: "Understanding Kalman Filters" provides a six-part walkthrough with practical examples like estimating the position of a pendulum. Watch at MathWorks Key Concepts for Beginners

For a beginner, you don't need to derive them. You just need to know:

% Run the Kalman filter x = zeros(2, length(t)); P = zeros(2, 2, length(t)); x(:, 1) = x0; P(:, :, 1) = P0; for i = 2:length(t) % Prediction step x_pred = A * x(:, i-1); P_pred = A * P(:, :, i-1) * A' + Q;

: It doesn't need to store old data; it only needs the previous estimate and the current measurement. Prediction vs. Update :

| Step | Equation Name | Formula (Simplified) | | :--- | :--- | :--- | | Predict | State Estimate | x_pred = F * x_prev | | Predict | Covariance Estimate | P_pred = F * P_prev * F' + Q | | Update | Kalman Gain | K = P_pred * H' / (H * P_pred * H' + R) | | Update | State Estimate (Corrected) | x_est = x_pred + K * (z - H * x_pred) | | Update | Covariance (Corrected) | P_est = (I - K * H) * P_pred |