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.