Cool, there are people out there struggling with the same problem so it is worth to spent some time 🙂
I agree with westsider’s statement as I spent a few weeks of experimenting with different approaches and ended up with poor results. I am sure that there won’t be an acceptable solution for either larger distances or slow motions lasting for more than 1 or 2 seconds. If you can live with some restrictions like small distances (< 10 cm) and a given minimum velocity for your motions, then I believe there might be the chance to find a solution – no guarantee at all. If so, it will take you a pretty hard time of research and a lot of frustration, but if you get it, it will be very very cool 🙂 Maybe you find these hints useful:
First of all to make things easy just look at one axis e.g x but consider both left (-x) and right (+x) to have a representable situation.
Yes you are right, you have to integrate twice to get the position as function of time. And for further processing you should store the first integration’s result (== velocity), because you will need it in a later stage for optimisation. Do it very careful because every tiny bug will lead to huge errors after short period of time.
Always bear in mind that even a very small error (e.g. <0.1%) will grow rapidly after doing integration twice. Situation will become even worse after one second if you configure accelerometer with let’s say 50 Hz, i.e. 50 ticks are processed and the tiny neglectable error will outrun the “true” value. I would strongly recommend to not rely on trapezoidal rule but to use at least Simpson or a higher degree Newton-Cotes formula.
If you managed this, you will have to keep an eye on setting up the right low pass filtering. I cannot give a general value but as a rule of thumb experimenting with filtering factors between 0.2 and 0.8 will be a good starting point. The right value depends on the business case you need, for instance what kind of game, how fast to react on events, …
Now you will have a solution which is working pretty good under certain circumstances and within a short period of time. But than after a few seconds you will run into trouble because your object is drifting away. Now you will enter the difficult part of the solution which I failed to handle eventually within the given time scope 🙁
One promising approach is to introduce something I call “synthectic forces” or “virtual forces”. This is some strategy to react on several bad situations triggering the object to drift away although the device remains fixed (? no native speaker, I mean without moving) in your hands. The most troubling one is a velocity greater than 0 without any acceleration. This is an unavoidable result of error propagation and can be handled by slowing down artificially that means introducing a virtual deceleration even if there is no real counterpart. A very simplified example:
if (vX > 0 && lastAccelerationXTimeStamp > 0.3sec) {
vX *= 0.9;
}
`
You will need a combination of such conditions to tame the beast. A lot of try and error is required to get a feeling for the right way to go and this will be the hard part of the problem.
If you ever managed to crack the code, pleeeease let me know, I am very curious to see if it is possible in general or not 🙂
Cheers Kay