rtkpos.c

/*------------------------------------------------------------------------------
* rtkpos.c : precise positioning
*
*          Copyright (C) 2007-2018 by T.TAKASU, All rights reserved.
*
* version : $Revision: 1.1 $ $Date: 2008/07/17 21:48:06 $
* history : 2007/01/12 1.0  new
*           2007/03/13 1.1  add slip detection by LLI flag
*           2007/04/18 1.2  add antenna pcv correction
*                           change rtkpos argin
*           2008/07/18 1.3  refactored
*           2009/01/02 1.4  modify rtk positioning api
*           2009/03/09 1.5  support glonass, gallileo and qzs
*           2009/08/27 1.6  fix bug on numerical exception
*           2009/09/03 1.7  add check of valid satellite number
*                           add check time sync for moving-base
*           2009/11/23 1.8  add api rtkopenstat(),rtkclosestat()
*                           add receiver h/w bias estimation
*                           add solution status output
*           2010/04/04 1.9  support ppp-kinematic and ppp-static modes
*                           support earth tide correction
*                           changed api:
*                               rtkpos()
*           2010/09/07 1.10 add elevation mask to hold ambiguity
*           2012/02/01 1.11 add extended receiver error model
*                           add glonass interchannel bias correction
*                           add slip detectior by L1-L5 gf jump
*                           output snr of rover receiver in residuals
*           2013/03/10 1.12 add otl and pole tides corrections
*           2014/05/26 1.13 support beidou and galileo
*                           add output of gal-gps and bds-gps time offset
*           2014/05/28 1.14 fix bug on memory exception with many sys and freq
*           2014/08/26 1.15 add functino to swap sol-stat file with keywords
*           2014/10/21 1.16 fix bug on beidou amb-res with pos2-bdsarmode=0
*           2014/11/08 1.17 fix bug on ar-degradation by unhealthy satellites
*           2015/03/23 1.18 residuals referenced to reference satellite
*           2018/01/29 1.19 unfix ambiguity between gps and qzss
*-----------------------------------------------------------------------------*/
#include <stdarg.h>
#include "rtklib.h"

static const char rcsid[]="$Id:$";

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

#define SQR(x)      ((x)*(x))
#define SQRT(x)     ((x)<=0.0?0.0:sqrt(x))
#define MIN(x,y)    ((x)<=(y)?(x):(y))
#define ROUND(x)    (int)floor((x)+0.5)

#define VAR_POS     SQR(30.0) /* initial variance of receiver pos (m^2) */
#define VAR_VEL     SQR(10.0) /* initial variance of receiver vel ((m/s)^2) */
#define VAR_ACC     SQR(10.0) /* initial variance of receiver acc ((m/ss)^2) */
#define VAR_HWBIAS  SQR(1.0)  /* initial variance of h/w bias ((m/MHz)^2) */
#define VAR_GRA     SQR(0.001) /* initial variance of gradient (m^2) */
#define INIT_ZWD    0.15     /* initial zwd (m) */

#define PRN_HWBIAS  1E-6     /* process noise of h/w bias (m/MHz/sqrt(s)) */
#define GAP_RESION  120      /* gap to reset ionosphere parameters (epochs) */
#define MAXACC      30.0     /* max accel for doppler slip detection (m/s^2) */

#define VAR_HOLDAMB 0.001    /* constraint to hold ambiguity (cycle^2) */

#define TTOL_MOVEB  (1.0+2*DTTOL)
                             /* time sync tolerance for moving-baseline (s) */

/* number of parameters (pos,ionos,tropos,hw-bias,phase-bias,real,estimated) */
#define NF(opt)     ((opt)->ionoopt==IONOOPT_IFLC?1:(opt)->nf)
#define NP(opt)     ((opt)->dynamics==0?3:9)
#define NI(opt)     ((opt)->ionoopt!=IONOOPT_EST?0:MAXSAT)
#define NT(opt)     ((opt)->tropopt<TROPOPT_EST?0:((opt)->tropopt<TROPOPT_ESTG?2:6))
#define NL(opt)     ((opt)->glomodear!=2?0:NFREQGLO)
#define NB(opt)     ((opt)->mode<=PMODE_DGPS?0:MAXSAT*NF(opt))
#define NR(opt)     (NP(opt)+NI(opt)+NT(opt)+NL(opt))
#define NX(opt)     (NR(opt)+NB(opt))

/* state variable index */
#define II(s,opt)   (NP(opt)+(s)-1)                 /* ionos (s:satellite no) */
#define IT(r,opt)   (NP(opt)+NI(opt)+NT(opt)/2*(r)) /* tropos (r:0=rov,1:ref) */
#define IL(f,opt)   (NP(opt)+NI(opt)+NT(opt)+(f))   /* receiver h/w bias */
#define IB(s,f,opt) (NR(opt)+MAXSAT*(f)+(s)-1) /* phase bias (s:satno,f:freq) */

#ifdef EXTGSI

extern int resamb_WLNL(rtk_t *rtk, const obsd_t *obs, const int *sat,
                       const int *iu, const int *ir, int ns, const nav_t *nav,
                       const double *azel);
extern int resamb_TCAR(rtk_t *rtk, const obsd_t *obs, const int *sat,
                       const int *iu, const int *ir, int ns, const nav_t *nav,
                       const double *azel);
#else

extern int resamb_WLNL(rtk_t *rtk, const obsd_t *obs, const int *sat,
                       const int *iu, const int *ir, int ns, const nav_t *nav,
                       const double *azel) {return 0;}
extern int resamb_TCAR(rtk_t *rtk, const obsd_t *obs, const int *sat,
                       const int *iu, const int *ir, int ns, const nav_t *nav,
                       const double *azel) {return 0;}
#endif

/* global variables ----------------------------------------------------------*/
static int statlevel=0;          /* rtk status output level (0:off) */
static FILE *fp_stat=NULL;       /* rtk status file pointer */
static char file_stat[1024]="";  /* rtk status file original path */
static gtime_t time_stat={0};    /* rtk status file time */

/* open solution status file ---------------------------------------------------
* open solution status file and set output level
* args   : char     *file   I   rtk status file
*          int      level   I   rtk status level (0: off)
* return : status (1:ok,0:error)
* notes  : file can constain time keywords (%Y,%y,%m...) defined in reppath().
*          The time to replace keywords is based on UTC of CPU time.
* output : solution status file record format
*
*   $POS,week,tow,stat,posx,posy,posz,posxf,posyf,poszf
*          week/tow : gps week no/time of week (s)
*          stat     : solution status
*          posx/posy/posz    : position x/y/z ecef (m) float
*          posxf/posyf/poszf : position x/y/z ecef (m) fixed
*
*   $VELACC,week,tow,stat,vele,veln,velu,acce,accn,accu,velef,velnf,veluf,accef,accnf,accuf
*          week/tow : gps week no/time of week (s)
*          stat     : solution status
*          vele/veln/velu    : velocity e/n/u (m/s) float
*          acce/accn/accu    : acceleration e/n/u (m/s^2) float
*          velef/velnf/veluf : velocity e/n/u (m/s) fixed
*          accef/accnf/accuf : acceleration e/n/u (m/s^2) fixed
*
*   $CLK,week,tow,stat,clk1,clk2,clk3,clk4
*          week/tow : gps week no/time of week (s)
*          stat     : solution status
*          clk1     : receiver clock bias GPS (ns)
*          clk2     : receiver clock bias GLO-GPS (ns)
*          clk3     : receiver clock bias GAL-GPS (ns)
*          clk4     : receiver clock bias BDS-GPS (ns)
*
*   $ION,week,tow,stat,sat,az,el,ion,ion-fixed
*          week/tow : gps week no/time of week (s)
*          stat     : solution status
*          sat      : satellite id
*          az/el    : azimuth/elevation angle(deg)
*          ion      : vertical ionospheric delay L1 (m) float
*          ion-fixed: vertical ionospheric delay L1 (m) fixed
*
*   $TROP,week,tow,stat,rcv,ztd,ztdf
*          week/tow : gps week no/time of week (s)
*          stat     : solution status
*          rcv      : receiver (1:rover,2:base station)
*          ztd      : zenith total delay (m) float
*          ztdf     : zenith total delay (m) fixed
*
*   $HWBIAS,week,tow,stat,frq,bias,biasf
*          week/tow : gps week no/time of week (s)
*          stat     : solution status
*          frq      : frequency (1:L1,2:L2,...)
*          bias     : h/w bias coefficient (m/MHz) float
*          biasf    : h/w bias coefficient (m/MHz) fixed
*
*   $SAT,week,tow,sat,frq,az,el,resp,resc,vsat,snr,fix,slip,lock,outc,slipc,rejc
*          week/tow : gps week no/time of week (s)
*          sat/frq  : satellite id/frequency (1:L1,2:L2,...)
*          az/el    : azimuth/elevation angle (deg)
*          resp     : pseudorange residual (m)
*          resc     : carrier-phase residual (m)
*          vsat     : valid data flag (0:invalid,1:valid)
*          snr      : signal strength (dbHz)
*          fix      : ambiguity flag  (0:no data,1:float,2:fixed,3:hold,4:ppp)
*          slip     : cycle-slip flag (bit1:slip,bit2:parity unknown)
*          lock     : carrier-lock count
*          outc     : data outage count
*          slipc    : cycle-slip count
*          rejc     : data reject (outlier) count
*
*-----------------------------------------------------------------------------*/
extern int rtkopenstat(const char *file, int level)
{
    gtime_t time=utc2gpst(timeget());
    char path[1024];
    
    trace(3,"rtkopenstat: file=%s level=%d\n",file,level);
    
    if (level<=0) return 0;
    
    reppath(file,path,time,"","");
    
    if (!(fp_stat=fopen(path,"w"))) {
        trace(1,"rtkopenstat: file open error path=%s\n",path);
        return 0;
    }
    strcpy(file_stat,file);
    time_stat=time;
    statlevel=level;
    return 1;
}
/* close solution status file --------------------------------------------------
* close solution status file
* args   : none
* return : none
*-----------------------------------------------------------------------------*/
extern void rtkclosestat(void)
{
    trace(3,"rtkclosestat:\n");
    
    if (fp_stat) fclose(fp_stat);
    fp_stat=NULL;
    file_stat[0]='\0';
    statlevel=0;
}
/* swap solution status file -------------------------------------------------*/
static void swapsolstat(void)
{
    gtime_t time=utc2gpst(timeget());
    char path[1024];
    
    if ((int)(time2gpst(time     ,NULL)/INT_SWAP_STAT)==
        (int)(time2gpst(time_stat,NULL)/INT_SWAP_STAT)) {
        return;
    }
    time_stat=time;
    
    if (!reppath(file_stat,path,time,"","")) {
        return;
    }
    if (fp_stat) fclose(fp_stat);
    
    if (!(fp_stat=fopen(path,"w"))) {
        trace(2,"swapsolstat: file open error path=%s\n",path);
        return;
    }
    trace(3,"swapsolstat: path=%s\n",path);
}
/* output solution status ----------------------------------------------------*/
static void outsolstat(rtk_t *rtk)
{
    ssat_t *ssat;
    double tow,pos[3],vel[3],acc[3],vela[3]={0},acca[3]={0},xa[3];
    int i,j,week,est,nfreq,nf=NF(&rtk->opt);
    char id[32];
    
    if (statlevel<=0||!fp_stat) return;
    
    trace(3,"outsolstat:\n");
    
