基于粒子滤波的移动传感器网络定位技术研究
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摘要
定位是无线传感器网络(WSN)投入实际应用所需的关键技术之一,高精度、低复杂度的定位算法对无线传感器网络具有重要意义。传统的无线传感器网络定位算法仅适用于节点静止的情况,当节点移动时,会因为周期性重复定位消耗大量的能量,降低网络使用寿命。因此,迫切需要研究适合于移动场景的无线传感器网络定位、目标跟踪技术。为此,本文重点研究了基于序列蒙特卡洛方法(SMC)的移动无线传感器网络定位技术和基于粒子滤波(PF)的无线传感器网络目标跟踪技术。
首先,在查阅大量相关文献的基础上,综述了国内外无线传感器网络定位的研究现状。分别从静态无线传感器网络定位和移动无线传感器网络定位两个方面进行了介绍,重点分析了其中的典型算法,并对典型算法的性能进行了比较,给出了移动无线传感器网络定位的性能评价标准。
其次,作为移动无线传感器网络定位和目标跟踪的理论基础,详细介绍了适用于非线性、非高斯情况下的贝叶斯滤波和粒子滤波技术,并对扩展卡尔曼滤波(EKF)、无迹卡尔曼滤波(UKF)和标准粒子滤波(PF)的性能进行了仿真分析。结合无线传感器网络能量受限的特性,文中还讨论了粒子滤波在无线传感器网络中的五种运行模式,对基于分布式粒子滤波的无线传感器网络目标跟踪算法进行了仿真分析。
再次,对序列蒙特卡洛定位(MCL)、蒙特卡罗盒定位(MCB)和多跳蒙特卡罗定位(MMCL)算法的特点、性能进行了详细的理论分析,并分别从定位精度、样本数、节点密度、锚节点密度、节点运动速度、定位覆盖率等方面进行了MATLAB仿真与性能分析。在此基础上,提出了一种基于自适应采样蒙特卡罗盒(AMCB)的移动传感器网络定位算法,仿真结果表明改进算法在保持定位精度的同时有效地减少了计算量。针对MMCL算法在锚节点密度低时定位精度高的特性,结合DRL动态洪泛锚节点信息节约通信量的优点,提出了一种跳数自适应的移动无线传感器网络蒙特卡罗定位(AMMCL)算法,仿真分析表明,AMMCL在提高定位精度的同时有效地减少了通信量。
最后,本文对开展的研究工作进行了总结,并给出了进一步研究的内容和建议。
Localization plays a crucial role in wireless sensor networks (WSN) as most of WSN applications need the awareness of the node's location. Localization algorithms with high accuracy and low complexity are very important for WSN. Traditional wireless sensor networks localization algorithms only apply to a static situation, when the nodes move, lots of energy will be consumed by the periodically repeated localization. Therefore, it is urgent to study the mobile localization and tracking algorithm which is suited for mobile wireless sensor networks. This thesis focuses on mobile wireless sensor networks location techniques based on Sequential Monte Carlo (SMC) method and target tracking based on particle filter (PF).
First of all, this thesis introduces an overview of wireless sensor networks localization algorithms at home and on abroad, and analyzes the classical localization algorithms of static wireless sensor networks and mobile wireless sensor networks, and then compares the performance of classical location algorithms. The criterion of performance evaluation of mobile wireless sensor networks localization is also summarized.
Secondly, this thesis introduces the particle filter which is suit for non-linear, non-Gaussian, the Bayesian filtering theory and particle filter (PF) are described in detail. The properties of Extended Kalman filter (EKF), unscented Kalman filter (UKF) and standard particle filter are simulated and analyzed. Take the energy-constrained characteristics of the wireless sensor networks into account, this thesis introduces five operating mode of particle filter which are applied in wireless sensor networks, simulates and analyzes the target tracking algorithms of distributed particle filter in wireless sensor networks.
