ukf代码python

以下是Python实现的无迹卡尔曼滤波（Unscented Kalman Filter，UKF）的示例代码：

import numpy as np

class UKF:
    def __init__(self, n, m, alpha, beta, kappa):
        self.n = n    # 状态向量维度
        self.m = m    # 观测向量维度
        self.alpha = alpha    # UKF参数
        self.beta = beta      # UKF参数
        self.kappa = kappa    # UKF参数
        self.lambda_ = alpha**2 * (n + kappa) - n
        self.Wm, self.Wc = self._compute_weights(n, kappa, alpha, beta)
        self.x = np.zeros((n, 1))    # 状态向量
        self.P = np.eye(n)           # 状态协方差矩阵
        self.Q = np.eye(n)           # 状态噪声协方差矩阵
        self.R = np.eye(m)           # 观测噪声协方差矩阵

    def _compute_weights(self, n, kappa, alpha, beta):
        lambda_ = alpha**2 * (n + kappa) - n
        c = n + lambda_
        Wm = np.zeros((2*n+1, 1))
        Wc = np.zeros((2*n+1, 1))
        Wm[0] = lambda_ / c
        Wc[0] = lambda_ / c + (1 - alpha**2 + beta)
        for i in range(1, 2*n+1):
            Wm[i] = 1 / (2*c)
            Wc[i] = 1 / (2*c)
        return Wm, Wc

    def _compute_sigma_points(self, x, P):
        n = x.shape[0]
        X = np.zeros((n, 2*n+1))
        L = np.linalg.cholesky((n+self.lambda_)*P)
        X[:,0] = x.flatten()
        for i in range(n):
            X[:,i+1] = (x + L[:,i]).flatten()
            X[:,i+1+n] = (x - L[:,i]).flatten()
        return X

    def predict(self, dt):
        X = self._compute_sigma_points(self.x, self.P)
        n = X.shape[0]
        X_pred = np.zeros((n, 2*n+1))
        for i in range(2*n+1):
            X_pred[:,i] = self._state_function(X[:,i], dt).flatten()
        x_pred = X_pred.dot(self.Wm)
        P_pred = self.Q
        for i in range(2*n+1):
            P_pred += self.Wc[i] * np.outer(X_pred[:,i]-x_pred, X_pred[:,i]-x_pred)
        self.x = x_pred
        self.P = P_pred

    def update(self, z):
        X = self._compute_sigma_points(self.x, self.P)
        n = X.shape[0]
        Z = np.zeros((self.m, 2*n+1))
        for i in range(2*n+1):
            Z[:,i] = self._observation_function(X[:,i]).flatten()
        z_pred = Z.dot(self.Wm)
        Pz_pred = self.R
        Pxz = np.zeros((n, self.m))
        for i in range(2*n+1):
            Pz_pred += self.Wc[i] * np.outer(Z[:,i]-z_pred, Z[:,i]-z_pred)
            Pxz += self.Wc[i] * np.outer(X[:,i]-self.x, Z[:,i]-z_pred)
        K = Pxz.dot(np.linalg.inv(Pz_pred))
        self.x += K.dot(z - z_pred)
        self.P -= K.dot(Pz_pred).dot(K.T)

    def _state_function(self, x, dt):
        # 状态转移函数
        pass

    def _observation_function(self, x):
        # 观测函数
        pass

其中，`n`表示状态向量的维度，`m`表示观测向量的维度，`alpha`、`beta`和`kappa`是UKF的参数。`_compute_weights()`方法用于计算权重矩阵，`_compute_sigma_points()`方法用于计算sigma点，`predict()`方法用于预测状态，`update()`方法用于更新状态。`_state_function()`方法是状态转移函数，`_observation_function()`方法是观测函数，需要根据具体问题实现。