    /* swap solution status file */
    swapsolstat();
    
    est=rtk->opt.mode>=PMODE_DGPS;
    nfreq=est?nf:1;
    tow=time2gpst(rtk->sol.time,&week);
    
    /* receiver position */
    if (est) {
        for (i=0;i<3;i++) xa[i]=i<rtk->na?rtk->xa[i]:0.0;
        fprintf(fp_stat,"$POS,%d,%.3f,%d,%.4f,%.4f,%.4f,%.4f,%.4f,%.4f\n",week,tow,
                rtk->sol.stat,rtk->x[0],rtk->x[1],rtk->x[2],xa[0],xa[1],xa[2]);
    }
    else {
        fprintf(fp_stat,"$POS,%d,%.3f,%d,%.4f,%.4f,%.4f,%.4f,%.4f,%.4f\n",week,tow,
                rtk->sol.stat,rtk->sol.rr[0],rtk->sol.rr[1],rtk->sol.rr[2],
                0.0,0.0,0.0);
    }
    /* receiver velocity and acceleration */
    if (est&&rtk->opt.dynamics) {
        ecef2pos(rtk->sol.rr,pos);
        ecef2enu(pos,rtk->x+3,vel);
        ecef2enu(pos,rtk->x+6,acc);
        if (rtk->na>=6) ecef2enu(pos,rtk->xa+3,vela);
        if (rtk->na>=9) ecef2enu(pos,rtk->xa+6,acca);
        fprintf(fp_stat,"$VELACC,%d,%.3f,%d,%.4f,%.4f,%.4f,%.5f,%.5f,%.5f,%.4f,%.4f,%.4f,%.5f,%.5f,%.5f\n",
                week,tow,rtk->sol.stat,vel[0],vel[1],vel[2],acc[0],acc[1],acc[2],
                vela[0],vela[1],vela[2],acca[0],acca[1],acca[2]);
    }
    else {
        ecef2pos(rtk->sol.rr,pos);
        ecef2enu(pos,rtk->sol.rr+3,vel);
        fprintf(fp_stat,"$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],
                0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0,0.0);
    }
    /* receiver clocks */
    fprintf(fp_stat,"$CLK,%d,%.3f,%d,%d,%.3f,%.3f,%.3f,%.3f\n",
            week,tow,rtk->sol.stat,1,rtk->sol.dtr[0]*1E9,rtk->sol.dtr[1]*1E9,
            rtk->sol.dtr[2]*1E9,rtk->sol.dtr[3]*1E9);
    
    /* ionospheric parameters */
    if (est&&rtk->opt.ionoopt==IONOOPT_EST) {
        for (i=0;i<MAXSAT;i++) {
            ssat=rtk->ssat+i;
            if (!ssat->vs) continue;
            satno2id(i+1,id);
            j=II(i+1,&rtk->opt);
            xa[0]=j<rtk->na?rtk->xa[j]:0.0;
            fprintf(fp_stat,"$ION,%d,%.3f,%d,%s,%.1f,%.1f,%.4f,%.4f\n",week,tow,rtk->sol.stat,
                    id,ssat->azel[0]*R2D,ssat->azel[1]*R2D,rtk->x[j],xa[0]);
        }
    }
    /* tropospheric parameters */
    if (est&&(rtk->opt.tropopt==TROPOPT_EST||rtk->opt.tropopt==TROPOPT_ESTG)) {
        for (i=0;i<2;i++) {
            j=IT(i,&rtk->opt);
            xa[0]=j<rtk->na?rtk->xa[j]:0.0;
            fprintf(fp_stat,"$TROP,%d,%.3f,%d,%d,%.4f,%.4f\n",week,tow,rtk->sol.stat,
                    i+1,rtk->x[j],xa[0]);
        }
    }
    /* receiver h/w bias */
    if (est&&rtk->opt.glomodear==2) {
        for (i=0;i<nfreq;i++) {
            j=IL(i,&rtk->opt);
            xa[0]=j<rtk->na?rtk->xa[j]:0.0;
            fprintf(fp_stat,"$HWBIAS,%d,%.3f,%d,%d,%.4f,%.4f\n",week,tow,rtk->sol.stat,
                    i+1,rtk->x[j],xa[0]);
        }
    }
    if (rtk->sol.stat==SOLQ_NONE||statlevel<=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_stat,"$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]);
        }
    }
}
/* save error message --------------------------------------------------------*/
static void errmsg(rtk_t *rtk, const char *format, ...)
{
    char buff[256],tstr[32];
    int n;
    va_list ap;
    time2str(rtk->sol.time,tstr,2);
    n=sprintf(buff,"%s: ",tstr+11);
    va_start(ap,format);
    n+=vsprintf(buff+n,format,ap);
    va_end(ap);
    n=n<MAXERRMSG-rtk->neb?n:MAXERRMSG-rtk->neb;
    memcpy(rtk->errbuf+rtk->neb,buff,n);
    rtk->neb+=n;
    trace(2,"%s",buff);
}
/* single-differenced observable ---------------------------------------------*/
static double sdobs(const obsd_t *obs, int i, int j, int f)
{
    double pi=f<NFREQ?obs[i].L[f]:obs[i].P[f-NFREQ];
    double pj=f<NFREQ?obs[j].L[f]:obs[j].P[f-NFREQ];
    return pi==0.0||pj==0.0?0.0:pi-pj;
}
/* single-differenced geometry-free linear combination of phase --------------*/
static double gfobs_L1L2(const obsd_t *obs, int i, int j, const double *lam)
{
    double pi=sdobs(obs,i,j,0)*lam[0],pj=sdobs(obs,i,j,1)*lam[1];
    return pi==0.0||pj==0.0?0.0:pi-pj;
}
static double gfobs_L1L5(const obsd_t *obs, int i, int j, const double *lam)
{
    double pi=sdobs(obs,i,j,0)*lam[0],pj=sdobs(obs,i,j,2)*lam[2];
    return pi==0.0||pj==0.0?0.0:pi-pj;
}
/* single-differenced measurement error variance -----------------------------*/
static double varerr(int sat, int sys, double el, double bl, double dt, int f,
                     const prcopt_t *opt)
{
    double a,b,c=opt->err[3]*bl/1E4,d=CLIGHT*opt->sclkstab*dt,fact=1.0;
    double sinel=sin(el);
    int i=sys==SYS_GLO?1:(sys==SYS_GAL?2:0),nf=NF(opt);
    
    /* extended error model */
    if (f>=nf&&opt->exterr.ena[0]) { /* code */
        a=opt->exterr.cerr[i][  (f-nf)*2];
        b=opt->exterr.cerr[i][1+(f-nf)*2];
        if (sys==SYS_SBS) {a*=EFACT_SBS; b*=EFACT_SBS;}
    }
    else if (f<nf&&opt->exterr.ena[1]) { /* phase */
        a=opt->exterr.perr[i][  f*2];
        b=opt->exterr.perr[i][1+f*2];
        if (sys==SYS_SBS) {a*=EFACT_SBS; b*=EFACT_SBS;}
    }
    else { /* normal error model */
        if (f>=nf) fact=opt->eratio[f-nf];
        if (fact<=0.0)  fact=opt->eratio[0];
        fact*=sys==SYS_GLO?EFACT_GLO:(sys==SYS_SBS?EFACT_SBS:EFACT_GPS);
        a=fact*opt->err[1];
        b=fact*opt->err[2];
    }
    return 2.0*(opt->ionoopt==IONOOPT_IFLC?3.0:1.0)*(a*a+b*b/sinel/sinel+c*c)+d*d;
}
/* baseline length -----------------------------------------------------------*/
static double baseline(const double *ru, const double *rb, double *dr)
{
    int i;
    for (i=0;i<3;i++) dr[i]=ru[i]-rb[i];
    return norm(dr,3);
}
/* 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;
    }
}
/* select common satellites between rover and reference station --------------*/
static int selsat(const obsd_t *obs, double *azel, int nu, int nr,
                  const prcopt_t *opt, int *sat, int *iu, int *ir)
{
    int i,j,k=0;
    
    trace(3,"selsat  : nu=%d nr=%d\n",nu,nr);
    
    for (i=0,j=nu;i<nu&&j<nu+nr;i++,j++) {
        if      (obs[i].sat<obs[j].sat) j--;
        else if (obs[i].sat>obs[j].sat) i--;
        else if (azel[1+j*2]>=opt->elmin) { /* elevation at base station */
            sat[k]=obs[i].sat; iu[k]=i; ir[k++]=j;
            trace(4,"(%2d) sat=%3d iu=%2d ir=%2d\n",k-1,obs[i].sat,i,j);
        }
    }
    return k;
}
/* temporal update of position/velocity/acceleration -------------------------*/
static void udpos(rtk_t *rtk, double tt)
{
    double *F,*FP,*xp,pos[3],Q[9]={0},Qv[9],var=0.0;
    int i,j;
    
    trace(3,"udpos   : tt=%.3f\n",tt);
    
    /* fixed mode */
    if (rtk->opt.mode==PMODE_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);
        if (rtk->opt.dynamics) {
            for (i=3;i<6;i++) initx(rtk,rtk->sol.rr[i],VAR_VEL,i);
            for (i=6;i<9;i++) initx(rtk,1E-6,VAR_ACC,i);
        }
    }
    /* static mode */
    if (rtk->opt.mode==PMODE_STATIC) return;
    
    /* kinmatic mode without dynamics */
    if (!rtk->opt.dynamics) {
        for (i=0;i<3;i++) initx(rtk,rtk->sol.rr[i],VAR_POS,i);
        return;
    }
    /* check variance of estimated postion */
    for (i=0;i<3;i++) var+=rtk->P[i+i*rtk->nx]; var/=3.0;
    
    if (var>VAR_POS) {
        /* reset position with large variance */
        for (i=0;i<3;i++) initx(rtk,rtk->sol.rr[i],VAR_POS,i);
        for (i=3;i<6;i++) initx(rtk,rtk->sol.rr[i],VAR_VEL,i);
        for (i=6;i<9;i++) initx(rtk,1E-6,VAR_ACC,i);
        trace(2,"reset rtk position due to large variance: var=%.3f\n",var);
        return;
    }
    /* state transition of position/velocity/acceleration */
    F=eye(rtk->nx); FP=mat(rtk->nx,rtk->nx); xp=mat(rtk->nx,1);
    
    for (i=0;i<6;i++) {
        F[i+(i+3)*rtk->nx]=tt;
    }
    /* x=F*x, P=F*P*F+Q */
    matmul("NN",rtk->nx,1,rtk->nx,1.0,F,rtk->x,0.0,xp);
    matcpy(rtk->x,xp,rtk->nx,1);
    matmul("NN",rtk->nx,rtk->nx,rtk->nx,1.0,F,rtk->P,0.0,FP);
    matmul("NT",rtk->nx,rtk->nx,rtk->nx,1.0,FP,F,0.0,rtk->P);
    
