ukf python代码

以下是一个简单的基于Python实现的UKF代码示例，供您参考：

import numpy as np

class UKF:
    def __init__(self, dim_x, dim_z, fx, hx, dt, alpha, beta, kappa):
        self.dim_x = dim_x
        self.dim_z = dim_z
        self.fx = fx
        self.hx = hx
        self.dt = dt
        self.alpha = alpha
        self.beta = beta
        self.kappa = kappa
        self.weights = self.compute_weights()
        self.mean = np.zeros(dim_x)
        self.cov = np.eye(dim_x)

    def predict(self, u=None):
        sigmas = self.compute_sigma_points(self.mean, self.cov, self.alpha, self.beta, self.kappa)
        sigmas = [self.fx(sigma, self.dt, u) for sigma in sigmas]
        self.mean, self.cov = self.compute_mean_cov(sigmas, self.weights)

    def update(self, z):
        sigmas = self.compute_sigma_points(self.mean, self.cov, self.alpha, self.beta, self.kappa)
        zs = [self.hx(sigma) for sigma in sigmas]
        z_mean, z_cov = self.compute_mean_cov(zs, self.weights)
        Pxz = np.zeros((self.dim_x, self.dim_z))
        for i in range(len(sigmas)):
            dx = sigmas[i] - self.mean
            dz = zs[i] - z_mean
            Pxz += self.weights[i] * np.outer(dx, dz)
        K = np.dot(Pxz, np.linalg.inv(z_cov))
        innovation = z - z_mean
        self.mean += np.dot(K, innovation)
        self.cov -= np.dot(K, np.dot(z_cov, K.T))

    def compute_sigma_points(self, mean, cov, alpha, beta, kappa):
        n = self.dim_x
        lamda = alpha ** 2 * (n + kappa) - n
        U = np.linalg.cholesky((n + lamda) * cov)
        X = np.zeros((2 * n + 1, n))
        X[0] = mean
        for k in range(n):
            X[k + 1] = mean + U[k]
            X[n + k + 1] = mean - U[k]
        return X

    def compute_weights(self):
        n = self.dim_x
        lamda = self.alpha ** 2 * (n + self.kappa) - n
        c = 0.5 / (n + lamda)
        weights = np.full(2 * n + 1, c)
        weights[0] = lamda / (n + lamda)
        return weights

    def compute_mean_cov(self, sigmas, weights):
        mean = np.average(sigmas, axis=0, weights=weights)
        cov = np.zeros((self.dim_x, self.dim_x))
        for i in range(len(sigmas)):
            dx = sigmas[i] - mean
            cov += weights[i] * np.outer(dx, dx)
        return mean, cov

使用方法：

1. 初始化UKF实例，指定状态向量和观测向量的维度、状态转移函数和观测函数、时间间隔、UKF参数（alpha、beta和kappa）。
2. 调用predict方法进行预测，传入控制向量（可选）。
3. 调用update方法进行更新，传入观测向量。
4. 重复步骤2和3，进行连续的预测和更新。