I am looking to figure out if a current filter algorithm I have built could be useful for some problems I am looking into at work. It isn't a Kalman filter, but is instead making estimations using a Neural Network and the latest $N$ time series measurements for some state.

I have tested it on a 2D particle tracking problem I put together with what I believe to be fairly large Gaussian noise, and it has performed decent as far as I can see. An example figure is below:

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However, I don't know if this sample problem is challenging enough to prove this algorithm works sufficiently well and I also don't have any reference algorithm results to compare against.

Is there any sample problems seen in the literature or elsewhere that I could run to test this filtering algorithm against so I have a reference of what's good or not?

  • $\begingroup$ You could compare it to a moving average filter. $\endgroup$
    – fibonatic
    May 12 '16 at 8:45
  • $\begingroup$ I think the problem is okay. I'd say compare with Kalman filter and particles filter. I also recommend the you compare the performance in case of model mismatch (e.g. you assume linear model but true system is either not linear or not always linear). $\endgroup$
    – ThP
    May 12 '16 at 9:01
  • $\begingroup$ @ThP good thoughts! Particular with model mismatch. $\endgroup$
    – spektr
    May 12 '16 at 14:05

This answer might give you one example problem and a KF implementation to solve it.

The usual problems are kinematics problems, where you want to track position, velocity, and acceleration in one or more dimensions.

There are some nonlinear problems, too, like frequency / phase tracking but that might be overkill. See how it works on linear problems first.

  • $\begingroup$ Cool, knowing what's normal is what I was looking for. I will probably end up tackling some nonlinear problems, as well. Thanks! $\endgroup$
    – spektr
    May 12 '16 at 14:06

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