Introduction and use of precise ephemeris

Precise ephemeris

SP3 Precise ephemeris format , namely The Extended Standard Product 3 Orbit Format.

Precise ephemeris download

Click here to download the precise ephemeris
The following picture shows the download 2005-04-02 A precise ephemeris , So you can download the precise ephemeris of this day .

Precise ephemeris format

#cP2009 4 1 0 0 0.00000000 96 ORBIT IGS05 BHN ESOC 
European Space Operations Centre
## 1525 259200.00000000   900.00000000 54922 0.0000000000000                    
+   48   G32G24G25G26G27G30G03G04G06G08G09G10G14G13G28G21G11                    
+        G22G20G18G16G19G23G02G31G17G12G15G29G07R04R06R07R10                    
+        R11R13R14R15R17R19R20R23R18R21R22R03R02R08  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  0  0  0  0  0  0  0  0  0  0  0  0                    
++         5  5  6  5  5  6  5  5  5  5  5  5  5  5  5  5  5                    
++         5  5  5  6  5  5  5  5  5  5  5  5  5  7  8  6  6                    
++         6  7  7  7  7  6  6  7  7  7  7  7  6  7  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  0  0  0  0  0  0  0  0  0  0  0  0                    
%c M  cc GPS ccc cccc cccc cccc cccc ccccc ccccc ccccc ccccc                    
%c cc cc ccc ccc cccc cccc cccc cccc ccccc ccccc ccccc ccccc                    
%f  0.0000000  0.000000000  0.00000000000  0.000000000000000                    
%f  0.0000000  0.000000000  0.00000000000  0.000000000000000                    
%i    0    0    0    0      0      0      0      0         0                    
%i    0    0    0    0      0      0      0      0         0                    
/* CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC /* CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC /* CCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCCC /* PCV:IGS05_1461 OL/AL:FES2004 NONE YN ORB:CoN CLK:CoN * 2009 4 1 0 0 0.00000000 PG32 -8588.723867 -20090.643282 15669.151907 280.381686 PG24 22871.271694 12675.543847 -3627.944084 177.697220 ... ( Several lines are omitted here ) PR08 5808.861773 17946.260291 -17172.857334 -102.035201 * 2009 4 1 0 15 0.00000000 PG32 -8297.565626 -21671.755580 13538.952491 280.377529 PG24 22933.972419 13075.825862 -790.871026 177.700812 

Simple interpretation

#cP2009 4 1 0 0 0.00000000 96 ORBIT IGS05 BHN ESOC 

• #c, edition

• P, Pos/Vel Sign a

• 2009 4 1 0 0 0.00000000, The year of the beginning of the precise ephemeris - month - Japan - when - branch - second

• 96, Epoch number

• IGS05
  http://acc.igs.org/igs-frames.html

• ESOC, European Space Operations Centre

## 1525 259200.00000000   900.00000000 54922 0.0000000000000                    

• 1525, GPS Zhou
• 259200.00000000, GPS Seconds in a week
• 900.00000000, Epoch interval Here is 900 second ,15 minute
• 54922, Julian day

+   48   G32G24G25G26G27G30G03G04G06G08G09G10G14G13G28G21G11                    
+        G22G20G18G16G19G23G02G31G17G12G15G29G07R04R06R07R10                    
+        R11R13R14R15R17R19R20R23R18R21R22R03R02R08  0  0  0                    

• 48, The number of satellites
• G32…R08, Satellite number

more SP Format description click here

rtklib Precise ephemeris applications

rtklib Support the use of precise ephemeris , As you can see from the code below , We can use parameters by specifying ephemeris EPHOPT_PREC, In this way, when solving the satellite position , The precise ephemeris is used .

extern int satpos(gtime_t time, gtime_t teph, int sat, int ephopt,
                  const nav_t *nav, double *rs, double *dts, double *var,
                  int *svh)
{
    
    trace(4,"satpos : time=%s sat=%2d ephopt=%d\n",time_str(time,3),sat,ephopt);
    
    *svh=0;
    
    switch (ephopt) {
    
        case EPHOPT_BRDC  : return ephpos     (time,teph,sat,nav,-1,rs,dts,var,svh);
        case EPHOPT_SBAS  : return satpos_sbas(time,teph,sat,nav,   rs,dts,var,svh);
        case EPHOPT_SSRAPC: return satpos_ssr (time,teph,sat,nav, 0,rs,dts,var,svh);
        case EPHOPT_SSRCOM: return satpos_ssr (time,teph,sat,nav, 1,rs,dts,var,svh);
        case EPHOPT_PREC  :
            if (!peph2pos(time,sat,nav,1,rs,dts,var)) break; else return 1;
    }
    *svh=-1;
    return 0;
}

If we use it directly rtklib Compiled executable file for data processing , So in option Just set a precise ephemeris in the .

Interpolation processing

The interval of precise ephemeris broadcasting is 15 minute , Therefore, interpolation processing is needed in practical application .rtklib Is used in Neville Interpolation method .

/* polynomial interpolation by Neville's algorithm ---------------------------*/
static double interppol(const double *x, double *y, int n)
{
    
    int i,j;
    
    for (j=1;j<n;j++) {
    
        for (i=0;i<n-j;i++) {
    
            y[i]=(x[i+j]*y[i]-x[i]*y[i+1])/(x[i+j]-x[i]);
        }
    }
    return y[0];
}

Neville Introduction to interpolation

Understand the direct skip of Neville interpolation

Neville Probably Not as well known as Newton and Lagrange interpolation , So here's a brief introduction . Neville interpolation is a method composed of two n-1 Construct an interpolation polynomial n Polynomial of degree Linear successive interpolation Method . What is linear successive interpolation ？ Let's take five points as an example .
First , Use all the $p_i$ and $p_{i+1}$, Such as $p_0$ and $p_1$ Linear interpolation , We get four first-order polynomials . Then, three second-order polynomials can be obtained by linear interpolation using four obtained first-order polynomials , Keep going like this , Get a fourth-order polynomial , This fourth-order polynomial passes through these five points .

If it still feels a little abstract , Look directly at the example below . For three points (-1,0)(0,1)(1,0) Conduct 2 Order Neville interpolation , give the result as follows .

Comparison between precise ephemeris solution and broadcast ephemeris

Precision ephemeris solution results

Broadcast ephemeris solution results