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.