[2578] | 1 |
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| 2 | #include <cmath>
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| 3 |
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[5801] | 4 | #include "pppModel.h"
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[2579] | 5 | #include "bncutils.h"
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[2578] | 6 |
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| 7 | using namespace std;
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| 8 |
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[5801] | 9 | double Frac (double x) { return x-floor(x); };
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| 10 | double Modulo (double x, double y) { return y*Frac(x/y); }
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[2578] | 11 |
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[5801] | 12 | Matrix t_astro::rotX(double Angle) {
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| 13 | const double C = cos(Angle);
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| 14 | const double S = sin(Angle);
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| 15 | Matrix UU(3,3);
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| 16 | UU[0][0] = 1.0; UU[0][1] = 0.0; UU[0][2] = 0.0;
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| 17 | UU[1][0] = 0.0; UU[1][1] = +C; UU[1][2] = +S;
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| 18 | UU[2][0] = 0.0; UU[2][1] = -S; UU[2][2] = +C;
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| 19 | return UU;
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| 20 | }
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[2578] | 21 |
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[5801] | 22 | Matrix t_astro::rotY(double Angle) {
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| 23 | const double C = cos(Angle);
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| 24 | const double S = sin(Angle);
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| 25 | Matrix UU(3,3);
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| 26 | UU[0][0] = +C; UU[0][1] = 0.0; UU[0][2] = -S;
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| 27 | UU[1][0] = 0.0; UU[1][1] = 1.0; UU[1][2] = 0.0;
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| 28 | UU[2][0] = +S; UU[2][1] = 0.0; UU[2][2] = +C;
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| 29 | return UU;
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| 30 | }
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[2578] | 31 |
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[5801] | 32 | Matrix t_astro::rotZ(double Angle) {
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| 33 | const double C = cos(Angle);
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| 34 | const double S = sin(Angle);
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| 35 | Matrix UU(3,3);
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| 36 | UU[0][0] = +C; UU[0][1] = +S; UU[0][2] = 0.0;
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| 37 | UU[1][0] = -S; UU[1][1] = +C; UU[1][2] = 0.0;
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| 38 | UU[2][0] = 0.0; UU[2][1] = 0.0; UU[2][2] = 1.0;
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| 39 | return UU;
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[2578] | 40 | }
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| 41 |
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| 42 | // Greenwich Mean Sidereal Time
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| 43 | ///////////////////////////////////////////////////////////////////////////
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[5801] | 44 | double t_astro::GMST(double Mjd_UT1) {
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[2578] | 45 |
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| 46 | const double Secs = 86400.0;
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| 47 |
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| 48 | double Mjd_0 = floor(Mjd_UT1);
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| 49 | double UT1 = Secs*(Mjd_UT1-Mjd_0);
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| 50 | double T_0 = (Mjd_0 -MJD_J2000)/36525.0;
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| 51 | double T = (Mjd_UT1-MJD_J2000)/36525.0;
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| 52 |
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| 53 | double gmst = 24110.54841 + 8640184.812866*T_0 + 1.002737909350795*UT1
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| 54 | + (0.093104-6.2e-6*T)*T*T;
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| 55 |
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| 56 | return 2.0*M_PI*Frac(gmst/Secs);
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| 57 | }
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| 58 |
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| 59 | // Nutation Matrix
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| 60 | ///////////////////////////////////////////////////////////////////////////
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[5801] | 61 | Matrix t_astro::NutMatrix(double Mjd_TT) {
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[2578] | 62 |
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| 63 | const double T = (Mjd_TT-MJD_J2000)/36525.0;
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| 64 |
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| 65 | double ls = 2.0*M_PI*Frac(0.993133+ 99.997306*T);
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| 66 | double D = 2.0*M_PI*Frac(0.827362+1236.853087*T);
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| 67 | double F = 2.0*M_PI*Frac(0.259089+1342.227826*T);
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| 68 | double N = 2.0*M_PI*Frac(0.347346- 5.372447*T);
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| 69 |
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| 70 | double dpsi = ( -17.200*sin(N) - 1.319*sin(2*(F-D+N)) - 0.227*sin(2*(F+N))
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| 71 | + 0.206*sin(2*N) + 0.143*sin(ls) ) / RHO_SEC;
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| 72 | double deps = ( + 9.203*cos(N) + 0.574*cos(2*(F-D+N)) + 0.098*cos(2*(F+N))
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| 73 | - 0.090*cos(2*N) ) / RHO_SEC;
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| 74 |
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| 75 | double eps = 0.4090928-2.2696E-4*T;