Thirdly, this thesis analyzes the performance and characteristics of Monte Carlo localization (MCL) and its improved algorithm, such as Monte Carlo localization Boxed (MCB), Multi-hop-based Monte Carlo localization (MMCL), then compares their performance from the aspects of localization accuracy, sample number, node density, anchor node density, node velocity and localization ratio base on MATLAB simulation. Based on MCB algorithm we propose a sample Adaptive Monte Carlo Localization Boxed (AMCB) mobile localization algorithm, simulation results demonstrate that the proposed algorithm produces good localization accuracy as well as low computational cost compared with MCL and MCB. Aim at the speciality of the localization accuracy of MMCL algorithm is high when the anchor density is low, take the merit of DRL dynamically changing of anchor's flooding-hop into account, we propose a Adaptive Multi-hop-based Monte Carlo Localization (AMMCL) algorithm. Simulation results show that the proposed algorithm produces better localization accuracy as well as low communication cost compared with MMCL.
Finally, the research work of this paper is concluded and the future research topics are presented.
首先,在查阅大量相关文献的基础上,综述了国内外无线传感器网络定位的研究现状。分别从静态无线传感器网络定位和移动无线传感器网络定位两个方面进行了介绍,重点分析了其中的典型算法,并对典型算法的性能进行了比较,给出了移动无线传感器网络定位的性能评价标准。
其次,作为移动无线传感器网络定位和目标跟踪的理论基础,详细介绍了适用于非线性、非高斯情况下的贝叶斯滤波和粒子滤波技术,并对扩展卡尔曼滤波(EKF)、无迹卡尔曼滤波(UKF)和标准粒子滤波(PF)的性能进行了仿真分析。结合无线传感器网络能量受限的特性,文中还讨论了粒子滤波在无线传感器网络中的五种运行模式,对基于分布式粒子滤波的无线传感器网络目标跟踪算法进行了仿真分析。
再次,对序列蒙特卡洛定位(MCL)、蒙特卡罗盒定位(MCB)和多跳蒙特卡罗定位(MMCL)算法的特点、性能进行了详细的理论分析,并分别从定位精度、样本数、节点密度、锚节点密度、节点运动速度、定位覆盖率等方面进行了MATLAB仿真与性能分析。在此基础上,提出了一种基于自适应采样蒙特卡罗盒(AMCB)的移动传感器网络定位算法,仿真结果表明改进算法在保持定位精度的同时有效地减少了计算量。针对MMCL算法在锚节点密度低时定位精度高的特性,结合DRL动态洪泛锚节点信息节约通信量的优点,提出了一种跳数自适应的移动无线传感器网络蒙特卡罗定位(AMMCL)算法,仿真分析表明,AMMCL在提高定位精度的同时有效地减少了通信量。
最后,本文对开展的研究工作进行了总结,并给出了进一步研究的内容和建议。
Localization plays a crucial role in wireless sensor networks (WSN) as most of WSN applications need the awareness of the node's location. Localization algorithms with high accuracy and low complexity are very important for WSN. Traditional wireless sensor networks localization algorithms only apply to a static situation, when the nodes move, lots of energy will be consumed by the periodically repeated localization. Therefore, it is urgent to study the mobile localization and tracking algorithm which is suited for mobile wireless sensor networks. This thesis focuses on mobile wireless sensor networks location techniques based on Sequential Monte Carlo (SMC) method and target tracking based on particle filter (PF).
First of all, this thesis introduces an overview of wireless sensor networks localization algorithms at home and on abroad, and analyzes the classical localization algorithms of static wireless sensor networks and mobile wireless sensor networks, and then compares the performance of classical location algorithms. The criterion of performance evaluation of mobile wireless sensor networks localization is also summarized.
Secondly, this thesis introduces the particle filter which is suit for non-linear, non-Gaussian, the Bayesian filtering theory and particle filter (PF) are described in detail. The properties of Extended Kalman filter (EKF), unscented Kalman filter (UKF) and standard particle filter are simulated and analyzed. Take the energy-constrained characteristics of the wireless sensor networks into account, this thesis introduces five operating mode of particle filter which are applied in wireless sensor networks, simulates and analyzes the target tracking algorithms of distributed particle filter in wireless sensor networks.
