extracting information in presence of noise Assume I have a vector of displacements, when I calculate the derivative I obtain velocity. The problem is, there are so many noisy points and I am looking for one number as a velocity. What do you think is the best technique to obtain the velocity ? I am taking derivative and then take the mean, this gives me good result when there is not much noise however this technique is not really robust to noise also taking the median is not giving good result. Can anyone suggest a better technique to handle this problem?
Usually removing noise is a process depends on the type of noise. 
Noises can be high or low frequency , you are using low frequency filters ( average and median) . 
1. You did not describe the source of noise, we can not tell if it is a high frequency or low frequency . 
2. Try to use a higher order low pass filter