WCDMA网络中的定位算法研究
摘要
随着第三代(3G)移动通信的发展和美国E911规定的颁布,蜂窝网络移动台(MS)无线定位技术得到了越来越广泛的注视。该服务能够提供有关移动台位置的信息。因此,在很多领域有着重要的应用,如网络优化、娱乐、紧急救护和国家安全等。同时,无线传播信道的复杂性又决定了蜂窝无线定位技术会面临很多困难。如何提高定位精度以更好地服务于大众已成为国际上相关领域的研究重点。
WCDMA全称为Wideband CDMA,也称为CDMA Direct Spread,意为宽频码分多重存取,这是基于GSM网发展出来的3G技术规范,是欧洲提出的宽带CDMA技术。它有较高的扩频增益,发展空间较大,全球漫游能力最强,技术成熟性最佳。它以宽带伪随机(PN)序列来区分用户。不同用户在频率和时间上共享,提高了资源的利用率。因此,本文针对WCDMA蜂窝网络,采用到达时间／时间差(TOA/TDOA)定位方式,以提高移动台定位精度为目标,从被动定位的角度出发,在定位性能参数、影响定位精度的因素、TDOA定位方式的多种算法、非视距(NLOS)环境下的定位算法等几个方面深入研究蜂窝网络移动台的无线定位技术。
首先,本文在理论分析和数据支持的基础上明确了技术路线和研究内容。论文简略地讨论了常用的定位算法,定性地比较了它们的性能；详细地分析了WCDMA蜂窝无线网络的特点,确立了移动台定位误差的来源；概括了目前国内外蜂窝无线定位技术的研究现状；进而通过综合分析,确定了研究的方法和重点。
其次,在深入研究TOA算法和TDOA算法后,搭建了WCDMA的仿真平台,分别对TOA算法中LOS和NLOS的两种情况进行仿真,对TDOA定位方式下的四种算法进行仿真,通过改变基站数目,观察定位误差方差的改变。仿真结果比较了各种算法的定位性能,分析了各种算法的优缺点,有利于在实际应用中选用合适的算法。
With the third-generation (3G) mobile communications development and promulgation of the provisions of the U.S. E911, cellular network mobile station (MS)wireless location technology has been more and more widely watched. The service can provide information about the location of the mobile station. Therefore, in many fields has important applications, such as network optimization, entertainment, emergency and national security. Meanwhile, the wireless propagation channel in turn determines the complexity of cellular location technology will face many difficulties. How to improve the positioning accuracy to better serve the public has become the international focus on research in related fields.
The full name of WCDMA Wideband CDMA, also known as CDMA Direct Spread, intended for the wideband code division multiple access, which is based on the GSM network developed 3G technology standard, is Europe's wideband CDMA technology. It has a high spreading gain, the development of larger space, the strongest global roaming capabilities, technical maturity of the best. It wideband pseudo-random (PN) sequence to differentiate between users. Different users sharing the frequency and time, improve resource utilization. Therefore, this paper WCDMA cellular network, using time of arrival/ time difference (TOA/TDOA)positioning methods to improve the mobile station positioning accuracy as the goal, from passive positioning point of view, the positioning performance parameters, affect the positioning accuracy of the factors, TDOA Location The way a variety of algorithms, non line of sight (NLOS) environment, the positioning algorithm-depth study of several aspects of cellular mobile wireless location technology.
Firstly, the theoretical analysis and data support on the basis of clear technology roadmap and research content. Paper briefly discusses the positioning algorithmused qualitatively compare their performance; a detailed analysis of the characteristics of WCDMA cellular radio network, established a mobile station positioning error sources; summarizes the cellular location technology at home and abroad Research Status; and then through a comprehensive analysis to determine the research methods and priorities.
Secondly, in-depth study of TOA and TDOA algorithms algorithms, the structures of the WCDMA simulation platform, respectively, LOS and NLOS TOA algorithm to simulate the two cases of the four TDOA positioning algorithm under the simulation, by changing the number of base stations To observe the change in location error variance.
