Control theory person here. In the linear case resulting "system" is a linear time-invariant system. That's the standard state space system that you can convert

Control theory person here. In the linear case resulting "system" is a linear time-invariant system. That's the standard state space system that you can convert and obtain a transfer function. But from a higher order transfer function, through partial fraction decomposition you can always write it as a sum of simple lead-lag and second order filters. So the distinction in the post and also discussion here is kind of orthogonal semantics. What NASA did was to "extend" the kalman filter for nonlinear cases (actually their extension was also not so big but if it works it works). In short every linear system can be written as a sum of trivial components such as low pass/notches/anti-notches etc. This is in fact how you implement higher order controllers real time. The MIMO distinction is also not super important. Since you can also have MIMO low pass filters. The real difficulty is obtaining the coefficients of these filters and hopefully find the best ones. That's where you start getting into the optimality and the real contribution of these tools. But as a side-effect you must assume that the noise is Gaussian otherwise you lose much of the niceties of the theoretical guarantees. This is basically the biggest control theoretical disadvantage of kalman filters and the reason why other domains keep rediscovering it while in control it is "kinda, sorta" falling out of grace.