    /* process noise added to only acceleration */
    Q[0]=Q[4]=SQR(rtk->opt.prn[3]); Q[8]=SQR(rtk->opt.prn[4]);
    ecef2pos(rtk->x,pos);
    covecef(pos,Q,Qv);
    for (i=0;i<3;i++) for (j=0;j<3;j++) {
        rtk->P[i+6+(j+6)*rtk->nx]+=Qv[i+j*3];
    }
    free(F); free(FP); free(xp);
}
/* temporal update of ionospheric parameters ---------------------------------*/
static void udion(rtk_t *rtk, double tt, double bl, const int *sat, int ns)
{
    double el,fact;
    int i,j;
    
    trace(3,"udion   : tt=%.1f bl=%.0f ns=%d\n",tt,bl,ns);
    
    for (i=1;i<=MAXSAT;i++) {
        j=II(i,&rtk->opt);
        if (rtk->x[j]!=0.0&&
            rtk->ssat[i-1].outc[0]>GAP_RESION&&rtk->ssat[i-1].outc[1]>GAP_RESION)
            rtk->x[j]=0.0;
    }
    for (i=0;i<ns;i++) {
        j=II(sat[i],&rtk->opt);
        
        if (rtk->x[j]==0.0) {
            initx(rtk,1E-6,SQR(rtk->opt.std[1]*bl/1E4),j);
        }
        else {
            /* elevation dependent factor of process noise */
            el=rtk->ssat[sat[i]-1].azel[1];
            fact=cos(el);
            rtk->P[j+j*rtk->nx]+=SQR(rtk->opt.prn[1]*bl/1E4*fact)*tt;
        }
    }
}
/* temporal update of tropospheric parameters --------------------------------*/
static void udtrop(rtk_t *rtk, double tt, double bl)
{
    int i,j,k;
    
    trace(3,"udtrop  : tt=%.1f\n",tt);
    
    for (i=0;i<2;i++) {
        j=IT(i,&rtk->opt);
        
        if (rtk->x[j]==0.0) {
            initx(rtk,INIT_ZWD,SQR(rtk->opt.std[2]),j); /* initial zwd */
            
            if (rtk->opt.tropopt>=TROPOPT_ESTG) {
                for (k=0;k<2;k++) initx(rtk,1E-6,VAR_GRA,++j);
            }
        }
        else {
            rtk->P[j+j*rtk->nx]+=SQR(rtk->opt.prn[2])*tt;
            
            if (rtk->opt.tropopt>=TROPOPT_ESTG) {
                for (k=0;k<2;k++) {
                    rtk->P[++j*(1+rtk->nx)]+=SQR(rtk->opt.prn[2]*0.3)*fabs(rtk->tt);
                }
            }
        }
    }
}
/* temporal update of receiver h/w biases ------------------------------------*/
static void udrcvbias(rtk_t *rtk, double tt)
{
    int i,j;
    
    trace(3,"udrcvbias: tt=%.1f\n",tt);
    
    for (i=0;i<NFREQGLO;i++) {
        j=IL(i,&rtk->opt);
        
        if (rtk->x[j]==0.0) {
            initx(rtk,1E-6,VAR_HWBIAS,j);
        }
        /* hold to fixed solution */
        else if (rtk->nfix>=rtk->opt.minfix&&rtk->sol.ratio>rtk->opt.thresar[0]) {
            initx(rtk,rtk->xa[j],rtk->Pa[j+j*rtk->na],j);
        }
        else {
            rtk->P[j+j*rtk->nx]+=SQR(PRN_HWBIAS)*tt;
        }
    }
}
/* detect cycle slip by LLI --------------------------------------------------*/
static void detslp_ll(rtk_t *rtk, const obsd_t *obs, int i, int rcv)
{
    unsigned char slip,LLI1,LLI2,LLI;
    int f,sat=obs[i].sat;
    
    trace(3,"detslp_ll: i=%d rcv=%d\n",i,rcv);
    
    for (f=0;f<rtk->opt.nf;f++) {
        
        if (obs[i].L[f]==0.0) continue;
        
        /* restore previous LLI */
        LLI1=(rtk->ssat[sat-1].slip[f]>>6)&3;
        LLI2=(rtk->ssat[sat-1].slip[f]>>4)&3;
        LLI=rcv==1?LLI1:LLI2;
        
        /* detect slip by cycle slip flag */
        slip=(rtk->ssat[sat-1].slip[f]|obs[i].LLI[f])&3;
        
        if (obs[i].LLI[f]&1) {
            errmsg(rtk,"slip detected (sat=%2d rcv=%d LLI%d=%x)\n",
                   sat,rcv,f+1,obs[i].LLI[f]);
        }
        /* detect slip by parity unknown flag transition */
        if (((LLI&2)&&!(obs[i].LLI[f]&2))||(!(LLI&2)&&(obs[i].LLI[f]&2))) {
            errmsg(rtk,"slip detected (sat=%2d rcv=%d LLI%d=%x->%x)\n",
                   sat,rcv,f+1,LLI,obs[i].LLI[f]);
            slip|=1;
        }
        /* save current LLI and slip flag */
        if (rcv==1) rtk->ssat[sat-1].slip[f]=(obs[i].LLI[f]<<6)|(LLI2<<4)|slip;
        else        rtk->ssat[sat-1].slip[f]=(obs[i].LLI[f]<<4)|(LLI1<<6)|slip;
    }
}
/* detect cycle slip by L1-L2 geometry free phase jump -----------------------*/
static void detslp_gf_L1L2(rtk_t *rtk, const obsd_t *obs, int i, int j,
                           const nav_t *nav)
{
    int sat=obs[i].sat;
    double g0,g1;
    
    trace(3,"detslp_gf_L1L2: i=%d j=%d\n",i,j);
    
    if (rtk->opt.nf<=1||(g1=gfobs_L1L2(obs,i,j,nav->lam[sat-1]))==0.0) return;
    
    g0=rtk->ssat[sat-1].gf; rtk->ssat[sat-1].gf=g1;
        
    if (g0!=0.0&&fabs(g1-g0)>rtk->opt.thresslip) {
        
        rtk->ssat[sat-1].slip[0]|=1;
        rtk->ssat[sat-1].slip[1]|=1;
        
        errmsg(rtk,"slip detected (sat=%2d GF_L1_L2=%.3f %.3f)\n",sat,g0,g1);
    }
}
/* detect cycle slip by L1-L5 geometry free phase jump -----------------------*/
static void detslp_gf_L1L5(rtk_t *rtk, const obsd_t *obs, int i, int j,
                           const nav_t *nav)
{
    int sat=obs[i].sat;
    double g0,g1;
    
    trace(3,"detslp_gf_L1L5: i=%d j=%d\n",i,j);
    
    if (rtk->opt.nf<=2||(g1=gfobs_L1L5(obs,i,j,nav->lam[sat-1]))==0.0) return;
    
    g0=rtk->ssat[sat-1].gf2; rtk->ssat[sat-1].gf2=g1;
        
    if (g0!=0.0&&fabs(g1-g0)>rtk->opt.thresslip) {
        
        rtk->ssat[sat-1].slip[0]|=1;
        rtk->ssat[sat-1].slip[2]|=1;
        
        errmsg(rtk,"slip detected (sat=%2d GF_L1_L5=%.3f %.3f)\n",sat,g0,g1);
    }
}
/* detect cycle slip by doppler and phase difference -------------------------*/
static void detslp_dop(rtk_t *rtk, const obsd_t *obs, int i, int rcv,
                       const nav_t *nav)
{
    /* detection with doppler disabled because of clock-jump issue (v.2.3.0) */
#if 0
    int f,sat=obs[i].sat;
    double tt,dph,dpt,lam,thres;
    
    trace(3,"detslp_dop: i=%d rcv=%d\n",i,rcv);
    
    for (f=0;f<rtk->opt.nf;f++) {
        if (obs[i].L[f]==0.0||obs[i].D[f]==0.0||rtk->ph[rcv-1][sat-1][f]==0.0) {
            continue;
        }
        if (fabs(tt=timediff(obs[i].time,rtk->pt[rcv-1][sat-1][f]))<DTTOL) continue;
        if ((lam=nav->lam[sat-1][f])<=0.0) continue;
        
        /* cycle slip threshold (cycle) */
        thres=MAXACC*tt*tt/2.0/lam+rtk->opt.err[4]*fabs(tt)*4.0;
        
        /* phase difference and doppler x time (cycle) */
        dph=obs[i].L[f]-rtk->ph[rcv-1][sat-1][f];
        dpt=-obs[i].D[f]*tt;
        
        if (fabs(dph-dpt)<=thres) continue;
        
        rtk->slip[sat-1][f]|=1;
        
        errmsg(rtk,"slip detected (sat=%2d rcv=%d L%d=%.3f %.3f thres=%.3f)\n",
               sat,rcv,f+1,dph,dpt,thres);
    }
#endif
}
/* temporal update of phase biases -------------------------------------------*/
static void udbias(rtk_t *rtk, double tt, const obsd_t *obs, const int *sat,
                   const int *iu, const int *ir, int ns, const nav_t *nav)
{
    double cp,pr,cp1,cp2,pr1,pr2,*bias,offset,lami,lam1,lam2,C1,C2;
    int i,j,f,slip,reset,nf=NF(&rtk->opt);
    
    trace(3,"udbias  : tt=%.1f ns=%d\n",tt,ns);
    
    for (i=0;i<ns;i++) {
        
        /* detect cycle slip by LLI */
        for (f=0;f<rtk->opt.nf;f++) rtk->ssat[sat[i]-1].slip[f]&=0xFC;
        detslp_ll(rtk,obs,iu[i],1);
        detslp_ll(rtk,obs,ir[i],2);
        
        /* detect cycle slip by geometry-free phase jump */
        detslp_gf_L1L2(rtk,obs,iu[i],ir[i],nav);
        detslp_gf_L1L5(rtk,obs,iu[i],ir[i],nav);
        
