針對利用無線感測網路(wireless sensor network)開發的定位系統而言，定位的準確度與感測器能量的使用效能可視為設計時主要考量的兩大重點。一些以距離為依據的定位技術已被提出使用分散式的架構來實現定位的估計運算，每個感測器只需與鄰近的感測器相互溝通與傳送資料，相較於集中式的架構而言，可省略掉將每個感測器蒐集到的資料全部傳送到中央處理器做運算時所需耗掉龐大的傳輸能量。而這些定位技術往往將每個感測器在做距離估測上的準確度視為相同，但實際上各個感測器隨著各種因素影響會有不同的準確性，因此不準確的感測器往往會造成目標位置估測上較大的誤差。
本篇論文當中，我們提出一個利用權重內插的方法並可以分散式架構實現的定位技術，其設計上主要考量實際在做距離估測時，每個感測器都會有不同的估測準確性，從數學推導的式子中可以發現，距離目標物越遠的感測器，其距離估測的準確性越低，因此我們利用權重的概念，根據每個感測器個別的準確性給予不同的權重，來達到更好的目標位置估計；此外，以權重內插的方法推導出的疊代式子能讓此定位演算法以分散式架構實現，每個感測器只要利用自己蒐集到的資訊對估測結果做修正，在傳送給下一個鄰近的感測器繼續計算直到收斂；另一方面，利用適應性更新得到的調整大小(step size)能使疊代的演算法收斂更為迅速準確；另外，針對分散式的定位技術提出一個環狀網路似(token ring-like)的方法加以實現，在實際的應用上能提供較佳的能量效益；由電腦模擬的結果中，可明顯的看出疊代演算法中使用適應性更新的調整大小能得到較佳的收斂效果，並且所提出考慮不同感測器的準確度給予不同權重的定位方法相較其他定位方法也能達到更加的定位準確性。

Abstract

Accuracy and energy efficiency are two major requirements for the development of a positioning system in wireless sensor networks. Some distance-based positioning approaches have been proposed to be implemented in a decentralized manner for energy saving, leaving out the need of transmitting all data to a central server for processing. These algorithms are usually formulated as a least square problem which assumes measurements from all sensors are accurate equally. As a matter of fact, the accuracy of distance estimation from each sensor varies according to the actual distance between the target and the sensor. Thus, some inaccurate distance estimation may cause serious error in location estimation for these methods.
In this thesis, we propose a decentralized positioning scheme based on weighted interpolation. We formulate the positioning problem as a weighted least square problem and distribute different weights among sensors according to the reliability of the distance estimation from each sensor. An iterative scheme is then derived from weighted interpolation such that the proposed positioning method can be implemented in a decentralized manner；Each sensor adjusts the estimate based on local data and then passes the modified result to its neighbor. In addition, an adaptive step size is used for the iterative procedure to have fast convergence. Moreover, a token ring-like distribution scheme is proposed for the decentralized positioning algorithms, which provides energy efficient design principle for practical implementation. Computer simulation results show that, as compared to a previous iterative decentralized positioning method based on the projection onto convex sets, the proposed scheme has faster convergence speed and achieves better positioning accuracy.

[1] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, “A survey on sensor networks,” IEEE Commun. Mag., vol. 40, pp. 102–114, Aug. 2002.

[2] K. Pahlavan, X. Li, and J. Makela, “Indoor geolocation science and technology,” IEEE Commun. Mag., vol. 40, pp. 112–118, Feb. 2002.

[3] N. Patwari, J. N. Ash, S. Kyperountas, A. O. Hero, III, R. L. Moses, and N. S. Correal, “Locating the nodes: Cooperative localization in wireless sensor Networks,” IEEE Signal Processing Mag., vol. 22, no. 4, July 2005, pp.54–69.

[4] Y.-C. Chen, J.-R. Chiang, H.-H. Chu, P. Huang, A. W. Tsui, “Sensor-assisted Wi-Fi indoor location system for adapting to environmental dynamics,” ACM/IEEE Int. Symp. on Modeling, Analysis and Simulation of Wireless and Mobile Systems (MSWiM 2005), Montreal, Qc. Canada, Oct. 2005, pp 118–125.

[5] K. Kaemarungsi and P. Krishnamurthy, “Properties of indoor received signal strength for WLAN location fingerprinting,” in Proc. of the The First Annual Int. Conf. on Mobile and Ubiquitous Systems: Networking and Services (MOBIQUITOUS), Boston, MA, 2004, pp. 14–23.

[6] G. L. , Principles of Mobile Communication. Norwell, MA: Kluwer, 1998.

[7] J. C. Libert, T. S. Rappaport, “Statistics of shasowing in indoor radio channels at 900 and 1900 MHz”, in Proc. 1992 IEEE Military Commun. Conf. (MILCOM ‘92), San Diego, CA, vol. 3, Oct. 1992, pp. 1060–1070.

[8] P. Bahl and V. N. Padmanabhan, “RADAR: An in-building RF-based user location and tracking system,” in Proc. IEEE INFOCOM 2000, Tel–Aviv, Israel, vol. 2, Mar. 2000, pp. 775–784.

[9] P. Bahl and V. N. Padmanabhan and A. Balachandran, “Enhencements to the RADAR user location and tracking system,” Microsoft Research Tech. Report: MSR-TR-00-12. Feb. 2000.

[10] Y. Chen and H. Kobayashi, “Signal strength based indoor geolocation,” in Proc. IEEE Int. Conf. Commun. (ICC 2002), New York, NY, vol. 1, pp. 436 – 439, May 2002.

[11] J. Kwon, B. Dundar, and P. Varaiya, “Hybrid algorithm for indoor positioning using wireless LAN,” in Proc. 2004 IEEE 60th Veh. Technol. Conf. (VTC 2004), vol. 7, Los Angeles, CA, Sep. 2004, pp. 4625–4629.

[12] P. Prasithsangaree, P. Krishnamurthy and P. K. Chrysanthis, “One indoor position location with wireless LANs,” in Proc. 2002 IEEE Int. Symp. Personal Indoor and Mobile Radio Commun. (PIMRC 2002), vol. 2, Sep. 2002, pp.720-724.

[13] M. G. Rabbat and R. D. Nowak, “Decentralized source localization and tracking,” in Proc. 2004 IEEE Int. Conf. Acoustics, Speech, Signal Processing, (ICASSP ’04), vol.3 , pp. 921–924 May. 2004.

[14] A. O. Hero and D. Blatt, “Sensor network source localization via projection onto convex sets (POCS),” in Proc. of the IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP 05), Philadelphia, PA , vol. 5, pp. 1065–1068, March 2005.

[15] N. Patwari, A.O. Hero, III, M. Perkins, N. Correal, and R. O’Dea, “Relative location estimation in wireless sensor networks,” IEEE Trans. Signal Processing, vol. 51, pp. 2137 – 2148, Aug. 2003.

[16] S. Y. Seidel and T. S. Rappaport, “914 MHz path loss prediction models for indoor wireless communications in multifloored build,” IEEE Trans. Antennas Propagat vol. 40, pp. 207 – 217, Feb. 1992.

[17] S. Phaiboon, “An empirically based path loss model for indoor wireless channels in laboratory building,” in Proc. IEEE TENCON 2002, Beijing, vol. 2, Oct. 2002, pp. 1020–1023.

[18] C. J. Liberti, Jr., T. S. Rappaport, Smart Antennas for Wireless Communications: IS-95 and Thied Generation CDMA Applications. Upper Saddle River, NJ: Prentice Hall PTR,1999.