ||
| 48 | bool ComboGravitationModel(const char* label, GravitationModel& gravitationModel); | ||
| 49 | |||
| 50 | /// @brief Returns a constant gravitation of 9.81 [m/s^2] in down direction | ||
| 51 | /// @return Gravitation vector in local-navigation frame coordinates in [m/s^2] | ||
| 52 | template<typename T> | ||
| 53 | ✗ | [[nodiscard]] Eigen::Vector3<T> n_calcGravitation_Const() | |
| 54 | { | ||
| 55 | ✗ | return { T(0.0), T(0.0), T(9.81) }; | |
| 56 | } | ||
| 57 | |||
| 58 | /// @brief Calculates the gravitation (acceleration due to mass attraction of the Earth) at the WGS84 reference ellipsoid | ||
| 59 | /// using the Somigliana model and makes corrections for altitude | ||
| 60 | /// @param[in] latitude Latitude in [rad] | ||
| 61 | /// @param[in] altitude Altitude in [m] | ||
| 62 | /// @return Gravitation vector in local-navigation frame coordinates in [m/s^2] | ||
| 63 | /// | ||
| 64 | /// @note See S. Gleason (2009) - GNSS Applications and Methods (Chapter 6.2.3.2 - eq. 6.16) | ||
| 65 | template<typename T> | ||
| 66 | 97530 | [[nodiscard]] Eigen::Vector3<T> n_calcGravitation_SomiglianaAltitude(const T& latitude, const T& altitude) | |
| 67 | { | ||
| 68 | // eq 6.16 has a fault in the denominator, it should be a sin^2(latitude) | ||
| 69 | 97530 | auto g_0 = 9.7803253359 * (1.0 + 1.931853e-3 * std::pow(std::sin(latitude), 2)) | |
| 70 | 97530 | / std::sqrt(1.0 - InsConst::WGS84::e_squared * std::pow(std::sin(latitude), 2)); | |
| 71 | |||
| 72 | // Altitude compensation (Matlab example from Chapter 6_GNSS_INS_1 - glocal.m) | ||
| 73 | 97530 | auto k = 1.0 | |
| 74 | 195060 | - (2.0 * altitude / InsConst::WGS84::a) | |
| 75 | 97530 | * (1.0 + InsConst::WGS84::f | |
| 76 | 97530 | + (std::pow(InsConst::omega_ie * InsConst::WGS84::a, 2)) | |
| 77 | 97530 | * (InsConst::WGS84::b / InsConst::WGS84::MU)) | |
| 78 | 97530 | + 3.0 * std::pow(altitude / InsConst::WGS84::a, 2.0); | |
| 79 | |||
| 80 |
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195060 | return { T(0.0), T(0.0), k * g_0 }; |
| 81 | } | ||
| 82 | |||
| 83 | /// @brief Calculates the gravitation (acceleration due to mass attraction of the Earth) at the WGS84 reference ellipsoid | ||
| 84 | /// 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' | ||
| 85 | /// @param[in] latitude Latitude in [rad] | ||
| 86 | /// @param[in] altitude Altitude in [m] | ||
| 87 | /// @return Gravitation vector in local-navigation frame coordinates in [m/s^2] | ||
| 88 | /// | ||
| 89 | /// @note See Skydel API plug-in 'skydel_plugin/source/library/inertial_math/Sources/source/gravity.cpp' | ||
| 90 | template<typename T> | ||
| 91 | 2890019 | [[nodiscard]] Eigen::Vector3<T> n_calcGravitation_WGS84_Skydel(const T& latitude, const T& altitude) | |
| 92 | { | ||
| 93 | // geocentric latitude determination from geographic latitude | ||
| 94 | 2890019 | auto latitudeGeocentric = std::atan((std::pow(InsConst::WGS84::b, 2.0) / std::pow(InsConst::WGS84::a, 2.0)) * std::tan(latitude)); | |
| 95 | // effective radius determination, i.e. earth radius on WGS84 spheroid plus local altitude --> possible error!! altitude in lla should be added rather than subtracted! | ||
| 96 | 2890019 | auto radiusSpheroid = InsConst::WGS84::a * (1.0 - InsConst::WGS84::f * std::pow(std::sin(latitudeGeocentric), 2.0)) - altitude; | |
| 97 | |||
| 98 | // Derivation of gravity, i.e. gravitational potential derived after effective radius | ||
| 99 | 2890019 | auto gravitationMagnitude = InsConst::WGS84::MU * std::pow(radiusSpheroid, -2.0) | |
| 100 | 2890019 | - 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) | |
| 101 | 2890019 | - std::pow(InsConst::omega_ie_Skydel, 2.0) * radiusSpheroid * std::pow(std::cos(latitudeGeocentric), 2.0); | |
| 102 | |||
| 103 |
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5771147 | return { T(0.0), T(0.0), gravitationMagnitude }; |
| 104 | } | ||
| 105 | |||
| 106 | /// @brief Calculates the gravitation (acceleration due to mass attraction of the Earth) at the WGS84 reference ellipsoid | ||
| 107 | /// using gravity as derived from the gravity potential. | ||
| 108 | /// @param[in] latitude Latitude in [rad] | ||
| 109 | /// @param[in] altitude Altitude in [m] | ||
