Semidefinite Relaxation for Source Localization with Quantized ToA Measurements and Transmission Uncertainty in Sensor Networks

Accurate location information is critical for many engineering applications (e.g., radar, sonar, autonomous robots, intelligent transportation systems). In traditional source localization algorithms, the perfect knowledge of noisy Time-of-Arrival (ToA) measurements are assumed to be obtained by the fusion center in a sensor network. This assumption is not practical for wireless sensor networks, especially for a resource-limited sensor network with stringent power and communication bandwidth constraints. In this paper, we propose a novel channel-aware source localization method based on quantized asynchronous ToA measurements, where the quantization errors as well as the imperfect communication link between each sensor and the fusion center are considered. The maximum-likelihood (ML) source localization by jointly estimating the signal transmission instant and source location is formulated. An efficient relaxation is provided to transform the non-convex ML optimization problem into a convex problem. The Cramér-Rao lower bounds (CRLBs) for the quantized ToA measurements with the uncertainty of data exchange are derived. Furthermore, a Fisher information based heuristic quantization scheme is proposed to design quantized thresholds for asynchronous ToA measurements. The simulation and experimental results demonstrate that our proposed method can yield an efficient estimate under different scenarios.