Thirdly, this thesis analyzes the performance and characteristics of Monte Carlo localization (MCL) and its improved algorithm, such as Monte Carlo localization Boxed (MCB), Multi-hop-based Monte Carlo localization (MMCL), then compares their performance from the aspects of localization accuracy, sample number, node density, anchor node density, node velocity and localization ratio base on MATLAB simulation. Based on MCB algorithm we propose a sample Adaptive Monte Carlo Localization Boxed (AMCB) mobile localization algorithm, simulation results demonstrate that the proposed algorithm produces good localization accuracy as well as low computational cost compared with MCL and MCB. Aim at the speciality of the localization accuracy of MMCL algorithm is high when the anchor density is low, take the merit of DRL dynamically changing of anchor's flooding-hop into account, we propose a Adaptive Multi-hop-based Monte Carlo Localization (AMMCL) algorithm. Simulation results show that the proposed algorithm produces better localization accuracy as well as low communication cost compared with MMCL.
Finally, the research work of this paper is concluded and the future research topics are presented.
引文
[1]孙利民,李建中等,无线传感器网络,清华大学出版社,北京,2005年5月.
[2]汪炀,无线传感器网络定位技术研究：[博士学位论文],安徽：中国科学技术大学,2007年
[3]Aspnes J, Eren T, and Goldenberg D, et al. A theory of network localization. IEEE Transactions on Mobile Computing.2006. vol.5(12):1663-1677.
[4]Priyantha N B, Chakraborty A, and Balakrishnan H. Cricket location-support system. MOBICOM 2000:32-43.
[5]Mao G, Fidan B, and Anderso B. Wireless sensor network localization techniques. Computer Networks,2007, val.51(10):2529-2553.
[6]Li X, Shi HC, and Shang Y. A sorted RSSI quantization based algorithm for sensor network localization. The 11th International Conference on Parallel and Distributed Systems Workshops. Fuduoka, Japan,2005,557-563.
[7]Wei X, Zhao J, and Liu X, et al.. EUL:An Efficient and Universal Localization Method for Wireless Sensor Network. ICDCS'2009,433-440.
[8]Niculescu D, Nath B. Ad-hoc positioning system (APS) using AOA. INFOCOM, San Francisco, 2003:1734-1743.
[9]Bulusu N, Heidemann J, and Estrin D. GPS-less Low Cost Outdoor Localization for very Small Devices. IEEE Personal Communications,2000.10, vol.71(5):28-34.
[10]Niculescu D and Nath B. Ad hoc positioning system (APS). IEEE GLOBECOM'01, San Antonio, TX USA, vol.5:2926-2931.
[11]He Tian, Huang Chengdu, and Brian M B, et al.. Range-Free Localization Schemes for Large Scale Sensor Networks. MobiCom 2003, San Diego, California, USA:ACM Press,2(1039):81-95.
[12]Doherty L, Pister KSJ, and Ghaoui LE. Convex position estimation in wireless sensor networks. INFOCOM 2001. Vol.3, Anchorage,2001.1655-1663.
[13]Shang Yi, Wheeler R, and Zhang Ying, et al.. Localization from mere connectivity. Proceedings of the 4th ACM international symposium on Mobile Ad hoc networking & computing. Annapolis, Maryland, USA,2003:201-212.
[14]王福豹,史龙,任丰原.无线传感器网络中的自身定位系统和算法.软件学报.2005,Vol.16,No.5.857-868.
