full_rls.m

System identification with adaptive filter using full and partial-update Recursive-Least-Squares

function [e,w] = full_rls(x,d,N,w0,lambda,epsilon)
%full_rls(x,d,N,w0,lambda,epsilon) implements full-update RLS algorithm
%   ----------------
%   input parameters
%   ----------------
%   x : Lx1 input signal
%   d : Lx1 desired response 
%   N : filter length
%   w0 : Nx1 initialization
%   lambda : exponential forgetting factor
%   epsilon: regularization parameter 
%   ----------------
%   function outputs
%   ----------------
%   e : Lx1 output error vector
%   w : LxN coefficients vectors

x = x(:);
d = d(:);
w0 = w0(:);

L = length(x);
w = zeros(L,N);
e = zeros(L,1);

w(1,:) = w0';
xvec = zeros(N,1);
P = (1/epsilon) * eye(N);
invlambda = 1/lambda;

for i = 1:L-1
    xvec = [x(i);xvec(1:N-1)];
    e(i) = d(i)-w(i,:)*xvec;    %error
    Px = invlambda*P*xvec;      %P(k) computation
    P = invlambda*P - Px*Px'/(1+Px'*xvec);

    w(i+1,:) = w(i,:) + (P*xvec*e(i))';
end
xvec = [x(L);xvec(1:N-1)];
e(L) = d(L)-w(L,:)*xvec;