Adaptive Networks Under Non-Stationary Conditions: Formulation, Performance Analysis, and Application

In this paper, we thoroughly investigate the tracking behavior of a wide range of adaptive networks under non-stationary conditions. Under these conditions, we study and analyze the mean-square-error performance of all centralized, incremental, and diffusion algorithms for adaptive networks. The closed forms of the steady-state mean-square deviation (MSD) and excess mean-square error (EMSE) criteria are extracted for these algorithms. In addition, we apply our findings to the time-varying autoregressive (TVAR) modeling problem, which is a significant and common engineering application. Generally, time-varying parameters are extracted from a single-point observation; however, the employment of numerous observations may be necessary in some cases. Therefore, we consider a set of observations in the corresponding model identification problem. It is shown that doing so improves the resolution of the estimated parameters. Moreover, we theoretically examine various types of adaptive algorithms for the TVAR model identification problem. Furthermore, node and network behavior analysis is performed for both transient and steady-state conditions. The analysis proves that regardless of the stationary conditions, neither centralized nor incremental adaptive algorithms dominate universally. However, among diffusion algorithms, the adapt-then-combine (ATC) approach demonstrates superior performance, followed by the combine-then-adapt (CTA) approach and the non-cooperative approach (treated as a special case of the diffusion strategy), in that order. The theoretical findings are well supported by simulation results.