IIR Filter Adaptation Using Branch-and-Bound: A Novel Approach

Adaptive infinite impulse response (IIR) filters provide significant advantages over equivalent finite impulse response (FIR) implementations because they are able to more accurately model physical plants that have pole-zero structures. Additionally, they are typically capable of meeting performance specifications using fewer filter parameters. This savings in parameters, which can be as much as 5-10 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 paper 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, which is an exhaustive search method, and employ interval arithmetic for all computations. Simulation results show that the resulting algorithm is viable and competitive and, when compared with a number of existing state-of-the-art algorithms, outperforms them in terms of the MSE of the final point.