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% ----------------------------------------------------------------------