matlab无迹卡尔曼滤波算法代码
时间: 2023-07-03 22:18:16 浏览: 51
以下是MATLAB中无迹卡尔曼滤波(Unscented Kalman Filter)算法的代码实现:
```matlab
function [x_k, P_k] = UKF(f_func, h_func, x_k_1, P_k_1, Q, R, y_k)
% f_func: 状态转移函数
% h_func: 观测函数
% x_k_1: 上一时刻的状态向量
% P_k_1: 上一时刻的状态协方差矩阵
% Q: 状态噪声协方差矩阵
% R: 观测噪声协方差矩阵
% y_k: 当前时刻的观测值
% 系统参数
n = length(x_k_1); % 状态向量的维数
alpha = 1; % UKF参数
kappa = 0; % UKF参数
beta = 2; % UKF参数
% 计算sigma点
lambda = alpha^2*(n+kappa)-n;
sigma_points = zeros(n,2*n+1);
sigma_points(:,1) = x_k_1;
P_k_1_sqrt = chol((n+lambda)*P_k_1)';
for i = 1:n
sigma_points(:,i+1) = x_k_1 + P_k_1_sqrt(i,:)';
sigma_points(:,i+n+1) = x_k_1 - P_k_1_sqrt(i,:)';
end
% 预测状态和状态协方差矩阵
x_k_minus = zeros(n,1);
for i = 1:2*n+1
x_k_minus = x_k_minus + f_func(sigma_points(:,i));
end
x_k_minus = x_k_minus/(2*n+1);
P_k_minus = Q;
for i = 1:2*n+1
P_k_minus = P_k_minus + (f_func(sigma_points(:,i))-x_k_minus)*(f_func(sigma_points(:,i))-x_k_minus)';
end
P_k_minus = P_k_minus/(2*n+1) + Q;
% 计算观测sigma点
lambda = alpha^2*(n+kappa)-n;
sigma_points_obs = zeros(n,2*n+1);
sigma_points_obs(:,1) = h_func(x_k_minus);
P_k_minus_sqrt = chol((n+lambda)*P_k_minus)';
for i = 1:n
sigma_points_obs(:,i+1) = h_func(x_k_minus) + P_k_minus_sqrt(i,:)';
sigma_points_obs(:,i+n+1) = h_func(x_k_minus) - P_k_minus_sqrt(i,:)';
end
% 计算预测观测和观测协方差矩阵
y_k_minus = zeros(n,1);
for i = 1:2*n+1
y_k_minus = y_k_minus + sigma_points_obs(:,i);
end
y_k_minus = y_k_minus/(2*n+1);
P_yy = R;
P_xy = zeros(n,n);
for i = 1:2*n+1
P_yy = P_yy + (sigma_points_obs(:,i)-y_k_minus)*(sigma_points_obs(:,i)-y_k_minus)';
P_xy = P_xy + (f_func(sigma_points(:,i))-x_k_minus)*(sigma_points_obs(:,i)-y_k_minus)';
end
P_yy = P_yy/(2*n+1) + R;
P_xy = P_xy/(2*n+1);
% 计算卡尔曼增益
K_k = P_xy/P_yy;
% 更新状态和状态协方差矩阵
x_k = x_k_minus + K_k*(y_k-y_k_minus);
P_k = P_k_minus - K_k*P_yy*K_k';
end
```
其中,`f_func`和`h_func`分别为状态转移函数和观测函数,输入参数为状态向量;`x_k_1`和`P_k_1`分别为上一时刻的状态向量和状态协方差矩阵;`Q`和`R`分别为状态噪声协方差矩阵和观测噪声协方差矩阵;`y_k`为当前时刻的观测值。函数的输出为当前时刻的状态向量`x_k`和状态协方差矩阵`P_k`。