Passive Source Localization Using Time Differences of Arrival and Gain Ratios of Arrival

A source signal will be subject to different amounts of time-delay as well as attenuation when it reaches a number of spatially separated sensors. Both time-delay and attenuation are dependent on the distance between the source and the receivers. This paper performs a fundamental investigation of whether the gain ratios of arrival (GROAs), defined here as the ratio of the received signal amplitudes at the referenced sensor to the other sensors, can be utilized in conjunction with the time differences of arrival (TDOAs) to improve the source localization accuracy. We begin with a Gaussian random signal model and derive the Cramer-Rao lower bound (CRLB) of a source location estimate based on both GROAs and TDOAs. Our conclusion is that the improvement from GROAs increases when the factor $c/\omega_{o}$ increases, where $c$ is the signal propagation speed and $\omega_{o}$ is the signal bandwidth. The paper proceeds to develop an algebraic closed-form solution for the source location using GROAs and TDOAs. The algebraic solution is proved theoretically to reach the CRLB accuracy under the Gaussian data model. Numerical simulations are included to support and corroborate the theoretical developments.