% Update K = P * H' / (H * P * H' + R); x = x + K * (measurements(k) - H*x); P = (eye(3) - K*H) * P;
The Kalman filter gives a smooth estimate much closer to the true position than the raw noisy measurements. 5. MATLAB Example 2: Tracking a Falling Object (Acceleration) Now let’s track an object in free fall (constant acceleration due to gravity).
estimated_positions(k) = x(1); end
est_pos(k) = x(1); end
% Filter est_pos = zeros(size(t)); for k = 1:length(t) % Predict x = A * x; P = A * P * A' + Q;
% Initial state guess x = [0; 10]; % start at 0 m, velocity 10 m/s P = eye(2); % initial uncertainty
dt = 0.1; A = [1 dt dt^2/2; 0 1 dt; 0 0 1]; H = [1 0 0]; % measure only position Q = 0.01 * eye(3); R = 5; % measurement noise variance x = [100; 0; -9.8]; % start at 100m, 0 velocity, gravity down P = eye(3); kalman filter for beginners with matlab examples download
% Update K = P * H' / (H * P * H' + R); % Kalman gain x = x + K * (measurements(k) - H * x); P = (eye(2) - K * H) * P;
% Run Kalman filter estimated_positions = zeros(size(measurements)); for k = 1:length(measurements) % Predict x = A * x; P = A * P * A' + Q;
1. What is a Kalman Filter? The Kalman filter is a recursive algorithm that estimates the state of a dynamic system from a series of incomplete and noisy measurements. It was developed by Rudolf E. Kálmán in 1960. % Update K = P * H' /
% Simulate t = 0:dt:5; true_pos = 100 + 0 t + 0.5 (-9.8)*t.^2; measurements = true_pos + sqrt(R)*randn(size(t));
% Measurement noise (GPS error) R = 10;
% Generate true motion and noisy measurements true_position = 0:dt:50; measurements = true_position + sqrt(R)*randn(size(true_position)); estimated_positions(k) = x(1); end est_pos(k) = x(1); end
State = [position; velocity; acceleration]