Diffusion Fractional Tap-length Algorithm with Adaptive Error Width and Step-size

Estimation in a cooperative and distributed manner in wireless sensor networks (WSNs) has considered much attention in recent years. When this distributed estimation is performed adaptively, the concept of adaptive networks will develop. In such networks, proper selection of the unknown parameter length is an issue in itself. A deficient filter length results in an additional steady-state error while selecting a large length will impose a more computational load on the nodes, which is critical in sensor networks due to the lack of energy resources. This motivates the use of variable tap-length adaptive filters in the context of the adaptive networks. This has been achieved in adaptive networks using the distributed fractional tap-length (FT) algorithm. This algorithm requires proper selection of the length adaptation parameters, such as error width and length adaptation step-size. This paper proposes an automatic method for selecting these parameters. In the proposed method, these parameters are adapted based on the estimated gradient vector. The proposed method is fully distributed and presented in a diffusion strategy. Simulation results show that the proposed algorithm has both the advantage of fast length convergence and an unbiased steady-state tap-length.