In order to obtain target velocity in radar systems we use Doppler filters. It is usual in such applications to use window functions with prespecified shape and length. For a good target velocity estimation, it is necessary to apply adaptive length window functions. The optimum length is primarily influenced by the target dynamics, expressed in its acceleration, and the signal to noise ratio of the obtained echo. In this paper, we have proposed a very simple and accurate procedure for an estimation of the target acceleration. We assumed signal to noise ratio to be constant. The efficiency of the procedure has been demonstrated through computer simulations.