无线传感器网络无需测距的高效定位算法的研究
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摘要
无线传感器网络一般是由数目众多的廉价传感器节点组成。这些传感器节点具有感知,计算和无线通信等能力。在许多无线传感器网络应用中,例如环境监测,灾难救援,地理路由等,传感器节点的位置信息十分重要。但是为每个传感器节点装置GPS接收器的代价巨大,一般只为其中小部分的节点安置GPS接收器(这些节点称为锚节点),其他节点(称为未知节点)的位置开始时是不知道的,它们利用锚节点信息来估计自己的位置。因此传感器节点的定位问题在许多无线传感器网络应用中是一个非常重要的问题。已提出的定位算法大体可以分为基于测距的和无需测距的。尽管基于测距的定位算法的定位精度较好,但是这类定位算法需要传感器节点装置额外的硬件,费用过高。而无需测距的定位算法不需要额外的硬件条件,是解决定位问题的一个比较经济适用的方法。
怎么克服无需测距的定位算法定位精度不高的缺点是本文的主要任务。如果传感节节点能得到更多有利于定位的信息,显然可以做到在已有算法的基础上提高定位的精度。但是更多有利信息的获取不应该是通过为传感器节点装置额外的硬件实现的,否者无需测距的定位算法将失去经济适用的特点。因此在不需要为传感器节点装置额外硬件的前提下,充分发掘现有硬件条件下能够获取到的信息并加以充分利用是本文研究的主要内容。同时传感器节点的能量是有限的,怎样减小定位算法的计算开销从而节省能量也是我们的研究内容。主要从以下几个方面展开了深入的研究,概括如下:
第一,传统的定位算法要么利用一跳内锚节点的信息进行定位,这时由于一跳内的锚节点数目较少,定位的精度不好;要么利用整个传感器网络中锚节点的信息进行定位,但是为了获取整个网络锚节点的信息,算法的通信开销非常大,且受到不规则网络拓扑的影响较大。因此,在两跳邻居范围内收集锚节点信息是一个折衷的方法。
第二,很多传统的定位算法并没有考虑到实际环境中通信模型的不规则带来的影响,即使有些算法描述了不规则通信模型给算法带来的影响,但是没有针对所带来的影响而专门改进或者扩展算法使之能更加适用于实际应用。
第三,接收信号强度,作为一个现有硬件条件下能够轻易测得,但是在早前的无需测距的定位算法中没有被充分利用的信息,如果能够加以利用,必然能够提高现有算法的定位精度。本文在仔细研究了不规则通信模型下接收信号强度与距离之间的关系后,设计了一个更加精确的使用接收信号强度的算法。
A wireless sensor network (WSN) usually consists of a large number of inexpensive sensor nodes with the ability of sensing, computing and wireless communicating. In many WSN applications, such as environmental monitoring, disaster rescue and geographic-base routing, the location information of sensor nodes is crucial. Owing to high cost of Global Positioning System (GPS) receivers, only a small portion of sensor nodes are equipped with GPS receivers and these nodes are called anchor nodes. The remaining nodes, called unknown nodes, are location-unaware initially, and need to be localized with the assistance of the anchor nodes. Therefore, a localization problem, which solves the location information of location-unaware nodes, is a very fundamental and essential issue in many WSN applications. Existing localization algorithms can be totally classified into two categories: the range-based algorithms and range-free algorithms. The range-based algorithm can achieve higher localization accuracy, especially in open scenarios; however, additional hardware is required. The range-free algorithm does not need additional hardware, and, thus, it is a cost-effective approach for the WSN localization problem.
In this paper, we aim to enhance the performance of the range-free algorithms. If more useful information is available, the localization accuracy of the existing range-free localization algorithms should be increased. However, it is not reasonable that the information is obtained by equipping sensor nodes with additional hardware, because the cost would be very high, which is just the reason why we choose range-free algorithm rather than range-based algorithm to solve the WSN localization problem. Therefore, how to exploit to utilize the information which is available and underutilized in present hardware to enhance the performance of the range-free algorithms is our main focus. Moreover, due to the energy limited of sensor nodes, we also concern how to decrease the computation cost of the localization algorithm.
