Multiple-source ellipsoidal localization using acoustic energy measurements

Fanqin Meng; Xiaojing Shen; Zhiguo Wang; Haiqi Liu; Junfeng Wang; Yunmin Zhu; Pramod K. Varshney

doi:10.1016/j.automatica.2019.108737

Multiple-source ellipsoidal localization using acoustic energy measurements

Fanqin Meng, Xiaojing Shen, Zhiguo Wang, Haiqi Liu, Junfeng Wang, Yunmin Zhu, Pramod K. Varshney

Department of Electrical Engineering & Computer Science

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

In this paper, the multiple-source ellipsoidal localization problem based on acoustic energy measurements is investigated via set-membership estimation theory. When the probability density function of measurement noise is unknown-but-bounded, multiple-source localization is a difficult problem since not only the acoustic energy measurements are complicated nonlinear functions of multiple sources, but also the multiple sources bring about a high-dimensional state estimation problem. First, when the energy parameter and the position of the source are bounded in an interval and a ball respectively, the nonlinear remainder bound of the Taylor series expansion is obtained analytically on-line. Next, based on the separability of the nonlinear measurement function, an efficient estimation procedure is developed. It solves the multiple-source localization problem by using an alternating optimization iterative algorithm, in which the remainder bound needs to be known on-line. For this reason, we first derive the remainder bound analytically. When the energy decay factor is unknown but bounded, an efficient estimation procedure is developed based on interval mathematics. Finally, numerical examples demonstrate the effectiveness of the ellipsoidal localization algorithms for multiple-source localization. In particular, our results show that when the noise is non-Gaussian, the set-membership localization algorithm performs better than the EM localization algorithm.

Original language	English (US)
Article number	108737
Journal	Automatica
Volume	112
DOIs	https://doi.org/10.1016/j.automatica.2019.108737
State	Published - Feb 2020

Keywords

Acoustic energy measurements
Multiple-source localization
Nonlinear measurements
Set-membership estimation

ASJC Scopus subject areas

Control and Systems Engineering
Electrical and Electronic Engineering

Access to Document

10.1016/j.automatica.2019.108737

Cite this

@article{2756b679580949629b2d0d8a0fb13468,

title = "Multiple-source ellipsoidal localization using acoustic energy measurements",

abstract = "In this paper, the multiple-source ellipsoidal localization problem based on acoustic energy measurements is investigated via set-membership estimation theory. When the probability density function of measurement noise is unknown-but-bounded, multiple-source localization is a difficult problem since not only the acoustic energy measurements are complicated nonlinear functions of multiple sources, but also the multiple sources bring about a high-dimensional state estimation problem. First, when the energy parameter and the position of the source are bounded in an interval and a ball respectively, the nonlinear remainder bound of the Taylor series expansion is obtained analytically on-line. Next, based on the separability of the nonlinear measurement function, an efficient estimation procedure is developed. It solves the multiple-source localization problem by using an alternating optimization iterative algorithm, in which the remainder bound needs to be known on-line. For this reason, we first derive the remainder bound analytically. When the energy decay factor is unknown but bounded, an efficient estimation procedure is developed based on interval mathematics. Finally, numerical examples demonstrate the effectiveness of the ellipsoidal localization algorithms for multiple-source localization. In particular, our results show that when the noise is non-Gaussian, the set-membership localization algorithm performs better than the EM localization algorithm.",

keywords = "Acoustic energy measurements, Multiple-source localization, Nonlinear measurements, Set-membership estimation",

author = "Fanqin Meng and Xiaojing Shen and Zhiguo Wang and Haiqi Liu and Junfeng Wang and Yunmin Zhu and Varshney, {Pramod K.}",

