function [afixed,sqnorm,Qahat,Z] = lambda2 (afloat,Qahat)%LAMBDA2: Integer ambiguity estimation using LAMBDA (basic version)%% This routine performs an integer ambiguity estimation using the % LAMBDA-method, as developed by the Delft University of Technology, % Mathematical Geodesy and Positioning.%% Input arguments:%    afloat: Float ambiguities (\hat{a}, must be a column!)%    Qahat : Variance/covariance matrix of ambiguities (Q_\hat{a})%% Output arguments:%    afixed: Estimated integers%    sqnorm: Distance between candidates and float ambiguity vector%    Qzhat : Decorrelated variance/covariance matrix%    Z     : Transformation matrix% ----------------------------------------------------------------------% File.....: lambda2.m% Date.....: 19-MAY-1999% Author...: Peter Joosten%            Mathematical Geodesy and Positioning%            Delft University of Technology% ----------------------------------------------------------------------% ----------------------------------------------------------------------% Initalise% ----------------------------------------------------------------------ncands = 2;n      = size (Qahat,1);afixed = zeros(n,ncands);sqnorm = zeros(1,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);% ----------------------------------------------------------------------% 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);% ----------------------------------------------------------------------% 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.% ----------------------------------------------------------------------Chi2 = chistart (D,L,afloat,ncands);% ----------------------------------------------------------------------% Find the requested number of candidates (search)% ----------------------------------------------------------------------[afixed,sqnorm,ierr] = lsearch (afloat,L,D,Chi2,ncands);if ierr == 1; error ('Not enough candidates were found!!'); end;% ----------------------------------------------------------------------% --- Perform the back-transformation and add the increments% ----------------------------------------------------------------------afixed = (afixed' * inv(Z))';afixed = round(afixed + repmat(incr,1,ncands));% ----------------------------------------------------------------------% End of routine: lambda2% ----------------------------------------------------------------------