Distributed Estimation of Spatially Varying Distributed Parameter System

Abstract

Adaptive filter shows a significant role in the field of digital signal processing and wireless communication. It integrates LMS algorithm in real time situations because of its low computational complexity and simplicity. The adaptive distributed strategy is built on the diffusion cooperation scheme among nodes at different locations that are dispersed over a wide topographical area. Computations have been performed in all the nodes and all the results are shared among them so as to obtain precise parameters of interest. There are some scenarios where estimation parameters vary over both space and time domains across the network. A set of basis functions i.e. Chebyshev polynomials is used to describe the space-varying nature of the parameters and diffusion least mean-squares strategy is proposed to recover these parameters. The parameters of our concern are assessed for both one dimensional and two dimensional networks. Stability and convergence of the proposed algorithm have been analysed and expressions are derived to predict the behavior. Network stochastic matrices are used to combine exchanged information between nodes. The results show that the performances of the networks also depend upon the combination matrices. The resulting algorithm is distributed, co-operative and able to respond to the real time changes in environment