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Added Ensemble Kalman Filter chapter.

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Had to rename and move directories around to allow the new chapter
to fit in.
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Roger Labbe 2014-12-07 19:44:42 -08:00
parent 3c6abb8899
commit a27ebac336
6 changed files with 955 additions and 22 deletions
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11_Ensemble_Kalman_Filter/Ensemble_Kalman_Filter.ipynb Normal file
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11_Designing_Nonlinear_Kalman_Filters/Designing_Nonlinear_Kalman_Filters.ipynb → 12_Designing_Nonlinear_Kalman_Filters/Designing_Nonlinear_Kalman_Filters.ipynb
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README.md
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@ -136,36 +136,41 @@ Kalman filter as covered only work for linear problems. Extended Kalman filters
* [**Chapter 10: Unscented Kalman Filters**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/10_Unscented_Kalman_Filters/Unscented_Kalman_Filter.ipynb)
Unscented Kalman filters (UKF) are a recent development in Kalman filter theory. They allow you to filter nonlinear problems without requiring a closed form solution like the Extended Kalman filter requires.
* [**Chapter 11: Designing Nonlinear Kalman Filters**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/11_Designing_Nonlinear_Kalman_Filters/Designing_Nonlinear_Kalman_Filters.ipynb)
[**Chapter 11: Ensemble Kalman Filters**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/11_Ensemble_Kalman_Filter/Ensemble_Kalman_Filter_Kalman_Filters.ipynb)
Discusses the ensemble Kalman Filter, which uses a Monte Carlo approach to deal with very large Kalman filter states in nonlinear systems.
* [**Chapter 12: Designing Nonlinear Kalman Filters**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/12_Designing_Nonlinear_Kalman_Filters/Designing_Nonlinear_Kalman_Filters.ipynb)
EKF and UKF are linear approximations of nonlinear problems. Unless programmed carefully, they are not numerically stable. We discuss some common approaches to this problem.
* [**Chapter 12: H-Infinity Filters**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/12_HInfinity_Filters/HInfinity_Filters.ipynb)
* [**Chapter 13: H-Infinity Filters**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/13_HInfinity_Filters/HInfinity_Filters.ipynb)
H-inifinity filters are a form of filter that is very robust in the presence of non-Gaussian noise. They do not perform as well as Kalman filters, but are less likely to diverge.
* [**Chapter 13: Numerical Stability**](not implemented)
Not written yet.
* [**Chapter 14: Smoothing**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/14_Smoothing/Smoothing.ipynb)
Kalman filters are recursive, and thus very suitable for real time filtering. However, they work well for post-processing data. We discuss some common approaches.
* [**Chapter XX: Numerical Stability**](not implemented)
Not written yet.
* [**Chapter 15: Particle Filters**](not implemented)
* [**Chapter XX: Particle Filters**](not implemented)
Not written yet
* [**Chapter 16: Multihypothesis Tracking**](not implemented)
* [**Chapter XX: Multihypothesis Tracking**](not implemented)
Not written yet.

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table_of_contents.ipynb
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@ -75,41 +75,40 @@
"\n",
"Unscented Kalman filters (UKF) are a recent development in Kalman filter theory. They allow you to filter nonlinear problems without requiring a closed form solution like the Extended Kalman filter requires.\n",
"\n",
"*Still early going.*\n",
"[**Chapter 11: Ensemble Kalman Filters**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/11_Ensemble_Kalman_Filter/Ensemble_Kalman_Filter_Kalman_Filters.ipynb)\n",
"\n",
"Discusses the ensemble Kalman Filter, which uses a Monte Carlo approach to deal with very large Kalman filter states in nonlinear systems.\n",
"\n",
"\n",
"[**Chapter 11: Designing Nonlinear Kalman Filters**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/11_Designing_Nonlinear_Kalman_Filters/Designing_Nonlinear_Kalman_Filters.ipynb)\n",
"[**Chapter 12: Designing Nonlinear Kalman Filters**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/12_Designing_Nonlinear_Kalman_Filters/Designing_Nonlinear_Kalman_Filters.ipynb)\n",
"\n",
"Works through some examples of the design of Kalman filters for nonlinear problems. *This is still very much a work in progress.*\n",
"\n",
"\n",
"[**Chapter 12: H-Infinity Filters**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/12_HInfinity_Filters/HInfinity_Filters.ipynb)\n",
"[**Chapter 13: H-Infinity Filters**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/13_HInfinity_Filters/HInfinity_Filters.ipynb)\n",
" \n",
"Describes the $H_\\infty$ filter. \n",
"\n",
"*I have code that implements the filter, but no supporting text yet.*\n",
"\n",
"\n",
"[**Chapter 13: Numerical Stability**](not implemented)\n",
"[**Chapter 14: Smoothing**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/14_Smoothing/Smoothing.ipynb)\n",
" \n",
"Kalman filters are recursive, and thus very suitable for real time filtering. However, they work well for post-processing data. We discuss some common approaches.\n",
" \n",
"[**Chapter XX: Numerical Stability**](not implemented)\n",
"\n",
"EKF and UKF are linear approximations of nonlinear problems. Unless programmed carefully, they are not numerically stable. We discuss some common approaches to this problem.\n",
"\n",
"*This chapter is not started. I'm likely to rearrange where this material goes - this is just a placeholder.*\n",
"\n",
"[**Chapter 14: Smoothing**](http://nbviewer.ipython.org/urls/raw.github.com/rlabbe/Kalman-and-Bayesian-Filters-in-Python/master/14_Smoothing/Smoothing.ipynb)\n",
" \n",
"Kalman filters are recursive, and thus very suitable for real time filtering. However, they work well for post-processing data. We discuss some common approaches.\n",
" \n",
" \n",
"[**Chapter 15: Particle Filters**](not implemented)\n",
"[**Chapter XX: Particle Filters**](not implemented)\n",
" \n",
"Particle filters uses a Monte Carlo technique to filter. \n",
"\n",
"*This is not implemented, and I have not decided if I want to make it part of this book or not.*\n",
" \n",
"\n",
"[**Chapter 16: Multihypothesis Tracking**](not implemented)\n",
"[**Chapter XX: Multihypothesis Tracking**](not implemented)\n",
" \n",
"*Not implemented yet.*\n",
"\n",