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

Author

Lirong Huang ; Hjalmarsson, Hakan

Author_Institution

Autom. Control Lab., KTH, Stockholm, Sweden

Volume

60

Issue

8

fYear

2015

fDate

Aug. 2015

Firstpage

2242

Lastpage

2247

Abstract

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.

Keywords

convergence; identification; recursive estimation; signal processing; stochastic processes; ARMAX systems; identically distributed input signals; multitime-scale generalization algorithm; multitime-scale modification; recursive identification algorithm; three-stage recursive scheme; Algorithm design and analysis; Approximation algorithms; Approximation methods; Convergence; Equations; Recursive estimation; Stochastic processes; $L$-mixing processes; ARMAX models; L-mixing processes; multi-time-scale method; quasi-stationary signals; recursive estimation; stochastic approximation;

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2014.2373711

Filename

6963298