The contents of our work are listed as follows:
Firstly, the conventional localization algorithms use the neighboring anchor nodes or all anchor nodes in the WSN to localize the unknown nodes. The localization accuracy of the former algorithms is coarse because of the limited information provided by the neighboring anchor nodes. The communication cost of the latter algorithms to collect the information of all the anchor nodes is very high, and they suffer from irregular network topology. Consequently, a tradeoff is that collecting the information of the anchor nodes in two hops.
Secondly, many conventional localization algorithms do not consider the influence of the radio irregularity in reality. Although some researchers mention the influence, further specialized improvement of their algorithms is not made. In our work, we took radio irregularity into consideration and proposed an algorithm which is more robust against radio irregularity.
Thirdly, the Received Signal Strength (RSS), which can be easily measured by present hardware, is underutilized before by range-free algorithms. In our work, we investigated the relationship between the RSS and the node-to-node distance, and then exploited to utilize it in a more elaborate way that the localization accuracy of the conventional algorithm is increased.
怎么克服无需测距的定位算法定位精度不高的缺点是本文的主要任务。如果传感节节点能得到更多有利于定位的信息,显然可以做到在已有算法的基础上提高定位的精度。但是更多有利信息的获取不应该是通过为传感器节点装置额外的硬件实现的,否者无需测距的定位算法将失去经济适用的特点。因此在不需要为传感器节点装置额外硬件的前提下,充分发掘现有硬件条件下能够获取到的信息并加以充分利用是本文研究的主要内容。同时传感器节点的能量是有限的,怎样减小定位算法的计算开销从而节省能量也是我们的研究内容。主要从以下几个方面展开了深入的研究,概括如下:
第一,传统的定位算法要么利用一跳内锚节点的信息进行定位,这时由于一跳内的锚节点数目较少,定位的精度不好;要么利用整个传感器网络中锚节点的信息进行定位,但是为了获取整个网络锚节点的信息,算法的通信开销非常大,且受到不规则网络拓扑的影响较大。因此,在两跳邻居范围内收集锚节点信息是一个折衷的方法。
第二,很多传统的定位算法并没有考虑到实际环境中通信模型的不规则带来的影响,即使有些算法描述了不规则通信模型给算法带来的影响,但是没有针对所带来的影响而专门改进或者扩展算法使之能更加适用于实际应用。
第三,接收信号强度,作为一个现有硬件条件下能够轻易测得,但是在早前的无需测距的定位算法中没有被充分利用的信息,如果能够加以利用,必然能够提高现有算法的定位精度。本文在仔细研究了不规则通信模型下接收信号强度与距离之间的关系后,设计了一个更加精确的使用接收信号强度的算法。
A wireless sensor network (WSN) usually consists of a large number of inexpensive sensor nodes with the ability of sensing, computing and wireless communicating. In many WSN applications, such as environmental monitoring, disaster rescue and geographic-base routing, the location information of sensor nodes is crucial. Owing to high cost of Global Positioning System (GPS) receivers, only a small portion of sensor nodes are equipped with GPS receivers and these nodes are called anchor nodes. The remaining nodes, called unknown nodes, are location-unaware initially, and need to be localized with the assistance of the anchor nodes. Therefore, a localization problem, which solves the location information of location-unaware nodes, is a very fundamental and essential issue in many WSN applications. Existing localization algorithms can be totally classified into two categories: the range-based algorithms and range-free algorithms. The range-based algorithm can achieve higher localization accuracy, especially in open scenarios; however, additional hardware is required. The range-free algorithm does not need additional hardware, and, thus, it is a cost-effective approach for the WSN localization problem.
In this paper, we aim to enhance the performance of the range-free algorithms. If more useful information is available, the localization accuracy of the existing range-free localization algorithms should be increased. However, it is not reasonable that the information is obtained by equipping sensor nodes with additional hardware, because the cost would be very high, which is just the reason why we choose range-free algorithm rather than range-based algorithm to solve the WSN localization problem. Therefore, how to exploit to utilize the information which is available and underutilized in present hardware to enhance the performance of the range-free algorithms is our main focus. Moreover, due to the energy limited of sensor nodes, we also concern how to decrease the computation cost of the localization algorithm.
