GPS from entry to abandonment (XIV), ionospheric delay

One 、 Ionosphere concept

the ionosphere （Ionosphere） It is an ionized region of the earth's atmosphere . It is the upper atmosphere ionized by solar high-energy radiation and cosmic rays .50 The whole earth's atmosphere over kilometers is in a state of partial ionization or complete ionization , The ionosphere is a partially ionized area of the atmosphere , The completely ionized atmospheric region is called the magnetosphere .

        The ionosphere ranges from about 50 It starts from km and stretches to about 1000 km The altitude of the earth's upper atmospheric airspace . The main characteristics of the ionosphere are determined by electron density 、 electron temperature 、 Collision frequency 、 Ion density 、 The basic parameters of spatial distribution such as ion temperature and ion composition .
        The research object of ionosphere is mainly the distribution of electron density with height . Electron density （ Or electron concentration ） Is the number of free electrons per unit volume , Changes with altitude and atmospheric composition at various altitudes 、 Atmospheric density, solar radiation flux and other factors . Electron density at any point in the ionosphere , It depends on the production of free electrons mentioned above 、 Disappearance and migration . In different areas , The relative functions of the three and their specific ways of action are also very different . There are quite a lot of free electrons and ions in the ionosphere , It can change the propagation speed of radio waves , Refraction occurs 、 Reflection and scattering , The polarization surface rotates and is absorbed to varying degrees .

Two 、 The influence of ionosphere on satellite navigation

3、 ... and 、 Dual frequency receiver eliminates ionospheric delay

Four 、 Single frequency receiver eliminates ionospheric delay

The last parentheses in each formula above indicate the unit of operation ,semi-circle It's a semicircle , The conversion relationship between it and radian is π  Radian equals a semicircle . Here's an excerpt from RTKLIB of use Klobuchar Function code for calculating ionospheric delay by 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 , So when converting to a semicircle, you need to divide by π .
 

double ionmodel(gtime_t t, const double *ion, const double *pos,
                       const double *azel)
{
	const double ion_default[]={ /* 2004/1/1 */
		0.1118E-07,-0.7451E-08,-0.5961E-07, 0.1192E-06,
	    0.1167E+06,-0.2294E+06,-0.1311E+06, 0.1049E+07
	};
    double tt,f,psi,phi,lam,amp,per,x;
    int week;
 
    if (pos[2]<-1E3||azel[1]<=0) return 0.0;
    if (norm(ion,8)<=0.0) ion=ion_default; // If there are no ionospheric parameters , With default parameters 
 
    /* earth centered angle (semi-circle) */
    psi=0.0137/(azel[1]/PI+0.11)-0.022;
 
    /* subionospheric latitude/longitude (semi-circle) */
    phi=pos[0]/PI+psi*cos(azel[0]);
    if      (phi> 0.416) phi= 0.416;
    else if (phi<-0.416) phi=-0.416;
    lam=pos[1]/PI+psi*sin(azel[0])/cos(phi*PI);
 
    /* geomagnetic latitude (semi-circle) */
    phi+=0.064*cos((lam-1.617)*PI);
 
    /* local time (s) */
    tt=43200.0*lam+time2gpst(t,&week);
    tt-=floor(tt/86400.0)*86400.0; /* 0<=tt<86400 */
 
    /* slant factor */
    f=1.0+16.0*pow(0.53-azel[1]/PI,3.0);
 
    /* ionospheric delay */
    amp=ion[0]+phi*(ion[1]+phi*(ion[2]+phi*ion[3]));
    per=ion[4]+phi*(ion[5]+phi*(ion[6]+phi*ion[7]));
    amp=amp<    0.0?    0.0:amp;
    per=per<72000.0?72000.0:per;
    x=2.0*PI*(tt-50400.0)/per;
 
    return CLIGHT*f*(fabs(x)<1.57?5E-9+amp*(1.0+x*x*(-0.5+x*x/24.0)):5E-9);
}

For single frequency receiver Klobuchar The ionospheric delay calculated by the model can roughly eliminate the effect of ionospheric delay 50%, The dual frequency method can eliminate most , The accuracy is 1m following .