www.pudn.com > gmm_utilities.zip > covariance_intersect.m

function [x,P,a] = covariance_intersect(x1,P1, x2,P2, a) 
%function [x,P,a] = covariance_intersect(x1,P1, x2,P2, a) 
% 
% For the time being I implement only a simple form of CI. 
% There is no transform between spaces and the numerics are basic. 
% The value for a is to minimise determinant. 
% 
% TODO: How does this derive from Bayes theorem? Is there any equivalent 
% of the denominator p(z=z0) normalising term for the CI? 
% 
% TODO:  
%   - update with linear transform H 
%   - closed form optimisation of a, or without optimisation (a as an input parameter) 
%   - more numerically stable implementation 
 
P1i = inv_posdef(P1); 
P2i = inv_posdef(P2); 
 
if nargin == 4 
    a = fminbnd(@det_ci, 0, 1, [], P1i, P2i); 
end 
 
P = inv_posdef(a*P1i + (1-a)*P2i); 
x = P*(a*P1i*x1 + (1-a)*P2i*x2); 
 
% 
% 
 
function d = det_ci(a, P1i, P2i) 
Ri = a*P1i + (1-a)*P2i; 
d = 1 / det(Ri); % det(R) == 1/det(inv(R))