Kalman Filter for Beginners: A Step-by-Step Guide with MATLAB Examples
: A practical guide focusing on usage rather than complex statistical derivation Tutorial: The Kalman Filter (MIT)
fprintf('RMS Error of Raw Measurements: %.2f meters\n', error_measurements); fprintf('RMS Error of Kalman Filter: %.2f meters\n', error_kalman); Kalman Filter for Beginners: A Step-by-Step Guide with
: A highly-rated, simplified tutorial example with nearly 20,000 downloads. Download from File Exchange Kalman Filtering for Beginners
% --- 1D Kalman Filter Example --- dt = 1; % Time step t = 0:dt:50; n = length(t); % True dynamics (constant velocity) true_pos = 0.5 * 0.1 * t.^2; % Accelerated motion true_vel = 0.1 * t; noise_sigma = 5; measured_pos = true_pos + randn(1, n) * noise_sigma; % Add noise % Kalman Filter Initialization x = [0; 0]; % Initial state: [position; velocity] P = eye(2); % Initial uncertainty matrix A = [1 dt; 0 1]; % State transition matrix H = [1 0]; % Measurement matrix Q = [0.1 0; 0 0.1]; % Process noise covariance R = noise_sigma^2; % Measurement noise covariance % Storage estimated_pos = zeros(1, n); % Kalman Filter Loop for i = 1:n % 1. Predict x = A * x; P = A * P * A' + Q; % 2. Update K = P * H' / (H * P * H' + R); % Kalman Gain x = x + K * (measured_pos(i) - H * x); P = (eye(2) - K * H) * P; estimated_pos(i) = x(1); end % Plot results figure; plot(t, measured_pos, 'r.', t, true_pos, 'k-', t, estimated_pos, 'b-', 'LineWidth', 2); legend('Measured Position', 'True Position', 'Kalman Estimate'); xlabel('Time (s)'); ylabel('Position'); title('1D Kalman Filter Tracking'); grid on; Use code with caution. Example 2: Using MATLAB’s kalman Function (Advanced) Update K = P * H' / (H
: Forecasts the future state based on past data and a physical model. Update (Correction) Step
| Project Difficulty | Application | MATLAB Feature to Learn | | :--- | :--- | :--- | | Beginner | Temperature sensor smoothing | Scalar Kalman filter | | Intermediate | Object tracking in 2D video | H = [1 0 0 0; 0 0 1 0] | | Advanced | GPS + IMU fusion (self-driving car) | Extended Kalman Filter (EKF) | | Expert | Drone attitude estimation | Unscented Kalman Filter (UKF) | However, the core concept is remarkably intuitive
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 Kalman Filter operates in a continuous loop comprising two main steps: A. The Prediction Step ("Time Update")