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ppp.c
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/*------------------------------------------------------------------------------
* ppp.c : precise point positioning
*
* Copyright (C) 2010-2013 by T.TAKASU, All rights reserved.
*
* options : -DIERS_MODEL use IERS tide model
*
* references :
* [1] D.D.McCarthy, IERS Technical Note 21, IERS Conventions 1996, July 1996
* [2] D.D.McCarthy and G.Petit, IERS Technical Note 32, IERS Conventions
* 2003, November 2003
* [3] D.A.Vallado, Fundamentals of Astrodynamics and Applications 2nd ed,
* Space Technology Library, 2004
* [4] J.Kouba, A Guide to using International GNSS Service (IGS) products,
* May 2009
* [5] RTCM Paper, April 12, 2010, Proposed SSR Messages for SV Orbit Clock,
* Code Biases, URA
* [6] MacMillan et al., Atmospheric gradients and the VLBI terrestrial and
* celestial reference frames, Geophys. Res. Let., 1997
* [7] G.Petit and B.Luzum (eds), IERS Technical Note No. 36, IERS
* Conventions (2010), 2010
*
* version : $Revision:$ $Date:$
* history : 2010/07/20 1.0 new
* added api:
* tidedisp()
* 2010/12/11 1.1 enable exclusion of eclipsing satellite
* 2012/02/01 1.2 add gps-glonass h/w bias correction
* move windupcorr() to rtkcmn.c
* 2013/03/11 1.3 add otl and pole tides corrections
* involve iers model with -DIERS_MODEL
* change initial variances
* suppress acos domain error
* 2013/09/01 1.4 pole tide model by iers 2010
* add mode of ionosphere model off
* 2014/05/23 1.5 add output of trop gradient in solution status
* 2014/10/13 1.6 fix bug on P0(a[3]) computation in tide_oload()
* fix bug on m2 computation in tide_pole()
*-----------------------------------------------------------------------------*/
#include "rtklib.h"
static const char rcsid[]="$Id:$";
#define SQR(x) ((x)*(x))
#define MIN(x,y) ((x)<=(y)?(x):(y))
#define AS2R (D2R/3600.0) /* arc sec to radian */
#define GME 3.986004415E+14 /* earth gravitational constant */
#define GMS 1.327124E+20 /* sun gravitational constant */
#define GMM 4.902801E+12 /* moon gravitational constant */
/* initial variances */
#define VAR_POS SQR(100.0) /* receiver position (m^2) */
#define VAR_CLK SQR(100.0) /* receiver clock (m^2) */
#define VAR_ZTD SQR( 0.3) /* ztd (m^2) */
#define VAR_GRA SQR(0.001) /* gradient (m^2) */
#define VAR_BIAS SQR(100.0) /* phase-bias (m^2) */
#define VAR_IONO_OFF SQR(10.0) /* variance of iono-model-off */
#define ERR_SAAS 0.3 /* saastamoinen model error std (m) */
#define ERR_BRDCI 0.5 /* broadcast iono model error factor */
#define ERR_CBIAS 0.3 /* code bias error std (m) */
#define REL_HUMI 0.7 /* relative humidity for saastamoinen model */
#define NP(opt) ((opt)->dynamics?9:3) /* number of pos solution */
#define IC(s,opt) (NP(opt)+(s)) /* state index of clocks (s=0:gps,1:glo) */
#define IT(opt) (IC(0,opt)+NSYS) /* state index of tropos */
#define NR(opt) (IT(opt)+((opt)->tropopt<TROPOPT_EST?0:((opt)->tropopt==TROPOPT_EST?1:3)))
/* number of solutions */
#define IB(s,opt) (NR(opt)+(s)-1) /* state index of phase bias */
#define NX(opt) (IB(MAXSAT,opt)+1) /* number of estimated states */
/* function prototypes -------------------------------------------------------*/
#ifdef IERS_MODEL
extern int dehanttideinel_(double *xsta, int *year, int *mon, int *day,
double *fhr, double *xsun, double *xmon,
double *dxtide);
#endif
/* output solution status for PPP --------------------------------------------*/
extern void pppoutsolstat(rtk_t *rtk, int level, FILE *fp)
{
ssat_t *ssat;
double tow,pos[3],vel[3],acc[3];
int i,j,week,nfreq=1;
char id[32];
if (level<=0||!fp) return;
