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function gpsPvt = GpsWlsPvt(gnssMeas,allGpsEph,bRaw) |
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%gpsPvt = GpsWlsPvt(gnssMeas,allGpsEph,bRaw) |
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%compute PVT from gnssMeas |
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% Input: gnssMeas, structure of pseudoranges, etc. from ProcessGnssMeas |
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% allGpsEph, structure with all ephemeris |
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% [bRaw], default true, true => use raw pr, false => use smoothed |
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% |
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% Output: |
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% gpsPvt.FctSeconds Nx1 time vector, same as gnssMeas.FctSeconds |
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% .allLlaDegDegM Nx3 matrix, (i,:) = [lat (deg), lon (deg), alt (m)] |
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% .sigmaLlaM Nx3 standard deviation of [lat,lon,alt] (m) |
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% .allBcMeters Nx1 common bias computed with llaDegDegM |
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% .allVelMps Nx3 (i,:) = velocity in NED coords |
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% .sigmaVelMps Nx3 standard deviation of velocity (m/s) |
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% .allBcDotMps Nx1 common freq bias computed with velocity |
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% .numSvs Nx1 number of satellites used in corresponding llaDegDegM |
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% .hdop Nx1 hdop of corresponding fix |
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% |
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%Algorithm: Weighted Least Squares |
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%Author: Frank van Diggelen |
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%Open Source code for processing Android GNSS Measurements |
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if nargin<3 |
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bRaw = true; |
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else |
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%check that smoothed pr fields exists in input |
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if any(~isfield(gnssMeas,{'PrSmM','PrSmSigmaM'})) |
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error('If bRaw is false, gnssMeas must have fields gnssMeas.PrSmM and gnssMeas.PrSmSigmaM') |
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end |
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end |
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xo =zeros(8,1);%initial state: [center of the Earth, bc=0, velocities = 0]' |
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weekNum = floor(gnssMeas.FctSeconds/GpsConstants.WEEKSEC); |
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N = length(gnssMeas.FctSeconds); |
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gpsPvt.FctSeconds = gnssMeas.FctSeconds; |
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gpsPvt.allLlaDegDegM = zeros(N,3)+NaN; |
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gpsPvt.sigmaLLaM = zeros(N,3)+NaN; |
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gpsPvt.allBcMeters = zeros(N,1)+NaN; |
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gpsPvt.allVelMps = zeros(N,3)+NaN; |
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gpsPvt.sigmaVelMps = zeros(N,3)+NaN; |
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gpsPvt.allBcDotMps = zeros(N,1)+NaN; |
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gpsPvt.numSvs = zeros(N,1); |
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gpsPvt.hdop = zeros(N,1)+inf; |
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for i=1:N |
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iValid = find(isfinite(gnssMeas.PrM(i,:))); %index into valid svid |
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svid = gnssMeas.Svid(iValid)'; |
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[gpsEph,iSv] = ClosestGpsEph(allGpsEph,svid,gnssMeas.FctSeconds(i)); |
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svid = svid(iSv); %svid for which we have ephemeris |
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numSvs = length(svid); %number of satellites this epoch |
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gpsPvt.numSvs(i) = numSvs; |
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if numSvs<4 |
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continue;%skip to next epoch |
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end |
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%% WLS PVT ----------------------------------------------------------------- |
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%for those svIds with valid ephemeris, pack prs matrix for WlsNav |
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prM = gnssMeas.PrM(i,iValid(iSv))'; |
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prSigmaM= gnssMeas.PrSigmaM(i,iValid(iSv))'; |
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prrMps = gnssMeas.PrrMps(i,iValid(iSv))'; |
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prrSigmaMps = gnssMeas.PrrSigmaMps(i,iValid(iSv))'; |
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tRx = [ones(numSvs,1)*weekNum(i),gnssMeas.tRxSeconds(i,iValid(iSv))']; |
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prs = [tRx, svid, prM, prSigmaM, prrMps, prrSigmaMps]; |
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xo(5:7) = zeros(3,1); %initialize speed to zero |
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[xHat,~,~,H,Wpr,Wrr] = WlsPvt(prs,gpsEph,xo);%compute WLS solution |
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xo = xo + xHat; |
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%extract position states |
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llaDegDegM = Xyz2Lla(xo(1:3)'); |
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gpsPvt.allLlaDegDegM(i,:) = llaDegDegM; |
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gpsPvt.allBcMeters(i) = xo(4); |
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%extract velocity states |
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RE2N = RotEcef2Ned(llaDegDegM(1),llaDegDegM(2)); |
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%NOTE: in real-time code compute RE2N once until position changes |
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vNed = RE2N*xo(5:7); %velocity in NED |
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gpsPvt.allVelMps(i,:) = vNed; |
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gpsPvt.allBcDotMps(i) = xo(8); |
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%compute HDOP |
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H = [H(:,1:3)*RE2N', ones(numSvs,1)]; %observation matrix in NED |
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P = inv(H'*H);%unweighted covariance |
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gpsPvt.hdop(i) = sqrt(P(1,1)+P(2,2)); |
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%compute variance of llaDegDegM |
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%inside LsPvt the weights are used like this: |
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% z = Hx, premultiply by W: Wz = WHx, and solve for x: |
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% x = pinv(Wpr*H)*Wpr*zPr; |
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% the point of the weights is to make sigma(Wz) = 1 |
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% therefore, the variances of x come from diag(inv(H'Wpr'WprH)) |
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P = inv(H'*(Wpr'*Wpr)*H); %weighted covariance |
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gpsPvt.sigmaLLaM(i,:) = sqrt(diag(P(1:3,1:3))); |
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%similarly, compute variance of velocity |
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P = inv(H'*(Wrr'*Wrr)*H); %weighted covariance |
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gpsPvt.sigmaVelMps(i,:) = sqrt(diag(P(1:3,1:3))); |
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%%end WLS PVT -------------------------------------------------------------- |
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end |
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end %end of function GpsWlsPvt |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% Copyright 2016 Google Inc. |
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% |
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% Licensed under the Apache License, Version 2.0 (the "License"); |
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% you may not use this file except in compliance with the License. |
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% You may obtain a copy of the License at |
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% |
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% http://www.apache.org/licenses/LICENSE-2.0 |
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% |
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% Unless required by applicable law or agreed to in writing, software |
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% distributed under the License is distributed on an "AS IS" BASIS, |
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% WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
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% See the License for the specific language governing permissions and |
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% limitations under the License. |
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