note = "Funding Information: In this paper, we have proposed new multiple-source localization methods in the unknown-but-bounded noise setting. We employed set-membership estimation theory to determine a state estimation ellipsoid. The main difficulties are that the acoustic energy decay model is a complicated nonlinear function and the multiple-source localization problem is a high-dimensional state estimation problem. In our approach, the nonlinear function is linearized by the first-order Taylor series expansion with a remainder error. The bounding box of the remainder has been derived on-line based on the bounding set of the state. A point that should be stressed is that the remainder bounding box is obtained analytically when the energy parameter and the position of the source are bounded in an interval and a ball respectively. An efficient procedure has been developed to deal with the multiple-source localization problem by alternately estimating the parameters of each source while the parameters of the other sources remain fixed. When the energy decay factor is unknown but bounded, a new estimation procedure has been developed. Numerical examples have shown that when the PDF of measurement noise is non-Gaussian, the performance of the ellipsoidal localization algorithm is better than the ML method. Future work may include sensor management and sensor placement, Byzantines and mitigation techniques, for the multiple-source localization problem in wireless sensor networks. Fanqin Meng is currently working as a post-Doctor in School of Aeronautics and Astronautics, Sichuan University, Chengdu, Sichuan 610064, China, and with School of Automation and Information Engineering, Sichuan University of Science and Engineering, Yibin, Sichuan 644000, China. His research interests include information fusion, target tracking, localization, machine learning and convex optimization. Xiaojing Shen graduated from Sichuan University in 2003, obtained his M.S. at Jilin University in 2006 and his Ph.D. at Sichuan University in 2009. He is the recipient of the China National Excellent Doctoral Dissertation Award (the highest honor of Ph.D. degree). During 2009–2011, he worked as a post-Doctor and assistant professor in school of computer science, Sichuan University. Since 2013, he has been working as a professor in school of Mathematics, Sichuan University, Chengdu, China. He was with Syracuse University as a postdoctoral research associate during 2012–2013. His current research interests are in the fields of multisensor decision and estimation fusion, multitarget data association and tracking, optimization theory with applications to information fusion, statistical theory with applications to information fusion. He is one of the authors of two books—Networked Multisensor Decision and Estimation Fusion: Based on Advanced Mathematical Methods (CRC Press, 2012) and Nonlinear Estimation and Applications to Industrial Systems Control (G. Rigatos, ed., ch. 3, pp. 61–88, Nova Science, 2012). He has also served as a cooperator to several major research institutes. Zhiguo Wang received the Ph.D. degree from Sichuan University, Chengdu, China, in 2018. He is currently working as a post-Doctor in school of science and engineering, The Chinese University of Hong Kong, Shenzhen, and Department of Electronic Engineering & Information Science, University of Science & Technology of China, Hefei, Anhui 230026, China. His research interests are in the fields of information fusion, target tracking, signal and data processing, machine learning, nonconvex optimization, and analysis and control of uncertain systems. Haiqi Liu is currently working as a Doctor candidate in school of Mathematics, Sichuan University, Chengdu, China. His research interests are in the fields of information fusion, target tracking, signal and data processing, machine learning, optimization, and analysis and control of uncertain systems. Junfeng Wang received the M.S. degree in computer application technology from the Chongqing University of Posts and Telecommunications, Chongqing, in 2001, and the Ph.D. degree in computer science from the University of Electronic Science and Technology of China, Chengdu, in 2004. From 2004 to 2006, he held a postdoctoral position with the Institute of Software, Chinese Academy of Sciences. Since 2006, he has been with the School of Aeronautics and Astronautics, College of Computer Science, Sichuan University, as a Professor. His current research interests include network and information security, spatial information networks, and data mining. He has been invited to serve as an Associate Editors for the IEEE ACCESS, the IEEE INTERNET OF THINGS JOURNAL, and Security and Communication Networks . Yunmin Zhu received the B.S. degree from the Department of Mathematics and Mechanics, Beijing University, Beijing, China, in 1968. From 1968 to 1978, he was with Luoyang Tractor Factory, Luoyang, Henan, China, as a steel worker and a machine engineer. From 1981 to 1994, he was with Institute of Mathematical Sciences, Chengdu Institute of Computer Applications, Chengdu Branch, Academia Sinica. Since 1995 he has been with Department of Mathematics, Sichuan University as a Professor. From 1986 to 1987, 1989–1990, 1993–1996, 1998–1999, 2001–2002, he was a Visiting Associate or Visiting Professor, at the Lefschetz Centre for Dynamical Systems and Division of Applied Mathematics, Brown University; Department of Electrical Engineering, McGill University; Communications Research Laboratory, McMaster University; and the Department of Electrical Engineering, University of New Orleans. He is the author or coauthor of over 80 papers in international and Chinese journals. He is the author of Multisensor Decision and Estimation Fusion (Kluwer Academic Publishers, 2002), Networked Multisensor Decision and Estimation Fusion: Based on Advanced Mathematical Methods (CRC Press, 2012), and Multisensor Distributed Statistical Decision (Science Press, Chinese Academy of Science, Beijing, 2000), and coauthor of Stochastic Approximations (Shanghai Scientific & Technical Publishers, 1996). He is on the editorial boards of the Journal of Systems Science and Complexity and Systems Science and Mathematics. His research interests include stochastic approximations, adaptive filtering, other stochastic recursive algorithms and their applications in estimations, optimizations, and decisions for dynamic system as well as for signal processing, information compression. In particular, his present major interest is multisensor distributed estimation and decision fusion. Pramod. K. Varshney was born in Allahabad, India, on July 1, 1952. He received the B.S. degree in electrical engineering and computer science (with highest honors), and the M.S. and Ph.D. degrees in electrical engineering from the University of Illinois at Urbana–Champaign in 1972, 1974, and 1976 respectively. During 1972–1976, he held teaching and research assistantships at the University of Illinois. Since 1976, he has been with Syracuse University, Syracuse, NY, where he is currently a Distinguished Professor of Electrical Engineering and Computer Science and the Director of CASE: Center for Advanced Systems and Engineering. He served as the Associate Chair of the department during 1993–1996. He is also an Adjunct Professor of Radiology at Upstate Medical University, Syracuse. His current research interests are in distributed sensor networks and data fusion, detection and estimation theory, wireless communications, image processing, radar signal processing and remote sensing. He has published extensively. He is the author of Distributed Detection and Data Fusion (New York: Springer-Verlag, 1997). He has also served as a consultant to several major companies. Dr. Varshney was a James Scholar, a Bronze Tablet Senior, and a Fellow while at the University of Illinois. He is a member of Tau Beta Pi and is the recipient of the 1981 ASEE Dow Outstanding Young Faculty Award. He was elected to the grade of Fellow of the IEEE in 1997 for his contributions in the area of distributed detection and data fusion. He was the Guest editor of the Special Issue on Data Fusion of the PROCEEDINGS OF THE IEEE, January 1997. In 2000, he received the Third Millennium Medal from the IEEE and Chancellor{\textquoteright}s Citation for exceptional academic achievement at Syracuse University. He is the recipient of the IEEE 2012 Judith A. Resnik Award. He is on the editorial board of the Journal on Advances in Information Fusion. He was the President of International Society of Information Fusion during 2001. Funding Information: This work was supported in part by the NSFC No. 61673282, U1836103 and the PCSIRT16R53. The material in this paper was presented at the 20th International Conference on Information Fusion (Fusion 2017), July 10?13, 2017, Xi'an, China. This paper was recommended for publication in revised form by Associate Editor Erik Weyer under the direction of Editor Torsten S?derstr?m Publisher Copyright: {\textcopyright} 2019 Elsevier Ltd",

