BFGS quasi-Newton location algorithm using TDOAs and GROAs

With the emergence of location-based applications in various fields, the higher accuracy of positioning is demanded. By utilizing the time differences of arrival （TDOAs） and gain ratios of arrival （GROAs）, an efficient algorithm for estimating the position is proposed, which exploits the Broyden-Fletcher-Goldfarb-Shanno （BFGS） quasi-Newton method to solve nonlinear equations at the source location under the additive measurement error. Although the accuracy of two-step weighted-least-square （WLS） method based on TDOAs and GROAs is very high, this method has a high computational complexity. While the proposed approach can achieve the same accuracy and bias with the lower computational complexity when the signal-to-noise ratio （SNR） is high, especially it can achieve better accuracy and smaller bias at a lower SNR. The proposed algorithm can be applied to the actual environment due to its real-time property and good robust performance. Simulation results show that with a good initial guess to begin with, the proposed estimator converges to the true solution and achieves the Cramer-Rao lower bound （CRLB） accuracy for both near-field and far-field sources.

Semidefinite programming approach for TDOA/GROA based source localization

Time-differences-of-arrival （TDOA） and gain-ratios-of- arrival （GROA） measurements are used to determine the passive source location. Based on the measurement models, the con- strained weighted least squares （CWLS） estimator is presented. Due to the nonconvex nature of the CWLS problem, it is difficult to obtain its globally optimal solution. However, according to the semidefinite relaxation, the CWLS problem can be relaxed as a convex semidefinite programming problem （SDP）, which can be solved by using modern convex optimization algorithms. Moreover, this relaxation can be proved to be tight, i.e., the SDP solves the relaxed CWLS problem, and this hence guarantees the good per- formance of the proposed method. Furthermore, this method is extended to solve the localization problem with sensor position errors. Simulation results corroborate the theoretical results and the good performance of the proposed method.

A novel bearing-assisted TDOA-GROA approach for passive source localization

Purpose–The passive source localization(PSL)problem using angles of arrival(AOA),time differences of arrival(TDOA)or gain ratios of arrival(GROA)is generally nonlinear and nontrival.In this research,the purpose of this paper is to design an accurate hybrid source localization approach to solve the PSL problem.The inspiration is drawn from the fact that the bearings,TDOAs and GROAs are complementary in terms of their geometry properties.Design/methodology/approach–The maximum-likelihood(ML)method is reexamined by using hybrid measurements.Being assisted by the bearings,a new hybrid weighted least-squares(WLS)method is then proposed by jointly utilizing the bearing,TDOA and GROA measurements.Findings–Theoretical performance analysis illustrates that the mean-square error of the ML or WLS method can attain the Cramér-Rao lower bound for Gaussian noiseover small error region.However,the WLS method has much lower computational complexity than the ML algorithm.Compared with the AOA-only,TDOA-only,AOA-TDOA,TDOA-GROA methods,the localization accuracy can be greatly improved by combining the AOAs,TDOAs and GROAs,especially for some specific geometries.Originality/value–A novel bearing-assisted TDOA-GROA method is proposed for source localization,and a new hybrid WLS estimator is presented inspired from the fact that the bearings,TDOAs and GROAs are complementary in terms of their geometry properties.