gnss-sdr/src/algorithms/libs/rtklib/rtklib_rtkpos.cc

/*!
 * \file rtklib_rtkpos.cc
 * \brief rtklib ppp-related functions
 * \authors <ul>
 *          <li> 2007-2013, T. Takasu
 *          <li> 2017, Javier Arribas
 *          <li> 2017, Carles Fernandez
 *          </ul>
 *
 * This is a derived work from RTKLIB http://www.rtklib.com/
 * The original source code at https://github.com/tomojitakasu/RTKLIB is
 * released under the BSD 2-clause license with an additional exclusive clause
 * that does not apply here. This additional clause is reproduced below:
 *
 * " The software package includes some companion executive binaries or shared
 * libraries necessary to execute APs on Windows. These licenses succeed to the
 * original ones of these software. "
 *
 * Neither the executive binaries nor the shared libraries are required by, used
 * or included in GNSS-SDR.
 *
 * -------------------------------------------------------------------------
 * Copyright (C) 2007-2013, T. Takasu
 * Copyright (C) 2017, Javier Arribas
 * Copyright (C) 2017, Carles Fernandez
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are
 * met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
 * A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
 * HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
 * SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
 * LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
 * DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
 * THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
 * OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 *
 *
 *----------------------------------------------------------------------------*/

#include <iostream>
#include "rtklib_rtkpos.h"
#include "rtklib_pntpos.h"
#include "rtklib_ephemeris.h"
#include "rtklib_ppp.h"
#include "rtklib_tides.h"
#include "rtklib_lambda.h"

static int resamb_WLNL(rtk_t *rtk __attribute((unused)), const obsd_t *obs __attribute((unused)), const int *sat __attribute((unused)),
                       const int *iu __attribute((unused)), const int *ir __attribute((unused)), int ns __attribute__((unused)), const nav_t *nav __attribute((unused)),
                       const double *azel __attribute((unused))) {return 0;}
static int resamb_TCAR(rtk_t *rtk __attribute((unused)), const obsd_t *obs __attribute((unused)), const int *sat __attribute((unused)),
                       const int *iu __attribute((unused)), const int *ir __attribute((unused)), int ns __attribute((unused)), const nav_t *nav __attribute((unused)),
                       const double *azel __attribute((unused))) {return 0;}

/* 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, 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
 *
 *-----------------------------------------------------------------------------*/
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
 *-----------------------------------------------------------------------------*/
void rtkclosestat(void)
{
    trace(3, "rtkclosestat:\n");

    if (fp_stat) fclose(fp_stat);
    fp_stat = NULL;
    file_stat[0] = '\0';
    statlevel = 0;
}


/* write solution status to buffer -------------------------------------------*/
void rtkoutstat(rtk_t *rtk,  char *buff)
{
  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(&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_RTK(i+1,&rtk->opt);
          xa[0]=j<rtk->na?rtk->xa[j]:0.0;
          fprintf(fp_stat,"$ION,%d,%.3f,%d,%s,%.1f,%.1f,%.4f,%.4f\n",week,tow,rtk->sol.stat,
                  id,ssat->azel[0]*R2D,ssat->azel[1]*R2D,rtk->x[j],xa[0]);
      }
  }
  /* tropospheric parameters */
  if (est&&(rtk->opt.tropopt==TROPOPT_EST||rtk->opt.tropopt==TROPOPT_ESTG)) {
      for (i=0;i<2;i++) {
          j=IT_RTK(i,&rtk->opt);
          xa[0]=j<rtk->na?rtk->xa[j]:0.0;
          fprintf(fp_stat,"$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_RTK(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]);
      }
  }
}