trace(3,"pppoutsolstat:\n");
tow=time2gpst(rtk->sol.time,&week);
/* receiver position */
fprintf(fp,"$POS,%d,%.3f,%d,%.4f,%.4f,%.4f,%.4f,%.4f,%.4f\n",week,tow,
rtk->sol.stat,rtk->x[0],rtk->x[1],rtk->x[2],0.0,0.0,0.0);
/* receiver velocity and acceleration */
if (rtk->opt.dynamics) {
ecef2pos(rtk->sol.rr,pos);
ecef2enu(pos,rtk->x+3,vel);
ecef2enu(pos,rtk->x+6,acc);
fprintf(fp,"$VELACC,%d,%.3f,%d,%.4f,%.4f,%.4f,%.5f,%.5f,%.5f,%.4f,%.4f,%.4f,%.5f,%.5f,%.5f\n",
week,tow,rtk->sol.stat,vel[0],vel[1],vel[2],acc[0],acc[1],acc[2],
0.0,0.0,0.0,0.0,0.0,0.0);
}
/* receiver clocks */
i=IC(0,&rtk->opt);
fprintf(fp,"$CLK,%d,%.3f,%d,%d,%.3f,%.3f,%.3f,%.3f\n",
week,tow,rtk->sol.stat,1,rtk->x[i]*1E9/CLIGHT,rtk->x[i+1]*1E9/CLIGHT,
0.0,0.0);
/* tropospheric parameters */
if (rtk->opt.tropopt==TROPOPT_EST||rtk->opt.tropopt==TROPOPT_ESTG) {
i=IT(&rtk->opt);
fprintf(fp,"$TROP,%d,%.3f,%d,%d,%.4f,%.4f\n",week,tow,rtk->sol.stat,
1,rtk->x[i],0.0);
}
if (rtk->opt.tropopt==TROPOPT_ESTG) {
i=IT(&rtk->opt);
fprintf(fp,"$TRPG,%d,%.3f,%d,%d,%.5f,%.5f,%.5f,%.5f\n",week,tow,
rtk->sol.stat,1,rtk->x[i+1],rtk->x[i+2],0.0,0.0);
}
if (rtk->sol.stat==SOLQ_NONE||level<=1) return;
/* residuals and status */
for (i=0;i<MAXSAT;i++) {
ssat=rtk->ssat+i;
if (!ssat->vs) continue;
satno2id(i+1,id);
for (j=0;j<nfreq;j++) {
fprintf(fp,"$SAT,%d,%.3f,%s,%d,%.1f,%.1f,%.4f,%.4f,%d,%.0f,%d,%d,%d,%d,%d,%d\n",
week,tow,id,j+1,ssat->azel[0]*R2D,ssat->azel[1]*R2D,
ssat->resp[j],ssat->resc[j],ssat->vsat[j],ssat->snr[j]*0.25,
ssat->fix[j],ssat->slip[j]&3,ssat->lock[j],ssat->outc[j],
ssat->slipc[j],ssat->rejc[j]);
}
}
}
/* solar/lunar tides (ref [2] 7) ---------------------------------------------*/
static void tide_pl(const double *eu, const double *rp, double GMp,
const double *pos, double *dr)
{
const double H3=0.292,L3=0.015;
double r,ep[3],latp,lonp,p,K2,K3,a,H2,L2,dp,du,cosp,sinl,cosl;
int i;
trace(4,"tide_pl : pos=%.3f %.3f\n",pos[0]*R2D,pos[1]*R2D);
if ((r=norm(rp,3))<=0.0) return;
for (i=0;i<3;i++) ep[i]=rp[i]/r;
K2=GMp/GME*SQR(RE_WGS84)*SQR(RE_WGS84)/(r*r*r);
K3=K2*RE_WGS84/r;
latp=asin(ep[2]); lonp=atan2(ep[1],ep[0]);
cosp=cos(latp); sinl=sin(pos[0]); cosl=cos(pos[0]);
/* step1 in phase (degree 2) */
p=(3.0*sinl*sinl-1.0)/2.0;
H2=0.6078-0.0006*p;
L2=0.0847+0.0002*p;
a=dot(ep,eu,3);
dp=K2*3.0*L2*a;
du=K2*(H2*(1.5*a*a-0.5)-3.0*L2*a*a);
/* step1 in phase (degree 3) */
dp+=K3*L3*(7.5*a*a-1.5);
du+=K3*(H3*(2.5*a*a*a-1.5*a)-L3*(7.5*a*a-1.5)*a);
/* step1 out-of-phase (only radial) */
du+=3.0/4.0*0.0025*K2*sin(2.0*latp)*sin(2.0*pos[0])*sin(pos[1]-lonp);
du+=3.0/4.0*0.0022*K2*cosp*cosp*cosl*cosl*sin(2.0*(pos[1]-lonp));
dr[0]=dp*ep[0]+du*eu[0];
dr[1]=dp*ep[1]+du*eu[1];
dr[2]=dp*ep[2]+du*eu[2];
trace(5,"tide_pl : dr=%.3f %.3f %.3f\n",dr[0],dr[1],dr[2]);
}
/* displacement by solid earth tide (ref [2] 7) ------------------------------*/
static void tide_solid(const double *rsun, const double *rmoon,
const double *pos, const double *E, double gmst, int opt,
double *dr)
{
double dr1[3],dr2[3],eu[3],du,dn,sinl,sin2l;
trace(3,"tide_solid: pos=%.3f %.3f opt=%d\n",pos[0]*R2D,pos[1]*R2D,opt);
/* step1: time domain */
eu[0]=E[2]; eu[1]=E[5]; eu[2]=E[8];
tide_pl(eu,rsun, GMS,pos,dr1);
tide_pl(eu,rmoon,GMM,pos,dr2);
/* step2: frequency domain, only K1 radial */
sin2l=sin(2.0*pos[0]);
du=-0.012*sin2l*sin(gmst+pos[1]);
dr[0]=dr1[0]+dr2[0]+du*E[2];
dr[1]=dr1[1]+dr2[1]+du*E[5];
dr[2]=dr1[2]+dr2[2]+du*E[8];
/* eliminate permanent deformation */
if (opt&8) {
sinl=sin(pos[0]);
du=0.1196*(1.5*sinl*sinl-0.5);
dn=0.0247*sin2l;
dr[0]+=du*E[2]+dn*E[1];
dr[1]+=du*E[5]+dn*E[4];
dr[2]+=du*E[8]+dn*E[7];
}
trace(5,"tide_solid: dr=%.3f %.3f %.3f\n",dr[0],dr[1],dr[2]);