| 110 | /// @return Gravitation vector in local-navigation frame coordinates in [m/s^2] | ||
| 111 | /// | ||
| 112 | /// @note See 'INS-Projects/INSTINCT/SpecificLiterature/GravityPotentialWGS84' in NC folder (eq. (3) derived after 'r') | ||
| 113 | template<typename T> | ||
| 114 | ✗ | [[nodiscard]] Eigen::Vector3<T> n_calcGravitation_WGS84(const T& latitude, const T& altitude) | |
| 115 | { | ||
| 116 | // Geocentric latitude determination from geographic latitude | ||
| 117 | ✗ | auto latitudeGeocentric = std::atan((std::pow(InsConst::WGS84::b, 2.0) / std::pow(InsConst::WGS84::a, 2.0)) * std::tan(latitude)); | |
| 118 | // Radius of spheroid determination | ||
| 119 | ✗ | auto radiusSpheroid = InsConst::WGS84::a * (1.0 - InsConst::WGS84::f * std::pow(std::sin(latitudeGeocentric), 2.0)) + altitude; | |
| 120 | |||
| 121 | // Magnitude of the gravity, i.e. without orientation | ||
| 122 | ✗ | auto gravitationMagnitude = InsConst::WGS84::MU * std::pow(radiusSpheroid, -2.0) | |
| 123 | ✗ | - 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) | |
| 124 | ✗ | - std::pow(InsConst::omega_ie, 2.0) * radiusSpheroid * std::pow(std::cos(latitudeGeocentric), 2.0); | |
| 125 | |||
| 126 | ✗ | return { T(0.0), T(0.0), gravitationMagnitude }; | |
| 127 | } | ||
| 128 | |||
| 129 | /// @brief Calculates the gravitation (acceleration due to mass attraction of the Earth) at the WGS84 reference ellipsoid | ||
| 130 | /// using the EGM96 spherical harmonic model (up to order 10) | ||
| 131 | /// @param[in] lla_position [ϕ, λ, h] Latitude, Longitude, Altitude in [rad, rad, m] | ||
| 132 | /// @param[in] ndegree Degree of the EGM96 (1 <= ndegree <= 10) | ||
| 133 | /// @return Gravitation vector in local-navigation frame coordinates in [m/s^2] | ||
| 134 | /// | ||
| 135 | /// @note See Groves (2013) Chapter 2.4.3 and 'GUT User Guide' (2018) Chapter 7.4 | ||
| 136 | template<typename Derived> | ||
| 137 | 99994 | [[nodiscard]] Eigen::Vector3<typename Derived::Scalar> n_calcGravitation_EGM96(const Eigen::MatrixBase<Derived>& lla_position, size_t ndegree = 10) | |
| 138 | { | ||
| 139 | using internal::egm96Coeffs; | ||
| 140 | using internal::associatedLegendre; | ||
| 141 | |||
| 142 |
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99994 | auto e_position = trafo::lla2ecef_WGS84(lla_position); |
| 143 | |||
| 144 | // Geocentric latitude determination from Groves (2013) - eq. (2.114) | ||
| 145 |
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99994 | auto latitudeGeocentric = std::atan(e_position(2) / std::sqrt(e_position(0) * e_position(0) + e_position(1) * e_position(1))); |
| 146 | |||
| 147 | // Spherical coordinates | ||
| 148 |
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99994 | auto radius = std::sqrt(e_position(0) * e_position(0) + e_position(1) * e_position(1) + e_position(2) * e_position(2)); |
| 149 | 99994 | auto elevation = M_PI_2 - latitudeGeocentric; // [rad] | |
| 150 |
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99994 | const auto& azimuth = lla_position(1); // [rad] |
| 151 | |||
| 152 | // Gravitation vector in local-navigation frame coordinates in [m/s^2] | ||
| 153 |
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99994 | Eigen::Vector3<typename Derived::Scalar> n_gravitation = Eigen::Vector3<typename Derived::Scalar>::Zero(); |
| 154 | |||
| 155 | 99994 | typename Derived::Scalar Pnm(0.0); | |
| 156 | 99994 | typename Derived::Scalar Pnmd(0.0); | |
| 157 | |||
| 158 | 99994 | auto coeffsRows = egm96Coeffs.size(); | |
| 159 | |||
| 160 | // Associated Legendre Polynomial Coefficients 'P' and their derivatives 'Pd' | ||
| 161 |
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99994 | auto [P, Pd] = associatedLegendre(elevation, ndegree); |
| 162 | |||
| 163 |
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6499610 | 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) |
| 164 | { | ||
| 165 | // Retrieving EGM96 coefficients | ||
| 166 |
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6399616 | auto n = static_cast<int>(egm96Coeffs.at(i).at(0)); // Degree of the Associated Legendre Polynomial |
| 167 |
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6399616 | auto m = static_cast<int>(egm96Coeffs.at(i).at(1)); // Order of the Associated Legendre Polynomial |
