Automatic algorithm for filtering kinematic signals with impacts in the Wigner representation

An automatic filtering algorithm is proposed for the accurate estimation of the second derivatives of kinematic signals with impacts. The impacts considered here occur when a moving object hits a rigid surface. The algorithm performs time-frequency filtering in the Wigner representation, to deal efficiently with the non-stationarities caused by such impacts, and adjusts the parameters of its time-frequency filtering function so that the filtering process adapts to the individual characteristics of the signal in hand. Performance analysis and comparative evaluation with experimentally acquired kinematic impact signals demonstrated a higher accuracy, with performance advantages over two widely used conventional automatic methods: linear phase autoregressive model-based derivative assessment (LAMBDA) and generalised cross-validation using quintic splines (GCVQS). For high impacts, the average absolute relative error in estimating the peak acceleration was 5.7% with the proposed method, 17.2% with a Butterworth low-pass filter optimised to yield minimum overall acceleration RMS error (best-case result), 18.3% with the LAMBDA method, and 37.2% with the GCVQS method. For signals with low impacts, the average absolute relative error was 19.4%, 6.9%, 8.3% and 19.1%, respectively, in each case, which indicates that, for signals with a low-frequency content, there is no need for such time-frequency filtering.