}
/* displacement by ocean tide loading (ref [2] 7) ----------------------------*/
static void tide_oload(gtime_t tut, const double *odisp, double *denu)
{
const double args[][5]={
{1.40519E-4, 2.0,-2.0, 0.0, 0.00}, /* M2 */
{1.45444E-4, 0.0, 0.0, 0.0, 0.00}, /* S2 */
{1.37880E-4, 2.0,-3.0, 1.0, 0.00}, /* N2 */
{1.45842E-4, 2.0, 0.0, 0.0, 0.00}, /* K2 */
{0.72921E-4, 1.0, 0.0, 0.0, 0.25}, /* K1 */
{0.67598E-4, 1.0,-2.0, 0.0,-0.25}, /* O1 */
{0.72523E-4,-1.0, 0.0, 0.0,-0.25}, /* P1 */
{0.64959E-4, 1.0,-3.0, 1.0,-0.25}, /* Q1 */
{0.53234E-5, 0.0, 2.0, 0.0, 0.00}, /* Mf */
{0.26392E-5, 0.0, 1.0,-1.0, 0.00}, /* Mm */
{0.03982E-5, 2.0, 0.0, 0.0, 0.00} /* Ssa */
};
const double ep1975[]={1975,1,1,0,0,0};
double ep[6],fday,days,t,t2,t3,a[5],ang,dp[3]={0};
int i,j;
trace(3,"tide_oload:\n");
/* angular argument: see subroutine arg.f for reference [1] */
time2epoch(tut,ep);
fday=ep[3]*3600.0+ep[4]*60.0+ep[5];
ep[3]=ep[4]=ep[5]=0.0;
days=timediff(epoch2time(ep),epoch2time(ep1975))/86400.0;
t=(27392.500528+1.000000035*days)/36525.0;
t2=t*t; t3=t2*t;
a[0]=fday;
a[1]=(279.69668+36000.768930485*t+3.03E-4*t2)*D2R; /* H0 */
a[2]=(270.434358+481267.88314137*t-0.001133*t2+1.9E-6*t3)*D2R; /* S0 */
a[3]=(334.329653+4069.0340329577*t-0.010325*t2-1.2E-5*t3)*D2R; /* P0 */
a[4]=2.0*PI;
/* displacements by 11 constituents */
for (i=0;i<11;i++) {
ang=0.0;
for (j=0;j<5;j++) ang+=a[j]*args[i][j];
for (j=0;j<3;j++) dp[j]+=odisp[j+i*6]*cos(ang-odisp[j+3+i*6]*D2R);
}
denu[0]=-dp[1];
denu[1]=-dp[2];
denu[2]= dp[0];
trace(5,"tide_oload: denu=%.3f %.3f %.3f\n",denu[0],denu[1],denu[2]);
}
/* iers mean pole (ref [7] eq.7.25) ------------------------------------------*/
static void iers_mean_pole(gtime_t tut, double *xp_bar, double *yp_bar)
{
const double ep2000[]={2000,1,1,0,0,0};
double y,y2,y3;
y=timediff(tut,epoch2time(ep2000))/86400.0/365.25;
if (y<3653.0/365.25) { /* until 2010.0 */
y2=y*y; y3=y2*y;
*xp_bar= 55.974+1.8243*y+0.18413*y2+0.007024*y3; /* (mas) */
*yp_bar=346.346+1.7896*y-0.10729*y2-0.000908*y3;
}
else { /* after 2010.0 */
*xp_bar= 23.513+7.6141*y; /* (mas) */
*yp_bar=358.891-0.6287*y;
}
}
/* displacement by pole tide (ref [7] eq.7.26) --------------------------------*/
static void tide_pole(gtime_t tut, const double *pos, const double *erpv,
double *denu)
{
double xp_bar,yp_bar,m1,m2,cosl,sinl;
trace(3,"tide_pole: pos=%.3f %.3f\n",pos[0]*R2D,pos[1]*R2D);
/* iers mean pole (mas) */
iers_mean_pole(tut,&xp_bar,&yp_bar);
/* ref [7] eq.7.24 */
m1= erpv[0]/AS2R-xp_bar*1E-3; /* (as) */
m2=-erpv[1]/AS2R+yp_bar*1E-3;
/* sin(2*theta) = sin(2*phi), cos(2*theta)=-cos(2*phi) */
cosl=cos(pos[1]);
sinl=sin(pos[1]);
denu[0]= 9E-3*sin(pos[0]) *(m1*sinl-m2*cosl); /* de= Slambda (m) */
denu[1]= -9E-3*cos(2.0*pos[0])*(m1*cosl+m2*sinl); /* dn=-Stheta (m) */
denu[2]=-33E-3*sin(2.0*pos[0])*(m1*cosl+m2*sinl); /* du= Sr (m) */
trace(5,"tide_pole : denu=%.3f %.3f %.3f\n",denu[0],denu[1],denu[2]);
}
/* tidal displacement ----------------------------------------------------------
* displacements by earth tides
* args : gtime_t tutc I time in utc
* double *rr I site position (ecef) (m)
* int opt I options (or of the followings)
* 1: solid earth tide
* 2: ocean tide loading
* 4: pole tide
* 8: elimate permanent deformation
* double *erp I earth rotation parameters (NULL: not used)
* double *odisp I ocean loading parameters (NULL: not used)
* odisp[0+i*6]: consituent i amplitude radial(m)
* odisp[1+i*6]: consituent i amplitude west (m)
* odisp[2+i*6]: consituent i amplitude south (m)
* odisp[3+i*6]: consituent i phase radial (deg)
* odisp[4+i*6]: consituent i phase west (deg)
* odisp[5+i*6]: consituent i phase south (deg)
