// Part of BNC, a utility for retrieving decoding and
// converting GNSS data streams from NTRIP broadcasters.
//
// Copyright (C) 2007
// German Federal Agency for Cartography and Geodesy (BKG)
// http://www.bkg.bund.de
// Czech Technical University Prague, Department of Geodesy
// http://www.fsv.cvut.cz
//
// Email: euref-ip@bkg.bund.de
//
// This program is free software; you can redistribute it and/or
// modify it under the terms of the GNU General Public License
// as published by the Free Software Foundation, version 2.
//
// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
// GNU General Public License for more details.
//
// You should have received a copy of the GNU General Public License
// along with this program; if not, write to the Free Software
// Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
/* -------------------------------------------------------------------------
* BKG NTRIP Client
* -------------------------------------------------------------------------
*
* Class: t_astro, t_tides, t_tropo
*
* Purpose: Observation model
*
* Author: L. Mervart
*
* Created: 29-Jul-2014
*
* Changes:
*
* -----------------------------------------------------------------------*/
#include <cmath>
#include "pppModel.h"
#include "bncutils.h"
using namespace BNC_PPP;
using namespace std;
const double t_astro::RHO_DEG = 180.0 / M_PI;
const double t_astro::RHO_SEC = 3600.0 * 180.0 / M_PI;
const double t_astro::MJD_J2000 = 51544.5;
Matrix t_astro::rotX(double Angle) {
const double C = cos(Angle);
const double S = sin(Angle);
Matrix UU(3,3);
UU[0][0] = 1.0; UU[0][1] = 0.0; UU[0][2] = 0.0;
UU[1][0] = 0.0; UU[1][1] = +C; UU[1][2] = +S;
UU[2][0] = 0.0; UU[2][1] = -S; UU[2][2] = +C;
return UU;
}
Matrix t_astro::rotY(double Angle) {
const double C = cos(Angle);
const double S = sin(Angle);
Matrix UU(3,3);
UU[0][0] = +C; UU[0][1] = 0.0; UU[0][2] = -S;
UU[1][0] = 0.0; UU[1][1] = 1.0; UU[1][2] = 0.0;
UU[2][0] = +S; UU[2][1] = 0.0; UU[2][2] = +C;
return UU;
}
Matrix t_astro::rotZ(double Angle) {
const double C = cos(Angle);
const double S = sin(Angle);
Matrix UU(3,3);
UU[0][0] = +C; UU[0][1] = +S; UU[0][2] = 0.0;
UU[1][0] = -S; UU[1][1] = +C; UU[1][2] = 0.0;
UU[2][0] = 0.0; UU[2][1] = 0.0; UU[2][2] = 1.0;
return UU;
}
// Greenwich Mean Sidereal Time
///////////////////////////////////////////////////////////////////////////
double t_astro::GMST(double Mjd_UT1) {
const double Secs = 86400.0;
double Mjd_0 = floor(Mjd_UT1);
double UT1 = Secs*(Mjd_UT1-Mjd_0);
double T_0 = (Mjd_0 -MJD_J2000)/36525.0;
double T = (Mjd_UT1-MJD_J2000)/36525.0;
double gmst = 24110.54841 + 8640184.812866*T_0 + 1.002737909350795*UT1
+ (0.093104-6.2e-6*T)*T*T;
return 2.0*M_PI*Frac(gmst/Secs);
}
// Nutation Matrix
///////////////////////////////////////////////////////////////////////////
Matrix t_astro::NutMatrix(double Mjd_TT) {
const double T = (Mjd_TT-MJD_J2000)/36525.0;
double ls = 2.0*M_PI*Frac(0.993133+ 99.997306*T);
double D = 2.0*M_PI*Frac(0.827362+1236.853087*T);
double F = 2.0*M_PI*Frac(0.259089+1342.227826*T);
double N = 2.0*M_PI*Frac(0.347346- 5.372447*T);
double dpsi = ( -17.200*sin(N) - 1.319*sin(2*(F-D+N)) - 0.227*sin(2*(F+N))
+ 0.206*sin(2*N) + 0.143*sin(ls) ) / RHO_SEC;
double deps = ( + 9.203*cos(N) + 0.574*cos(2*(F-D+N)) + 0.098*cos(2*(F+N))
- 0.090*cos(2*N) ) / RHO_SEC;
double eps = 0.4090928-2.2696E-4*T;
return rotX(-eps-deps)*rotZ(-dpsi)*rotX(+eps);
}
// Precession Matrix
///////////////////////////////////////////////////////////////////////////
