easy5.m

% EASY5  computes vector components of a baseline. With given C/A code
%	     and phase observations we estimate the ambiguities using the
%	     Lambda method and next estimate the baseline components by a
%	     least-squares procedure. The code does not handle
%	     1. cycle slips, and
%	     2. outliers.
%	     The present code is no real RTK code as all computational steps
%	     do not happen on an epoch-by-epoch basis

%Kai Borre 27-07-2002
%Copyright (c) by Kai Borre
%$Revision: 1.1 $  $Date: 2005/01/20  $ %%to run with Matlab version 7.0

% Initial computations of constants
v_light = 299792458;	     % vacuum speed of light m/s
f1 = 154*10.23E6;		     % L1 frequency Hz
f2 = 120*10.23E6;			 % L2 frequency Hz
lambda1 = v_light/f1;	     % wavelength on L1:  .19029367  m
lambda2 = v_light/f2;	     % wavelength on L2:  .244210213 m

% Read RINEX ephemerides file and convert to internal Matlab format
rinexe('site247j.01n','eph.dat'); 
Eph = get_eph('eph.dat'); 

% We identify the master observation file and open it
ofile1 = 'site247j.01o'; 
fid1 = fopen(ofile1,'rt');
[Obs_types1, ant_delta1, ifound_types1, eof11] = anheader(ofile1);
NoObs_types1 = size(Obs_types1,2)/2;

% We start by estimating the master position
[time1, dt1, sats1, eof1] = fepoch_0(fid1);
NoSv1 = size(sats1, 1);
m = NoSv1;
obs1raw = grabdata(fid1, NoSv1, NoObs_types1);
i = fobs_typ(Obs_types1,'C1'); % We use C/A pseudoranges
[X_i, el] = recpo_ls(obs1raw(:,i), sats1, time1, Eph);
[phi_i,lambda_i,h_i] =	...
    togeod(6378137,298.257223563,X_i(1),X_i(2),X_i(3));
% We close all files to ensure that the next reading starts
% at the top of the observation files
fclose all;

% Finding columns in Eph for each SV
for t = 1:m
	col_Eph(t) = find_eph(Eph,sats1(t),time1);
end

% Computation of elevation angle to all SVs.
all_sats1 = sats1;
% Delete Sv with elevation smaller than 10 degrees
sats1(el<10) = [];
del_sat = setdiff(all_sats1,sats1);

no_del_sat = [];
for t = 1:length(del_sat)
    no_dels = find(del_sat(t) == all_sats1);
    no_del_sat = [no_del_sat; no_dels];
end
No_del_sat = length(no_del_sat);

% The SV with largest elevation is taken as reference SV
[y,ind] = max(el);
rearr = sort(all_sats1);
refsv = rearr(ind);
fid1 = fopen(ofile1,'rt');
ofile2 = 'site24~1.01o'; 
fid2 = fopen(ofile2,'rt');

% We start reading both observation files
[Obs_types1, ant_delta1, ifound_types1, eof11] = anheader(ofile1);
NoObs_types1 = size(Obs_types1,2)/2;
obsstr(1,1:2) = 'P1'; % P1
obsstr(2,1:2) = 'P2'; % P2
obsstr(3,1:2) = 'L1'; % Phi1
obsstr(4,1:2) = 'L2'; % Phi2
match = zeros(1,4);
for t = 1:4
    for ii = 1:NoObs_types1
	mat = strmatch(obsstr(t,1:2),Obs_types1(1,2*ii-1:2*ii),'exact');
	if isempty(mat) == 0, match(1,t) = ii; end
    end
end
Oc = match;
[Obs_types2, ant_delta2, ifound_types2, eof12] = anheader(ofile2);
NoObs_types2 = size(Obs_types2,2)/2;

m1 = m-No_del_sat; % original number of SVs - deleted SVs due to low elevations
X_a = [];
X_j = X_i(1:3,1);
X = zeros(3+2*m1-2,1);

% We process three epochs for estimating ambiguities; the present data evidently
% need three or more epochs for getting reliable estimates of the float ambiguities
for q = 1:5
    X_j = X_i(1:3,1)+X(1:3,1);
    [time1, dt1, sats1, eof1] = fepoch_0(fid1);
    [time2, dt2, sats2, eof2] = fepoch_0(fid2);
    if time1 ~= time2
	disp('Epochs do not correspond in time')
	break
    end;
    time = time1;
    NoSv1 = size(sats1,1);
    NoSv2 = size(sats2,1);
    obsm = grabdata(fid1, NoSv1, NoObs_types1);
    obsr = grabdata(fid2, NoSv2, NoObs_types2);
    % Deleting SVs that are only observed at one receiver
    if NoSv1 ~= NoSv2
	kk = intersect(sats1, sats2); 
    else
	kk = sats1;
    end
    if q ==1, X = zeros(3+2*(length(kk)-length(no_del_sat)),1); end;  % coord.diff., N1, N2
    refrow = find(refsv == kk);
    % Reordering of rows in master and rover observations corresponding to
    % increasing SV numbers and deletion of non-used observation columns
    for s = 1:length(kk)
	j1 = find(kk(s) == sats1);
	j2 = find(kk(s) == sats2);
	obs1(s,1:length(Oc)) = obsm(j1,Oc);
	obs2(s,1:length(Oc)) = obsr(j2,Oc);
    end

    tt = 0;
    A1 = [];
    t0 = 1:length(kk);
    t1 = setdiff(t0,no_del_sat); % we delete the low satellites

