粒子滤波四种基本重采样实例代码

以下是基于Python的四种基本重采样算法的代码实现：

1. 系统重采样

import numpy as np

def system_resampling(particles, weights):
    n_particles = len(weights)
    cum_weights = np.cumsum(weights)
    cum_weights[-1] = 1.0
    indexes = np.zeros(n_particles, dtype=int)
    u0 = np.random.uniform(0, 1/n_particles)
    j = 0
    for i in range(n_particles):
        u = u0 + i/n_particles
        while u > cum_weights[j]:
            j += 1
        indexes[i] = j
    return particles[indexes]

2. 伯努利重采样

import numpy as np

def bernoulli_resampling(particles, weights):
    n_particles = len(weights)
    cum_weights = np.cumsum(weights)
    cum_weights[-1] = 1.0
    indexes = np.zeros(n_particles, dtype=int)
    u = np.random.uniform(0, 1/n_particles)
    j = 0
    for i in range(n_particles):
        u += np.random.uniform(0, 1/n_particles)
        while u > cum_weights[j]:
            j += 1
        indexes[i] = j
    return particles[indexes]

3. 残差重采样

import numpy as np

def residual_resampling(particles, weights):
    n_particles = len(weights)
    indexes = np.zeros(n_particles, dtype=int)
    cum_weights = np.cumsum(weights)
    cum_weights[-1] = 1.0
    step = 1.0/n_particles
    u = np.random.uniform(0, step)
    j = 0
    for i in range(n_particles):
        while u > cum_weights[j]:
            j += 1
        indexes[i] = j
        u += step
    return particles[indexes]

4. 分层重采样

import numpy as np

def stratified_resampling(particles, weights):
    n_particles = len(weights)
    indexes = np.zeros(n_particles, dtype=int)
    cum_weights = np.cumsum(weights)
    cum_weights[-1] = 1.0
    step = 1.0/n_particles
    u = np.random.uniform(0, step)
    j = 0
    for i in range(n_particles):
        while u > cum_weights[j]:
            j += 1
        indexes[i] = j
        u += step
    return particles[indexes]

注意：以上代码中，`particles`表示粒子集合，`weights`表示对应的权重。在系统重采样、伯努利重采样和残差重采样中，`cum_weights`表示累计权重，`indexes`表示选择的粒子下标。在分层重采样中，`step`表示步长。