基于移动锚节点的无线传感器网络定位技术研究
|
摘要
无线传感器网络(Wireless Sensor Networks, WSN)通过引入网络技术使具有数据采集能力、信息处理能力和无线通信能力的传感器节点不再是单个的感知单元,而是能够交换信息、协调控制的有机结合体。无线传感器网络已成为一种全新的信息获取、处理、传输和控制系统,并在军事、工业、商业、医疗、环境监测等领域有着广阔应用前景。无线传感器网络广泛应用在环境恶劣、不可到达区域,实现监测与跟踪任务。在这些应用中,节点的位置信息起到很重要的作用,因此,对节点自身定位方法的研究具有重要的理论意义和极强的实用价值。本文在详细分析现有定位算法的基础上,重点对基于移动锚节点的无线传感器网络节点定位算法和移动锚节点路径规划方法进行了研究。
首先,在查阅大量相关文献的基础上,本文综述了无线传感器网络技术在国内外的研究现状,介绍了无线传感器网络定位计算方法和定位算法分类方法,并详细分析了近年来该领域具有代表性的算法和研究成果。
其次,考虑到无线传感器网络中的节点是随机部署在二维空间内的特定应用环境中,移动锚节点利用周围节点信息进行动态路径规划是一个重要研究方向。本文针对静态路径规划缺少灵活性的缺点,提出了一种禁忌搜索动态路径规划方法,通过仿真分析验证了该方法在节点非均匀分布情况下的有效性。
然后,研究分析了基于半定规划的定位模型,仿真分析了该研究领域内主要算法的定位性能。针对集中式半定规划定位算法存在计算复杂度大的问题,本文重点探讨了一种基于多功率移动锚节点的分布式半定规划定位算法,仿真结果表明该算法可以大大减小算法的计算复杂度。
最后,通过分析研究近年来移动锚节点辅助定位领域内的研究成果,本文提出了一种基于移动锚节点结合正三角形路径的多坐标系定位算法,结合正三角形路径,该算法可以取得很好的定位性能。在研究一种分布式移动锚节点辅助定位算法的基础上,针对该算法存在依赖直线移动路径的缺点,结合动态路径规划,提出了一种改进的分布式多功率移动锚节点辅助定位算法。仿真结果表明,改进算法在网络节点非均匀分布和网络区域存在障碍物的情况下可以取得比原算法更好的定位性能。
The application of network technology has made wireless sensor networks (WSN) node which is consisted of sensing, data processing, and communicaiting components not only to be a sensor unit, but also to be a combination unit which can exchange information, collaborate and control. As a new information acquisition and process platform, Wireless sensor networks possess wide application prospects in military, industry, medical treatment, environment monitoring and other fields. Wireless sensor networks have widely used in the areas of poor conditions, to achieve the monitoring and tracking tasks. In these applications, the location of nodes play an important role in wireless sensor networks. Therefore, the study of node location method has important theoretical and practical value. This thesis focuses on the study of localization algorithm and path planning of the mobile anchor for wireless sensor networks based on the analysis of related literatures.
First of all, the research status of wireless location techniques for wireless sensor networks at home and abroad are summarized based on the analysis of a lot of related literatures. The classification methods of localization systems and algorithms for wireless sensor networks are introduced and the principles and characteristics of recent representative localization algorithms are analyzed and discussed.
Secondly, as sensor nodes are randomly deployed in two-dimensional applications, in the localization algorithm with a mobile beacon, how to choose the appropriate beacon trajectory is very important. At present relatively little research has been made. In this paper, a new dynamic path planning method is proposed. When mobile anchor nodes receive messages sent from neighbor nodes, the path that the mobile anchor should travel along is determined according to the information of neighbor nodes based on this search algorithm.
Then, several semi-definite programming relaxation models are analyzed, the advantages and the disadvantages of several location algorithms in these fields are researched based on the simulation. Focus on the computation costs of semi-definite programming, in this thesis a new convex position estimation algorithm is studied. In this algorithm, a mobile anchor broadcasts packets with multi-power level on its trajectory. Simulation results show that this algorithm can greatly reduce the computational complexity and also perform well.
