77ba700e39
Pretty happy with it now. Needs copy editing, and probably an easier introduction to convey the basic idea. Moved from a class based approach to a procedural approach, and I like that very much.
266 lines
7.5 KiB
Python
266 lines
7.5 KiB
Python
# -*- coding: utf-8 -*-
|
|
|
|
"""Copyright 2015 Roger R Labbe Jr.
|
|
|
|
|
|
Code supporting the book
|
|
|
|
Kalman and Bayesian Filters in Python
|
|
https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
|
|
|
|
|
|
This is licensed under an MIT license. See the LICENSE.txt file
|
|
for more information.
|
|
"""
|
|
|
|
from __future__ import (absolute_import, division, print_function,
|
|
unicode_literals)
|
|
|
|
import numpy as np
|
|
|
|
from numpy.random import randn, random, uniform
|
|
import scipy.stats
|
|
|
|
|
|
class RobotLocalizationParticleFilter(object):
|
|
|
|
def __init__(self, N, x_dim, y_dim, landmarks, measure_std_error):
|
|
self.particles = np.empty((N, 3)) # x, y, heading
|
|
self.N = N
|
|
self.x_dim = x_dim
|
|
self.y_dim = y_dim
|
|
self.landmarks = landmarks
|
|
self.R = measure_std_error
|
|
|
|
# distribute particles randomly with uniform weight
|
|
self.weights = np.empty(N)
|
|
#self.weights.fill(1./N)
|
|
'''self.particles[:, 0] = uniform(0, x_dim, size=N)
|
|
self.particles[:, 1] = uniform(0, y_dim, size=N)
|
|
self.particles[:, 2] = uniform(0, 2*np.pi, size=N)'''
|
|
|
|
|
|
def create_uniform_particles(self, x_range, y_range, hdg_range):
|
|
self.particles[:, 0] = uniform(x_range[0], x_range[1], size=N)
|
|
self.particles[:, 1] = uniform(y_range[0], y_range[1], size=N)
|
|
self.particles[:, 2] = uniform(hdg_range[0], hdg_range[1], size=N)
|
|
self.particles[:, 2] %= 2 * np.pi
|
|
|
|
def create_gaussian_particles(self, mean, var):
|
|
self.particles[:, 0] = mean[0] + randn(self.N)*var[0]
|
|
self.particles[:, 1] = mean[1] + randn(self.N)*var[1]
|
|
self.particles[:, 2] = mean[2] + randn(self.N)*var[2]
|
|
self.particles[:, 2] %= 2 * np.pi
|
|
|
|
|
|
def predict(self, u, std, dt=1.):
|
|
""" move according to control input u (heading change, velocity)
|
|
with noise std"""
|
|
|
|
self.particles[:, 2] += u[0] + randn(self.N) * std[0]
|
|
self.particles[:, 2] %= 2 * np.pi
|
|
|
|
d = u[1]*dt + randn(self.N) * std[1]
|
|
self.particles[:, 0] += np.cos(self.particles[:, 2]) * d
|
|
self.particles[:, 1] += np.sin(self.particles[:, 2]) * d
|
|
|
|
|
|
def update(self, z):
|
|
self.weights.fill(1.)
|
|
for i, landmark in enumerate(self.landmarks):
|
|
distance = np.linalg.norm(self.particles[:, 0:2] - landmark, axis=1)
|
|
self.weights *= scipy.stats.norm(distance, self.R).pdf(z[i])
|
|
#self.weights *= Gaussian(distance, self.R, z[i])
|
|
|
|
self.weights += 1.e-300
|
|
self.weights /= sum(self.weights) # normalize
|
|
|
|
|
|
def neff(self):
|
|
return 1. / np.sum(np.square(self.weights))
|
|
|
|
|
|
def resample(self):
|
|
cumulative_sum = np.cumsum(self.weights)
|
|
cumulative_sum[-1] = 1. # avoid round-off error
|
|
indexes = np.searchsorted(cumulative_sum, random(self.N))
|
|
|
|
# resample according to indexes
|
|
self.particles = self.particles[indexes]
|
|
self.weights = self.weights[indexes]
|
|
self.weights /= np.sum(self.weights) # normalize
|
|
|
|
|
|
def resample_from_index(self, indexes):
|
|
assert len(indexes) == self.N
|
|
|
|
self.particles = self.particles[indexes]
|
|
self.weights = self.weights[indexes]
|
|
self.weights /= np.sum(self.weights)
|
|
|
|
|
|
def estimate(self):
|
|
""" returns mean and variance """
|
|
pos = self.particles[:, 0:2]
|
|
mu = np.average(pos, weights=self.weights, axis=0)
|
|
var = np.average((pos - mu)**2, weights=self.weights, axis=0)
|
|
|
|
return mu, var
|
|
|
|
def mean(self):
|
|
""" returns weighted mean position"""
|
|
return np.average(self.particles[:, 0:2], weights=self.weights, axis=0)
|
|
|
|
|
|
|
|
def residual_resample(w):
|
|
|
|
N = len(w)
|
|
|
|
w_ints = np.floor(N*w).astype(int)
|
|
residual = w - w_ints
|
|
residual /= sum(residual)
|
|
|
|
indexes = np.zeros(N, 'i')
|
|
k = 0
|
|
for i in range(N):
|
|
for j in range(w_ints[i]):
|
|
indexes[k] = i
|
|
k += 1
|
|
cumsum = np.cumsum(residual)
|
|
cumsum[N-1] = 1.
