kalman filter noise signal in matlab

main.m
% Define system model
A = 1;
B = 0;
C = 1;
D = 0;

% Define system noise covariance
Q = 0.1;

% Define measurement noise covariance
R = 1;

% Initialize state estimate
x_prev = 0;
P_prev = 1;

% Initialize Kalman filter parameters
x_pred = 0;
P_pred = 0;

% Load noisy signal data
NoisySignal = your_noisy_signal_data_here;

FilteredSignal = zeros(size(NoisySignal));

for k = 1:length(NoisySignal)
    % Prediction (time update)
    x_pred = A * x_prev;
    P_pred = A * P_prev * A' + Q;

    % Correction (measurement update)
    K = P_pred * C' * inv(C * P_pred * C' + R);
    x_corrected = x_pred + K * (NoisySignal(k) - C * x_pred);
    P_corrected = (1 - K * C) * P_pred;

    % Update variables for next iteration
    x_prev = x_corrected;
    P_prev = P_corrected;

    FilteredSignal(k) = x_corrected;
end

% Plot the original signal and the filtered signal
figure;
plot(1:length(NoisySignal), NoisySignal, 'b', 1:length(FilteredSignal), FilteredSignal, 'r');
legend('Noisy Signal', 'Filtered Signal');
title('Kalman Filtered Signal');
1045 chars
48 lines