Time-delay metric for TDE of SISO delay systems

The time-delay intrinsic in the time series sampled from dynamic systems results in the chaotic correspondence between the elements of the time series. Therefore, accurate estimation of the time-delay is essential in time series-based tasks. In this paper, we propose two time-delay metrics for time-delay estimation (TDE) of single -input single-output (SISO) delay systems with unknown structures. The two proposed metrics are based on the ellipse shape ratio (ESR) and called the linear ellipse shape ratio (LESR), and the nonlinear ellipse shape ratio (NESR). In the devised TDE process employing the proposed metrics, an iteratively updated ellipse is used to filter out the outliers from the system input and output samples. Simulation experiments confirm the efficiency of the proposed time-delay metrics.