        /* detect cycle slip by doppler and phase difference */
        detslp_dop(rtk,obs,iu[i],1,nav);
        detslp_dop(rtk,obs,ir[i],2,nav);
    }
    for (f=0;f<nf;f++) {
        /* reset phase-bias if instantaneous AR or expire obs outage counter */
        for (i=1;i<=MAXSAT;i++) {
            
            reset=++rtk->ssat[i-1].outc[f]>(unsigned int)rtk->opt.maxout;
            
            if (rtk->opt.modear==ARMODE_INST&&rtk->x[IB(i,f,&rtk->opt)]!=0.0) {
                initx(rtk,0.0,0.0,IB(i,f,&rtk->opt));
            }
            else if (reset&&rtk->x[IB(i,f,&rtk->opt)]!=0.0) {
                initx(rtk,0.0,0.0,IB(i,f,&rtk->opt));
                trace(3,"udbias : obs outage counter overflow (sat=%3d L%d n=%d)\n",
                      i,f+1,rtk->ssat[i-1].outc[f]);
            }
            if (rtk->opt.modear!=ARMODE_INST&&reset) {
                rtk->ssat[i-1].lock[f]=-rtk->opt.minlock;
            }
        }
        /* reset phase-bias if detecting cycle slip */
        for (i=0;i<ns;i++) {
            j=IB(sat[i],f,&rtk->opt);
            rtk->P[j+j*rtk->nx]+=rtk->opt.prn[0]*rtk->opt.prn[0]*tt;
            slip=rtk->ssat[sat[i]-1].slip[f];
            if (rtk->opt.ionoopt==IONOOPT_IFLC) slip|=rtk->ssat[sat[i]-1].slip[1];
            if (rtk->opt.modear==ARMODE_INST||!(slip&1)) continue;
            rtk->x[j]=0.0;
            rtk->ssat[sat[i]-1].lock[f]=-rtk->opt.minlock;
        }
        bias=zeros(ns,1);
        
        /* estimate approximate phase-bias by phase - code */
        for (i=j=0,offset=0.0;i<ns;i++) {
            
            if (rtk->opt.ionoopt!=IONOOPT_IFLC) {
                cp=sdobs(obs,iu[i],ir[i],f); /* cycle */
                pr=sdobs(obs,iu[i],ir[i],f+NFREQ);
                lami=nav->lam[sat[i]-1][f];
                if (cp==0.0||pr==0.0||lami<=0.0) continue;
                
                bias[i]=cp-pr/lami;
            }
            else {
                cp1=sdobs(obs,iu[i],ir[i],0);
                cp2=sdobs(obs,iu[i],ir[i],1);
                pr1=sdobs(obs,iu[i],ir[i],NFREQ);
                pr2=sdobs(obs,iu[i],ir[i],NFREQ+1);
                lam1=nav->lam[sat[i]-1][0];
                lam2=nav->lam[sat[i]-1][1];
                if (cp1==0.0||cp2==0.0||pr1==0.0||pr2==0.0||lam1<=0.0||lam2<=0.0) continue;
                
                C1= SQR(lam2)/(SQR(lam2)-SQR(lam1));
                C2=-SQR(lam1)/(SQR(lam2)-SQR(lam1));
                bias[i]=(C1*lam1*cp1+C2*lam2*cp2)-(C1*pr1+C2*pr2);
            }
            if (rtk->x[IB(sat[i],f,&rtk->opt)]!=0.0) {
                offset+=bias[i]-rtk->x[IB(sat[i],f,&rtk->opt)];
                j++;
            }
        }
        /* correct phase-bias offset to enssure phase-code coherency */
        if (j>0) {
            for (i=1;i<=MAXSAT;i++) {
                if (rtk->x[IB(i,f,&rtk->opt)]!=0.0) rtk->x[IB(i,f,&rtk->opt)]+=offset/j;
            }
        }
        /* set initial states of phase-bias */
        for (i=0;i<ns;i++) {
            if (bias[i]==0.0||rtk->x[IB(sat[i],f,&rtk->opt)]!=0.0) continue;
            initx(rtk,bias[i],SQR(rtk->opt.std[0]),IB(sat[i],f,&rtk->opt));
        }
        free(bias);
    }
}
/* temporal update of states --------------------------------------------------*/
static void udstate(rtk_t *rtk, const obsd_t *obs, const int *sat,
                    const int *iu, const int *ir, int ns, const nav_t *nav)
{
    double tt=fabs(rtk->tt),bl,dr[3];
    
    trace(3,"udstate : ns=%d\n",ns);
    
    /* temporal update of position/velocity/acceleration */
    udpos(rtk,tt);
    
    /* temporal update of ionospheric parameters */
    if (rtk->opt.ionoopt>=IONOOPT_EST) {
        bl=baseline(rtk->x,rtk->rb,dr);
        udion(rtk,tt,bl,sat,ns);
    }
    /* temporal update of tropospheric parameters */
    if (rtk->opt.tropopt>=TROPOPT_EST) {
        udtrop(rtk,tt,bl);
    }
    /* temporal update of eceiver h/w bias */
    if (rtk->opt.glomodear==2&&(rtk->opt.navsys&SYS_GLO)) {
        udrcvbias(rtk,tt);
    }
    /* temporal update of phase-bias */
    if (rtk->opt.mode>PMODE_DGPS) {
        udbias(rtk,tt,obs,sat,iu,ir,ns,nav);
    }
}
/* undifferenced phase/code residual for satellite ---------------------------*/
static void zdres_sat(int base, double r, const obsd_t *obs, const nav_t *nav,
                      const double *azel, const double *dant,
                      const prcopt_t *opt, double *y)
{
    const double *lam=nav->lam[obs->sat-1];
    double f1,f2,C1,C2,dant_if;
    int i,nf=NF(opt);
    
    if (opt->ionoopt==IONOOPT_IFLC) { /* iono-free linear combination */
        if (lam[0]==0.0||lam[1]==0.0) return;
        
        if (testsnr(base,0,azel[1],obs->SNR[0]*0.25,&opt->snrmask)||
            testsnr(base,1,azel[1],obs->SNR[1]*0.25,&opt->snrmask)) return;
        
        f1=CLIGHT/lam[0];
        f2=CLIGHT/lam[1];
        C1= SQR(f1)/(SQR(f1)-SQR(f2));
        C2=-SQR(f2)/(SQR(f1)-SQR(f2));
        dant_if=C1*dant[0]+C2*dant[1];
        
        if (obs->L[0]!=0.0&&obs->L[1]!=0.0) {
            y[0]=C1*obs->L[0]*lam[0]+C2*obs->L[1]*lam[1]-r-dant_if;
        }
        if (obs->P[0]!=0.0&&obs->P[1]!=0.0) {
            y[1]=C1*obs->P[0]+C2*obs->P[1]-r-dant_if;
        }
    }
    else {
        for (i=0;i<nf;i++) {
            if (lam[i]==0.0) continue;
            
            /* check snr mask */
            if (testsnr(base,i,azel[1],obs->SNR[i]*0.25,&opt->snrmask)) {
                continue;
            }
            /* residuals = observable - pseudorange */
            if (obs->L[i]!=0.0) y[i   ]=obs->L[i]*lam[i]-r-dant[i];
            if (obs->P[i]!=0.0) y[i+nf]=obs->P[i]       -r-dant[i];
        }
    }
}
/* undifferenced phase/code residuals ----------------------------------------*/
static int zdres(int base, const obsd_t *obs, int n, const double *rs,
                 const double *dts, const int *svh, const nav_t *nav,
                 const double *rr, const prcopt_t *opt, int index, double *y,
                 double *e, double *azel)
{
    double r,rr_[3],pos[3],dant[NFREQ]={0},disp[3];
    double zhd,zazel[]={0.0,90.0*D2R};
    int i,nf=NF(opt),sys,sva=-1;

    eph_t *eph;
    
    trace(3,"zdres   : n=%d\n",n);
    
    for (i=0;i<n*nf*2;i++) y[i]=0.0;
    
    if (norm(rr,3)<=0.0) return 0; /* no receiver position */
    
    for (i=0;i<3;i++) rr_[i]=rr[i];
    
    /* earth tide correction */
    if (opt->tidecorr) {
        tidedisp(gpst2utc(obs[0].time),rr_,opt->tidecorr,&nav->erp,
                 opt->odisp[base],disp);
        for (i=0;i<3;i++) rr_[i]+=disp[i];
    }
    ecef2pos(rr_,pos);
    
    for (i=0;i<n;i++) {
        /* compute geometric-range and azimuth/elevation angle */
        if ((r=geodist(rs+i*6,rr_,e+i*3))<=0.0) continue;
        if (satazel(pos,e+i*3,azel+i*2)<opt->elmin) continue;
        
        /* if Gal satellite, check SISA is not NAPA*/
        if (!(sys=satsys(obs[i].sat,NULL))) continue;
        if (sys==SYS_GAL){
        	if (!(eph=seleph(obs[i].time,obs[i].sat,-1,nav))) continue;
        	sva = eph->sva;
        }
        /* excluded satellite? */
        if (satexclude(obs[i].sat,svh[i],sva,opt)) continue;
        
        /* satellite clock-bias */
        r+=-CLIGHT*dts[i*2];
        
        /* troposphere delay model (hydrostatic) */
        zhd=tropmodel(obs[0].time,pos,zazel,0.0);
        r+=tropmapf(obs[i].time,pos,azel+i*2,NULL)*zhd;
        
        /* receiver antenna phase center correction */
        antmodel(opt->pcvr+index,opt->antdel[index],azel+i*2,opt->posopt[1],
                 dant);
        
        /* undifferenced phase/code residual for satellite */
        zdres_sat(base,r,obs+i,nav,azel+i*2,dant,opt,y+i*nf*2);
    }
    trace(4,"rr_=%.3f %.3f %.3f\n",rr_[0],rr_[1],rr_[2]);
    trace(4,"pos=%.9f %.9f %.3f\n",pos[0]*R2D,pos[1]*R2D,pos[2]);
    for (i=0;i<n;i++) {
        trace(4,"sat=%2d %13.3f %13.3f %13.3f %13.10f %6.1f %5.1f\n",
              obs[i].sat,rs[i*6],rs[1+i*6],rs[2+i*6],dts[i*2],azel[i*2]*R2D,
              azel[1+i*2]*R2D);
    }
    trace(4,"y=\n"); tracemat(4,y,nf*2,n,13,3);
    
    return 1;
}
/* test valid observation data -----------------------------------------------*/
static int validobs(int i, int j, int f, int nf, double *y)
{
    /* if no phase observable, psudorange is also unusable */
    return y[f+i*nf*2]!=0.0&&y[f+j*nf*2]!=0.0&&
           (f<nf||(y[f-nf+i*nf*2]!=0.0&&y[f-nf+j*nf*2]!=0.0));
}
/* double-differenced measurement error covariance ---------------------------*/
static void ddcov(const int *nb, int n, const double *Ri, const double *Rj,
                  int nv, double *R)
{
    int i,j,k=0,b;
    
    trace(3,"ddcov   : n=%d\n",n);
    
    for (i=0;i<nv*nv;i++) R[i]=0.0;
    for (b=0;b<n;k+=nb[b++]) {
        
        for (i=0;i<nb[b];i++) for (j=0;j<nb[b];j++) {
            R[k+i+(k+j)*nv]=Ri[k+i]+(i==j?Rj[k+i]:0.0);
        }
    }
    trace(5,"R=\n"); tracemat(5,R,nv,nv,8,6);
}
/* baseline length constraint ------------------------------------------------*/
static int constbl(rtk_t *rtk, const double *x, const double *P, double *v,
                   double *H, double *Ri, double *Rj, int index)
{
    const double thres=0.1; /* threshold for nonliearity (v.2.3.0) */
    double xb[3],b[3],bb,var=0.0;
    int i;
     
    trace(3,"constbl : \n");
    
