Global Optimization Methods for Adaptive IIR Filters

Abstract

Adaptive filtering systems mimic the ability of biological systems to change their internal configuration so as to better survive in their environment. This ability is critical because adaptive filters operate in noisy, time-varying environments. At design time, although performance objectives are well-defined, there is limited a priori information about the characteristics of the input signals. As a result, systems capable of meeting performance specifications while operating under such conditions need to be able to make on-the-fly changes to their structure so as to constantly improve performance. Over the last couple of decades, their efficacy and robustness have been demonstrated in numerous applications and today, they are used in a wide variety of applications ranging from radar, sonar and active noise control to channel equalization, adaptive antenna systems and hearing aids.

Adaptive IIR filters provide significant advantages over equivalent adaptive FIR filters implementations. First, they more accurately model physical plants that have pole-zero structures. Secondly, they are typically capable of meeting performance specifications using fewer filter parameters. This savings in parameters, which can be as much as 5 to 10 times, leads to the use of fewer multiplier blocks and therefore, lower power consumption. Despite these advantages, adaptive IIR filters have not found widespread use because the associated Mean Squared Error (MSE) cost function is multimodal and therefore, significantly difficult to minimize. Additionally, the filter can become unstable during adaptation. These two properties pose several problems for adaptive algorithms, causing them to be sensitive to initial conditions, produce biased solutions, unstable filter configurations or converge to local minima. These problems prevent the widespread use of adaptive IIR filters in practice and if such filter structures are to become more practical, new, innovative solutions are required.

This dissertation proposes a new algorithm for minimizing the MSE cost function of adaptive IIR filters, aimed at addressing some of the aforementioned issues. We adopt the approach of using a Branch-and-Bound algorithm because it is guaranteed to locate global minima. Furthermore, we employ interval arithmetic for all computations. Its use allows for all numerical errors that accrue during computations to be accounted for. Simulation results show that the resulting algorithm is a viable one, and when compared to a number of existing, state-of-the-art algorithms, outperforms them in a number of categories.