The model should be responsible for changes to the state and calculating the probability of state changes. This includes things like the constant velocity model knowing that it should set accelerations to zero.
When calculating the probability of the state change, be careful of which elements have been set deterministically. Going from CA to CV, the acceleration is set to zero and there is no sampling involved, so the probability of the change in acceleration shouldn't be considered. Similarly, when going from CV to CA, acceleration is included. The mean acceleration is set by the parameters of the model, so it is just the noise of these now non-zero values, whose probability we wish to calculate. This could mean that when calculating x_k-x_k-1, you augment x_k-1 with the mean acceleration values to make this calculation valid.
The model should be responsible for changes to the state and calculating the probability of state changes. This includes things like the constant velocity model knowing that it should set accelerations to zero.
When calculating the probability of the state change, be careful of which elements have been set deterministically. Going from CA to CV, the acceleration is set to zero and there is no sampling involved, so the probability of the change in acceleration shouldn't be considered. Similarly, when going from CV to CA, acceleration is included. The mean acceleration is set by the parameters of the model, so it is just the noise of these now non-zero values, whose probability we wish to calculate. This could mean that when calculating x_k-x_k-1, you augment x_k-1 with the mean acceleration values to make this calculation valid.