Time-of-Arrival Simultaneous Sensor and Target Localization With Dynamic Optimal Sensor Placements

This paper focuses on optimizing the performance of simultaneous sensor and target localization (SSTL) using multiple mobile monostatic sensors. It leverages time-of-arrival (TOA) measurements received from the target, as well as from passive anchors located at known positions and the sensors themselves. The sensor positions are not known due to the limited accessibility of the global positioning system (GPS) in challenging environments. Firstly, we formulate the SSTL problem and conclude from the feasibility study the necessity of the presence of position-known anchors. Besides, the minimal number of sensors and anchors are derived to ensure a unique SSTL solution. Secondly, the positive effect of having the inter-sensor TOA measurements on the localization accuracy is analyzed. Thirdly, to break through the performance limit of the SSTL problem, an optimization problem is formulated based on the A-optimality criterion to minimize the estimation error lower bound with respect to the sensor positions. Fourthly, to tackle the proposed sensor placement problem to achieve better performance of SSTL, a fast convergence optimization algorithm, namely SPSA-Adam*, is developed by utilizing the simultaneous perturbation stochastic approximation (SPSA) and adaptive momentum estimation (Adam). An in-depth discussion of the proposed sensor placement optimization method is made. Furthermore, a comprehensive localization system for practical applications is established. Simulation examples demonstrate the effectiveness of the proposed methods and the correctness of the developments.