Mean-Convergence behavior of Adaptive Identification Algorithms for Pole-Zero Systems

Abstract

Adaptive methods for the estimation of unknown system parameters has the advantage of tracking time-varying systems. Identification algorithms for recursive systems produce nonquadratic performance functions. In such problems it is very difficult to estimate the nature of convergence in a stochastic frame work. Recently, it has been shown that the ensemble mean parameter updating equations of IIR adaptive algorithm can be represened by associated ordinary differential equations (ODEs). A method of solving the ODEs in order to analyze the mean- convergence behavior of these algorithms, given the mean description of the input in the form of power spectral density, has been presented recently. In this paper, this procedure is applied to study the convergence behavior of recursive adaptive algorithms applied for the identification of pole-zero systems. Effectiveness of this method is shown through analytical and simulation results.

Indexing terms:

• System identification
• Adaptive
• Pole-zero systems
• ODE
• Mean-convergence