The contents of our work are listed as follows:
Firstly, the conventional localization algorithms use the neighboring anchor nodes or all anchor nodes in the WSN to localize the unknown nodes. The localization accuracy of the former algorithms is coarse because of the limited information provided by the neighboring anchor nodes. The communication cost of the latter algorithms to collect the information of all the anchor nodes is very high, and they suffer from irregular network topology. Consequently, a tradeoff is that collecting the information of the anchor nodes in two hops.
Secondly, many conventional localization algorithms do not consider the influence of the radio irregularity in reality. Although some researchers mention the influence, further specialized improvement of their algorithms is not made. In our work, we took radio irregularity into consideration and proposed an algorithm which is more robust against radio irregularity.
Thirdly, the Received Signal Strength (RSS), which can be easily measured by present hardware, is underutilized before by range-free algorithms. In our work, we investigated the relationship between the RSS and the node-to-node distance, and then exploited to utilize it in a more elaborate way that the localization accuracy of the conventional algorithm is increased.
引文
[1]任丰原,黄海宁,林闯,“无线传感器网络”,软件学报,vol. 14, no. 7, pp. 1282-1291, 2003.
[2] DARPA Program, http://dtsn.darpa.mil/ixo/programs.asp
[3] Chris Savarese, Jan M.Rabaey, Jan Beutel. Locationing in Distributed Ad-Hoc wireless sensor network. In Proc. of IEEE International Conference on Acoustics, Speech, and Signal (ICASSP'01 ), Salt Lake, USA: IEEE Computer Society. 2001.5,vol 4:2037-2040.
[4] Seapahn Meguerdichian, Farinaz Koushantar. Miodrag Potkonjak, and Mani B Srivastava. Coverage problems in wireless ad-hoc sensor networks. In Proc. of Twentieth Annual Joint Conference of the IEEE Computer and Comnninications Societies (INFOCOM 2001), Anchorage, Alaska, USA: IEEE Compter and Communications Societies, 2001 4, vol 3 1380-1387.
[5] Jae-Hwan Chang and Leandros Tassiulas. Energy conserving routing in wireless ad-hoc networking, In Proc. of Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2000), Tel Aviv, Israel: IEEE Computer and Communications Societies, 2000.3. Vol.1 22-31.
[6] JM Rabaey, MJ Ammer, JL da Silva Jr, D. Patel, and S. Roundy,“PicoRadio Supports Ad Hoc Ultra-low Power Wireless Networking,”Computer, vol. 33, no. 7, pp. 42-48, Aug, 2000
[7] S. Capkun, M. Hamdi and J.P. Hubaux,“GPS-Free Positioning in Mobile Ad-Hoc Networks,”In Proc. of the 34th Annual Hawaii International Conference on System Sciences, IEEE Computer Society, 2001.1, 3481-3490.
[8] Lance Doherty, Laurent EI Ghaoui and Kristofer S.J.Pister. Convex Position Estimation in Wireless Sensor Networks In Proc. of Twentieth Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2001), Anchorage, AK, USA:IEEE Computer and Communications Societies.2001.4,vol 3:1655-1663.
[9] J. Caffery,“A new approach to the geometry of TOA location”, Proc. of IEEE Vehicular Technology Conference (VTC), pp. 1943-1950, September 2000.
[10] J. Beutel,“Geolocation in a PicoRadio environment”, M.S. Thesis, ETH Aurich, Electronics Laboratory, UC-Berkley, December 1999.
[11] D. Niculescu and B. Nath,“Ad Hoc Positioning System (APS) using AoA,”Proc. of IEEE INFOCOM, pp. 1734-1743, March 2003.
[12] N.B. Priyantha, A. Chakraborty, and H. Balakrishnan,“The Cricket Location-Support System,”Proc. ACM MobiCom’00, pp. 32-43, Aug. 2000.
[13] P. Bahl, and V.N. Padmanabhan,“PADAR: an in-building RF based user location and tracking system”, Proc. of IEEE INFOCOM, pp. 775-784, March 2000.
