You asked about choosing a set of four parameters for processing some accelerometer data, with the goal of minimizing disagreement between the accelerometer measurements prediction of location and what a "high precision camera" records as location (or "displacement" to use your term).
You have twelve sessions of experimental data, from which you hope to extract the best parameter set with respect to a least squares error criterion.
The computation applied to your accelerometer data is described at a moderately high level: essentially that the acceleration is integrated twice to provide an offset position. Both integration steps involve a threshold parameter that is continuous (a floating point number) and a moving average window parameter that is discrete (a positive integer number of steps).
What could the Math.SE Community do to help you? We could encourage clarification of your goals and your approach. At this time there is no explicit model to which mathematical reasoning can be applied, though since you have coded something up and gotten an initial set of parameters that gave an acceptable result for at least one session, there surely is a model implicit in your thinking.
What could the StackOverflow Community do to help you? Putting on our programming hats, there could be suggestions based on the SciPy platform you mentioned, e.g. about constructing a "testing harness" to extensively check various parameter sets against your twelve recorded sessions. Before asking a new Question there, search for earlier posts that seem relevant.
How about other SE Communities? The one that closely matches your mix of math modelling and coding is Computational Science. You might have a look at the existing Questions there tagged SciPy.
Given your participation in StackOverflow, I don't expect you would literally crosspost there the Question you asked on Math.SE. As Gerry Myerson suggested, links between posts could be helpful.
