LAMBDA.rar_GPS LAMBDA算法_figure1v3_lambda_lambda算法_差分 GPS

function [afixed,sqnorm,Ps,Qzhat,Z,nfixed,mu]=LAMBDA(ahat,Qahat,method,varargin) % % [afixed,sqnorm,Ps,Qzhat,Z,nfixed,mu]=LAMBDA(ahat,Qahat,method,varargin) % % This is the main routin of the LAMBDA software package. By default the ILS % method will be used for integer estimation based on the provided float % ambiguity vector ahat and associated variance-covariance matrix Qahat. % However, the user may also select other methods: integer rounding, % bootstrapping or Partial Ambiguity Resolution (PAR). Furthermore, there is % the option to apply the Ratio Test to decide on acceptance of the fixed % solution. % % NOTE 1: LAMBDA always first applies a decorrelation before the integer % estimation (for ILS this is required to guarantee an efficient search, for % rounding and bootstrapping it is required in order to get higher success % rates). % % NOTE 2: Two different ILS search strategies are implemented (see % documentation). The solution will be the same with both methods, but the % search-and-shrink method is known to be faster. % % INPUTS: % % ahat: Float ambiguities (must be a column!) % Qahat: Variance/covariance matrix of ambiguities % method: 1: ILS method based on search-and-shrink [DEFAULT] % 2: ILS method based enumeration in search % 3: integer rounding method % 4: integer bootstrapping method % 5: PAR with the input P0 of user-defined success rate % 6: ILS method with Ratio Test (uses search-and shrink) % varargin: Optional input arguments, see below % % OUTPUTS: % % afixed: Array of size (n x ncands) with the estimated integer % candidates, sorted according to the corresponding squared norms, % best candidate first. % For integer rounding and bootstrapping: ncands = 1 % sqnorm: Distance between integer candidate and float ambiguity vectors % in the metric of the variance-covariance matrix Qahat. % Only available for ILS. % Ps: Bootstrapped success rate. % If ILS/PAR is used, Ps is its lower bound; % If rounding is used, Ps is its upper bound; % If bootstrapping is used, Ps is the exact success rate. % Qzhat: Variance-covariance matrix of decorrelated ambiguities % (corresponding to fixed subset in case of PAR). % Z: Transformation matrix with % - dimension (n x n) for methods 1-4, 6 % - dimension (n x nfixed) for method 5 (PAR). % nfixed: Number of fixed ambiguities % - with methods 1 to 4: will always be equal to n % - with method 5 (PAR): will be equal to the number of % fixed decorrelated ambiguities % - with method 6 (ILS + Ratio test): will be equal to n if fixed % solution is accepted, and 0 otherwise % mu: Threshold value used for Ratio Test % % % [AFIXED,...] = LAMBDA(ahat,Qahat,method,'option',value,...) can be used % to specify various options. Possible options are % % 'ncands',value Number of requested integer candidate vectors % (only used with ILS/PAR, DEFAULT = 2) % 'P0',value - with method 5 (PAR): Minimum required success rate % [DEFAULT=0.995] % - with method 6 (ILS + Ratio test): Fixed failure rate % (available options: 0.01 or 0.001) [DEFAULT=0.001] % 'MU',value Fixed threshold value for Ratio Test % (value must be between 0 and 1) % % The Ratio Test will only be applied if method 6 is selected. By default % the Fixed Failure rate Ratio Test will be applied. The threshold value MU % is then determined such that the failure rate will not exceed the % specified P0 (DEFAULT 0.001). % If MU is specified, the value for P0 is ignored. % NOTE: the Ratio Test used here is % % Accept afixed iff: sqnorm(1)/sqnorm(2) <= MU % % Hence, the squared norm of the best (ILS) integer solution is in the % numerator. In literature often the reciprocal is used; the corresponding % critical value is then c = 1/MU. % %-------------------------------------------------------------------------- % Release date : 1-SEPT-2012 % Authors : Bofeng LI and Sandra VERHAGEN % % GNSS Research Centre, Curtin University % Mathematical Geodesy and Positioning, Delft University of Technology %-------------------------------------------------------------------------- % % REFERENCES: % 1. LAMBDA Software Package: Matlab implementation, Version 3.0. % Documentation provided with this software package. % 2. Teunissen P (1993) Least-squares estimation of the integer GPS % ambiguities. In: Invited lecture, section IV theory and methodology, % IAG General Meeting, Beijing, China % 3. Teunissen P (1995) The least-squares ambiguity decorrelation % adjustment: a method for fast GPS ambiguity estitmation. J Geod % 70:651-7 % 4. De Jonge P, Tiberius C (1996) The LAMBDA method of intger ambiguity % estimation:implementation aspects. % 5. Chang X ,Yang X, Zhou T (2005) MLAMBDA: a modified LAMBDA method for % integer least-squares estimation %=============================START PROGRAM===============================% if(nargin<2) error(['Not enough inputs: float solution', ... 'and its variance-covariance matrix must be specified']); end %By default use ILS with search-and-shrink if(nargin<3) method = 1; end %If ILS/PAR method is not used, only a unique solution is available if(ismember(method,[3,4])), ncands = 1; else ncands = 2; end %For PAR method, the user-defined success rate is necessary. %Default value is 0.995 if(method==5) P0 = 0.995; end %Default values for Ratio Test if(method==6) P0 = 0.001; FFRT = 1; else mu = 1; end % Set the values of the optional input arguments in varargin i = 0; while i < length(varargin) switch upper(varargin{i+1}) case 'P0' P0 = varargin{i+2}; if(method == 6 && (~ismember(P0,[0.01,0.001]))) error('Fixed failure rate must be either 0.01 or 0.001.'); elseif(method == 5 && P0>1.0) error('User-defined success rate P0 cannot be larger than 1'); end i=i+2; case {'MU'} mu = varargin{i+2}; if(method == 6 && mu>1) error('MU must be between 0 and 1'); end if ~isempty(mu), FFRT = 0; end i=i+2; case {'NCANDS'} if ismember(method,[1,2,5]) ncands = varargin{i+2}; end i=i+2; otherwise error('Unrecognised input option.') end end n = size (Qahat,1); zfixed = zeros(n,ncands); nfixed = n; sqnorm = []; %----------------------------------------------------------------- %Tests on Inputs ahat and Qahat %Is the Q-matrix symmetric? if ~isequal(Qahat-Qahat'<1E-8,ones(size(Qahat))); error ('Variance-covariance matrix is not symmetric!'); end; %Is the Q-matrix positive-definite? if sum(eig(Qahat)>0) ~= size(Qahat,1); error ('Variance-covariance matrix is not positive definite!'); end; %Do the Q-matrix and ambiguity-vector have identical dimensions? if length(ahat) ~= size(Qahat,1); error (['Variance-covariance matrix and vector of ambiguities do', ... 'not have identical dimensions!']); end; %Is the ambiguity vector a column? if size(ahat,2) ~= 1; error ('Ambiguity vector should be a column vector'); end; %remove integer numbers from float solution, so that all values are between %-1 and 1 (for computational convenience only) incr = ahat - rem(ahat,1); ahat = rem(ahat,1); %Compute Z matrix ba