chistart.m

This a source code for ambiguity resolution in GPS Receivers that run in matlab software

function Chi2 = chistart (D,L,a,ncands,factor)
%CHISTART: Computes the initial size of the search ellipsoid
%
% This routine computes or approximates the initial size of the search
% ellipsoid. If the requested number of candidates is not more than the
% dimension + 1, this is done by computing the squared distances of partially
% conditionally rounded float vectors to the float vector in the metric of the
% covariance matrix. Otherwise an approximation is used.
%
% Input arguments
%    L,D   : LtDL-decomposition of the variance-covariance matrix of
%            the float ambiguities (preferably decorrelated)
%    a     : float ambiguites (preferably decorrelated)
%    ncands: Requested number of candidates (default = 2)
%    factor: Multiplication factor for the volume of the resulting
%            search ellipsoid (default = 1.5)
%
% Output arguments:
%    Chi2  : Size of the search ellipsoid

% ----------------------------------------------------------------------
% File.....: chistart.m
% Date.....: 19-MAY-1999
% Modified.: 05-MAR-2001, by P. Joosten
% Author...: Peter Joosten
%            Mathematical Geodesy and Positioning
%            Delft University of Technology
% ----------------------------------------------------------------------

% ------------------
% --- Initialize ---
% ------------------

if nargin < 4; ncands = 2  ; end;
if nargin < 5; factor = 1.5; end;

n = max(size(a));

% ----------------------------------------------------------------------
% --- Computation depends on the number of candidates to be computed ---
% ----------------------------------------------------------------------

if ncands <= n+1;

  % --------------------------------------------------------
  % --- Computation based on the bootstrapping estimator ---
  % --------------------------------------------------------

  Chi = [];

  for k = n:-1:0;

    afloat = a;
    afixed = a;
  
    for i = n:-1:1;
    
      dw = 0;
      for j = n:-1:i;
	dw = dw + L(j,i) * (afloat(j) - afixed(j));
      end;
    
      afloat(i) = afloat(i) - dw;
      if (i ~= k);
	afixed(i) = round (afloat(i));
      else;
	if isequal (afloat(i),afixed(i));
	  afixed(i) = round(afixed(i) + 1);
	else;
	  afixed(i) = round (afloat(i) + sign (afloat(i) - afixed(i)));
	end;
      end;
    
    end;

    Chi = [Chi (a-afixed)' * inv(L'*diag(D)*L) * (a-afixed)];

  end;

  % ---------------------------------------------------------------
  % --- Sort the results, and return the appropriate number     ---
  % --- Add an "eps", to make sure there is no boundary problem ---
  % ---------------------------------------------------------------

  Chi  = sort(Chi);
  Chi2 = Chi(ncands) + 1d-6;
   
else

  % -----------------------------------------------------
  % An approximation for the squared norm is computed ---
  % -----------------------------------------------------
  
  Linv = inv(L);
  Dinv = 1./D;
   
  Vn   = (2/n) * (pi ^ (n/2) / gamma(n/2));
  Chi2 = factor * (ncands / sqrt((prod(1 ./ Dinv)) * Vn)) ^ (2/n);

end;

% ----------------------------------------------------------------------
% End of routine: chistart
% ----------------------------------------------------------------------