write an extended kalman filter script in matlab

main.m
% Define the system dynamics and measurement functions
f = @(x, u) [x(1) + u(1)*cos(x(3))*0.1; x(2) + u(1)*sin(x(3))*0.1; x(3) + u(2)*0.1];
h = @(x) [x(1); x(2)];

% Define the initial state and covariance matrices
x0 = [0; 0; 0];
P0 = [1 0 0; 0 1 0; 0 0 1];

% Define the process and measurement noise covariance matrices
R = [0.1 0; 0 0.1];
Q = [0.1 0 0; 0 0.1 0; 0 0 0.01];

% Generate some noisy measurements
N = 100;
x = zeros(3, N);
y = zeros(2, N);
u = [1; 0.5];
for i = 1:N
    x(:,i) = f(x(:,max(i-1, 1)), u) + mvnrnd(zeros(3,1), R)';
    y(:,i) = h(x(:,i)) + mvnrnd(zeros(2,1), Q)';
end

% Initialize the EKF state estimate and covariance
xhat = x0;
Phat = P0;

% Loop over the measurements and update the EKF estimates
for i = 1:N
    % Propagate the state estimate and covariance
    F = [1 0 -u(1)*sin(xhat(3))*0.1; 0 1 u(1)*cos(xhat(3))*0.1; 0 0 1];
    G = [cos(xhat(3))*0.1 0; sin(xhat(3))*0.1 0; 0 0.1];
    xhat = f(xhat, u);
    Phat = F*Phat*F' + G*R*G';

    % Calculate the Kalman gain and update the state estimate and covariance
    H = [1 0 0; 0 1 0];
    K = Phat*H'/(H*Phat*H' + Q);
    xhat = xhat + K*(y(:,i) - h(xhat));
    Phat = (eye(3) - K*H)*Phat;
end
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