IIR system identification using cat swarm optimization Ganapati Panda a , Pyari Mohan Pradhan a,⇑ , Babita Majhi b a School of Electrical Sciences, Indian Institute of Technology Bhubaneswar, India b Department of Information Technology, ITER, SOA University Bhubaneswar, India article info Keywords: System identification IIR system Cat swarm optimization abstract Conventional derivative based learning rule poses stability problem when used in adaptive identification of infinite impulse response (IIR) systems. In addition the performance of these methods substantially deteriorates when reduced order adaptive models are used for such identification. In this paper the IIR system identification task is formulated as an optimization problem and a recently introduced cat swarm optimization (CSO) is used to develop a new population based learning rule for the model. Both actual and reduced order identification of few benchmarked IIR plants is carried out through simulation study. The results demonstrate superior identification performance of the new method compared to that achieved by genetic algorithm (GA) and particle swarm optimization (PSO) based identification. Ó 2011 Elsevier Ltd. All rights reserved. 1. Introduction Adaptive IIR filtering is an active area of research for many years and has been used for applications in signal processing and com- munication. There has been substantial effort to establish adaptive IIR filters as alternative to adaptive FIR filters. In this filter the out- put feedback generates an infinite impulse response with only a fi- nite number of parameters. Hence with same number of coefficients, an adaptive IIR filter performs better than an adaptive FIR filter. Alternatively, to achieve a particular level of perfor- mance, an IIR filter requires less number of coefficients than the corresponding FIR filter. This is because the desired response can be approximated more effectively by the output of a filter that has both poles and zeros compared to one that has only zeros (Shy- nk, 1989a). As a result an adaptive IIR filter with sufficient number of poles and zeros can exactly model an unknown pole-zero sys- tem, whereas an adaptive FIR filter with higher order can only approximate it. A major concern in adaptive IIR filtering applications is that the error surface is usually non-quadratic and multimodal with respect to the filter coefficients. The gradient-based learning algorithms such as least mean square algorithm tries to find out the global minimum of the error surface by moving in the direction of nega- tive gradient and hence can easily be struck at local minima and cannot converge to global minimum (Widrow & Strearns, 1985). In addition the IIR filters become unstable if the poles move out- side the unit circle during the learning process. Therefore, for learning of higher order adaptive IIR filters, stability-monitoring is very essential. The properties of an adaptive IIR filter are consid- erably more complex than an adaptive FIR filter, and hence it is more difficult to predict the behavior of an adaptive IIR algorithm. Another drawback of adaptive IIR filters is slow convergence which needs further attention. In order to overcome these problems, sev- eral new structures and algorithms have been proposed in the lit- erature (David, 1981; Regalia, 1992; Shynk, 1989b). Most of the adaptive IIR filters are realized in direct form due to its simple implementation and analysis. However, some disadvantages of the direct form such as finite-precision effects and the complexity of stability monitoring have led to the development of alternative structures like cascade (David, 1981), lattice (Regalia, 1992) and parallel (Shynk, 1989b). The computational complexity and con- vergence properties of adaptive algorithms depend on the filter realization. In past few years several efforts have been made for studying alternative structures and algorithms for adaptive IIR filters. Re- cently evolutionary algorithms, such as GA, PSO, evolutionary pro- gramming (EP) and evolutionary strategies (ES) have received much attention for global optimization problems. These evolution- ary algorithms are heuristic population-based search techniques and incorporate random search and selection principle to achieve the global optimal solution. 2. Related work A number of adaptive system identification techniques have been reported in literature (Astriim & Eykhoff, 1971; Friedlander, 1982; Ljung, 1987; Siiderstrom, Ljung, & Gustavsson, 1978). An early attempt to implement adaptive IIR filter was made by White (1975). Johnson (1984) presented a tutorial on adaptive filtering in 0957-4174/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.eswa.2011.04.054 ⇑ Corresponding author. Tel.: +91 9238000246. E-mail addresses: ganapati.panda@gmail.com (G. Panda), pyarimohan.pradhan@ gmail.com (P.M. Pradhan), babita.majhi@gmail.com (B. Majhi). Expert Systems with Applications 38 (2011) 12671–12683 Contents lists available at ScienceDirect Expert Systems with Applications journal homepage: www.elsevier.com/locate/eswa