    /* no constraint */
    if (rtk->opt.baseline[0]<=0.0) return 0;
    
    /* time-adjusted baseline vector and length */
    for (i=0;i<3;i++) {
        xb[i]=rtk->rb[i]+rtk->rb[i+3]*rtk->sol.age;
        b[i]=x[i]-xb[i];
    }
    bb=norm(b,3);
    
    /* approximate variance of solution */
    if (P) {
        for (i=0;i<3;i++) var+=P[i+i*rtk->nx];
        var/=3.0;
    }
    /* check nonlinearity */
    if (var>thres*thres*bb*bb) {
        trace(3,"constbl : equation nonlinear (bb=%.3f var=%.3f)\n",bb,var);
        return 0;
    }
    /* constraint to baseline length */
    v[index]=rtk->opt.baseline[0]-bb;
    if (H) {
        for (i=0;i<3;i++) H[i+index*rtk->nx]=b[i]/bb;
    }
    Ri[index]=0.0;
    Rj[index]=SQR(rtk->opt.baseline[1]);
    
    trace(4,"baseline len   v=%13.3f R=%8.6f %8.6f\n",v[index],Ri[index],Rj[index]);
    
    return 1;
}
/* precise tropspheric model -------------------------------------------------*/
static double prectrop(gtime_t time, const double *pos, int r,
                       const double *azel, const prcopt_t *opt, const double *x,
                       double *dtdx)
{
    double m_w=0.0,cotz,grad_n,grad_e;
    int i=IT(r,opt);
    
    /* wet mapping function */
    tropmapf(time,pos,azel,&m_w);
    
    if (opt->tropopt>=TROPOPT_ESTG&&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[i+1]+grad_e*x[i+2];
        dtdx[1]=grad_n*x[i];
        dtdx[2]=grad_e*x[i];
    }
    else dtdx[1]=dtdx[2]=0.0;
    dtdx[0]=m_w;
    return m_w*x[i];
}
/* glonass inter-channel bias correction -------------------------------------*/
static double gloicbcorr(int sat1, int sat2, const prcopt_t *opt, double lam1,
                         double lam2, int f)
{
    double dfreq;
    
    if (f>=NFREQGLO||f>=opt->nf||!opt->exterr.ena[2]) return 0.0;
    
    dfreq=(CLIGHT/lam1-CLIGHT/lam2)/(f==0?DFRQ1_GLO:DFRQ2_GLO);
    
    return opt->exterr.gloicb[f]*0.01*dfreq; /* (m) */
}
/* test navi system (m=0:gps/sbs,1:glo,2:gal,3:bds,4:qzs) --------------------*/
static int test_sys(int sys, int m)
{
    switch (sys) {
        case SYS_GPS: return m==0;
        case SYS_QZS: return m==4;
        case SYS_SBS: return m==0;
        case SYS_GLO: return m==1;
        case SYS_GAL: return m==2;
        case SYS_CMP: return m==3;
    }
    return 0;
}
/* double-differenced phase/code residuals -----------------------------------*/
static int ddres(rtk_t *rtk, const nav_t *nav, double dt, const double *x,
                 const double *P, const int *sat, double *y, double *e,
                 double *azel, const int *iu, const int *ir, int ns, double *v,
                 double *H, double *R, int *vflg)
{
    prcopt_t *opt=&rtk->opt;
    double bl,dr[3],posu[3],posr[3],didxi=0.0,didxj=0.0,*im;
    double *tropr,*tropu,*dtdxr,*dtdxu,*Ri,*Rj,lami,lamj,fi,fj,df,*Hi=NULL;
    int i,j,k,m,f,ff,nv=0,nb[NFREQ*4*2+2]={0},b=0,sysi,sysj,nf=NF(opt);
    
    trace(3,"ddres   : dt=%.1f nx=%d ns=%d\n",dt,rtk->nx,ns);
    
    bl=baseline(x,rtk->rb,dr);
    ecef2pos(x,posu); ecef2pos(rtk->rb,posr);
    
    Ri=mat(ns*nf*2+2,1); Rj=mat(ns*nf*2+2,1); im=mat(ns,1);
    tropu=mat(ns,1); tropr=mat(ns,1); dtdxu=mat(ns,3); dtdxr=mat(ns,3);
    
    for (i=0;i<MAXSAT;i++) for (j=0;j<NFREQ;j++) {
        rtk->ssat[i].resp[j]=rtk->ssat[i].resc[j]=0.0;
    }
    /* compute factors of ionospheric and tropospheric delay */
    for (i=0;i<ns;i++) {
        if (opt->ionoopt>=IONOOPT_EST) {
            im[i]=(ionmapf(posu,azel+iu[i]*2)+ionmapf(posr,azel+ir[i]*2))/2.0;
        }
        if (opt->tropopt>=TROPOPT_EST) {
            tropu[i]=prectrop(rtk->sol.time,posu,0,azel+iu[i]*2,opt,x,dtdxu+i*3);
            tropr[i]=prectrop(rtk->sol.time,posr,1,azel+ir[i]*2,opt,x,dtdxr+i*3);
        }
    }
    for (m=0;m<5;m++) /* m=0:gps/sbs,1:glo,2:gal,3:bds,4:qzs */
    
    for (f=opt->mode>PMODE_DGPS?0:nf;f<nf*2;f++) {
        
        /* search reference satellite with highest elevation */
        for (i=-1,j=0;j<ns;j++) {
            sysi=rtk->ssat[sat[j]-1].sys;
            if (!test_sys(sysi,m)) continue;
            if (!validobs(iu[j],ir[j],f,nf,y)) continue;
            if (i<0||azel[1+iu[j]*2]>=azel[1+iu[i]*2]) i=j;
        }
        if (i<0) continue;
        
        /* make double difference */
        for (j=0;j<ns;j++) {
            if (i==j) continue;
            sysi=rtk->ssat[sat[i]-1].sys;
            sysj=rtk->ssat[sat[j]-1].sys;
            if (!test_sys(sysj,m)) continue;
            if (!validobs(iu[j],ir[j],f,nf,y)) continue;
            
            ff=f%nf;
            lami=nav->lam[sat[i]-1][ff];
            lamj=nav->lam[sat[j]-1][ff];
            if (lami<=0.0||lamj<=0.0) continue;
            if (H) Hi=H+nv*rtk->nx;
            
            /* double-differenced residual */
            v[nv]=(y[f+iu[i]*nf*2]-y[f+ir[i]*nf*2])-
                  (y[f+iu[j]*nf*2]-y[f+ir[j]*nf*2]);
            
            /* partial derivatives by rover position */
            if (H) {
                for (k=0;k<3;k++) {
                    Hi[k]=-e[k+iu[i]*3]+e[k+iu[j]*3];
                }
            }
            /* double-differenced ionospheric delay term */
            if (opt->ionoopt==IONOOPT_EST) {
                fi=lami/lam_carr[0]; fj=lamj/lam_carr[0];
                didxi=(f<nf?-1.0:1.0)*fi*fi*im[i];
                didxj=(f<nf?-1.0:1.0)*fj*fj*im[j];
                v[nv]-=didxi*x[II(sat[i],opt)]-didxj*x[II(sat[j],opt)];
                if (H) {
                    Hi[II(sat[i],opt)]= didxi;
                    Hi[II(sat[j],opt)]=-didxj;
                }
            }
            /* double-differenced tropospheric delay term */
            if (opt->tropopt==TROPOPT_EST||opt->tropopt==TROPOPT_ESTG) {
                v[nv]-=(tropu[i]-tropu[j])-(tropr[i]-tropr[j]);
                for (k=0;k<(opt->tropopt<TROPOPT_ESTG?1:3);k++) {
                    if (!H) continue;
                    Hi[IT(0,opt)+k]= (dtdxu[k+i*3]-dtdxu[k+j*3]);
                    Hi[IT(1,opt)+k]=-(dtdxr[k+i*3]-dtdxr[k+j*3]);
                }
            }
            /* double-differenced phase-bias term */
            if (f<nf) {
                if (opt->ionoopt!=IONOOPT_IFLC) {
                    v[nv]-=lami*x[IB(sat[i],f,opt)]-lamj*x[IB(sat[j],f,opt)];
                    if (H) {
                        Hi[IB(sat[i],f,opt)]= lami;
                        Hi[IB(sat[j],f,opt)]=-lamj;
                    }
                }
                else {
                    v[nv]-=x[IB(sat[i],f,opt)]-x[IB(sat[j],f,opt)];
                    if (H) {
                        Hi[IB(sat[i],f,opt)]= 1.0;
                        Hi[IB(sat[j],f,opt)]=-1.0;
                    }
                }
            }
            /* glonass receiver h/w bias term */
            if (rtk->opt.glomodear==2&&sysi==SYS_GLO&&sysj==SYS_GLO&&ff<NFREQGLO) {
                df=(CLIGHT/lami-CLIGHT/lamj)/1E6; /* freq-difference (MHz) */
                v[nv]-=df*x[IL(ff,opt)];
                if (H) Hi[IL(ff,opt)]=df;
            }
            /* glonass interchannel bias correction */
            else if (sysi==SYS_GLO&&sysj==SYS_GLO) {
                
                v[nv]-=gloicbcorr(sat[i],sat[j],&rtk->opt,lami,lamj,f);
            }
            if (f<nf) rtk->ssat[sat[j]-1].resc[f   ]=v[nv];
            else      rtk->ssat[sat[j]-1].resp[f-nf]=v[nv];
            
            /* test innovation */
            if (opt->maxinno>0.0&&fabs(v[nv])>opt->maxinno) {
                if (f<nf) {
                    rtk->ssat[sat[i]-1].rejc[f]++;
                    rtk->ssat[sat[j]-1].rejc[f]++;
                }
                errmsg(rtk,"outlier rejected (sat=%3d-%3d %s%d v=%.3f)\n",
                       sat[i],sat[j],f<nf?"L":"P",f%nf+1,v[nv]);
                continue;
            }
            /* single-differenced measurement error variances */
            Ri[nv]=varerr(sat[i],sysi,azel[1+iu[i]*2],bl,dt,f,opt);
            Rj[nv]=varerr(sat[j],sysj,azel[1+iu[j]*2],bl,dt,f,opt);
            
