State = [position; velocity; acceleration]
dt = 0.1; A = [1 dt dt^2/2; 0 1 dt; 0 0 1]; H = [1 0 0]; % measure only position Q = 0.01 * eye(3); R = 5; % measurement noise variance x = [100; 0; -9.8]; % start at 100m, 0 velocity, gravity down P = eye(3); kalman filter for beginners with matlab examples download
The Kalman filter gives a smooth estimate much closer to the true position than the raw noisy measurements. 5. MATLAB Example 2: Tracking a Falling Object (Acceleration) Now let’s track an object in free fall (constant acceleration due to gravity). State = [position; velocity; acceleration] dt = 0
% Update K = P * H' / (H * P * H' + R); % Kalman gain x = x + K * (measurements(k) - H * x); P = (eye(2) - K * H) * P; % Update K = P * H' /
% Plot results plot(0:dt:50, true_position, 'g-', 'LineWidth', 2); hold on; plot(0:dt:50, measurements, 'rx'); plot(0:dt:50, estimated_positions, 'b--', 'LineWidth', 2); legend('True', 'Noisy GPS', 'Kalman Estimate'); xlabel('Time (s)'); ylabel('Position (m)'); title('Kalman Filter for Constant Velocity'); grid on;