GPS from entry to abandonment (XVII), tropospheric delay

One 、 Tropospheric concept

The troposphere （Troposphere） The layer of the earth's atmosphere near the ground . It is also the densest layer in the earth's atmosphere , It contains the entire atmosphere about 75% The quality of the , And almost all water vapor and aerosols .

• The lower boundary of the troposphere is connected with the ground , The upper bound height varies with geographical latitude and season , In low latitudes, the average altitude is 17 ~ 18 km , In mid latitudes, the average is 10 ~ 12 km , In high-dimensional areas, the average is 8 ~ 9 km , And summer is higher than winter .
• The troposphere in the field of satellite navigation is different from the strict definition of troposphere in Atmospheric Science . Tropospheric delay should be considered in the field of satellite navigation , Therefore, the region from the earth's surface to the ionosphere is regarded as the troposphere , From 0km To about 50km Atmospheric region .
• cloud 、 Fog 、 rain 、 Many weather phenomena such as snow occur in the troposphere .
• The main propagation modes or effects in the troposphere are ： Atmospheric refraction 、 Waveguide propagation 、 Tropospheric scattering 、 Multipath propagation 、 Atmospheric absorption , And the absorption and scattering of water vapor condensates and other atmospheric particles .

Two 、 The influence of troposphere on satellite navigation

Because satellites are outside the atmosphere , Satellite signals must pass through the troposphere in the atmosphere to spread to the earth , So it must be affected by the troposphere . The troposphere is a non dispersive medium , That is, the dielectric constant of the medium is independent of frequency , So in the troposphere , Electromagnetic waves of different frequencies have the same propagation speed . Therefore, the method of using dual frequency receiver to eliminate ionospheric delay used in the article of ionospheric delay cannot be used in the troposphere . This makes us generally use mathematical models to estimate tropospheric delay in practice . Of course , When there is a base station , The tropospheric delay can also be eliminated by differential method （ Refer to the article Difference GPS）.
 

3、 ... and 、 Tropospheric model

It may be because there are too many tropospheric models , The accuracy is not so high , stay GPS The official reference troposphere model is not given in the interface description document of . Here we have RTKLIB Used in Saastamoinen The model says .

The standard atmosphere model can be expressed as ：

Here's an excerpt from RTKLIB of use Saastamoinen The function code for calculating tropospheric delay by the model , It can correspond to the above formula one by one . Note the unit conversion during calculation ,azel[0], azel[1] They are azimuth and elevation ,pos[0], pos[1] They are the latitude and longitude of the receiver , Their units are radians ,pos[2] Is the receiver height , The unit is rice. .

/* troposphere model -----------------------------------------------------------
* compute tropospheric delay by standard atmosphere and saastamoinen model
* args   : gtime_t time     I   time
*          double *pos      I   receiver position {lat,lon,h} (rad,m)
*          double *azel     I   azimuth/elevation angle {az,el} (rad)
*          double humi      I   relative humidity
* return : tropospheric delay (m)
*-----------------------------------------------------------------------------*/
extern double tropmodel(gtime_t time, const double *pos, const double *azel,
                        double humi)
{
    const double temp0=15.0; /* temparature at sea level */
    double hgt,pres,temp,e,z,trph,trpw;
 
    if (pos[2]<-100.0||1E4<pos[2]||azel[1]<=0) return 0.0;
 
    /* standard atmosphere */
    hgt=pos[2]<0.0?0.0:pos[2];
 
    pres=1013.25*pow(1.0-2.2557E-5*hgt,5.2568);
    temp=temp0-6.5E-3*hgt+273.16;
    e=6.108*humi*exp((17.15*temp-4684.0)/(temp-38.45));
 
    /* saastamoninen model */
    z=PI/2.0-azel[1];
    trph=0.0022768*pres/(1.0-0.00266*cos(2.0*pos[0])-0.00028*hgt/1E3)/cos(z);
    trpw=0.002277*(1255.0/temp+0.05)*e/cos(z);
    return trph+trpw;
}