WCDMA全称为Wideband CDMA,也称为CDMA Direct Spread,意为宽频码分多重存取,这是基于GSM网发展出来的3G技术规范,是欧洲提出的宽带CDMA技术。它有较高的扩频增益,发展空间较大,全球漫游能力最强,技术成熟性最佳。它以宽带伪随机(PN)序列来区分用户。不同用户在频率和时间上共享,提高了资源的利用率。因此,本文针对WCDMA蜂窝网络,采用到达时间／时间差(TOA/TDOA)定位方式,以提高移动台定位精度为目标,从被动定位的角度出发,在定位性能参数、影响定位精度的因素、TDOA定位方式的多种算法、非视距(NLOS)环境下的定位算法等几个方面深入研究蜂窝网络移动台的无线定位技术。
首先,本文在理论分析和数据支持的基础上明确了技术路线和研究内容。论文简略地讨论了常用的定位算法,定性地比较了它们的性能；详细地分析了WCDMA蜂窝无线网络的特点,确立了移动台定位误差的来源；概括了目前国内外蜂窝无线定位技术的研究现状；进而通过综合分析,确定了研究的方法和重点。
其次,在深入研究TOA算法和TDOA算法后,搭建了WCDMA的仿真平台,分别对TOA算法中LOS和NLOS的两种情况进行仿真,对TDOA定位方式下的四种算法进行仿真,通过改变基站数目,观察定位误差方差的改变。仿真结果比较了各种算法的定位性能,分析了各种算法的优缺点,有利于在实际应用中选用合适的算法。
With the third-generation (3G) mobile communications development and promulgation of the provisions of the U.S. E911, cellular network mobile station (MS)wireless location technology has been more and more widely watched. The service can provide information about the location of the mobile station. Therefore, in many fields has important applications, such as network optimization, entertainment, emergency and national security. Meanwhile, the wireless propagation channel in turn determines the complexity of cellular location technology will face many difficulties. How to improve the positioning accuracy to better serve the public has become the international focus on research in related fields.
The full name of WCDMA Wideband CDMA, also known as CDMA Direct Spread, intended for the wideband code division multiple access, which is based on the GSM network developed 3G technology standard, is Europe's wideband CDMA technology. It has a high spreading gain, the development of larger space, the strongest global roaming capabilities, technical maturity of the best. It wideband pseudo-random (PN) sequence to differentiate between users. Different users sharing the frequency and time, improve resource utilization. Therefore, this paper WCDMA cellular network, using time of arrival/ time difference (TOA/TDOA)positioning methods to improve the mobile station positioning accuracy as the goal, from passive positioning point of view, the positioning performance parameters, affect the positioning accuracy of the factors, TDOA Location The way a variety of algorithms, non line of sight (NLOS) environment, the positioning algorithm-depth study of several aspects of cellular mobile wireless location technology.
Firstly, the theoretical analysis and data support on the basis of clear technology roadmap and research content. Paper briefly discusses the positioning algorithmused qualitatively compare their performance; a detailed analysis of the characteristics of WCDMA cellular radio network, established a mobile station positioning error sources; summarizes the cellular location technology at home and abroad Research Status; and then through a comprehensive analysis to determine the research methods and priorities.
Secondly, in-depth study of TOA and TDOA algorithms algorithms, the structures of the WCDMA simulation platform, respectively, LOS and NLOS TOA algorithm to simulate the two cases of the four TDOA positioning algorithm under the simulation, by changing the number of base stations To observe the change in location error variance.
引文
[1]王莹,刘宝玲WCDMA无线网络规划与优化[M].北京：人民邮电出版社,2007：16.17.
[2]范平志,邓平,刘林.蜂窝网无线定位.北京：电子工业出版社,2002.
