Continuous-time tracking algorithms involving two-time-scale Markov chains

摘要: This work is concerned with least-mean-squares (LMS) algorithms in continuous time for tracking a time-varying parameter process. A distinctive feature that the true process changing at fast pace driven by finite-state Markov chain. The states of chain are divisible into number groups. Within each group, transitions take place rapidly; among different groups, infrequent. Introducing small generator leads to two-time-scale formulation. objective difficult achieve. Nevertheless, limit result derived yielding systems. Moreover, rates variation error sequence analyzed. Under simple conditions, it shown scaled errors converges weakly switching diffusion. In addition, numerical example provided and an adaptive step-size algorithm developed.