% Update K = P * H' / (H * P * H' + R); % Kalman gain x = x + K * (measurements(k) - H * x); P = (eye(2) - K * H) * P;
est_pos(k) = x(1); end
% Measurement noise (GPS error) R = 10;
% 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; kalman filter for beginners with matlab examples download
% Run Kalman filter estimated_positions = zeros(size(measurements)); for k = 1:length(measurements) % Predict x = A * x; P = A * P * A' + Q; % Update K = P * H' /
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). % Generate true motion and noisy measurements true_position
% Generate true motion and noisy measurements true_position = 0:dt:50; measurements = true_position + sqrt(R)*randn(size(true_position));