Here are two references for linking GPS data to street centerlines:
Schussler, N. & Axhausen, K. (2009a), ‘Map-matching of GPS traces on
high-resolution navigation networks using the multiple hypothesis
technique’, Working paper 568. IVT, ETH Zu ̈rich, Zu ̈rich.
Schussler, N. & Axhausen, K. (2009b), ‘Processing raw data from global
positioning systems without additional information’, Transportation
Research Record: Journal of the Transportation Research Board 2105,
Reference link (for those with access).
I know SF City implemented one of these algorithms to process gps tracks from a smart phone app they are using to track cyclists (cycletracks); and they released all of the code under an open-source license (because they are wonderful!). I think their issue was mainly to do with urban-canyon inaccuracies; I'm not sure if they had a problem with acceleration also.