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| 76 |
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| 77 | return rotX(-eps-deps)*rotZ(-dpsi)*rotX(+eps);
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| 78 | }
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| 79 |
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| 80 | // Precession Matrix
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| 81 | ///////////////////////////////////////////////////////////////////////////
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[5801] | 82 | Matrix t_astro::PrecMatrix(double Mjd_1, double Mjd_2) {
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[2578] | 83 |
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| 84 | const double T = (Mjd_1-MJD_J2000)/36525.0;
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| 85 | const double dT = (Mjd_2-Mjd_1)/36525.0;
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| 86 |
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| 87 | double zeta = ( (2306.2181+(1.39656-0.000139*T)*T)+
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| 88 | ((0.30188-0.000344*T)+0.017998*dT)*dT )*dT/RHO_SEC;
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| 89 | double z = zeta + ( (0.79280+0.000411*T)+0.000205*dT)*dT*dT/RHO_SEC;
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| 90 | double theta = ( (2004.3109-(0.85330+0.000217*T)*T)-
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| 91 | ((0.42665+0.000217*T)+0.041833*dT)*dT )*dT/RHO_SEC;
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| 92 |
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| 93 | return rotZ(-z) * rotY(theta) * rotZ(-zeta);
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| 94 | }
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| 95 |
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| 96 | // Sun's position
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| 97 | ///////////////////////////////////////////////////////////////////////////
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[5801] | 98 | ColumnVector t_astro::Sun(double Mjd_TT) {
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[2578] | 99 |
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| 100 | const double eps = 23.43929111/RHO_DEG;
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| 101 | const double T = (Mjd_TT-MJD_J2000)/36525.0;
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| 102 |
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| 103 | double M = 2.0*M_PI * Frac ( 0.9931267 + 99.9973583*T);
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[2586] | 104 | double L = 2.0*M_PI * Frac ( 0.7859444 + M/2.0/M_PI +
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[2578] | 105 | (6892.0*sin(M)+72.0*sin(2.0*M)) / 1296.0e3);
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| 106 | double r = 149.619e9 - 2.499e9*cos(M) - 0.021e9*cos(2*M);
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| 107 |
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| 108 | ColumnVector r_Sun(3);
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| 109 | r_Sun << r*cos(L) << r*sin(L) << 0.0; r_Sun = rotX(-eps) * r_Sun;
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| 110 |
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| 111 | return rotZ(GMST(Mjd_TT))
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| 112 | * NutMatrix(Mjd_TT)
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| 113 | * PrecMatrix(MJD_J2000, Mjd_TT)
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| 114 | * r_Sun;
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| 115 | }
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| 116 |
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| 117 | // Moon's position
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| 118 | ///////////////////////////////////////////////////////////////////////////
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[5801] | 119 | ColumnVector t_astro::Moon(double Mjd_TT) {
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[2578] | 120 |
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| 121 | const double eps = 23.43929111/RHO_DEG;
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| 122 | const double T = (Mjd_TT-MJD_J2000)/36525.0;
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| 123 |
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| 124 | double L_0 = Frac ( 0.606433 + 1336.851344*T );
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| 125 | double l = 2.0*M_PI*Frac ( 0.374897 + 1325.552410*T );
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| 126 | double lp = 2.0*M_PI*Frac ( 0.993133 + 99.997361*T );
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| 127 | double D = 2.0*M_PI*Frac ( 0.827361 + 1236.853086*T );
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| 128 | double F = 2.0*M_PI*Frac ( 0.259086 + 1342.227825*T );
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| 129 |
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| 130 | double dL = +22640*sin(l) - 4586*sin(l-2*D) + 2370*sin(2*D) + 769*sin(2*l)
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| 131 | -668*sin(lp) - 412*sin(2*F) - 212*sin(2*l-2*D)- 206*sin(l+lp-2*D)
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| 132 | +192*sin(l+2*D) - 165*sin(lp-2*D) - 125*sin(D) - 110*sin(l+lp)
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| 133 | +148*sin(l-lp) - 55*sin(2*F-2*D);
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| 134 |
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| 135 | double L = 2.0*M_PI * Frac( L_0 + dL/1296.0e3 );
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| 136 |
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| 137 | double S = F + (dL+412*sin(2*F)+541*sin(lp)) / RHO_SEC;
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| 138 | double h = F-2*D;
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| 139 | double N = -526*sin(h) + 44*sin(l+h) - 31*sin(-l+h) - 23*sin(lp+h)
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| 140 | +11*sin(-lp+h) - 25*sin(-2*l+F) + 21*sin(-l+F);
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| 141 |
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| 142 | double B = ( 18520.0*sin(S) + N ) / RHO_SEC;
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| 143 |
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| 144 | double cosB = cos(B);
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| 145 |