[3]熊瑾煜,王巍,朱中梁.基于泰勒级数展开的蜂窝TDOA定位算法[J].通信学报,2004,25(4)：144.150
[4]M Aso, et al. A new location estimation method based on maximum likelihood function in cellular systems. IEEE,2001,3(1):106.110
[5]J. A. Stankovic, Wireless Sensor Networks, Computer, v01.41, no.10, PP.92 —95, Oct.2008
[6]邓平,范志平.蜂窝系统无线定位原理及应用.移动通信,V01.24,N05,2000.9,pp.19-22.
[7]E Weinstein. Decentralization of the gaussian maximum likelihood estimator and its applications to passive array processing[J]. IEEE Trans on ASSP,1981, ASSP(29):945.951
[8]PicoRadioproject.URL:http:/bwrc.eecs.Berkeley.edu/Research/Pico_Radio/Default
[9]Kahn J.M., Katz R.H., Pister K.S.J. Next Century Challenges:Mobile Networking for Smart Dust[C], In:Proceedings of the 5th Annual ACM/IEEE International Conference on Mobile Computing and Networking, ACM SIGMOBILE, Seattle, Washington,1999,483-492.
[10]WINS(Wireless Integrated Network Sensors) Project:http://www.janet.ecla.edu/
[11]MIT uAMPS project. URL:http://www-mtl.mit.edu/research/icsystems/uamps/
[12]NMS project.URL:http://nms.csail.mit.edu/
[13]SCADDS project. URL:http://www.isi.edu/scadds/.89
[14]Codeblue project. URL:http://www.eecs.harvard.edu/}mdw/proj/codeblue/
[15]Exscal project. URL:http://www.cast.cse.ohio-state.edu/exscal/
[16]ESP project. URL:http://projects.cerias.purdue.edu/esp/
[17]Caccamo,M.,Zhang,L.Y.,Lui Sha,et al, An Implicit Prioritized Access Protocol for Wireless Sensor Networks[C].In:Proceedings of the 23rd IEEE Real-Time Systems Symposium,(RTSS'02),2002,39-48.
[18]Warneke,B.,Last,M.,Liebowitz,B. Smart dust:communicating with a cubic-millimeter computer[J].Computer,2001,34(1):44-51
[19]http://www.xbow.com/Products/Wireless Sensor Networks.htm.
[20]http://bibliotecnica.upc.es/PFC/arxius/migrats/50838-2.pdf.
[21]Want R,Hopper A,Falcao V. The active badge location system[J].ACM Transaction on Information System(TOIS).1992,10(1).91-102.
[22]彭林,朱小敏,朱凌霄.WCDMA无线通信技术及演化[M].北京：中国铁道出版社,200.4：148.151.
[23]Hopper A,Steggles P,Ward A. The Anatomy of a Context-Aware Application[C].Proc.of 5th Annual Int'Conf. Mobile Computing and Networking (Mobicom 99).1999.59-68.
[24]Welch G, Bishop G,Vicci L. The HiBall Tracker:high-performance wide-area tracking for virtual and augmented environments[J]. Proceedings of the ACM symposium on Virtual reality software and technology.1999.1-10
[25]Hightower J. An indoor 3D location sensing technology based on RF signal strength[D].University of Washington, Department of Computer Science and Engineering.2000.
[26]Tian H,Chengdu H,Brian M.B.Range-free localization schemes for large scale sensor networks[C].Proceedings of the 9th annual international conference on Mobile computing and networking, San Diego,CA,USA.2003.81-95.
[27]Orr R.J, Abowd G..D.A Mechanism for Natural User Identification and Trackong[C].Proc.2000 Conf.Human Factors in Computing System.2000.275-276.
[28]Priyantha N.B,Chakraborty A,Balakrishnan H. The Cricket location-support system [C]. Proceedings of the 6th annual international conference on Mobile computing andnetworking.2000.32-43
[29]Shang Y, Ruml W,Zhang Y. Localization from mere connectivity[C].Proceedings of the 4th ACM international symposium on Mobile ad-hoc networking&computing. 2003.201-212.
