Estimation of time-varying delay time in nonstationary linear systems: an approach to monitor human operator adaptation in manual tracking tasks

Adaptability is one of man´s advantages over machines. Perhaps one of the reasons for our limited understanding about human adaptation during manual tracking tasks is that we have only limited tools to identify the model coefficients (especially delay time) of an adapting human operator. In this paper, we introduce a discrete time recursive delay identifier (RDI) capable of simultaneously estimating a human operator´s nonstationary delay time and linear model coefficients. At its core lies the extended Kalman filter (EKF). Our goal to obtain fractional delay time estimates was realized by using the bicubic interpolation scheme as part of the EKF to provide subsample magnitude and derivative estimates of the observed input/output time series. While this theoretically limits the RDI applicability to band-limited or differentiable signals, this is seldom a concern in practice. Based on data from simulated and experimental time varying tracking tasks, we show the RDI´s potential to substantially increase our understanding about human adaptations thus perhaps offering new avenues for machine adaptation