无迹卡尔曼滤波 python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。下面是一个简单的无迹卡尔曼滤波的Python代码示例：

import numpy as np

def unscented_kalman_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
    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
    predicted_sigma_points = np.zeros((n, 2*n+1))
    for i in range(2*n+1):
        predicted_sigma_points[:, i] = f(sigma_points[:, i])

    # Calculate predicted state and covariance
    x_pred = np.sum(predicted_sigma_points, axis=1) / c
    P_pred = np.zeros((n, n))
    for i in range(2*n+1):
        diff = predicted_sigma_points[:, i] - x_pred
        P_pred += (diff.reshape(-1, 1) @ diff.reshape(1, -1)) / c
    P_pred += Q

    # Calculate predicted measurement and covariance
    predicted_measurements = np.zeros((m, 2*n+1))
    for i in range(2*n+1):
        predicted_measurements[:, i] = h(predicted_sigma_points[:, i])
    z_pred = np.sum(predicted_measurements, axis=1) / c
    Pz_pred = np.zeros((m, m))
    for i in range(2*n+1):
        diff = predicted_measurements[:, i] - z_pred
        Pz_pred += (diff.reshape(-1, 1) @ diff.reshape(1, -1)) / c
    Pz_pred += R

    # Calculate cross-covariance matrix
    Pxz = np.zeros((n, m))
    for i in range(2*n+1):
        x_diff = predicted_sigma_points[:, i] - x_pred
        z_diff = predicted_measurements[:, i] - z_pred
        Pxz += (x_diff.reshape(-1, 1) @ z_diff.reshape(1, -1)) / c

    # 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

# 定义非线性过程模型函数 f(x)
def process_model(x):
    return np.array([x + x, x])

# 定义非线性测量模型函数 h(x)
def measurement_model(x):
    return np.array([x])

# 初始化状态和协方差矩阵
x = np.array([0, 0])
P = np.eye(2)

# 测量噪声协方差矩阵
R = np.array([[0.1]])

# 过程噪声协方差矩阵
Q = np.array([[0.01, 0], [0, 0.01]])

# 测量值
z = np.array()

# 使用无迹卡尔曼滤波进行状态估计
x_est, P_est = unscented_kalman_filter(x, P, z, Q, R, process_model, measurement_model)

print("Estimated state:", x_est)
print("Estimated covariance:", P_est)