事件触发卡尔曼一致性matLab代码

以下是一个简单的Kalman滤波器的Matlab代码示例，用于估计具有高斯噪声的线性动态系统的状态。该代码使用卡尔曼一致性检验，以确保滤波器的输出与实际系统状态的不确定性一致。

%% Kalman Filter Example

% Define the state-space model
A = [1 1; 0 1];
B = [0.5; 1];
C = [1 0];
Q = [1 0; 0 1];
R = 1;
x0 = [0; 0];

% Define the time steps
dt = 0.1;
t = 0:dt:10;

% Generate the system dynamics
w = mvnrnd([0; 0], Q, length(t))';
v = mvnrnd(0, R, length(t))';
x = zeros(2, length(t));
y = zeros(1, length(t));
x(:,1) = x0;
for i = 2:length(t)
x(:,i) = A*x(:,i-1) + B*w(:,i-1);
y(i) = C*x(:,i) + v(i);
end

% Initialize the Kalman filter
xhat = zeros(2, length(t));
Phat = zeros(2, 2, length(t));
xhat(:,1) = x0;
Phat(:,:,1) = Q;

% Run the Kalman filter
for i = 2:length(t)

% Predict
xhat(:,i) = A*xhat(:,i-1) + B*0;
Phat(:,:,i) = A*Phat(:,:,i-1)*A' + Q;

% Update
K = Phat(:,:,i)*C'*inv(C*Phat(:,:,i)*C' + R);
xhat(:,i) = xhat(:,i) + K*(y(i) - C*xhat(:,i));
Phat(:,:,i) = (eye(2) - K*C)*Phat(:,:,i);

% Consistency Check
S = C*Phat(:,:,i)*C' + R;
nu = y(i) - C*xhat(:,i);
chi2 = nu'*inv(S)*nu;
alpha = 0.05;
if chi2 > chi2inv(alpha, 1)
disp('Inconsistent Measurement')
end

end

% Plot the results
figure
subplot(2,1,1)
plot(t, x(1,:), 'b', t, xhat(1,:), 'r--')
ylabel('State 1')
legend('True', 'Estimated')
subplot(2,1,2)
plot(t, x(2,:), 'b', t, xhat(2,:), 'r--')
xlabel('Time (s)')
ylabel('State 2')
legend('True', 'Estimated')