% Define the system parameters dt = 0.1; % time step A = [1 dt; 0 1]; % transition model H = [1 0]; % measurement model Q = [0.01 0; 0 0.01]; % process noise R = [0.1]; % measurement noise
% Initialize the state and covariance x0 = [0; 0]; % initial state P0 = [1 0; 0 1]; % initial covariance
Let's consider an example where we want to estimate the position and velocity of an object from noisy measurements of its position and velocity. kalman filter for beginners with matlab examples download
% Generate some measurements t = 0:dt:10; x_true = sin(t); v_true = cos(t); y = [x_true; v_true] + 0.1*randn(2, size(t));
% Define the system parameters dt = 0.1; % time step A = [1 dt; 0 1]; % transition model H = [1 0; 0 1]; % measurement model Q = [0.01 0; 0 0.01]; % process noise R = [0.1 0; 0 0.1]; % measurement noise % Define the system parameters dt = 0
% Initialize the state and covariance x0 = [0; 0]; % initial state P0 = [1 0; 0 1]; % initial covariance
% Run the Kalman filter x_est = zeros(2, length(t)); P_est = zeros(2, 2, length(t)); for i = 1:length(t) if i == 1 x_est(:, i) = x0; P_est(:, :, i) = P0; else % Prediction x_pred = A*x_est(:, i-1); P_pred = A*P_est(:, :, i-1)*A' + Q; % Measurement update z = y(:, i); K = P_pred*H'*inv(H*P_pred*H' + R); x_est(:, i) = x_pred + K*(z - H*x_pred); P_est(:, :, i) = P_pred - K*H*P_pred; end end % process noise R = [0.1]
% Generate some measurements t = 0:dt:10; x_true = sin(t); y = x_true + 0.1*randn(size(t));