Reduced Complexity Semidefinite Relaxation Algorithms for Source Localization Based on Time Difference of Arrival

We investigate the problem of source localization based on measuring time difference of signal arrivals (TDOA) from the source emitter. Taking into account the colored measurement noise, we adopt a min-max principle to develop two lower complexity semidefinite relaxation algorithms that can be reliably solved using semidefinite programming. The reduction of algorithm complexity is achieved through a simple, but effective method to select a reference node among participating measurement nodes such that only selective time differences of signal arrival are exploited. Our estimation methods are insensitive to the source locations and can be used either as the final location estimate or as the initial point for more traditional search algorithms.

1 Introduction

Wireless source localization has been a problem that maintains a considerable level of research interest because of its broad applications in areas such as target tracking, signal routing, interference mitigation, and emergency response, among others [2]. Source localization typically involves estimating the positions of signal emitters in a network of sensors that measure distinct source signal characteristics. Utilizing the collective signal measurements from the sensors, a data fusion center can generate the source location estimate. In practice, the various data fusing methods include time of arrival (TOA), time difference of arrival (TDOA), received signal strength (RSS), angle of arrival (AOA), and various combinations of these [3]. Similarly, an equivalent problem of sensor navigation involves a sensor trying to estimate its own location based on signals received from multiple (coordinated) emitters.