[30]Capkun S,Hamdi M,Hubaux J.P. GPS-free Positioning in Mobile Ad Hoc Networks [J]. Cluster Computing.2002,5(2).157-167.
[31]Doherty L, Pister K.S.J, El Ghaoui L. Convex position estimation in wireless sensor networks[C]. INFOCOM 2001.Twentieth Annual Joint Conference of the IEEE Computer and communication Societies. Proceedings, IEEE, Anchorage, AK, USA.2001.1655-1663.
[32]Savvides A. The Ad-Hoc Localization System. Department of Electrical Engineering, University of California, Los Angeles.
[33]Niculescu D, Nath B. Ad-hoc positioning system (APS)[C]. Global Telecommunications Conference,2001.IEEE, San Antonio,TX.2001.2926-2931.
[34]Niculescu D, Badri N.Ad-hoc positioning system(APS) using AOA[C]. Twenty-Second Annual Joint Conference of the IEEE Computer and Communications Societies. IEEE, San Francisco, California,USA.2003.1734-1743.
[35]Ahmed A.A, Shi H, Shang Y. A new approach to relative localization in wireless sensor networks[C].25th IEEE International Conference on.2005.892-898.
[36]Lazos L, Poovendran R. High-resolution robust localization for wireless sensor networks[J].Selected Areas in Communications, IEEE Journal on.2006,24(2).233-246
[37]田孝华,廖桂生.减轻TOA和AOA定位系统非视距影响的方法[J].电子与信息学报,2003,25(12)：1664.1667
[38]陈茜.移动自组织网络中的定位技术研究[D].国防科学技术大学硕士学位论文.2004
[39]Z.-Z Zheng, X.-L. Luo, Z.-J. Wu:A geometric buildup algorithm for the solution of the sensor network localization problem, Computational Optimization and Applications (SCI),2010.
[40]余晖,邢燕霞WCDMA网络中的位置业务[M].北京：中国电信集团北京研究院,2003：317.325
[41]DRAGO, SNICULESCU and BADRI NATH:DV Based Positioning in Ad Hoc Networks. Telecommunication Systems 22:1-4,267-280,2003
[42]郭房富WCDMA系统中的移动台定位技术评估.硕士学位论文,浙江,浙江大学,2001
[43]Braginsky D, Estrin D. Rumor routing algorithm for sensor networks[C]. In:Proc. of the 1st workshop on sensor networks and applications. Atlanta:AVM Press.2002:22-31.
[44]Savarese C, Rabaey J,Beutel J. Locationing in Distributed Ad Hoc Wireless Sensor Networks[C]. In Proceeding of ICASSP.May 2001.2037-2040.
[45]Priyantha N,Balakrishnan H,Demaine E,et al. Anchor Free Distributed localization in Sensor Networks[R].Technical Report TR-892,MIT LCS.April 2003.
[46]Wang Shu, Liu Kezhong, Hu Fuping, et al. A Distributed Sensor Network Localization Scheme Motivated by Graph Rigidity Theory [J].The Mediterranean Journal of Measurement and Control.2005,1(4).185-190.
[47]De Oliveira H A B F, Nakamure E F, Loureiro A A F, et al. Directed Estimation: a Recursive Localization Approach for Wireless Sensor networks[C].In Proceeding of the 14th International Conference on Computer Communication and Networks. October,2005.557-562.
[48]Bulusu N, Heidemann J, Estrin D. GPS-less low-cost outdoor localization for very small devices[J].Personal Communication,IEEE.2000,7(5).28-34.
[49]Ss K-F,Ou C-H,Jiau H C. Localization with Mobile Anchor Points in Wireless Sensor Networks [J].IEEE Transactions on Vehicular Technology. May 2005,54(3).1187-1197.