Finally, a new distributed multi-coordinate localization algorithm using multi-power mobile anchors is proposed based on the study of a lot of recent representative localization algorithms. The algorithm can achieve very good positioning performance when it using triangle path. Based on the study of a distributed mobile anchor localization algorithm, aim at the defect of node beeline movement and using dynamic path planning method, a improved localization algorithm is proposed for the case of nodes non-uniform distribution. The simulation results show that this improved algorithm can obtain higher localization precision compared with the original algorithm in the network environments where the sensor nodes are non-uniform deployed and obstacles still occur in the area.
首先,在查阅大量相关文献的基础上,本文综述了无线传感器网络技术在国内外的研究现状,介绍了无线传感器网络定位计算方法和定位算法分类方法,并详细分析了近年来该领域具有代表性的算法和研究成果。
其次,考虑到无线传感器网络中的节点是随机部署在二维空间内的特定应用环境中,移动锚节点利用周围节点信息进行动态路径规划是一个重要研究方向。本文针对静态路径规划缺少灵活性的缺点,提出了一种禁忌搜索动态路径规划方法,通过仿真分析验证了该方法在节点非均匀分布情况下的有效性。
然后,研究分析了基于半定规划的定位模型,仿真分析了该研究领域内主要算法的定位性能。针对集中式半定规划定位算法存在计算复杂度大的问题,本文重点探讨了一种基于多功率移动锚节点的分布式半定规划定位算法,仿真结果表明该算法可以大大减小算法的计算复杂度。
最后,通过分析研究近年来移动锚节点辅助定位领域内的研究成果,本文提出了一种基于移动锚节点结合正三角形路径的多坐标系定位算法,结合正三角形路径,该算法可以取得很好的定位性能。在研究一种分布式移动锚节点辅助定位算法的基础上,针对该算法存在依赖直线移动路径的缺点,结合动态路径规划,提出了一种改进的分布式多功率移动锚节点辅助定位算法。仿真结果表明,改进算法在网络节点非均匀分布和网络区域存在障碍物的情况下可以取得比原算法更好的定位性能。
The application of network technology has made wireless sensor networks (WSN) node which is consisted of sensing, data processing, and communicaiting components not only to be a sensor unit, but also to be a combination unit which can exchange information, collaborate and control. As a new information acquisition and process platform, Wireless sensor networks possess wide application prospects in military, industry, medical treatment, environment monitoring and other fields. Wireless sensor networks have widely used in the areas of poor conditions, to achieve the monitoring and tracking tasks. In these applications, the location of nodes play an important role in wireless sensor networks. Therefore, the study of node location method has important theoretical and practical value. This thesis focuses on the study of localization algorithm and path planning of the mobile anchor for wireless sensor networks based on the analysis of related literatures.
First of all, the research status of wireless location techniques for wireless sensor networks at home and abroad are summarized based on the analysis of a lot of related literatures. The classification methods of localization systems and algorithms for wireless sensor networks are introduced and the principles and characteristics of recent representative localization algorithms are analyzed and discussed.
Secondly, as sensor nodes are randomly deployed in two-dimensional applications, in the localization algorithm with a mobile beacon, how to choose the appropriate beacon trajectory is very important. At present relatively little research has been made. In this paper, a new dynamic path planning method is proposed. When mobile anchor nodes receive messages sent from neighbor nodes, the path that the mobile anchor should travel along is determined according to the information of neighbor nodes based on this search algorithm.
Then, several semi-definite programming relaxation models are analyzed, the advantages and the disadvantages of several location algorithms in these fields are researched based on the simulation. Focus on the computation costs of semi-definite programming, in this thesis a new convex position estimation algorithm is studied. In this algorithm, a mobile anchor broadcasts packets with multi-power level on its trajectory. Simulation results show that this algorithm can greatly reduce the computational complexity and also perform well.
