Representing continuous probability distributions

Question

I have a problem involving a collection of continuous probability distribution functions, most of which are determined empirically (e.g. departure times, transit times). What I

Answer 1

Autonomous mobile robotics deals with similar issue in localization and navigation, in particular the Markov localization and Kalman filter (sensor fusion). See An experimental comparison of localization methods continued for example.

Another approach you could borrow from mobile robots is path planning using potential fields.