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Estimating velocity from known position and acceleration

I am stuck at modeling a system model, i.e. getting my state vector and input vector. My guess is that position and velocity are state vector and acceleration is input vector. My 2nd guess is that all three quantities are in state vector and none in input vector.

So... what is state vector and what is input vector in my case?

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I get measurements from position sensor and acceleration sensor. Everything is happening in 1D, for example on a straight line. I want to merge these readings (and remove the noise) to get an estimation of velocity for each timestep.

These equations describe the system; I am not sure if they're modeled right though. If I understand correctly it's safe to predict that acceleration is constant (even though in reality it changes) - because process covariance matrix fixes this assumption (right?).

I have also some sample data to work with (input values aren't noised here for simplicity):

 time    pos     acc      what I should get as output (velocity)
[0.0s]  0.000, -0.000  | 18.850
[0.1s]  1.885, -0.113  | 18.850
[0.2s]  3.768, -0.227  | 18.839
[0.3s]  5.650, -0.340  | 18.816
[0.4s]  7.528, -0.452  | 18.782
[0.5s]  9.401, -0.565  | 18.737