A Comparison of Evolutionary Algorithms for Tracking Time-Varying Recursive Systems
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A Comparison of Evolutionary Algorithms for Tracking Time-Varying Recursive Systems Michael S. White Royal Holloway, University of London, Egham Hill, Egham, Surrey, TW20 0EX, UK Email: [email protected]
Stuart J. Flockton Royal Holloway, University of London, Egham Hill, Egham, Surrey, TW20 0EX, UK Email: [email protected] Received 28 June 2002 and in revised form 29 November 2002 A comparison is made of the behaviour of some evolutionary algorithms in time-varying adaptive recursive filter systems. Simulations show that an algorithm including random immigrants outperforms a more conventional algorithm using the breeder genetic algorithm as the mutation operator when the time variation is discontinuous, but neither algorithms performs well when the time variation is rapid but smooth. To meet this deficit, a new hybrid algorithm which uses a hill climber as an additional genetic operator, applied for several steps at each generation, is introduced. A comparison is made of the effect of applying the hill climbing operator a few times to all members of the population or a larger number of times solely to the best individual; it is found that applying to the whole population yields the better results, substantially improved compared with those obtained using earlier methods. Keywords and phrases: recursive filters, evolutionary algorithms, tracking.
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INTRODUCTION
Many problems in signal processing may be viewed as system identification. A block diagram of a typical system identification configuration is shown in Figure 1. The information available to the user is typically the input and the noisecorrupted output signals, x(n) and a(n), respectively, and the aim is to identify the properties of the “unknown system” by, for example, putting an adaptive filter of a suitable structure in parallel to the unknown system and altering the parameters of this filter to minimise the error signal (n). When the nature of the unknown system requires pole-zero modelling, there is a difficulty in adjusting the parameters of the adaptive filter, as the mean square error (MSE) is a nonquadratic function of the recursive filter coefficients, so the error surface of such a filter may have local minima as well as the global minimum that is being sought. The ability of evolutionary algorithms (EAs) to find global minima of multimodal functions has led to their application in this area [1, 2, 3, 4]. All these authors have considered only time-invariant unknown systems. However in many real-life applications, time variations are an ever-present feature. In noise or echo cancellation, for example, the unknown system represents
the path between the primary and reference microphones. Movements inside or outside of the recording environment cause the characteristics of this filter to change with time. The system to be identified in an HF transmission system corresponds to the varying propagation path through the atmosphere. Hence there is an interest in investigating the applicability of evolutionary-based adaptive system identification algori
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