[15]Lazos L and Poovendran R. SeRLoc:Secure range independent localization for wireless sensor networks. In ACM workshop on Wireless security (ACM WiSe'04), Philadelphia, PA, October 2004:21-30
[16]Lazos L and Poovendran R. HiRLoc:High-Resolution Robust Localization for Wireless Sensor Networks. IEEE Journal on Selected Areas in Communications, Vol.24, No.2, February 2006:233-246
[17]Li Mo and Liu Yunhao. Rendered path:Range-free localization in anisotropic sensor networks with holes. Proceedings of the Thirteenth ACM International Conference on Mobile Computing and Networking,2007:51-62
[18]Peralta and Laura M. Rodriguez. Collaborative Localization in Wireless Sensor Networks. Sensor Comm 2007. Oct.2007,94-100.
[19]王伟东,移动传感器网络定位技术研究：[博士学位论文],成都：电子科技大学,2008年.
[20]Doucet A, Freitas N, and Gordon N. (2001) An introduction to sequential Monte Carlo methods., 3-13.
[21]Doucet A and Johansen A M. (2009) A tutorial on particle filtering and smoothing:Fifteen years later. In Oxford Handbook of Nonlinear Filtering, D. Crisan and B. Rozovsky (eds.). Oxford University Press.
[22]Alhmiedat T A and Yang S H. A Survey:Localization and Tracking Mobile Targets through Wireless Sensors Network. In the Eighth Annual Post Graduate Symposium on the Convergence of Telecommunications, Networking and Broadcasting (PGNET),2007.
[23]Peng R and Sichitiu M L. Localization of wireless sensor networks with a mobile beacon. MASS 2004, Fort Lauderdale, FL, USA, October 2004.
[24]Priyantha N B, Balakrishnan H, and Demaine ED, et al.. Mobile-assisted localization in wireless sensor networks. INFOCOM 2005, Miami, FL, USA, March 2005.
[25]Yoon J, Liu M, and Noble B. Random waypoint considered harmful. In IEEE INFOCOM, San Fransciso, CA, USA,2003, March-April.
[26]Hu L and Evans D. Localization for mobile sensor networks, MobiCom'04, Pennsylvania, USA, 2004:45-57.
[27]Baggio A and Langendoen K. Monte-Carlo localization for mobile wireless sensor networks, MSN 2006, Hong Kong, China, December 2006, vol.6(5):718-733.
[28]Masoomeh R and Suprakash D. Localization in wireless sensor networks, Proceedings of the 6th International Symposium on Information processing in sensor networks, Cambridge, Massachusetts, USA. April,2007:51-60.
[29]Wang WD and Zhu QX. RSS-based Monte Carlo localisation for mobile sensor networks. IET Communication.2008, vol.2(5):673-681.
[30]Dil B, Dulman S, and Havinga P. Range-based localization in mobile sensor networks. EWSN2006, Springer, Zurich, Switzerland,2006, val.3868:164-179.
[31]Yi Jiyoung, YangSungwon, and Cha Hojung. Multi-hop-based Monte Carlo Localization for Mobile Sensor Networks. June 2007:163-171.
[32]Hsieh Y.L and Wang K. Efficient localization in mobile wireless sensor networks. SUTC'06: Proceeding of IEEE International Conference on Sensor Networks, Ubiquitous, and Trustworthy Computing. Washington, DC, USA,2006:292-296.
[33]Shee S.-H, Wang K.-C, and Hsieh I.-L. Color-theory-based Dynamic Localization in Mobile Wireless Sensor Networks. In Proceedings of Workshop on Wireless Ad Hoc Sensor Networks, Aug 2005.
[34]Chang Tzu-Chien, Wang Kuochen, and Hsieh Yi-Ling. Enhanced Color-Theory-Based Dynamic Localization in Mobile Wireless Sensor Networks. WCNC 2007:3064-3069.
[35]Zhan P and Martonosi M. LOCALE:Collaborative Localization Estimation for Sparse Mobile Sensor Networks, IPSN 2008, April 2008.
[36]Koo Jahyoung, Yi Jiyoung and Cha Hojung. Localization in mobile ad hoc networks using cumulative route information. Proceedings of the 10th international conference on Ubiquitous computing, ACM International Conference Proceeding Series; 2008, vol.344:124-133.
