Yes, you can describe tracking and Kalman filter using bayesian statistics. Although, my prof said that originally it was not developed that way, but it is easier to describe it using normal distributions as priors and likelihoods of the position of the object being tracked.
And I guess thanks to those crazy generalizing mathematicians, nowadays you can use something like Kalman filtering with distribution other than normal ones.
Check out particle filters if you want crazy mathematicians. Fun stuff.
In any case, many years ago, I worked on a radar system for a fighter plane. Its air-to-ground radar (at the very least; this was the part I was involved in) did indeed use a Kalman filter.