RLS Adaptive Filter Implementation in MATLAB

This is the code for implementing the RLS adaptive algorithm filter. The RLS (Recursive Least Squares) algorithm is widely used in adaptive filtering applications. Below is the MATLAB implementation of the RLS adaptive filter which helps in understanding the core concepts of adaptive filtering and recursive algorithms.

% MATLAB code for RLS adaptive filter
N = 1000; % Number of filter coefficients
M = 32; % Filter order
lambda = 0.99; % Forgetting factor
delta = 10; % Initialization constant

% Initialize filter coefficients and variables
w = zeros(M, 1); % Filter weights
P = delta * eye(M); % Inverse correlation matrix

% Simulate the input signal and desired output
x = randn(N, 1); % Input signal
d = filter([1, -0.9], 1, x); ?sired signal

% RLS adaptive filtering loop
for n = M+1:N
    x_n = x(n:-1:n-M+1); % Input vector
    e = d(n) - w' * x_n; % Error signal
    k = P * x_n / (lambda + x_n' * P * x_n); % Gain vector
    w = w + k * e; % Update weights
    P = (P - k * x_n' * P) / lambda; % Update inverse correlation matrix
end

% Display results
figure; plot(d, 'b'); hold on; plot(filter(w, 1, x), 'r');
legend('Desired', 'Filtered Output');

This code illustrates how to apply the RLS adaptive filter to adjust its coefficients to minimize the error between the desired signal and the filter output.