Norio Watanabe

Chuo University, JAPAN

Estimation of average trajectory of nearly periodic motion

In this study we discuss an estimation problem for the data obtained from almost periodic movement. For example, successive strokes of the swimmer or location of some body part of a walking man can provide such data by setting the center of the body. Similar data are found in the sports analysis or health science. Usually data is obtained through motion capture and can be converted to 2-dimensional time series. A purpose is to find the average movement. A usual approach for estimation of the average trajectory is based on the functional data analysis. In this approach whole time series is devided into piecewise series according to each periods and regarded as the functional data. And the average trajectory can be estimated as the mean of the functional data. For successive movement, however, the obtained trajectory is not necessarily closed. Moreover the registration is a bothering problem. Our approach is based on the time series analysis. First we fit some nonlinear time series model to the data. Then we can estimate the average trajectory as an attractor of a nonlinear system by using the estimated model. In this study we use a multilayered neural network as a nonlinear time series model and discuss applicability of our approach by simulation studies.