6维ukf 展示matlab代码

以下是一个简单的6维UKF实现的MATLAB代码示例：

% 定义状态转移函数
f = @(x, dt) [x(1) + dt*x(4); x(2) + dt*x(5); x(3) + dt*x(6); x(4); x(5); x(6)];

% 定义观测函数
h = @(x) x(1:3);

% 初始化状态向量和协方差矩阵
x = [0; 0; 0; 1; 1; 1];
P = eye(6);

% 定义过程噪声和观测噪声的协方差矩阵
Q = diag([0.1, 0.1, 0.1, 0.01, 0.01, 0.01]);
R = diag([0.5, 0.5, 0.5]);

% 定义UKF参数
alpha = 0.001;
beta = 2;
kappa = 0;
n = 6;

% 生成sigma点
lambda = alpha^2*(n+kappa)-n;
c = n+lambda;
Wm = [lambda/c 0.5/c+zeros(1,2*n)];
Wc = Wm;
Wc(1) = Wc(1)+(1-alpha^2+beta);
sigma = zeros(n,2*n+1);
sigma(:,1) = x;
A = sqrt(c)*chol(P)';
for i = 1:n
    sigma(:,i+1) = x+A(:,i);
    sigma(:,n+i+1) = x-A(:,i);
end

% 对sigma点进行传播
dt = 0.1;
for i = 1:2*n+1
    sigma(:,i) = f(sigma(:,i), dt);
end

% 计算预测状态和协方差矩阵
x = sum(Wm.*sigma,2);
P = Q;
for i = 1:2*n+1
    P = P + Wc(i)*(sigma(:,i)-x)*(sigma(:,i)-x)';
end

% 生成新的sigma点
A = sqrt(c)*chol(P)';
sigma = zeros(n,2*n+1);
sigma(:,1) = x;
for i = 1:n
    sigma(:,i+1) = x+A(:,i);
    sigma(:,n+i+1) = x-A(:,i);
end

% 对sigma点进行更新
for i = 1:2*n+1
    y(:,i) = h(sigma(:,i));
end

% 计算预测观测和协方差矩阵
y_hat = sum(Wm.*y,2);
S = R;
for i = 1:2*n+1
    S = S + Wc(i)*(y(:,i)-y_hat)*(y(:,i)-y_hat)';
end

% 计算卡尔曼增益和最终状态和协方差矩阵
C = zeros(n,3);
for i = 1:2*n+1
    C = C + Wc(i)*(sigma(:,i)-x)*(y(:,i)-y_hat)';
end
K = C/S;
x = x + K*(z-y_hat);
P = P - K*S*K';

% 输出最终状态向量
disp(x);

这只是一个简单的示例，实际应用中需要根据具体问题进行相应的修改和调整。