Design and Analysis of Reciprocal Zhang Neuronet Handling Temporally-Variant Linear Matrix-Vector Equations Applied to Mobile Localization

Abstract

Linear matrix-vector equations (LMVE) problem is widely encountered in science and engineering. Numerous methods have been proposed and studied to solve static (i.e., temporally-invariant) LMVE problem. However, many practical LMVE problems are temporally-variant. The static methods are not efficient and accurate enough. Originated from the research of Hopfield neuronet (HN), Zhang neuronet (ZN) is widely used to solve temporally-variant problems, but the traditional continuous ZN (TCZN) model needs to compute the inverse or pseudoinverse of the coefficient matrix, being less efficient. In this paper, a novel reciprocal ZN (RZN) model that does not need to compute the inverse or pseudoinverse of the coefficient matrix is proposed, and the detailed derivation procedure is first given. In addition, theoretical analyses show the global convergence performance of the RZN model. Moreover, the comparative numerical experiments with gradient neuronet (GN) model and TCZN model show the correctness and efficiency of RZN. Finally, the application of mobile localization further validates the superiority of RZN model over TCZN and GN models.