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# Is acceleration noise modelled differently in EKF and UKF Kalman Filters?

In a lecture on basic Kalman filter, I came across the following assumption about acceleration noise.

Every component of the noise vector $$\nu$$ is itself a product of time and acceleration values. Nothing is known about the accelerations $$a_x$$ and $$a_y$$ but each component of $$\nu$$ is assumed to have zero mean and every pair of components $$\nu_j$$, $$\nu_k$$ has some known variance $$\sigma^2_{\nu_j\nu_k}$$. As a consequence the last term in each of the four equations is set to zero (not shown here). The covariance matrix Q contains time though as in the screenshot below.

In a latter lecture on Unscented Kalman Filter the assumption was changed as below.

Here the components of noise vector $$\nu$$ do not contain any effect of time. These time-free components are assumed to have mean zero and covariance $$Q$$. As a result their effect on the mean state vector $$x$$ cannot be set to zero. Also $$Q$$ is independent of time.

Is it standard practice to make different kind of assumptions?