* (i=0:M2,1:S2,2:N2,3:K2,4:K1,5:O1,6:P1,7:Q1,
* 8:Mf,9:Mm,10:Ssa)
* double *dr O displacement by earth tides (ecef) (m)
* return : none
* notes : see ref [1], [2] chap 7
* see ref [4] 5.2.1, 5.2.2, 5.2.3
* ver.2.4.0 does not use ocean loading and pole tide corrections
*-----------------------------------------------------------------------------*/
extern void tidedisp(gtime_t tutc, const double *rr, int opt, const erp_t *erp,
const double *odisp, double *dr)
{
gtime_t tut;
double pos[2],E[9],drt[3],denu[3],rs[3],rm[3],gmst,erpv[5]={0};
int i;
#ifdef IERS_MODEL
double ep[6],fhr;
int year,mon,day;
#endif
trace(3,"tidedisp: tutc=%s\n",time_str(tutc,0));
if (erp) geterp(erp,tutc,erpv);
tut=timeadd(tutc,erpv[2]);
dr[0]=dr[1]=dr[2]=0.0;
if (norm(rr,3)<=0.0) return;
pos[0]=asin(rr[2]/norm(rr,3));
pos[1]=atan2(rr[1],rr[0]);
xyz2enu(pos,E);
if (opt&1) { /* solid earth tides */
/* sun and moon position in ecef */
sunmoonpos(tutc,erpv,rs,rm,&gmst);
#ifdef IERS_MODEL
time2epoch(tutc,ep);
year=(int)ep[0];
mon =(int)ep[1];
day =(int)ep[2];
fhr =ep[3]+ep[4]/60.0+ep[5]/3600.0;
/* call DEHANTTIDEINEL */
dehanttideinel_((double *)rr,&year,&mon,&day,&fhr,rs,rm,drt);
#else
tide_solid(rs,rm,pos,E,gmst,opt,drt);
#endif
for (i=0;i<3;i++) dr[i]+=drt[i];
}
if ((opt&2)&&odisp) { /* ocean tide loading */
tide_oload(tut,odisp,denu);
matmul("TN",3,1,3,1.0,E,denu,0.0,drt);
for (i=0;i<3;i++) dr[i]+=drt[i];
}
if ((opt&4)&&erp) { /* pole tide */
tide_pole(tut,pos,erpv,denu);
matmul("TN",3,1,3,1.0,E,denu,0.0,drt);
for (i=0;i<3;i++) dr[i]+=drt[i];
}
trace(5,"tidedisp: dr=%.3f %.3f %.3f\n",dr[0],dr[1],dr[2]);
}
/* exclude meas of eclipsing satellite (block IIA) ---------------------------*/
static void testeclipse(const obsd_t *obs, int n, const nav_t *nav, double *rs)
{
double rsun[3],esun[3],r,ang,erpv[5]={0},cosa;
int i,j;
const char *type;
trace(3,"testeclipse:\n");
/* unit vector of sun direction (ecef) */
sunmoonpos(gpst2utc(obs[0].time),erpv,rsun,NULL,NULL);
normv3(rsun,esun);
for (i=0;i<n;i++) {
type=nav->pcvs[obs[i].sat-1].type;
if ((r=norm(rs+i*6,3))<=0.0) continue;
#if 1
/* only block IIA */
if (*type&&!strstr(type,"BLOCK IIA")) continue;
#endif
/* sun-earth-satellite angle */
cosa=dot(rs+i*6,esun,3)/r;
cosa=cosa<-1.0?-1.0:(cosa>1.0?1.0:cosa);
ang=acos(cosa);
/* test eclipse */
if (ang<PI/2.0||r*sin(ang)>RE_WGS84) continue;
trace(2,"eclipsing sat excluded %s sat=%2d\n",time_str(obs[0].time,0),
obs[i].sat);
for (j=0;j<3;j++) rs[j+i*6]=0.0;
}
}
/* measurement error variance ------------------------------------------------*/
static double varerr(int sat, int sys, double el, int type, const prcopt_t *opt)
{
double a,b,a2,b2,fact=1.0;
double sinel=sin(el);
int i=sys==SYS_GLO?1:(sys==SYS_GAL?2:0);
/* extended error model */
if (type==1&&opt->exterr.ena[0]) { /* code */
a=opt->exterr.cerr[i][0];
b=opt->exterr.cerr[i][1];
if (opt->ionoopt==IONOOPT_IFLC) {
a2=opt->exterr.cerr[i][2];
b2=opt->exterr.cerr[i][3];
a=sqrt(SQR(2.55)*a*a+SQR(1.55)*a2*a2);
b=sqrt(SQR(2.55)*b*b+SQR(1.55)*b2*b2);
}
}
else if (type==0&&opt->exterr.ena[1]) { /* phase */
a=opt->exterr.perr[i][0];
b=opt->exterr.perr[i][1];
if (opt->ionoopt==IONOOPT_IFLC) {
a2=opt->exterr.perr[i][2];
b2=opt->exterr.perr[i][3];
a=sqrt(SQR(2.55)*a*a+SQR(1.55)*a2*a2);
b=sqrt(SQR(2.55)*b*b+SQR(1.55)*b2*b2);
}
}
else { /* normal error model */
if (type==1) fact*=opt->eratio[0];
fact*=sys==SYS_GLO?EFACT_GLO:(sys==SYS_SBS?EFACT_SBS:EFACT_GPS);
if (opt->ionoopt==IONOOPT_IFLC) fact*=3.0;
a=fact*opt->err[1];
b=fact*opt->err[2];
}
return a*a+b*b/sinel/sinel;
}
/* initialize state and covariance -------------------------------------------*/
