Problems and solutions

I had a very productive session with my advisor yesterday. I feel a little more confidence about being able to obtain a solution for the problem I am working on, but I still think I am a long way off. I will try to create and parallel analogy to the problem that I am working on.

Suppose you observe a ball flying through the air and it could have only came from two places; and the first place would have made the ball fly in the air at a different speed than the second place. There is also a certain probability that it came from the first place. Now if you observed many such balls, The E.M. algorithm can be used to estimates the probability of the balls coming from the first place, the speed if it came from the first place, and the speed if it came from the second place. This is a well known problem with well known solutions.

My issues is suppose that the speeds change every day and you observe one ball every days for several days. Can you still estimate the speeds and the probability? I am not so sure because in the earlier problem there were just two speeds to estimate; in this problem you would have to estimate the speeds at each day.

This is just the 1st issue in my problems, it actually becomes harder because supposed you dont' actually observes the balls, you just observed the winds changes that might occur if a ball is flying in the air. Given only the wind measure can you estimate, the speed, probabilities, and where the balls are in the air? Yep, I have alot on my plate.