%% 2. KALMAN FILTER INITIALIZATION % State vector: [Position; Velocity] x_est = [0; 0]; % Initial guess: position 0, velocity 0 P_est = [100, 0; % High uncertainty in initial position 0, 10]; % Lower uncertainty in initial velocity
%% Noisy measurement (measuring position only) meas_noise_std = 0.5; % 0.5 meter noise measurements = true_pos + meas_noise_std * randn(1, N); If you rely solely on the GPS, your
Introduction: The Magic of "Noisy" Measurements Imagine you are trying to track the position of a speeding car using a GPS. Your GPS device updates every second, but the reading is never perfect—it jumps around by a few meters due to atmospheric interference or urban canyons. If you rely solely on the GPS, your tracking line will look jagged and erratic. % Update covariance estimate
x_est = x_pred + K * y; % Update state estimate P_est = (eye(2) - K * H) * P_pred; % Update covariance estimate Velocity] x_est = [0