无迹卡尔曼python代码

无迹卡尔曼滤波（Unscented Kalman Filter，简称UKF）是一种基于无迹变换（Unscented Transformation）的卡尔曼滤波算法，它在非线性系统中的估计问题上表现出了很好的性能。相对于传统的扩展卡尔曼滤波（Extended Kalman Filter，简称EKF），UKF不需要对非线性函数进行泰勒展开，因此可以避免扰动方差的引入和计算复杂度的增加。

以下是一个用Python实现的简单的无迹卡尔曼滤波器代码，仅供参考：

import numpy as np

class UnscentedKalmanFilter:
    def __init__(self, dim_x, dim_z, fx, hx, dt):
        self.dim_x = dim_x
        self.dim_z = dim_z
        self.fx = fx
        self.hx = hx
        self.dt = dt
        
        self.x = np.zeros((dim_x, 1))
        self.P = np.eye(dim_x)
        self.Q = np.eye(dim_x)
        self.R = np.eye(dim_z)
        
        self.alpha = 1e-3
        self.beta = 2
        self.kappa = 0
        
        self.weights_mean = np.zeros((2 * dim_x + 1,))
        self.weights_cov = np.zeros((2 * dim_x + 1,))
        
        lambda_ = self.alpha**2 * (dim_x + self.kappa) - dim_x
        c = dim_x + lambda_
        Wm = np.zeros((2 * dim_x + 1,))
        Wc = np.zeros((2 * dim_x + 1,))
        
        for i in range(2 * dim_x + 1):
            if i == 0:
                Wm[i] = lambda_ / c
                Wc[i] = lambda_ / c + (1 - self.alpha**2 + self.beta)
            else:
                Wm[i] = 1 / (2 * c)
                Wc[i] = 1 / (2 * c)
                
        self.Wm = Wm
        self.Wc = Wc
        
    def predict(self):
        sigmas = self._compute_sigma_points(self.x, self.P)
        
        x_pred = np.zeros((self.dim_x, 1))
        
        for i in range(len(sigmas)):
            x_pred += self.weights_mean[i] * self.fx(sigmas[i], self.dt)
            
        P_pred = np.zeros((self.dim_x, self.dim_x))
        
        for i in range(len(sigmas)):
            err = self.fx(sigmas[i], self.dt) - x_pred
            P_pred += self.weights_cov[i] * np.outer(err, err)
            
        P_pred += self.Q
        
        self.x = x_pred
        self.P = P_pred
        
    def update(self, z):
        sigmas = self._compute_sigma_points(self.x, self.P)
        
        z_pred = np.zeros((self.dim_z, 1))
        
        for i in range(len(sigmas)):
            z_pred += self.weights_mean[i] * self.hx(sigmas[i])
            
        Pzz = np.zeros((self.dim_z, self.dim_z))
        
        for i in range(len(sigmas)):
            err = self.hx(sigmas[i]) - z_pred
            Pzz += self.weights_cov[i] * np.outer(err, err)
            
        Pzz += self.R
        
        Pxz = np.zeros((self.dim_x, self.dim_z))
        
        for i in range(len(sigmas)):
            err_x = sigmas[i] - self.x
            err_z = self.hx(sigmas[i]) - z_pred
            Pxz += self.weights_cov[i] * np.outer(err_x, err_z)
            
        K = np.dot(Pxz, np.linalg.inv(Pzz))
        
        y = z - z_pred
        x_post = self.x + np.dot(K, y)
        P_post = self.P - np.dot(K, np.dot(Pzz, K.T))
        
        self.x = x_post
        self.P = P_post
        
    def _compute_sigma_points(self, x, P):
        lambda_ = self.alpha**2 * (self.dim_x + self.kappa) - self.dim_x
        c = self.dim_x + lambda_
        U = np.linalg.cholesky(c * P)
        
        sigmas = np.zeros((2 * self.dim_x + 1, self.dim_x))
        sigmas = x.flatten()
        
        for k in range(self.dim_x):
            sigmas[k + 1] = (x + U[k]).flatten()
            sigmas[self.dim_x + k + 1] = (x - U[k]).flatten()
            
        return sigmas

该代码实现了一个基本的无迹卡尔曼滤波器类，包括了初始化、预测、更新和计算sigma点等基本操作。其中fx和hx分别为状态转移函数和观测函数，dt为时间步长。使用时，需要根据具体的问题定义对应的状态转移函数和观测函数，并将其传递给无迹卡尔曼滤波器类的构造函数。