Open AccessClosed‐form formula of Cramer–Rao lower bound for 3D TOA target localisation
Author(s) -
Li YinYa,
Wang ChangCheng,
Qi GuoQing,
Sheng AnDong
Publication year - 2020
Publication title -
electronics letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.375
H-Index - 146
eISSN - 1350-911X
pISSN - 0013-5194
DOI - 10.1049/el.2019.2669
Subject(s) - cramér–rao bound , upper and lower bounds , time of arrival , singularity , metric (unit) , algorithm , fisher information , computer science , non line of sight propagation , gravitational singularity , mathematics , mathematical analysis , wireless , statistics , telecommunications , engineering , operations management
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.