A Multi-Time-Scale Generalization of Recursive Identification Algorithm for ARMAX Systems

Recently, Chen (2010) presented a new approach to recursive identification for ARMAX systems, which is a three-stage recursive scheme and assumes independent and identically distributed input signals. Here, we observe that, unless the time scale of the algorithm at one stage is reasonably faster than those at the previous stages, convergence to the true value may not take place. To remedy this issue, this note proposes a multi-time-scale modification of the algorithm in [5] such that convergence is achieved. In addition, the new scheme handles a wider class of input signals so that the input can be designed for some purpose.The advantage of the multi-time scale algorithm is verified with numerical examples.