This paper discusses the application of Lagrange interpolation and cubic spline interpolation to predict acceleration/ velocity and to adapt better window lengths for any range of target acceleration. The estimated velocity/ acceleration is then smoothed using Kalman and adaptive Kalman filters. Simulation results show that in a 'high-level noise' scenario, the interpolated adaptive filter gives a more accurate estimation than the existing method of using a rectangular window function. Track initialization error minimized with spline interpolation was comparable to that minimized with Lagrange interpolation. © 2013 Walter de Gruyter GmbH, Berlin/Boston.