Localization by Signals of Opportunity in the Absence of Transmitter Position

Localization of an object by signals of opportunity may not have the transmitter position and the synchronization with the transmitter. Additionally, a receiver may not be able to resolve the separate time delays of the line of sight signal from the transmitter and the back-scattered signal by the object, and it is only able to obtain the difference between the two. This paper investigates the use of such differential time delays (DTDs), one from each receiver by itself without the need of synchronization with the others, for positioning the object; and shows that localization is possible in absence of transmitter position. The performance is not necessarily worse than, and indeed can be better than, the TDOA approach that can operate without the transmitter position but dictates receiver synchronization. We then propose the use of both DTDs and TDOAs for improving the positioning accuracy and analyze the expected performance. Algebraic solutions are next derived for localization by DTDs, and by DTDs together with TDOAs. Theoretical study illustrates that the solutions attain the Cramer-Rao Lower Bound accuracy under the Gaussian noise model. A refinement step is also developed to extend the noise level for matching with the CRLB performance.