Geolocation with FDOA Measurements via Polynomial Systems and RANSAC

The problem of geolocation of a transmitter via time difference of arrival (TDOA) and frequency difference of arrival (FDOA) is given as a system of polynomial equations. This allows for the use of homotopy continuation-based methods from numerical algebraic geometry. A novel geolocation algorithm employs numerical algebraic geometry techniques in conjunction with the random sample consensus (RANSAC) method. This is all developed and demonstrated in the setting of only FDOA measurements, without loss of generality. Additionally, the problem formulation as polynomial systems immediately provides lower bounds on the number of receivers or measurements required for the solution set to consist of only isolated points.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl

FDOA-based passive source localization: a geometric perspective

2018 Fall.Includes bibliographical references.We consider the problem of passively locating the source of a radio-frequency signal using observations by several sensors. Received signals can be compared to obtain time difference of arrival (TDOA) and frequency difference of arrival (FDOA) measurements. The geometric relationship satisfied by these measurements allow us to make inferences about the emitter's location. In this research, we choose to focus on the FDOA-based source localization problem. This problem has been less widely studied and is more difficult than solving for an emitter's location using TDOA measurements. When the FDOA-based source localization problem is formulated as a system of polynomials, the source's position is contained in the corresponding algebraic variety. This provides motivation for the use of methods from algebraic geometry, specifically numerical algebraic geometry (NAG), to solve for the emitter's location and gain insight into this system's interesting structure