Identification of models of long lines on the basis of adaptive filters with fractional-order differences

Abstract

In many applications, objects are distributed and described by equations of mathematical physics. Such objects are often described by models with lumped parameters. Therefore, improving the accuracy of the description of a distributed object on the basis of a model with lumped parameters is an urgent problem. The aim of this paper is to develop a method for adaptive identification of long-line models on the basis of equations with fractional-order differences in the presence of noise. In many applications, the spatial coordinate can be considered constant and measurements can be performed at the beginning and at the end of the line. For such cases, the object transfer function is an irrational function of variable p. It is shown that an object with an irrational transfer function can be approximated by equations with fractional-order differences. A mathematical model of a long line in the form of a finite impulse-response filter with fractional-order differences is proposed. Such a filter combines the advantages of the known infinite impulse-response and finite impulse-response filters: it has a comparatively small number of coefficients and remains stable at any limited values of the coefficients. On the basis of the recurrent least-squares method, an algorithm for adaptive identification of long-line models with fractional-order differences was developed. A computer experiment showed a high accuracy of the proposed model as compared with the known infinite impulse-response and finite impulse-response filters. In addition, the identification algorithm on the basis of the proposed model showed the higher noise immunity. The obtained results can be used in the development of adaptive-filtering algorithms for long lines (communication channels, track circuits, power lines).