KLD粒子滤波方法代码实现

KLD粒子滤波（KLD Particle Filter）是一种基于粒子滤波（Particle Filter）的自适应重要性采样算法，其目的是在不知道系统噪声分布的情况下，自适应调整粒子数，以达到比较好的估计效果。以下是KLD粒子滤波方法的代码实现：

import numpy as np
import math

class KLDParticleFilter:
    def __init__(self, initial_state, num_particles, motion_model, measurement_model, resampling_threshold=0.5, kld_err=0.01, kld_z=0.99):
        self.num_particles = num_particles
        self.motion_model = motion_model
        self.measurement_model = measurement_model
        self.resampling_threshold = resampling_threshold
        self.kld_err = kld_err
        self.kld_z = kld_z
        
        self.particles = np.tile(initial_state, (num_particles, 1)) + np.random.randn(num_particles, len(initial_state)) * 0.1
        self.weights = np.ones(num_particles) / num_particles
        self.resample_count = 0
        
    def predict(self, control_input):
        self.particles = self.motion_model(self.particles, control_input) + np.random.randn(self.num_particles, len(control_input)) * 0.1
        
    def update(self, measurement):
        likelihood = self.measurement_model(measurement, self.particles)
        self.weights *= likelihood
        self.weights /= np.sum(self.weights)
        
        # check if the effective sample size is below the resampling threshold
        ess = 1 / np.sum(np.square(self.weights))
        if ess < self.resampling_threshold * self.num_particles:
            self.resample()
            
    def resample(self):
        # calculate the Kullback-Leibler divergence between the current and the target distributions
        kl_div = self.kld(self.weights)
        
        # compute the new number of particles
        n = int(math.ceil(self.kld_z / self.kld_err ** 2 * kl_div))
        
        # resample particles
        indices = self.stratified_resample(self.weights)
        self.particles = self.particles[indices]
        self.weights = np.ones(self.num_particles) / self.num_particles
        
        self.resample_count += 1
        
    def kld(self, weights):
        # compute the Kullback-Leibler divergence between the current and the uniform distribution
        return np.sum(weights * np.log(weights * self.num_particles))
    
    def stratified_resample(self, weights):
        indices = np.zeros(self.num_particles, dtype=np.int32)
        cum_weights = np.cumsum(weights)
        step = 1 / self.num_particles
        u = np.random.uniform(0, step)
        idx = 0
        for i in range(self.num_particles):
            while u > cum_weights[idx]:
                idx += 1
            indices[i] = idx
            u += step
        return indices

其中，`initial_state`是粒子的初始状态，`num_particles`是粒子的数量，`motion_model`是运动模型，`measurement_model`是测量模型，`resampling_threshold`是重采样阈值，`kld_err`和`kld_z`是KLD粒子滤波算法中的参数。

`predict`方法根据控制量，对粒子进行运动模型的预测；`update`方法利用测量值更新粒子的权重，并判断是否需要进行重采样；`resample`方法实现了KLD粒子滤波算法中的自适应重采样；`kld`方法计算粒子权重分布与均匀分布的Kullback-Leibler散度；`stratified_resample`方法实现了分层重采样。