python的ukf代码

以下是Python中的UKF（无迹卡尔曼滤波器）实现代码，使用NumPy库：

import numpy as np

class UnscentedKalmanFilter:
    def __init__(self, dim_x, dim_z, fx, hx, dt, points, sqrt_fn=None, sqrt_x=None, x_mean_fn=None, z_mean_fn=None):
        self.dim_x = dim_x
        self.dim_z = dim_z
        self.fx = fx
        self.hx = hx
        self.dt = dt
        self.points = points
        
        if sqrt_fn is None:
            self.sqrt_fn = np.linalg.cholesky
        else:
            self.sqrt_fn = sqrt_fn
            
        if sqrt_x is None:
            self.sqrt_x = np.linalg.cholesky
        else:
            self.sqrt_x = sqrt_x
            
        if x_mean_fn is None:
            self.x_mean_fn = self.mean
        else:
            self.x_mean_fn = x_mean_fn
            
        if z_mean_fn is None:
            self.z_mean_fn = self.mean
        else:
            self.z_mean_fn = z_mean_fn
            
        self.reset()
        
    def reset(self):
        self.x = np.zeros((self.dim_x, 1))
        self.P = np.eye(self.dim_x)
        self.Q = np.eye(self.dim_x)
        self.R = np.eye(self.dim_z)
        self.y = np.zeros((self.dim_z, 1))
        self.sigma_points = np.zeros((self.dim_x, self.points * 2 + 1))
        self.sigmas_f = np.zeros((self.dim_x, self.points * 2 + 1))
        self.sigmas_h = np.zeros((self.dim_z, self.points * 2 + 1))
        
    def mean(self, sigmas, Wm):
        return np.dot(sigmas, Wm)
    
    def residual(self, a, b):
        y = a - b
        y[1] = self.wrap_angle(y[1])
        return y
    
    def wrap_angle(self, angle):
        return angle - 2 * np.pi * np.floor((angle + np.pi) / (2 * np.pi))
    
    def predict(self, u=None):
        self.sigma_points = self.compute_sigma_points(self.x, self.P)
        
        for i in range(self.points * 2 + 1):
            self.sigmas_f[:, [i]] = self.fx(self.sigma_points[:, [i]], self.dt, u)
            
        x, P = self.unscented_transform(self.sigmas_f, self.x_mean_fn, self.sqrt_fn, self.Q)
        self.x = x
        self.P = P
        
    def update(self, z):
        self.sigma_points = self.compute_sigma_points(self.x, self.P)
        
        for i in range(self.points * 2 + 1):
            self.sigmas_h[:, [i]] = self.hx(self.sigma_points[:, [i]])
            
        z_mean, S = self.unscented_transform(self.sigmas_h, self.z_mean_fn, self.sqrt_x, self.R)
        Pxz = np.zeros((self.dim_x, self.dim_z))
        
        for i in range(self.points * 2 + 1):
            Pxz += np.dot(self.residual(self.sigmas_f[:, [i]], self.x), self.residual(self.sigmas_h[:, [i]], z_mean).T) * self.points
        
        K = np.dot(Pxz, np.linalg.inv(S))
        self.y = self.residual(z, z_mean)
        self.x += np.dot(K, self.y)
        self.P -= np.dot(K, np.dot(S, K.T))
        
    def compute_sigma_points(self, x, P):
        sigmas = np.zeros((self.dim_x, self.points * 2 + 1))
        sigmas[:, [0]] = x
        
        sqrt_P = self.sqrt_fn(P)
        
        for i in range(self.dim_x):
            sigmas[:, [i + 1]] = x + sqrt_P[:, [i]] * self.points
            sigmas[:, [i + 1 + self.dim_x]] = x - sqrt_P[:, [i]] * self.points
            
        return sigmas
    
    def unscented_transform(self, sigmas, mean_fn, sqrt_fn, cov=None, add_noise=False, noise=None):
        Wm = np.ones(2 * self.dim_x + 1) / (2 * self.dim_x)
        Wc = Wm.copy()
        Wc[0] = Wc[0] + (1 - np.square(self.dim_x)) + 2 * add_noise
        
        if noise is None:
            noise = np.zeros((self.dim_x, 1))
            
        x = mean_fn(sigmas, Wm)
        y = sigmas - x
        
        P = np.dot(y, np.dot(np.diag(Wc), y.T))
        
        if cov is not None:
            P += cov
            
        sqrt_P = sqrt_fn(P)
        
        return x + noise, sqrt_P
        

其中，`dim_x`和`dim_z`分别是状态向量和观测向量的维度，`fx`和`hx`分别是状态转移函数和观测函数，`dt`是时间间隔，`points`是Sigma点的数量，`sqrt_fn`和`sqrt_x`是函数，用于计算协方差矩阵的平方根，`x_mean_fn`和`z_mean_fn`分别是函数，用于计算均值。`reset`方法用于重置滤波器状态。`mean`方法用于计算均值，`residual`方法用于计算残差，`wrap_angle`方法用于对角度进行约束。`predict`方法用于预测，`update`方法用于更新。`compute_sigma_points`方法用于计算Sigma点，`unscented_transform`方法用于实现无迹变换。