[14] N. Bulusu, J. Heidemann, and D. Estrin,“GPS-less low-cost outdoor localization for very small devices”, IEEE, Personal Comm., vol. 7, no. 5, pp. 28-34, Oct. 2000.
[15] T. He, C. Huang, B.M. Blum, J.A. Stankovic, and T. Abdelzaher,“Rang-Free Localization Schemes for Large Scale Sensor Networks”, Proc. ACM Mobicom’03, pp. 81-95, Sept. 2003.
[16] D. Niculescu and B. Nath,“DV Based Positioning in AD Hoc Networks,”J. Telecomm. Systems, vol. 22, pp. 267-280, Jan.-Apr. 2003.
[17] S.N. Simic and S. Sastry,“Distributed localization in wireless ad hoc networks,”UC Berkeley ERL report, 2001
[18] Y. Shang, W. Ruml, Y. Zhang, and M.P.J. Fromherz,“Localization from Mere Connectivity,”Proc. ACM MobiHoc’03, pp. 201-212, Jun. 2003.
[19] M.L. Sichitiu and V. Ramadurai,“Localization of Wireless Sensor Networks with a mobile beacon,”In Proc. of Mobile Ad-hoc and Sensor Systems, pp. 174-183, 2004
[20]周正,“无线传感器网络的节点自定位技术”,《中兴通讯技术》,第II卷第4期, 2005
[21] Nirupama Bulusu and Deborah Estrin and John Heidemann. Tradeoffs in Location Support Systems: The Case for Quality-Expressive Location Models far Applications. In Proc. of the Ubicomp 2001 Workshop on Location Modeling, Atlanta, Georgia, USA: 2001.9,7-12.
[22] R. Nagpal, H. E. Shrobe and J. Bachrach,“Organizing a Global Coordinate System from Local Information on an Ad Hoc Sensor Network,”Lecture notes in computer science, ISSN 0302-9743
[23] Y. Shang and W. Ruml,“Improved MDS-Based Localization”, In Proc. of IEEE INFOCOM’04, vol. 4, pp. 2640-2651, 2004.
[24] Y. Shang, W. Ruml, Y. Zhang and M. Fromherz,“Localization from Connectivity in Sensor Networks,”IEEE Trans. on Parallel and Distributed Systems, vol. 15, no. 11, pp. 961-974, 2004.
[25] L. Doherty, K.S.J. Pister, and L.E. Ghaoui,“Convex Position Estimation in Wireless Sensor Networks,”Proc. IEEE INFOCOM’01, vol. 3, pp. 1655-1663, Apr. 2001.
[26] T.S. Rappaport,“Wireless Communications: Principles and Practice,”Prentice Hall, 1999
[27] H. Hashemi,“The Indoor Radio Propagation Channel,”Proc. IEEE, vol. 81, no. 7, pp. 943-968, July 1993.
[28] M. Zuniga and B. Krishnamachari,“Analyzing the Transitional Region in Low Power Wireless Links,”Proc. First IEEE Int’l Conf. Sensor and Ad Hoc Comm. and Networks(SECON’04), Oct. 2004.
[29] J.P. Sheu, P.C. Chen and C.S. Hsu,“A Distributed Localization Scheme for Wireless Sensor Networks with Improved Grid-Scan and Vector-Based Refinement,”IEEE Trans. on Mobile Computing, vol. 7, no. 9, pp. 1110-1123, Sept. 2008.
[30] B. Xiao, L. Chen, Q.J. Xiao and M.L. Li,“Reliable Anchor-Based Sensor Localization in Irregular Areas,”IEEE Trans. on Mobile Computing, vol. 9, no. 1, pp. 60-72, Jan. 2009.
[31] C. Wang and L. Xiao,“Sensor Localization in Concave Environments,”ACM Trans. on Sensor Networks, vol. 4, no. 1, Jan. 2008.
[32] H. Lim and J.C. Hou,“Distributed Localization for Anisotropic Sensor Networks,”ACM Trans. on Sensor Networks, vol. 5, no. 2, Mar. 2009.
