On the Cramer-Rao bound of multiple sources localization using RDOAs and GROAs in the presence of sensor location uncertainties

Passive source localization has been the focus of considerable research efforts due to its usefulness in various applications. This paper performs a fundamental investigation of whether the gain ratios of arrival (GROAs) can be utilized in conjunction with the range differences of arrival (RDOAs) to improve the multiple sources localization accuracy in the presence of sensor location uncertainties. In this paper, we derive the Cramer-Rao lower bound (CRLB) of multiple source location estimate using both RDOAs and GROAs when sensor positions have errors. Simulations show that the localization accuracy improvements contributed by GROA measurements are significant for two far-field sources, two near-field sources and two enclosed sources as the SNR, jamming signal bandwidth factor C/ωo or sensor position error power σs2 increases. The CRLB will provide reasonable reference for localization algorithm research in the future.