一致性卡尔曼滤波，matlab程序

一致性卡尔曼滤波（Consistent Kalman Filter）是一种针对非线性系统的滤波方法，它能够有效地解决传统卡尔曼滤波在非线性系统中存在的问题。下面是一份MATLAB程序实现一致性卡尔曼滤波算法：

function [x, P] = CKF(f,h,x0,P0,Q,R,y,u)
% Consistent Kalman Filter
% f: state transition function handle
% h: observation function handle
% x0: initial state
% P0: initial covariance
% Q: process noise covariance
% R: measurement noise covariance
% y: observations
% u: control inputs (optional)

% Dimensions
n = length(x0);
m = size(y,1);
T = size(y,2);

% Allocate memory
x = zeros(n,T);
P = zeros(n,n,T);

% Initialize
x(:,1) = x0;
P(:,:,1) = P0;

% Consistency parameter
alpha = 1;

% Sigma-point weights
lambda = n + alpha^2 - 1;
Wm = [lambda/(n+lambda) 0.5/(n+lambda)*ones(1,2*n)]';
Wc = Wm;
Wc(1) = Wc(1) + (1 - alpha^2 + beta);
c = sqrt(n+lambda);

% Sigma-points
X = zeros(n,2*n+1);
X(:,1) = x0;
for j = 1:n
    X(:,j+1) = x0 + c*chol(P0)'(:,j);
    X(:,n+j+1) = x0 - c*chol(P0)'(:,j);
end

% Time update
for k = 2:T
    % Propagate sigma-points
    Xf = f(X,u(:,k-1));
    % Compute predicted mean and covariance
    x(:,k) = Xf*Wm;
    P(:,:,k) = Q;
    for j = 1:2*n+1
        P(:,:,k) = P(:,:,k) + Wc(j)*(Xf(:,j)-x(:,k))*(Xf(:,j)-x(:,k))';
    end
    % Compute predicted observations
    Yf = h(Xf);
    % Compute cross-covariance
    Pxy = zeros(n,m);
    for j = 1:2*n+1
        Pxy = Pxy + Wc(j)*(Xf(:,j)-x(:,k))*(Yf(:,j)-h(x(:,k)))';
    end
    % Compute innovation covariance
    S = R;
    for j = 1:2*n+1
        S = S + Wc(j)*(Yf(:,j)-h(x(:,k)))*(Yf(:,j)-h(x(:,k)))';
    end
    % Compute Kalman gain
    K = Pxy/S;
    % Update state and covariance
    x(:,k) = x(:,k) + K*(y(:,k)-h(x(:,k)));
    P(:,:,k) = P(:,:,k) - K*S*K';
end
end

在这个程序中，参数`f`和`h`分别是状态转移函数和观测函数的句柄。`x0`和`P0`是初始状态和协方差矩阵，`Q`和`R`是过程噪声和测量噪声的协方差矩阵，`y`是观测数据，`u`是控制输入（可选）。函数的输出`x`和`P`分别是估计的状态和协方差矩阵。

需要注意的是，一致性卡尔曼滤波需要调整一些参数，例如一致性参数`alpha`和加权系数`beta`，这些参数需要根据具体问题进行调整。