%% Plotting figure; plot(t, true_pos, 'g-', 'LineWidth', 2); hold on; plot(t, measurements, 'r.', 'MarkerSize', 4); plot(t, stored_x(1,:), 'b-', 'LineWidth', 2); xlabel('Time (s)'); ylabel('Position (m)'); title('Tracking a Falling Object with Kalman Filter'); legend('True Position', 'Noisy Measurements', 'Kalman Estimate'); grid on;
You combine your step count with the feel of the wall to figure out your exact location.
% State transition with known input (gravity) % x(k+1) = F x(k) + B u(k) F = [1, dt; 0, 1]; B = [0.5*dt^2; dt]; % Control input matrix for acceleration u = g; % Control input (gravity) %% Plotting figure; plot(t, true_pos, 'g-', 'LineWidth', 2);
What your physics equations say should happen. The Measurement: What your sensors say is happening. The Boat Analogy Imagine you are navigating a boat at night.
If you are new to estimation theory, the math behind Kalman filters can look intimidating. However, the core concept is remarkably intuitive. This article provides a beginner-friendly introduction to Kalman filters, explains the underlying mechanics, and provides top MATLAB examples for you to download and run. What is a Kalman Filter? The Boat Analogy Imagine you are navigating a boat at night
Goal: estimate x_k given measurements z_1..z_k.
% plot figure; plot(true_traj(1,:), true_traj(2,:), '-k'); hold on; plot(meas(1,:), meas(2,:), '.r'); plot(est(1,:), est(2,:), '-b'); legend('True','Measurements','Estimate'); xlabel('x'); ylabel('y'); axis equal; % plot figure
: A student-focused thesis detailing standard and Extended Kalman Filters (EKF) with satellite orbit examples. A Kalman Filtering Tutorial for Undergraduate Students
He downloaded it without hesitation. Inside:
Used for non-linear systems (like tracking a turning car).