/*------------------------------------------------------------------------------
* pntpos.c : standard positioning
*
*          Copyright (C) 2007-2020 by T.TAKASU, All rights reserved.
*
* version : $Revision:$ $Date:$
* history : 2010/07/28 1.0  moved from rtkcmn.c
*                           changed api:
*                               pntpos()
*                           deleted api:
*                               pntvel()
*           2011/01/12 1.1  add option to include unhealthy satellite
*                           reject duplicated observation data
*                           changed api: ionocorr()
*           2011/11/08 1.2  enable snr mask for single-mode (rtklib_2.4.1_p3)
*           2012/12/25 1.3  add variable snr mask
*           2014/05/26 1.4  support galileo and beidou
*           2015/03/19 1.5  fix bug on ionosphere correction for GLO and BDS
*           2018/10/10 1.6  support api change of satexclude()
*           2020/11/30 1.7  support NavIC/IRNSS in pntpos()
*                           no support IONOOPT_LEX option in ioncorr()
*                           improve handling of TGD correction for each system
*                           use E1-E5b for Galileo dual-freq iono-correction
*                           use API sat2freq() to get carrier frequency
*                           add output of velocity estimation error in estvel()
*-----------------------------------------------------------------------------*/
#include <stdbool.h>
#include "rtklib.h"
#include "time.h"

/* constants/macros ----------------------------------------------------------*/

#define SQR(x)      ((x)*(x))
#define MAX(x,y)    ((x)>=(y)?(x):(y))

#if 0 /* enable GPS-QZS time offset estimation */
#define NX          (4+5)       /* # of estimated parameters */
#else
#define NX          (4+3)       /* # of estimated parameters */
#endif
#define MAXITR      10          /* max number of iteration for point pos */
#define ERR_ION     5.0         /* ionospheric delay Std (m) */
#define ERR_TROP    3.0         /* tropspheric delay Std (m) */
#define ERR_SAAS    0.3         /* Saastamoinen model error Std (m) */
#define ERR_BRDCI   0.5         /* broadcast ionosphere model error factor */
#define ERR_CBIAS   0.3         /* code bias error Std (m) */
#define REL_HUMI    0.7         /* relative humidity for Saastamoinen model */
#define MIN_EL      (5.0*D2R)   /* min elevation for measurement error (rad) */
#define STDOPP      0.1        /* doppler measurement standard variance */


/* jacobian of pseudorange measurement by ins attitude error states-----------
 * args  :  double *e    I  line-of-sight vector (ecef)
 *          double *l    I  lever arm of body frame to gps antenna
 *          double *Cbe  I  transform matrix of body frame to ecef
 *          double *dpda O  jacobian of ins attitude error states
 * return : none
 * --------------------------------------------------------------------------*/
static void jacob_dp_da(const double *e,const double *l,const double *Cbe,
                        double *dpda)
{
    double T[9];

    matmul("NN",3,1,3,-1.0,Cbe,l,0.0,dpda);
    skewsym3(dpda,T);
    matmul("NN",1,3,3,1.0,e,T,0.0,dpda);
}

/* pseudorange measurement error variance ------------------------------------*/
static double varerr(const prcopt_t *opt, const ssat_t *ssat, const obsd_t *obs, double el, int sys)
{
    double fact=1.0,varr,snr_rover;

    switch (sys) {
        case SYS_GPS: fact *= EFACT_GPS; break;
        case SYS_GLO: fact *= EFACT_GLO; break;
        case SYS_SBS: fact *= EFACT_SBS; break;
        case SYS_CMP: fact *= EFACT_CMP; break;
        case SYS_QZS: fact *= EFACT_QZS; break;
        case SYS_IRN: fact *= EFACT_IRN; break;
        default:      fact *= EFACT_GPS; break;
    }
    if (el<MIN_EL) el=MIN_EL;
    /* var = R^2*(a^2 + (b^2/sin(el) + c^2*(10^(0.1*(snr_max-snr_rover)))) + (d*rcv_std)^2) */
    varr=SQR(opt->err[1])+SQR(opt->err[2])/sin(el);
    if (opt->err[6]>0.0) {  /* if snr term not zero */
        snr_rover=(ssat)?SNR_UNIT*ssat->snr_rover[0]:opt->err[5];
        varr+=SQR(opt->err[6])*pow(10,0.1*MAX(opt->err[5]-snr_rover,0));
    }
    varr*=SQR(opt->eratio[0]);
    if (opt->err[7]>0.0) {
        varr+=SQR(opt->err[7]*0.01*(1<<(obs->Pstd[0]+5)));  /* 0.01*2^(n+5) m */
    }
    if (opt->ionoopt==IONOOPT_IFLC) varr*=SQR(3.0); /* iono-free */
    return SQR(fact)*varr;
}
/* get group delay parameter (m) ---------------------------------------------*/
static double gettgd(int sat, const nav_t *nav, int type)
{
    int i,sys=satsys(sat,NULL);
    
    if (sys==SYS_GLO) {
        for (i=0;i<nav->ng;i++) {
            if (nav->geph[i].sat==sat) break;
        }
        return (i>=nav->ng)?0.0:-nav->geph[i].dtaun*CLIGHT;
    }
    else {
        for (i=0;i<nav->n;i++) {
            if (nav->eph[i].sat==sat) break;
        }
        return (i>=nav->n)?0.0:nav->eph[i].tgd[type]*CLIGHT;
    }
}
/* test SNR mask -------------------------------------------------------------*/
static int snrmask(const obsd_t *obs, const double *azel, const prcopt_t *opt)
{
    int f2;

    if (testsnr(0,0,azel[1],obs->SNR[0]*SNR_UNIT,&opt->snrmask)) {
        return 0;
    }
    if (opt->ionoopt==IONOOPT_IFLC) {
        f2=seliflc(opt->nf,satsys(obs->sat,NULL));
        if (testsnr(0,f2,azel[1],obs->SNR[f2]*SNR_UNIT,&opt->snrmask)) return 0;
    }
    return 1;
}
static double prange(const obsd_t *obs, const nav_t *nav, const prcopt_t *opt,
                     double *var)
{
    double P1,P2,gamma,b1,b2;
    int sat,sys,f2;

    sat=obs->sat;
    sys=satsys(sat,NULL);
    P1=obs->P[0];
    f2=seliflc(opt->nf,satsys(obs->sat,NULL));
    P2=obs->P[f2];
    *var=0.0;

    if (P1==0.0||(opt->ionoopt==IONOOPT_IFLC&&P2==0.0)) return 0.0;