Finally, a new distributed multi-coordinate localization algorithm using multi-power mobile anchors is proposed based on the study of a lot of recent representative localization algorithms. The algorithm can achieve very good positioning performance when it using triangle path. Based on the study of a distributed mobile anchor localization algorithm, aim at the defect of node beeline movement and using dynamic path planning method, a improved localization algorithm is proposed for the case of nodes non-uniform distribution. The simulation results show that this improved algorithm can obtain higher localization precision compared with the original algorithm in the network environments where the sensor nodes are non-uniform deployed and obstacles still occur in the area.
引文
[1]孙利民等.无线传感器网络.清华大学出版社,2005
[2]王殊等.无线传感器网络的理论及应用.北京航空航天大学出版社,2007
[3]Byrne J A.21 ideas for 21st Century[J]. Business Week.1999,8:78-167
[4]Wade R, Mitehel W M, Petter F. Ten Emerging Technologies that will Change the Word[J]. Technology Review.2003,106(1):33-49
[5]朱红松,孙利民.无线传感器网络技术发展现状.中兴通讯技术.2009,第15卷,第5期
[6]HU L and EVANS D. Localization for mobile sensor networks. Tenth International Conference on Mobile Computing and Networking, Philadelphia, Pennsylvania, USA, 2004.2004:45-57
[7]BAGGIO A, LANGENDOEN K. Monte-Carlo localization for mobile wireless sensor networks. Second International Conference on Mobile Ad-hoc and Sensor Networks, Hong Kong,2006, December.2006:718-733
[8]P. ZHAN, M. MARTONOSI. LOCALE:Collaborative Localization Estimation for Sparse Mobile Sensor Networks. International Conference on Information Processing in Sensor Networks (IPSN 2008), April,2008
[9]Guoqiang Mao, B. Fidan, Brian D.O. Anderso. Wireless sensor network localization techniques. Computer Networks,2007, val.51(10):2529-2553
[10]Sichitiu M L, Ramadurai V. Localization of wireless sensor networks with a mobile beacon. In:Proc. of the 2004 IEEE International Conference on Mobile Ad-Hoc and Sensor Systems,2004. Fort Lauderdale,2004:174-183
[11]K Kim, W Lee. MBAL:A mobile beacon-assisted localization scheme for wireless sensor networks. Proceeding of the 16th International Conference on Computer Communications and Networks, Hawaii,2007. IEEE Society Communications,2007:57-62
[12]任丽婕,无线传感器网络中节点部署和优化算法研究.中国海洋大学硕士毕业论文.2009.6
[13]Zhang L, Cheng Q, Wang Y and Zeadally S. A novel high performance distributed sensor positioning system. Wireless And Mobile Computing, Networking And Communications, 2005. Vol.3:430-437
[14]Weiwei Hu, Huibin Qin, Haiyun Huang. A Mobile Beacon Based Method for Wireless Sensor Networks Localization.11th IEEE International Conference on Communication Technology Proceedings,2008:144-147
[15]Melike Erol, Luiz F. M.Vieira, Antonio Caruso, etl. Multi Stage Underwater Sensor Localization using Mobile Beacons. SENSORCOMM 2008, Cap. Esterel, France, August 2008
[16]Azzedine Boukerche, Horacio A.B.F. Oliveira, Eduardo F. Nakamura, etl. Localization in Time and Space for Wireless Sensor Networks:A Mobile Beacon Approach.2008 IEEE international symposium on a world of wireless, mobile and multimedia networks,2008: 1-8
[17]Z.J XIA, C.J CHEN. A localization scheme with mobile beacon for wireless sensor networks. Proceeding of the 6th International Conference on ITS Telecommunications, Chengdu,2006:1017-1020
[18]E. Guerrero, H. G. Xiong, Q. Gao, G. Cova, R. Ricardo and J. Estevez. ADAL:A Distributed Range-Free Localization Algorithm Based on a Mobile Beacon for Wireless Sensor Networks.. ICUMT'09. Ultra Modern Telecommunications & Workshops,2009:1-7
