NDLI: Closed-form formula of Cramer–Rao lower bound for 3D TOA target localisation

Content Provider	IET Digital Library
Author	Li, Yin Ya Wang, Chang Cheng Qi, Guo Qing Sheng, An Dong
Abstract	This Letter focuses on the problem of analytically evaluating the performance metric using the Cramer–Rao lower bound (CRLB) for three-dimensional (3D) time-of-arrival (TOA) target localisation. The necessary and sufficient condition on the invertibility (non-singularity) of the Fisher information matrix (FIM) is presented, and then the existence of the CRLB is analysed. Two types of equivalent closed-form formulas of the CRLB are proposed, and any one of which can be adopted to analytically evaluate the best achievable accuracy of 3D TOA localisation. Moreover, three types of the worst sensor-target geometries described by the unit vectors of line-of-sight of TOA sensors are extensively illustrated, which will lead to a worse localisation accuracy or even result in singularities of the FIM and should be avoided in the deployment of 3D TOA sensors.
Starting Page	43
Ending Page	45
Page Count	3
ISSN	00135194
Volume Number	56
e-ISSN	1350911X
Issue Number	Issue 1, Jan (2020)
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/el/56/1
Alternate Webpage(s)	https://digital-library.theiet.org/content/journals/10.1049/el.2019.2669
Journal	Electronics Letters
Publisher Date	2019-10-25
Access Restriction	Open
Rights Holder	© The Institution of Engineering and Technology
Subject Keyword	3D TOA Localisation 3D TOA Target Localisation Algebra Combinatorial Mathematics Cramer-Rao Lower Bound CRLB Equivalent Closed-form Formulas Fisher Information Matrix Geometry Matrix Algebra Performance Metric Signal Processing And Detection Signal Processing Theory Time-of-arrival Estimation Time-of-arrival Target Localisation TOA Sonsor Worse Localisation Accuracy Worst Sensor-target Geometries
Content Type	Text
Resource Type	Article
Subject	Electrical and Electronic Engineering

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