A novel nonlinear filter, which incorporates the concept of exponential sinusoidal models into nonlinear filters based on functional link networks (FLNs) has been developed in this paper. The proposed filter is designed to provide improved convergence characteristics over traditional FLN filters. The conventional trigonometric FLN may be considered as a special case of the proposed adaptive exponential FLN (AEFLN). An adaptive exponential least mean square (AELMS) algorithm has been derived and the same has been successfully applied for identification of a couple of nonlinear plants. The AEFLN-based nonlinear active noise control (ANC) system has also been designed and an adaptive exponential filtered-s least mean square (AEFsLMS) algorithm has been developed to update the weights as well as the exponential factor. Simulation study has revealed the improved noise mitigation offered by the AEFLN-based nonlinear ANC system.

In recent years, correntropy-based algorithms which include maximum correntropy criterion (MCC), generalized MCC (GMCC), kernel MCC (KMCC) and hyperbolic cosine function-based algorithms such as hyperbolic cosine adaptive filter (HCAF), logarithmic HCAF (LHCAF), least lncosh (Llncosh) have been widely utilized in adaptive filtering due to their robustness towards non-Gaussian/impulsive background noises. However, the performance of such algorithms suffers from high steady-state misalignment. To minimize the steady-state misalignment along with having comparable computational complexity, an exponential hyperbolic cosine function (EHCF) based new robust norm is introduced and a corresponding EHCF based adaptive filter called exponential hyperbolic cosine adaptive filter (EHCAF) is developed in this letter. Further, computational complexity and bound on learning rate for stability of the proposed algorithm is also studied. A set of simulation studies has been carried out for system identification scenario to assess the performance of the proposed algorithm. Further, EHCAF algorithm has been extended and the filtered-x EHCAF (Fx-EHCAF) algorithm is proposed for robust room equalization.

This paper proposes a functional-link-artificial-neural-network-based (FLANN) multichannel nonlinear active noise control (ANC) system trained using a particle swarm optimization (PSO) algorithm suitable for nonlinear noise processes. The use of PSO algorithm in a multichannel ANC environment not only reduces the local minima problem but also removes the requirement of computationally expensive modeling of the secondary-path transfer functions. A decentralized version of a multichannel nonlinear ANC is also developed, which facilitates scaling up of an existing ANC setup without rederiving the learning rules. This is possible as the controller module of each channel is independent of others. Simulation study of the two new multichannel ANC systems demonstrates comparable mitigation performance. However, the decentralized one is preferred to as it possesses the added advantage of scalability.