Ok so based on the vast amount of responses - I realize i did a great job on laying out the problem.

The Main question is : How do you fit data to SDEs with Mathematica which have a drift, and a diffusion coefficient that is not constant?

Here is the model again - and hopefully a bit clearer.

And here is a sample data - acceleration in the Y-directions:

{0.59, 0.311, 0.094, -0.063, -0.307, -0.552, -0.867, -1.144, -1.405, -1.58, -1.742, -1.753, -1.541, -1.1, -0.551, -0.012, 0.343, 0.357, 0.361, 0.283, 0.084, -0.743, 0.45, -0.482, 0.042, -0.024}

I will also like to post the link from a presentation given by Oleksandr Pavlyk. At 15:46 he presents a similar model, however he does not have much time there to go in depth. Awesome presentation though. I wish we could see more of that.

Stochastic Calculus and Applications

So, any help would be greatly appreciated. Let's make this an open conversation and if someone wants to bring his own example - that would also be very helpful.

Cheers!