[50]MiodragPotkonjak, JessieaFeng, Lewis Girod. Location discovery using data drive Statistical error modeling[J] · IEEE IN FOCOM,2006,26(8):43-47
[51]HDernaine, TellerS, Priyantha, N.B.Balakrishnan. Mobile assisted localization in Wireless sensor networks[J] Inproc · of IEEE In foeom 05,2005,65(3):323-329
[52]Borg I, Groener P. Modern multidimensional scaling theory and applications. New York:Springer-Verlag,1997,10-35.
[53]顾杰,何芳,龚耀寰.一种新的无线蜂窝定位跟踪技术[J].电子与信息学报,2004,26(4)：511-516
[54]C H Lin,J Y Cheng YCheng, et al. Mobile location estimation by density-based clustering for NLOS enviroments[J]. International conference on advanced information networking and applications,2006,1(18-20):295-300
[55]Yi Sharig, Wheeler Ruml. Improved MDS-Based Localization. IEEE INFOCOM 2004.0-7803-8356-7
[56]Chris Savarese, Jan Rabaey. Robust Positioning Algorithms for Distributed Ad-Hoc Wireless Sensor Networks. Faculty of Information Technology and Systems Delft University of Technology.
[57]Andreas Savvides, Heemin Park and Mani B. Srivastava. The Bits and Flops of the N-hop Multilateration Primitive for Node Localization Problems. WSNA, September 28,2002, Atlanta, Georgia, USA. ACM 1-58113-589-0/02/0009
[58]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
[59]X.-L. Luo and Z.-J. Wu:Least-square approximations in geometric buildup for solving distance geometry problems, Journal of Optimization Theory and Applications (SCI),2010.
[60]R.-Z. Li, X.-L. Luo and J.-R. Lin:Weighted centroid correction localization in cellular systems, American Journal of Engineering and Applied Sciences,2010.
[2]范平志,邓平,刘林.蜂窝网无线定位.北京：电子工业出版社,2002.
[3]熊瑾煜,王巍,朱中梁.基于泰勒级数展开的蜂窝TDOA定位算法[J].通信学报,2004,25(4)：144.150
[4]M Aso, et al. A new location estimation method based on maximum likelihood function in cellular systems. IEEE,2001,3(1):106.110
[5]J. A. Stankovic, Wireless Sensor Networks, Computer, v01.41, no.10, PP.92 —95, Oct.2008
[6]邓平,范志平.蜂窝系统无线定位原理及应用.移动通信,V01.24,N05,2000.9,pp.19-22.
[7]E Weinstein. Decentralization of the gaussian maximum likelihood estimator and its applications to passive array processing[J]. IEEE Trans on ASSP,1981, ASSP(29):945.951
[8]PicoRadioproject.URL:http:/bwrc.eecs.Berkeley.edu/Research/Pico_Radio/Default
[9]Kahn J.M., Katz R.H., Pister K.S.J. Next Century Challenges:Mobile Networking for Smart Dust[C], In:Proceedings of the 5th Annual ACM/IEEE International Conference on Mobile Computing and Networking, ACM SIGMOBILE, Seattle, Washington,1999,483-492.
[10]WINS(Wireless Integrated Network Sensors) Project:http://www.janet.ecla.edu/
[11]MIT uAMPS project. URL:http://www-mtl.mit.edu/research/icsystems/uamps/
[12]NMS project.URL:http://nms.csail.mit.edu/
[13]SCADDS project. URL:http://www.isi.edu/scadds/.89
[14]Codeblue project. URL:http://www.eecs.harvard.edu/}mdw/proj/codeblue/
[15]Exscal project. URL:http://www.cast.cse.ohio-state.edu/exscal/
[16]ESP project. URL:http://projects.cerias.purdue.edu/esp/
[17]Caccamo,M.,Zhang,L.Y.,Lui Sha,et al, An Implicit Prioritized Access Protocol for Wireless Sensor Networks[C].In:Proceedings of the 23rd IEEE Real-Time Systems Symposium,(RTSS'02),2002,39-48.
