Hybrid DTD-AOA Multi-Object Localization in 3-D by Single Receiver Without Synchronization and Some Transmitter Positions: Solutions and Analysis

Abstract

This paper addresses the multi-object localization problem by using a hybrid of differential time delay (DTD) and angle-of-arrival (AOA) measurements collected by a single receiver in an unsynchronized multistatic localization system, where two kinds of transmitters, intentional transmitters at known positions and unintentional transmitters at unknown positions, are used for the illumination of the objects. By integrating the DTD and AOA measurements, we first derive a new set of transformed observation models relating to the object positions, and then investigate the three cases of intentional transmitters only, a mix of intentional and unintentional transmitters, and unintentional transmitters only. Localization for the first case is addressed by a linear weighted least squares (LWLS) estimator and the other two are solved by applying semidefinite relaxation followed with an LWLS estimator. Furthermore, we conduct a thorough theoretical analysis. It shows that incorporating unintentional transmitters at unknown positions is beneficial to improve the localization performance, and increasing the number of objects will also improve the positioning accuracy when unintentional transmitters are used. Additionally, a theoretical bias analysis is conducted, based on which a bias-subtracted solution is given. Both theoretical mean square error analysis and simulations validate well the good performance of the proposed methods.