filterpy 0.0.9

Kalman filtering and optimal estimation library

FilterPy - Kalman filters and other optimal and non-optimal estimation filters in Python.
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This library provides Kalman filtering and various related optimal and
non-optimal filtering software written in Python. It contains Kalman
filters, Extended Kalman filters, Unscented Kalman filters, Kalman
smoothers, Least Squares filters, fading memory filters, g-h filters,
discrete Bayes, and more.

This is code I am developing in conjunction with my book Kalman Filters
and Random Signals in Python, which you can read/download at
https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/

My aim is largely pedalogical - I opt for clear code that matches the
equations in the relevant texts on a 1-to-1 basis, even when that has a
performance cost. There are places where this tradeoff is unclear - for
example, I find it somewhat clearer to write a small set of equations
using linear algebra, but numpy's overhead on small matrices makes it
run slower than writing each equation out by hand, and books such as
Zarchan present the written out form, not the linear algebra form. It is
hard for me to choose which presentation is 'clearer' - it depends on
the audience. In that case I usually opt for the faster implementation.

I use NumPy and SciPy for all of the computations. I have experimented
with Numba, Continuum Analytics' just in time compiler, and it yields
impressive speed ups with minimal costs, but I am not convinced that I
want to add that requirement to my project. It is still on my list of
things to figure out, however.

As it evolves from alpha status I am adding documentation, tests, and
examples, but at the moment the my book linked above serves as the best
documentation. I am developing both in parallel, so one or the other has
to suffer during the development phase. Reach out to me if you have
questions or needs and I will either answer directly or shift my
development to address your problem (assuming your question is a planned
part of this library.

Sphinx generated documentation lives at http://filterpy.readthedocs.org/.
Generation is triggered by git when I do a check in, so this will always
be bleeding edge development version - it will often be ahead of the
released version.

You can also find the documentation at https://pythonhosted.org/filterpy/
but that currently requires me to manually upload the documentation, so
it is possible that it will be out of date. It will never be of a development
version, however.

Installation
------------

::
pip install filterpy

If you prefer to download the source yourself

::
cd <directory you want to install to>
git clone http://github.com/rlabbe/filterpy
python setup.py install

And, if you want to install from the bleeding edge git version

::

pip install git+https://github.com/rlabbe/filterpy.git

Note: at the moment github will probably be much more 'bleeding edge' than
the pip install. I need to formalize this into a dev and stable path, but
have yet to do so.


Basic use
---------

First, import the filters and helper functions.

::
import numpy as np
from filterpy.kalman import KalmanFilter
from filterpy.common import Q_discrete_white_noise

Now, create the filter

::
my_filter = KalmanFilter(dim_x=2, dim_z=1)


Initialize the filter's matrices.

::
f.x = np.array([[2.],
[0.]]) # initial state (location and velocity)

f.F = np.array([[1.,1.],
[0.,1.]]) # state transition matrix

f.H = np.array([[1.,0.]]) # Measurement function
f.P *= 1000. # covariance matrix
f.R = 5 # state uncertainty
f.Q = Q_discrete_white_noise(2, dt, .1) # process uncertainty


Finally, run the filter.

::
while True:
my_filter.predict()
my_filter.update(get_some_measurement())

# do something with the output
x = my_filter.x
do_something_amazing(x)

Sorry, that is the extent of the documentation here. However, the library
is broken up into subdirectories: gh, kalman, memory, leastsq, and so on.
Each subdirectory contains python files relating to that form of filter.
The functions and methods contain pretty good docstrings on use.

My book https://github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/
uses this library, and is the place to go if you are trying to learn
about Kalman filtering and/or this library. These two are not exactly in
sync - my normal development cycle is to add files here, test them, figure
out how to present them pedalogically, then write the appropriate section
or chapterin the book. So there is code here that is not discussed
yet in the book.


Requirements
------------

This library uses NumPy, SciPy, Matplotlib, and Python.

I haven't extensively tested backwards compatibility - I use the
Anaconda distribution, and so I am on Python 3.4 and 2.7.5, along with
whatever version of numpy, scipy, and matplotlib they provide. But I am
using pretty basic Python - numpy.array, maybe a list comprehension in
my tests.

I import from **__future__** to ensure the code works in Python 2 and 3.

The matplotlib library is required because, *for now*, 'tests' are very
visual. Meaning I generate some data, plot the data against the filtered
results, and eyeball it. That is great for my personal development, and
terrible as a foundation for regression testing. If you don't have
matplotlib installed you won't be able to run the tests, but I'm not
sure the tests will have a lot of meaning to you anyway.

There is one import from the code from my book to plot ellipses. That
dependency needs to be removed. This only affects the tests.

Testing
-------

All tests are written to work with py.test. Just type *py.text* at the
command line.

As explained above, the tests are not robust. I'm still at the stage
where visual plots are the best way to see how things are working.
Apologies, but I think it is a sound choice for development. It is easy
for a filter to perform within theoretical limits (which we can write a
non-visual test for) yet be 'off' in some way. The code itself contains
tests in the form of asserts and properties that ensure that arrays are
of the proper dimension, etc.

References
----------

I use three main texts as my refererence, though I do own the majority
of the Kalman filtering literature. First is Paul Zarchan's
'Fundamentals of Kalman Filtering: A Practical Approach'. I think it by
far the best Kalman filtering book out there if you are interested in
practical applications more than writing a thesis. The second book I use
is Eli Brookner's 'Tracking and Kalman Filtering Made Easy'. This is an
astonishingly good book; its first chapter is actually readable by the
layperson! Brookner starts from the g-h filter, and shows how all other
filters - the Kalman filter, least squares, fading memory, etc., all
derive from the g-h filter. It greatly simplifies many aspects of
analysis and/or intuitive understanding of your problem. In contrast,
Zarchan starts from least squares, and then moves on to Kalman
filtering. I find that he downplays the predict-update aspect of the
algorithms, but he has a wealth of worked examples and comparisons
between different methods. I think both viewpoints are needed, and so I
can't imagine discarding one book. Brookner also focuses on issues that
are ignored in other books - track initialization, detecting and
discarding noise, tracking multiple objects, an so on.

I said three books. I also like and use Bar-Shalom's Estimation with
Applications to Tracking and Navigation. Much more mathmatical than the
previous two books, I would not recommend it as a first text unless you
already have a background in control theory or optimal estimation. Once
you have that experience, this book is a gem. Every sentence is crystal
clear, his language is precise, but each abstract mathematical statement
is followed with something like "and this means...".

License
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Copyright (c) 2014 Roger R Labbe Jr

Permission is hereby granted, free of charge, to any person obtaining a
copy of this software and associated documentation files (the
"Software"), to deal in the Software without restriction, including
without limitation the rights to use, copy, modify, merge, publish,
distribute, sublicense, and/or sell copies of the Software, and to
permit persons to whom the Software is furnished to do so, subject to
the following conditions:

The above copyright notice and this permission notice shall be included
in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.
IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY
CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,
TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE
SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.