[37]Yi Jiyoung, Koo Jahyoung, and Cha Hojung. A. Localization Technique for Mobile Sensor Networks using Archived Anchor Information. SECON'08. June 2008:64-72.
[38]Garrick Ing. Distributed particle filters for object tracking in sensor networks, McGill University,2005,1-102
[39]匡兴红,无线传感器网络中定位跟踪技术的研究：[博士学位论文],上海：上海交通大学,2008
[40]Kalman R.E. A new approach to linear filtering and prediction and prediction problems, Trans.
ASME, Journal of basic Engineering, 1960,82D(1):35-45
[41]Arulampalam S, Maskell S, Gordon N, and Clapp T. (2002) A tutorial on particle filters for on-line nonlinear/non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing, 50(2):174-188.
[42]Wan EA, Van Der, and Merwe R. The unscented Kalman filter for nonlinear estimation. proceeding of the Symposium on Adaptive Systems for Signal Processing, Communication and control,2000, pp:153-158.
[43]Julier SJ. The scaled unscented transformation, In:Proceeding of America Control Conference, Anchorage Alaska:IEEE,2002,6:4555-4559.
[44]Gordon NJ, Salmond DJ, and Smith AF. Novel approach to nonlinear/non Gaussian Bayesian state estimation, IEE Proceedings-F(0143-7070),1993,140(2):107-113.
[45]Liu JS and Chen R. Sequential Monte Carlo methods for dynamic system, Journal of the American Statistical Association,1998,93(443):1032-1044
[46]Kitagawa G. Monte carlo filter and smoother for Non-Gaussian nonlinear state space models, Journal of computation and graphical statistics,1996,5(1):1-25.
[47]Musso C, Oudjane N, and Legland F. Improving regularised particle filters [M] De DOUCET A. Sequential Monte Carlo methods in practice. New York:Springer-Verlag,2001.
[48]Pressw H and Farrar GR. Recursive stratified sampling for multi-dimensional Monte Carlo integration [J]. Computers in Physics,1990,4 (2):190-195.
[49]Doucet A. On sequential simulation-based methods for Bayesian filtering, Technical ReportCUED-F-ENG-TR310, Dept. of. Engineering, University of Cambridge,1998.
[50]Chen H Y and Martins M H T. Cooperative node localization for mobile sensor networks. International Conference on Embedded and Ubiquitous Computing. Shanghai, China:Inst of Elec and Elec Eng Computer Society,2008:302-308.
[51]Martins M.H.T, Chen HY, and Sezaki K. OTMCL:Orientation Tracking-based Monte Carlo Localization for Mobile Sensor Networks. In Proceedings of the 6th International Conference on Networked Systems (INSS), Pittsburgh, PA, USA, June 2009:151-158.
[2]汪炀,无线传感器网络定位技术研究：[博士学位论文],安徽：中国科学技术大学,2007年
[3]Aspnes J, Eren T, and Goldenberg D, et al. A theory of network localization. IEEE Transactions on Mobile Computing.2006. vol.5(12):1663-1677.
[4]Priyantha N B, Chakraborty A, and Balakrishnan H. Cricket location-support system. MOBICOM 2000:32-43.
[5]Mao G, Fidan B, and Anderso B. Wireless sensor network localization techniques. Computer Networks,2007, val.51(10):2529-2553.
[6]Li X, Shi HC, and Shang Y. A sorted RSSI quantization based algorithm for sensor network localization. The 11th International Conference on Parallel and Distributed Systems Workshops. Fuduoka, Japan,2005,557-563.
[7]Wei X, Zhao J, and Liu X, et al.. EUL:An Efficient and Universal Localization Method for Wireless Sensor Network. ICDCS'2009,433-440.
[8]Niculescu D, Nath B. Ad-hoc positioning system (APS) using AOA. INFOCOM, San Francisco, 2003:1734-1743.