[19]GUO Z, GUO Y, HONG F, etc. Perpendicular Intersection:Locating Wireless Sensors with Mobile Beacon. Proceeding of the 2008 Real-Time Systems Symposium.2008:93-102
[20]Kuo-Feng Ssu, Chia-Ho Ou, Jiau,.H C. Localization With Mobile Anchor Points in Wireless Sensor Networks. IEEE transactions on vehicular technology.2005,5 (3)
[21]Ganggang Yu, Fengqi Yul and Lei Feng. A Localization Algorithm Using a Mobile Anchor Node Under Wireless Channel.2007 IEEE International Conference on Robotics and Biomimetics, December,15-18,2007, Sanya, china.2007:1104-1108
[22]Baoli Zhang and Fengqi Yu. An Energy Efficient Localization Algorithm for Wireless Sensor Networks Using a Mobile Anchor Node. Proceedings of the 2008 IEEE International Conference on Information and Automation, Zhangjiajie, China,2008: 215-219
[23]Ganggang Yu, Fengqi yu, Lei feng. A Three Dimensional Localization Algorithm Using a Mobile Anchor Node under Wireless Channel. IEEE World Congress on Computational Intelligence,2008:477-483
[24]Bin Xiao, Hekang Chen, and Shuigeng Zhou. Distributed Localization Using a Moving Beacon in Wireless Sensor Networks. IEEE transactions on parallel and distributed systems.2008, VOL.19, NO.5
[25]Galstyan, B. Krishnamachari, K. Lerman and S. Pattern. Distributed Online Localization in Sensor Networks Using a Moving Target. Proc. Third Int'l Symp. Information Processing in Sensor Networks (IPSN'04),2004:61-70,2004
[26]张正勇,孙智,王刚等.基于移动信标节点的无线传感器网络节点定位.清华大学学报(自然科学版).2007,47(4)：534-537
[27]Ranjeet Kumar Patro. localization in wireless sensor network with mobile beacons. Electrical and Electronics Engineers in Israel,2004:22-24
[28]Sichitiu M L, Ramadurai V. Localization of wireless sensor networks with a mobile beacon. Proc of MASS.Piscataway, NJ:IEEE,2004:174-183
[29]Koutsonilas D, Das S M, Hu Y Charlie. Path planning of mobile landmarks for localization in wireless sensor networks. Computer Communication.2007,30(13): 2577-2592
[30]Rui Huang, Zaruba Gergely V. Static path planning for mobile beacons to localize sensor networks. Proc of IEEE PerComW. Piscataway, NJ:IEEE,2007:323-330
[31]Jacques M.,Bahi Abdallah Makhoul. A Mobile Beacon Based Approach for Sensor Network Localization. WiMobIEEE Computer Society,2007:44
[32]Hongjun Li, Jianwen Wang, Xun Li and Hongxu Ma. Real-time Path Planning of Mobile Anchor Node in Localization for Wireless Sensor Networks. Proceedings of the 2008 IEEE International Conference on Information and Automation, Zhangjiajie,China, June,20-23,2008
[33]Glover F. Tabu search-Part Ⅰ. ORSA Journal on Computing.1989,1(3):190-206
[34]Glover F. Tabu search-Part Ⅱ. ORSA Journal on Computing.1989,2(1):4-32
[35]王建新,李健,朱贤曼.MANET中节点的运动模型和性能分析.计算机工程.2006,32(19)：125-130
[36]Camp T, Boleng J, Davies V. A Survey of Mobility Models for Ad Hoc Network Research. Wireless Communication& Mobile Computing:Special issue on Mobile Ad Hoc Networking:Research, Trends and Applications,2002,2(5):483-502
[37]L. Doherty, L.E. Ghaoui, and S.J. Pister. Convex position estimation in wireless sensor networks. IEEE Infocom.2001,3:1655-1663
[38]S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM,1994
[39]P.Biswas and Y. Ye. Semidefinite Programming for Ad Hoc Wireless Sensor Network Localization. IEEE Conf.on Information Processing in Sensor Networks. April,2004: 46-54
[40]P.Biswas, Y.Ye. A distributed method for solving semidefinite programming arising from ad hoc wireless sensor network localization. Tchnical report, Dept of Management Science and Engineering, stanford university,2006
