% Define the system parameters
spreadFactor = 10;
bandwidth = 1;
sigmaNoise = 0.1;
sigmaInterference = 1;
% Define the Kalman filter parameters
A = 1;
B = 1;
C = spreadFactor;
Q = sigmaNoise^2;
R = sigmaInterference^2;
% Initialize the state and covariance matrices
x = [0; 0];
P = [0 0; 0 0];
% Preallocate the arrays for storing the results
xEstimate = zeros(2, 1000);
y = zeros(1, 1000);
% Generate the signals
for k = 1:1000
% Generate the noise and interference
noise = sigmaNoise * randn;
interference = sigmaInterference * randn;
% Generate the spread signal
x(1) = bandwidth * randn;
x(2) = x(1) * spreadFactor + noise + interference;
% Kalman filter prediction step
xEstimate(:, k) = A * x;
P = A * P * A' + Q;
% Kalman filter update step
y(k) = C * x + interference;
K = P * C' / (C * P * C' + R);
xEstimate(:, k) = xEstimate(:, k) + K * (y(k) - C * xEstimate(:, k));
P = (eye(2) - K * C) * P;
end
% Plot the results
figure
subplot(2, 1, 1)
plot(xEstimate(1, :))
title('Estimated Signal')
subplot(2, 1, 2)
plot(y)
title('Observed Signal')
