ukf算法的python实现

以下是一个简单的用Python实现UKF算法的示例代码：

import numpy as np

def ukf_filter(x, P, z, Q, R, f, h):
    n = len(x)
    m = len(z)
    alpha = 0.001
    kappa = 0
    beta = 2

    lambda_ = alpha**2 * (n + kappa) - n
    
    # Generate sigma points
    sqrt_P = np.linalg.cholesky((n + lambda_) * P)
    sigma_points = np.zeros((n, 2*n+1))
    sigma_points[:, 0] = x
    for i in range(n):
        sigma_points[:, i+1] = x + sqrt_P[:, i]
        sigma_points[:, n+i+1] = x - sqrt_P[:, i]
    
    # Propagate sigma points through the nonlinear process function f
    propagated_points = np.zeros((n, 2*n+1))
    for i in range(2*n+1):
        propagated_points[:, i] = f(sigma_points[:, i])
    
    # Calculate predicted state and covariance
    x_pred = np.sum(propagated_points, axis=1) / (2*n+1)
    P_pred = ((propagated_points - x_pred[:, np.newaxis]) @ (propagated_points - x_pred[:, np.newaxis]).T) / (2*n+1) + Q
    
    # Calculate predicted measurement mean and covariance
    sqrt_P_pred = np.linalg.cholesky((n + lambda_) * P_pred)
    sigma_points_pred = np.zeros((m, 2*n+1))
    for i in range(2*n+1):
        sigma_points_pred[:, i] = h(propagated_points[:, i])
    z_pred = np.sum(sigma_points_pred, axis=1) / (2*n+1)
    Pz_pred = ((sigma_points_pred - z_pred[:, np.newaxis]) @ (sigma_points_pred - z_pred[:, np.newaxis]).T) / (2*n+1) + R
    
    # Calculate cross-covariance matrix
    Pxz = ((propagated_points - x_pred[:, np.newaxis]) @ (sigma_points_pred - z_pred[:, np.newaxis]).T) / (2*n+1)
    
    # Calculate Kalman gain
    K = Pxz @ np.linalg.inv(Pz_pred)
    
    # Update state and covariance
    x = x_pred + K @ (z - z_pred)
    P = P_pred - K @ Pz_pred @ K.T
    
    return x, P

在使用该代码时，需要自定义状态转移函数 `f` 和观测函数 `h`，以及指定初始状态 `x`、初始协方差矩阵 `P`、过程噪声协方差矩阵 `Q`、测量噪声协方差矩阵 `R`，并提供观测值 `z`。函数 `f` 和 `h` 接受一个状态向量作为输入，并返回相应的状态转移值和观测值。

请注意，这只是UKF算法的简单实现示例，可能需要根据具体问题进行调整和优化。