渐消卡尔曼滤波的matlab代码

以下是一个简单的渐消卡尔曼滤波（CDKF）的Matlab代码示例：

% CDKF Demo

% State transition matrix
F = [1 1; 0 1];

% Measurement matrix
H = [1 0];

% Process noise covariance
Q = [0.01 0; 0 0.01];

% Measurement noise covariance
R = 1;

% Initial state
x0 = [0; 0];

% Initial state covariance
P0 = [1 0; 0 1];

% Number of time steps
N = 100;

% Generate true state and measurements
w = sqrt(Q) * randn(2, N);
v = sqrt(R) * randn(1, N);
x_true = zeros(2, N);
y = zeros(1, N);
x_true(:, 1) = x0;
y(1) = H * x_true(:, 1) + v(1);
for i = 2:N
    x_true(:, i) = F * x_true(:, i-1) + w(:, i);
    y(i) = H * x_true(:, i) + v(i);
end

% CDKF parameters
alpha = 1; % Scaling factor
beta = 2; % Optimal for Gaussian distributions
kappa = 0; % Optimal for state dimension of 2

% CDKF initialization
x_est = x0;
P_est = P0;
x_est_hist = zeros(2, N);
P_est_hist = zeros(2, 2, N);
x_est_hist(:, 1) = x_est;
P_est_hist(:, :, 1) = P_est;

% CDKF loop
for i = 2:N
    % Predict
    [X, Wm, Wc] = sigma_points(x_est, P_est, alpha, beta, kappa);
    X_pred = F * X;
    x_pred = sum(Wm .* X_pred, 2);
    P_pred = Q;
    for j = 1:2*kappa+1
        P_pred = P_pred + Wc(j) * (X_pred(:, j) - x_pred) * (X_pred(:, j) - x_pred)';
    end

    % Update
    Y = H * X_pred;
    y_pred = sum(Wm .* Y, 2);
    S = R;
    for j = 1:2*kappa+1
        S = S + Wc(j) * (Y(j) - y_pred) * (Y(j) - y_pred)';
    end
    K = P_pred * H' * inv(S);
    x_est = x_pred + K * (y(i) - y_pred);
    P_est = P_pred - K * H * P_pred;

    % Save estimates
    x_est_hist(:, i) = x_est;
    P_est_hist(:, :, i) = P_est;
end

% Plot results
figure;
subplot(2,1,1);
plot(1:N, x_true(1,:), 'b', 1:N, x_est_hist(1,:), 'r');
legend('True', 'Estimate');
title('State 1');
subplot(2,1,2);
plot(1:N, x_true(2,:), 'b', 1:N, x_est_hist(2,:), 'r');
legend('True', 'Estimate');
title('State 2');

这个例子演示了如何使用CDKF来估计一个带有高斯噪声的一维运动状态。在这里，我们使用一个简单的线性状态转移模型和线性测量模型，但是CDKF可以很容易地扩展到非线性模型。输出是一个包含两个子图的图形，其中每个子图显示真实状态和估计状态随时间的变化。