www.pudn.com > easy8.rar > rls.m

function rls(A,b,Sigma) 
%RLS      Recursive Least Squares 
%         A is the coefficient matrix, b the observations and  
%         Sigma a vector containing the diagonal entries of 
%         the covariance matrix for the problem. 
%         We include one additional observation for increasing i by 1 
 
%Copyright (c) by Kai Borre 
%$Revision: 1.0 $  %Date:1999/10/24  $ 
 
if nargin == 0 
   A = [1 1;1 2;-1 1]; 
   b = [2;1;0]; 
   Sigma = diag([1,.5,1]); 
end 
 
% Initial weight 
P = A(1,:)'*Sigma(1,1)*A(1,:); 
if rcond(P) == 0 
   P = 1.e10*eye(size(A,2)); 
else  
   P = inv(P); 
end  
P 
% Initial solution 
x = pinv(A(1,:)'*Sigma(1,1)*A(1,:))*A(1,:)'*Sigma(1,1)*b(1)%; 
 
for i = 1:size(b,1) 
   K = P*A(i,:)'*inv(A(i,:)*P*A(i,:)'+Sigma(i,i))%; 
   P = (eye(size(A,2))-K*A(i,:))*P%; 
   x = x+K*(b(i)-A(i,:)*x)%; 
%   fprintf('\nSolution:\n'); 
%   for j = 1:size(A,2) 
%      fprintf('  x(%2g) = %6.3f\n',j,x(j)); 
%   end 
end 
 
break 
 
dof = size(b,1)-size(A,2); 
if dof ~= 0 
   P = (norm(b-A*x))^2*P/dof; 
else 
   P = (norm(b-A*x))^2*pinv(A'*Sigma*A);   
end       
fprintf('\nFinal Covariance matrix:\n'); 
for j = 1:size(A,2) 
   for k = 1:size(A,2) 
      fprintf('%12.7f',P(j,k)); 
   end 
   fprintf('\n'); 
end 
fprintf('\nTrace of Covariance matrix: %12.7f\n',trace(P)); 
%%%%%%%%%%%%%%%%% end rls.m %%%%%%%%%%%%%%%%%%%