Design of adaptive IIR filter with modified firefly algorithm for parameter estimation

This article presents a design of digital infinite impulse response (IIR) filter with traditional and modified firefly algorithms for parameter estimation of unknown systems. The parameters of the filter to be designed are considered as an optimization vector. Traditional learning techniques create stability problem and the performance drastically deteriorates in case of reduced order adaptive models. This article presents both uni-modal and multi modal design of digital IIR filter. The modified firefly algorithm always tries to explore the search space for improved solutions without getting trapped in the local optima and diverged situations. The results of actual and reduced order estimation for standard system by modified firefly method exhibit superior performance as compared to traditional firefly algorithm and variable step size firefly algorithm. The superiority can be visualized in terms of mean square error, convergence speed and estimation of coefficients.

I. Introduction

Design of digital filter plays an essential role in the area of signal processing, communication systems, parameters estimation and system modelling. In this case, unknown IIR filter parameters are taken as a vector to be optimized. The objective of optimization procedure is to adjust coefficients of digital filter for estimating actual parameters of an unknown system. IIR filters use finite number of parameters to generate an infinite impulse response. The adaptive IIR filter provides enhanced performance than corresponding FIR filters with identical number of coefficients. Similarly for a standard level of performance, the number of coefficients in IIR filter is less as compared to FIR filter. Generally the error surface provided by IIR filter is non-quadratic and multimodal. Another problem significant to IIR filter is stability. In addition to that IIR filters also become unstable if there is a movement of poles outside unit circle during the process of learning. So, stability monitoring of higher order IIR filter is very essential during learning process. The behavior of traditional algorithm offers difficult prediction as IIR filter with adaptive nature have more complex properties than a similar type FIR filter. The convergence of the IIR filter is also very slow.