Node Localization in Unsynchronized Time of Arrival Sensor Networks

Abstract:
We present a method for solving the previously unstudied

problem of localizing a set of receivers and directions

from transmitters placed far from the receivers,

measuring unsynchronized time of arrival data. The

same problem is present in node localization of microphone

and antenna arrays. The solution algorithm using

5 receivers and 9 transmitters is extended to the

overdetermined case in a straightforward manner. Degenerate

cases are shown to be when i) the measurement

matrix has rank 4 or less or ii) the directions from

the transmitters to the receivers lie on an intersection

between the unit sphere and another quadric surface.

In simulated experiments we explore how sensitive the

solution is with respect to different degrees of far field

approximations of the transmitters and with respect to

noise in the data. Using real data we get a reconstruction

of the receivers with a relative error of 14%.