[18]Warneke,B.,Last,M.,Liebowitz,B. Smart dust:communicating with a cubic-millimeter computer[J].Computer,2001,34(1):44-51
[19]http://www.xbow.com/Products/Wireless Sensor Networks.htm.
[20]http://bibliotecnica.upc.es/PFC/arxius/migrats/50838-2.pdf.
[21]Want R,Hopper A,Falcao V. The active badge location system[J].ACM Transaction on Information System(TOIS).1992,10(1).91-102.
[22]彭林,朱小敏,朱凌霄.WCDMA无线通信技术及演化[M].北京：中国铁道出版社,200.4：148.151.
[23]Hopper A,Steggles P,Ward A. The Anatomy of a Context-Aware Application[C].Proc.of 5th Annual Int'Conf. Mobile Computing and Networking (Mobicom 99).1999.59-68.
[24]Welch G, Bishop G,Vicci L. The HiBall Tracker:high-performance wide-area tracking for virtual and augmented environments[J]. Proceedings of the ACM symposium on Virtual reality software and technology.1999.1-10
[25]Hightower J. An indoor 3D location sensing technology based on RF signal strength[D].University of Washington, Department of Computer Science and Engineering.2000.
[26]Tian H,Chengdu H,Brian M.B.Range-free localization schemes for large scale sensor networks[C].Proceedings of the 9th annual international conference on Mobile computing and networking, San Diego,CA,USA.2003.81-95.
[27]Orr R.J, Abowd G..D.A Mechanism for Natural User Identification and Trackong[C].Proc.2000 Conf.Human Factors in Computing System.2000.275-276.
[28]Priyantha N.B,Chakraborty A,Balakrishnan H. The Cricket location-support system [C]. Proceedings of the 6th annual international conference on Mobile computing andnetworking.2000.32-43
[29]Shang Y, Ruml W,Zhang Y. Localization from mere connectivity[C].Proceedings of the 4th ACM international symposium on Mobile ad-hoc networking&computing. 2003.201-212.
[30]Capkun S,Hamdi M,Hubaux J.P. GPS-free Positioning in Mobile Ad Hoc Networks [J]. Cluster Computing.2002,5(2).157-167.
[31]Doherty L, Pister K.S.J, El Ghaoui L. Convex position estimation in wireless sensor networks[C]. INFOCOM 2001.Twentieth Annual Joint Conference of the IEEE Computer and communication Societies. Proceedings, IEEE, Anchorage, AK, USA.2001.1655-1663.
[32]Savvides A. The Ad-Hoc Localization System. Department of Electrical Engineering, University of California, Los Angeles.
[33]Niculescu D, Nath B. Ad-hoc positioning system (APS)[C]. Global Telecommunications Conference,2001.IEEE, San Antonio,TX.2001.2926-2931.
[34]Niculescu D, Badri N.Ad-hoc positioning system(APS) using AOA[C]. Twenty-Second Annual Joint Conference of the IEEE Computer and Communications Societies. IEEE, San Francisco, California,USA.2003.1734-1743.
[35]Ahmed A.A, Shi H, Shang Y. A new approach to relative localization in wireless sensor networks[C].25th IEEE International Conference on.2005.892-898.
[36]Lazos L, Poovendran R. High-resolution robust localization for wireless sensor networks[J].Selected Areas in Communications, IEEE Journal on.2006,24(2).233-246
[37]田孝华,廖桂生.减轻TOA和AOA定位系统非视距影响的方法[J].电子与信息学报,2003,25(12)：1664.1667
[38]陈茜.移动自组织网络中的定位技术研究[D].国防科学技术大学硕士学位论文.2004
[39]Z.-Z Zheng, X.-L. Luo, Z.-J. Wu:A geometric buildup algorithm for the solution of the sensor network localization problem, Computational Optimization and Applications (SCI),2010.
