Kalman filtering and optimal estimation library
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but that currently requires me to manually upload the documentation, so it is possible that it will be out of date.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.
The most general installation is just to use pip, which should come with any modern Python distribution.
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
If you use Anaconda, you can install from the conda-forge channel. You will need to add the conda-forge channel if you haven’t already done so:
and then install with:
And, if you want to install from the bleeding edge git version
pip install git+https://github.com/rlabbe/filterpy.git
Note: I make no guarantees that everything works if you install from here. I’m the only developer, and so I don’t worry about dev/release branches and the like. Unless I fix a bug for you and tell you to get this version because I haven’t made a new release yet, I strongly advise not installing from git.
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.
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.
All tests are written to work with py.test. Just type py.test 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.
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…”.
Move to minor version numbering doesn’t mean anything other than it got absurd to be using 3 digits for version numbers. We are far past alpha here. I will be moving to 1.0.0 soon, probably after I finish the book and flesh out a few points.
Color on this: There are various recusive equations for the fixed point filter that I have found in various book - Simon, Crassidis, and Grewal. None seem to work very well. I have code that works pretty good when R is < 0.5 or so, but then the filter diverges when R is larger. I’m not seeing much in the literature that explains this very well, nor any evidence of this smoother actually being used in practice. I will give this a bit more effort, and if I can’t get something reliable I’ll put it in a branch and remove from trunk. Someone will have to tackle this on a rainy day.
The MIT License (MIT)
Copyright (c) 2015 Roger R. Labbe Jr
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