Mobile localization based on online solution of linear matrix–vector equations using inverse-free acceleration-layer Zhang neurodynamics

The solution of temporal-dependent linear matrix–vector equations (TDLMVE) problem has become a research hotspot. Many methods have been presented to solve the problem. However, existing methods often only consider the velocity layer and inevitably require temporal-dependent matrix inversion (TDMI) computation, limiting the efficiency of solving the problem. Therefore, exploring a solution to the TDLMVE problem without TDMI computation from the viewpoint of acceleration-layer control is of significant research value. In this paper, we propose an innovative acceleration-layer TDLMVE (AL-TDLMVE) problem, that is, how to solve TDLMVE problem from the viewpoint of acceleration-layer control. To solve the proposed problem, a groundbreaking inverse-free acceleration-layer Zhang neurodynamics (IFALZN) controller is designed and proposed, reducing computational complexity and enhancing computational precision. Besides, theoretical analyses show the convergence performance of the proposed IFALZN controller. Numerical experiments are conducted to verify the effectiveness and validity of the proposed controller. Finally, the IFALZN controller successfully and efficiently solves the mobile localization problem. Furthermore, comparative experiments with some state-of-the-art controllers further substantiate the robustness and superiority of the IFALZN controller.