在無線定位系統中，因基地台 (Base Station, BS) 陣列與行動台 (Mobile Station, MS) 的幾何相對關係不同而影響定位精準度，此現象稱為幾何精度稀釋 (Geometric Dilution of Precision, GDOP)，幾何精度稀釋理論值可由基地台架構及行動台的已知位置計算求得。事實上，幾何精度稀釋可做為一項定位效能指標，數值大小可用來描述定位誤差及量測誤差之間的關係，幾何精度稀釋理論值越大，則代表定位誤差越大，定位精準度越差。當行動台位於不同基地台幾何架構下，觀察其定位精準度，藉由基地台及行動台幾何分布的改變，可以使得定位精準度提升。本論文以幾何精度稀釋做為提升無線定位系統中定位精準度的依據，在訊號抵達時間差 (Time Difference of Arrival, TDOA) 定位系統下提出以移動式基地台 (Mobile Base Station, MBS) 的機動運作，藉由移動式基地台的位置改變，進而形成基地台與行動台間的新幾何架構，達到降低幾何精度稀釋效應並提升定位精準度的目的。對於移動式基地台在幾何架構中的最佳位置找尋，由於模擬退火法 (Simulated Annealing, SA) 具有跳脫區域最小值 (local minimum) 的特性，為搜索全域最小值 (global minimum) 的演算法，我們利用模擬退火法來找尋幾何精度稀釋理論最小值及其平面位置，其位置可視為移動式基地台的最佳位置。在得到最佳位置後，移動式基地台可由現在位置以機動方式前往該最佳位置。在不考慮空間中障礙物或地形等影響移動的因素下，移動式基地台由初始位置移動至最佳位置的過程，將有可能會進入高幾何精度稀釋理論值的區域。為了避開此區域，我們採用最速下降法 (Steepest Descent, SD) 來規劃移動式基地台的移動路徑，利用現在位置與最終位置的資訊建立目標函數，目標函數可由幾何精度稀釋資訊及移動角度所組成；之後利用最速下降法逐次搜索位置週遭下一次移動範圍中最小目標函數值的位置，直到抵達最佳位置。在電腦模擬中，我們針對單一移動式基地台、單一固定式基地台及全移動式基地台等三種情況下進行模擬與探討，由模擬結果可以發現，移動式基地台移動至最佳位置，能有效降低幾何精度稀釋效應，在移動過程中，移動式基地台能有效避開高幾何精度稀釋理論值的區域，降低幾何精度稀釋效應的影響並維持穩定的平均定位精準度。

In wireless location system, geometric relationship between the base station (BS) and the mobile station (MS) may affect the accuracy of MS location estimate. The effect is called Geometric Dilution of Precision (GDOP). Given the information of geometric configuration of BS and MS locations, the GDOP value can be calculated accordingly. In fact, the GDOP value is considered as ratio factor between the location error and measurement noise. A higher GDOP value indicates larger location error in the location estimator. Therefore the GDOP can be utilized as an index for observing the location precision of the MS under different geometric layout. The accuracy of location estimation can be improved by changing the BS device element locations. In the thesis, a time different of arrival (TDOA) wireless location system with mobile base station (MBS) is considered. Changing the geometric layout between the BS and the MS by relocating the MBS, the GDOP effect can be reduced and the accuracy of location estimation also can therefore be improved. Since the simulated annealing (SA) is capable of escaping the local minimum and finding the global minimum in an objective function, the SA algorithm is used in finding the best solution in a defined function based on the GDOP distribution. The best solution is then the destination of an MBS in the process of MS location estimation. When relocating an MBS from its initial location to the best location, it is likely that the MBS enters regions with high GDOP effects. To avoid the problem, the steepest descent (SD) algorithm is utilized for path planning. First, we establish the objective function which consists of the GDOP information and the angle of movement. A nearby location that has the minimum value of objective function is selected as the next move. The process continues until the MBS reaches the destination. A variety of cases are investigated by computer simulations. Simulation results show that the proposed approach can effectively find the best locations for MBSs to relocate. Based on the relocation and path planning, the GDOP effects can be reasonably reduced, and therefore the higher location accuracy is achieved.

誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
表目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
1 序論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 研究背景及文獻探討. . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 移動式基地台. . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 無線定位演算法. . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.3 幾何精度稀釋效應. . . . . . . . . . . . . . . . . . . . . . . . 3
1.1.4 移動式基地台之最佳位置. . . . . . . . . . . . . . . . . . . . . 4
1.1.5 移動式基地台之路徑規劃. . . . . . . . . . . . . . . . . . . . . 4
1.2 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 論文架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2 幾何精度稀釋理論值分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
2.1 幾何分布對無線定位誤差的影響. . . . . . . . . . . . . . . . . . . . . 6
2.1.1 訊號抵達時間(Time of Arrival, TOA) . . . . . . . . . . . . . 7
2.1.2 訊號抵達時間差(Time Difference of Arrival, TDOA) . . . . . 13
2.2 TDOA 定位系統的GDOP 理論值探討. . . . . . . . . . . . . . . . . 13
2.3 基地台位置不變情況下GDOP 理論值分析. . . . . . . . . . . . . . . 19
2.3.1 基地台數量之影響. . . . . . . . . . . . . . . . . . . . . . . . 21
2.3.2 基地台幾何分布範圍之影響. . . . . . . . . . . . . . . . . . . 26
2.4 行動台位置不變情況下GDOP 理論值分析. . . . . . . . . . . . . . . 28
2.4.1 定義GT 函數. . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4.2 行動台與基地台角度之影響. . . . . . . . . . . . . . . . . . . 29
3 移動式基地台之最佳位置與路徑規劃. . . . . . . . . . . . . . . . . . . . . . 36
3.1 移動式基地台之最佳位置. . . . . . . . . . . . . . . . . . . . . . . . . 36
3.1.1 模擬退火法原理介紹. . . . . . . . . . . . . . . . . . . . . . . 38
3.1.2 利用模擬退火法找尋最佳位置. . . . . . . . . . . . . . . . . . 41
3.2 移動式基地台之路徑規劃. . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2.1 建立目標函數. . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.2.2 利用最速下降法進行路徑規劃. . . . . . . . . . . . . . . . . . 44
3.3 路徑規劃效能判斷依據. . . . . . . . . . . . . . . . . . . . . . . . . . 46
4 電腦模擬與分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.1 無線定位模擬環境之參數設定. . . . . . . . . . . . . . . . . . . . . . 48
4.2 移動式基地台路徑規劃模擬. . . . . . . . . . . . . . . . . . . . . . . 49
4.2.1 具單一移動式基地台之系統. . . . . . . . . . . . . . . . . . . 49
4.2.2 具單一固定式基地台之系統. . . . . . . . . . . . . . . . . . . 53
4.2.3 全移動式基地台之系統. . . . . . . . . . . . . . . . . . . . . . 54
5 結論與建議. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.2 建議. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

[1] S. Swales, J. Maloney, and J. Stevenson, “Locating mobile phones and the US wireless E-911 mandate,” in Proceedings of the IEE Colloquium on Novel Methods of Location and Tracking of Cellular Mobiles and Their System Applications, 1999, pp. 2/1–2/6.
[2] A. Sayed, A. Tarighat, and N. Khajehnouri, “Network-based wireless location: challenges faced in developing techniques for accurate wireless location information,” IEEE Signal Processing Magazine, vol. 22, no. 4, pp. 24–40, 2005.
[3] FCC, “Revision of the commissions rules to ensure compatibility with enhanced 911 emergency calling systems,” in Report and Order and Further Notice of Proposed Rulemaking. Washington, DC: Federal Communications Commission, June 1996.
[4] T. Rappaport, J. Reed, and B. Woerner, “Position location using wireless communications on highways of the future,” IEEE Communications Magazine, vol. 34, no. 10, pp. 33–41, 1996.
[5] K. Krizman, T. Biedka, and T. Rappaport, “Wireless position location: fundamentals, implementation strategies, and sources of error,” in Proceedings of the 47th IEEE Vehicular Technology Conference, vol. 2, 1997, pp. 919–923 vol.2.
[6] IEEE 802.16j-06/026r2, “Baseline document for draft standard for local and metropolitan area networks.”
[7] K. Pahlavan, X. Li, and J. Makela, “Indoor geolocation science and technology,” IEEE Communications Magazine, vol. 40, no. 2, pp. 112–118, 2002.
[8] K. Pahlavan, P. Krishnamurthy, and A. Beneat, “Wideband radio propagation modeling for indoor geolocation applications,” IEEE Communications Magazine, vol. 36, no. 4, pp. 60–65, 1998.
[9] W. Hirt, “Ultra-wideband radio technology: overview and future research,” Computer Communications, vol. 26, no. 1, pp. 46–52, Jan. 2003. [Online]. Available: http://www.sciencedirect.com/science/article/B6TYP-461XPFR-9/2/b8ad11078d732637bf9b70ba10f4baea
[10] D. Porcino and W. Hirt, “Ultra-wideband radio technology: potential and challenges ahead,” IEEE Communications Magazine, vol. 41, no. 7, pp. 66–74, 2003.
[11] W. Alsalih, S. Akl, and H. Hassanein, “Placement of multiple mobile base stations in wireless sensor networks,” in Proceedings of the IEEE International Symposium on Signal Processing and Information Technology, 2007, pp. 229–233.
[12] A. Azad and A. Chockalingam, “Mobile base stations placement and energy aware routing in wireless sensor networks,” in Proceedings of the IEEE Wireless Communications and Networking Conference, vol. 1, 2006, pp. 264–269.
[13] H. Su and X. Zhang, “Power-efficiency data gathering schemes for wireless sensor networks,” in Proceedings of the International Conference on Computer Communications and Networks, 2006, pp. 328–333.
[14] P. Pathirana, A. Savkin, and S. Jha, “Location estimation and trajectory prediction for cellular networks with mobile base stations,” IEEE Transactions on Vehicular Technology, vol. 53, no. 6, pp. 1903–1913, 2004.