    /* P1-C1,P2-C2 DCB correction */
    if (sys==SYS_GPS||sys==SYS_GLO) {
        if (obs->code[0]==CODE_L1C) P1+=nav->cbias[sat-1][1]; /* C1->P1 */
        if (obs->code[1]==CODE_L2C) P2+=nav->cbias[sat-1][2]; /* C2->P2 */
    }
    if (opt->ionoopt==IONOOPT_IFLC) { /* dual-frequency */

        if (sys==SYS_GPS||sys==SYS_QZS) { /* L1-L2 or L1-L5 */
            gamma=f2==1?SQR(FREQL1/FREQL2):SQR(FREQL1/FREQL5);
            return (P2-gamma*P1)/(1.0-gamma);
        }
        else if (sys==SYS_GLO) { /* G1-G2 or G1-G3 */
            gamma=f2==1?SQR(FREQ1_GLO/FREQ2_GLO):SQR(FREQ1_GLO/FREQ2_GLO);
            return (P2-gamma*P1)/(1.0-gamma);
        }
        else if (sys==SYS_GAL) { /* E1-E5b, E1-E5a */
            gamma=f2==1?SQR(FREQL1/FREQE5b):SQR(FREQL1/FREQL5);
            if (f2==1&&getseleph(SYS_GAL)) { /* F/NAV */
                P2-=gettgd(sat,nav,0)-gettgd(sat,nav,1); /* BGD_E5aE5b */
            }
            return (P2-gamma*P1)/(1.0-gamma);
        }
        else if (sys==SYS_CMP) { /* B1-B2 */
            gamma=SQR(((obs->code[0]==CODE_L2I)?FREQ1_CMP:FREQL1)/FREQ2_CMP);
            if      (obs->code[0]==CODE_L2I) b1=gettgd(sat,nav,0); /* TGD_B1I */
            else if (obs->code[0]==CODE_L1P) b1=gettgd(sat,nav,2); /* TGD_B1Cp */
            else b1=gettgd(sat,nav,2)+gettgd(sat,nav,4); /* TGD_B1Cp+ISC_B1Cd */
            b2=gettgd(sat,nav,1); /* TGD_B2I/B2bI (m) */
            return ((P2-gamma*P1)-(b2-gamma*b1))/(1.0-gamma);
        }
        else if (sys==SYS_IRN) { /* L5-S */
            gamma=SQR(FREQL5/FREQs);
            return (P2-gamma*P1)/(1.0-gamma);
        }
    }
    else { /* single-freq (L1/E1/B1) */
        *var=SQR(ERR_CBIAS);

        if (sys==SYS_GPS||sys==SYS_QZS) { /* L1 */
            b1=gettgd(sat,nav,0); /* TGD (m) */
            return P1-b1;
        }
        else if (sys==SYS_GLO) { /* G1 */
            gamma=SQR(FREQ1_GLO/FREQ2_GLO);
            b1=gettgd(sat,nav,0); /* -dtaun (m) */
            return P1-b1/(gamma-1.0);
        }
        else if (sys==SYS_GAL) { /* E1 */
            if (getseleph(SYS_GAL)) b1=gettgd(sat,nav,0); /* BGD_E1E5a */
            else                    b1=gettgd(sat,nav,1); /* BGD_E1E5b */
            return P1-b1;
        }
        else if (sys==SYS_CMP) { /* B1I/B1Cp/B1Cd */
            if      (obs->code[0]==CODE_L2I) b1=gettgd(sat,nav,0); /* TGD_B1I */
            else if (obs->code[0]==CODE_L1P) b1=gettgd(sat,nav,2); /* TGD_B1Cp */
            else b1=gettgd(sat,nav,2)+gettgd(sat,nav,4); /* TGD_B1Cp+ISC_B1Cd */
            return P1-b1;
        }
        else if (sys==SYS_IRN) { /* L5 */
            gamma=SQR(FREQs/FREQL5);
            b1=gettgd(sat,nav,0); /* TGD (m) */
            return P1-gamma*b1;
        }
    }
    return P1;
}
/* ionospheric correction ------------------------------------------------------
* compute ionospheric correction
* args   : gtime_t time     I   time
*          nav_t  *nav      I   navigation data
*          int    sat       I   satellite number
*          double *pos      I   receiver position {lat,lon,h} (rad|m)
*          double *azel     I   azimuth/elevation angle {az,el} (rad)
*          int    ionoopt   I   ionospheric correction option (IONOOPT_???)
*          double *ion      O   ionospheric delay (L1) (m)
*          double *var      O   ionospheric delay (L1) variance (m^2)
* return : status(1:ok,0:error)
*-----------------------------------------------------------------------------*/
extern int ionocorr(gtime_t time, const nav_t *nav, int sat, const double *pos,
                    const double *azel, int ionoopt, double *ion, double *var)
{
    int err=0;

    trace(4,"ionocorr: time=%s opt=%d sat=%2d pos=%.3f %.3f azel=%.3f %.3f\n",
          time_str(time,3),ionoopt,sat,pos[0]*R2D,pos[1]*R2D,azel[0]*R2D,
          azel[1]*R2D);
    
    /* SBAS ionosphere model */
    if (ionoopt==IONOOPT_SBAS) {
        if (sbsioncorr(time,nav,pos,azel,ion,var)) return 1;
        err=1;
    }
    /* IONEX TEC model */
    if (ionoopt==IONOOPT_TEC) {
        if (iontec(time,nav,pos,azel,1,ion,var)) return 1;
        err=1;
    }
    /* QZSS broadcast ionosphere model */
    if (ionoopt==IONOOPT_QZS&&norm(nav->ion_qzs,8)>0.0) {
        *ion=ionmodel(time,nav->ion_qzs,pos,azel);
        *var=SQR(*ion*ERR_BRDCI);
        return 1;
    }
    /* GPS broadcast ionosphere model */
    if (ionoopt==IONOOPT_BRDC||err==1) {
        *ion=ionmodel(time,nav->ion_gps,pos,azel);
        *var=SQR(*ion*ERR_BRDCI);
        return 1;
    }
    *ion=0.0;
    *var=ionoopt==IONOOPT_OFF?SQR(ERR_ION):0.0;
    return 1;
}
/* tropospheric correction -----------------------------------------------------
* compute tropospheric correction
* args   : gtime_t time     I   time
*          nav_t  *nav      I   navigation data
*          double *pos      I   receiver position {lat,lon,h} (rad|m)
*          double *azel     I   azimuth/elevation angle {az,el} (rad)
*          int    tropopt   I   tropospheric correction option (TROPOPT_???)
*          double *trp      O   tropospheric delay (m)
*          double *var      O   tropospheric delay variance (m^2)
* return : status(1:ok,0:error)
*-----------------------------------------------------------------------------*/
extern int tropcorr(gtime_t time, const nav_t *nav, const double *pos,
                    const double *azel, int tropopt, double *trp, double *var)
{
    trace(4,"tropcorr: time=%s opt=%d pos=%.3f %.3f azel=%.3f %.3f\n",
          time_str(time,3),tropopt,pos[0]*R2D,pos[1]*R2D,azel[0]*R2D,
          azel[1]*R2D);
    
    /* Saastamoinen model */
    if (tropopt==TROPOPT_SAAS||tropopt==TROPOPT_EST||tropopt==TROPOPT_ESTG) {
        *trp=tropmodel(time,pos,azel,REL_HUMI);
        *var=SQR(ERR_SAAS/(sin(azel[1])+0.1));
        return 1;
    }
    /* SBAS (MOPS) troposphere model */
    if (tropopt==TROPOPT_SBAS) {
        *trp=sbstropcorr(time,pos,azel,var);
        return 1;
    }
    /* no correction */
    *trp=0.0;
    *var=tropopt==TROPOPT_OFF?SQR(ERR_TROP):0.0;
    return 1;
}
/* pseudorange residuals -----------------------------------------------------*/
static int rescode(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, const prcopt_t *opt,
                   const ssat_t *ssat, double *v, double *H, double *var,
                   double *azel, int *vsat, double *resp, int *ns)
{
    gtime_t time;
    double r,freq,dion=0.0,dtrp=0.0,vmeas,vion=0.0,vtrp=0.0,rr[3],pos[3],dtr,e[3],P;
    int i,j,nv=0,sat,sys,mask[NX-3]={0};
    
    trace(3,"resprng : n=%d\n",n);
    
    for (i=0;i<3;i++) rr[i]=x[i];
    dtr=x[3];
    
    ecef2pos(rr,pos);
    
    for (i=*ns=0;i<n&&i<MAXOBS;i++) {
        vsat[i]=0; azel[i*2]=azel[1+i*2]=resp[i]=0.0;
        time=obs[i].time;
        sat=obs[i].sat;
        if (!(sys=satsys(sat,NULL))) continue;
        
