svpeph.m

Matlab GPS Toolbox

%                          svpeph.m
%  Scope:   This MATLAB macro computes ECEF satellite position based on 
%           satellite ephemeris data; WGS-84 constants are used.
%  Usage:   pse = svpeph(tsim,edata)
%  Description of parameters:
%           tsim      - input, tsim, GPS system time at time of transmission,
%                       i.e. GPS time corrected for transit time 
%                       (range/speed of light), in seconds
%           edata(1)  - input, toe, reference time ephemeris, in seconds         
%           edata(2)  - input, smaxis (a), semi-major axis, in meters
%           edata(3)  - input, ecc (e), satellite eccentricity  
%           edata(4)  - input, izero (I_0), inclination angle at reference time, 
%                       in radians 
%           edata(5)  - input, razero (OMEGA_0), right ascension at reference 
%                       time, in radians (longitude of ascending node of orbit 
%                       plane at weekly epoch)
%           edata(6)  - input, argper (omega), argument of perigee, in radians
%           edata(7)  - input, mzero (M_0), mean anomaly at reference time, in 
%                       radians      
%           edata(8)  - input, radot (OMEGA_DOT), rate of right ascension, in 
%                       radians/second 
%           edata(9)  - input, deln (delta_n), mean motion difference from 
%                       computed value, in radians/second 
%           edata(10) - input, idot (I_DOT), rate of inclination angle, in 
%                       radians/second 
%           edata(11) - input, cic, amplitude of the cosine harmonic
%                       correction term to the angle of inclination, in radians
%           edata(12) - input, cis, amplitude of the sine harmonic correction
%                       term to the angle of inclination, in radians
%           edata(13) - input, crc, amplitude of the cosine harmonic correction
%                       term to the orbit radius, in meters
%           edata(14) - input, crs, amplitude of the sine harmonic correction
%                       term to the orbit radius, in meters
%           edata(15) - input, cuc, amplitude of the cosine harmonic correction
%                       term to the argument of latitude, in radians
%           edata(16) - input, cus, amplitude of the sine harmonic correction
%                       term to the argument of latitude, in radians
%           pse       - output, ECEF satellite position vector, the components 
%                       are in meters
%  External Matlab macros used:  wgs84con
%  Last update:  11/09/00
%  Copyright (C) 1996-00 by LL Consulting. All Rights Reserved.

function   pse = svpeph(tsim,edata) 

[nrow,ncol] = size(edata);
if  ncol ~= 16
   error('Error  -  SVPEPH; check the dimension of the inputs');
end

%  Constants and initialization

wgs84con;
% global constants used: gravpar, rot_rate

toe    = edata(1); 
smaxis = edata(2); 
ecc    = edata(3); 
izero  = edata(4); 
razero = edata(5); 
argper = edata(6); 
mzero  = edata(7); 
radot  = edata(8);
deln   = edata(9); 
idot   = edata(10);
cic    = edata(11);
cis    = edata(12);
crc    = edata(13);
crs    = edata(14);
cuc    = edata(15);
cus    = edata(16);

%  Compute GPS time of week at which SV position is computed

ttr = tsim;   
tk = ttr - toe;   %  time from ephemeris reference epoch, in seconds
if  tk > 302400.
  tk = tk - 604800;
elseif  tk < -302400.
  tk = tk + 604800;
end

%  Initialization 
          
mmot = sqrt(gravpar/smaxis/smaxis/smaxis) + deln;
r1mecc2 = sqrt(1. - ecc * ecc);
sinw = sin(argper);
cosw = cos(argper);
izero = izero + idot * tk;
sinio = sin(izero);
cosio = cos(izero);

%  Compute mean anomaly

meanom = mzero + mmot * tk;

%  Compute eccentric anomaly  (Keppler's equation)

eccano = meanom + ecc * sin(meanom);  %  initial guess 
for j = 1:6     % number of iterations can be changed if necessary
   temp1 = 1. - ecc * cos(eccano);
   temp2 = sin(eccano) - eccano * cos(eccano);
   eccano = (ecc * temp2 + meanom) / temp1;
end

%  Compute sine and cosine of eccentric anomaly, and rho

sine = sin(eccano);
cose = cos(eccano);
rho = 1. - ecc * cose;

%  Compute sine and cosine of true anomaly

cosv = (cose - ecc) / rho;
sinv = r1mecc2 * sine / rho;

%  Compute sine and cosine of argument of latitude

sinphi = cosv * sinw + cosw * sinv;
cosphi = cosv * cosw - sinv * sinw;
cos2phi = 1. - 2. * sinphi * sinphi;
sin2phi = 2. * sinphi * cosphi;

%  Correct argument of latitude

delu = cus * sin2phi + cuc * cos2phi;
sindelu = sin(delu);
cosdelu = cos(delu);
sinu = cosdelu * sinphi + sindelu * cosphi;
cosu = cosdelu * cosphi - sindelu * sinphi;

%  Compute satellite position in orbital plane

delr = crs * sin2phi + crc * cos2phi;
orbrad = smaxis * rho + delr;
xprime = orbrad * cosu;
yprime = orbrad * sinu;

%  Correct inclination

deli = cis * sin2phi + cic * cos2phi;
sindeli = sin(deli);
cosdeli = cos(deli);
sini = cosdeli * sinio + sindeli * cosio;
cosi = cosdeli * cosio - sindeli * sinio;

%  Compute longitude of ascending node, its sine and cosine

omega = razero + radot * tk - rot_rate * ttr;
sinome = sin(omega);
cosome = cos(omega);

%  Compute satellite position in ECEF, in meters

pse(1) = xprime * cosome - yprime * cosi * sinome;
pse(2) = xprime * sinome + yprime * cosi * cosome;
pse(3) = yprime * sini;