Fundamental Limitations on the Number of Resolvable Emitters Using a Geolocation System

Abstract

We derive conditions for unique geolocation of multiple radio-frequency emitters using a general observation model. These conditions specify the maximum number of emitters that can be uniquely located by a geolocation system, often referred to as the resolution capacity (RC). Our derivations extend previously published results for geolocation based on angle-of-arrival (AOA) estimation. We show that with no prior information, the RC is upper bounded by the total number of antenna elements in the system, i.e., LM, where M is the number of elements in each array and L is the number of arrays. In contrast, the RC of geolocation based on AOA is upper bounded by M. In addition, if the signals are known to be uncorrelated, and the arrays are uniform and linear, the RC is upper bounded by (LM) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -L(M-1) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> -1. However, more emitters can be resolved using different types of arrays. Our results lead to the inevitable conclusion that geolocation based on AOA is suboptimal, and new methods should be developed that can jointly exploit the information collected by all the antenna arrays