$H_\infty$ filter¶
In [1]:
#format the book
%matplotlib inline
from __future__ import division, print_function
import book_format
book_format.load_style()
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I am still mulling over how to write this chapter. In the meantime, Dan Simon has an accessible introduction here:
http://academic.csuohio.edu/simond/courses/eec641/hinfinity.pdf
In one sentence the $H_\infty$ (H infinity) filter is like a Kalman filter, but it is robust in the face of non-Gaussian, non-predictable inputs.
My FilterPy library contains an H-Infinity filter. I've pasted some test code below which implements the filter designed by Simon in the article above. Hope it helps.
In [2]:
from __future__ import (absolute_import, division, print_function,
unicode_literals)
from numpy import array
import matplotlib.pyplot as plt
from filterpy.hinfinity import HInfinityFilter
dt = 0.1
f = HInfinityFilter(2, 1, dim_u=1, gamma=.01)
f.F = array([[1., dt],
[0., 1.]])
f.H = array([[0., 1.]])
f.G = array([[dt**2 / 2, dt]]).T
f.P = 0.01
f.W = array([[0.0003, 0.005],
[0.0050, 0.100]])/ 1000 #process noise
f.V = 0.01
f.Q = 0.01
u = 1. #acceleration of 1 f/sec**2
xs = []
vs = []
for i in range(1,40):
f.update (5)
#print(f.x.T)
xs.append(f.x[0,0])
vs.append(f.x[1,0])
f.predict(u=u)
plt.subplot(211)
plt.plot(xs)
plt.title('position')
plt.subplot(212)
plt.plot(vs)
plt.title('velocity')
plt.show()
