What learning algorithm is appropriate for predicting one time-series from another?
If I understand your question right, you want to model two stochastic processes, where the 'student' process is driven by the 'teacher' process.

A hidden Markov model can represent such a relationship, but is restricted to a discrete state space. This means that you can only model a finite set of points on your map rather than continuous (x/y) coordinates. A Linear Dynamical System might suit better to your problem.

You could also use recurrent neural networks to model your system.