/* swap solution status file -------------------------------------------------*/
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 ----------------------------------------------------*/
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(&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_RTK(i+1,&rtk->opt);
       xa[0]=j<rtk->na?rtk->xa[j]:0.0;
       fprintf(fp_stat,"$ION,%d,%.3f,%d,%s,%.1f,%.1f,%.4f,%.4f\n",week,tow,rtk->sol.stat,
               id,ssat->azel[0]*R2D,ssat->azel[1]*R2D,rtk->x[j],xa[0]);
   }
}
/* tropospheric parameters */
if (est&&(rtk->opt.tropopt==TROPOPT_EST||rtk->opt.tropopt==TROPOPT_ESTG)) {
   for (i=0;i<2;i++) {
       j=IT_RTK(i,&rtk->opt);
       xa[0]=j<rtk->na?rtk->xa[j]:0.0;
       fprintf(fp_stat,"$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_RTK(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 --------------------------------------------------------*/
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 ---------------------------------------------*/
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 --------------*/
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;
}


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 -----------------------------*/
double varerr(int sat __attribute((unused)), int sys, double el, double bl, double dt, int f,
        const prcopt_t *opt)
{
    double a, b, c = opt->err[3]*bl/1e4, d = SPEED_OF_LIGHT * opt->sclkstab*dt, fact = 1.0;
    double sinel = sin(el);
    int i = sys == SYS_GLO ? 1 : (sys == SYS_GAL ? 2 : 0), nf = NF_RTK(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 -----------------------------------------------------------*/
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_rtk(dr, 3);
}


/* initialize state and covariance -------------------------------------------*/
void initx_rtk(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 --------------*/
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 -------------------------*/
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, rtk->opt.ru[i], 1E-8, i);
            return;
        }
    /* initialize position for first epoch */
    if (norm_rtk(rtk->x, 3)  <= 0.0)
        {
            for (i = 0;i<3;i++) initx_rtk(rtk, rtk->sol.rr[i], VAR_POS, i);
            if (rtk->opt.dynamics)
                {
                    for (i = 3;i<6;i++) initx_rtk(rtk, rtk->sol.rr[i], VAR_VEL, i);
                    for (i = 6;i<9;i++) initx_rtk(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, 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, rtk->sol.rr[i], VAR_POS, i);
            for (i = 3;i<6;i++) initx_rtk(rtk, rtk->sol.rr[i], VAR_VEL, i);
            for (i = 6;i<9;i++) initx_rtk(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] = std::pow(rtk->opt.prn[3],  2.0); Q[8] = std::pow(rtk->opt.prn[4],  2.0);
    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 ---------------------------------*/
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_RTK(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_RTK(sat[i], &rtk->opt);

            if (rtk->x[j] == 0.0)
                {
                    initx_rtk(rtk, 1E-6, std::pow(rtk->opt.std[1]*bl/1e4,  2.0), 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] += std::pow(rtk->opt.prn[1]*bl/1e4*fact, 2.0)*tt;
                }
        }
}


/* temporal update of tropospheric parameters --------------------------------*/
void udtrop(rtk_t *rtk, double tt, double bl __attribute((unused)))
{
    int i, j, k;

    trace(3, "udtrop  : tt=%.1f\n", tt);

    for (i = 0;i<2;i++)
        {
            j = IT_RTK(i, &rtk->opt);

            if (rtk->x[j] == 0.0)
                {
                    initx_rtk(rtk, INIT_ZWD, std::pow(rtk->opt.std[2],  2.0), j); /* initial zwd */

                    if (rtk->opt.tropopt >= TROPOPT_ESTG)
                        {
                            for (k = 0;k<2;k++) initx_rtk(rtk, 1e-6, VAR_GRA, ++j);
                        }
                }
            else
                {
                    rtk->P[j+j*rtk->nx] += std::pow(rtk->opt.prn[2],  2.0)*tt;

                    if (rtk->opt.tropopt >= TROPOPT_ESTG)
                        {
                            for (k = 0;k<2;k++)
                                {
                                    rtk->P[++j*(1+rtk->nx)]+=std::pow(rtk->opt.prn[2]*0.3,  2.0)*fabs(rtk->tt);
                                }
                        }
                }
        }
}


