Convergence speed analysis and new algorithms for adaptive IIR filtering based on the theory of balanced realization

• Grant number: 06/01113-0
• Support Opportunities: Regular Research Grants
• Start date: June 01, 2006
• End date: January 31, 2009
• Field of knowledge: Engineering - Electrical Engineering
• Principal Investigator: Phillip Mark Seymour Burt
• Grantee: Phillip Mark Seymour Burt
• Host Institution: Escola Politécnica (EP). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

Adaptive IIR filters can be an attractive alternative to FIR adaptive filters. However, some problems have to be considered, such as the possibility of very slow convergence. A considerable gain in the understanding of this aspect was attained by the author in previous works, where, based on the theory of balanced realization, the relation of convergence speed with the Hankel singular values of the system being identified and with the parameterization of the adpative filter's poles was showed.Moreover, based on this analysis, a new adaptive IIR algorithm was proposed (sucessive approximations algorithm, or SA), whose convergence speed can be much higher than that of more conventional algorithms, at the cost of a relatively small increase in computational complexity.The analysis method that was introduced in the mencioned works as well as the SA algorithm, constitute a very distinct approach from other ones found up to now in the area of adaptive IIR filtering. As a consequence, they present several aspects yet to be investigated. This work is under way and some results on the convergence of the SA algorithm and its computational complexity were presented in the author's thesis for Associate Professorship.The main motivation of this research project is the continuity of the investigations already under way and the investigation of new aspects such as: the extension of the analysis to the inverse identification adaptive filtering configuration; to other parameterizations (in particular, Laguerre filters) and for non-white inputs; the real-time implementation of the SA algorithm. (AU)