二维轨迹的无迹卡尔曼预测 python

以下是二维轨迹的无迹卡尔曼预测 Python 代码示例：

import numpy as np

def unscented_transform(sigma_points, weights):
    mean = np.sum(sigma_points * weights, axis=1)
    residual = sigma_points - mean[:, np.newaxis]
    covariance = np.dot(residual, np.dot(np.diag(weights), residual.T))
    return mean, covariance

class UnscentedKalmanFilter(object):
    def __init__(self, dt, state_dim, measurement_dim, process_noise_cov, measurement_noise_cov):
        self.dt = dt
        self.state_dim = state_dim
        self.measurement_dim = measurement_dim
        self.process_noise_cov = process_noise_cov
        self.measurement_noise_cov = measurement_noise_cov

        self.n_sigma = 2 * state_dim + 1
        self.alpha = 1e-3
        self.beta = 2
        self.kappa = 0
        self.lambda_ = self.alpha ** 2 * (state_dim + self.kappa) - state_dim

        self.weights_mean = np.zeros(self.n_sigma)
        self.weights_cov = np.zeros(self.n_sigma)

        self.sigma_points = np.zeros((state_dim, self.n_sigma))
        self.measurement_sigma_points = np.zeros((measurement_dim, self.n_sigma))

        self.x = np.zeros(state_dim)
        self.P = np.eye(state_dim) * 1e-6

    def predict(self, u=None):
        sigma_points = self._generate_sigma_points(self.x, self.P)
        self.sigma_points = sigma_points

        if u is not None:
            sigma_points = self._add_control_input(sigma_points, u)

        sigma_points = self._propagate(sigma_points, self.dt)

        self.x, self.P = unscented_transform(sigma_points, self.weights_cov)
        self.P += self.process_noise_cov

    def update(self, z):
        self.measurement_sigma_points = self._generate_measurement_sigma_points(self.sigma_points)
        z_mean, z_cov = unscented_transform(self.measurement_sigma_points, self.weights_mean)
        S = z_cov + self.measurement_noise_cov

        residual = self.measurement_sigma_points - z_mean[:, np.newaxis]
        cross_cov = np.dot(self.sigma_points - self.x[:, np.newaxis], np.dot(np.diag(self.weights_cov), residual.T))

        K = np.dot(cross_cov, np.linalg.inv(S))
        self.x += np.dot(K, z - z_mean)
        self.P -= np.dot(K, np.dot(S, K.T))

    def _generate_sigma_points(self, x, P):
        sigma_points = np.zeros((self.state_dim, self.n_sigma))
        L = np.linalg.cholesky((self.state_dim + self.lambda_) * P)

        sigma_points[:, 0] = x
        for i in range(self.state_dim):
            sigma_points[:, i+1] = x + L[:, i]
            sigma_points[:, i+1+self.state_dim] = x - L[:, i]

        self.weights_mean[0] = self.lambda_ / (self.state_dim + self.lambda_)
        self.weights_cov[0] = self.weights_mean[0] + (1 - self.alpha**2 + self.beta)

        for i in range(1, self.n_sigma):
            self.weights_mean[i] = 1 / (2 * (self.state_dim + self.lambda_))
            self.weights_cov[i] = self.weights_mean[i]

        return sigma_points

    def _generate_measurement_sigma_points(self, sigma_points):
        measurement_sigma_points = np.zeros((self.measurement_dim, self.n_sigma))
        for i in range(self.n_sigma):
            measurement_sigma_points[:, i] = self._measurement_model(sigma_points[:, i])
        return measurement_sigma_points

    def _add_control_input(self, sigma_points, u):
        for i in range(self.n_sigma):
            sigma_points[:, i] = self._state_transition_model(sigma_points[:, i], u)
        return sigma_points

    def _propagate(self, sigma_points, dt):
        for i in range(self.n_sigma):
            sigma_points[:, i] = self._state_transition_model(sigma_points[:, i], None, dt)
        return sigma_points

    def _state_transition_model(self, state, control_input=None, dt=None):
        # TODO: Implement state transition model
        pass

    def _measurement_model(self, state):
        # TODO: Implement measurement model
        pass

在实现代码时需要替换 `_state_transition_model` 和 `_measurement_model` 函数，以适应具体问题。