Matrix t_astro::PrecMatrix(double Mjd_1, double Mjd_2) {
const double T = (Mjd_1-MJD_J2000)/36525.0;
const double dT = (Mjd_2-Mjd_1)/36525.0;
double zeta = ( (2306.2181+(1.39656-0.000139*T)*T)+
((0.30188-0.000344*T)+0.017998*dT)*dT )*dT/RHO_SEC;
double z = zeta + ( (0.79280+0.000411*T)+0.000205*dT)*dT*dT/RHO_SEC;
double theta = ( (2004.3109-(0.85330+0.000217*T)*T)-
((0.42665+0.000217*T)+0.041833*dT)*dT )*dT/RHO_SEC;
return rotZ(-z) * rotY(theta) * rotZ(-zeta);
}
// Sun's position
///////////////////////////////////////////////////////////////////////////
ColumnVector t_astro::Sun(double Mjd_TT) {
const double eps = 23.43929111/RHO_DEG;
const double T = (Mjd_TT-MJD_J2000)/36525.0;
double M = 2.0*M_PI * Frac ( 0.9931267 + 99.9973583*T);
double L = 2.0*M_PI * Frac ( 0.7859444 + M/2.0/M_PI +
(6892.0*sin(M)+72.0*sin(2.0*M)) / 1296.0e3);
double r = 149.619e9 - 2.499e9*cos(M) - 0.021e9*cos(2*M);
ColumnVector r_Sun(3);
r_Sun << r*cos(L) << r*sin(L) << 0.0; r_Sun = rotX(-eps) * r_Sun;
return rotZ(GMST(Mjd_TT))
* NutMatrix(Mjd_TT)
* PrecMatrix(MJD_J2000, Mjd_TT)
* r_Sun;
}
// Moon's position
///////////////////////////////////////////////////////////////////////////
ColumnVector t_astro::Moon(double Mjd_TT) {
const double eps = 23.43929111/RHO_DEG;
const double T = (Mjd_TT-MJD_J2000)/36525.0;
double L_0 = Frac ( 0.606433 + 1336.851344*T );
double l = 2.0*M_PI*Frac ( 0.374897 + 1325.552410*T );
double lp = 2.0*M_PI*Frac ( 0.993133 + 99.997361*T );
double D = 2.0*M_PI*Frac ( 0.827361 + 1236.853086*T );
double F = 2.0*M_PI*Frac ( 0.259086 + 1342.227825*T );
double dL = +22640*sin(l) - 4586*sin(l-2*D) + 2370*sin(2*D) + 769*sin(2*l)
-668*sin(lp) - 412*sin(2*F) - 212*sin(2*l-2*D)- 206*sin(l+lp-2*D)
+192*sin(l+2*D) - 165*sin(lp-2*D) - 125*sin(D) - 110*sin(l+lp)
+148*sin(l-lp) - 55*sin(2*F-2*D);
double L = 2.0*M_PI * Frac( L_0 + dL/1296.0e3 );
double S = F + (dL+412*sin(2*F)+541*sin(lp)) / RHO_SEC;
double h = F-2*D;
double N = -526*sin(h) + 44*sin(l+h) - 31*sin(-l+h) - 23*sin(lp+h)
+11*sin(-lp+h) - 25*sin(-2*l+F) + 21*sin(-l+F);
double B = ( 18520.0*sin(S) + N ) / RHO_SEC;
double cosB = cos(B);
double R = 385000e3 - 20905e3*cos(l) - 3699e3*cos(2*D-l) - 2956e3*cos(2*D)
-570e3*cos(2*l) + 246e3*cos(2*l-2*D) - 205e3*cos(lp-2*D)
-171e3*cos(l+2*D) - 152e3*cos(l+lp-2*D);
ColumnVector r_Moon(3);
r_Moon << R*cos(L)*cosB << R*sin(L)*cosB << R*sin(B);
r_Moon = rotX(-eps) * r_Moon;
return rotZ(GMST(Mjd_TT))
* NutMatrix(Mjd_TT)
* PrecMatrix(MJD_J2000, Mjd_TT)
* r_Moon;
}
// Tidal Correction
////////////////////////////////////////////////////////////////////////////
ColumnVector t_tides::displacement(const bncTime& time, const ColumnVector& xyz) {
if (time.undef()) {
ColumnVector dX(3); dX = 0.0;
return dX;
}
double Mjd = time.mjd() + time.daysec() / 86400.0;
if (Mjd != _lastMjd) {
_lastMjd = Mjd;
_xSun = t_astro::Sun(Mjd);
_rSun = sqrt(DotProduct(_xSun,_xSun));
_xSun /= _rSun;
_xMoon = t_astro::Moon(Mjd);
_rMoon = sqrt(DotProduct(_xMoon,_xMoon));
_xMoon /= _rMoon;
}
double rRec = sqrt(DotProduct(xyz, xyz));
ColumnVector xyzUnit = xyz / rRec;
// Love's Numbers
// --------------
const double H2 = 0.6078;
const double L2 = 0.0847;
// Tidal Displacement
// ------------------
double scSun = DotProduct(xyzUnit, _xSun);
double scMoon = DotProduct(xyzUnit, _xMoon);
double p2Sun = 3.0 * (H2/2.0-L2) * scSun * scSun - H2/2.0;
double p2Moon = 3.0 * (H2/2.0-L2) * scMoon * scMoon - H2/2.0;
double x2Sun = 3.0 * L2 * scSun;
double x2Moon = 3.0 * L2 * scMoon;
const double gmWGS = 398.6005e12;
