When SBAS encounters rtklib

brief introduction

SBAS It's a satellite based enhancement system Satellite-Based Augmentation System Abbreviation . for example USA Of WAAS It's just one. SBAS System .

Satellite based augmentation system （SBAS） And foundation reinforcement system （CORS） Just a word , So how does the satellite based enhancement system work ?CORS A reference station is required to work . Allied SBAS need GEO satellite （ To avoid confusion , This is called SBAS satellite ） Only by cooperating with the ground station can it work , But these don't need our users' attention .SBAS Satellites can broadcast ephemeris errors to users 、 Satellite clock error 、 Ionospheric delay parameters and other correction information , So as to improve the positioning accuracy .

in addition , It is worth noting that SBAS A satellite is more than just a signal forwarding device , It is also a navigation satellite , You can also issue broadcast ephemeris , The receiver can also obtain SBAS Satellite carrier phase, pseudo range and other observation information . therefore ,SBAS A satellite can be used as an ordinary navigation satellite .

RTKLib Chinese vs SBAS Support for

rtklib It's supporting sbas Participating in the solution , And both of the above methods support .

SBAS Satellite as an ordinary navigation satellite

since SBAS Satellites should be used as ordinary navigation satellites , Then we need to know the position and observation value of the satellite , Of course, the satellite position is calculated through its own ephemeris . Here are SBAS Calculation method of satellite position , Follow GLONASS The calculation method is very similar to .

/* sbas ephemeris to satellite position and clock bias */
extern void seph2pos(gtime_t time, const seph_t *seph, double *rs, 
double *dts,double *var)
{
    
    double t;
    int i;
    
    trace(4,"seph2pos: time=%s sat=%2d\n",time_str(time,3),seph->sat);
    
    t=timediff(time,seph->t0);
    for (i=0;i<3;i++) {
    
        rs[i]=seph->pos[i]+seph->vel[i]*t+seph->acc[i]*t*t/2.0;
    }
    *dts=seph->af0+seph->af1*t;
    
    *var=var_uraeph(SYS_SBS,seph->sva);
}

Here are Rinex in ,SBAS Ephemeris format .

The following is a rtklib in SBAS Ephemeris Rinex analysis .

    seph->af0=data[0];
    seph->af1=data[1];
    
    seph->pos[0]=data[3]*1E3; seph->pos[1]=data[7]*1E3; seph->pos[2]=data[11]*1E3;
    seph->vel[0]=data[4]*1E3; seph->vel[1]=data[8]*1E3; seph->vel[2]=data[12]*1E3;
    seph->acc[0]=data[5]*1E3; seph->acc[1]=data[9]*1E3; seph->acc[2]=data[13]*1E3;
    
    seph->svh=(int)data[6];
    seph->sva=uraindex(data[10]);

Again ,Rinex You can read in the observation file SBAS Observation information .

for example , The following example is an example Rinex Observation information , among S20 by SBAS satellite .

Now we have ephemeris and observations , You can solve the positioning problem , Click here to read rtklib Single point positioning explanation . Oh , And a little bit more , The observation values of different satellites should be given different weights .SBAS Satellites are no exception .

static double varerr(const prcopt_t *opt, double el, int sys)
{
    
    double fact,varr;
    fact=sys==SYS_GLO?EFACT_GLO:(sys==SYS_SBS?EFACT_SBS:EFACT_GPS);
    if (el<MIN_EL) el=MIN_EL;
    varr=SQR(opt->err[0])*(SQR(opt->err[1])+SQR(opt->err[2])/sin(el));
    if (opt->ionoopt==IONOOPT_IFLC) varr*=SQR(3.0); /* iono-free */
    return SQR(fact)*varr;
}

SBAS Satellite based enhancement

Of course ,SBAS As an ordinary navigation satellite, satellite is a sideline after all , Let's get down to business . Look at a watch first ,SBAS The satellite sent those messages ？ You can also see from the table below Message Type=9 Namely SBAS Ephemeris news .

Message Type	Messages Contents	Update Period (sec)
0	Don’t use this GEO for safety-of-life (it is only for testing)	6
1	PRN Mask assignments, set up to 51 of 210 bits	120
2	5 Fast corrections (satellite clock error)	6-60
6	Integrity information (UDREI)	6
7	Fast correction degradation factors	120
9	GEO navigation message (X, Y, Z, time, etc.)	120
10	Degradation parameters	120
12	WAAS network time/UTC offset parameters	300
17	GEO satellite almanacs	300
18	Ionospheric grid point masks	300
24	Mixed fast/long term satellite error corrections	6-60
25	Long term satellite error corrections	120
26	Ionospheric delay corrections	300
27	WAAS service message	300
28	Clock/ephemeris covariance matrix	120
63	Null message	-

The messages in the above table rtklib All supported , We take SBAS Ionospheric correction to see .

1. First , Analytical ionospheric delay parameters , Ionospheric delay id Number is 26,5 Send it once every ten minutes

/* decode type 26: ionospheric deley corrections -----------------------------*/
static int decode_sbstype26(const sbsmsg_t *msg, sbsion_t *sbsion){
    }

2. So when we make the ionospheric correction of pseudo range , You can use SBAS The ionospheric correction parameters

extern int ionocorr(gtime_t time, const nav_t *nav, int sat, const double *pos,
                    const double *azel, int ionoopt, double *ion, double *var)

extern int sbsioncorr(gtime_t time, const nav_t *nav, const double *pos,
                      const double *azel, double *delay, double *var)

About IPP—— Ionospheric entry point

When calculating the ionospheric delay , We found the following function , This function is used to calculate the coordinates of the ionospheric entry point .

/* ipp (ionospheric pierce point) position */
    fp=ionppp(pos,azel,re,hion,posp);

What is the ionospheric entry point ？ First look at the picture below . To put it simply , We connect the user location point with the satellite in a straight line , The intersection of this line and the ionospheric height is the ionospheric entry point .

Below is the calculation method of ionospheric entry point , First of all, the calculation of latitude is relatively simple , as follows ：
$${\varphi }_{pp}=si{n}^{-1}(sin{\varphi }_{u}cos{\psi }_{pp}+cos{\varphi }_{u}sin{\psi }_{pp}cosA)$$

among ,$A$ Is the azimuth of the satellite ,${\varphi }_u$ For the user ,${\psi }_{pp}$ For user location and IPP The corner of the earth's Center , The calculation method is as follows
$${\psi }_{pp}=\frac{\pi }{2}-E-si{n}^{-1}(\frac{R_e}{R_e+h_I}cosE)$$
among $E$ It's satellite elevation ,$R_e$ Is the radius of the earth ,$h_I$ Is the ionospheric height , take 350Km.
Look down , The longitude calculation method of the entry point ,
If the following conditions are true ,
(${\varphi }_u>70^{\circ }$ && $tan{\psi }_{pp}cosA>tan(\frac{\pi }{2}-{\varphi }_u)$) ||(${\varphi }_u<-70^{\circ }$ && $tan{\psi }_{pp}cos(A+\pi )>tan(\frac{\pi }{2}+{\varphi }_u)$ )
be ,
$${\lambda }_{pp}={\lambda }_u+\pi -si{n}^{-1}\frac{sin{\psi }_{pp}sinA}{cos{\varphi }_{pp}}$$
otherwise , Calculate the entry point coordinates according to the following formula ,
$${\lambda }_{pp}={\lambda }_u+si{n}^{-1}\frac{sin{\psi }_{pp}sinA}{cos{\varphi }_{pp}}$$

Interpolation processing

SBAS Interpolation processing is needed for ionospheric correction , Click here for details .