/* temporal update of receiver h/w biases ------------------------------------*/
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_RTK(i, &rtk->opt);

            if (rtk->x[j] == 0.0)
                {
                    initx_rtk(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, rtk->xa[j], rtk->Pa[j+j*rtk->na], j);
                }
            else
                {
                    rtk->P[j+j*rtk->nx]+=std::pow(PRN_HWBIAS,  2.0)*tt;
                }
        }
}


/* detect cycle slip by LLI --------------------------------------------------*/
void detslp_ll(rtk_t *rtk, const obsd_t *obs, int i, int rcv)
{
    unsigned int slip, 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 */
            if (rcv == 1) LLI = getbitu(&rtk->ssat[sat-1].slip[f], 0, 2); /* rover */
            else        LLI = getbitu(&rtk->ssat[sat-1].slip[f], 2, 2); /* base  */

            /* detect slip by cycle slip flag in LLI */
            if (rtk->tt >= 0.0) { /* forward */
                    if (obs[i].LLI[f]&1)
                        {
                            errmsg(rtk, "slip detected forward (sat=%2d rcv=%d F=%d LLI=%x)\n",
                                    sat, rcv, f+1, obs[i].LLI[f]);
                        }
                    slip = obs[i].LLI[f];
            }
            else
                { /* backward */
                    if (LLI&1)
                        {
                            errmsg(rtk, "slip detected backward (sat=%2d rcv=%d F=%d LLI=%x)\n",
                                    sat, rcv, f+1, LLI);
                        }
                    slip = LLI;
                }
            /* detect slip by parity unknown flag transition in LLI */
            if (((LLI&2) && !(obs[i].LLI[f]&2)) || (!(LLI&2) && (obs[i].LLI[f]&2)))
                {
                    errmsg(rtk, "slip detected half-cyc (sat=%2d rcv=%d F=%d LLI=%x->%x)\n",
                            sat, rcv, f+1, LLI, obs[i].LLI[f]);
                    slip|=1;
                }
            /* save current LLI */
            if (rcv == 1) setbitu(&rtk->ssat[sat-1].slip[f], 0, 2, obs[i].LLI[f]);
            else        setbitu(&rtk->ssat[sat-1].slip[f], 2, 2, obs[i].LLI[f]);

            /* save slip and half-cycle valid flag */
            rtk->ssat[sat-1].slip[f]|=(unsigned char)slip;
            rtk->ssat[sat-1].half[f] = (obs[i].LLI[f]&2) ? 0 : 1;
        }
}


/* detect cycle slip by L1-L2 geometry free phase jump -----------------------*/
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 -----------------------*/
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 -------------------------*/
void detslp_dop(rtk_t *rtk __attribute__((unused)), const obsd_t *obs __attribute__((unused)), int i __attribute__((unused)), int rcv __attribute__((unused)),
        const nav_t *nav __attribute__((unused)))
{
    /* 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 -------------------------------------------*/
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(&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);

            /* update half-cycle valid flag */
            for (f = 0;f<nf;f++)
                {
                    rtk->ssat[sat[i]-1].half[f] =
                            !((obs[iu[i]].LLI[f]&2) || (obs[ir[i]].LLI[f]&2));
                }
        }
    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_RTK(i, f, &rtk->opt)] != 0.0)
                        {
                            initx_rtk(rtk, 0.0, 0.0, IB_RTK(i, f, &rtk->opt));
                        }
                    else if (reset && rtk->x[IB_RTK(i, f, &rtk->opt)] != 0.0)
                        {
                            initx_rtk(rtk, 0.0, 0.0, IB_RTK(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_RTK(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 =  std::pow(lam2, 2.0)/(std::pow(lam2, 2.0)-std::pow(lam1, 2.0));
                            C2 = -std::pow(lam1, 2.0)/(std::pow(lam2, 2.0)-std::pow(lam1, 2.0));
                            bias[i] = (C1*lam1*cp1+C2*lam2*cp2)-(C1*pr1+C2*pr2);
                        }
                    if (rtk->x[IB_RTK(sat[i], f, &rtk->opt)] != 0.0)
                        {
                            offset+=bias[i]-rtk->x[IB_RTK(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_RTK(i, f, &rtk->opt)] != 0.0) rtk->x[IB_RTK(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_RTK(sat[i], f, &rtk->opt)] != 0.0) continue;
                    initx_rtk(rtk, bias[i], std::pow(rtk->opt.std[0],  2.0), IB_RTK(sat[i], f, &rtk->opt));
                }
            free(bias);
        }
}


