I'm running a CMDeviceMotion processing queue on iPhone 4, which gives me user-induced acceleration, along with the rotation rates. I can filter this data myself.
What I'm trying to understand is how to convert these discrete samples of acceleration, device attitude and rotational rate into a 3 dimensional displacement. This is possible with classical mechanics for straight lines, but I"m thinking of more advanced calculations - for example curves. This can be handled with GPS, but I'm looking for a much better resolution - lets say within 10 feet. GPS under clear sky has an average accuracy of about 30 feet.
Is there some sort of a physics engine or physics processor that can take a set of device motion or acceleration/turn rate events and give me a distance of how far the phone is from the original location?
I know that there are various pedometer and bike GPS trackers for iPhone. Are they based on GPS or do they actually do the acceleration integration like I'm describing?
Unfortunately, the acceleration integration you are describing won't work in itself.
However, you may improve the accuracy by fusing with the GPS signal and/or make domain specific assumptions. For details, see the above link.