year = "2020",

month = feb,

doi = "10.1016/j.automatica.2019.108737",

language = "English (US)",

volume = "112",

journal = "Automatica",

issn = "0005-1098",

publisher = "Elsevier",

}

TY - JOUR

T1 - Multiple-source ellipsoidal localization using acoustic energy measurements

AU - Meng, Fanqin

AU - Shen, Xiaojing

AU - Wang, Zhiguo

AU - Liu, Haiqi

AU - Wang, Junfeng

AU - Zhu, Yunmin

AU - Varshney, Pramod K.

N1 - Funding Information: In this paper, we have proposed new multiple-source localization methods in the unknown-but-bounded noise setting. We employed set-membership estimation theory to determine a state estimation ellipsoid. The main difficulties are that the acoustic energy decay model is a complicated nonlinear function and the multiple-source localization problem is a high-dimensional state estimation problem. In our approach, the nonlinear function is linearized by the first-order Taylor series expansion with a remainder error. The bounding box of the remainder has been derived on-line based on the bounding set of the state. A point that should be stressed is that the remainder bounding box is obtained analytically when the energy parameter and the position of the source are bounded in an interval and a ball respectively. An efficient procedure has been developed to deal with the multiple-source localization problem by alternately estimating the parameters of each source while the parameters of the other sources remain fixed. When the energy decay factor is unknown but bounded, a new estimation procedure has been developed. Numerical examples have shown that when the PDF of measurement noise is non-Gaussian, the performance of the ellipsoidal localization algorithm is better than the ML method. Future work may include sensor management and sensor placement, Byzantines and mitigation techniques, for the multiple-source localization problem in wireless sensor networks. Fanqin Meng is currently working as a post-Doctor in School of Aeronautics and Astronautics, Sichuan University, Chengdu, Sichuan 610064, China, and with School of Automation and Information Engineering, Sichuan University of Science and Engineering, Yibin, Sichuan 644000, China. His research interests include information fusion, target tracking, localization, machine learning and convex optimization. Xiaojing Shen graduated from Sichuan University in 2003, obtained his M.S. at Jilin University in 2006 and his Ph.D. at Sichuan University in 2009. He is the recipient of the China National Excellent Doctoral Dissertation Award (the highest honor of Ph.D. degree). During 2009–2011, he worked as a post-Doctor and assistant professor in school of computer science, Sichuan University. Since 2013, he has been working as a professor in school of Mathematics, Sichuan University, Chengdu, China. He was with Syracuse University as a postdoctoral research associate during 2012–2013. His current research interests are in the fields of multisensor decision and estimation fusion, multitarget data association and tracking, optimization theory with applications to information fusion, statistical theory with applications to information fusion. He is one of the authors of two books—Networked Multisensor Decision and Estimation Fusion: Based on Advanced Mathematical Methods (CRC Press, 2012) and Nonlinear Estimation and Applications to Industrial Systems Control (G. Rigatos, ed., ch. 3, pp. 61–88, Nova Science, 2012). He has also served as a cooperator to several major research institutes. Zhiguo Wang received the Ph.D. degree from Sichuan University, Chengdu, China, in 2018. He is currently working as a post-Doctor in school of science and engineering, The Chinese University of Hong Kong, Shenzhen, and Department of Electronic Engineering & Information Science, University of Science & Technology of China, Hefei, Anhui 230026, China. His research interests are in the fields of information fusion, target tracking, signal and data processing, machine learning, nonconvex optimization, and analysis and control of uncertain systems. Haiqi Liu is currently working as a Doctor candidate in school of Mathematics, Sichuan University, Chengdu, China. His research interests are in the fields of information fusion, target tracking, signal and data processing, machine learning, optimization, and analysis and control of uncertain systems. Junfeng Wang received the M.S. degree in computer application technology from the Chongqing University of Posts and Telecommunications, Chongqing, in 2001, and the Ph.D. degree in computer science from the University of Electronic Science and Technology of China, Chengdu, in 2004. From 2004 to 2006, he held a postdoctoral position with the Institute of Software, Chinese