简单无迹kalman的matlab程序,卡尔曼滤波原理及应用——MATLAB仿真

以下是一个简单的无迹卡尔曼滤波的 MATLAB 程序：

function [x, P] = ukf_filter(z, x0, P0, Q, R, ffun, hfun)
% UKF_FILTER   Unscented Kalman Filter for nonlinear dynamic systems
%
% [x, P] = ukf_filter(z, x0, P0, Q, R, ffun, hfun)
%
% INPUTS
% z     - measurements (column vector)
% x0    - initial state (column vector)
% P0    - initial covariance matrix
% Q     - process noise covariance matrix
% R     - measurement noise covariance matrix
% ffun  - function handle to state transition function
% hfun  - function handle to measurement function
%
% OUTPUTS
% x     - state estimate (column vector)
% P     - state covariance matrix

n = length(x0);

% Define scaling parameters
alpha = 1e-3;
kappa = 0;
beta  = 2;

% Calculate sigma points
L = chol(P0)';
X = [zeros(n,1), L, -L];
X = sqrt(n+lambda)*X + x0(:,ones(2*n+1,1));

% Calculate weights
lambda = alpha^2*(n+kappa)-n;
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);

% Initialize state estimate and covariance
x = x0;
P = P0;

% Perform unscented Kalman filtering
for k = 1:length(z)
    
    % Propagate sigma points through state transition function
    X = ffun(X);
    
    % Calculate predicted state and covariance
    x_pred = X*Wm';
    P_pred = zeros(n,n);
    for j = 1:2*n+1
        P_pred = P_pred + Wc(j)*(X(:,j)-x_pred)*(X(:,j)-x_pred)';
    end
    P_pred = P_pred + Q;
    
    % Propagate sigma points through measurement function
    Y = hfun(X);
    
    % Calculate predicted measurements and innovation covariance
    z_pred = Y*Wm';
    S = zeros(length(z_pred),length(z_pred));
    for j = 1:2*n+1
        S = S + Wc(j)*(Y(:,j)-z_pred)*(Y(:,j)-z_pred)';
    end
    S = S + R;
    
    % Calculate cross-covariance matrix
    Pxy = zeros(n,length(z_pred));
    for j = 1:2*n+1
        Pxy = Pxy + Wc(j)*(X(:,j)-x_pred)*(Y(:,j)-z_pred)';
    end
    
    % Calculate Kalman gain
    K = Pxy/S;
    
    % Update state estimate and covariance
    x = x_pred + K*(z(k)-z_pred);
    P = P_pred - K*S*K';
    
end

其中，输入参数为：

- `z`：测量向量（列向量）。
- `x0`：初始状态向量（列向量）。
- `P0`：初始协方差矩阵。
- `Q`：过程噪声协方差矩阵。
- `R`：测量噪声协方差矩阵。
- `ffun`：状态转移函数的函数句柄。
- `hfun`：测量函数的函数句柄。

输出参数为：

- `x`：状态估计向量（列向量）。
- `P`：状态协方差矩阵。

这个程序实现了一个无迹卡尔曼滤波器，可以用于非线性动态系统的状态估计。