"all models are wrong, but some are useful" - Box.
I think the Bayesian approach is a good place to start, and provides a coherent way to think about things.
Pragmatically, one might end up needing to introduce a few approximations into the model, to make it computationally tractable, for example, but it is good to be able to view this in the context of what the gold-plated theoretical modelling approach would be.
Instead of doing something ad-hoc that appears to work, say.
You can also augment the state to take this into account.
I have a model that says my system does F with Q amount of uncertainty, and my measurements are Z with R uncertainty. But I have to give precise numbers for R, when it is just an imprecise model or SWAG. I can add to my state a parameter for how precise R is, and let the filter estimate it over time. Not always, and it is noisy, but it can be done.
There are other approaches - use a filter bank, each with a different set of assumptions. Run 'em all, and either pick one or blend them, depending on your scenario. 'Depending' being the topic of many a PhD thesis, but again, very doable in practice for many problems.
I think the Bayesian approach is a good place to start, and provides a coherent way to think about things.
Pragmatically, one might end up needing to introduce a few approximations into the model, to make it computationally tractable, for example, but it is good to be able to view this in the context of what the gold-plated theoretical modelling approach would be.
Instead of doing something ad-hoc that appears to work, say.