I'm developing (actually adopting existing solution) a Kalman filter to model motion of a vehicle (UAV or automobile). The state vector will include position, velocity, and, possibly, acceleration.
In that existing solution acceleration is included; state transition is something like $(\vec x,\vec v, \vec a) \to (\vec x+\Delta t\cdot \vec v,\vec v+\Delta t \cdot \vec a,\vec a+\xi)$, where $\xi$ is a process noise.
I think that such model is good when acceleration is changing somewhat smoothly, but when there are bursts of acceleration, removing $\vec a$ from state and adding noise to velocity should be more suitable: $(\vec x,\vec v)\to(\vec x+\Delta t\cdot\vec v,\vec v+\xi)$.
Tests show that there is almost no difference in precision of solution between both models (turns out that the observation data provides more effect on position than the velocity).
So the question is, when should I include acceleration in state, and when should not? What things should I consider?