用matlab写一个分别采用 KF、EKF和UKF测试IEEE-14 测试系统节点 9电压幅值的估计值的代码

以下是一个简单的 MATLAB 代码，用于使用 KF、EKF 和 UKF 估计 IEEE-14 测试系统节点 9 的电压幅值。请注意，这只是一个简单的示例，实际的应用可能需要更复杂的模型和参数调整。

% Load IEEE-14 test system data
load('ieee14.mat');

% Define measurement model for voltage amplitude at node 9
H = zeros(1,14);
H(9) = 1;

% Define process noise covariance matrix
Q = eye(14) * 1e-6;

% Define measurement noise covariance matrix
R = 0.1;

% Define initial state estimate and covariance
x0 = zeros(14,1);
P0 = eye(14);

% Initialize filter parameters
kf_x = x0;
kf_P = P0;
ekf_x = x0;
ekf_P = P0;
ukf_x = x0;
ukf_P = P0;

% Loop through measurements
for k = 1:size(V,2)
    % Get measurement
    z = abs(V(9,k));
    
    % Kalman filter
    kf_x_ = A * kf_x;
    kf_P_ = A * kf_P * A' + Q;
    K = kf_P_ * H' / (H * kf_P_ * H' + R);
    kf_x = kf_x_ + K * (z - H * kf_x_);
    kf_P = (eye(14) - K * H) * kf_P_;
    
    % Extended Kalman filter
    ekf_f = @(x) A * x;
    ekf_h = @(x) abs(x(9));
    ekf_x_ = ekf_f(ekf_x);
    J = jacobianest(ekf_h,ekf_x);
    ekf_P_ = A * ekf_P * A' + Q;
    K = ekf_P_ * J' / (J * ekf_P_ * J' + R);
    ekf_x = ekf_x_ + K * (z - ekf_h(ekf_x_));
    ekf_P = (eye(14) - K * J) * ekf_P_;
    
    % Unscented Kalman filter
    ukf_f = @(x) A * x;
    ukf_h = @(x) abs(x(9));
    [ukf_x_,ukf_P_] = unscented_transform(ukf_f,ukf_x,ukf_P,2);
    [z_,ukf_Pz_] = unscented_transform(ukf_h,ukf_x_,ukf_P_,2);
    [x_,P_] = unscented_kalman_update(ukf_x_,ukf_P_,z_,ukf_Pz_,R,ukf_f,ukf_h);
    ukf_x = x_;
    ukf_P = P_;
end

% Plot results
figure;
plot(abs(V(9,:)),'k');
hold on;
plot(abs(kf_x(9,:)),'b');
plot(abs(ekf_x(9,:)),'g');
plot(abs(ukf_x(9,:)),'r');
legend('True','KF','EKF','UKF');
xlabel('Time');
ylabel('Voltage Amplitude');

请注意，这个代码使用了一个名为 `unscented_transform` 和 `unscented_kalman_update` 的函数，这些函数可以在 MATLAB 的 Control System Toolbox 中找到。