const double gms = 1.3271250e20;
const double gmm = 4.9027890e12;
double facSun = gms / gmWGS *
(rRec * rRec * rRec * rRec) / (_rSun * _rSun * _rSun);
double facMoon = gmm / gmWGS *
(rRec * rRec * rRec * rRec) / (_rMoon * _rMoon * _rMoon);
ColumnVector dX = facSun * (x2Sun * _xSun + p2Sun * xyzUnit) +
facMoon * (x2Moon * _xMoon + p2Moon * xyzUnit);
return dX;
}
// Constructor
///////////////////////////////////////////////////////////////////////////
t_windUp::t_windUp() {
for (unsigned ii = 0; ii <= t_prn::MAXPRN; ii++) {
sumWind[ii] = 0.0;
lastEtime[ii] = 0.0;
}
}
// Phase Wind-Up Correction
///////////////////////////////////////////////////////////////////////////
double t_windUp::value(const bncTime& etime, const ColumnVector& rRec,
t_prn prn, const ColumnVector& rSat) {
if (etime.mjddec() != lastEtime[prn.toInt()]) {
// Unit Vector GPS Satellite --> Receiver
// --------------------------------------
ColumnVector rho = rRec - rSat;
rho /= rho.norm_Frobenius();
// GPS Satellite unit Vectors sz, sy, sx
// -------------------------------------
ColumnVector sz = -rSat / rSat.norm_Frobenius();
ColumnVector xSun = t_astro::Sun(etime.mjddec());
xSun /= xSun.norm_Frobenius();
ColumnVector sy = crossproduct(sz, xSun);
ColumnVector sx = crossproduct(sy, sz);
// Effective Dipole of the GPS Satellite Antenna
// ---------------------------------------------
ColumnVector dipSat = sx - rho * DotProduct(rho,sx)
- crossproduct(rho, sy);
// Receiver unit Vectors rx, ry
// ----------------------------
ColumnVector rx(3);
ColumnVector ry(3);
double recEll[3]; xyz2ell(rRec.data(), recEll) ;
double neu[3];
neu[0] = 1.0;
neu[1] = 0.0;
neu[2] = 0.0;
neu2xyz(recEll, neu, rx.data());
neu[0] = 0.0;
neu[1] = -1.0;
neu[2] = 0.0;
neu2xyz(recEll, neu, ry.data());
// Effective Dipole of the Receiver Antenna
// ----------------------------------------
ColumnVector dipRec = rx - rho * DotProduct(rho,rx)
+ crossproduct(rho, ry);
// Resulting Effect
// ----------------
double alpha = DotProduct(dipSat,dipRec) /
(dipSat.norm_Frobenius() * dipRec.norm_Frobenius());
if (alpha > 1.0) alpha = 1.0;
if (alpha < -1.0) alpha = -1.0;
double dphi = acos(alpha) / 2.0 / M_PI; // in cycles
if ( DotProduct(rho, crossproduct(dipSat, dipRec)) < 0.0 ) {
dphi = -dphi;
}
if (lastEtime[prn.toInt()] == 0.0) {
sumWind[prn.toInt()] = dphi;
}
else {
sumWind[prn.toInt()] = nint(sumWind[prn.toInt()] - dphi) + dphi;
}
lastEtime[prn.toInt()] = etime.mjddec();
}
return sumWind[prn.toInt()];
}
// Tropospheric Model (Saastamoinen)
////////////////////////////////////////////////////////////////////////////
double t_tropo::delay_saast(const ColumnVector& xyz, double Ele) {
Tracer tracer("bncModel::delay_saast");
if (xyz[0] == 0.0 && xyz[1] == 0.0 && xyz[2] == 0.0) {
return 0.0;
}
double ell[3];
xyz2ell(xyz.data(), ell);
double height = ell[2];
double pp = 1013.25 * pow(1.0 - 2.26e-5 * height, 5.225);
double TT = 18.0 - height * 0.0065 + 273.15;
double hh = 50.0 * exp(-6.396e-4 * height);
double ee = hh / 100.0 * exp(-37.2465 + 0.213166*TT - 0.000256908*TT*TT);
double h_km = height / 1000.0;
if (h_km < 0.0) h_km = 0.0;
if (h_km > 5.0) h_km = 5.0;
int ii = int(h_km + 1); if (ii > 5) ii = 5;
double href = ii - 1;
double bCor[6];
bCor[0] = 1.156;
bCor[1] = 1.006;
bCor[2] = 0.874;
bCor[3] = 0.757;
bCor[4] = 0.654;
bCor[5] = 0.563;
double BB = bCor[ii-1] + (bCor[ii]-bCor[ii-1]) * (h_km - href);
double zen = M_PI/2.0 - Ele;
return (0.002277/cos(zen)) * (pp + ((1255.0/TT)+0.05)*ee - BB*(tan(zen)*tan(zen)));
}