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| 146 | double R = 385000e3 - 20905e3*cos(l) - 3699e3*cos(2*D-l) - 2956e3*cos(2*D)
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| 147 | -570e3*cos(2*l) + 246e3*cos(2*l-2*D) - 205e3*cos(lp-2*D)
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| 148 | -171e3*cos(l+2*D) - 152e3*cos(l+lp-2*D);
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| 149 |
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| 150 | ColumnVector r_Moon(3);
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| 151 | r_Moon << R*cos(L)*cosB << R*sin(L)*cosB << R*sin(B);
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| 152 | r_Moon = rotX(-eps) * r_Moon;
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| 153 |
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| 154 | return rotZ(GMST(Mjd_TT))
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| 155 | * NutMatrix(Mjd_TT)
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| 156 | * PrecMatrix(MJD_J2000, Mjd_TT)
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| 157 | * r_Moon;
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| 158 | }
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[2579] | 159 |
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| 160 | // Tidal Correction
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| 161 | ////////////////////////////////////////////////////////////////////////////
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[5801] | 162 | ColumnVector t_tides::displacement(const bncTime& time, const ColumnVector& xyz) {
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[2579] | 163 |
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| 164 | double Mjd = time.mjd() + time.daysec() / 86400.0;
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| 165 |
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[5801] | 166 | if (Mjd != _lastMjd) {
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| 167 | _lastMjd = Mjd;
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| 168 | _xSun = t_astro::Sun(Mjd);
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| 169 | _rSun = sqrt(DotProduct(_xSun,_xSun));
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| 170 | _xSun /= _rSun;
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| 171 | _xMoon = t_astro::Moon(Mjd);
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| 172 | _rMoon = sqrt(DotProduct(_xMoon,_xMoon));
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| 173 | _xMoon /= _rMoon;
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[2579] | 174 | }
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| 175 |
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| 176 | double rRec = sqrt(DotProduct(xyz, xyz));
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| 177 | ColumnVector xyzUnit = xyz / rRec;
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| 178 |
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| 179 | // Love's Numbers
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| 180 | // --------------
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[4151] | 181 | const double H2 = 0.6078;
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| 182 | const double L2 = 0.0847;
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[2579] | 183 |
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| 184 | // Tidal Displacement
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| 185 | // ------------------
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[5801] | 186 | double scSun = DotProduct(xyzUnit, _xSun);
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| 187 | double scMoon = DotProduct(xyzUnit, _xMoon);
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[2579] | 188 |
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| 189 | double p2Sun = 3.0 * (H2/2.0-L2) * scSun * scSun - H2/2.0;
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| 190 | double p2Moon = 3.0 * (H2/2.0-L2) * scMoon * scMoon - H2/2.0;
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| 191 |
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| 192 | double x2Sun = 3.0 * L2 * scSun;
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| 193 | double x2Moon = 3.0 * L2 * scMoon;
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| 194 |
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| 195 | const double gmWGS = 398.6005e12;
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| 196 | const double gms = 1.3271250e20;
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| 197 | const double gmm = 4.9027890e12;
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| 198 |
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| 199 | double facSun = gms / gmWGS *
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[5801] | 200 | (rRec * rRec * rRec * rRec) / (_rSun * _rSun * _rSun);
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[2581] | 201 |
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[2579] | 202 | double facMoon = gmm / gmWGS *
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[5801] | 203 | (rRec * rRec * rRec * rRec) / (_rMoon * _rMoon * _rMoon);
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[2579] | 204 |
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[5801] | 205 | ColumnVector dX = facSun * (x2Sun * _xSun + p2Sun * xyzUnit) +
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| 206 | facMoon * (x2Moon * _xMoon + p2Moon * xyzUnit);
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[2579] | 207 |
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[5801] | 208 | return dX;
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[2579] | 209 | }
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[5802] | 210 |
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| 211 | // Constructor
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| 212 | ///////////////////////////////////////////////////////////////////////////
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| 213 | t_windUp::t_windUp() {
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| 214 | for (unsigned ii = 0; ii <= t_prn::MAXPRN; ii++) {
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| 215 | sumWind[ii] = 0.0;
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| 216 | lastEtime[ii] = 0.0;
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| 217 | }
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| 218 | }
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| 219 |
