Kalman Filter For Beginners With Matlab Examples Pdf ◆

% Update K = P_pred * H' / (H * P_pred * H' + R); x_hat = x_pred + K * (measurements(k) - H * x_pred); P = (eye(2) - K * H) * P_pred;

x_hat_log(:,k) = x_hat; end

% Run Kalman filter x_hat_log = zeros(2, num_steps); for k = 1:num_steps % Predict x_pred = A * x_hat; P_pred = A * P * A' + Q;

x_k = A * x_k-1 + B * u_k + w_k Measurement equation: z_k = H * x_k + v_k

% Noise covariances Q = [0.01 0; 0 0.01]; % process noise (small) R = 1; % measurement noise (variance)

% Plot results t = 1:num_steps; plot(t, measurements, 'r.', 'MarkerSize', 8); hold on; plot(t, x_hat_log(1,:), 'b-', 'LineWidth', 1.5); xlabel('Time step'); ylabel('Position'); legend('Noisy measurements', 'Kalman filter estimate'); title('1D Position Tracking with Kalman Filter'); grid on;