[41]So and Y. Ye. Theory of semidefinite programming for sensor network localization. Mathematical Programming, published online, DOI:10.1007/s10107-006-0040-1,2006
[42]Zizhuo Wang, Song Zheng, Stephen Boydy and Yinyu Ye. Further Relaxations of the SDP Approach to sensor Network Localization. working paper, Dept of Man-agement Science and Engineering., Stanford university,2006
[43]Gu ler and Y.Ye. Convergence behavior of interior point algorithms. Math. Programming, 1993,60:215-228
[44]T.-C. Liang, T.-C. Wang, and Y. Ye, A gradient search method to round the semidefinite programming relaxation for ad hoc wireless sensor network localization, Standford University, Tech. Rep, August,26,2004
[45]H. Aghajan, P. Biswas, and Y. Ye. Semidefinite programming algorithms for sensor network localization using angle of arrival information.39th Annual Asilomar Conference on Signals, Systems and Computers,2005
[46]P.Biswas,Y.Ye. A distributed method for solving semidefinite programming arising from ad hoc wireless sensor network localization. Tchnical report, Dept of Management Science and Engineering, stanford university,2006
[47]Qingjiang Shi, Chen He. A SDP Approach for Range-free Localization in Wireless Sensor Networks. IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings,2008:4214-4218
[48]J F Sturm, Using SeDuMi 1.02. a Matlab toolbox for optimization over symmetric cones, Optimiz. Meth. Softw.1999,vol.11-12:625-653
[49]V.Vivekanandan and V.W.S. Wong. Concentric Anchor Beacon Localization Algorithm for Wireless Sensor Networks. IEEE Trasactions on Vehicular Technology.2007,56(5):2733-2744
[50]Hongyang Chen, Q. Shi, P. Huang, H. Vincent Poor, and K. Sezaki. Mobile Anchor Assisted Node Localization for Wireless Sensor Networks. Proc. IEEE PIMRC'09, Tokyo, Japan, Sept,2009
[51]Biswas P, Lian T C, Wang T C, Ye Y. Semidefinite programming based algorithms for sensor network localization. ACM Trans on Sensor Networks.2006,2(2):188-220
[52]Zhi Li, Hui Chen, Jing Qian, Shouyin Liu. A Distributed Multi-Coordinate Localization Algorithm For Wireless Sensor Networks.2008 International Symposiums on Information Processing,2008
[2]王殊等.无线传感器网络的理论及应用.北京航空航天大学出版社,2007
[3]Byrne J A.21 ideas for 21st Century[J]. Business Week.1999,8:78-167
[4]Wade R, Mitehel W M, Petter F. Ten Emerging Technologies that will Change the Word[J]. Technology Review.2003,106(1):33-49
[5]朱红松,孙利民.无线传感器网络技术发展现状.中兴通讯技术.2009,第15卷,第5期
[6]HU L and EVANS D. Localization for mobile sensor networks. Tenth International Conference on Mobile Computing and Networking, Philadelphia, Pennsylvania, USA, 2004.2004:45-57
[7]BAGGIO A, LANGENDOEN K. Monte-Carlo localization for mobile wireless sensor networks. Second International Conference on Mobile Ad-hoc and Sensor Networks, Hong Kong,2006, December.2006:718-733
[8]P. ZHAN, M. MARTONOSI. LOCALE:Collaborative Localization Estimation for Sparse Mobile Sensor Networks. International Conference on Information Processing in Sensor Networks (IPSN 2008), April,2008
[9]Guoqiang Mao, B. Fidan, Brian D.O. Anderso. Wireless sensor network localization techniques. Computer Networks,2007, val.51(10):2529-2553
[10]Sichitiu M L, Ramadurai V. Localization of wireless sensor networks with a mobile beacon. In:Proc. of the 2004 IEEE International Conference on Mobile Ad-Hoc and Sensor Systems,2004. Fort Lauderdale,2004:174-183
[11]K Kim, W Lee. MBAL:A mobile beacon-assisted localization scheme for wireless sensor networks. Proceeding of the 16th International Conference on Computer Communications and Networks, Hawaii,2007. IEEE Society Communications,2007:57-62
