138 lines
4.6 KiB
C++
138 lines
4.6 KiB
C++
#include "Igrf13Model.h"
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Igrf13Model::Igrf13Model() {}
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Igrf13Model::~Igrf13Model() {}
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void Igrf13Model::magFieldComp(const double longitude, const double gcLatitude,
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const double altitude, timeval timeOfMagMeasurement,
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double* magFieldModelInertial) {
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double magFieldModel[3] = {0, 0, 0};
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double phi = longitude, theta = gcLatitude; // geocentric
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/* Here is the co-latitude needed*/
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theta -= 90. * M_PI / 180.;
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theta *= (-1);
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double rE = 6371200.0; // radius earth [m]
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/* Predefine recursive associated Legendre polynomials */
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double P11 = 1;
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double P10 = P11; // P10 = P(n-1,m-0)
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double dP11 = 0; // derivative
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double dP10 = dP11; // derivative
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double P2 = 0, dP2 = 0, P20 = 0, dP20 = 0, K = 0;
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for (int m = 0; m <= igrfOrder; m++) {
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for (int n = 1; n <= igrfOrder; n++) {
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if (m <= n) {
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/* Calculation of Legendre Polynoms (normalised) */
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if (n == m) {
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P2 = sin(theta) * P11;
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dP2 = sin(theta) * dP11 + cos(theta) * P11;
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P11 = P2;
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P10 = P11;
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P20 = 0;
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dP11 = dP2;
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dP10 = dP11;
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dP20 = 0;
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} else if (n == 1) {
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P2 = cos(theta) * P10;
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dP2 = cos(theta) * dP10 - sin(theta) * P10;
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P20 = P10;
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P10 = P2;
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dP20 = dP10;
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dP10 = dP2;
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} else {
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K = (pow((n - 1), 2) - pow(m, 2)) / ((2 * n - 1) * (2 * n - 3));
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P2 = cos(theta) * P10 - K * P20;
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dP2 = cos(theta) * dP10 - sin(theta) * P10 - K * dP20;
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P20 = P10;
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P10 = P2;
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dP20 = dP10;
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dP10 = dP2;
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}
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/* gradient of scalar potential towards radius */
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magFieldModel[0] +=
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pow(rE / (altitude + rE), (n + 2)) * (n + 1) *
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((updatedG[m][n - 1] * cos(m * phi) + updatedH[m][n - 1] * sin(m * phi)) * P2);
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/* gradient of scalar potential towards theta */
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magFieldModel[1] +=
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pow(rE / (altitude + rE), (n + 2)) *
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((updatedG[m][n - 1] * cos(m * phi) + updatedH[m][n - 1] * sin(m * phi)) * dP2);
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/* gradient of scalar potential towards phi */
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magFieldModel[2] +=
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pow(rE / (altitude + rE), (n + 2)) *
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((-updatedG[m][n - 1] * sin(m * phi) + updatedH[m][n - 1] * cos(m * phi)) * P2 * m);
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}
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}
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}
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magFieldModel[1] *= -1;
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magFieldModel[2] *= (-1 / sin(theta));
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double JD2000 = 0;
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Clock::convertTimevalToJD2000(timeOfMagMeasurement, &JD2000);
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double UT1 = JD2000 / 36525.;
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double gst =
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280.46061837 + 360.98564736629 * JD2000 + 0.0003875 * pow(UT1, 2) - 2.6e-8 * pow(UT1, 3);
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gst = std::fmod(gst, 360.);
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gst *= M_PI / 180.;
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double lst = gst + longitude; // local sidereal time [rad]
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magFieldModelInertial[0] =
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(magFieldModel[0] * cos(gcLatitude) + magFieldModel[1] * sin(gcLatitude)) * cos(lst) -
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magFieldModel[2] * sin(lst);
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magFieldModelInertial[1] =
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(magFieldModel[0] * cos(gcLatitude) + magFieldModel[1] * sin(gcLatitude)) * sin(lst) +
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magFieldModel[2] * cos(lst);
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magFieldModelInertial[2] =
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magFieldModel[0] * sin(gcLatitude) - magFieldModel[1] * cos(gcLatitude);
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// convert nT to uT
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VectorOperations<double>::mulScalar(magFieldModelInertial, 1e-3, magFieldModelInertial, 3);
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}
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void Igrf13Model::updateCoeffGH(timeval timeOfMagMeasurement) {
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double JD2000Igrf = (2458850.0 - 2451545); // Begin of IGRF-13 (2020-01-01,00:00:00) in JD2000
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double JD2000 = 0;
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Clock::convertTimevalToJD2000(timeOfMagMeasurement, &JD2000);
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double days = ceil(JD2000 - JD2000Igrf);
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for (int i = 0; i <= igrfOrder; i++) {
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for (int j = 0; j <= (igrfOrder - 1); j++) {
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updatedG[i][j] = coeffG[i][j] + svG[i][j] * (days / 365);
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updatedH[i][j] = coeffH[i][j] + svH[i][j] * (days / 365);
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}
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}
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}
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void Igrf13Model::schmidtNormalization() {
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double kronDelta = 0;
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schmidtFactors[0][0] = 1;
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for (int n = 1; n <= igrfOrder; n++) {
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if (n == 1) {
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schmidtFactors[0][n - 1] = 1;
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} else {
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schmidtFactors[0][n - 1] = schmidtFactors[0][n - 2] * (2 * n - 1) / n;
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}
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for (int m = 1; m <= igrfOrder; m++) {
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if (m == 1) {
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kronDelta = 1;
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} else {
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kronDelta = 0;
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}
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schmidtFactors[m][n - 1] =
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schmidtFactors[m - 1][n - 1] * sqrt((n - m + 1) * (kronDelta + 1) / (n + m));
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}
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}
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for (int i = 0; i <= igrfOrder; i++) {
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for (int j = 0; j <= (igrfOrder - 1); j++) {
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coeffG[i][j] = schmidtFactors[i][j] * coeffG[i][j];
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coeffH[i][j] = schmidtFactors[i][j] * coeffH[i][j];
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svG[i][j] = schmidtFactors[i][j] * svG[i][j];
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svH[i][j] = schmidtFactors[i][j] * svH[i][j];
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}
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}
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}
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