Kalman filter after lowpass filter: bad idea? I am new to Kalman filter and am enjoying playing with it. However, I generated some random velocities and acceleration and Kalman filter (with the covariance matrices I have chosen) is comparable with lowpass filtering. 

So I thought maybe both lowpass filtering and Kalman filter could be combined, however this completely ruins the assumption of white Gaussian noise. My numerical experiments indicates that Kalman filter does not bring anything interesting after LP filtering for the cases I tried.

What are good preprocessing practices, if any, before applying a Kalman filter?
The Kalman filter is the optimal filter under various assumptions. You need to check whether those assumptions hold in your case:

a) the model perfectly matches the real system,
b) the entering noise is white and Gaussian and
c) the covariances of the noise are exactly known.

Without further detail I can't say whether your statement My experiments indicates that Kalman filter does not bring anything interesting after LP filtering. is true or not.
Use Occam's Razor: the simplest approach that works is the best. That is, it may well be that for your situation a low pass filter is all you need.