/* temporal update of states --------------------------------------------------*/
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 = 0.0, 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 ---------------------------*/
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_RTK(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 = SPEED_OF_LIGHT/lam[0];
            f2 = SPEED_OF_LIGHT/lam[1];
            C1 =  std::pow(f1, 2.0)/(std::pow(f1, 2.0)-std::pow(f2, 2.0));
            C2 = -std::pow(f2, 2.0)/(std::pow(f1, 2.0)-std::pow(f2, 2.0));
            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 ----------------------------------------*/
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_RTK(opt);

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

    for (i = 0;i<n*nf*2;i++) y[i] = 0.0;

    if (norm_rtk(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;

            /* excluded satellite? */
            if (satexclude(obs[i].sat, svh[i], opt)) continue;

            /* satellite clock-bias */
            r+=-SPEED_OF_LIGHT*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 -----------------------------------------------*/
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 ---------------------------*/
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 ------------------------------------------------*/
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_rtk(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] = std::pow(rtk->opt.baseline[1],  2.0);

    trace(4, "baseline len   v=%13.3f R=%8.6f %8.6f\n", v[index], Ri[index], Rj[index]);

    return 1;
}


/* precise tropspheric model -------------------------------------------------*/
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_RTK(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 -------------------------------------*/
double gloicbcorr(int sat1 __attribute((unused)), int sat2 __attribute((unused)), 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 = (SPEED_OF_LIGHT/lam1-SPEED_OF_LIGHT/lam2)/(f == 0 ? DFRQ1_GLO : DFRQ2_GLO);

    return opt->exterr.gloicb[f]*0.01*dfreq; /* (m) */
}


/* test navi system (m=0:gps/qzs/sbs,1:glo,2:gal,3:bds) ----------------------*/
int test_sys(int sys, int m)
{
    switch (sys)
    {
    case SYS_GPS: return m == 0;
    case SYS_QZS: return m == 0;
    case SYS_SBS: return m == 0;
    case SYS_GLO: return m == 1;
    case SYS_GAL: return m == 2;
    case SYS_BDS: return m == 3;
    }
    return 0;
}


/* double-differenced phase/code residuals -----------------------------------*/
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_RTK(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<4;m++) /* m=0:gps/qzs/sbs, 1:glo, 2:gal, 3:bds */

        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;
                                for (k = 0;k<rtk->nx;k++) Hi[k] = 0.0;
                            }
                        /* 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_RTK(sat[i], opt)]-didxj*x[II_RTK(sat[j], opt)];
                                if (H)
                                    {
                                        Hi[II_RTK(sat[i], opt)] =  didxi;
                                        Hi[II_RTK(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_RTK(0, opt)+k] =  (dtdxu[k+i*3]-dtdxu[k+j*3]);
                                        Hi[IT_RTK(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_RTK(sat[i], f, opt)]-lamj*x[IB_RTK(sat[j], f, opt)];
                                        if (H)
                                            {
                                                Hi[IB_RTK(sat[i], f, opt)] =  lami;
                                                Hi[IB_RTK(sat[j], f, opt)] = -lamj;
                                            }
                                    }
                                else
                                    {
                                        v[nv] -= x[IB_RTK(sat[i], f, opt)]-x[IB_RTK(sat[j], f, opt)];
                                        if (H)
                                            {
                                                Hi[IB_RTK(sat[i], f, opt)] =  1.0;
                                                Hi[IB_RTK(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 = (SPEED_OF_LIGHT/lami-SPEED_OF_LIGHT/lamj)/1E6; /* freq-difference (MHz) */
                                v[nv] -= df*x[IL_RTK(ff, opt)];
                                if (H) Hi[IL_RTK(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) ------------------------*/
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_RTK(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') --------------------*/
int ddmat(rtk_t *rtk, double *D)
{
    int i, j, k, m, f, nb = 0, nx = rtk->nx, na = rtk->na, nf = NF_RTK(&rtk->opt), nofix;

