Kalman Filter For Beginners With Matlab Examples — Download !free! Top
% 2D Kalman Filter Example: Vehicle Tracking clear; clc; close all; dt = 0.1; % Time step (seconds) num_steps = 50; % State Matrix: [Position; Velocity] X_true = zeros(2, num_steps); X_true(:,1) = [0; 5]; % Start at 0 meters, moving at 5 m/s % Transition Matrix (Physics Model) A = [1 dt; 0 1]; % Generate True Trajectory for k = 2:num_steps X_true(:,k) = A * X_true(:,k-1); end % Generate Noisy Position Measurements (Velocity is hidden/not measured) R = 4; % Measurement noise variance noise = sqrt(R) * randn(1, num_steps); Z = X_true(1, :) + noise; % Kalman Filter Setup X_hat = [0; 0]; % Initial state estimate [pos; vel] P = [10 0; 0 10]; % Initial state covariance Q = [0.01 0; 0 0.01]; % Process noise covariance H = [1 0]; % Measurement matrix (we only observe position) pos_est = zeros(1, num_steps); vel_est = zeros(1, num_steps); % Recursive Loop for k = 1:num_steps % Predict X_hat_minus = A * X_hat; P_minus = A * P * A' + Q; % Update K = P_minus * H' / (H * P_minus * H' + R); X_hat = X_hat_minus + K * (Z(k) - H * X_hat_minus); P = (eye(2) - K * H) * P_minus; % Save data pos_est(k) = X_hat(1); vel_est(k) = X_hat(2); end % Plotting Position Results figure; subplot(2,1,1); plot(X_true(1,:), 'g-', 'LineWidth', 2); hold on; plot(Z, 'r.', 'MarkerSize', 10); plot(pos_est, 'b--', 'LineWidth', 2); ylabel('Position (m)'); title('Tracking Position & Velocity'); legend('True', 'Measured', 'Kalman', 'Location', 'Best'); grid on; % Plotting Velocity Results subplot(2,1,2); plot(X_true(2,:), 'g-', 'LineWidth', 2); hold on; plot(vel_est, 'b--', 'LineWidth', 2); xlabel('Time Step'); ylabel('Velocity (m/s)'); legend('True', 'Kalman', 'Location', 'Best'); grid on; Use code with caution. Download and Run the Top Scripts To download and run these examples locally: Open on your machine. Click New Script in the Home tab. Copy either the 1D or 2D code block provided above.
% 3. State Update x_hat = x_hat_pred + K * y;
: The process noise covariance (unmodeled environmental disruptions). % 2D Kalman Filter Example: Vehicle Tracking clear;
4. MATLAB Example 2: Tracking a Moving Object (2D Kalman Filter)
For a beginner, the Kalman Filter is simply two alternating steps: Copy either the 1D or 2D code block provided above
In practice, your primary task as a beginner is often to correctly tune the two key trust parameters, Q and R . Q reflects the trust in your model (a higher Q means you trust your model less), and R reflects the trust in your sensor measurements (a higher R means you trust the measurements less). Getting these right is the key to a successful filter.
Example command to clone (if you have Git): Share public link
Your GPS signal (measurement) becomes noisy or drops completely.
A Kalman filter solves this problem. It combines the predictable physics of the car (speedometer) with the noisy measurements (GPS) to find the absolute best estimate of where the car actually is. The Two-Step Cycle
To help tailor the next steps for your project, tell me: Are you tracking an object in (like a drone or car) or filtering a 1D signal (like sensor data)? If you are using specific sensors like an IMU, GPS, or encoder , let me know so I can provide the exact transition matrix setup. Share public link