Appendix-D-HInfinity-Filters.ipynb

Kernel: Python 3

Table of Contents

H Infinity filter

%matplotlib inline

#format the book
import book_format
book_format.set_style()

I am still mulling over how to write this chapter. In the meantime, Professor Dan Simon at Cleveland State University 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.

import numpy as np
import matplotlib.pyplot as plt

from filterpy.hinfinity import HInfinityFilter

dt = 0.1
f = HInfinityFilter(2, 1, dim_u=1, gamma=.01)

f.F = np.array([[1., dt],
                [0., 1.]])

f.H = np.array([[0., 1.]])
f.G = np.array([[dt**2 / 2, dt]]).T

f.P = 0.01
f.W = np.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');