Update: K_k = P_k-1 H^T (H P_k H^T + R)^-1 x̂_k = x̂_k + K_k (z_k - H x̂_k-1) P_k = (I - K_k H) P_k
The algorithm runs recursively in a continuous loop using two main steps:
The Kalman filter runs continuously in a two-step loop: and Update (Correct) .
% State Transition Matrix (The Physics Model) % x_new = x_old + v_old * dt % v_new = v_old F = [1 dt; 0 1]; Update: K_k = P_k-1 H^T (H P_k H^T
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The filter works in two repeating steps to minimize uncertainty: 1. The Prediction Step
It works in a two-step loop:
% Plot the results figure; plot(t, x(1, :)); hold on; plot(t, y); legend('Estimated position', 'Measurement');
We defined F = [1 dt; 0 1] . This matrix tells the filter how the object moves based on high-school physics:
true_traj(:,k) = x; meas(:,k) = z; est(:,k) = xhat; end The Prediction Step It works in a two-step
% Store data for plotting est_position(i) = x(1); est_velocity(i) = x(2);
If you want to use MATLAB's built-in control system functions (such as the kalman command), the official MathWorks documentation offers a deep-dive tutorial. It shows you how to design a filter for a simple mass-spring-damper system, define your noise covariances (
Imagine you are in a car trying to measure your speed. Your speedometer is good, but it's a bit noisy (it fluctuates when you hit bumps). You also have a GPS that measures your position, but it updates slowly and is sometimes inaccurate. Your speedometer is good, but it's a bit