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mirror of https://github.com/gnss-sdr/gnss-sdr synced 2024-10-30 06:36:21 +00:00
gnss-sdr/utils/matlab/libs/geoFunctions/leastSquarePos.m

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