        /* reject duplicated observation data */
        if (i<n-1&&i<MAXOBS-1&&sat==obs[i+1].sat) {
            trace(2,"duplicated obs data %s sat=%d\n",time_str(time,3),sat);
            i++;
            continue;
        }
        /* excluded satellite? */
        if (satexclude(sat,vare[i],svh[i],opt)) continue;
        
        /* geometric distance and elevation mask*/
        if ((r=geodist(rs+i*6,rr,e))<=0.0) continue;
        if (satazel(pos,e,azel+i*2)<opt->elmin) continue;
        
        if (iter>0) {
            /* test SNR mask */
            if (!snrmask(obs+i,azel+i*2,opt)) continue;
        
            /* ionospheric correction */
            if (!ionocorr(time,nav,sat,pos,azel+i*2,opt->ionoopt,&dion,&vion)) {
                continue;
            }
            if ((freq=sat2freq(sat,obs[i].code[0],nav))==0.0) continue;
            dion*=SQR(FREQL1/freq);
            vion*=SQR(FREQL1/freq);
        
            /* tropospheric correction */
            if (!tropcorr(time,nav,pos,azel+i*2,opt->tropopt,&dtrp,&vtrp)) {
                continue;
            }
        }
        /* psendorange with code bias correction */
        if ((P=prange(obs+i,nav,opt,&vmeas))==0.0) continue;
        
        /* pseudorange residual */
        v[nv]=P-(r+dtr-CLIGHT*dts[i*2]+dion+dtrp);
        
        /* design matrix */
        for (j=0;j<NX;j++) {
            H[j+nv*NX]=j<3?-e[j]:(j==3?1.0:0.0);
        }
        /* time system offset and receiver bias correction */
        if      (sys==SYS_GLO) {v[nv]-=x[4]; H[4+nv*NX]=1.0; mask[1]=1;}
        else if (sys==SYS_GAL) {v[nv]-=x[5]; H[5+nv*NX]=1.0; mask[2]=1;}
        else if (sys==SYS_CMP) {v[nv]-=x[6]; H[6+nv*NX]=1.0; mask[3]=1;}
        else if (sys==SYS_IRN) {v[nv]-=x[7]; H[7+nv*NX]=1.0; mask[4]=1;}
#if 0 /* enable QZS-GPS time offset estimation */
        else if (sys==SYS_QZS) {v[nv]-=x[8]; H[8+nv*NX]=1.0; mask[5]=1;}
#endif
        else mask[0]=1;

        vsat[i]=1; resp[i]=v[nv]; (*ns)++;
        
        /* variance of pseudorange error */
        var[nv++]=varerr(opt,&ssat[i],&obs[i],azel[1+i*2],sys)+vare[i]+vmeas+vion+vtrp;
        trace(4,"sat=%2d azel=%5.1f %4.1f res=%7.3f sig=%5.3f\n",obs[i].sat,
              azel[i*2]*R2D,azel[1+i*2]*R2D,resp[i],sqrt(var[nv-1]));
    }
    /* constraint to avoid rank-deficient */
    for (i=0;i<NX-3;i++) {
        if (mask[i]) continue;
        v[nv]=0.0;
        for (j=0;j<NX;j++) H[j+nv*NX]=j==i+3?1.0:0.0;
        var[nv++]=0.01;
    }
    return nv;
}

/* jacobian of doppler measurement by ins velocity---------------------------*/
static void jaco_dop_dv(const double *e,const double *rs,double *dopdv)
{
    dopdv[0]=e[0]-OMGE/CLIGHT*rs[1];
    dopdv[1]=e[1]+OMGE/CLIGHT*rs[0];
    dopdv[2]=e[2];
}

/* jacobian of doppler measurement by attitude error-------------------------
 * args   :  double *dr    I  jacobian matrix of ins position
 *           double *Cbe   I  transform matrix from b-frame to ecef
 *           double *l     I  lever arm of b-frame to antenna position
 *           double *dopdv I  jacobian matrix of velocity
 *           double *gyro  I  gyro measurement data
 *           double *dopda O  output jacobian matrix
 * return : none
 * --------------------------------------------------------------------------*/
static void jaco_dop_da(const double *dr,const double *Cbe,const double *l,
                        const double *dopdv,const double *gyro,double *dopda)
{
    int i;
    double T[9],sl[3],S[9];

    /* partial matrix by ins position */
    matmul("NN",3,1,3,-1.0,Cbe,l,0.0,dopda);
    skewsym3(dopda,T);
    matmul("NN",1,3,3,1.0,dr,T,0.0,dopda);

    /* partial matrix by ins velocity */
    skewsym3(gyro,T);
    matmul33("NNN",Cbe,T,l,3,3,3,1,sl);
    skewsym3(sl,T);
    matmul("NN",1,3,3,1.0,dopdv,T,0.0,S);
    for (i=0;i<3;i++) dopda[i]-=S[i];

    matmul("NN",3,1,3,1.0,Cbe,l,0.0,sl);
    skewsym3(sl,T);
    matmul("NN",3,3,3,1.0,Omge,T,0.0,S);
    matmul("NN",1,3,3,1.0,dopdv,S,0.0,T);
    for (i=0;i<3;i++) dopda[i]+=T[i];
}

/* jacobian of doppler measurement by ins position---------------------------
 * args   :  double *rs     I  satellite position
 *           double *rr     I  receiver position
 *           double *vs     I  satellite velocity
 *           double *dopdp  O  output jacobian matrix
 * return : none
 * --------------------------------------------------------------------------*/
static void jaco_dop_dp(const double *rs,const double *rr,const double *vs,
                        const double *vr,double *dopdp)
{
    int i;
    double dv[3],dp[3],pr,t;

    for (i=0;i<3;i++) dp[i]=rs[i]-rr[i]; pr=norm(dp,3);
    for (i=0;i<3;i++) dv[i]=vs[i]-vr[i];

    t=pow(SQR(pr),1.5);

    dopdp[0]=2.0*dv[2]*dp[2]*dp[0]/(2.0*t)-dv[0]/pr+2.0*dv[0]*dp[0]*dp[0]/(2.0*t)+
             2.0*dv[1]*dp[1]*dp[0]/(2.0*t)+OMGE/CLIGHT*vs[1];
    dopdp[1]=2.0*dv[1]*dp[1]*dp[0]/(2.0*t)-dv[1]/pr+2.0*dv[2]*dp[2]*dp[1]/(2.0*t)+
             2.0*dv[0]*dp[0]*dp[1]/(2.0*t)-OMGE/CLIGHT*vs[0];
    dopdp[2]=2.0*dv[0]*dp[0]*dp[2]/(2.0*t)-dv[1]/pr+2.0*dv[1]*dp[1]*dp[2]/(2.0*t)+
             2.0*dv[2]*dp[2]*dp[2]/(2.0*t);
    for (i=0;i<3;i++) dopdp[i]=-dopdp[i];
}

