function [afixed,sqnorm,Qahat,Z] = lambda1 (afloat,Qahat,ncands,fidlog)%LAMBDA1: Integer ambiguity estimation using LAMBDA (extended version)%% This routine performs an integer ambiguity estimation using the % LAMBDA-method, as developed by the Delft University of Technology, % Mathematical Geodesy and Positioning.%% This version (lambda1) is intended to be used mainly for research.% It has more options than the original code, such as output of% intermediate results, optional number of candidates to be returned% and so on. If you are not interested in these options, you can use % "lambda2"%% Input arguments:%    afloat: Float ambiguities (\hat{a}, must be a column!)%    Qahat : Variance/covariance matrix of ambiguities (Q_\hat{a})%    ncands: Number of candidates to be returned (default 2)%    fidlog: File-id for intermediate results (default 0, no output)%% Output arguments:%    afixed: Estimated integers%    sqnorm: Distance between candidates and float ambiguity vector%    Qzhat : Decorrelated variance/covariance matrix%    Z     : Transformation matrix% ----------------------------------------------------------------------% File.....: lambda1.m% Date.....: 19-MAY-1999% Version..: 2.0b% Author...: Peter Joosten%            Mathematical Geodesy and Positioning%            Delft University of Technology% ----------------------------------------------------------------------% ----------------------------------------------------------------------% Initialise% ----------------------------------------------------------------------if nargin < 3; ncands = 2; end;if nargin < 4; fidlog = 0; end;n      = size (Qahat,1);afixed = zeros(n,ncands);sqnorm = zeros(1,ncands);if fidlog ~= 0;   if fidlog == 1; clc; end;   fprintf (fidlog, '\n');   fprintf (fidlog, ' -----------------------------------------------------------------------\n');   fprintf (fidlog, ' "LAMBDA" - Least Squares Ambiguity Decorrelation Adjustment            \n');   fprintf (fidlog, ' Rel. 2.0b d.d. 19 MAY 1999                                             \n');   fprintf (fidlog, ' (c) Department of Mathematical Geodesy and Positioning (MGP)           \n');   fprintf (fidlog, '     Faculty of Civil Engineering and Geosciences                       \n');   fprintf (fidlog, '     Delft University of Technology, The Netherlands                    \n');   fprintf (fidlog, ' -----------------------------------------------------------------------\n');   fprintf (fidlog, '\n');end;% ----------------------------------------------------------------------% Display the input-arguments% ----------------------------------------------------------------------writemat (fidlog,'Original float ambiguities',afloat);writemat (fidlog,'Original variance/covariance matrix (Qahat)',Qahat);writemat (fidlog,'Number of candidates requested',ncands);% ----------------------------------------------------------------------% --- Perform tests on the input, these tests are rather extensive   ---% --- and can be switched off (by commenting-out) if necessary       ---% --- Tests: Is the Q-matrix symmetric?                              ---% ---        Is the Q-matrix positive-definite?                      ---% ---        Do the Q-matrix and ambiguity-vector have identical     ---% ---        dimensions?                                             ---% ---        Is the ambiguity vector a column?                       ---% ----------------------------------------------------------------------if ~isequal(Qahat-Qahat'<1E-12,ones(size(Qahat)));  error ('Variance/covariance matrix is not symmetric!');end;if sum(eig(Qahat)>0) ~= size(Qahat,1);  error ('Variance/covariance matrix is not positive definite!');end;if length(afloat) ~= size(Qahat,1);  error (['Variance/covariance matrix and vector of ambiguities do not have' ...	  ' identical dimensions!']);end;if size(afloat,2) ~= 1;  error ('Ambiguity-vector should be a column-vector');end;% ----------------------------------------------------------------------% Make estimates in 'a' between -1 and +1 by subtracting an% integer number, store the increments in 'incr' (= shift the centre% of the ellipsoid over the grid by an integer translation)% ----------------------------------------------------------------------incr   = afloat - rem(afloat,1);afloat = rem(afloat,1);writemat (fidlog,'shifted ambiguities - increments',[afloat incr]);% ----------------------------------------------------------------------% Compute the Z-transformation based on L and D of Q, ambiguities% are transformed according to \hat{z} = Z^T\hat{a}, Q is transformed% according to Q_\hat{z} = Z^T * Q_\hat{a} * Z% ----------------------------------------------------------------------[Qahat,Z,L,D,afloat] = decorrel (Qahat,afloat);writemat (fidlog,'Decorrelated Q-matrix',Qahat);writemat (fidlog,'Transformation matrix (Z)',Z);writemat (fidlog,'L-matrix, as used in ''search''',L);writemat (fidlog,'D-matrix, as used in ''search''',D);writemat (fidlog,'Transformed reduced ambiguities',afloat);% ----------------------------------------------------------------------% If the number of requested candidates is no more than "n+1", with "n"% the dimension of Q_\hat(a), we can compute a suitable Chi^2 such that% we have the requested number of candidates at minimum; use an eps% to make sure the candidates are inside the ellipsoid and not exactly% on the border.%% If the requested number of canditates is larger, we have to "guess"% the volume of the search-space, it can not be guarenteed the requested% number of canditates will actually be found.% ----------------------------------------------------------------------Chi2 = chistart (D,L,afloat,ncands);writemat (fidlog,'Chi-squared, size of the search-ellipsoid',Chi2);% ----------------------------------------------------------------------% Find the requested number of candidates (search)% ----------------------------------------------------------------------[afixed,sqnorm,ierr] = lsearch (afloat,L,D,Chi2,ncands);if ierr == 1;   fprintf (1,'Warning: Not enough candidates were found!!\n');   fprintf (1,'         Requested number.: %2d\n',ncands);end;writemat (fidlog,'Fixed transformed ''reduced'' ambiguities',afixed);writemat (fidlog,'Corresponding squared norms',sqnorm);% ----------------------------------------------------------------------% Finally, perform the back-transformation and add the increments% ----------------------------------------------------------------------afixed = (afixed' * inv(Z))';afixed = round(afixed + repmat(incr,1,ncands));writemat (fidlog,'Final fixed ambiguities',afixed);% ----------------------------------------------------------------------% End of routine: lambda1% ----------------------------------------------------------------------