IMPROVED EXTRAPOLATION TECHNIQUES IN RECURSIVE DIGITAL FILTERING - A COMPARISON OF LEAST-SQUARES AND PREDICTION

Two extrapolation techniques for recursive digital filtering are prese nted and compared with common padding methods such as linear and refle ction (reverse mirror) extrapolation. The case in which the endpoints of position data lead to peak accelerations after filtering and differ entiation is examined. The first technique, 'least squares', is based on fitting a third-degree polynomial to the final 10 data points in bo th the forward and backward directions and extending the signal by 20 data points using the polynomial coefficients. The second technique, ' prediction', is based on a linear autoregressive model with 20 coeffic ients, which is applied in both directions and the signal is extrapola ted by 20 points. The lowest cumulative error of the endpoint accelera tions (22.8 rads(-2)) represented just one-third of the error when the common padding methods were used in optimal digital filtering (69.7 r ads(-2)). It also represented approximately half the lowest cumulative error in optimal smoothing with quintic splines (48.0 rads(-2)). (C) 1998 Elsevier Science Ltd. All rights reserved.