/* jacobian of doppler measurement by gyro bias------------------------------*/
static void jaco_dop_bg(const double *dopdv,const double *Cbe,const double *l,
                        double *dopbg)
{
    double T[9],S[9];

    skewsym3(l,T);
    matmul("NN",3,3,3,-1.0,Cbe,T,0.0,S);
    matmul("NN",1,3,3, 1.0,dopdv,S,0.0,dopbg);
}

/* pseudorange and doppler residuals -----------------------------------------------------*/
static int tc_rescode(int iter, const obsd_t *obs, int n, const double *rs,
                   const double *dts, const double *vare, const int *svh,
                   const nav_t *nav, double *x, const prcopt_t *opt,
                   const ssat_t *ssat,
                   const ins_t *ins,
                   double *v, double *H, double *var,
                   double *azel, int *vsat, double *resp, int *ns)
{
    gtime_t time;
    double r,freq,dion=0.0,dtrp=0.0,vmeas,vion=0.0,vtrp=0.0,rr[3],vr[3],pos[3],e[3],P;
    int i,j,nv=0,sat,sys,mask[3]={0};
    int nx,index_GPS,index_GLO,index_GAL,index_BDS,index_IRN,index_dtrr;
    double dpda[3];

    trace(3,"rescode: n=%d\n");

    /* receiver clock state index */
    index_GPS = 15;/* receiver clock state index */
    index_GAL=index_GPS+1;
    index_BDS=index_GPS+2;

    index_dtrr = 18;

    nx = ins->nx;
    /* lever arm */
    rmlever(NULL,ins->position,ins->velocity,ins->L_ba_b,ins->Cbe,ins->omgb,rr,vr);
    /* receiver clock */
    for(i=0;i<3;i++) {
        x[index_GPS + i] = ins->clk[i] + ins->dtrr[i];
        x[index_dtrr + i]= ins->dtrr[i];
    }
    ecef2pos(rr,pos);

    for (i=*ns=0;i<n&&i<MAXOBS;i++) {
        vsat[i]=0;
        azel[i*2]=azel[1+i*2]=resp[i]=0.0;
        time=obs[i].time;
        sat=obs[i].sat;
        if (!(sys=satsys(sat,NULL))) continue;

        /* reject duplicated observation data */
        if (i<n-1&&i<MAXOBS-1&&sat==obs[i+1].sat) {
            trace(2,"duplicated obs data %s sat=%d\n",time_str(time,3),sat);
            i++;
            continue;
        }
        /* excluded satellite? */
        if (satexclude(sat,vare[i],svh[i],opt)) continue;

        /* geometric distance and elevation mask */
        if ((r=geodist(rs+i*6,rr,e))<=0.0||satazel(pos,e,azel+i*2)<opt->elmin) continue;

        if (iter>0) {
            /* test SNR mask */
            if (!snrmask(obs+i,azel+i*2,opt)) continue;

            /* ionospheric correction */
            if (!ionocorr(time,nav,sat,pos,azel+i*2,opt->ionoopt,&dion,&vion)) {
                continue;
            }
            if ((freq=sat2freq(sat,obs[i].code[0],nav))==0.0) continue;
            dion*=SQR(FREQL1/freq);
            vion*=SQR(FREQL1/freq);

            /* tropospheric correction */
            if (!tropcorr(time,nav,pos,azel+i*2,opt->tropopt,&dtrp,&vtrp)) {
                continue;
            }
        }
        /* psendorange with code bias correction */
        if ((P=prange(obs+i,nav,opt,&vmeas))==0.0) continue;
        /* pseudorange residual */
        v[2*nv]=P-(r-CLIGHT*dts[i*2]+dion+dtrp);
        /* design matrix */
        jacob_dp_da(e,ins->L_ba_b,ins->Cbe,dpda);
        /* position index = 6 */
        for(j=6;j<9;j++) H[j+2*nv*nx]=e[j-6];
        for (j=0;j<0+3;j++) H[j+2*nv*nx]=dpda[j-0];


        /* time system offset and receiver bias correction */
        if      (sys==SYS_GPS) {v[2*nv]-=x[index_GPS];H[index_GPS+2*nv*nx]=1.0;}
        else if (sys==SYS_GAL) {v[2*nv]-=x[index_GAL];H[index_GAL+2*nv*nx]=1.0;mask[1]=1;}
        else if (sys==SYS_CMP) {v[2*nv]-=x[index_BDS];H[index_BDS+2*nv*nx]=1.0;mask[2]=1;}
        else mask[0]=1;

        vsat[i]=1;
        resp[i]=v[2*nv];
        (*ns)++;

        /* doppler residuals */
        double rate,vs[3]={0},dopdv[3]={0},dopdp[3]={0},dopda[3]={0},dopbg[3]={0};

        /* satellite velocity relative to receiver in ecef */
        vs[0]=rs[0+3+i*6]-vr[0];
        vs[1]=rs[1+3+i*6]-vr[1];
        vs[2]=rs[2+3+i*6]-vr[2];
        /* range rate with earth rotation correction */
        rate=dot(vs,e,3)+OMGE/CLIGHT*(rs[4+i*6]*rr[0]+rs[1+i*6]*vr[0]-
                                      rs[3+i*6]*rr[1]-rs[  i*6]*vr[1]);
        /* doppler residual */
#ifdef LG69T
        v[2*nv+1]=(-obs[i].D[0]*CLIGHT/freq-(rate-CLIGHT*dts[1+i*2]));
#elif defined(MPU6050)
        v[2*nv+1]=(obs[i].D[0]*CLIGHT/freq-(rate-CLIGHT*dts[1+i*2]));
#endif

        if(1){
            jaco_dop_dp(rs+6*i,rr,rs+3+6*i,vr,dopdp);
            jaco_dop_da(dopdp,ins->Cbe,ins->L_ba_b,dopdv,ins->omgb,dopda);
            jaco_dop_dv(e,rs+6*i,dopdv);
            jaco_dop_bg(dopdv,ins->Cbe,ins->L_ba_b,dopbg);

            for (j=0;j<0+3;j++) H[j+(2*nv+1)*nx]=dopda[j-0];
            for (j=3;j<3+3;j++) H[j+(2*nv+1)*nx]=dopdv[j-3];
            for (j=6;j<6+3;j++) H[j+(2*nv+1)*nx]=dopdp[j-6];
            H[12+0+(2*nv+1)*nx]=dopbg[0];
            H[12+1+(2*nv+1)*nx]=dopbg[1];
            H[12+2+(2*nv+1)*nx]=dopbg[2];

            if (sys == SYS_GPS) {
                v[(2*nv+1)] -= x[index_dtrr+0];
                H[index_dtrr+0 + (2*nv+1) * nx] = 1.0;
            }
            else if (sys == SYS_GAL) {
                v[(2*nv+1)] -= x[index_dtrr+1];
                H[index_dtrr+1 + (2*nv+1) * nx] = 1.0;
            }
            else if (sys == SYS_CMP) {
                v[(2*nv+1)] -= x[index_dtrr+2];
                H[index_dtrr+2 + (2*nv+1) * nx] = 1.0;
            }
        }