static void initx(rtk_t *rtk, double xi, double var, int i)
{
int j;
rtk->x[i]=xi;
for (j=0;j<rtk->nx;j++) {
rtk->P[i+j*rtk->nx]=rtk->P[j+i*rtk->nx]=i==j?var:0.0;
}
}
/* dual-frequency iono-free measurements -------------------------------------*/
static int ifmeas(const obsd_t *obs, const nav_t *nav, const double *azel,
const prcopt_t *opt, const double *dantr, const double *dants,
double phw, double *meas, double *var)
{
const double *lam=nav->lam[obs->sat-1];
double c1,c2,L1,L2,P1,P2,P1_C1,P2_C2,gamma;
int i=0,j=1,k;
trace(4,"ifmeas :\n");
/* L1-L2 for GPS/GLO/QZS, L1-L5 for GAL/SBS */
if (NFREQ>=3&&(satsys(obs->sat,NULL)&(SYS_GAL|SYS_SBS))) j=2;
if (NFREQ<2||lam[i]==0.0||lam[j]==0.0) return 0;
/* test snr mask */
if (testsnr(0,i,azel[1],obs->SNR[i]*0.25,&opt->snrmask)||
testsnr(0,j,azel[1],obs->SNR[j]*0.25,&opt->snrmask)) {
return 0;
}
gamma=SQR(lam[j])/SQR(lam[i]); /* f1^2/f2^2 */
c1=gamma/(gamma-1.0); /* f1^2/(f1^2-f2^2) */
c2=-1.0 /(gamma-1.0); /* -f2^2/(f1^2-f2^2) */
L1=obs->L[i]*lam[i]; /* cycle -> m */
L2=obs->L[j]*lam[j];
P1=obs->P[i];
P2=obs->P[j];
P1_C1=nav->cbias[obs->sat-1][1];
P2_C2=nav->cbias[obs->sat-1][2];
if (opt->sateph==EPHOPT_LEX) {
P1_C1=nav->lexeph[obs->sat-1].isc[0]*CLIGHT; /* ISC_L1C/A */
}
if (L1==0.0||L2==0.0||P1==0.0||P2==0.0) return 0;
/* iono-free phase with windup correction */
meas[0]=c1*L1+c2*L2-(c1*lam[i]+c2*lam[j])*phw;
/* iono-free code with dcb correction */
if (obs->code[i]==CODE_L1C) P1+=P1_C1; /* C1->P1 */
if (obs->code[j]==CODE_L2C) P2+=P2_C2; /* C2->P2 */
meas[1]=c1*P1+c2*P2;
var[1]=SQR(ERR_CBIAS);
if (opt->sateph==EPHOPT_SBAS) meas[1]-=P1_C1; /* sbas clock based C1 */
/* gps-glonass h/w bias correction for code */
if (opt->exterr.ena[3]&&satsys(obs->sat,NULL)==SYS_GLO) {
meas[1]+=c1*opt->exterr.gpsglob[0]+c2*opt->exterr.gpsglob[1];
}
/* antenna phase center variation correction */
for (k=0;k<2;k++) {
if (dants) meas[k]-=c1*dants[i]+c2*dants[j];
if (dantr) meas[k]-=c1*dantr[i]+c2*dantr[j];
}
return 1;
}
/* get tgd parameter (m) -----------------------------------------------------*/
static double gettgd(int sat, const nav_t *nav)
{
int i;
for (i=0;i<nav->n;i++) {
if (nav->eph[i].sat!=sat) continue;
return CLIGHT*nav->eph[i].tgd[0];
}
return 0.0;
}
/* slant ionospheric delay ---------------------------------------------------*/
static int corr_ion(gtime_t time, const nav_t *nav, int sat, const double *pos,
const double *azel, int ionoopt, double *ion, double *var,
int *brk)
{
#ifdef EXTSTEC
double rate;
#endif
/* sbas ionosphere model */
if (ionoopt==IONOOPT_SBAS) {
return sbsioncorr(time,nav,pos,azel,ion,var);
}
/* ionex tec model */
if (ionoopt==IONOOPT_TEC) {
return iontec(time,nav,pos,azel,1,ion,var);
}
#ifdef EXTSTEC
/* slant tec model */
if (ionoopt==IONOOPT_STEC) {
return stec_ion(time,nav,sat,pos,azel,ion,&rate,var,brk);
}
#endif
/* broadcast model */
if (ionoopt==IONOOPT_BRDC) {
*ion=ionmodel(time,nav->ion_gps,pos,azel);
*var=SQR(*ion*ERR_BRDCI);
return 1;
}
/* ionosphere model off */
*ion=0.0;
*var=VAR_IONO_OFF;
return 1;
}
/* ionosphere and antenna corrected measurements -----------------------------*/
static int corrmeas(const obsd_t *obs, const nav_t *nav, const double *pos,
const double *azel, const prcopt_t *opt,
const double *dantr, const double *dants, double phw,
double *meas, double *var, int *brk)
{
const double *lam=nav->lam[obs->sat-1];
double ion=0.0,L1,P1,PC,P1_P2,P1_C1,vari,gamma;
int i;
trace(4,"corrmeas:\n");
meas[0]=meas[1]=var[0]=var[1]=0.0;
/* iono-free LC */
if (opt->ionoopt==IONOOPT_IFLC) {
return ifmeas(obs,nav,azel,opt,dantr,dants,phw,meas,var);
}
if (lam[0]==0.0||obs->L[0]==0.0||obs->P[0]==0.0) return 0;
