kalman matlab

In MATLAB, you can implement the Kalman filter using the `kalman` or `kalmanf` functions, depending on your specific requirements.

The `kalman` function is used for discrete-time systems, while `kalmanf` is used for continuous-time systems. Both functions require defining the system dynamics and measurement equations, as well as the covariance matrices representing the process and measurement noise.

Here's a basic example of how to use the `kalman` function in MATLAB:

% Define system matrices
A = [1 1; 0 1];     % State transition matrix
B = [0.5; 1];       % Control input matrix
C = [1 0];          % Measurement matrix
Q = [0.01 0; 0 0.01];   % Process noise covariance
R = 1;              % Measurement noise covariance

% Initialize state and covariance
x0 = [0; 0];        % Initial state
P0 = eye(2);        % Initial state covariance

% Generate noisy measurements
t = 0:0.1:10;
u = sin(t);
y = C * x + randn(size(t));

% Run Kalman filter
[xhat, P] = kalman(A, B, C, Q, R, y, u, x0, P0);

% Plot estimated and true state
figure;
plot(t, xhat(1,:), 'r-', t, xhat(2,:), 'b--');
hold on;
plot(t, x(1,:), 'k-', t, x(2,:), 'k--');
legend('Estimated x1', 'Estimated x2', 'True x1', 'True x2');

This example assumes a simple 2D system with a single measurement. You can modify the system dynamics and measurement equations according to your specific application.