        /* variance of pseudorange error */
        var[2*nv]=varerr(opt,&ssat[i],&obs[i],azel[1+i*2],sys)+vare[i]+vmeas+vion+vtrp;
        var[2*nv+1]=STDOPP/sin(azel[1]);

        trace(3,"sat=%2d azel=%5.1f %4.1f res=%7.3f doppler_res=%7.3f sig=%5.3f，sys=%d\n",obs[i].sat,
              azel[i*2]*R2D,azel[1+i*2]*R2D,resp[i],v[2*nv+1],sqrt(var[2*nv]),sys);

        nv++;

    }

    return nv;
}
/* validate solution ---------------------------------------------------------*/
static int valsol(const double *azel, const int *vsat, int n,
                  const prcopt_t *opt, const double *v, int nv, int nx,
                  char *msg)
{
    double azels[MAXOBS*2],dop[4],vv;
    int i,ns;
    
    trace(3,"valsol  : n=%d nv=%d\n",n,nv);
    
    /* Chi-square validation of residuals */
    vv=dot(v,v,nv);
    if (nv>nx&&vv>chisqr[nv-nx-1]) {
        sprintf(msg,"Warning: large chi-square error nv=%d vv=%.1f cs=%.1f",nv,vv,chisqr[nv-nx-1]);
        /* return 0; */ /* threshold too strict for all use cases, report error but continue on */
    }
    /* large GDOP check */
    for (i=ns=0;i<n;i++) {
        if (!vsat[i]) continue;
        azels[  ns*2]=azel[  i*2];
        azels[1+ns*2]=azel[1+i*2];
        ns++;
    }
    dops(ns,azels,opt->elmin,dop);
    if (dop[0]<=0.0||dop[0]>opt->maxgdop) {
        sprintf(msg,"gdop error nv=%d gdop=%.1f",nv,dop[0]);
        return 0;
    }
    return 1;
}
/* estimate receiver position ------------------------------------------------*/
static int estpos(const obsd_t *obs, int n, const double *rs, const double *dts,
                  const double *vare, const int *svh, const nav_t *nav,
                  const prcopt_t *opt, const ssat_t *ssat, sol_t *sol, double *azel,
                  int *vsat, double *resp, char *msg)
{
    double x[NX]={0},dx[NX],Q[NX*NX],*v,*H,*var,sig;
    int i,j,k,info,stat,nv,ns;
    
    trace(3,"estpos  : n=%d\n",n);
    
    v=mat(n+4,1);
    H=mat(NX,n+4);
    var=mat(n+4,1);
    
    for (i=0;i<3;i++) x[i]=sol->rr[i];

    for (i=0;i<MAXITR;i++) {

        /* pseudorange residuals (m) */
        nv=rescode(i,obs,n,rs,dts,vare,svh,nav,x,opt,ssat,v,H,var,azel,vsat,resp,
                   &ns);
        
        if (nv<NX) {
            sprintf(msg,"lack of valid sats ns=%d",nv);
            break;
        }
        /* weight by variance (lsq uses sqrt of weight */
        for (j=0;j<nv;j++) {
            sig=sqrt(var[j]);
            v[j]/=sig;
            for (k=0;k<NX;k++) H[k+j*NX]/=sig;
        }
        /* least square estimation */
        if ((info=lsq(H,v,NX,nv,dx,Q))) {
            sprintf(msg,"lsq error info=%d",info);
            break;
        }
        for (j=0;j<NX;j++) {
            x[j]+=dx[j];
        }
        if (norm(dx,NX)<1E-4) {
            sol->type=0;
            sol->time=timeadd(obs[0].time,-x[3]/CLIGHT);
            sol->dtr[0]=x[3]/CLIGHT; /* receiver clock bias (s) */
            sol->dtr[1]=x[4]/CLIGHT; /* GLO-GPS time offset (s) */
            sol->dtr[2]=x[5]/CLIGHT; /* GAL-GPS time offset (s) */
            sol->dtr[3]=x[6]/CLIGHT; /* BDS-GPS time offset (s) */
            sol->dtr[4]=x[7]/CLIGHT; /* IRN-GPS time offset (s) */
            for (j=0;j<6;j++) sol->rr[j]=j<3?x[j]:0.0;
            for (j=0;j<3;j++) sol->qr[j]=(float)Q[j+j*NX];
            sol->qr[3]=(float)Q[1];    /* cov xy */
            sol->qr[4]=(float)Q[2+NX]; /* cov yz */
            sol->qr[5]=(float)Q[2];    /* cov zx */
            sol->ns=(uint8_t)ns;
            sol->age=sol->ratio=0.0;
            
            /* validate solution */
            if ((stat=valsol(azel,vsat,n,opt,v,nv,NX,msg))) {
                sol->stat=opt->sateph==EPHOPT_SBAS?SOLQ_SBAS:SOLQ_SINGLE;
            }
            free(v); free(H); free(var);
            return stat;
        }
    }
    if (i>=MAXITR) sprintf(msg,"iteration divergent i=%d",i);
    
    free(v); free(H); free(var);
    return 0;
}
/* RAIM FDE (failure detection and exclution) -------------------------------*/
static int raim_fde(const obsd_t *obs, int n, const double *rs,
                    const double *dts, const double *vare, const int *svh,
                    const nav_t *nav, const prcopt_t *opt, const ssat_t *ssat, 
                    sol_t *sol, double *azel, int *vsat, double *resp, char *msg)
{
    obsd_t *obs_e;
    sol_t sol_e={{0}};
    char tstr[32],name[16],msg_e[128];
    double *rs_e,*dts_e,*vare_e,*azel_e,*resp_e,rms_e,rms=100.0;
    int i,j,k,nvsat,stat=0,*svh_e,*vsat_e,sat=0;
    
    trace(3,"raim_fde: %s n=%2d\n",time_str(obs[0].time,0),n);
    
    if (!(obs_e=(obsd_t *)malloc(sizeof(obsd_t)*n))) return 0;
    rs_e = mat(6,n); dts_e = mat(2,n); vare_e=mat(1,n); azel_e=zeros(2,n);
    svh_e=imat(1,n); vsat_e=imat(1,n); resp_e=mat(1,n); 
    
    for (i=0;i<n;i++) {
        
        /* satellite exclusion */
        for (j=k=0;j<n;j++) {
            if (j==i) continue;
            obs_e[k]=obs[j];
            matcpy(rs_e +6*k,rs +6*j,6,1);
            matcpy(dts_e+2*k,dts+2*j,2,1);
            vare_e[k]=vare[j];
            svh_e[k++]=svh[j];
        }
        /* estimate receiver position without a satellite */
        if (!estpos(obs_e,n-1,rs_e,dts_e,vare_e,svh_e,nav,opt,ssat,&sol_e,azel_e,
                    vsat_e,resp_e,msg_e)) {
            trace(3,"raim_fde: exsat=%2d (%s)\n",obs[i].sat,msg);
            continue;
        }
        for (j=nvsat=0,rms_e=0.0;j<n-1;j++) {
            if (!vsat_e[j]) continue;
            rms_e+=SQR(resp_e[j]);
            nvsat++;
        }
        if (nvsat<5) {
            trace(3,"raim_fde: exsat=%2d lack of satellites nvsat=%2d\n",
                  obs[i].sat,nvsat);
            continue;
        }
        rms_e=sqrt(rms_e/nvsat);
        
        trace(3,"raim_fde: exsat=%2d rms=%8.3f\n",obs[i].sat,rms_e);
        
        if (rms_e>rms) continue;
        