[9]Bulusu N, Heidemann J, and Estrin D. GPS-less Low Cost Outdoor Localization for very Small Devices. IEEE Personal Communications,2000.10, vol.71(5):28-34.
[10]Niculescu D and Nath B. Ad hoc positioning system (APS). IEEE GLOBECOM'01, San Antonio, TX USA, vol.5:2926-2931.
[11]He Tian, Huang Chengdu, and Brian M B, et al.. Range-Free Localization Schemes for Large Scale Sensor Networks. MobiCom 2003, San Diego, California, USA:ACM Press,2(1039):81-95.
[12]Doherty L, Pister KSJ, and Ghaoui LE. Convex position estimation in wireless sensor networks. INFOCOM 2001. Vol.3, Anchorage,2001.1655-1663.
[13]Shang Yi, Wheeler R, and Zhang Ying, et al.. Localization from mere connectivity. Proceedings of the 4th ACM international symposium on Mobile Ad hoc networking & computing. Annapolis, Maryland, USA,2003:201-212.
[14]王福豹,史龙,任丰原.无线传感器网络中的自身定位系统和算法.软件学报.2005,Vol.16,No.5.857-868.
[15]Lazos L and Poovendran R. SeRLoc:Secure range independent localization for wireless sensor networks. In ACM workshop on Wireless security (ACM WiSe'04), Philadelphia, PA, October 2004:21-30
[16]Lazos L and Poovendran R. HiRLoc:High-Resolution Robust Localization for Wireless Sensor Networks. IEEE Journal on Selected Areas in Communications, Vol.24, No.2, February 2006:233-246
[17]Li Mo and Liu Yunhao. Rendered path:Range-free localization in anisotropic sensor networks with holes. Proceedings of the Thirteenth ACM International Conference on Mobile Computing and Networking,2007:51-62
[18]Peralta and Laura M. Rodriguez. Collaborative Localization in Wireless Sensor Networks. Sensor Comm 2007. Oct.2007,94-100.
[19]王伟东,移动传感器网络定位技术研究：[博士学位论文],成都：电子科技大学,2008年.
[20]Doucet A, Freitas N, and Gordon N. (2001) An introduction to sequential Monte Carlo methods., 3-13.
[21]Doucet A and Johansen A M. (2009) A tutorial on particle filtering and smoothing:Fifteen years later. In Oxford Handbook of Nonlinear Filtering, D. Crisan and B. Rozovsky (eds.). Oxford University Press.
[22]Alhmiedat T A and Yang S H. A Survey:Localization and Tracking Mobile Targets through Wireless Sensors Network. In the Eighth Annual Post Graduate Symposium on the Convergence of Telecommunications, Networking and Broadcasting (PGNET),2007.
[23]Peng R and Sichitiu M L. Localization of wireless sensor networks with a mobile beacon. MASS 2004, Fort Lauderdale, FL, USA, October 2004.
[24]Priyantha N B, Balakrishnan H, and Demaine ED, et al.. Mobile-assisted localization in wireless sensor networks. INFOCOM 2005, Miami, FL, USA, March 2005.
[25]Yoon J, Liu M, and Noble B. Random waypoint considered harmful. In IEEE INFOCOM, San Fransciso, CA, USA,2003, March-April.
[26]Hu L and Evans D. Localization for mobile sensor networks, MobiCom'04, Pennsylvania, USA, 2004:45-57.
[27]Baggio A and Langendoen K. Monte-Carlo localization for mobile wireless sensor networks, MSN 2006, Hong Kong, China, December 2006, vol.6(5):718-733.
[28]Masoomeh R and Suprakash D. Localization in wireless sensor networks, Proceedings of the 6th International Symposium on Information processing in sensor networks, Cambridge, Massachusetts, USA. April,2007:51-60.
[29]Wang WD and Zhu QX. RSS-based Monte Carlo localisation for mobile sensor networks. IET Communication.2008, vol.2(5):673-681.
[30]Dil B, Dulman S, and Havinga P. Range-based localization in mobile sensor networks. EWSN2006, Springer, Zurich, Switzerland,2006, val.3868:164-179.
