CB-MLE: Time-Delay Estimation Method for SISO Delay Systems

A time-delay estimation method is proposed for single-input single-output (SISO) delay systems. A copula is constructed from uniformly sampled input-output data to build the relationship between the input and output of the system. Taking time-delay as the parameter to be estimated, the logarithm likelihood function is formulated and separated into two parts, i.e., the dependence structure likelihood and the margin-related part. Then, the time-delay is obtained through maximizing the dependence structure likelihood. The highlight of this method is that the structure prior to the studied system is not required to estimate the time-delay. Comparative simulation examples are provided to demonstrate the validity of this method.