        /* save result */
        for (j=k=0;j<n;j++) {
            if (j==i) continue;
            matcpy(azel+2*j,azel_e+2*k,2,1);
            vsat[j]=vsat_e[k];
            resp[j]=resp_e[k++];
        }
        stat=1;
        sol_e.eventime = sol->eventime;
        *sol=sol_e;
        sat=obs[i].sat;
        rms=rms_e;
        vsat[i]=0;
        strcpy(msg,msg_e);
    }
    if (stat) {
        time2str(obs[0].time,tstr,2); satno2id(sat,name);
        trace(2,"%s: %s excluded by raim\n",tstr+11,name);
    }
    free(obs_e);
    free(rs_e ); free(dts_e ); free(vare_e); free(azel_e);
    free(svh_e); free(vsat_e); free(resp_e);
    return stat;
}
/* range rate residuals ------------------------------------------------------*/
static int resdop(const obsd_t *obs, int n, const double *rs, const double *dts,
                  const nav_t *nav, const double *rr, const double *x,
                  const double *azel, const int *vsat, double err, double *v,
                  double *H)
{
    double freq,rate,pos[3],E[9],a[3],e[3],vs[3],cosel,sig;
    int i,j,nv=0;

    trace(3,"resdop  : n=%d\n",n);

    ecef2pos(rr,pos); xyz2enu(pos,E);

    for (i=0;i<n&&i<MAXOBS;i++) {

        freq=sat2freq(obs[i].sat,obs[i].code[0],nav);

        if (obs[i].D[0]==0.0||freq==0.0||!vsat[i]||norm(rs+3+i*6,3)<=0.0) {
            continue;
        }
        /* LOS (line-of-sight) vector in ECEF */
        cosel=cos(azel[1+i*2]);
        a[0]=sin(azel[i*2])*cosel;
        a[1]=cos(azel[i*2])*cosel;
        a[2]=sin(azel[1+i*2]);
        matmul("TN",3,1,3,1.0,E,a,0.0,e);

        /* satellite velocity relative to receiver in ECEF */
        for (j=0;j<3;j++) {
            vs[j]=rs[j+3+i*6]-x[j];
        }
        /* range rate with earth rotation correction */
        rate=dot(vs,e,3)+OMGE/CLIGHT*(rs[4+i*6]*rr[0]+rs[1+i*6]*x[0]-
                                      rs[3+i*6]*rr[1]-rs[  i*6]*x[1]);

        /* Std of range rate error (m/s) */
        sig=(err<=0.0)?1.0:err*CLIGHT/freq;

        /* range rate residual (m/s) */
        v[nv]=(obs[i].D[0]*CLIGHT/freq-(rate+x[3]-CLIGHT*dts[1+i*2]))/sig;

        /* design matrix */
        for (j=0;j<4;j++) {
            H[j+nv*4]=((j<3)?-e[j]:1.0)/sig;
        }
        nv++;
    }
    return nv;
}
/* estimate receiver velocity ------------------------------------------------*/
static void estvel(const obsd_t *obs, int n, const double *rs, const double *dts,
                   const nav_t *nav, const prcopt_t *opt, sol_t *sol,
                   const double *azel, const int *vsat)
{
    double x[4]={0},dx[4],Q[16],*v,*H;
    double err=opt->err[4]; /* Doppler error (Hz) */
    int i,j,nv;

    v=mat(n,1);
    H=mat(4,n);

    for (i=0;i<MAXITR;i++) {

        /* range rate residuals (m/s) */
        if ((nv=resdop(obs,n,rs,dts,nav,sol->rr,x,azel,vsat,err,v,H))<4) {
            break;
        }
        /* least square estimation */
        if (lsq(H,v,4,nv,dx,Q)) break;

        for (j=0;j<4;j++) x[j]+=dx[j];

        if (norm(dx,4)<1E-6) {
            trace(3,"estvel : vx=%.3f vy=%.3f vz=%.3f, n=%d\n",x[0],x[1],x[2],n);
            matcpy(sol->rr+3,x,3,1); /* velocity */
            sol->dtrr[0] = x[3];
            sol->qv[0]=(float)Q[0];  /* xx */
            sol->qv[1]=(float)Q[5];  /* yy */
            sol->qv[2]=(float)Q[10]; /* zz */
            sol->qv[3]=(float)Q[1];  /* xy */
            sol->qv[4]=(float)Q[6];  /* yz */
            sol->qv[5]=(float)Q[2];  /* zx */
            break;
        }
    }
    free(v);
    free(H);
}
/* single-point positioning ----------------------------------------------------
* compute receiver position, velocity, clock bias by single-point positioning
* with pseudorange and doppler observables
* args   : obsd_t *obs      I   observation data
*          int    n         I   number of observation data
*          nav_t  *nav      I   navigation data
*          prcopt_t *opt    I   processing options
*          sol_t  *sol      IO  solution
*          double *azel     IO  azimuth/elevation angle (rad) (NULL: no output)
*          ssat_t *ssat     IO  satellite status              (NULL: no output)
*          char   *msg      O   error message for error exit
* return : status(1:ok,0:error)
*-----------------------------------------------------------------------------*/
extern int pntpos(const obsd_t *obs, int n, const nav_t *nav,
                  const prcopt_t *opt, sol_t *sol, double *azel, ssat_t *ssat,
                  char *msg)
{
    prcopt_t opt_=*opt;
    double *rs,*dts,*var,*azel_,*resp;
    int i,stat,vsat[MAXOBS]={0},svh[MAXOBS];
    
    trace(3,"pntpos  : tobs=%s n=%d\n",time_str(obs[0].time,3),n);
    
    sol->stat=SOLQ_NONE;
    
    if (n<=0) {
        strcpy(msg,"no observation data");
        return 0;
    }
    sol->time=obs[0].time;
    msg[0]='\0';
    sol->eventime = obs[0].eventime;
    
    rs=mat(6,n); dts=mat(2,n); var=mat(1,n); azel_=zeros(2,n); resp=mat(1,n);
    
    if (ssat) {
        for (i=0;i<MAXSAT;i++) {
            ssat[i].snr_rover[0]=0;
            ssat[i].snr_base[0]=0;
        }
        for (i=0;i<n;i++)
            ssat[obs[i].sat-1].snr_rover[0]=obs[i].SNR[0];
    }
    
    if (opt_.mode!=PMODE_SINGLE) { /* for precise positioning */
        opt_.ionoopt=IONOOPT_BRDC;
        opt_.tropopt=TROPOPT_SAAS;
    }
    /* satellite positons, velocities and clocks */
    satposs(sol->time,obs,n,nav,opt_.sateph,rs,dts,var,svh);
    
    /* estimate receiver position and time with pseudorange */
    stat=estpos(obs,n,rs,dts,var,svh,nav,&opt_,ssat,sol,azel_,vsat,resp,msg);
    
