期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 67, 期 19, 页码 5018-5031出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2019.2932872
关键词
3D time-of-arrival (TOA) localization; Cramer-Rao lower bound (CRLB); Fisher information matrix (FIM); A-optimality criterion; optimal sensor placement
资金
- National Natural Science Foundation of China [61803363, U1613210]
- Guangdong Special Support Program [2017TX04X265]
- Primary Research and Development Plan of Guangdong Province [2019B090915002]
- Shenzhen Fundamental Research Programs [JCYJ20170413165528221, JCYJ2016428154842603]
- China Postdoctoral Science Foundation [2018M643254]
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 Cramer-Rao lower bound (CRLB) = 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)= 9/4 (Sigma(N)(i=1) 1/sigma(2)(i))(-1) of using different noise variances is also presented. The analytical results are verified by simulation examples.
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