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access icon free Performance analysis of the generalised projection identification for time-varying systems

  • Author(s): Feng Ding 1 ; Ling Xu 1, 2 ; Quanmin Zhu 3
    • View affiliations
    • Affiliations: 1: Key Laboratory of Advanced Process Control for Light Industry, Ministry of Education, School of Internet of Things Engineering, Jiangnan University, Wuxi 214122, People's Republic of China ;
      2: School of Internet of Things Technology, Wuxi Vocational Institute of Commerce, Wuxi 214153, People's Republic of China ;
      3: Department of Engineering Design and Mathematics, University of the West of England, Bristol BS16 1QY, UK
  • Source: Volume 10, Issue 18, 12 December 2016, p. 2506 – 2514
    DOI:  10.1049/iet-cta.2016.0202 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 23/02/2016, Accepted 19/08/2016, Revised 04/07/2016, Published 08/09/2016

The least mean square methods include two typical parameter estimation algorithms, which are the projection algorithm and the stochastic gradient algorithm, the former is sensitive to noise and the latter is not capable of tracking the time-varying parameters. On the basis of these two typical algorithms, this study presents a generalised projection identification algorithm (or a finite data window stochastic gradient identification algorithm) for time-varying systems and studies its convergence by using the stochastic process theory. The analysis indicates that the generalised projection algorithm can track the time-varying parameters and requires less computational effort compared with the forgetting factor recursive least squares algorithm. The way of choosing the data window length is stated so that the minimum parameter estimation error upper bound can be obtained. The numerical examples are provided.

Inspec keywords: time-varying systems; stochastic processes; parameter estimation; gradient methods; least mean squares methods

Other keywords: stochastic gradient algorithm; least mean square methods; data window length; parameter estimation algorithms; stochastic process theory; performance analysis; forgetting factor recursive least squares algorithm; minimum parameter estimation error; time-varying systems; generalised projection identification algorithm; generalised projection algorithm; time-varying parameters

Subjects: Optimisation techniques; Time-varying control systems; Other topics in statistics; Interpolation and function approximation (numerical analysis); Simulation, modelling and identification

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