在無線定位環境中，影響定位精準度的因素除了通道的干擾外，感測節點與定位
目標的位置佈建也是因素之一，這種幾何位置關係的影響現象稱為幾何精度稀釋效應
(Geometric Dilution of Precision, GDOP) 。幾何精度稀釋效應可以作為定位效能的
指標之ㄧ，用於描述定位誤差與量測誤差之間的關係，數值愈大代表定位誤差愈大，
則定位精確度愈差。本文欲使用訊號抵達時間差(Time Difference of Arrival, TDOA)
量測法，與擴展式卡爾曼濾波器(Extended Kalman Filter, EKF) 追蹤一個連續移動
的目標，當目標位置隨時間變動，感測節點與定位目標的幾何架構也將改變，故為了盡
量維持良好的幾何架構，採用移動式感測節點(Mobile Sensor Node, MSN) 的設計概
念，利用移動式感測節點的機動性改善感測節點與目標所形成的幾何位置關係，降低幾
何精度稀釋效應。針對某個瞬間的目標，其位置是固定的，我們將計算幾何精度稀釋的
過程定義成GT 函數，並且計算整個範圍的GDOP 值後得到GT 分布，為了找尋移
動式感測節點的最佳位置，使用模擬退火法(Simulated Annealing) 具不易落入區域最
小值的特性，將模擬退火法作為最佳化演算法，找出GT 函數最小值之處當作移動式
感測節點的最佳位置。當移動式感測節點要移動到最佳位置時，可能會因自身速度不夠
快到足以一步抵達最佳位置，而停留在高幾何精度稀釋理論值的區域造成較差的定位效
能，所以必須為移動式感測節點的移動路徑做規劃，讓移動式感測節點移動的過程可以
選擇轉彎或直走，為此我們建立一目標函數，並且選擇往最小目標函數值的位置移動。
透過電腦模擬，針對系統中具單一移動式感測節點與系統中具單一固定式感測節點的情
況進行模擬，結果驗證移動式感測節點會隨目標移動而改變其位置，透過模擬退火法的
搜尋，固定式感測節點與移動式感測節點都能形成一個良好的範圍包圍目標，使幾何精
度稀釋理論值降低

In wireless positioning system, in addition to channel error, the geometric re-
lationship between sensor nodes and the target may also affect the positioning
accuracy. The effect is called geometric dilution of precision (GDOP). GDOP is
determined as ratio factor between location error and measurement error. A higher
GDOP value indicates a larger location error in location estimation. Accordingly,
the location performance will be poor. The GDOP can therefore be used as an in-
dex of the positioning performance. In this thesis, approaches of tracking a moving
target with extended Kalman filter (EKF) in a time-difference-of-arrival (TDOA)
wireless positioning system are discussed. While the target changes its position with
time, the geometric layout between sensor nodes and the target will become differ-
ent. To maintain the good layout, the positioning system with mobile sensor nodes
is considered. Therefore, the geometric layout can be possibly improved and GDOP
effect can be reduced by the mobility of mobile sensor nodes. In order to find the
positions that mobile sensor nodes should move to, a time-varying function based
on the GDOP distribution is defined for finding the best solutions. Since the simu-
lated annealing is capable of escaping local minima and finding the global minimum
in an objective function, the simulated annealing algorithm is used in finding the
best solutions in the defined function. Thus the best solutions can be determined
as the destinations of mobile sensor nodes. When relocating mobile sensor nodes
from their current positions to the destinations, they may pass through or stay in
high GDOP regions before arriving at the destinations. To avoid the problem, we
establish an objective function for path planning of mobile sensor nodes in order to
minimize the overall positioning accuracy. Simulation results show that the mobile
sensor nodes will accordingly change their positions while the target is moving. All
the sensor nodes will maintain a surrounding region to localize the target and the
GDOP effect can be effectively reduced.