    % Computing rho for refsv
    [tcorr,rhok_j,Xk_ECF] = get_rho(time, obs2(refrow,1), Eph(:,col_Eph(refrow)), X_j);
    [tcorr,rhok_i,Xk_ECF] = get_rho(time, obs1(refrow,1), Eph(:,col_Eph(refrow)), X_i);

    for t = t1
	tt = tt+1;
	[tcorr,rhol_j,Xl_ECF] = get_rho(time,obs2(t,1), Eph(:,col_Eph(t)), X_j);
	[tcorr,rhol_i,Xl_ECF] = get_rho(time,obs1(t,1), Eph(:,col_Eph(t)), X_i);
	A0 = [(Xk_ECF(1)-X_j(1))/rhok_j - (Xl_ECF(1)-X_j(1))/rhol_j  ...
		(Xk_ECF(2)-X_j(2))/rhok_j - (Xl_ECF(2)-X_j(2))/rhol_j ...
		(Xk_ECF(3)-X_j(3))/rhok_j - (Xl_ECF(3)-X_j(3))/rhol_j];
	A1 = [A1; A0];
	Phi1 = (obs1(refrow,3)-obs1(t,3)-obs2(refrow,3)+obs2(t,3))*lambda1;
	Phi2 = (obs1(refrow,4)-obs1(t,4)-obs2(refrow,4)+obs2(t,4))*lambda2;
	b(tt,:) = Phi1-lambda1*X(3+tt,1);
	b(length(t1)+tt,:) = Phi2-lambda2*X(3+length(t1)+tt,1);
	bk(tt,:) =  rhok_i-rhok_j-rhol_i+rhol_j;
	bk(length(t1)+tt,:) =  rhok_i-rhok_j-rhol_i+rhol_j;
    end;
    m1 = length(t1); % New m1: we have deleted non-common and low satellites
    N = zeros(3+2*m1,3+2*m1);	  % initialization of normals
    rs = zeros(3+2*m1,1);	      % initialization of right side
    % Computation of covariance matrix Sigma for double differenced observations
    D = [ones(m1,1) -eye(m1) -ones(m1,1) eye(m1)];
    Sigma = D*D';
    A_modi = eye(m1);	    	  % modified coefficient matrix
    col = find(refsv == sats1);   % find column for reference PRN
    A_modi(:,col) = -ones(m1,1);
    A_aug = [A1 lambda1*A_modi 0*eye(m1); A1 0*eye(m1) lambda2*A_modi];
    N = N+A_aug'*kron(eye(2),Sigma)*A_aug;
    rs = rs+A_aug'*kron(eye(2),Sigma)*(b-bk);
end %q
PP = pinv(N);
% X contains the three preliminary baseline components and the float ambiguities
X = PP*rs %;

% Estimation of ambiguities by means of the Lambda method
[a,sqnorm,Sigma_afixed,Z] = lambda(X(4:4+2*m1-1,1),PP(4:4+2*m1-1,4:4+2*m1-1));
% Correcting to baseline vector as consequence of changing float ambiguities to fixed ones
X(1:3,1) = X(1:3,1)-PP(1:3,4:4+2*m1-1)*inv(PP(4:4+2*m1-1,4:4+2*m1-1))*...
    (X(4:4+2*m1-1,1)-a(:,1)); %select first set of candidates
X(4:4+2*m1-1,1) = a(:,1);
fprintf('\n N1 for PRN %3.0f: %3.0f',[sats1(t1)'; a(1:m1,1)'])
fprintf('\n')
fprintf('\n N2 for PRN %3.0f: %3.0f',[sats1(t1)';a(m1+1:2*m1,1)'])

% We close and reopen all files in order to start reading at a known position
fclose all;
ofile1 = 'site247j.01o';
fid1 = fopen(ofile1,'rt');
ofile2 = 'site24~1.01o';
fid2 = fopen(ofile2,'rt');