|
|
for j in range(k, N):
|
|
indexes[j] = np.searchsorted(cumsum, random())
|
|
|
|
return indexes
|
|
|
|
|
|
|
|
def residual_resample2(w):
|
|
|
|
N = len(w)
|
|
|
|
w_ints =np.floor(N*w).astype(int)
|
|
|
|
R = np.sum(w_ints)
|
|
m_rdn = N - R
|
|
|
|
Ws = (N*w - w_ints)/ m_rdn
|
|
indexes = np.zeros(N, 'i')
|
|
i = 0
|
|
for j in range(N):
|
|
for k in range(w_ints[j]):
|
|
indexes[i] = j
|
|
i += 1
|
|
cumsum = np.cumsum(Ws)
|
|
cumsum[N-1] = 1 # just in case
|
|
|
|
for j in range(i, N):
|
|
indexes[j] = np.searchsorted(cumsum, random())
|
|
|
|
return indexes
|
|
|
|
|
|
|
|
def systemic_resample(w):
|
|
N = len(w)
|
|
Q = np.cumsum(w)
|
|
indexes = np.zeros(N, 'int')
|
|
t = np.linspace(0, 1-1/N, N) + random()/N
|
|
|
|
i, j = 0, 0
|
|
while i < N and j < N:
|
|
while Q[j] < t[i]:
|
|
j += 1
|
|
indexes[i] = j
|
|
i += 1
|
|
|
|
return indexes
|
|
|
|
|
|
|
|
|
|
|
|
def Gaussian(mu, sigma, x):
|
|
|
|
# calculates the probability of x for 1-dim Gaussian with mean mu and var. sigma
|
|
g = (np.exp(-((mu - x) ** 2) / (sigma ** 2) / 2.0) /
|
|
np.sqrt(2.0 * np.pi * (sigma ** 2)))
|
|
for i in range(len(g)):
|
|
g[i] = max(g[i], 1.e-229)
|
|
return g
|
|
|
|
|
|
if __name__ == '__main__':
|
|
|
|
DO_PLOT_PARTICLES = False
|
|
from numpy.random import seed
|
|
import matplotlib.pyplot as plt
|
|
|
|
#plt.figure()
|
|
|
|
seed(5)
|
|
for count in range(10):
|
|
print()
|
|
print(count)
|
|
#numpy.random.set_state(fail_state)
|
|
#if count == 12:
|
|
# #fail_state = numpy.random.get_state()
|
|
# DO_PLOT_PARTICLES = True
|
|
|
|
N = 4000
|
|
sensor_std_err = .1
|
|
landmarks = np.array([[-1, 2], [2,4], [10,6], [18,25]])
|
|
NL = len(landmarks)
|
|
|
|
#landmarks = [[-1, 2], [2,4]]
|
|
|
|
pf = RobotLocalizationParticleFilter(N, 20, 20, landmarks, sensor_std_err)
|
|
#pf.create_gaussian_particles([3, 2, 0], [5, 5, 2])
|
|
pf.create_uniform_particles((0,20), (0,20), (0, 6.28))
|
|
|
|
if DO_PLOT_PARTICLES:
|
|
plt.scatter(pf.particles[:, 0], pf.particles[:, 1], alpha=.2, color='g')
|
|
|
|
xs = []
|
|
for x in range(18):
|
|
zs = []
|
|
pos=(x+1, x+1)
|
|
|
|
for landmark in landmarks:
|
|
d = np.sqrt((landmark[0]-pos[0])**2 + (landmark[1]-pos[1])**2)
|
|
zs.append(d + randn()*sensor_std_err)
|
|
|
|
|
|
zs = np.linalg.norm(landmarks - pos, axis=1) + randn(NL)*sensor_std_err
|
|
|
|
|
|
# move diagonally forward to (x+1, x+1)
|
|
pf.predict((0.00, 1.414), (.2, .05))
|
|
|
|
pf.update(z=zs)
|
|
if x == 0:
|
|
print(max(pf.weights))
|
|
#while abs(pf.neff() -N) < .1:
|
|
# print('neffing')
|
|
# pf.create_uniform_particles((0,20), (0,20), (0, 6.28))
|
|
# pf.update(z=zs)
|
|
#print(pf.neff())
|
|
#indexes = residual_resample2(pf.weights)
|
|
indexes = systemic_resample(pf.weights)
|
|
|
|
pf.resample_from_index(indexes)
|
|
#pf.resample()
|
|
|
|
mu, var = pf.estimate()
|
|
xs.append(mu)
|
|
if DO_PLOT_PARTICLES:
|
|
plt.scatter(pf.particles[:, 0], pf.particles[:, 1], alpha=.2)
|
|
plt.scatter(pos[0], pos[1], marker='*', color='r')
|
|
plt.scatter(mu[0], mu[1], marker='s', color='r')
|
|
plt.pause(.01)
|
|
|
|
xs = np.array(xs)
|
|
plt.plot(xs[:, 0], xs[:, 1])
|
|
plt.show()
|