AOA Sensor Placement for Anchor-Assisted Target Localization in GNSS-Denied Environment: Formulation, Bounds and Optimization

Target localization technology is widely applied in various applications, such as rescue missions, robot navigation, and the Internet of Things. However, in some scenarios, the positions of sensors are unknown due to the load limitation of the sensor carriers and environmental interferences, resulting in the instability of the global navigation satellite system (GNSS). This paper focuses on optimal angle-of-arrival (AOA) sensor placement using multiple position-unknown sensors for target localization accuracy improvement. To guarantee the uniqueness of the target coordinate, at least two anchors are needed. The anchors are some static benchmark objects in the environment with priori known positions. Firstly, a new optimization problem for AOA target localization accuracy improvement incorporating position-unknown sensors and anchors is formulated. Secondly, the optimal theoretical localization accuracies of the unknown sensors and target are derived by minimizing the trace of the Cramér-Rao lower bounds (CRLBs). Thirdly, a mixture optimization method, including a geometrical initialization and the new proposed simultaneous perturbation stochastic approximation and adaptive momentum estimation (SPSA-Adam) algebraic algorithm, is developed. Then, the correctness of the new theoretical findings and the effectiveness of the proposed sensor placement optimization method are verified by simulation examples.