[15] M. Pozzo and V. Tralli, “Data collection in wireless sensor networks using mobile base stations and geographic forwarding,” in Proceedings of the International Conference on Information Networking, 2008, pp. 1–5.
[16] M. A. Birchler, “E911 Phase II location technologies,” IEEE Vehicular Technology Society News, November 2002.
[17] J. Hightower and G. Borriello, “Location systems for ubiquitous computing,” Computer, vol. 34, no. 8, pp. 57–66, 2001.
[18] H. Liu, H. Darabi, P. Banerjee, and J. Liu, “Survey of wireless indoor positioning techniques and systems,” IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews, vol. 37, no. 6, pp. 1067–1080, 2007.
[19] M. Hata and T. Nagatsu, “Mobile location using signal strength measurements
in a cellular system,” IEEE Transactions on Vehicular Technology, vol. 29, no. 2, pp. 245–252, 1980.
[20] C. Alippi and G. Vanini, “A RSSI-based and calibrated centralized localization technique for wireless sensor networks,” in Proceedings of the IEEE International Conference on Pervasive Computing and Communications Workshops, 2006, pp. 5 pp.–305.
[21] S. Sakagami, S. Aoyama, K. Kuboi, S. Shirota, and A. Akeyama, “Vehicle position estimates by multibeam antennas in multipath environments,” IEEE Transactions on Vehicular Technology, vol. 41, no. 1, pp. 63–68, 1992.
[22] J. Caffery, Jr. and G. Stuber, “Subscriber location in CDMA cellular networks,” IEEE Transactions on Vehicular Technology, vol. 47, no. 2, pp. 406–416, 1998.
[23] M. Spirito and A. Mattioli, “On the hyperbolic positioning of GSM mobile stations,” in Proceedings of the International Symposium on Signals, Systems, and Electronics, 1998, pp. 173–177.
[24] P. Bahl and V. Padmanabhan, “RADAR: an in-building RF-based user location and tracking system,” in Proceedings of the IEEE Nineteenth Annual Joint Conference of the IEEE Computer and Communications Societies., vol. 2, 2000, pp. 775–784 vol.2.
[25] K. Lorincz, D. J.Malan, T. R. Fulford-Jones, A. Nawoj, A. Clavel, V. Shnayder, G. Mainland, M. Welsh, and S. Moulton, “Sensor networks for emergency response: Challenges and opportunities,” IEEE Pervasive Computing, vol. 3, no. 4, pp. 16–23, 2004.
[26] N. B. Priyantha, A. Chakraborty, and H. Balakrishnan, “The cricket location support system,” in Proceedings of the 6th annual international conference on Mobile computing and networking. Boston, Massachusetts, United States: ACM, 2000, pp. 32–43.
[27] J. Liberti and T. Rappaport, “A geometrically based model for line-of-sight multipath radio channels,” in Proceedings of the IEEE 46th Vehicular Technology Conference, vol. 2, 1996, pp. 844–848 vol.2.
[28] N. Levanon, “Lowest GDOP in 2-D scenarios,” IEE Proceedings on Radar, Sonar and Navigation, vol. 147, no. 3, pp. 149–155, 2000.
[29] R. Kelly, “Reducing geometric dilution of precision using ridge regression,” IEEE Transactions on Aerospace and Electronic Systems, vol. 26, no. 1, pp. 154–168, 1990.
[30] C.-H. Chen, K.-T. Feng, C.-L. Chen, and P.-H. Tseng, “Wireless location estimation with the assistance of virtual base stations,” IEEE Transactions on Vehicular Technology, vol. 58, no. 1, pp. 93–106, 2009.
[31] N. Metropolis, R. AE, and T. AH, “Equations of calculation by fast computing machines,” Journal of Chemical Physics, pp. 1087–1092, 1953.
[32] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated annealing,” Science, vol. 220, no. 4598, pp. 671–680, May 1983.
[33] J. A. Snyman, Practical Mathematical Optimization: An Introduction to Basic Optimization Theory and Classical and New Gradient-Based Algorithms. Springer Publishing, 2005.
[34] M. Mitchell, An introduction to genetic algorithms. The MIT Press, 1998.
[35] C. Warren, “A technique for autonomous underwater vehicle route planning,” IEEE Journal of Oceanic Engineering, vol. 15, no. 3, pp. 199–204, 1990.
[36] S. Vougioukas, “Optimization of robot paths computed by randomized planners,” in Proceedings of the 2005 IEEE International Conference on Robotics and Automation, 2005, pp. 2148–2153.
[37] J. Zelek and M. Levine, “Local-global concurrent path planning and execution,” IEEE Transactions on Systems, Man and Cybernetics, Part A: Systems and Humans, vol. 30, no. 6, pp. 865–870, 2000.
[38] S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory. Prentice Hall, 1993.
[39] H. Lee, “A novel procedure for assessing the accuracy of hyperbolic multilateration systems,” IEEE Transactions on Aerospace and Electronic Systems, vol. AES-11, no. 1, pp. 2–15, 1975.