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In the tutorials on particle filters that I have seen, it seems that the state transition function is already known. This example from Matlab, for example, states the the Plant or State Transition function is provided ahead of time.

This video, also from Matlab, talks about predicting future state to move particles forward based on the ded reckoning done by a robot. In that case, the robot knows what it's motion vector is (with process noise) at each step, but it is solving for its position and orientation. So the particle filter isn't involved in predicting this delta that results in future state.

I noticed the same thing in Matlab's description of the Unscented Kalman filter, where the state transition function is given a priori, when the filter is instantiated.

I'm looking for an explanation on how to use the particle filter (and the UKF) to estimate the parameters of the state transition function, but I'm not finding anything about that.

I suppose I can treat the parameters of the state transition function as the space in which I want to generate the particles, and transate those into the same space as the measurements. But for a simpel case of constant velocity in 3 dimensions, that would mean generating particles in 6 dimensions. Is this how it's done with a particle filter? If not, what am I missing and where can I get a simple explanation of how this would be done?

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I suppose I can treat the parameters of the state transition function as the space in which I want to generate the particles ... Is this how it's done with a particle filter?

More or less, yes. You'll find the richest sources of information on this if you look for books on system identification and on adaptive control (of which one important branch is doing system identification on-line, then adapting one's controller to match the identified system).

I can't recommend a good system identification book, but Karl Åström and Björn Wittenmark's "Adaptive Control" is a pretty good book on that topic.

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