    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<4;m++)
        { /* m=0:gps/qzs/sbs, 1:glo, 2:gal, 3:bds */
            nofix = (m == 1 && rtk->opt.glomodear == 0) || (m == 3 && rtk->opt.bdsmodear == 0);

            for (f = 0, k = na;f<nf;f++, k+=MAXSAT)
                {
                    for (i = k;i<k+MAXSAT;i++)
                        {
#if 0
                            if (rtk->x[i] == 0.0||!test_sys(rtk->ssat[i-k].sys,m)||
                                    !rtk->ssat[i-k].vsat[f])
                                {
#else
                            if (rtk->x[i] == 0.0 || !test_sys(rtk->ssat[i-k].sys, m) ||
                                            !rtk->ssat[i-k].vsat[f] || !rtk->ssat[i-k].half[f])
                                {
#endif
                                    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 && !nofix)
                                {
                                    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 && !nofix)
                                {
                                    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 --------------------------------------*/
void restamb(rtk_t *rtk, const double *bias, int nb __attribute((unused)), double *xa)
{
    int i, n, m, f, index[MAXSAT], nv = 0, nf = NF_RTK(&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<4;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_RTK(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 ----------------------------------------------------*/
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(&rtk->opt);

    trace(3, "holdamb :\n");

    v = mat(nb, 1); H = zeros(nb, rtk->nx);

    for (m = 0;m<4;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_RTK(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 ---------------------------------------*/
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 ----------------------------------------------------*/
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], std::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 ------------------------------------------------------*/
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_RTK(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_RTK(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
 *-----------------------------------------------------------------------------*/
void rtkinit(rtk_t *rtk,  const prcopt_t *opt)
{
    sol_t sol0 = { {0,  0},  {},  {},  {},  '0',  '0',  '0',  0.0,  0.0,  0.0};
    ambc_t ambc0 = {{ {0, 0},  {0,  0},  {0,  0},  {0,  0} },  {},  {},  {} ,  0,  {}};
    ssat_t ssat0 = {0, 0, {0.0}, {0.0}, {0.0}, {'0'}, {'0'}, {'0'}, {'0'}, {'0'}, {}, {}, {}, {}, 0.0, 0.0, 0.0, 0.0, {{0,0},{0,0}}, {{},{}}};
    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_RTK(opt) : pppnx(opt);
    rtk->na = opt->mode <= PMODE_FIXED ? NR_RTK(opt) : pppnx(opt);
    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
 *-----------------------------------------------------------------------------*/
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
 *-----------------------------------------------------------------------------*/
int rtkpos(rtk_t *rtk, const obsd_t *obs, int n, const nav_t *nav)
{
    prcopt_t *opt = &rtk->opt;
    sol_t solb = { {0, 0}, {}, {}, {}, '0', '0', '0', 0.0, 0.0, 0.0};
    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 <= POSOPT_RINEX && 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;
        }
    /* suppress output of single solution */
    if (!opt->outsingle)
        {
            rtk->sol.stat = SOLQ_NONE;
        }
    /* precise point positioning */
    if (opt->mode >= PMODE_PPP_KINEMA)
        {
            pppos(rtk, obs, nu, nav);
            outsolstat(rtk);
            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;
}