    /* RAIM FDE */
    if (!stat&&n>=6&&opt->posopt[4]) {
        stat=raim_fde(obs,n,rs,dts,var,svh,nav,&opt_,ssat,sol,azel_,vsat,resp,msg);
    }
    /* estimate receiver velocity with Doppler */
    if (stat) {
        estvel(obs,n,rs,dts,nav,&opt_,sol,azel_,vsat);
    }
    if (azel) {
        for (i=0;i<n*2;i++) azel[i]=azel_[i];
    }
    if (ssat) {
        for (i=0;i<MAXSAT;i++) {
            ssat[i].vs=0;
            ssat[i].azel[0]=ssat[i].azel[1]=0.0;
            ssat[i].resp[0]=ssat[i].resc[0]=0.0;
        }
        for (i=0;i<n;i++) {
            ssat[obs[i].sat-1].azel[0]=azel_[  i*2];
            ssat[obs[i].sat-1].azel[1]=azel_[1+i*2];
            if (!vsat[i]) continue;
            ssat[obs[i].sat-1].vs=1;
            ssat[obs[i].sat-1].resp[0]=resp[i];
        }
    }
    free(rs); free(dts); free(var); free(azel_); free(resp);
    return stat;
}
/* validate solution for ins filter-------------------------------------------*/
static int valins(const double *azel, const int *vsat, int n,const prcopt_t *opt,
                  const double *v, int nv,const double *x,const double *R,
                  double thres,char *msg)
{
    const insopt_t *insopt=&opt->insopt;
    double azels[MAXOBS*2],dop[4],fact=SQR(thres);
    int i,ns,nba=0,iba=0,nbg=0,ibg=0;

    trace(3,"valins  : n=%d nv=%d\n",n,nv);

    nba=3; iba=9;
    nbg=3; ibg=12;

    /* check estimated states */
//    if (norm(x,3)>15.0*D2R||(nba?norm(x+iba,3)>1E4*Mg2M:false)
//        ||(nbg?norm(x+ibg,3)>5.0*D2R:false)) {
//        /* 输出 状态 */
//        trace(2,"%lf,%lf,%lf\n",norm(x,3),norm(x+iba,3),norm(x+ibg,3));
//        trace(2,"too large estimated state error\n");
//        return 0;
//    }
    /* post-fit residual test */
    for (i=0;i<nv;i++) {
        if (v[2*i]*v[2*i]<fact*R[2*i+2*i*2*nv]) continue;
        trace(2,"large residual (v=%6.3f sig=%.3f)\n",v[i],SQRT(R[2*i+2*i*2*nv]));
        return 0;
    }
    /* large gdop check */
//    for (i=ns=0;i<n;i++) {
//        if (!vsat[i]) continue;
//        azels[  ns*2]=azel[  i*2];
//        azels[1+ns*2]=azel[1+i*2];
//        ns++;
//    }
//    dops(ns,azels,opt->elmin,dop);
//    if (dop[0]<=0.0||dop[0]>opt->maxgdop) {
//        sprintf(msg,"gdop error nv=%d gdop=%.1f",nv,dop[0]);
//        return 0;
//    }
    return 1;
}

/* outlier -----------------------------------------------------
 * args:
 *         double *v    IO  residual vector
 *         int     n    I   number of states
 *         int     m    I   number of measurement
 *         double  *H   IO  design matirx
 *         double  *var IO  variance
 * -----------------------------------------------------------*/
static int outlier(double *v,int n, int m, double *H,double *var)
{
    double mean_psr=0.0,sigma_psr=0.0, mean_dp=0.0,sigma_dp=0.0;

    for(int i=0;i<m;i++) {
        mean_psr+=v[2*i];
        mean_dp+=v[2*i+1];
    }
    mean_psr/=m;
    mean_dp/=m;

    for(int i=0;i<m;i++) {
        sigma_psr+=(v[2*i]-mean_psr)*(v[2*i]-mean_psr);
        sigma_dp+=(v[2*i+1]-mean_dp)*(v[2*i+1]-mean_dp);
    }
    sigma_psr/=m;
    sigma_dp/=m;

    int k=0;
    for(int i=0;i<m;i++) {
        if((v[2*i]-mean_psr)<sqrt(sigma_psr)*3) {
            v[2*k]=v[2*i];
            v[2*k+1]=v[2*i+1];
            for(int j=0;j<n;j++) {
                H[j+2*k*n]=H[j+2*i*n];
                H[j+(2*k+1)*n]=H[j+(2*i+1)*n];
                var[2*k]=var[2*i];
                var[2*k+1]=var[2*i+1];
            }
            k++;
        }
    }
    return k;
}

/* iteration for tightly coupled ---------------------------------------------*/
static int itertc(const obsd_t *obs,int n,const double *rs,const double *dts,
                  const double *vare,const int *svh,const nav_t *nav,
                  const prcopt_t *opt,sol_t *sol,double *Pp,double *azel,ins_t *ins,
                  int *vsat,double *resp, char *msg,ssat_t *ssat)
{
    int nx,nv,ns,n_dtrr,stat=0,clk_index,ddtr_index;
    double *x,*R,*v,*H,*var;
    const insopt_t *insopt=&opt->insopt;
    static ins_t inss={0};
    trace(3,"estinspr:\n");

    nx = ins->nx;
    n_dtrr = 1;

    clk_index = 15;
    ddtr_index = 18;

    x = zeros(nx,1);
    R = zeros(2*n,2*n);
    H = zeros(nx, 2*n);
    v = zeros(2*n,1);
    var = mat(2*n,1);

    /* prefit residuals */
    nv = tc_rescode(1,obs,n,rs,dts,vare,svh,nav,x,opt,ssat,ins,v,H,var,azel,vsat,
                    resp,&ns);

    /* outlier */
    nv = outlier(v,nx,nv,H,var);

    for (int i=0;i<15;i++) {
        x[i]=1E-20;
    }
    /* tightly coupled */
    if(nv>=1){
//        matcpy(P,ins->P,nx,nx);
        trace(3,"P=\n");
        tracemat(3,Pp,nx,nx,15,10);
        trace(3,"H=\n");
        tracemat(3,H,nx,2*nv,15,6);

        /* measurement variance */
        for (int i=0;i<nv;i++) {
//            R[2*i+2*i*2*nv]= sqrt(var[2*i]);
//            R[(2*i+1)+(2*i+1)*2*nv]= SQR(var[(2*i+1)]);
            R[2*i+2*i*2*nv]=1.0;
            R[(2*i+1)+(2*i+1)*2*nv]=0.01;
        }
        trace(3,"R=\n");
        tracemat(3,R,2*nv,2*nv,15,6);

        /* ekf filter */
        stat=robust_filter(x,Pp,H,v,R,nx,2*nv);

        if(stat){
            trace(3,"ekf filter error info=%d\n",stat);
            stat=0;
        }
        else{
//            matcpy(ins->P0,Pp,nx,nx);

            /* correction for receiver clock */
            for (int i=0;i<3;i++) {
                ins->clk[i]=x[clk_index+i];
                ins->dtrr[i]=x[ddtr_index+i];
            }

            /* close loop */
            clp(ins,insopt,x);

            /* postfit residuals */
            nv = tc_rescode(1,obs,n,rs,dts,vare,svh,nav,x,opt,ssat,ins,v,H,var,azel,vsat,
                            resp,&ns);

