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I have a very basic question about particle filters and their applications. I know Kalman filters and I have implemented some of them. Taking a linear and unimodal Kalman filter, then I need a mathematical model of my dynamic system, like:

$\dot{\bf{x}} = \bf{f}(\bf{x}, \bf{u})$

Now... as far as I understood, this should be the same even for a particle filter.

You need a dynamic model (like in this question, where they speak about motion model)

That's ok.

What I don't understand is: how can I implement a particle filter without a dynamic model? Let's say I have a GNSS receiver. Only that sensor. Nothing else. If I need a motion model, then I need to extract the motion model from the same sensor (in this case the GNSS receiver) that I use to measure the state of the system. This is to me a vicious cirle.

In case I would like to implement a particle filter to increase accuracy of GNSS using a particle filter, than I would have many readings (the GNSS position in coordinates). If I use the velocity coming from the GNSS readings to update my motion or dynamic model, than I'm going to move my model exactly on the same quantity that I'm going to measure few milliseconds later...

Or am I wrong?

I hope the question is clear.

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