Academy of Sciences. Since 2006, he has been with the School of Aeronautics and Astronautics, College of Computer Science, Sichuan University, as a Professor. His current research interests include network and information security, spatial information networks, and data mining. He has been invited to serve as an Associate Editors for the IEEE ACCESS, the IEEE INTERNET OF THINGS JOURNAL, and Security and Communication Networks . Yunmin Zhu received the B.S. degree from the Department of Mathematics and Mechanics, Beijing University, Beijing, China, in 1968. From 1968 to 1978, he was with Luoyang Tractor Factory, Luoyang, Henan, China, as a steel worker and a machine engineer. From 1981 to 1994, he was with Institute of Mathematical Sciences, Chengdu Institute of Computer Applications, Chengdu Branch, Academia Sinica. Since 1995 he has been with Department of Mathematics, Sichuan University as a Professor. From 1986 to 1987, 1989–1990, 1993–1996, 1998–1999, 2001–2002, he was a Visiting Associate or Visiting Professor, at the Lefschetz Centre for Dynamical Systems and Division of Applied Mathematics, Brown University; Department of Electrical Engineering, McGill University; Communications Research Laboratory, McMaster University; and the Department of Electrical Engineering, University of New Orleans. He is the author or coauthor of over 80 papers in international and Chinese journals. He is the author of Multisensor Decision and Estimation Fusion (Kluwer Academic Publishers, 2002), Networked Multisensor Decision and Estimation Fusion: Based on Advanced Mathematical Methods (CRC Press, 2012), and Multisensor Distributed Statistical Decision (Science Press, Chinese Academy of Science, Beijing, 2000), and coauthor of Stochastic Approximations (Shanghai Scientific & Technical Publishers, 1996). He is on the editorial boards of the Journal of Systems Science and Complexity and Systems Science and Mathematics. His research interests include stochastic approximations, adaptive filtering, other stochastic recursive algorithms and their applications in estimations, optimizations, and decisions for dynamic system as well as for signal processing, information compression. In particular, his present major interest is multisensor distributed estimation and decision fusion. Pramod. K. Varshney was born in Allahabad, India, on July 1, 1952. He received the B.S. degree in electrical engineering and computer science (with highest honors), and the M.S. and Ph.D. degrees in electrical engineering from the University of Illinois at Urbana–Champaign in 1972, 1974, and 1976 respectively. During 1972–1976, he held teaching and research assistantships at the University of Illinois. Since 1976, he has been with Syracuse University, Syracuse, NY, where he is currently a Distinguished Professor of Electrical Engineering and Computer Science and the Director of CASE: Center for Advanced Systems and Engineering. He served as the Associate Chair of the department during 1993–1996. He is also an Adjunct Professor of Radiology at Upstate Medical University, Syracuse. His current research interests are in distributed sensor networks and data fusion, detection and estimation theory, wireless communications, image processing, radar signal processing and remote sensing. He has published extensively. He is the author of Distributed Detection and Data Fusion (New York: Springer-Verlag, 1997). He has also served as a consultant to several major companies. Dr. Varshney was a James Scholar, a Bronze Tablet Senior, and a Fellow while at the University of Illinois. He is a member of Tau Beta Pi and is the recipient of the 1981 ASEE Dow Outstanding Young Faculty Award. He was elected to the grade of Fellow of the IEEE in 1997 for his contributions in the area of distributed detection and data fusion. He was the Guest editor of the Special Issue on Data Fusion of the PROCEEDINGS OF THE IEEE, January 1997. In 2000, he received the Third Millennium Medal from the IEEE and Chancellor’s Citation for exceptional academic achievement at Syracuse University. He is the recipient of the IEEE 2012 Judith A. Resnik Award. He is on the editorial board of the Journal on Advances in Information Fusion. He was the President of International Society of Information Fusion during 2001. Funding Information: This work was supported in part by the NSFC No. 61673282, U1836103 and the PCSIRT16R53. The material in this paper was presented at the 20th International Conference on Information Fusion (Fusion 2017), July 10?13, 2017, Xi'an, China. This paper was recommended for publication in revised form by Associate Editor Erik Weyer under the direction of Editor Torsten S?derstr?m Publisher Copyright: © 2019 Elsevier Ltd