[33] M.D. Penrsose,“On k-connectivity for a geometric random graph,”Random Structures and Algorithms, vol. 15, no. 2, pp. 145-164, Jul. 1999.
[34] M. Barbeau, E. Kranakis, D. Krizanc and P. Morin,“Improving Distance Based Geographic Location Techniques in Sensor Networks,”ADHOC-NOW’04, LNCS 3158, pp. 197-210, 2004.
[35] P.D. Tinh, T. Noguchi and M. Kawai,“Localization Scheme for Large Scale Wireless Sensor Networks,”Proc. of ISSNIP’08, pp. 25-30, 2008.
[36] K. Yedavalli, and B. Krishnamachari,“Sequence-Based Localization in Wireless Sensor Networks,”IEEE Trans. on Mobile Computing, vol. 7, no. 1, pp. 81-94, Jan. 2008.
[37] Z.G. Zhong, and T. He,“Achieving Range-free Localization Beyond Connectivity,”Proc. ACM SenSys’09, pp. 281-294, Nov. 2009.
[38] R. Huang and G.V. Zaruba,“Beacon Deployment for Sensor Network Localization,”Proc. of Wireless Communications and Networking Conference, WCNC’07, pp. 3181-3193.
[39] P.K. Sahoo, I. Hwang and S.Y. Lin,“A Distributed Localization Scheme for Wireless Sensor Networks,”Int’l Conf. on Mobile Technology, Applications, and Systems, 2008.
[40] A.P. Peng, X.S. Guo, W. Cai and H.B. Li,“A Distributed Lolization Scheme for Wireless Sensor Networks Based on Bounding Box Algorithm,”the 9th Int’l Conf. on Electronic Measurement and Instruments, (ICEMI’09), pp. 2984-2988.
[41] M. L. Sichitiu, and V. Ramadurai,“Localization of Wireless Sensor Networks with a Mobile Beacon,”Proc. of IEEE Int. Conf. on Mobile Ad-hoc and Sensor Systems, pp. 174- 183, Oct. 2004.
[42] P. Dutta and S. Bergbreiter,“MobiLoc: mobility enhanced localization,”Berkeley, University of California, 2003.
[43] K.-F. Ssu; C.-H. Ou, H-C. Jiau,“Localization with mobile anchor points in wireless sensornetworks”, IEEE Trans. on Vehicular Technology, vol. 54, no. 3, pp 1187– 1197, May 2005.
[44] B. Xiao, H. Chen, S. Zhou,“A Walking Beacon-Assisted Localization in Wireless Sensor Networks”, Proc. of IEEE ICC, pp. 3070-3075, June 2007.
[2] DARPA Program, http://dtsn.darpa.mil/ixo/programs.asp
[3] Chris Savarese, Jan M.Rabaey, Jan Beutel. Locationing in Distributed Ad-Hoc wireless sensor network. In Proc. of IEEE International Conference on Acoustics, Speech, and Signal (ICASSP'01 ), Salt Lake, USA: IEEE Computer Society. 2001.5,vol 4:2037-2040.
[4] Seapahn Meguerdichian, Farinaz Koushantar. Miodrag Potkonjak, and Mani B Srivastava. Coverage problems in wireless ad-hoc sensor networks. In Proc. of Twentieth Annual Joint Conference of the IEEE Computer and Comnninications Societies (INFOCOM 2001), Anchorage, Alaska, USA: IEEE Compter and Communications Societies, 2001 4, vol 3 1380-1387.
[5] Jae-Hwan Chang and Leandros Tassiulas. Energy conserving routing in wireless ad-hoc networking, In Proc. of Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2000), Tel Aviv, Israel: IEEE Computer and Communications Societies, 2000.3. Vol.1 22-31.
[6] JM Rabaey, MJ Ammer, JL da Silva Jr, D. Patel, and S. Roundy,“PicoRadio Supports Ad Hoc Ultra-low Power Wireless Networking,”Computer, vol. 33, no. 7, pp. 42-48, Aug, 2000
[7] S. Capkun, M. Hamdi and J.P. Hubaux,“GPS-Free Positioning in Mobile Ad-Hoc Networks,”In Proc. of the 34th Annual Hawaii International Conference on System Sciences, IEEE Computer Society, 2001.1, 3481-3490.
