856775e906
I've derived the x + Ky form for the univariate kalman filter. I completely reordered material, cutting about 10 pages (pdf) of material. I made the connection between the bayesian form and orthogonal form more explicit. Probably there are a lot of grammatical errors, but I wanted to get these checked in. I also altered the css - mainly the font.
94 lines
2.7 KiB
Python
94 lines
2.7 KiB
Python
# -*- coding: utf-8 -*-
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"""Copyright 2015 Roger R Labbe Jr.
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Code supporting the book
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Kalman and Bayesian Filters in Python
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https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python
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This is licensed under an MIT license. See the LICENSE.txt file
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for more information.
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"""
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from __future__ import (absolute_import, division, print_function,
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unicode_literals)
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import book_plots as bp
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import filterpy.stats as stats
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from math import sqrt
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import matplotlib.pyplot as plt
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import numpy as np
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from numpy.random import randn, seed
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def plot_dog_track(xs, dog, measurement_var, process_var):
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N = len(xs)
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bp.plot_track(dog)
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bp.plot_measurements(xs, label='Sensor')
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bp.set_labels('variance = {}, process variance = {}'.format(
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measurement_var, process_var), 'time', 'pos')
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plt.ylim([0, N])
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bp.show_legend()
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plt.show()
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def print_gh(predict, update, z):
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predict_template = ' {: 7.3f} {: 8.3f}'
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update_template = '{: 7.3f} {: 7.3f}\t {:.3f}'
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print(predict_template.format(predict[0], predict[1]),end='\t')
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print(update_template.format(update[0], update[1], z))
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def print_variance(positions):
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print('Variance:')
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for i in range(0, len(positions), 5):
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print('\t{:.4f} {:.4f} {:.4f} {:.4f} {:.4f}'.format(
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*[v[1] for v in positions[i:i+5]]))
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def gaussian_vs_histogram():
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seed(15)
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xs = np.arange(0, 20, 0.1)
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ys = np.array([stats.gaussian(x-10, 0, 2) for x in xs])
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bar_ys = abs(ys + randn(len(xs)) * stats.gaussian(xs-10, 0, 10)/2)
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plt.gca().bar(xs[::5]-.25, bar_ys[::5], width=0.5, color='g')
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plt.plot(xs, ys, lw=3, color='k')
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plt.xlim(5, 15)
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class DogSimulation(object):
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def __init__(self, x0=0, velocity=1,
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measurement_var=0.0,
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process_var=0.0):
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""" x0 : initial position
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velocity: (+=right, -=left)
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measurement_var: variance in measurement m^2
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process_var: variance in process (m/s)^2
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"""
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self.x = x0
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self.velocity = velocity
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self.meas_std = sqrt(measurement_var)
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self.process_std = sqrt(process_var)
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def move(self, dt=1.0):
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"""Compute new position of the dog in dt seconds."""
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dx = self.velocity + randn()*self.process_std
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self.x += dx * dt
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def sense_position(self):
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""" Returns measurement of new position in meters."""
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measurement = self.x + randn()*self.meas_std
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return measurement
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def move_and_sense(self):
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""" Move dog, and return measurement of new position in meters"""
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self.move()
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return self.sense_position()
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