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I am using Kalman filter for filtering noise on 2D object movement. I read a lot of examples, but no one has been explained, why noise model is distance powered by 2:

$$ s \times s = \dfrac{T^2}{2} \times \dfrac{T^2}{2} = \dfrac{T^4}{4}; $$

My process noise model is: $$ \begin{bmatrix} T^4/4 & 0 & T^3/2 & 0 \\ 0 & T^4/4 & 0 & T^3/2 \\ T^3/2 & 0 & T^2 &0 \\ 0 & T^3/2 & 0 &T^2 \end{bmatrix} $$

My state model is standard:

$$ \begin{bmatrix} x & y & \dot{x} & \dot{y} \end{bmatrix} $$

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