[jvanderbot]

Forgive me, I'm thoroughly confused by that dichotomy. How are they different? Approaching from bayes rule or a "maximum likelihood" approach produces the same results.

The problems of the filter are present in both.

[hgomersall]

The result is identical, the understanding is different. I would suggest that the Bayesian perspective leads to insights like the UKF [1] which IME is all round much better than the apparently better known EKF for approximating non linear systems.

[1] That is, it is generally easier to approximate a distribution than a non linear function.

[eutectic]

Well, the derivations are different, and your comment seemed to imply that the maximum likelihood perspective was easier to understand.