无迹卡尔曼滤波ukf代码

无迹卡尔曼滤波（Unscented Kalman Filter，UKF）是一种非线性滤波算法，用于估计系统状态。相比于传统的扩展卡尔曼滤波（Extended Kalman Filter，EKF），UKF使用迹变换来更准确地估计线性系统的。

以下是一个简单的无迹卡尔曼滤波的代码示例：

import numpy as np

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

    lambda_ = alpha**2 * (n + kappa) - n
    c = n + lambda_

    Generate sigma points
    sigma_points = np.zeros((n, 2*n+1))
    sigma_points[:, 0] = x
    sqrt_P = np.linalg.cholesky(c*P)
    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 model
    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 = np.zeros((n, n))
    for i in range(2*n+1):
        P_pred += ((propagated_points[:, i] - x_pred) @ (propagated_points[:, i] - x_pred).T) / (2*n+1)
    P_pred += Q

    # Calculate predicted measurement and covariance
    z_pred = np.zeros((m, 1))
    for i in range(2*n+1):
        z_pred += h(propagated_points[:, i])
    z_pred /= (2*n+1)

    Pzz = np.zeros((m, m))
    Pxz = np.zeros((n, m))
    for i in range(2*n+1):
        Pzz += ((h(propagated_points[:, i]) - z_pred) @ (h(propagated_points[:, i]) - z_pred).T) / (2*n+1)
        Pxz += ((propagated_points[:, i] - x_pred) @ (h(propagated_points[:, i]) - z_pred).T) / (2*n+1)

    Pzz += R

    # Calculate Kalman gain
    K = Pxz @ np.linalg.inv(Pzz)

    # Update state and covariance
    x = x_pred + K @ (z - z_pred)
    P = P_pred - K @ Pzz @ K.T

    return x, P

在上述代码中，`x`是系统状态向量，`P`是状态协方差矩阵，`z`是测量向量，`Q`是过程噪声协方差矩阵，`R`是测量噪声协方差矩阵，`f`是非线性过程模型函数，`h`是非线性测量模型函数。函数`unscented_kalman_filter`实现了无迹卡尔曼滤波的主要逻辑，通过传入相应的参数进行状态估计。