Kalman filter: motion model

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Hi all,

I'm using a Kalman filter to estimate the position of an object ( (x,y) coordinates ). Regarding the state equations, I've seen the following approaches in different examples:

1) Auto regressive model:

x[t+1] = x[t] + V[t] + noise

where V[t] = (x[t] - x[t-1])

Thus: x[t+1] = x[t] + (x[t] - x[t-1]) + noise = 2x[t] - x[t-1] + noise

In this case, both x[t] and x[t-1] are kept in the state vector

2) Velocity estimation:

x[t+1] = x[t] + V[t] + noise

where V[t] = V[t-1] + noise

In this case, only x[t] and V[t] are kept in the state vector.

So my question is: is there really a difference between both approaches? Is any of them better than the other in certain situations?

Thanks a lot!

Kind regards, Arno