            /* set valid data flags */
            if (opt->mode>PMODE_DGPS) {
                if (f<nf) rtk->ssat[sat[i]-1].vsat[f]=rtk->ssat[sat[j]-1].vsat[f]=1;
            }
            else {
                rtk->ssat[sat[i]-1].vsat[f-nf]=rtk->ssat[sat[j]-1].vsat[f-nf]=1;
            }
            trace(4,"sat=%3d-%3d %s%d v=%13.3f R=%8.6f %8.6f\n",sat[i],
                  sat[j],f<nf?"L":"P",f%nf+1,v[nv],Ri[nv],Rj[nv]);
            
            vflg[nv++]=(sat[i]<<16)|(sat[j]<<8)|((f<nf?0:1)<<4)|(f%nf);
            nb[b]++;
        }
#if 0 /* residuals referenced to reference satellite (2.4.2 p11) */
        /* restore single-differenced residuals assuming sum equal zero */
        if (f<nf) {
            for (j=0,s=0.0;j<MAXSAT;j++) s+=rtk->ssat[j].resc[f];
            s/=nb[b]+1;
            for (j=0;j<MAXSAT;j++) {
                if (j==sat[i]-1||rtk->ssat[j].resc[f]!=0.0) rtk->ssat[j].resc[f]-=s;
            }
        }
        else {
            for (j=0,s=0.0;j<MAXSAT;j++) s+=rtk->ssat[j].resp[f-nf];
            s/=nb[b]+1;
            for (j=0;j<MAXSAT;j++) {
                if (j==sat[i]-1||rtk->ssat[j].resp[f-nf]!=0.0)
                    rtk->ssat[j].resp[f-nf]-=s;
            }
        }
#endif
        b++;
    }
    /* end of system loop */
    
    /* baseline length constraint for moving baseline */
    if (opt->mode==PMODE_MOVEB&&constbl(rtk,x,P,v,H,Ri,Rj,nv)) {
        vflg[nv++]=3<<4;
        nb[b++]++;
    }
    if (H) {trace(5,"H=\n"); tracemat(5,H,rtk->nx,nv,7,4);}
    
    /* double-differenced measurement error covariance */
    ddcov(nb,b,Ri,Rj,nv,R);
    
    free(Ri); free(Rj); free(im);
    free(tropu); free(tropr); free(dtdxu); free(dtdxr);
    
    return nv;
}
/* time-interpolation of residuals (for post-mission) ------------------------*/
static double intpres(gtime_t time, const obsd_t *obs, int n, const nav_t *nav,
                      rtk_t *rtk, double *y)
{
    static obsd_t obsb[MAXOBS];
    static double yb[MAXOBS*NFREQ*2],rs[MAXOBS*6],dts[MAXOBS*2],var[MAXOBS];
    static double e[MAXOBS*3],azel[MAXOBS*2];
    static int nb=0,svh[MAXOBS*2];
    prcopt_t *opt=&rtk->opt;
    double tt=timediff(time,obs[0].time),ttb,*p,*q;
    int i,j,k,nf=NF(opt);
    
    trace(3,"intpres : n=%d tt=%.1f\n",n,tt);
    
    if (nb==0||fabs(tt)<DTTOL) {
        nb=n; for (i=0;i<n;i++) obsb[i]=obs[i];
        return tt;
    }
    ttb=timediff(time,obsb[0].time);
    if (fabs(ttb)>opt->maxtdiff*2.0||ttb==tt) return tt;
    
    satposs(time,obsb,nb,nav,opt->sateph,rs,dts,var,svh);
    
    if (!zdres(1,obsb,nb,rs,dts,svh,nav,rtk->rb,opt,1,yb,e,azel)) {
        return tt;
    }
    for (i=0;i<n;i++) {
        for (j=0;j<nb;j++) if (obsb[j].sat==obs[i].sat) break;
        if (j>=nb) continue;
        for (k=0,p=y+i*nf*2,q=yb+j*nf*2;k<nf*2;k++,p++,q++) {
            if (*p==0.0||*q==0.0) *p=0.0; else *p=(ttb*(*p)-tt*(*q))/(ttb-tt);
        }
    }
    return fabs(ttb)>fabs(tt)?ttb:tt;
}
/* single to double-difference transformation matrix (D') --------------------*/
static int ddmat(rtk_t *rtk, double *D)
{
    int i,j,k,m,f,nb=0,nx=rtk->nx,na=rtk->na,nf=NF(&rtk->opt);
    
    trace(3,"ddmat   :\n");
    
    for (i=0;i<MAXSAT;i++) for (j=0;j<NFREQ;j++) {
        rtk->ssat[i].fix[j]=0;
    }
    for (i=0;i<na;i++) D[i+i*nx]=1.0;
    
    for (m=0;m<5;m++) { /* m=0:gps/sbs,1:glo,2:gal,3:bds,4:qzs */
        
        if (m==1&&rtk->opt.glomodear==0) continue;
        if (m==3&&rtk->opt.bdsmodear==0) continue;
        
        for (f=0,k=na;f<nf;f++,k+=MAXSAT) {
            
            for (i=k;i<k+MAXSAT;i++) {
                if (rtk->x[i]==0.0||!test_sys(rtk->ssat[i-k].sys,m)||
                    !rtk->ssat[i-k].vsat[f]) {
                    continue;
                }
                if (rtk->ssat[i-k].lock[f]>0&&!(rtk->ssat[i-k].slip[f]&2)&&
                    rtk->ssat[i-k].azel[1]>=rtk->opt.elmaskar) {
                    rtk->ssat[i-k].fix[f]=2; /* fix */
                    break;
                }
                else rtk->ssat[i-k].fix[f]=1;
            }
            for (j=k;j<k+MAXSAT;j++) {
                if (i==j||rtk->x[j]==0.0||!test_sys(rtk->ssat[j-k].sys,m)||
                    !rtk->ssat[j-k].vsat[f]) {
                    continue;
                }
                if (rtk->ssat[j-k].lock[f]>0&&!(rtk->ssat[j-k].slip[f]&2)&&
                    rtk->ssat[i-k].vsat[f]&&
                    rtk->ssat[j-k].azel[1]>=rtk->opt.elmaskar) {
                    D[i+(na+nb)*nx]= 1.0;
                    D[j+(na+nb)*nx]=-1.0;
                    nb++;
                    rtk->ssat[j-k].fix[f]=2; /* fix */
                }
                else rtk->ssat[j-k].fix[f]=1;
            }
        }
    }
    trace(5,"D=\n"); tracemat(5,D,nx,na+nb,2,0);
    return nb;
}
/* restore single-differenced ambiguity --------------------------------------*/
static void restamb(rtk_t *rtk, const double *bias, int nb, double *xa)
{
    int i,n,m,f,index[MAXSAT],nv=0,nf=NF(&rtk->opt);
    
    trace(3,"restamb :\n");
    
    for (i=0;i<rtk->nx;i++) xa[i]=rtk->x [i];
    for (i=0;i<rtk->na;i++) xa[i]=rtk->xa[i];
    
    for (m=0;m<5;m++) for (f=0;f<nf;f++) {
        
        for (n=i=0;i<MAXSAT;i++) {
            if (!test_sys(rtk->ssat[i].sys,m)||rtk->ssat[i].fix[f]!=2) {
                continue;
            }
            index[n++]=IB(i+1,f,&rtk->opt);
        }
        if (n<2) continue;
        
        xa[index[0]]=rtk->x[index[0]];
        
        for (i=1;i<n;i++) {
            xa[index[i]]=xa[index[0]]-bias[nv++];
        }
    }
}
/* hold integer ambiguity ----------------------------------------------------*/
static void holdamb(rtk_t *rtk, const double *xa)
{
    double *v,*H,*R;
    int i,n,m,f,info,index[MAXSAT],nb=rtk->nx-rtk->na,nv=0,nf=NF(&rtk->opt);
    
    trace(3,"holdamb :\n");
    
    v=mat(nb,1); H=zeros(nb,rtk->nx);
    
    for (m=0;m<5;m++) for (f=0;f<nf;f++) {
        
        for (n=i=0;i<MAXSAT;i++) {
            if (!test_sys(rtk->ssat[i].sys,m)||rtk->ssat[i].fix[f]!=2||
                rtk->ssat[i].azel[1]<rtk->opt.elmaskhold) {
                continue;
            }
            index[n++]=IB(i+1,f,&rtk->opt);
            rtk->ssat[i].fix[f]=3; /* hold */
        }
        /* constraint to fixed ambiguity */
        for (i=1;i<n;i++) {
            v[nv]=(xa[index[0]]-xa[index[i]])-(rtk->x[index[0]]-rtk->x[index[i]]);
            
            H[index[0]+nv*rtk->nx]= 1.0;
            H[index[i]+nv*rtk->nx]=-1.0;
            nv++;
        }
    }
    if (nv>0) {
        R=zeros(nv,nv);
        for (i=0;i<nv;i++) R[i+i*nv]=VAR_HOLDAMB;
        
        /* update states with constraints */
        if ((info=filter(rtk->x,rtk->P,H,v,R,rtk->nx,nv))) {
            errmsg(rtk,"filter error (info=%d)\n",info);
        }
        free(R);
    }
    free(v); free(H);
}
/* resolve integer ambiguity by LAMBDA ---------------------------------------*/
static int resamb_LAMBDA(rtk_t *rtk, double *bias, double *xa)
{
    prcopt_t *opt=&rtk->opt;
    int i,j,ny,nb,info,nx=rtk->nx,na=rtk->na;
    double *D,*DP,*y,*Qy,*b,*db,*Qb,*Qab,*QQ,s[2];
    
    trace(3,"resamb_LAMBDA : nx=%d\n",nx);
    
    rtk->sol.ratio=0.0;
    
    if (rtk->opt.mode<=PMODE_DGPS||rtk->opt.modear==ARMODE_OFF||
        rtk->opt.thresar[0]<1.0) {
        return 0;
    }
    /* single to double-difference transformation matrix (D') */
    D=zeros(nx,nx);
    if ((nb=ddmat(rtk,D))<=0) {
        errmsg(rtk,"no valid double-difference\n");
        free(D);
        return 0;
    }
    ny=na+nb; y=mat(ny,1); Qy=mat(ny,ny); DP=mat(ny,nx);
    b=mat(nb,2); db=mat(nb,1); Qb=mat(nb,nb); Qab=mat(na,nb); QQ=mat(na,nb);
    
    /* transform single to double-differenced phase-bias (y=D'*x, Qy=D'*P*D) */
    matmul("TN",ny, 1,nx,1.0,D ,rtk->x,0.0,y );
    matmul("TN",ny,nx,nx,1.0,D ,rtk->P,0.0,DP);
    matmul("NN",ny,ny,nx,1.0,DP,D     ,0.0,Qy);
    
    /* phase-bias covariance (Qb) and real-parameters to bias covariance (Qab) */
    for (i=0;i<nb;i++) for (j=0;j<nb;j++) Qb [i+j*nb]=Qy[na+i+(na+j)*ny];
    for (i=0;i<na;i++) for (j=0;j<nb;j++) Qab[i+j*na]=Qy[   i+(na+j)*ny];
    
    trace(4,"N(0)="); tracemat(4,y+na,1,nb,10,3);
    
