% Kalman Filter for Beginners - Simple Example clear all; % 1. Initialization dt = 0.1; % Time step t = 0:dt:10; % Total time true_val = 14.4; % The actual value we are trying to find z_noise = 2 * randn(size(t)); z = true_val + z_noise; % Simulated noisy measurements % Kalman Variables A = 1; H = 1; Q = 0.01; R = 2; x = 0; % Initial estimate P = 1; % Initial error covariance % Results storage history = zeros(size(t)); % 2. The Kalman Loop for i = 1:length(t) % --- Step 1: Predict --- xp = A * x; Pp = A * P * A' + Q; % --- Step 2: Update (The Correction) --- K = Pp * H' * inv(H * Pp * H' + R); % Kalman Gain x = xp + K * (z(i) - H * xp); P = Pp - K * H * Pp; history(i) = x; end % 3. Visualization plot(t, z, 'r.', t, history, 'b-', t, repmat(true_val, size(t)), 'g--'); legend('Noisy Measurement', 'Kalman Filter Estimate', 'True Value'); title('Simple Kalman Filter Performance'); xlabel('Time (sec)'); ylabel('Value'); Use code with caution. Why this works:
At its heart, a Kalman Filter is an . It’s used to estimate the state of a system (like where a car is) when you have two imperfect sources of information:
(measurement noise) to balance filter responsiveness vs. smoothness. Part III: Advanced Filters Extended Kalman Filter (EKF)
Real-world systems are rarely linear. The book progresses to the Extended Kalman Filter, a non-linear adaptation. This is crucial for real-world applications like GPS navigation, where distances and angles introduce non-linearities. Kim demonstrates how to use Jacobians (derivatives) to linearize the system for the filter. % Kalman Filter for Beginners - Simple Example
The best way to build an intuitive understanding of the Kalman filter is to experiment with the code parameters. Try changing the measurement noise variance ( R ) in the scripts above to watch how the filter alters its reliance on sensor data versus physical predictions.
Used when a system scales across multiple dimensions but still moves in linear paths. For example, tracking an object moving along an X-Y plane using a standard linear acceleration equation. 2. The Extended Kalman Filter (EKF)
For those looking for a "PDF" of this work, the author encourages purchasing the book while sharing the code for free to aid learning. Visualization plot(t, z, 'r
Adjust the prediction by adding the measurement multiplied by the Kalman Gain.
Do you need help expanding the MATLAB code to handle ?
Kalman Filter for Beginners: A Practical Guide with MATLAB Examples smoothness
Demystifying the Kalman Filter: A Beginner's Guide with Phil Kim's MATLAB Examples
Notice that the filter doesn't lag behind like a simple moving average would; it accurately finds the true value and locks onto it. Advancing to Higher Dimensions: Beyond the Basics
The Kalman filter has several benefits, including:
—like a self-driving car sim or a drone controller—where you need a more complex matrix model ?