mirror of
https://github.com/gnss-sdr/gnss-sdr
synced 2024-10-30 14:46:23 +00:00
117 lines
4.2 KiB
Matlab
117 lines
4.2 KiB
Matlab
function [pos, el, az, dop] = leastSquarePos(satpos, obs, settings)
|
|
% Function calculates the Least Square Solution.
|
|
%
|
|
% [pos, el, az, dop] = leastSquarePos(satpos, obs, settings);
|
|
%
|
|
% Inputs:
|
|
% satpos - Satellites positions (in ECEF system: [X; Y; Z;] -
|
|
% one column per satellite)
|
|
% obs - Observations - the pseudorange measurements to each
|
|
% satellite:
|
|
% (e.g. [20000000 21000000 .... .... .... .... ....])
|
|
% settings - receiver settings
|
|
%
|
|
% Outputs:
|
|
% pos - receiver position and receiver clock error
|
|
% (in ECEF system: [X, Y, Z, dt])
|
|
% el - Satellites elevation angles (degrees)
|
|
% az - Satellites azimuth angles (degrees)
|
|
% dop - Dilutions Of Precision ([GDOP PDOP HDOP VDOP TDOP])
|
|
|
|
%--------------------------------------------------------------------------
|
|
% SoftGNSS v3.0
|
|
%--------------------------------------------------------------------------
|
|
% Based on Kai Borre
|
|
%
|
|
% GNSS-SDR is a Global Navigation Satellite System software-defined receiver.
|
|
% This file is part of GNSS-SDR.
|
|
%
|
|
% SPDX-FileCopyrightText: Kai Borre
|
|
% SPDX-License-Identifier: GPL-3.0-or-later
|
|
|
|
%==========================================================================
|
|
|
|
%=== Initialization =======================================================
|
|
nmbOfIterations = 7;
|
|
|
|
dtr = pi/180;
|
|
pos = zeros(4, 1);
|
|
X = satpos;
|
|
nmbOfSatellites = size(satpos, 2);
|
|
|
|
A = zeros(nmbOfSatellites, 4);
|
|
omc = zeros(nmbOfSatellites, 1);
|
|
az = zeros(1, nmbOfSatellites);
|
|
el = az;
|
|
|
|
%=== Iteratively find receiver position ===================================
|
|
for iter = 1:nmbOfIterations
|
|
|
|
for i = 1:nmbOfSatellites
|
|
if iter == 1
|
|
%--- Initialize variables at the first iteration --------------
|
|
Rot_X = X(:, i);
|
|
trop = 2;
|
|
else
|
|
%--- Update equations -----------------------------------------
|
|
rho2 = (X(1, i) - pos(1))^2 + (X(2, i) - pos(2))^2 + ...
|
|
(X(3, i) - pos(3))^2;
|
|
traveltime = sqrt(rho2) / settings.c ;
|
|
|
|
%--- Correct satellite position (do to earth rotation) --------
|
|
Rot_X = e_r_corr(traveltime, X(:, i));
|
|
|
|
%--- Find the elevation angel of the satellite ----------------
|
|
[az(i), el(i), dist] = topocent(pos(1:3, :), Rot_X - pos(1:3, :));
|
|
|
|
if (settings.useTropCorr == 1)
|
|
%--- Calculate tropospheric correction --------------------
|
|
trop = tropo(sin(el(i) * dtr), ...
|
|
0.0, 1013.0, 293.0, 50.0, 0.0, 0.0, 0.0);
|
|
else
|
|
% Do not calculate or apply the tropospheric corrections
|
|
trop = 0;
|
|
end
|
|
end % if iter == 1 ... ... else
|
|
|
|
%--- Apply the corrections ----------------------------------------
|
|
omc(i) = (obs(i) - norm(Rot_X - pos(1:3), 'fro') - pos(4) - trop);
|
|
|
|
%--- Construct the A matrix ---------------------------------------
|
|
A(i, :) = [ (-(Rot_X(1) - pos(1))) / obs(i) ...
|
|
(-(Rot_X(2) - pos(2))) / obs(i) ...
|
|
(-(Rot_X(3) - pos(3))) / obs(i) ...
|
|
1 ];
|
|
end % for i = 1:nmbOfSatellites
|
|
|
|
% These lines allow the code to exit gracefully in case of any errors
|
|
if rank(A) ~= 4
|
|
pos = zeros(1, 4);
|
|
return
|
|
end
|
|
|
|
%--- Find position update ---------------------------------------------
|
|
x = A \ omc;
|
|
|
|
%--- Apply position update --------------------------------------------
|
|
pos = pos + x;
|
|
|
|
end % for iter = 1:nmbOfIterations
|
|
|
|
pos = pos';
|
|
|
|
%=== Calculate Dilution Of Precision ======================================
|
|
if nargout == 4
|
|
%--- Initialize output ------------------------------------------------
|
|
dop = zeros(1, 5);
|
|
|
|
%--- Calculate DOP ----------------------------------------------------
|
|
Q = inv(A'*A);
|
|
|
|
dop(1) = sqrt(trace(Q)); % GDOP
|
|
dop(2) = sqrt(Q(1,1) + Q(2,2) + Q(3,3)); % PDOP
|
|
dop(3) = sqrt(Q(1,1) + Q(2,2)); % HDOP
|
|
dop(4) = sqrt(Q(3,3)); % VDOP
|
|
dop(5) = sqrt(Q(4,4)); % TDOP
|
|
end
|