            /* valid solutions */
            if(nv&&(stat=valins(azel,vsat,n,opt,v,nv,x,R,30.0,msg))){
                trace(3,"att and vel and pos and acc_bias %lf,%lf,%lf,%lf,%lf,%lf,%lf,%lf,%lf,%.15lf,%.15lf,%.15lf\n",x[0],x[1],x[2],x[3],x[4],x[5],x[6],x[7],x[8],x[9],x[10],x[11]);
                trace(3,"clk : %lf,%lf,%lf\n",ins->clk[0],ins->clk[1],ins->clk[2]);
                trace(3,"dtrr : %lf,%lf,%lf\n",ins->dtrr[0],ins->dtrr[1],ins->dtrr[2]);
                trace(3,"velocity: %lf，%lf,%lf\n", ins->velocity[0],ins->velocity[1],ins->velocity[2]);

                double rpy[3];
                getatt(ins,rpy);
                trace(3,"roll=%lf, pitch=%lf, yaw=%lf\n",rpy[0]*R2D,rpy[1]*R2D,rpy[2]*R2D);

                ins->ns=(unsigned char)ns;
                stat = 1;
                sol->stat=opt->sateph==EPHOPT_SBAS?SOLQ_SBAS:SOLQ_SINGLE;
                ins->gstat=opt->sateph==EPHOPT_SBAS?SOLQ_SBAS:SOLQ_SINGLE;
            }
            else {
                trace(2,"tightly coupled valid solutions fail\n");
                stat=0;
            }
        }
    }
    else {
        trace(2,"no observation data\n");
        stat=0;
    }
    free(v); free(H); free(var);
    free(x); free(R);
    return stat;
}

/* update ins states----------------------------------------------------------*/
static void updinsstate(const ins_t *insp,const double *Pp,ins_t *ins)
{

    matcpy(ins->p_position,ins->position,1,3);
    matcpy(ins->p_velocity,ins->velocity,1,3);
    /* update ins states if solution is ok */
    matcpy(ins->position ,insp->position ,1,3);
    matcpy(ins->velocity ,insp->velocity ,1,3);
    matcpy(ins->Cbe,insp->Cbe,3,3);
    /* no update ba/bg/Ma/Mg */
    matcpy(ins->acc_bias,insp->acc_bias,1,3);
    matcpy(ins->gyro_bias,insp->gyro_bias,1,3);

    matcpy(ins->P,Pp,ins->nx,ins->nx);

    for(int i=0;i<3;i++){
        ins->clk[i]=insp->clk[i];
        ins->dtrr[i]=insp->dtrr[i];
    }

    ins->ns=insp->ns;
    ins->gstat=insp->gstat;
}

/* ins estimate states by using pseudorange measurement-----------------------*/
static int est_ins_pr(const obsd_t *obs,int n,const double *rs,const double *dts,
                      const double *vare,const int *svh,const nav_t *nav,
                      const prcopt_t *opt,sol_t *sol,
                      ssat_t *ssat,
                      ins_t *ins,
                      double *azel,
                      int *vsat,double *resp, char *msg)
{
    static ins_t insp={0};
    double *Pp;
    int i,nx=ins->nx,info=1;

    trace(3,"estinspr: time=%lf n=%d\n",ins->time,n);

    Pp=mat(ins->nx,ins->nx);
    insp=*ins;

    for (i=0;i<1;i++) {
        matcpy(Pp,ins->P,nx,nx);
        /* iteration for tightly coupled */
        info&=itertc(obs,n,rs,dts,vare,svh,nav,opt,sol,Pp,azel,&insp,vsat,resp,msg,ssat);
        if (!info) {
            trace(2,"iteration for tightly coupled fail\n");
            break;
        }
    }
    if (info) {
//        sol->stat=(unsigned char)ins->gstat;
        updinsstate(&insp,Pp,ins);
    }
    free(Pp);
    return info;
}
/* single-point positioning/TC coupled ----------------------------------------------------
* compute receiver position, velocity, clock bias by single-point positioning
* with pseudorange and doppler observables
* args   : obsd_t *obs          I   observation data
*          int      n           I   number of observation data
*          nav_t    *nav        I   navigation data
*          prcopt_t *opt        I   processing options
*          sol_t    *sol        IO  solution
*          ins_t    *ins        IO  ins state
*          double   *azel       IO  azimuth/elevation angle (rad) (NULL: no output)
*          ssat_t   *ssat       IO  satellite status              (NULL: no output)
*          char     *msg        O   error message for error exit
* return : status(1:ok,0:error)
*-----------------------------------------------------------------------------*/
extern int tc_pntpos(const obsd_t *obs, int n, const nav_t *nav,
                  const prcopt_t *opt, sol_t *sol, ins_t *ins,double *azel, ssat_t *ssat,
                  char *msg)
{
    prcopt_t opt_=*opt;
    double *rs,*dts,*var,*azel_,*resp;
    int i,stat,stat2,vsat[MAXOBS]={0},svh[MAXOBS];
    int tc=0;

    trace(3,"pntpos  : tobs=%s n=%d\n",time_str(obs[0].time,3),n);

    sol->stat=SOLQ_NONE;
    tc = opt_.mode==PMODE_INS_TGNSS&&opt_.insopt.tc>=INSTC_SINGLE&&ins;

    if (n<=0) {
        strcpy(msg,"no observation data");
        return 0;
    }
    sol->time=obs[0].time;
    msg[0]='\0';
    sol->eventime = obs[0].eventime;

    rs=mat(6,n);
    dts=mat(2,n);
    var=mat(1,n);
    azel_=zeros(2,n);
    resp=mat(1,2*n);

    if (ssat) {
        for (i=0;i<MAXSAT;i++) {
            ssat[i].snr_rover[0]=0;
            ssat[i].snr_base[0]=0;
        }
        for (i=0;i<n;i++){
            ssat[obs[i].sat-1].snr_rover[0]=obs[i].SNR[0];
        }
    }

    if (opt_.mode!=PMODE_SINGLE) { /* for precise positioning */
        opt_.ionoopt=IONOOPT_BRDC;
        opt_.tropopt=TROPOPT_SAAS;
    }
    /* satellite positons, velocities and clocks */
    satposs(sol->time,obs,n,nav,opt_.sateph,rs,dts,var,svh);

    if(tc){
        /* tightly coupled */
        stat=est_ins_pr(obs,n,rs,dts,var,svh,nav,&opt_,
                      sol,ssat,ins,azel_,vsat,resp,msg);
    }
    else{
        /* estimate receiver position and time with pseudorange */
        stat=estpos(obs,n,rs,dts,var,svh,nav,&opt_,ssat,sol,azel_,vsat,resp,msg);
    }

    /* RAIM FDE */
    if (!stat&&n>=6&&opt->posopt[4]) {
        stat=raim_fde(obs,n,rs,dts,var,svh,nav,&opt_,ssat,sol,azel_,vsat,resp,msg);
    }
    /* estimate receiver velocity with Doppler */
    if (stat&&!tc) {
        estvel(obs,n,rs,dts,nav,&opt_,sol,azel_,vsat);
    }
    if (azel) {
        for (i=0;i<n*2;i++) azel[i]=azel_[i];
    }
    if (ssat) {
        for (i=0;i<MAXSAT;i++) {
            ssat[i].vs=0;
            ssat[i].azel[0]=ssat[i].azel[1]=0.0;
            ssat[i].resp[0]=ssat[i].resc[0]=0.0;
        }
        for (i=0;i<n;i++) {
            ssat[obs[i].sat-1].azel[0]=azel_[  i*2];
            ssat[obs[i].sat-1].azel[1]=azel_[1+i*2];
            if (!vsat[i]) continue;
            ssat[obs[i].sat-1].vs=1;
            ssat[obs[i].sat-1].resp[0]=resp[i];
        }
    }
    free(rs); free(dts); free(var); free(azel_); free(resp);
    return stat;
}