if (testsnr(0,0,azel[1],obs->SNR[0]*0.25,&opt->snrmask)) return 0;
L1=obs->L[0]*lam[0];
P1=obs->P[0];
/* dcb correction */
gamma=SQR(lam[1]/lam[0]); /* f1^2/f2^2 */
P1_P2=nav->cbias[obs->sat-1][0];
P1_C1=nav->cbias[obs->sat-1][1];
if (P1_P2==0.0&&(satsys(obs->sat,NULL)&(SYS_GPS|SYS_GAL|SYS_QZS))) {
P1_P2=(1.0-gamma)*gettgd(obs->sat,nav);
}
if (obs->code[0]==CODE_L1C) P1+=P1_C1; /* C1->P1 */
PC=P1-P1_P2/(1.0-gamma); /* P1->PC */
/* slant ionospheric delay L1 (m) */
if (!corr_ion(obs->time,nav,obs->sat,pos,azel,opt->ionoopt,&ion,&vari,brk)) {
trace(2,"iono correction error: time=%s sat=%2d ionoopt=%d\n",
time_str(obs->time,2),obs->sat,opt->ionoopt);
return 0;
}
/* ionosphere and windup corrected phase and code */
meas[0]=L1+ion-lam[0]*phw;
meas[1]=PC-ion;
var[0]+=vari;
var[1]+=vari+SQR(ERR_CBIAS);
/* antenna phase center variation correction */
for (i=0;i<2;i++) {
if (dants) meas[i]-=dants[0];
if (dantr) meas[i]-=dantr[0];
}
return 1;
}
/* L1/L2 geometry-free phase measurement -------------------------------------*/
static double gfmeas(const obsd_t *obs, const nav_t *nav)
{
const double *lam=nav->lam[obs->sat-1];
if (lam[0]==0.0||lam[1]==0.0||obs->L[0]==0.0||obs->L[1]==0.0) return 0.0;
return lam[0]*obs->L[0]-lam[1]*obs->L[1];
}
/* temporal update of position -----------------------------------------------*/
static void udpos_ppp(rtk_t *rtk)
{
int i;
trace(3,"udpos_ppp:\n");
/* fixed mode */
if (rtk->opt.mode==PMODE_PPP_FIXED) {
for (i=0;i<3;i++) initx(rtk,rtk->opt.ru[i],1E-8,i);
return;
}
/* initialize position for first epoch */
if (norm(rtk->x,3)<=0.0) {
for (i=0;i<3;i++) initx(rtk,rtk->sol.rr[i],VAR_POS,i);
}
/* static ppp mode */
if (rtk->opt.mode==PMODE_PPP_STATIC) return;
/* kinmatic mode without dynamics */
for (i=0;i<3;i++) {
initx(rtk,rtk->sol.rr[i],VAR_POS,i);
}
}
/* temporal update of clock --------------------------------------------------*/
static void udclk_ppp(rtk_t *rtk)
{
double dtr;
int i;
trace(3,"udclk_ppp:\n");
/* initialize every epoch for clock (white noise) */
for (i=0;i<NSYS;i++) {
if (rtk->opt.sateph==EPHOPT_PREC) {
/* time of prec ephemeris is based gpst */
/* negelect receiver inter-system bias */
dtr=rtk->sol.dtr[0];
}
else {
dtr=i==0?rtk->sol.dtr[0]:rtk->sol.dtr[0]+rtk->sol.dtr[i];
}
initx(rtk,CLIGHT*dtr,VAR_CLK,IC(i,&rtk->opt));
}
}
/* temporal update of tropospheric parameters --------------------------------*/
static void udtrop_ppp(rtk_t *rtk)
{
double pos[3],azel[]={0.0,PI/2.0},ztd,var;
int i=IT(&rtk->opt),j;
trace(3,"udtrop_ppp:\n");
if (rtk->x[i]==0.0) {
ecef2pos(rtk->sol.rr,pos);
ztd=sbstropcorr(rtk->sol.time,pos,azel,&var);
initx(rtk,ztd,var,i);
if (rtk->opt.tropopt>=TROPOPT_ESTG) {
for (j=0;j<2;j++) initx(rtk,1E-6,VAR_GRA,++i);
}
}
else {
rtk->P[i*(1+rtk->nx)]+=SQR(rtk->opt.prn[2])*fabs(rtk->tt);
if (rtk->opt.tropopt>=TROPOPT_ESTG) {
for (j=0;j<2;j++) {
rtk->P[++i*(1+rtk->nx)]+=SQR(rtk->opt.prn[2]*0.1)*fabs(rtk->tt);
}
}
}
}
/* detect cycle slip by LLI --------------------------------------------------*/
static void detslp_ll(rtk_t *rtk, const obsd_t *obs, int n)
{
int i,j;
trace(3,"detslp_ll: n=%d\n",n);
for (i=0;i<n&&i<MAXOBS;i++) for (j=0;j<rtk->opt.nf;j++) {
if (obs[i].L[j]==0.0||!(obs[i].LLI[j]&3)) continue;
trace(3,"detslp_ll: slip detected sat=%2d f=%d\n",obs[i].sat,j+1);
rtk->ssat[obs[i].sat-1].slip[j]=1;
}
}
/* detect cycle slip by geometry free phase jump -----------------------------*/
static void detslp_gf(rtk_t *rtk, const obsd_t *obs, int n, const nav_t *nav)
{
double g0,g1;
int i,j;
trace(3,"detslp_gf: n=%d\n",n);
for (i=0;i<n&&i<MAXOBS;i++) {
if ((g1=gfmeas(obs+i,nav))==0.0) continue;
g0=rtk->ssat[obs[i].sat-1].gf;