    /* lambda/mlambda integer least-square estimation */
    if (!(info=lambda(nb,2,y+na,Qb,b,s))) {
        
        trace(4,"N(1)="); tracemat(4,b   ,1,nb,10,3);
        trace(4,"N(2)="); tracemat(4,b+nb,1,nb,10,3);
        
        rtk->sol.ratio=s[0]>0?(float)(s[1]/s[0]):0.0f;
        if (rtk->sol.ratio>999.9) rtk->sol.ratio=999.9f;
        
        /* validation by popular ratio-test */
        if (s[0]<=0.0||s[1]/s[0]>=opt->thresar[0]) {
            
            /* transform float to fixed solution (xa=xa-Qab*Qb\(b0-b)) */
            for (i=0;i<na;i++) {
                rtk->xa[i]=rtk->x[i];
                for (j=0;j<na;j++) rtk->Pa[i+j*na]=rtk->P[i+j*nx];
            }
            for (i=0;i<nb;i++) {
                bias[i]=b[i];
                y[na+i]-=b[i];
            }
            if (!matinv(Qb,nb)) {
                matmul("NN",nb,1,nb, 1.0,Qb ,y+na,0.0,db);
                matmul("NN",na,1,nb,-1.0,Qab,db  ,1.0,rtk->xa);
                
                /* covariance of fixed solution (Qa=Qa-Qab*Qb^-1*Qab') */
                matmul("NN",na,nb,nb, 1.0,Qab,Qb ,0.0,QQ);
                matmul("NT",na,na,nb,-1.0,QQ ,Qab,1.0,rtk->Pa);
                
                trace(3,"resamb : validation ok (nb=%d ratio=%.2f s=%.2f/%.2f)\n",
                      nb,s[0]==0.0?0.0:s[1]/s[0],s[0],s[1]);
                
                /* restore single-differenced ambiguity */
                restamb(rtk,bias,nb,xa);
            }
            else nb=0;
        }
        else { /* validation failed */
            errmsg(rtk,"ambiguity validation failed (nb=%d ratio=%.2f s=%.2f/%.2f)\n",
                   nb,s[1]/s[0],s[0],s[1]);
            nb=0;
        }
    }
    else {
        errmsg(rtk,"lambda error (info=%d)\n",info);
    }
    free(D); free(y); free(Qy); free(DP);
    free(b); free(db); free(Qb); free(Qab); free(QQ);
    
    return nb; /* number of ambiguities */
}
/* validation of solution ----------------------------------------------------*/
static int valpos(rtk_t *rtk, const double *v, const double *R, const int *vflg,
                  int nv, double thres)
{
#if 0
    prcopt_t *opt=&rtk->opt;
    double vv=0.0;
#endif
    double fact=thres*thres;
    int i,stat=1,sat1,sat2,type,freq;
    char *stype;
    
    trace(3,"valpos  : nv=%d thres=%.1f\n",nv,thres);
    
    /* post-fit residual test */
    for (i=0;i<nv;i++) {
        if (v[i]*v[i]<=fact*R[i+i*nv]) continue;
        sat1=(vflg[i]>>16)&0xFF;
        sat2=(vflg[i]>> 8)&0xFF;
        type=(vflg[i]>> 4)&0xF;
        freq=vflg[i]&0xF;
        stype=type==0?"L":(type==1?"L":"C");
        errmsg(rtk,"large residual (sat=%2d-%2d %s%d v=%6.3f sig=%.3f)\n",
              sat1,sat2,stype,freq+1,v[i],SQRT(R[i+i*nv]));
    }
#if 0 /* omitted v.2.4.0 */
    if (stat&&nv>NP(opt)) {
        
        /* chi-square validation */
        for (i=0;i<nv;i++) vv+=v[i]*v[i]/R[i+i*nv];
        
        if (vv>chisqr[nv-NP(opt)-1]) {
            errmsg(rtk,"residuals validation failed (nv=%d np=%d vv=%.2f cs=%.2f)\n",
                   nv,NP(opt),vv,chisqr[nv-NP(opt)-1]);
            stat=0;
        }
        else {
            trace(3,"valpos : validation ok (%s nv=%d np=%d vv=%.2f cs=%.2f)\n",
                  rtk->tstr,nv,NP(opt),vv,chisqr[nv-NP(opt)-1]);
        }
    }
#endif
    return stat;
}
/* relative positioning ------------------------------------------------------*/
static int relpos(rtk_t *rtk, const obsd_t *obs, int nu, int nr,
                  const nav_t *nav)
{
    prcopt_t *opt=&rtk->opt;
    gtime_t time=obs[0].time;
    double *rs,*dts,*var,*y,*e,*azel,*v,*H,*R,*xp,*Pp,*xa,*bias,dt;
    int i,j,f,n=nu+nr,ns,ny,nv,sat[MAXSAT],iu[MAXSAT],ir[MAXSAT],niter;
    int info,vflg[MAXOBS*NFREQ*2+1],svh[MAXOBS*2];
    int stat=rtk->opt.mode<=PMODE_DGPS?SOLQ_DGPS:SOLQ_FLOAT;
    int nf=opt->ionoopt==IONOOPT_IFLC?1:opt->nf;
    
    trace(3,"relpos  : nx=%d nu=%d nr=%d\n",rtk->nx,nu,nr);
    
    dt=timediff(time,obs[nu].time);
    
    rs=mat(6,n); dts=mat(2,n); var=mat(1,n); y=mat(nf*2,n); e=mat(3,n);
    azel=zeros(2,n);
    
    for (i=0;i<MAXSAT;i++) {
        rtk->ssat[i].sys=satsys(i+1,NULL);
        for (j=0;j<NFREQ;j++) rtk->ssat[i].vsat[j]=rtk->ssat[i].snr[j]=0;
    }
    /* satellite positions/clocks */
    satposs(time,obs,n,nav,opt->sateph,rs,dts,var,svh);
    
    /* undifferenced residuals for base station */
    if (!zdres(1,obs+nu,nr,rs+nu*6,dts+nu*2,svh+nu,nav,rtk->rb,opt,1,
               y+nu*nf*2,e+nu*3,azel+nu*2)) {
        errmsg(rtk,"initial base station position error\n");
        
        free(rs); free(dts); free(var); free(y); free(e); free(azel);
        return 0;
    }
    /* time-interpolation of residuals (for post-processing) */
    if (opt->intpref) {
        dt=intpres(time,obs+nu,nr,nav,rtk,y+nu*nf*2);
    }
    /* select common satellites between rover and base-station */
    if ((ns=selsat(obs,azel,nu,nr,opt,sat,iu,ir))<=0) {
        errmsg(rtk,"no common satellite\n");
        
        free(rs); free(dts); free(var); free(y); free(e); free(azel);
        return 0;
    }
    /* temporal update of states */
    udstate(rtk,obs,sat,iu,ir,ns,nav);
    
    trace(4,"x(0)="); tracemat(4,rtk->x,1,NR(opt),13,4);
    
    xp=mat(rtk->nx,1); Pp=zeros(rtk->nx,rtk->nx); xa=mat(rtk->nx,1);
    matcpy(xp,rtk->x,rtk->nx,1);
    
    ny=ns*nf*2+2;
    v=mat(ny,1); H=zeros(rtk->nx,ny); R=mat(ny,ny); bias=mat(rtk->nx,1);
    
    /* add 2 iterations for baseline-constraint moving-base */
    niter=opt->niter+(opt->mode==PMODE_MOVEB&&opt->baseline[0]>0.0?2:0);
    
    for (i=0;i<niter;i++) {
        /* undifferenced residuals for rover */
        if (!zdres(0,obs,nu,rs,dts,svh,nav,xp,opt,0,y,e,azel)) {
            errmsg(rtk,"rover initial position error\n");
            stat=SOLQ_NONE;
            break;
        }
        /* double-differenced residuals and partial derivatives */
        if ((nv=ddres(rtk,nav,dt,xp,Pp,sat,y,e,azel,iu,ir,ns,v,H,R,vflg))<1) {
            errmsg(rtk,"no double-differenced residual\n");
            stat=SOLQ_NONE;
            break;
        }
        /* kalman filter measurement update */
        matcpy(Pp,rtk->P,rtk->nx,rtk->nx);
        if ((info=filter(xp,Pp,H,v,R,rtk->nx,nv))) {
            errmsg(rtk,"filter error (info=%d)\n",info);
            stat=SOLQ_NONE;
            break;
        }
        trace(4,"x(%d)=",i+1); tracemat(4,xp,1,NR(opt),13,4);
    }
    if (stat!=SOLQ_NONE&&zdres(0,obs,nu,rs,dts,svh,nav,xp,opt,0,y,e,azel)) {
        
        /* post-fit residuals for float solution */
        nv=ddres(rtk,nav,dt,xp,Pp,sat,y,e,azel,iu,ir,ns,v,NULL,R,vflg);
        
        /* validation of float solution */
        if (valpos(rtk,v,R,vflg,nv,4.0)) {
            
            /* update state and covariance matrix */
            matcpy(rtk->x,xp,rtk->nx,1);
            matcpy(rtk->P,Pp,rtk->nx,rtk->nx);
            
            /* update ambiguity control struct */
            rtk->sol.ns=0;
            for (i=0;i<ns;i++) for (f=0;f<nf;f++) {
                if (!rtk->ssat[sat[i]-1].vsat[f]) continue;
                rtk->ssat[sat[i]-1].lock[f]++;
                rtk->ssat[sat[i]-1].outc[f]=0;
                if (f==0) rtk->sol.ns++; /* valid satellite count by L1 */
            }
            /* lack of valid satellites */
            if (rtk->sol.ns<4) stat=SOLQ_NONE;
        }
        else stat=SOLQ_NONE;
    }
    /* resolve integer ambiguity by WL-NL */
    if (stat!=SOLQ_NONE&&rtk->opt.modear==ARMODE_WLNL) {
        
        if (resamb_WLNL(rtk,obs,sat,iu,ir,ns,nav,azel)) {
            stat=SOLQ_FIX;
        }
    }
    /* resolve integer ambiguity by TCAR */
    else if (stat!=SOLQ_NONE&&rtk->opt.modear==ARMODE_TCAR) {
        
        if (resamb_TCAR(rtk,obs,sat,iu,ir,ns,nav,azel)) {
            stat=SOLQ_FIX;
        }
    }
    /* resolve integer ambiguity by LAMBDA */
    else if (stat!=SOLQ_NONE&&resamb_LAMBDA(rtk,bias,xa)>1) {
        
        if (zdres(0,obs,nu,rs,dts,svh,nav,xa,opt,0,y,e,azel)) {
            
            /* post-fit reisiduals for fixed solution */
            nv=ddres(rtk,nav,dt,xa,NULL,sat,y,e,azel,iu,ir,ns,v,NULL,R,vflg);
            
            /* validation of fixed solution */
            if (valpos(rtk,v,R,vflg,nv,4.0)) {
                
