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Adaptive filter has become an active field of research due to its brobdingnagian scope of application in different fields of engineering such as communication, sonar, navigation, control, biomedical engineering, seismology, radar and many more. In this field different types of applications are noticed, namely system identification, inverse system identification, prediction and array processing etc.
An adaptive filter behaves like a filter with the exception of iteration based coefficient values due to incorporation of an adaptive algorithm to cope up with ever changing environmental condition (Haykin, 1996). Apart from adaptive system identification, adaptive filter may be applied for adaptive prediction, adaptive inverse modelling and adaptive array processing. In case of adaptive system identification the adaptive algorithm varies the filter’s characteristics by manipulating or varying the filter coefficient values iteratively according to the performance criterion of the system. In most of the cases error between output signal of the unknown system and output signal of the adaptive identifying filter is considered as the error fitness or objective function and the adaptive identifying filter works toward the minimization of error fitness function with the proper adjustment of the filter coefficients (Ljung, 1999; Goodwin & Sin, 1984).
Finite impulse response (FIR) and infinite impulse response (IIR) filters are two types of digital filters. For adaptive IIR filter, due to recursive nature, the present output depends not only on present and past inputs as in FIR but also on the previous outputs. Thus an IIR filter requires lower order as compared to FIR filter. In the present work adaptive IIR filter is considered for identifying / modelling an unknown plant / system.
In adaptive IIR filtering applications, non-differentiable, multimodal nature of error fitness surface is a major point of concern.
Classical optimization methods like gradient based optimization methods are incapable to handle such complex system identification problems due to following inherent deficiencies:
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Requirement of continuous and differentiable cost function,
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Usually converges to the local optimum solution or revisits the same sub-optimal solution,
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Incapable to search the large problem space,
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Requirement of the piecewise linear cost approximation (linear programming),
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Highly sensitive to starting points when the number of solution variables is increased and as a result the solution space is also increased.