Design and Analysis of Reciprocal Zhang Neuronet Handling Temporally-Variant Linear Matrix-Vector Equations Applied to Mobile Localization
Chen, Jielong; Pan, Yan; Li, Shuai; Zhang, Yunong (2024-02-12)
IEEE
12.02.2024
J. Chen, Y. Pan, S. Li and Y. Zhang, "Design and Analysis of Reciprocal Zhang Neuronet Handling Temporally-Variant Linear Matrix-Vector Equations Applied to Mobile Localization," in IEEE Transactions on Emerging Topics in Computational Intelligence, vol. 8, no. 2, pp. 2065-2074, April 2024, doi: 10.1109/TETCI.2024.3359512.
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© 2024 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
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Julkaisun pysyvä osoite on
https://urn.fi/URN:NBN:fi:oulu-202405294055
https://urn.fi/URN:NBN:fi:oulu-202405294055
Tiivistelmä
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.
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.
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