| 168 |
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6399616 | auto C = egm96Coeffs.at(i).at(2); |
| 169 |
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6399616 | auto S = egm96Coeffs.at(i).at(3); |
| 170 | |||
| 171 |
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6399616 | if (static_cast<size_t>(n) == ndegree + 1) |
| 172 | { | ||
| 173 | // Ending of the for-loop once the iterated 'n' becomes larger than the user-defined 'ndegree' | ||
| 174 | 99994 | i = coeffsRows; | |
| 175 | } | ||
| 176 | else | ||
| 177 | { | ||
| 178 | // Retrieving the parameters of the associated Legendre Polynomials | ||
| 179 |
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6299622 | Pnm = P(n, m); |
| 180 |
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6299622 | Pnmd = Pd(n, m); |
| 181 | |||
| 182 | 6299622 | auto nd = static_cast<double>(n); | |
| 183 | 6299622 | auto md = static_cast<double>(m); | |
| 184 | |||
| 185 | // Gravity vector from differentiation of the gravity potential in spherical coordinates (see 'GUT User Guide' eq. 7.4.2) | ||
| 186 |
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6299622 | n_gravitation(0) += std::pow((InsConst::WGS84::a / radius), nd) * (C * std::cos(md * azimuth) + S * std::sin(md * azimuth)) * Pnmd; |
| 187 |
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6299622 | n_gravitation(1) += std::pow((InsConst::WGS84::a / radius), nd) * md * (C * std::sin(md * azimuth) - S * std::cos(md * azimuth)) * Pnm; |
| 188 |
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6299622 | n_gravitation(2) += (nd + 1.0) * std::pow((InsConst::WGS84::a / radius), nd) * (C * std::cos(md * azimuth) + S * std::sin(md * azimuth)) * Pnm; |
| 189 | } | ||
| 190 | } | ||
| 191 | |||
| 192 |
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99994 | return { -InsConst::WGS84::MU / (radius * radius) * n_gravitation(0), |
| 193 |
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99994 | (1.0 / std::sin(elevation)) * (-InsConst::WGS84::MU / (radius * radius)) * n_gravitation(1), |
| 194 |
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199988 | InsConst::WGS84::MU / (radius * radius) * (1.0 + n_gravitation(2)) }; |
| 195 | 99994 | } | |
| 196 | |||
| 197 | /// @brief Calculates the gravitation (acceleration due to mass attraction of the Earth) | ||
| 198 | /// @param[in] lla_position [ϕ, λ, h] Latitude, Longitude, Altitude in [rad, rad, m] | ||
| 199 | /// @param[in] gravitationModel Gravitation model to use | ||
| 200 | /// @return Gravitation vector in local-navigation frame coordinates in [m/s^2] | ||
| 201 | template<typename Derived> | ||
| 202 | 2976029 | [[nodiscard]] Eigen::Vector3<typename Derived::Scalar> n_calcGravitation(const Eigen::MatrixBase<Derived>& lla_position, | |
| 203 | GravitationModel gravitationModel = GravitationModel::EGM96) | ||
| 204 | { | ||
| 205 | 2976029 | const typename Derived::Scalar& latitude = lla_position(0); | |
| 206 | 2975727 | const typename Derived::Scalar& altitude = lla_position(2); | |
| 207 | |||
| 208 |
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2984939 | switch (gravitationModel) |
| 209 | { | ||
| 210 | ✗ | case NAV::GravitationModel::None: | |
| 211 | ✗ | return Eigen::Vector3<typename Derived::Scalar>::Zero(); | |
| 212 | ✗ | case NAV::GravitationModel::Const: | |
| 213 | ✗ | return n_calcGravitation_Const<typename Derived::Scalar>(); | |
| 214 | ✗ | case GravitationModel::WGS84: | |
| 215 | ✗ | return n_calcGravitation_WGS84(latitude, altitude); | |
| 216 | 2887409 | case GravitationModel::WGS84_Skydel: | |
| 217 | 2887409 | return n_calcGravitation_WGS84_Skydel(latitude, altitude); | |
| 218 | 97530 | case GravitationModel::Somigliana: | |
| 219 | 97530 | return n_calcGravitation_SomiglianaAltitude(latitude, altitude); | |
| 220 | ✗ | case GravitationModel::EGM96: | |
| 221 | ✗ | return n_calcGravitation_EGM96(lla_position); | |
| 222 | ✗ | case NAV::GravitationModel::COUNT: | |
| 223 | ✗ | return Eigen::Vector3<typename Derived::Scalar>::Zero(); | |
| 224 | } | ||
| 225 | |||
| 226 | ✗ | return Eigen::Vector3<typename Derived::Scalar>::Zero(); | |
| 227 | } | ||
| 228 | |||
| 229 | } // namespace NAV | ||
| 230 |