                /* hold integer ambiguity */
                if (++rtk->nfix>=rtk->opt.minfix&&
                    rtk->opt.modear==ARMODE_FIXHOLD) {
                    holdamb(rtk,xa);
                }
                stat=SOLQ_FIX;
            }
        }
    }
    /* save solution status */
    if (stat==SOLQ_FIX) {
        for (i=0;i<3;i++) {
            rtk->sol.rr[i]=rtk->xa[i];
            rtk->sol.qr[i]=(float)rtk->Pa[i+i*rtk->na];
        }
        rtk->sol.qr[3]=(float)rtk->Pa[1];
        rtk->sol.qr[4]=(float)rtk->Pa[1+2*rtk->na];
        rtk->sol.qr[5]=(float)rtk->Pa[2];
    }
    else {
        for (i=0;i<3;i++) {
            rtk->sol.rr[i]=rtk->x[i];
            rtk->sol.qr[i]=(float)rtk->P[i+i*rtk->nx];
        }
        rtk->sol.qr[3]=(float)rtk->P[1];
        rtk->sol.qr[4]=(float)rtk->P[1+2*rtk->nx];
        rtk->sol.qr[5]=(float)rtk->P[2];
        rtk->nfix=0;
    }
    for (i=0;i<n;i++) for (j=0;j<nf;j++) {
        if (obs[i].L[j]==0.0) continue;
        rtk->ssat[obs[i].sat-1].pt[obs[i].rcv-1][j]=obs[i].time;
        rtk->ssat[obs[i].sat-1].ph[obs[i].rcv-1][j]=obs[i].L[j];
    }
    for (i=0;i<ns;i++) for (j=0;j<nf;j++) {
        
        /* output snr of rover receiver */
        rtk->ssat[sat[i]-1].snr[j]=obs[iu[i]].SNR[j];
    }
    for (i=0;i<MAXSAT;i++) for (j=0;j<nf;j++) {
        if (rtk->ssat[i].fix[j]==2&&stat!=SOLQ_FIX) rtk->ssat[i].fix[j]=1;
        if (rtk->ssat[i].slip[j]&1) rtk->ssat[i].slipc[j]++;
    }
    free(rs); free(dts); free(var); free(y); free(e); free(azel);
    free(xp); free(Pp);  free(xa);  free(v); free(H); free(R); free(bias);
    
    if (stat!=SOLQ_NONE) rtk->sol.stat=stat;
    
    return stat!=SOLQ_NONE;
}
/* initialize rtk control ------------------------------------------------------
* initialize rtk control struct
* args   : rtk_t    *rtk    IO  rtk control/result struct
*          prcopt_t *opt    I   positioning options (see rtklib.h)
* return : none
*-----------------------------------------------------------------------------*/
extern void rtkinit(rtk_t *rtk, const prcopt_t *opt)
{
    sol_t sol0={{0}};
    ambc_t ambc0={{{0}}};
    ssat_t ssat0={0};
    int i;
    
    trace(3,"rtkinit :\n");
    
    rtk->sol=sol0;
    for (i=0;i<6;i++) rtk->rb[i]=0.0;
    rtk->nx=opt->mode<=PMODE_FIXED?NX(opt):pppnx(opt);
    rtk->na=opt->mode<=PMODE_FIXED?NR(opt):0;
    rtk->tt=0.0;
    rtk->x=zeros(rtk->nx,1);
    rtk->P=zeros(rtk->nx,rtk->nx);
    rtk->xa=zeros(rtk->na,1);
    rtk->Pa=zeros(rtk->na,rtk->na);
    rtk->nfix=rtk->neb=0;
    for (i=0;i<MAXSAT;i++) {
        rtk->ambc[i]=ambc0;
        rtk->ssat[i]=ssat0;
    }
    for (i=0;i<MAXERRMSG;i++) rtk->errbuf[i]=0;
    rtk->opt=*opt;
}
/* free rtk control ------------------------------------------------------------
* free memory for rtk control struct
* args   : rtk_t    *rtk    IO  rtk control/result struct
* return : none
*-----------------------------------------------------------------------------*/
extern void rtkfree(rtk_t *rtk)
{
    trace(3,"rtkfree :\n");
    
    rtk->nx=rtk->na=0;
    free(rtk->x ); rtk->x =NULL;
    free(rtk->P ); rtk->P =NULL;
    free(rtk->xa); rtk->xa=NULL;
    free(rtk->Pa); rtk->Pa=NULL;
}
/* precise positioning ---------------------------------------------------------
* input observation data and navigation message, compute rover position by 
* precise positioning
* args   : rtk_t *rtk       IO  rtk control/result struct
*            rtk->sol       IO  solution
*                .time      O   solution time
*                .rr[]      IO  rover position/velocity
*                               (I:fixed mode,O:single mode)
*                .dtr[0]    O   receiver clock bias (s)
*                .dtr[1]    O   receiver glonass-gps time offset (s)
*                .Qr[]      O   rover position covarinace
*                .stat      O   solution status (SOLQ_???)
*                .ns        O   number of valid satellites
*                .age       O   age of differential (s)
*                .ratio     O   ratio factor for ambiguity validation
*            rtk->rb[]      IO  base station position/velocity
*                               (I:relative mode,O:moving-base mode)
*            rtk->nx        I   number of all states
*            rtk->na        I   number of integer states
*            rtk->ns        O   number of valid satellite
*            rtk->tt        O   time difference between current and previous (s)
*            rtk->x[]       IO  float states pre-filter and post-filter
*            rtk->P[]       IO  float covariance pre-filter and post-filter
*            rtk->xa[]      O   fixed states after AR
*            rtk->Pa[]      O   fixed covariance after AR
*            rtk->ssat[s]   IO  sat(s+1) status
*                .sys       O   system (SYS_???)
*                .az   [r]  O   azimuth angle   (rad) (r=0:rover,1:base)
*                .el   [r]  O   elevation angle (rad) (r=0:rover,1:base)
*                .vs   [r]  O   data valid single     (r=0:rover,1:base)
*                .resp [f]  O   freq(f+1) pseudorange residual (m)
*                .resc [f]  O   freq(f+1) carrier-phase residual (m)
*                .vsat [f]  O   freq(f+1) data vaild (0:invalid,1:valid)
*                .fix  [f]  O   freq(f+1) ambiguity flag
*                               (0:nodata,1:float,2:fix,3:hold)
*                .slip [f]  O   freq(f+1) slip flag
*                               (bit8-7:rcv1 LLI, bit6-5:rcv2 LLI,
*                                bit2:parity unknown, bit1:slip)
*                .lock [f]  IO  freq(f+1) carrier lock count
*                .outc [f]  IO  freq(f+1) carrier outage count
*                .slipc[f]  IO  freq(f+1) cycle slip count
*                .rejc [f]  IO  freq(f+1) data reject count
*                .gf        IO  geometry-free phase (L1-L2) (m)
*                .gf2       IO  geometry-free phase (L1-L5) (m)
*            rtk->nfix      IO  number of continuous fixes of ambiguity
*            rtk->neb       IO  bytes of error message buffer
*            rtk->errbuf    IO  error message buffer
*            rtk->tstr      O   time string for debug
*            rtk->opt       I   processing options
*          obsd_t *obs      I   observation data for an epoch
*                               obs[i].rcv=1:rover,2:reference
*                               sorted by receiver and satellte
*          int    n         I   number of observation data
*          nav_t  *nav      I   navigation messages
* return : status (0:no solution,1:valid solution)
* notes  : before calling function, base station position rtk->sol.rb[] should
*          be properly set for relative mode except for moving-baseline
*-----------------------------------------------------------------------------*/
extern int rtkpos(rtk_t *rtk, const obsd_t *obs, int n, const nav_t *nav)
{
    prcopt_t *opt=&rtk->opt;
    sol_t solb={{0}};
    gtime_t time;
    int i,nu,nr;
    char msg[128]="";
    
    trace(3,"rtkpos  : time=%s n=%d\n",time_str(obs[0].time,3),n);
    trace(4,"obs=\n"); traceobs(4,obs,n);
    /*trace(5,"nav=\n"); tracenav(5,nav);*/
    
    /* set base staion position */
    if (opt->refpos<=3&&opt->mode!=PMODE_SINGLE&&opt->mode!=PMODE_MOVEB) {
        for (i=0;i<6;i++) rtk->rb[i]=i<3?opt->rb[i]:0.0;
    }
    /* count rover/base station observations */
    for (nu=0;nu   <n&&obs[nu   ].rcv==1;nu++) ;
    for (nr=0;nu+nr<n&&obs[nu+nr].rcv==2;nr++) ;
    
    time=rtk->sol.time; /* previous epoch */
    
    /* rover position by single point positioning */
    if (!pntpos(obs,nu,nav,&rtk->opt,&rtk->sol,NULL,rtk->ssat,msg)) {
        errmsg(rtk,"point pos error (%s)\n",msg);
        
        if (!rtk->opt.dynamics) {
            outsolstat(rtk);
            return 0;
        }
    }
    if (time.time!=0) rtk->tt=timediff(rtk->sol.time,time);
    
    /* single point positioning */
    if (opt->mode==PMODE_SINGLE) {
        outsolstat(rtk);
        return 1;
    }
    /* precise point positioning */
    if (opt->mode>=PMODE_PPP_KINEMA) {
        pppos(rtk,obs,nu,nav);
        pppoutsolstat(rtk,statlevel,fp_stat);
        return 1;
    }
    /* check number of data of base station and age of differential */
    if (nr==0) {
        errmsg(rtk,"no base station observation data for rtk\n");
        outsolstat(rtk);
        return 1;
    }
    if (opt->mode==PMODE_MOVEB) { /*  moving baseline */
        
        /* estimate position/velocity of base station */
        if (!pntpos(obs+nu,nr,nav,&rtk->opt,&solb,NULL,NULL,msg)) {
            errmsg(rtk,"base station position error (%s)\n",msg);
            return 0;
        }
        rtk->sol.age=(float)timediff(rtk->sol.time,solb.time);
        
        if (fabs(rtk->sol.age)>TTOL_MOVEB) {
            errmsg(rtk,"time sync error for moving-base (age=%.1f)\n",rtk->sol.age);
            return 0;
        }
        for (i=0;i<6;i++) rtk->rb[i]=solb.rr[i];
        
        /* time-synchronized position of base station */
        for (i=0;i<3;i++) rtk->rb[i]+=rtk->rb[i+3]*rtk->sol.age;
    }
    else {
        rtk->sol.age=(float)timediff(obs[0].time,obs[nu].time);
        
        if (fabs(rtk->sol.age)>opt->maxtdiff) {
            errmsg(rtk,"age of differential error (age=%.1f)\n",rtk->sol.age);
            outsolstat(rtk);
            return 1;
        }
    }
    /* relative potitioning */
    relpos(rtk,obs,nu,nr,nav);
    outsolstat(rtk);
    
    return 1;
}