[12]任丽婕,无线传感器网络中节点部署和优化算法研究.中国海洋大学硕士毕业论文.2009.6
[13]Zhang L, Cheng Q, Wang Y and Zeadally S. A novel high performance distributed sensor positioning system. Wireless And Mobile Computing, Networking And Communications, 2005. Vol.3:430-437
[14]Weiwei Hu, Huibin Qin, Haiyun Huang. A Mobile Beacon Based Method for Wireless Sensor Networks Localization.11th IEEE International Conference on Communication Technology Proceedings,2008:144-147
[15]Melike Erol, Luiz F. M.Vieira, Antonio Caruso, etl. Multi Stage Underwater Sensor Localization using Mobile Beacons. SENSORCOMM 2008, Cap. Esterel, France, August 2008
[16]Azzedine Boukerche, Horacio A.B.F. Oliveira, Eduardo F. Nakamura, etl. Localization in Time and Space for Wireless Sensor Networks:A Mobile Beacon Approach.2008 IEEE international symposium on a world of wireless, mobile and multimedia networks,2008: 1-8
[17]Z.J XIA, C.J CHEN. A localization scheme with mobile beacon for wireless sensor networks. Proceeding of the 6th International Conference on ITS Telecommunications, Chengdu,2006:1017-1020
[18]E. Guerrero, H. G. Xiong, Q. Gao, G. Cova, R. Ricardo and J. Estevez. ADAL:A Distributed Range-Free Localization Algorithm Based on a Mobile Beacon for Wireless Sensor Networks.. ICUMT'09. Ultra Modern Telecommunications & Workshops,2009:1-7
[19]GUO Z, GUO Y, HONG F, etc. Perpendicular Intersection:Locating Wireless Sensors with Mobile Beacon. Proceeding of the 2008 Real-Time Systems Symposium.2008:93-102
[20]Kuo-Feng Ssu, Chia-Ho Ou, Jiau,.H C. Localization With Mobile Anchor Points in Wireless Sensor Networks. IEEE transactions on vehicular technology.2005,5 (3)
[21]Ganggang Yu, Fengqi Yul and Lei Feng. A Localization Algorithm Using a Mobile Anchor Node Under Wireless Channel.2007 IEEE International Conference on Robotics and Biomimetics, December,15-18,2007, Sanya, china.2007:1104-1108
[22]Baoli Zhang and Fengqi Yu. An Energy Efficient Localization Algorithm for Wireless Sensor Networks Using a Mobile Anchor Node. Proceedings of the 2008 IEEE International Conference on Information and Automation, Zhangjiajie, China,2008: 215-219
[23]Ganggang Yu, Fengqi yu, Lei feng. A Three Dimensional Localization Algorithm Using a Mobile Anchor Node under Wireless Channel. IEEE World Congress on Computational Intelligence,2008:477-483
[24]Bin Xiao, Hekang Chen, and Shuigeng Zhou. Distributed Localization Using a Moving Beacon in Wireless Sensor Networks. IEEE transactions on parallel and distributed systems.2008, VOL.19, NO.5
[25]Galstyan, B. Krishnamachari, K. Lerman and S. Pattern. Distributed Online Localization in Sensor Networks Using a Moving Target. Proc. Third Int'l Symp. Information Processing in Sensor Networks (IPSN'04),2004:61-70,2004
[26]张正勇,孙智,王刚等.基于移动信标节点的无线传感器网络节点定位.清华大学学报(自然科学版).2007,47(4)：534-537
[27]Ranjeet Kumar Patro. localization in wireless sensor network with mobile beacons. Electrical and Electronics Engineers in Israel,2004:22-24
[28]Sichitiu M L, Ramadurai V. Localization of wireless sensor networks with a mobile beacon. Proc of MASS.Piscataway, NJ:IEEE,2004:174-183
[29]Koutsonilas D, Das S M, Hu Y Charlie. Path planning of mobile landmarks for localization in wireless sensor networks. Computer Communication.2007,30(13): 2577-2592
[30]Rui Huang, Zaruba Gergely V. Static path planning for mobile beacons to localize sensor networks. Proc of IEEE PerComW. Piscataway, NJ:IEEE,2007:323-330
[31]Jacques M.,Bahi Abdallah Makhoul. A Mobile Beacon Based Approach for Sensor Network Localization. WiMobIEEE Computer Society,2007:44
