Here is a sample using deadline variables.
On the subject of the analysis of movement, ancient astronomers would accumulate lists of measurements, that could be used discover patterns of movement among heavenly bodies.
AI2 has some easy graph components that could be used to display measurements across time, if you feed them the appropriate lists of readings. Maybe you could spot patterns in the graphs that would give you clues?
Your problem reminds me of the problem of how to deduce your present location while locked into the trunk of a moving car.