daviddoji/Kalman-and-Bayesian-Filters-in-Python
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Major work on the UKF chapter.

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Text is still not organized well, but I got the unscented transform fully documented. Probably needs more citations to the original article, and some revisions - I think there is some duplication of info.
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Roger Labbe 2014-07-20 00:39:27 -07:00
parent 23e283e7fe
commit e5f968a2e3
2 changed files with 261 additions and 193 deletions
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421
Unscented_Kalman_Filter.ipynb
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33
ukf_internal.py
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@ -8,6 +8,7 @@ import matplotlib.pyplot as plt
from matplotlib.patches import Ellipse,Arrow
import stats
import numpy as np
import math
def arrow(x1,y1,x2,y2):
@ -65,7 +66,37 @@ def show_sigma_selections():
def show_sigmas_for_2_kappas():
# generate the Gaussian data
xs = np.arange(-4, 4, 0.1)
mean = 0
sigma = 1.5
ys = [stats.gaussian(x, mean, sigma*sigma) for x in xs]
def sigma_points(mean, sigma, kappa):
sigma1 = mean + math.sqrt((1+kappa)*sigma)
sigma2 = mean - math.sqrt((1+kappa)*sigma)
return mean, sigma1, sigma2
#generate our samples
kappa = 2
x0,x1,x2 = sigma_points(mean, sigma, kappa)
samples = [x0,x1,x2]
for x in samples:
p1 = plt.scatter([x], [stats.gaussian(x, mean, sigma*sigma)], s=80, color='k')
kappa = -.5
x0,x1,x2 = sigma_points(mean, sigma, kappa)
samples = [x0,x1,x2]
for x in samples:
p2 = plt.scatter([x], [stats.gaussian(x, mean, sigma*sigma)], s=80, color='b')
plt.legend([p1,p2], ['$kappa$=2', '$kappa$=-0.5'])
plt.plot(xs, ys)
plt.show()