I am stuck at modeling a system model, i.e. getting my state vector and input vector for navigating just using navaid and ins (tactical). My guess is that position is my only state vector and INS output (acceleration or velocity) is input vector. What is state vector and what is input vector in my case? As I just need 2 position which sensor must be used for update and which must be used for predict. Should I use 1d 2 kalman implementation for lat and lon or no etc?

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In general, for position-related Kalman filters, you want your state vector to contain $x$, and $\dot{x}$ (location and velocity) components. See, for example, the Wikipedia page or this question and answer here.

If you have a measure of velocity, then it can certainly also be an input to the Kalman filter.

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