Optimal Sensor Placement for Source Tracking Under Synchronization Offsets and Sensor Location Errors with Distance-Dependent Noises

Abstract This paper focuses on the problem of source tracking in the 3-D space using a time-difference-of-arrival (TDOA)-based localization system. Different from existing studies, we consider a more realistic data model that includes synchronization offsets, sensor location errors and distance-dependent noises, which dramatically complicates source tracking with a TDOA-based localization system. Then, we address the optimal sensor placement under the restriction of geographical conditions and derive the closed-form determinant expression of the Fisher information matrix (FIM) with the minimum amount of the sensors, which forms the criterion for designing the optimal sensor configuration. Finally, combining with the maximum likelihood estimation (MLE), Kalman filtering and sensor motion strategy, we propose a source tracking scheme guided by the optimal sensor placement configuration. Mathematical analyses and numerical simulations validate the optimal sensor placement and efficiencies of the source tracking scheme.