rtk->ssat[obs[i].sat-1].gf=g1;
trace(4,"detslip_gf: sat=%2d gf0=%8.3f gf1=%8.3f\n",obs[i].sat,g0,g1);
if (g0!=0.0&&fabs(g1-g0)>rtk->opt.thresslip) {
trace(3,"detslip_gf: slip detected sat=%2d gf=%8.3f->%8.3f\n",
obs[i].sat,g0,g1);
for (j=0;j<rtk->opt.nf;j++) rtk->ssat[obs[i].sat-1].slip[j]|=1;
}
}
}
/* temporal update of phase biases -------------------------------------------*/
static void udbias_ppp(rtk_t *rtk, const obsd_t *obs, int n, const nav_t *nav)
{
double meas[2],var[2],bias[MAXOBS]={0},offset=0.0,pos[3]={0};
int i,j,k,sat,brk=0;
trace(3,"udbias : n=%d\n",n);
for (i=0;i<MAXSAT;i++) for (j=0;j<rtk->opt.nf;j++) {
rtk->ssat[i].slip[j]=0;
}
/* detect cycle slip by LLI */
detslp_ll(rtk,obs,n);
/* detect cycle slip by geometry-free phase jump */
detslp_gf(rtk,obs,n,nav);
/* reset phase-bias if expire obs outage counter */
for (i=0;i<MAXSAT;i++) {
if (++rtk->ssat[i].outc[0]>(unsigned int)rtk->opt.maxout) {
initx(rtk,0.0,0.0,IB(i+1,&rtk->opt));
}
}
ecef2pos(rtk->sol.rr,pos);
for (i=k=0;i<n&&i<MAXOBS;i++) {
sat=obs[i].sat;
j=IB(sat,&rtk->opt);
if (!corrmeas(obs+i,nav,pos,rtk->ssat[sat-1].azel,&rtk->opt,NULL,NULL,
0.0,meas,var,&brk)) continue;
if (brk) {
rtk->ssat[sat-1].slip[0]=1;
trace(2,"%s: sat=%2d correction break\n",time_str(obs[i].time,0),sat);
}
bias[i]=meas[0]-meas[1];
if (rtk->x[j]==0.0||
rtk->ssat[sat-1].slip[0]||rtk->ssat[sat-1].slip[1]) continue;
offset+=bias[i]-rtk->x[j];
k++;
}
/* correct phase-code jump to enssure phase-code coherency */
if (k>=2&&fabs(offset/k)>0.0005*CLIGHT) {
for (i=0;i<MAXSAT;i++) {
j=IB(i+1,&rtk->opt);
if (rtk->x[j]!=0.0) rtk->x[j]+=offset/k;
}
trace(2,"phase-code jump corrected: %s n=%2d dt=%12.9fs\n",
time_str(rtk->sol.time,0),k,offset/k/CLIGHT);
}
for (i=0;i<n&&i<MAXOBS;i++) {
sat=obs[i].sat;
j=IB(sat,&rtk->opt);
rtk->P[j+j*rtk->nx]+=SQR(rtk->opt.prn[0])*fabs(rtk->tt);
if (rtk->x[j]!=0.0&&
!rtk->ssat[sat-1].slip[0]&&!rtk->ssat[sat-1].slip[1]) continue;
if (bias[i]==0.0) continue;
/* reinitialize phase-bias if detecting cycle slip */
initx(rtk,bias[i],VAR_BIAS,IB(sat,&rtk->opt));
trace(5,"udbias_ppp: sat=%2d bias=%.3f\n",sat,meas[0]-meas[1]);
}
}
/* temporal update of states --------------------------------------------------*/
static void udstate_ppp(rtk_t *rtk, const obsd_t *obs, int n, const nav_t *nav)
{
trace(3,"udstate_ppp: n=%d\n",n);
/* temporal update of position */
udpos_ppp(rtk);
/* temporal update of clock */
udclk_ppp(rtk);
/* temporal update of tropospheric parameters */
if (rtk->opt.tropopt>=TROPOPT_EST) {
udtrop_ppp(rtk);
}
/* temporal update of phase-bias */
udbias_ppp(rtk,obs,n,nav);
}
/* satellite antenna phase center variation ----------------------------------*/
static void satantpcv(const double *rs, const double *rr, const pcv_t *pcv,
double *dant)
{
double ru[3],rz[3],eu[3],ez[3],nadir,cosa;
int i;
for (i=0;i<3;i++) {
ru[i]=rr[i]-rs[i];
rz[i]=-rs[i];
}
if (!normv3(ru,eu)||!normv3(rz,ez)) return;
cosa=dot(eu,ez,3);
cosa=cosa<-1.0?-1.0:(cosa>1.0?1.0:cosa);
nadir=acos(cosa);
antmodel_s(pcv,nadir,dant);
}
/* precise tropospheric model ------------------------------------------------*/
static double prectrop(gtime_t time, const double *pos, const double *azel,
const prcopt_t *opt, const double *x, double *dtdx,
double *var)
{
const double zazel[]={0.0,PI/2.0};
double zhd,m_h,m_w,cotz,grad_n,grad_e;
/* zenith hydrostatic delay */
zhd=tropmodel(time,pos,zazel,0.0);
/* mapping function */
m_h=tropmapf(time,pos,azel,&m_w);
if ((opt->tropopt==TROPOPT_ESTG||opt->tropopt==TROPOPT_CORG)&&azel[1]>0.0) {
/* m_w=m_0+m_0*cot(el)*(Gn*cos(az)+Ge*sin(az)): ref [6] */
cotz=1.0/tan(azel[1]);
grad_n=m_w*cotz*cos(azel[0]);
