% --- Kalman gain --- K = P_pred / (P_pred + measurement_noise_std^2);
% Noisy measurement z = true_pos + meas_noise_pos * randn; meas_traj(k) = z;
% Noise parameters process_noise_std = 0.5; % uncertainty in model (e.g., window opens) measurement_noise_std = 2; % sensor noise
% Noise parameters process_noise_pos = 0.1; process_noise_vel = 0.1; meas_noise_pos = 3; % GPS-like noise
% --- Update --- x_est = x_pred + K * (z - H * x_pred); P_est = (eye(2) - K * H) * P_pred;
est_traj(k) = x_est(1); end
If you are an engineering student, a robotics hobbyist, or a data scientist venturing into signal processing, you have likely heard of the Kalman filter . It sounds complex, but at its heart, it is a brilliant algorithm for estimating the state of a dynamic system from noisy measurements.