Gyroscopic signal smoothness assessment by geometric jolt estimation. (17th May 2017)

• Record Type: Journal Article
• Authors: Fiori, Simone
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 16(2017)
• Page Start: 5893
• Page End: 5905
• Publication Date: 2017-05-17
• Subjects: gyroscopic signal -- human body movement -- complex body movement -- signal smoothness assessment -- geometric jolt; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4441
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : The present contribution focuses on the estimation of the geometric acceleration and of the geometric jolt (namely, the derivative of the acceleration) of a multidimensional, structured gyroscopic signal. A gyroscopic signal encodes the instantaneous orientation of a rigid body during a full three‐dimensional rotation that is regarded as a trajectory in the curved space SO(3) of the special orthogonal matrices. The geometric acceleration and jolt associated to a gyroscopic signal are evaluated through the rules of calculus prescribed by differential geometry. Such an endeavor is motivated by recent studies on the smoothness of human body movement in biomechanical engineering, sports science, and rehabilitation neuroengineering. Two indexes of smoothness are compared, namely, a normalized proper geometric acceleration index and a normalized proper geometric jolt index. Our investigation concludes that, in the considered experiments with measured signals, for relatively low values of the acceleration and of the jolt indexes, such indexes are strongly positively correlated. Copyright © 2017 John Wiley & Sons, Ltd.