grad_e=m_w*cotz*sin(azel[0]);
m_w+=grad_n*x[1]+grad_e*x[2];
dtdx[1]=grad_n*(x[0]-zhd);
dtdx[2]=grad_e*(x[0]-zhd);
}
dtdx[0]=m_w;
*var=SQR(0.01);
return m_h*zhd+m_w*(x[0]-zhd);
}
/* phase and code residuals --------------------------------------------------*/
static int res_ppp(int iter, const obsd_t *obs, int n, const double *rs,
const double *dts, const double *vare, const int *svh,
const nav_t *nav, const double *x, rtk_t *rtk, double *v,
double *H, double *R, double *azel)
{
prcopt_t *opt=&rtk->opt;
double r,rr[3],disp[3],pos[3],e[3],meas[2],dtdx[3],dantr[NFREQ]={0};
double dants[NFREQ]={0},var[MAXOBS*2],dtrp=0.0,vart=0.0,varm[2]={0};
int i,j,k,sat,sys,nv=0,nx=rtk->nx,brk,tideopt;
trace(3,"res_ppp : n=%d nx=%d\n",n,nx);
for (i=0;i<MAXSAT;i++) rtk->ssat[i].vsat[0]=0;
for (i=0;i<3;i++) rr[i]=x[i];
/* earth tides correction */
if (opt->tidecorr) {
tideopt=opt->tidecorr==1?1:7; /* 1:solid, 2:solid+otl+pole */
tidedisp(gpst2utc(obs[0].time),rr,tideopt,&nav->erp,opt->odisp[0],
disp);
for (i=0;i<3;i++) rr[i]+=disp[i];
}
ecef2pos(rr,pos);
for (i=0;i<n&&i<MAXOBS;i++) {
sat=obs[i].sat;
if (!(sys=satsys(sat,NULL))||!rtk->ssat[sat-1].vs) continue;
/* geometric distance/azimuth/elevation angle */
if ((r=geodist(rs+i*6,rr,e))<=0.0||
satazel(pos,e,azel+i*2)<opt->elmin) continue;
/* excluded satellite? */
if (satexclude(obs[i].sat,svh[i],opt)) continue;
/* tropospheric delay correction */
if (opt->tropopt==TROPOPT_SAAS) {
dtrp=tropmodel(obs[i].time,pos,azel+i*2,REL_HUMI);
vart=SQR(ERR_SAAS);
}
else if (opt->tropopt==TROPOPT_SBAS) {
dtrp=sbstropcorr(obs[i].time,pos,azel+i*2,&vart);
}
else if (opt->tropopt==TROPOPT_EST||opt->tropopt==TROPOPT_ESTG) {
dtrp=prectrop(obs[i].time,pos,azel+i*2,opt,x+IT(opt),dtdx,&vart);
}
else if (opt->tropopt==TROPOPT_COR||opt->tropopt==TROPOPT_CORG) {
dtrp=prectrop(obs[i].time,pos,azel+i*2,opt,x,dtdx,&vart);
}
/* satellite antenna model */
if (opt->posopt[0]) {
satantpcv(rs+i*6,rr,nav->pcvs+sat-1,dants);
}
/* receiver antenna model */
antmodel(opt->pcvr,opt->antdel[0],azel+i*2,opt->posopt[1],dantr);
/* phase windup correction */
if (opt->posopt[2]) {
windupcorr(rtk->sol.time,rs+i*6,rr,&rtk->ssat[sat-1].phw);
}
/* ionosphere and antenna phase corrected measurements */
if (!corrmeas(obs+i,nav,pos,azel+i*2,&rtk->opt,dantr,dants,
rtk->ssat[sat-1].phw,meas,varm,&brk)) {
continue;
}
/* satellite clock and tropospheric delay */
r+=-CLIGHT*dts[i*2]+dtrp;
trace(5,"sat=%2d azel=%6.1f %5.1f dtrp=%.3f dantr=%6.3f %6.3f dants=%6.3f %6.3f phw=%6.3f\n",
sat,azel[i*2]*R2D,azel[1+i*2]*R2D,dtrp,dantr[0],dantr[1],dants[0],
dants[1],rtk->ssat[sat-1].phw);
for (j=0;j<2;j++) { /* for phase and code */
if (meas[j]==0.0) continue;
for (k=0;k<nx;k++) H[k+nx*nv]=0.0;
v[nv]=meas[j]-r;
for (k=0;k<3;k++) H[k+nx*nv]=-e[k];
if (sys!=SYS_GLO) {
v[nv]-=x[IC(0,opt)];
H[IC(0,opt)+nx*nv]=1.0;
}
else {
v[nv]-=x[IC(1,opt)];
H[IC(1,opt)+nx*nv]=1.0;
}
if (opt->tropopt>=TROPOPT_EST) {
for (k=0;k<(opt->tropopt>=TROPOPT_ESTG?3:1);k++) {
H[IT(opt)+k+nx*nv]=dtdx[k];
}
}
if (j==0) {
v[nv]-=x[IB(obs[i].sat,opt)];
H[IB(obs[i].sat,opt)+nx*nv]=1.0;
}
var[nv]=varerr(obs[i].sat,sys,azel[1+i*2],j,opt)+varm[j]+vare[i]+vart;
if (j==0) rtk->ssat[sat-1].resc[0]=v[nv];
else rtk->ssat[sat-1].resp[0]=v[nv];
/* test innovation */
#if 0
if (opt->maxinno>0.0&&fabs(v[nv])>opt->maxinno) {
#else
if (opt->maxinno>0.0&&fabs(v[nv])>opt->maxinno&&sys!=SYS_GLO) {
#endif
trace(2,"ppp outlier rejected %s sat=%2d type=%d v=%.3f\n",
time_str(obs[i].time,0),sat,j,v[nv]);
rtk->ssat[sat-1].rejc[0]++;
continue;
}
if (j==0) rtk->ssat[sat-1].vsat[0]=1;
nv++;
}
}
for (i=0;i<nv;i++) for (j=0;j<nv;j++) {
R[i+j*nv]=i==j?var[i]:0.0;