[8] Lance Doherty, Laurent EI Ghaoui and Kristofer S.J.Pister. Convex Position Estimation in Wireless Sensor Networks In Proc. of Twentieth Annual Joint Conference of the IEEE Computer and Communications Societies (INFOCOM 2001), Anchorage, AK, USA:IEEE Computer and Communications Societies.2001.4,vol 3:1655-1663.
[9] J. Caffery,“A new approach to the geometry of TOA location”, Proc. of IEEE Vehicular Technology Conference (VTC), pp. 1943-1950, September 2000.
[10] J. Beutel,“Geolocation in a PicoRadio environment”, M.S. Thesis, ETH Aurich, Electronics Laboratory, UC-Berkley, December 1999.
[11] D. Niculescu and B. Nath,“Ad Hoc Positioning System (APS) using AoA,”Proc. of IEEE INFOCOM, pp. 1734-1743, March 2003.
[12] N.B. Priyantha, A. Chakraborty, and H. Balakrishnan,“The Cricket Location-Support System,”Proc. ACM MobiCom’00, pp. 32-43, Aug. 2000.
[13] P. Bahl, and V.N. Padmanabhan,“PADAR: an in-building RF based user location and tracking system”, Proc. of IEEE INFOCOM, pp. 775-784, March 2000.
[14] N. Bulusu, J. Heidemann, and D. Estrin,“GPS-less low-cost outdoor localization for very small devices”, IEEE, Personal Comm., vol. 7, no. 5, pp. 28-34, Oct. 2000.
[15] T. He, C. Huang, B.M. Blum, J.A. Stankovic, and T. Abdelzaher,“Rang-Free Localization Schemes for Large Scale Sensor Networks”, Proc. ACM Mobicom’03, pp. 81-95, Sept. 2003.
[16] D. Niculescu and B. Nath,“DV Based Positioning in AD Hoc Networks,”J. Telecomm. Systems, vol. 22, pp. 267-280, Jan.-Apr. 2003.
[17] S.N. Simic and S. Sastry,“Distributed localization in wireless ad hoc networks,”UC Berkeley ERL report, 2001
[18] Y. Shang, W. Ruml, Y. Zhang, and M.P.J. Fromherz,“Localization from Mere Connectivity,”Proc. ACM MobiHoc’03, pp. 201-212, Jun. 2003.
[19] M.L. Sichitiu and V. Ramadurai,“Localization of Wireless Sensor Networks with a mobile beacon,”In Proc. of Mobile Ad-hoc and Sensor Systems, pp. 174-183, 2004
[20]周正,“无线传感器网络的节点自定位技术”,《中兴通讯技术》,第II卷第4期, 2005
[21] Nirupama Bulusu and Deborah Estrin and John Heidemann. Tradeoffs in Location Support Systems: The Case for Quality-Expressive Location Models far Applications. In Proc. of the Ubicomp 2001 Workshop on Location Modeling, Atlanta, Georgia, USA: 2001.9,7-12.
[22] R. Nagpal, H. E. Shrobe and J. Bachrach,“Organizing a Global Coordinate System from Local Information on an Ad Hoc Sensor Network,”Lecture notes in computer science, ISSN 0302-9743
[23] Y. Shang and W. Ruml,“Improved MDS-Based Localization”, In Proc. of IEEE INFOCOM’04, vol. 4, pp. 2640-2651, 2004.
[24] Y. Shang, W. Ruml, Y. Zhang and M. Fromherz,“Localization from Connectivity in Sensor Networks,”IEEE Trans. on Parallel and Distributed Systems, vol. 15, no. 11, pp. 961-974, 2004.
[25] L. Doherty, K.S.J. Pister, and L.E. Ghaoui,“Convex Position Estimation in Wireless Sensor Networks,”Proc. IEEE INFOCOM’01, vol. 3, pp. 1655-1663, Apr. 2001.