% At end of ofile2 we overwrite empty observations with NaN's to obtain 22 valid epochs
qend = 22;
X_jacc = [];
base = [];
for q = 1:qend
    X_j = X_i(1:3,1)+X(1:3,1);
    [phi_j,lambda_j,h_j] = togeod(6378137,298.257223563,X_j(1),X_j(2),X_j(3));
    [time1, dt1, sats1, eof1] = fepoch_0(fid1);
    [time2, dt2, sats2, eof2] = fepoch_0(fid2);
    if time1 ~= time2
	disp('Epochs do not correspond in time')
	break
    end;
    time = time1;
    NoSv1 = size(sats1,1);
    NoSv2 = size(sats2,1);
    obsm = grabdata(fid1, NoSv1, NoObs_types1);
    obsr = grabdata(fid2, NoSv2, NoObs_types2);
    obs1 = obsm(:,Oc); % P1 P2 Phi1 Phi2
    % Reordering of rows in obsr to correspond to obsm
    for s = 1:m
	Ind = find(sats1(s) == sats2(:));
	obs2(s,:) = obsr(Ind,Oc);
    end
    % Computing rho for refsv
    [tcorr,rhok_j,Xk_ECF] = get_rho(time, obs2(1,1), Eph(:,col_Eph(1)), X_j);
    [tcorr,rhok_i,Xk_ECF] = get_rho(time, obs1(1,1), Eph(:,col_Eph(1)), X_i);
    tt = 0;
    A1 = [];
    for t = t1
	tt = tt+1;
	[tcorr,rhol_j,Xl_ECF] = get_rho(time,obs2(t,1), Eph(:,col_Eph(t)), X_j);
	[tcorr,rhol_i,Xl_ECF] = get_rho(time,obs1(t,1), Eph(:,col_Eph(t)), X_i);
	A0 = [(Xk_ECF(1)-X_j(1))/rhok_j - (Xl_ECF(1)-X_j(1))/rhol_j  ...
		(Xk_ECF(2)-X_j(2))/rhok_j - (Xl_ECF(2)-X_j(2))/rhol_j ...
		(Xk_ECF(3)-X_j(3))/rhok_j - (Xl_ECF(3)-X_j(3))/rhol_j];
	A1 = [A1; A0];
	% Tropospheric correction using standard meteorological parameters
       %[az,el_ki,d] = topocent(X_i(1:3),Xk_ECF-X_i(1:3));
       %[az,el_li,d] = topocent(X_i(1:3),Xl_ECF-X_i(1:3));
       %[az,el_kj,d] = topocent(X_j(1:3),Xk_ECF-X_j(1:3));
       %[az,el_lj,d] = topocent(X_j(1:3),Xl_ECF-X_j(1:3));
	%el_ki,    el_li,    el_kj,    el_lj
       %t_corr = tropo(sin(el_lj*pi/180),...
	%    h_j*1.e-3,1013,293,50,0,0,0)...
	%    -tropo(sin(el_li*pi/180),....
	%    h_i*1.e-3,1013,293,50,0,0,0)...
	%    -tropo(sin(el_kj*pi/180),...
	%    h_j*1.e-3,1013,293,50,0,0,0)...
	%    +tropo(sin(el_ki*pi/180),...
	%    h_i*1.e-3,1013,293,50,0,0,0);
	Phi1 = (obs1(refrow,3)-obs1(t,3)-obs2(refrow,3)+obs2(t,3))*lambda1; %-t_corr;
	Phi2 = (obs1(refrow,4)-obs1(t,4)-obs2(refrow,4)+obs2(t,4))*lambda2; %-t_corr;
	b(tt,:) = Phi1-lambda1*a(tt,1);
	b(m1+tt,:) = Phi2-lambda2*a(m1+tt,1);
	bk(tt,:) =  rhok_i-rhok_j-rhol_i+rhol_j;
	bk(m1+tt,:) =  rhok_i-rhok_j-rhol_i+rhol_j;
    end; % t
    N = [A1;A1]'*[Sigma zeros(m1,m1);zeros(m1,m1) Sigma]*[A1;A1];
    rs = [A1;A1]'*[Sigma zeros(m1,m1); zeros(m1,m1) Sigma]*(b-bk);
    x = inv(N)*rs;
    X_j = X_j+x;
    base = [base X_j-X_i(1:3)];
    X_jacc = [X_jacc X_j];
end %q
X = X_j-X_i(1:3,1);
% Transformation of geocentric baseline coordinates into topocentric coordinates
for i = 1:qend
    [e(i),n(i),u(i)] = xyz2enu(phi_j,lambda_j,base(1,i),base(2,i),base(3,i));
end
fprintf('\n\nBaseline Components\n')
fprintf('\nX: %8.3f m,  Y: %8.3f m,  Z: %8.3f m\n',X(1),X(2),X(3))
fprintf('\nE: %8.3f m,  N: %8.3f m,  U: %8.3f m\n',mean(e),mean(n),mean(u))

figure(1);
plot(1:qend,[(e-e(1))' (n-n(1))' (u-u(1))']*1000,'linewidth',2)
title('Differential Position Estimates From Phase Observations','fontsize',16)
ylabel('Corrections to Initial Position [mm]','fontsize',16)
xlabel('Epochs [1 s interval]','fontsize',16)
legend('East','North','Up')
set(gca,'fontsize',16)
legend