[40]余晖,邢燕霞WCDMA网络中的位置业务[M].北京：中国电信集团北京研究院,2003：317.325
[41]DRAGO, SNICULESCU and BADRI NATH:DV Based Positioning in Ad Hoc Networks. Telecommunication Systems 22:1-4,267-280,2003
[42]郭房富WCDMA系统中的移动台定位技术评估.硕士学位论文,浙江,浙江大学,2001
[43]Braginsky D, Estrin D. Rumor routing algorithm for sensor networks[C]. In:Proc. of the 1st workshop on sensor networks and applications. Atlanta:AVM Press.2002:22-31.
[44]Savarese C, Rabaey J,Beutel J. Locationing in Distributed Ad Hoc Wireless Sensor Networks[C]. In Proceeding of ICASSP.May 2001.2037-2040.
[45]Priyantha N,Balakrishnan H,Demaine E,et al. Anchor Free Distributed localization in Sensor Networks[R].Technical Report TR-892,MIT LCS.April 2003.
[46]Wang Shu, Liu Kezhong, Hu Fuping, et al. A Distributed Sensor Network Localization Scheme Motivated by Graph Rigidity Theory [J].The Mediterranean Journal of Measurement and Control.2005,1(4).185-190.
[47]De Oliveira H A B F, Nakamure E F, Loureiro A A F, et al. Directed Estimation: a Recursive Localization Approach for Wireless Sensor networks[C].In Proceeding of the 14th International Conference on Computer Communication and Networks. October,2005.557-562.
[48]Bulusu N, Heidemann J, Estrin D. GPS-less low-cost outdoor localization for very small devices[J].Personal Communication,IEEE.2000,7(5).28-34.
[49]Ss K-F,Ou C-H,Jiau H C. Localization with Mobile Anchor Points in Wireless Sensor Networks [J].IEEE Transactions on Vehicular Technology. May 2005,54(3).1187-1197.
[50]MiodragPotkonjak, JessieaFeng, Lewis Girod. Location discovery using data drive Statistical error modeling[J] · IEEE IN FOCOM,2006,26(8):43-47
[51]HDernaine, TellerS, Priyantha, N.B.Balakrishnan. Mobile assisted localization in Wireless sensor networks[J] Inproc · of IEEE In foeom 05,2005,65(3):323-329
[52]Borg I, Groener P. Modern multidimensional scaling theory and applications. New York:Springer-Verlag,1997,10-35.
[53]顾杰,何芳,龚耀寰.一种新的无线蜂窝定位跟踪技术[J].电子与信息学报,2004,26(4)：511-516
[54]C H Lin,J Y Cheng YCheng, et al. Mobile location estimation by density-based clustering for NLOS enviroments[J]. International conference on advanced information networking and applications,2006,1(18-20):295-300
[55]Yi Sharig, Wheeler Ruml. Improved MDS-Based Localization. IEEE INFOCOM 2004.0-7803-8356-7
[56]Chris Savarese, Jan Rabaey. Robust Positioning Algorithms for Distributed Ad-Hoc Wireless Sensor Networks. Faculty of Information Technology and Systems Delft University of Technology.
[57]Andreas Savvides, Heemin Park and Mani B. Srivastava. The Bits and Flops of the N-hop Multilateration Primitive for Node Localization Problems. WSNA, September 28,2002, Atlanta, Georgia, USA. ACM 1-58113-589-0/02/0009
[58]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
[59]X.-L. Luo and Z.-J. Wu:Least-square approximations in geometric buildup for solving distance geometry problems, Journal of Optimization Theory and Applications (SCI),2010.
[60]R.-Z. Li, X.-L. Luo and J.-R. Lin:Weighted centroid correction localization in cellular systems, American Journal of Engineering and Applied Sciences,2010.