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Implementing the GM-PHD filter

I'm implementing the GM-PHD filter. (The what? The Gaussian mixture Probability Hypothesis Density filter, which is for tracking multiple objects.) Implementing it in python, which is nice, but I'm not completely clear if it's working as intended yet.

Here's a screenshot of progress so far. Look at the first four plots in this picture, which are:

  1. The true trajectory of two simulated objects moving in 1D over time.
  2. Observations received, with "clutter" and occasional missed detections.
  3. The "intensity" calculated by the GM-PHD filter. This is the core state variable of the filter's model.
  4. Filtered trajectories output from the PHD filter.

So what do you think? Good results?

Not sure. It's clearly got rid of lots of the clutter - good. In fact yes it's got rid of the majority of the noise, hooray hooray. But the clutter right close to the the targets is still there, seems a bit mucky, in a kind of way that suggests it's not going to be easy to clear that up.

And there's also a significant "cold start" problem - it takes up to about 20 frames for the filter to be convinced that there's anything there at all. That's no real surprise, since there's an underlying "birth" model which says that a trail could spring into being at any point, but there's no model for "pre-existing" targets. There's nothing in the PHD and GMPHD papers which I've read which even mentions this, let alone accounts for it - I'm pretty sure that we'll either need to initialise the state to account for this, or always do some kind of "warmup" before getting any results out of the filter. That's not great, especially when we might be tracking things that only have a short lifespan themselves.

One thing: this is a one-dimensional problem I'm testing it on. PHD filters are usually used for 2D or 3D problems - and maybe there needs to be enough entropy in the representation for clutter to be distinguished more clearly from signals. That would be a shame, since I'd like to use it on 1D things like spectrogram frames.

More tests needed. Any thoughts gratefully received too

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