I'd like to know if there is any implemented python library for GPS trajectory pre-processing such as compression, smoothing, filtering, etc.
Expanding on my comment, a Kalman filter is the usual choice for estimating position and velocity from noisy sensor readings.
Here's what Wikipedia has to say on the topic (emphasis mine:)

The Kalman filter is an algorithm, commonly used since the 1960s for
  improving vehicle navigation (among other applications, although
  aerospace is typical), that yields an optimized estimate of the
  system's state (e.g. position and velocity). The algorithm works
  recursively in real time on streams of noisy input observation data
  (typically, sensor measurements) and filters out errors using a
  least-squares curve-fit optimized with a mathematical prediction of
  the future state generated through a modeling of the system's physical
  characteristics.

The Kalman filter is the basic version; there's also the extended Kalman filter and unscented Kalman filter (though my control systems lecturer never got around to telling us what those were actually used for.)
@stark has provided a link to an implementation of the Kalman filter in Python (not sure of the quality.) You may be able to find others, or roll your own with scipy.
Python library for GPS trajectory pre-processing?