Joint two‐stage multi‐innovation recursive least squares parameter and fractional‐order estimation algorithm for the fractional‐order input nonlinear output‐error autoregressive model

• Published in: International journal of adaptive control and signal processing Vol. 37; no. 7; pp. 1650 - 1670
• Main Authors: Hu, Chong, Ji, Yan, Ma, Caiqing
• Format: Journal Article
• Language: English
• Published: Bognor Regis Wiley Subscription Services, Inc 01.07.2023
• Subjects: Algorithms; Autoregressive models; Error analysis; fractional‐order model; gradient search; hierarchical identification; Identification methods; Innovations; key term separation; Least squares; multi‐innovation theory; Parameter estimation; Parameter identification
• ISSN: 0890-6327; 1099-1115
• DOI: 10.1002/acs.3593

Summary This paper mainly investigates the issue of parameter identification for the fractional‐order input nonlinear output error autoregressive (IN‐OEAR) model. In order to avoid the problem of large computation of redundant parameter estimation, the output form of the system can be expressed by a linear combination of unknown parameters through the key term separation. Through employing the hierarchial identification principle, the fractional‐order IN‐OEAR model is decomposed into two sub‐models with a smaller number of parameters. On the basis of the recursive identification methods, a recursive least squares sub‐algorithm and a gradient stochastic sub‐algorithm are proposed to estimate the parameters and the fractional‐order, respectively. With the aim of achieving more accurate parameter estimates, a two‐stage multi‐innovation least recursive algorithm is proposed by means of the multi‐innovation identification theory. The numerical simulation results test the effectiveness of the proposed methods.