I've worked on mode of transportation detection using smartphone accelerometers. The main result I've found is that almost any classifier will do; the key problem is then the set of features. (This is no different from many other machine learning problems.) My feature set ended up containing time-domain and frequency-domain values, both taken from time-series sliding-window segmentation.
Another problem is that the accelerometer can be placed anywhere. On the body, it can be anywhere and in any orientation. If the user is driving, is the phone in a pocket, in a bag, on a car seat, attached to a suction-cup window mount, etc.?
If you want to avoid these problems, use GPS instead of the accelerometer. You can make relatively accurate classifications with that sensor, but the cost is the battery usage.