PY - 2020/2

Y1 - 2020/2

N2 - In this paper, the multiple-source ellipsoidal localization problem based on acoustic energy measurements is investigated via set-membership estimation theory. When the probability density function of measurement noise is unknown-but-bounded, multiple-source localization is a difficult problem since not only the acoustic energy measurements are complicated nonlinear functions of multiple sources, but also the multiple sources bring about a high-dimensional state estimation problem. First, when the energy parameter and the position of the source are bounded in an interval and a ball respectively, the nonlinear remainder bound of the Taylor series expansion is obtained analytically on-line. Next, based on the separability of the nonlinear measurement function, an efficient estimation procedure is developed. It solves the multiple-source localization problem by using an alternating optimization iterative algorithm, in which the remainder bound needs to be known on-line. For this reason, we first derive the remainder bound analytically. When the energy decay factor is unknown but bounded, an efficient estimation procedure is developed based on interval mathematics. Finally, numerical examples demonstrate the effectiveness of the ellipsoidal localization algorithms for multiple-source localization. In particular, our results show that when the noise is non-Gaussian, the set-membership localization algorithm performs better than the EM localization algorithm.

AB - In this paper, the multiple-source ellipsoidal localization problem based on acoustic energy measurements is investigated via set-membership estimation theory. When the probability density function of measurement noise is unknown-but-bounded, multiple-source localization is a difficult problem since not only the acoustic energy measurements are complicated nonlinear functions of multiple sources, but also the multiple sources bring about a high-dimensional state estimation problem. First, when the energy parameter and the position of the source are bounded in an interval and a ball respectively, the nonlinear remainder bound of the Taylor series expansion is obtained analytically on-line. Next, based on the separability of the nonlinear measurement function, an efficient estimation procedure is developed. It solves the multiple-source localization problem by using an alternating optimization iterative algorithm, in which the remainder bound needs to be known on-line. For this reason, we first derive the remainder bound analytically. When the energy decay factor is unknown but bounded, an efficient estimation procedure is developed based on interval mathematics. Finally, numerical examples demonstrate the effectiveness of the ellipsoidal localization algorithms for multiple-source localization. In particular, our results show that when the noise is non-Gaussian, the set-membership localization algorithm performs better than the EM localization algorithm.

KW - Acoustic energy measurements

KW - Multiple-source localization

KW - Nonlinear measurements

KW - Set-membership estimation

UR - http://www.scopus.com/inward/record.url?scp=85075801277&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85075801277&partnerID=8YFLogxK

U2 - 10.1016/j.automatica.2019.108737

DO - 10.1016/j.automatica.2019.108737

M3 - Article

AN - SCOPUS:85075801277

SN - 0005-1098

VL - 112

JO - Automatica

JF - Automatica

M1 - 108737

ER -

Multiple-source ellipsoidal localization using acoustic energy measurements

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