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                                   gmphd
                   GM-PHD filter implementation in python
                              by Dan Stowell
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This is a Python implementation of the Gaussian mixture PHD filter
(probability hypothesis density filter) described in:

B. N. Vo and W. K. Ma. The gaussian mixture probability hypothesis density filter. 
   IEEE Transactions on Signal Processing, 54(11):4091--4104, 2006.
   DOI: 10.1109/TSP.2006.881190

It requires Numpy, and the demo scripts require matplotlib.
Tested with Python 2.7.

This implementation was developed as part of the following research:

D. Stowell and M. D. Plumbley, Multi-target pitch tracking of vibrato sources in
   noise using the GM-PHD filter. In: Proceedings of Proceedings of the 5th
   International Workshop on Machine Learning and Music (MML12), July 2012.
   http://c4dm.eecs.qmul.ac.uk/papers/2012/StowellPlumbley2012mml.pdf

The figures in that paper were produced by running the following commands:

* Fig 1: `python syntheticexample.py`
* Fig 2: `python syntheticroc.py`

DIFFERENCES FROM VO & MA
========================

There are some differences from the GM-PHD algorithm described in Vo & Ma's paper:

* I have not implemented "spawning" of new targets from old ones, since I don't 
  need it. It would be straightforward to add it - see the original paper.

* Weights are adjusted at the end of pruning, so that pruning doesn't affect
  the total weight allocation.

* I provide an alternative approach to state-extraction (an alternative to
  Table 3 in the original paper) which makes use of the integral to decide how
  many states to extract.


USAGE
=====

The file "syntheticexample.py" is a python script which runs the filter over a
synthetic randomly-generated scene, in which objects have 3D state and generate
chirp-like observations. I suggest you start by looking at that script. But
for a quick look at the API here's a very simple bit of python:

from gmphd import *
g = Gmphd([GmphdComponent(1, [100], [[10]])], 0.9, 0.9, [[1]], [[1]], [[1]], [[1]], 0.000002)
g.update([[30], [67.5]])
g.gmmplot1d()
g.prune()
g.gmmplot1d()


LICENCE
=======

(c) 2012 Dan Stowell and Queen Mary University of London.
All rights reserved.

    gmphd is free software: you can redistribute it and/or modify
    it under the terms of the GNU General Public License as published by
    the Free Software Foundation, either version 3 of the License, or
    (at your option) any later version.

    gmphd is distributed in the hope that it will be useful,
    but WITHOUT ANY WARRANTY; without even the implied warranty of
    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
    GNU General Public License for more details.

    You should have received a copy of the GNU General Public License
    along with gmphd.  If not, see <http://www.gnu.org/licenses/>.