Optimal Sensor Placement for 3-D Time-of-Arrival Target Localization

• Published in: IEEE transactions on signal processing 2019-10, Vol.67 (19), p.5018-5031
• Main Authors: Xu, Sheng, Ou, Yongsheng, Wu, Xinyu
• Format: Article
• Language: English
• Subjects: 3D time-of-arrival (TOA) localization; A-optimality criterion; Cramer-Rao bounds; Cramér-Rao lower bound (CRLB); Elevation angle; Estimation; Fisher information; Fisher information matrix (FIM); Geometry; Localization; Lower bounds; Mathematical analysis; Noise; Noise measurement; optimal sensor placement; Optimality criteria; Optimization; Placement; Receivers; Robot sensing systems; Sensors; Three-dimensional displays; Two dimensional displays
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2019.2932872

This paper focuses on finding the optimal sensor placement strategies for circular time-of-arrival (TOA) localization in the three-dimensional (3D) space. The A-optimality criterion, minimizing the trace of the inverse Fisher information matrix (FIM), is applied to determine optimal sensor placements under the Gaussian measurement noise. A comprehensive analysis of optimal sensor-target geometries is provided in the general circumstance with no restriction on the number of sensors, sensor elevation angle and sensor-target range. The analysis is divided into two detailed sub-cases with uniform sensor measurement noise variance. The reachable minimum trace of Cramér-Rao lower bound (CRLB)=\frac{9\sigma ^2}{4N} is derived. Two new closed-form solutions, i.e., the resistor network and special solution methods, are developed to quickly determine the optimal geometries. Furthermore, the theoretical smallest tr(CRLB)=\frac{9}{4} (\sum _{i=1}^N\frac{1}{\sigma _{i}^{2}})^{-1} of using different noise variances is also presented. The analytical results are verified by simulation examples.