Recurrent least square method for estimation of varying parameters

Authors

  • Igor Spectorsky Educational and Scientific Complex "Institute for Applied System Analysis" of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine https://orcid.org/0000-0003-4863-7986

DOI:

https://doi.org/10.20535/SRIT.2308-8893.2021.4.11

Keywords:

recursive less square methods, RLS, estimating

Abstract

In this paper, linear object yt=a1y1+...anyn+b1u1+...bmym+δ is considered. The aim is to estimate the object parameters with an assumption that they are changing linearly: ai=ai,0+ai,1t (i=1,2,...,n), bj=bj,0+bj,1t (j=1,2,...,m), δ=δ01t, parameters ai,0, ai,1 (i=1,2,...,n), bj,0, bj,1 (j=1,2,...,m), δ0, δ1 are assumed to be constants (almost constants during long time). For this object, the recursive least square (RLS) method is generalized. Provided examples show that the obtained RLS generalization gives higher precision (in comparison with the classical RLS method) for a case when parameters change with constant (almost constant) speed during long time. When parameters change unpredictably, the precision of the proposed RLS generalization is worse then the precision of the classical method, but it is still high.

Author Biography

Igor Spectorsky, Educational and Scientific Complex "Institute for Applied System Analysis" of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv

Igor Ya. Spectorsky,

Candidate of Physical and Mathematical Sciences (Ph.D.), an associate professor at the Department of Mathematical Methods of System Analysis of Educational and Scientific Complex "Institute for Applied System Analysis" of the National Technical University of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kyiv, Ukraine.

References

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R. Iserman, Digital control systems. Moscow: Mir, 1984, 541 p.

Adaptive filters; ed. K.F.N. Cowen and P.M. Grant. Moscow: Mir, 1988, 392 p.

Nicholas J. Higham, Accuracy and stability of numerical algorithms. Philadelphia: Society for Industrial and Applied Mathematics, 2002, 680 p.

Published

2021-12-22

Issue

Section

Mathematical methods, models, problems and technologies for complex systems research