Mutual Information for Quaternion Time Series
Mutual Information method is a widely used method for estimation of time delay value in the process of time delay embedding. It’s designed for a univariate scalar time series. In the real systems often many outputs of investigated system are available. In this case a multivariate time delay estimation method is necessary if one may require to perform the uniform time delay embedding. The special case of multivariate data is a kinematic time series(e.g. quaternion time series or Euler angles time series). The main goal of this paper is to provide a method for this case: Mutual Information method’s extension for quaternion time series. The results are also compared with previosly presented quaternion’s angle method. The method was tested on the real kinematic data - the recordings of human gait.
KeywordsMutual information Quaternions Deterministic chaos Nonlinear time series analysis Human motion analysis Human gait data
This work has been supported by the “Młoda Kadra” project from the Wrocław University of Science and Technology.
The author also would like to acknowledge the Polish-Japanese Institute of Information Technology for the gait sequences recorded in the Human Motion Laboratory (HML).
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