[32]Hongjun Li, Jianwen Wang, Xun Li and Hongxu Ma. Real-time Path Planning of Mobile Anchor Node in Localization for Wireless Sensor Networks. Proceedings of the 2008 IEEE International Conference on Information and Automation, Zhangjiajie,China, June,20-23,2008
[33]Glover F. Tabu search-Part Ⅰ. ORSA Journal on Computing.1989,1(3):190-206
[34]Glover F. Tabu search-Part Ⅱ. ORSA Journal on Computing.1989,2(1):4-32
[35]王建新,李健,朱贤曼.MANET中节点的运动模型和性能分析.计算机工程.2006,32(19)：125-130
[36]Camp T, Boleng J, Davies V. A Survey of Mobility Models for Ad Hoc Network Research. Wireless Communication& Mobile Computing:Special issue on Mobile Ad Hoc Networking:Research, Trends and Applications,2002,2(5):483-502
[37]L. Doherty, L.E. Ghaoui, and S.J. Pister. Convex position estimation in wireless sensor networks. IEEE Infocom.2001,3:1655-1663
[38]S. Boyd, L. El Ghaoui, E. Feron, and V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM,1994
[39]P.Biswas and Y. Ye. Semidefinite Programming for Ad Hoc Wireless Sensor Network Localization. IEEE Conf.on Information Processing in Sensor Networks. April,2004: 46-54
[40]P.Biswas, Y.Ye. A distributed method for solving semidefinite programming arising from ad hoc wireless sensor network localization. Tchnical report, Dept of Management Science and Engineering, stanford university,2006
[41]So and Y. Ye. Theory of semidefinite programming for sensor network localization. Mathematical Programming, published online, DOI:10.1007/s10107-006-0040-1,2006
[42]Zizhuo Wang, Song Zheng, Stephen Boydy and Yinyu Ye. Further Relaxations of the SDP Approach to sensor Network Localization. working paper, Dept of Man-agement Science and Engineering., Stanford university,2006
[43]Gu ler and Y.Ye. Convergence behavior of interior point algorithms. Math. Programming, 1993,60:215-228
[44]T.-C. Liang, T.-C. Wang, and Y. Ye, A gradient search method to round the semidefinite programming relaxation for ad hoc wireless sensor network localization, Standford University, Tech. Rep, August,26,2004
[45]H. Aghajan, P. Biswas, and Y. Ye. Semidefinite programming algorithms for sensor network localization using angle of arrival information.39th Annual Asilomar Conference on Signals, Systems and Computers,2005
[46]P.Biswas,Y.Ye. A distributed method for solving semidefinite programming arising from ad hoc wireless sensor network localization. Tchnical report, Dept of Management Science and Engineering, stanford university,2006
[47]Qingjiang Shi, Chen He. A SDP Approach for Range-free Localization in Wireless Sensor Networks. IEEE Communications Society subject matter experts for publication in the ICC 2008 proceedings,2008:4214-4218
[48]J F Sturm, Using SeDuMi 1.02. a Matlab toolbox for optimization over symmetric cones, Optimiz. Meth. Softw.1999,vol.11-12:625-653
[49]V.Vivekanandan and V.W.S. Wong. Concentric Anchor Beacon Localization Algorithm for Wireless Sensor Networks. IEEE Trasactions on Vehicular Technology.2007,56(5):2733-2744
[50]Hongyang Chen, Q. Shi, P. Huang, H. Vincent Poor, and K. Sezaki. Mobile Anchor Assisted Node Localization for Wireless Sensor Networks. Proc. IEEE PIMRC'09, Tokyo, Japan, Sept,2009
[51]Biswas P, Lian T C, Wang T C, Ye Y. Semidefinite programming based algorithms for sensor network localization. ACM Trans on Sensor Networks.2006,2(2):188-220
[52]Zhi Li, Hui Chen, Jing Qian, Shouyin Liu. A Distributed Multi-Coordinate Localization Algorithm For Wireless Sensor Networks.2008 International Symposiums on Information Processing,2008