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

Multichannel source separation and tracking with phase differences by random sample consensus

Blind audio source separation (BASS) is a fascinating problem that has been tackled from many different angles. The use case of interest in this thesis is that of multiple moving and simultaneously-active speakers in a reverberant room. This is a common situation, for example, in social gatherings. We human beings have the remarkable ability to focus attention on a particular speaker while effectively ignoring the rest. This is referred to as the ``cocktail party effect'' and has been the holy grail of source separation for many decades. Replicating this feat in real-time with a machine is the goal of BASS. Single-channel methods attempt to identify the individual speakers from a single recording. However, with the advent of hand-held consumer electronics, techniques based on microphone array processing are becoming increasingly popular. Multichannel methods record a sound field from various locations to incorporate spatial information. If the speakers move over time, we need an algorithm capable of tracking their positions in the room. For compact arrays with 1-10 cm of separation between the microphones, this can be accomplished by applying a temporal filter on estimates of the directions-of-arrival (DOA) of the speakers. In this thesis, we review recent work on BSS with inter-channel phase difference (IPD) features and provide extensions to the case of moving speakers. It is shown that IPD features compose a noisy circular-linear dataset. This data is clustered with the RANdom SAmple Consensus (RANSAC) algorithm in the presence of strong reverberation to simultaneously localize and separate speakers. The remarkable performance of RANSAC is due to its natural tendency to reject outliers. To handle the case of non-stationary speakers, a factorial wrapped Kalman filter (FWKF) and a factorial von Mises-Fisher particle filter (FvMFPF) are proposed that track source DOAs directly on the unit circle and unit sphere, respectively. These algorithms combine directional statistics, Bayesian filtering theory, and probabilistic data association techniques to track the speakers with mixtures of directional distributions