[31]Yi Jiyoung, YangSungwon, and Cha Hojung. Multi-hop-based Monte Carlo Localization for Mobile Sensor Networks. June 2007:163-171.
[32]Hsieh Y.L and Wang K. Efficient localization in mobile wireless sensor networks. SUTC'06: Proceeding of IEEE International Conference on Sensor Networks, Ubiquitous, and Trustworthy Computing. Washington, DC, USA,2006:292-296.
[33]Shee S.-H, Wang K.-C, and Hsieh I.-L. Color-theory-based Dynamic Localization in Mobile Wireless Sensor Networks. In Proceedings of Workshop on Wireless Ad Hoc Sensor Networks, Aug 2005.
[34]Chang Tzu-Chien, Wang Kuochen, and Hsieh Yi-Ling. Enhanced Color-Theory-Based Dynamic Localization in Mobile Wireless Sensor Networks. WCNC 2007:3064-3069.
[35]Zhan P and Martonosi M. LOCALE:Collaborative Localization Estimation for Sparse Mobile Sensor Networks, IPSN 2008, April 2008.
[36]Koo Jahyoung, Yi Jiyoung and Cha Hojung. Localization in mobile ad hoc networks using cumulative route information. Proceedings of the 10th international conference on Ubiquitous computing, ACM International Conference Proceeding Series; 2008, vol.344:124-133.
[37]Yi Jiyoung, Koo Jahyoung, and Cha Hojung. A. Localization Technique for Mobile Sensor Networks using Archived Anchor Information. SECON'08. June 2008:64-72.
[38]Garrick Ing. Distributed particle filters for object tracking in sensor networks, McGill University,2005,1-102
[39]匡兴红,无线传感器网络中定位跟踪技术的研究：[博士学位论文],上海：上海交通大学,2008
[40]Kalman R.E. A new approach to linear filtering and prediction and prediction problems, Trans.
ASME, Journal of basic Engineering, 1960,82D(1):35-45
[41]Arulampalam S, Maskell S, Gordon N, and Clapp T. (2002) A tutorial on particle filters for on-line nonlinear/non-Gaussian Bayesian tracking. IEEE Transactions on Signal Processing, 50(2):174-188.
[42]Wan EA, Van Der, and Merwe R. The unscented Kalman filter for nonlinear estimation. proceeding of the Symposium on Adaptive Systems for Signal Processing, Communication and control,2000, pp:153-158.
[43]Julier SJ. The scaled unscented transformation, In:Proceeding of America Control Conference, Anchorage Alaska:IEEE,2002,6:4555-4559.
[44]Gordon NJ, Salmond DJ, and Smith AF. Novel approach to nonlinear/non Gaussian Bayesian state estimation, IEE Proceedings-F(0143-7070),1993,140(2):107-113.
[45]Liu JS and Chen R. Sequential Monte Carlo methods for dynamic system, Journal of the American Statistical Association,1998,93(443):1032-1044
[46]Kitagawa G. Monte carlo filter and smoother for Non-Gaussian nonlinear state space models, Journal of computation and graphical statistics,1996,5(1):1-25.
[47]Musso C, Oudjane N, and Legland F. Improving regularised particle filters [M] De DOUCET A. Sequential Monte Carlo methods in practice. New York:Springer-Verlag,2001.
[48]Pressw H and Farrar GR. Recursive stratified sampling for multi-dimensional Monte Carlo integration [J]. Computers in Physics,1990,4 (2):190-195.
[49]Doucet A. On sequential simulation-based methods for Bayesian filtering, Technical ReportCUED-F-ENG-TR310, Dept. of. Engineering, University of Cambridge,1998.
[50]Chen H Y and Martins M H T. Cooperative node localization for mobile sensor networks. International Conference on Embedded and Ubiquitous Computing. Shanghai, China:Inst of Elec and Elec Eng Computer Society,2008:302-308.
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