create a kalman filter in matlab

main.m
% Define the state-space model
A = [1.1 1; 0 1]; % state transition matrix
B = [0.5; 1]; % input matrix
C = [1 0]; % output matrix
D = 0; % feedforward matrix
sys = ss(A,B,C,D);

% Design the Kalman filter gains
Q = eye(2); % process noise covariance
R = 2; % measurement noise covariance
[K,P,E] = kalman(sys,Q,R); % Kalman gain, covariance, and estimator

% Simulate the system
t = 0:0.1:10;
u = sin(t);
w = mvnrnd(zeros(size(t)), Q, size(t))'; % system noise
v = mvnrnd(zeros(size(t)), R, size(t))'; % measurement noise
[y,t,xhat] = lsim(sys, u+w, t, [], [], K*u'+v');

% Plot the results
figure;
plot(t, xhat(:,1), '-b', 'LineWidth', 2);
hold on;
plot(t, xhat(:,2), '-r', 'LineWidth', 2);
xlabel('Time');
ylabel('State');
title('Kalman Filter Example');
legend('State 1', 'State 2');
grid on;
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