GPS from getting started to giving up (16), satellite clock error and satellite ephemeris error

One 、 Satellite clock error

GPS Satellite clock error （ Referred to as satellite clock error ） Refer to GPS Satellite clock and GPS The difference between standard times . Even though GPS The satellite adopts high precision Atomic clock to ensure the accuracy of the clock , It has long-term stability ; But atomic clocks still have the problems of frequency shift and aging , Cause them to interact with GPS There will be a difference between standard time . This deviation must be corrected . Of course, the others GNSS Systems such as Beidou will have similar problems , Here we only use GPS For example, .
 

Let's talk about the treatment of the relativistic effect correction term in the formula . Relativistic effect includes special relativistic effect and general relativistic effect . Even though GPS The satellite has adjusted the clock frequency according to the relativistic effect , But because the satellite orbit is not a regular circle , It's oval , Therefore, the influence of relativistic effect on the frequency of clock at different orbital positions is different , Therefore, it needs to be revised .

GPS The relativistic correction given in the interface description document of is ：

Two 、 Satellite ephemeris error

When the satellite is in space , Its orbit will be affected by various factors , Such as the force caused by the uneven mass of the earth 、 Tidal influence 、 Atmospheric drag 、 Sunlight pressure and so on , Resulting in complex and irregular satellite orbit . Therefore, there is always a deviation between the satellite position calculated through the ephemeris and the actual position of the satellite , We call this error satellite ephemeris error .

        The error of satellite ephemeris belongs to systematic error . It is a three-dimensional vector , It can be divided into three directions ： Radial component 、 Tangential component and normal component . among Radial component It is the component in the direction of the connection between the receiver and the satellite ; The tangential component is perpendicular to the radial component in the satellite orbital plane to the direction of the satellite's flight speed ; The normal component is perpendicular to the orbital plane . Of these three components , The influence of tangential classification and normal component on pseudo range observation can be basically ignored , The radial component mainly affects the pseudo range observation .

At present, the commonly used ephemeris is Broadcast ephemeris and precision ephemeris

•   Broadcast ephemeris It's broadcast by positioning satellite . Its accuracy is unstable , Subject to ephemeris age 、 Whether the track is adjusted 、 Whether it is in the shadow of the earth and the moon, and many other factors are accidental for users . Broadcast ephemeris error is current GPS One of the important error sources of positioning . At present, the satellite ephemeris error calculated according to the broadcast ephemeris can be reduced to decimeter level .
• Precise ephemeris It is the satellite orbit information used for satellite precise positioning . It consists of observation data from several satellite tracking stations , After the post-processing, it can be calculated . current GPS There are mainly two kinds of precise ephemeris ： By the Defense Mapping Agency (DMA) The precision ephemeris produced by IGS Precision ephemeris produced . The ephemeris accuracy of the former is about 2cm, The ephemeris accuracy of the latter is about 5cm.

3、 ... and 、 Error elimination

Satellite clock error and satellite ephemeris error are the same for all receivers , So you can use Difference To eliminate .

double geodist(const double *rs, const double *rr, double *e)
{
    double r;
    int i;
 
    if (norm(rs,3)<RE_WGS84) return -1.0;
    for (i=0;i<3;i++) e[i]=rs[i]-rr[i];
    r=norm(e,3);
    for (i=0;i<3;i++) e[i]/=r;
    return r+OMGE*(rs[0]*rr[1]-rs[1]*rr[0])/CLIGHT;
}