recurrsive least square filter(RLS)

recurrsive least square filter(RLS) in matlab





function [W,e]=rls(x,d,N,delta,lambda,I,Wini,Pini,Xini)

if (~exist('I'))
itr = 1;
else
itr = I;
end

if (~exist('Wini'))
W = zeros(N,1);
else
if (length(Wini)~=N)
error('Weight initialization must match filter length');
end
W = Wini;
end

if (~exist('Pini'))
P = diag((ones(N,1)/delta));
else
if ((size(Pini,1)~=N) | (size(Pini,2)~=N))
error('Initial inverse must me square NxN');
end
P = Pini;
end

Lx = length(x);
[m,n] = size(x);
if (n>m)
x = x.';
end

if (~exist('Xini'))
x = [zeros(N-1,1); x];
else
if (length(Xini)~=(N-1))
error('State initialization must match filter length minus one');
end
x = [Xini; x];
end

for j=1:itr
for i = 2:Lx
X = x(i+N-1:-1:i);
Pi = P*X;
k = Pi/(lambda + X'*Pi);
y(i,1) = W'*X;
e(i,1) = d(i,1) - y(i,1)
W = W + k*e(i,1)
P = (P - (k*(X')*P))/lambda;
end
end