Discrete-Time ZND Algorithms for Time-Dependent LQ Decomposition Applied to Sound Source Localization

Abstract

To solve discrete-time LQ decomposition (DTLQD) problem, a 5-step Adams-Bashforth-type (5SAB-type) discrete-time zeroing neural dynamics (DTZND) algorithm is proposed by combining 5-step Adams-Bashforth (AB) method with continuous-time zeroing neural dynamics (CTZND) model. For comparison, general 4-step and 3-step Zhang et al. discretization (ZeaD) formulas are also presented and used to discretize the CTZND model. The corresponding 4-step ZeaD-type (4SZeaDtype) and 3-step ZeaD-type (3SZeaD-type) DTZND algorithms are thus developed. Theoretical analyses and results show that the proposed 5SAB-type DTZND algorithm has higher computational precision than the 4SZeaD-type and 3SZeaD-type DTZND algorithms. Two numerical examples further validate the availability of the three DTZND algorithms and the superiority of the proposed 5SAB-type DTZND algorithm. Moreover, the proposed DTZND algorithms are applied to the sound source localization based on the time difference of arrival (TDOA) technique.