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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/>.