Optimal 3D Angle of Arrival Sensor Placement with Gaussian Priors

Sensor placement is an important factor that may significantly affect the localization performance of a sensor network. This paper investigates the sensor placement optimization problem in three-dimensional (3D) space for angle of arrival (AOA) target localization with Gaussian priors. We first show...

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Autores principales:	Rongyan Zhou, Jianfeng Chen, Weijie Tan, Qingli Yan, Chang Cai
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	3D angle of arrival (AOA) localization Cramér–Rao lower bound (CRLB) optimal sensor placement covariance matrix fisher information matrix (FIM) Science Q Astrophysics QB460-466 Physics QC1-999
Acceso en línea:	https://doaj.org/article/265cb0b53aa44b1b92b87653647db378
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id	oai:doaj.org-article:265cb0b53aa44b1b92b87653647db378
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spelling	oai:doaj.org-article:265cb0b53aa44b1b92b87653647db3782021-11-25T17:29:08ZOptimal 3D Angle of Arrival Sensor Placement with Gaussian Priors10.3390/e231113791099-4300https://doaj.org/article/265cb0b53aa44b1b92b87653647db3782021-10-01T00:00:00Zhttps://www.mdpi.com/1099-4300/23/11/1379https://doaj.org/toc/1099-4300Sensor placement is an important factor that may significantly affect the localization performance of a sensor network. This paper investigates the sensor placement optimization problem in three-dimensional (3D) space for angle of arrival (AOA) target localization with Gaussian priors. We first show that under the A-optimality criterion, the optimization problem can be transferred to be a diagonalizing process on the AOA-based Fisher information matrix (FIM). Secondly, we prove that the FIM follows the invariance property of the 3D rotation, and the Gaussian covariance matrix of the FIM can be diagonalized via 3D rotation. Based on this finding, an optimal sensor placement method using 3D rotation was created for when prior information exists as to the target location. Finally, several simulations were carried out to demonstrate the effectiveness of the proposed method. Compared with the existing methods, the mean squared error (MSE) of the maximum a posteriori (MAP) estimation using the proposed method is lower by at least <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>25</mn><mo>%</mo></mrow></semantics></math></inline-formula> when the number of sensors is between 3 and 6, while the estimation bias remains very close to zero (smaller than 0.15 m).Rongyan ZhouJianfeng ChenWeijie TanQingli YanChang CaiMDPI AGarticle3D angle of arrival (AOA) localizationCramér–Rao lower bound (CRLB)optimal sensor placementcovariance matrixfisher information matrix (FIM)ScienceQAstrophysicsQB460-466PhysicsQC1-999ENEntropy, Vol 23, Iss 1379, p 1379 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	3D angle of arrival (AOA) localization Cramér–Rao lower bound (CRLB) optimal sensor placement covariance matrix fisher information matrix (FIM) Science Q Astrophysics QB460-466 Physics QC1-999
spellingShingle	3D angle of arrival (AOA) localization Cramér–Rao lower bound (CRLB) optimal sensor placement covariance matrix fisher information matrix (FIM) Science Q Astrophysics QB460-466 Physics QC1-999 Rongyan Zhou Jianfeng Chen Weijie Tan Qingli Yan Chang Cai Optimal 3D Angle of Arrival Sensor Placement with Gaussian Priors
description	Sensor placement is an important factor that may significantly affect the localization performance of a sensor network. This paper investigates the sensor placement optimization problem in three-dimensional (3D) space for angle of arrival (AOA) target localization with Gaussian priors. We first show that under the A-optimality criterion, the optimization problem can be transferred to be a diagonalizing process on the AOA-based Fisher information matrix (FIM). Secondly, we prove that the FIM follows the invariance property of the 3D rotation, and the Gaussian covariance matrix of the FIM can be diagonalized via 3D rotation. Based on this finding, an optimal sensor placement method using 3D rotation was created for when prior information exists as to the target location. Finally, several simulations were carried out to demonstrate the effectiveness of the proposed method. Compared with the existing methods, the mean squared error (MSE) of the maximum a posteriori (MAP) estimation using the proposed method is lower by at least <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>25</mn><mo>%</mo></mrow></semantics></math></inline-formula> when the number of sensors is between 3 and 6, while the estimation bias remains very close to zero (smaller than 0.15 m).
format	article
author	Rongyan Zhou Jianfeng Chen Weijie Tan Qingli Yan Chang Cai
author_facet	Rongyan Zhou Jianfeng Chen Weijie Tan Qingli Yan Chang Cai
author_sort	Rongyan Zhou
title	Optimal 3D Angle of Arrival Sensor Placement with Gaussian Priors
title_short	Optimal 3D Angle of Arrival Sensor Placement with Gaussian Priors
title_full	Optimal 3D Angle of Arrival Sensor Placement with Gaussian Priors
title_fullStr	Optimal 3D Angle of Arrival Sensor Placement with Gaussian Priors
title_full_unstemmed	Optimal 3D Angle of Arrival Sensor Placement with Gaussian Priors
title_sort	optimal 3d angle of arrival sensor placement with gaussian priors
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/265cb0b53aa44b1b92b87653647db378
work_keys_str_mv	AT rongyanzhou optimal3dangleofarrivalsensorplacementwithgaussianpriors AT jianfengchen optimal3dangleofarrivalsensorplacementwithgaussianpriors AT weijietan optimal3dangleofarrivalsensorplacementwithgaussianpriors AT qingliyan optimal3dangleofarrivalsensorplacementwithgaussianpriors AT changcai optimal3dangleofarrivalsensorplacementwithgaussianpriors
_version_	1718412273538564096

Optimal 3D Angle of Arrival Sensor Placement with Gaussian Priors

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