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| 220 | // Phase Wind-Up Correction
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| 221 | ///////////////////////////////////////////////////////////////////////////
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| 222 | double t_windUp::value(const bncTime& etime, const ColumnVector& rRec,
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| 223 | t_prn prn, const ColumnVector& rSat) {
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| 224 |
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| 225 | if (etime.mjddec() != lastEtime[prn.toInt()]) {
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| 226 |
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| 227 | // Unit Vector GPS Satellite --> Receiver
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| 228 | // --------------------------------------
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| 229 | ColumnVector rho = rRec - rSat;
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| 230 | rho /= rho.norm_Frobenius();
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| 231 |
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| 232 | // GPS Satellite unit Vectors sz, sy, sx
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| 233 | // -------------------------------------
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| 234 | ColumnVector sz = -rSat / rSat.norm_Frobenius();
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| 235 |
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| 236 | ColumnVector xSun = Sun(etime.mjddec());
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| 237 | xSun /= xSun.norm_Frobenius();
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| 238 |
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| 239 | ColumnVector sy = crossproduct(sz, xSun);
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| 240 | ColumnVector sx = crossproduct(sy, sz);
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| 241 |
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| 242 | // Effective Dipole of the GPS Satellite Antenna
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| 243 | // ---------------------------------------------
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| 244 | ColumnVector dipSat = sx - rho * DotProduct(rho,sx)
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| 245 | - crossproduct(rho, sy);
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| 246 |
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| 247 | // Receiver unit Vectors rx, ry
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| 248 | // ----------------------------
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| 249 | ColumnVector rx(3);
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| 250 | ColumnVector ry(3);
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| 251 |
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| 252 | double recEll[3]; xyz2ell(rRec.data(), recEll) ;
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| 253 | double neu[3];
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| 254 |
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| 255 | neu[0] = 1.0;
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| 256 | neu[1] = 0.0;
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| 257 | neu[2] = 0.0;
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| 258 | neu2xyz(recEll, neu, rx.data());
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| 259 |
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| 260 | neu[0] = 0.0;
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| 261 | neu[1] = -1.0;
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| 262 | neu[2] = 0.0;
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| 263 | neu2xyz(recEll, neu, ry.data());
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| 264 |
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| 265 | // Effective Dipole of the Receiver Antenna
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| 266 | // ----------------------------------------
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| 267 | ColumnVector dipRec = rx - rho * DotProduct(rho,rx)
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| 268 | + crossproduct(rho, ry);
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| 269 |
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| 270 | // Resulting Effect
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| 271 | // ----------------
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| 272 | double alpha = DotProduct(dipSat,dipRec) /
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| 273 | (dipSat.norm_Frobenius() * dipRec.norm_Frobenius());
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| 274 |
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| 275 | if (alpha > 1.0) alpha = 1.0;
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| 276 | if (alpha < -1.0) alpha = -1.0;
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| 277 |
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| 278 | double dphi = acos(alpha) / 2.0 / M_PI; // in cycles
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| 279 |
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| 280 | if ( DotProduct(rho, crossproduct(dipSat, dipRec)) < 0.0 ) {
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| 281 | dphi = -dphi;
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| 282 | }
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| 283 |
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| 284 | if (lastEtime[prn.toInt()] == 0.0) {
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| 285 | sumWind[prn.toInt()] = dphi;
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| 286 | }
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| 287 | else {
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| 288 | sumWind[prn.toInt()] = nint(sumWind[prn.toInt()] - dphi) + dphi;
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| 289 | }
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| 290 |
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| 291 | lastEtime[prn.toInt()] = etime.mjddec();
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| 292 | }
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| 293 |
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| 294 | return sumWind[prn.toInt()];
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| 295 | }
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