Q:

GPS data comparison after smoothing

I'm trying to compare multiple algorithms that are used to smooth GPS data. I'm wondering what should be the standard way to compare the results to see which one provides better smoothing.
I was thinking on a machine learning approach. To crate a car model based on a classifier and check on which tracks provides better behaviour.
For the guys who have more experience on this stuff, is this a good approach? Are there other ways to do this?

A:

Generally, there is no universally valid way for comparing two datasets, since it completely depends on the applied/required quality criterion.
For your appoach

I was thinking on a machine learning approach. To crate a car model
  based on a classifier and check on which tracks provides better
  behaviour.

this means that you will need to define your term "better behavior" mathematically. 
One possible quality criterion for your application is as follows (it consists of two parts that express opposing quality aspects):
First part (deviation from raw data): Compute the RMSE (root mean squared error) between the smoothed data and the raw data. This gives you a measure for the deviation of your smoothed track from the given raw coordinates. This means, that the error (RMSE) increases, if you are smoothing more. And it decreases if you are smoothing less.
Second part (track smoothness): Compute the mean absolute lateral acceleration that the car will experience along the track (second deviation). This will decrease if you are smoothing more, and it will increase if you are smoothing less. I.e., it behaves in contrary to the RMSE.
Result evaluation: 
(1) Find a sequence of your data where you know that the underlying GPS track is a straight line or where the tracked object is not moving. Note, that for those tracks, the (lateral) acceleration is zero by definition(!). 
For these, compute RMSE and mean absolute lateral acceleration. 
The RMSE of appoaches that have (almost) zero acceleration results from measurement inaccuracies!
(2) Plot the results in a coordinate system with the RMSE on the x axis and the mean acceleration on the y axis. 
(3) Pick all approaches that have an RMSE similar to what you found in step (1).
(4) From those approaches, pick the one(s) with the smallest acceleration. Those give you the smoothest track with an error explained through measurement inaccuracies!
(5) You're done :)

