Time-Delay Estimation Based on Graph Global Smoothness

Time delay is an essential factor affecting the performance of time series-related tasks, such as time series forecasting, system modeling, and so on. Therefore, the time-delay estimation (TDE) issue has attracted more and more attention. In this article, a TDE method for the open-loop multi-in multi-out (MIMO) delay system with an unknown structure is proposed. In our approach, the theory of graph Laplacian is introduced to the TDE task for the first time. The correspondence between a delay system and a graph is established by constructing an N-linked graph from input–output samples of the delay system, and the global smoothness of the N-linked graph is considered as a time-delay metric. The TDE process of a delay system is then implemented by tracking the minimum of the global smoothness. The sparsity of the N-linked graph is further leveraged to effectively reduce the computational load of the TDE process. Simulation experiments and wind speed forecasting based on real data validate the effectiveness of the proposed method.