Improved extrapolation techniques in recursive digital filtering: a comparison of least squares and prediction

Two extrapolation techniques for recursive digital filtering are presented and compared with common padding methods such as linear and reflection (reverse mirror) extrapolation. The case in which the endpoints of position data lead to peak accelerations after filtering and differentiation is examined. The first technique, ‘least squares’, is based on fitting a third-degree polynomial to the final 10 data points in both 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 coefficients, which is applied in both directions and the signal is extrapolated by 20 points. The lowest cumulative error of the endpoint accelerations (22.8 rad s-2) represented just one-third of the error when the common padding methods were used in optimal digital filtering (69.7 rad s-2). It also represented approximately half the lowest cumulative error in optimal smoothing with quintic splines (48.0 rad s-2).