Distributed sparse diffusion estimation based on set membership and affine projection algorithm

The wireless sensor networks (WSNs) is the result of evolution of wireless and networking technologies, micro-electromechanical systems, and micro-services. One important task which can be performed by nodes in WSNs is to find a common solution to a problem by using distributed processing. In this paper, we study the problem of distributed estimation, where a group of nodes are required to collectively estimate a sparse parameter vector of interest, and we solve it by an estimation algorithm based on the set membership (SM) and affine projection (AP) methods. At each iteration of the algorithm, in addition to the current data, the proposed algorithm uses data obtained from previous measurements to attain faster convergence rate. A method is also proposed to select the constraint bound for set membership such that the computational load is uniformly distributed among the nodes of network. Then the distributed estimation algorithm is analyzed and a closed form expression for the steady state mean square deviation (MSD) is developed. The performance of proposed method is assessed via computer simulations. The simulation results show that the proposed algorithm provides faster convergence rate and smaller steady state MSD value when compared to conventional methods such as diffusion least mean squares (LMS), distributed set membership normalized LMS (DSM-NLMS), and distributed APA. Moreover, it achieves lower computational load compared to the AP method. These advantages make the proposed method useful in sparse parameter vector estimation whenever the nodes have sufficient memory size.