[26] T.S. Rappaport,“Wireless Communications: Principles and Practice,”Prentice Hall, 1999
[27] H. Hashemi,“The Indoor Radio Propagation Channel,”Proc. IEEE, vol. 81, no. 7, pp. 943-968, July 1993.
[28] M. Zuniga and B. Krishnamachari,“Analyzing the Transitional Region in Low Power Wireless Links,”Proc. First IEEE Int’l Conf. Sensor and Ad Hoc Comm. and Networks(SECON’04), Oct. 2004.
[29] J.P. Sheu, P.C. Chen and C.S. Hsu,“A Distributed Localization Scheme for Wireless Sensor Networks with Improved Grid-Scan and Vector-Based Refinement,”IEEE Trans. on Mobile Computing, vol. 7, no. 9, pp. 1110-1123, Sept. 2008.
[30] B. Xiao, L. Chen, Q.J. Xiao and M.L. Li,“Reliable Anchor-Based Sensor Localization in Irregular Areas,”IEEE Trans. on Mobile Computing, vol. 9, no. 1, pp. 60-72, Jan. 2009.
[31] C. Wang and L. Xiao,“Sensor Localization in Concave Environments,”ACM Trans. on Sensor Networks, vol. 4, no. 1, Jan. 2008.
[32] H. Lim and J.C. Hou,“Distributed Localization for Anisotropic Sensor Networks,”ACM Trans. on Sensor Networks, vol. 5, no. 2, Mar. 2009.
[33] M.D. Penrsose,“On k-connectivity for a geometric random graph,”Random Structures and Algorithms, vol. 15, no. 2, pp. 145-164, Jul. 1999.
[34] M. Barbeau, E. Kranakis, D. Krizanc and P. Morin,“Improving Distance Based Geographic Location Techniques in Sensor Networks,”ADHOC-NOW’04, LNCS 3158, pp. 197-210, 2004.
[35] P.D. Tinh, T. Noguchi and M. Kawai,“Localization Scheme for Large Scale Wireless Sensor Networks,”Proc. of ISSNIP’08, pp. 25-30, 2008.
[36] K. Yedavalli, and B. Krishnamachari,“Sequence-Based Localization in Wireless Sensor Networks,”IEEE Trans. on Mobile Computing, vol. 7, no. 1, pp. 81-94, Jan. 2008.
[37] Z.G. Zhong, and T. He,“Achieving Range-free Localization Beyond Connectivity,”Proc. ACM SenSys’09, pp. 281-294, Nov. 2009.
[38] R. Huang and G.V. Zaruba,“Beacon Deployment for Sensor Network Localization,”Proc. of Wireless Communications and Networking Conference, WCNC’07, pp. 3181-3193.
[39] P.K. Sahoo, I. Hwang and S.Y. Lin,“A Distributed Localization Scheme for Wireless Sensor Networks,”Int’l Conf. on Mobile Technology, Applications, and Systems, 2008.
[40] A.P. Peng, X.S. Guo, W. Cai and H.B. Li,“A Distributed Lolization Scheme for Wireless Sensor Networks Based on Bounding Box Algorithm,”the 9th Int’l Conf. on Electronic Measurement and Instruments, (ICEMI’09), pp. 2984-2988.
[41] M. L. Sichitiu, and V. Ramadurai,“Localization of Wireless Sensor Networks with a Mobile Beacon,”Proc. of IEEE Int. Conf. on Mobile Ad-hoc and Sensor Systems, pp. 174- 183, Oct. 2004.
[42] P. Dutta and S. Bergbreiter,“MobiLoc: mobility enhanced localization,”Berkeley, University of California, 2003.
[43] K.-F. Ssu; C.-H. Ou, H-C. Jiau,“Localization with mobile anchor points in wireless sensornetworks”, IEEE Trans. on Vehicular Technology, vol. 54, no. 3, pp 1187– 1197, May 2005.
[44] B. Xiao, H. Chen, S. Zhou,“A Walking Beacon-Assisted Localization in Wireless Sensor Networks”, Proc. of IEEE ICC, pp. 3070-3075, June 2007.