Particle Filter 粒子滤波 原理以及python实践

本笔记学习于优达学城 Artificial Intelligence for Robotics课程

什么是粒子滤波器，请看下面几幅图片

在整个空间内有无数关于机器人的位置坐标以及方向的粒子 [x,y,orientation],随着机器人的移动感知周围空间，这些粒子将获得自己的权重，然后进行筛选，最后粒子逐渐收敛到一起。这个就是粒子滤波器的基本原理。

首先创建好一个机器人的类，机器人可以移动，设定方向，设定误差

# -*- coding: utf-8 -*-   from math import *import random#机器人四个参照物landmarks  = [[20.0, 20.0], [80.0, 80.0], [20.0, 80.0], [80.0, 20.0]]#地图大小world_size = 100.0class robot:    def __init__(self):        self.x = random.random() * world_size        self.y = random.random() * world_size        self.orientation = random.random() * 2.0 * pi        #给机器人初试化一个坐标和方向        self.forward_noise = 0.0;        self.turn_noise    = 0.0;        self.sense_noise   = 0.0;        def set(self, new_x, new_y, new_orientation):#设定机器人的坐标　方向        if new_x < 0 or new_x >= world_size:            raise ValueError, 'X coordinate out of bound'        if new_y < 0 or new_y >= world_size:            raise ValueError, 'Y coordinate out of bound'        if new_orientation < 0 or new_orientation >= 2 * pi:            raise ValueError, 'Orientation must be in [0..2pi]'        self.x = float(new_x)        self.y = float(new_y)        self.orientation = float(new_orientation)            def set_noise(self, new_f_noise, new_t_noise, new_s_noise):        # makes it possible to change the noise parameters        # this is often useful in particle filters        #设定一下机器人的噪声        self.forward_noise = float(new_f_noise);        self.turn_noise    = float(new_t_noise);        self.sense_noise   = float(new_s_noise);            def sense(self):#测量机器人到四个参照物的距离　可以添加一些高斯噪声        Z = []        for i in range(len(landmarks)):            dist = sqrt((self.x - landmarks[i][0]) ** 2 + (self.y - landmarks[i][1]) ** 2)            dist += random.gauss(0.0, self.sense_noise)            Z.append(dist)        return Z            def move(self, turn, forward):        #机器人转向　前进　并返回更新后的机器人新的坐标和噪声大小        if forward < 0:            raise ValueError, 'Robot cant move backwards'                         # turn, and add randomness to the turning command        orientation = self.orientation + float(turn) + random.gauss(0.0, self.turn_noise)        orientation %= 2 * pi                # move, and add randomness to the motion command        dist = float(forward) + random.gauss(0.0, self.forward_noise)        x = self.x + (cos(orientation) * dist)        y = self.y + (sin(orientation) * dist)        x %= world_size    # cyclic truncate        y %= world_size                # set particle        res = robot()        res.set(x, y, orientation)        res.set_noise(self.forward_noise, self.turn_noise, self.sense_noise)        return res        def Gaussian(self, mu, sigma, x):                # calculates the probability of x for 1-dim Gaussian with mean mu and var. sigma        return exp(- ((mu - x) ** 2) / (sigma ** 2) / 2.0) / sqrt(2.0 * pi * (sigma ** 2))            def measurement_prob(self, measurement):                # calculates how likely a measurement should be        #计算出的距离相对于正确正确的概率　离得近肯定大　离得远就小        prob = 1.0;        for i in range(len(landmarks)):            dist = sqrt((self.x - landmarks[i][0]) ** 2 + (self.y - landmarks[i][1]) ** 2)            prob *= self.Gaussian(dist, self.sense_noise, measurement[i])        return prob

让机器人移动一下吧

# 初始化一个机器人myrobot = robot()#设定噪声myrobot.set_noise(5.0,0.1,5.0)#设定初始位置myrobot.set(30,50,0.5)#打印位置方向print myrobot#打印与四个参照物的距离Z=myrobot.sense()print Z#机器人移动　myrobot=myrobot.move(pi/2,10.0)print myrobotZ=myrobot.sense()print Z

接下来就是粒子滤波部分，首先在运动初期给机器人初始化1000个位置粒子，这些粒子随机分布在整个地图，就上上面的第一张图片一样。然后机器人移动，粒子跟随移动，然后计算各个粒子的权重

myrobot=robot()myrobot.move(0.1,5.0)Z=myrobot.sense()N=1000#初始化一千个粒子p=[]for i in range( N):x=robot()x.set_noise(0.05,0.05,5.0)p.append(x)print len(p)p2=[]for i in range(N):p2.append(p[i].move(0.1,5.0))p=p2#计算各个粒子的权重w=[]for i in range(N):w.append(p[i].measurement_prob(Z))print w

下一篇　更新粒子滤波器　Resampling 降低粒子个数　挑选出重要的粒子　完成粒子滤波器的设计