誌謝. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . i
中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii
英文摘要. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
圖目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
表目錄. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
1 緒論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 研究背景. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 定位精準度的影響因素. . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 幾何精度稀釋效應(GDOP) . . . . . . . . . . . . . . . . . . . 2
1.1.3 移動式感測節點之設置. . . . . . . . . . . . . . . . . . . . . . 2
1.2 研究動機. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.3 論文架構. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
2 藉由改善幾何精度稀釋效應提升定位效能. . . . . . . . . . . . . . . . . . . 4
2.1 訊號抵達時間差定位法中的GDOP 效應. . . . . . . . . . . . . . . . 4
2.2 針對固定式目標之探討. . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.3 針對移動式目標之探討. . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.3.1 移動式目標之初始位置估測. . . . . . . . . . . . . . . . . . . 11
2.3.2 移動式目標之預測與追蹤. . . . . . . . . . . . . . . . . . . . . 14
3 移動式感測節點的最佳位置搜尋與路徑規劃. . . . . . . . . . . . . . . . . . 19
3.1 搜尋移動式感測節點之最佳位置. . . . . . . . . . . . . . . . . . . . . 19
3.2 移動式感測節點之路徑規劃. . . . . . . . . . . . . . . . . . . . . . . 22
3.3 移動式感測節點之位置改變. . . . . . . . . . . . . . . . . . . . . . . 31
4 電腦模擬與分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.1 模擬環境之參數設定. . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.2 模擬結果分析. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
4.2.1 系統中具單一移動式感測節點之模擬結果. . . . . . . . . . . . 33
4.2.2 系統中具單一固定式感測節點之模擬結果. . . . . . . . . . . . 59
5 結論與建議. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.1 結論. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.2 建議. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
參考文獻. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

[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 Ap-
plications, 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 infor-
mation,” IEEE Signal Processing Magazine, vol. 22, no. 4, pp. 24–40, 2005.
[3] A. Waadt, G. Bruck, and P. Jung, “An overview of positioning systems and
technologies,” in Proceedings of the 2nd International Symposium on Applied
Sciences in Biomedical and Communication Technologies, 2009, pp. 1–5.
[4] M. A. Birchler, “E911 Phase II location technologies,” IEEE Vehicular Tech-
nology Society News, pp. 4–9, November 2002.
[5] H. Lee, “A novel procedure for assessing the accuracy of hyperbolic multilater-
ation systems,” IEEE Transactions on Aerospace and Electronic Systems, vol.
AES-11, no. 1, pp. 2–15, 1975.
[6] I. Sharp, K. Yu, and Y. Guo, “GDOP analysis for positioning system design,”
IEEE Transactions on Vehicular Technology, vol. 58, no. 7, pp. 3371–3382,
2009.
[7] Y. Zhao, C.-H. Lung, I. Lambadaris, and N. Goel, “Improving location identifi-
cation in wireless Ad Hoc/sensor networks using GDOP theory,” in Proceedings
of the Third International Conference on Sensor Technologies and Applications,
2009, pp. 223–228.
[8] K. Bronk and J. Stefanski, “Bad geometry influence on positioning accuracy in
wireless networks,” in Proceedings of the International Conference on ”Com-
puter as a Tool”, 2007, pp. 1131–1135.
[9] N. Levanon, “Lowest GDOP in 2-D scenarios,” IEE Proceedings on Radar,
Sonar and Navigation, vol. 147, no. 3, pp. 149–155, 2000.
[10] S. Maheswararajah and S. Halgamuge, “Mobile sensor management for tar-
get tracking,” in Proceedings of the 2nd International Symposium on Wireless
Pervasive Computing, 2007, pp. 506–510.
[11] 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.
[12] K. Pahlavan, X. Li, and J. Makela, “Indoor geolocation science and technol-
ogy,” IEEE Communications Magazine, vol. 40, no. 2, pp. 112–118, 2002.
[13] S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory.
Prentice Hall, 1993.
[14] Y.-T. Yen, C.-D.Wann, and Y.-S. Huang, “Mobile base station for performance
improvement in wireless positioning systems,” in Proceedings of 2009 National
Symposium of Telecommunications, 2009, pp. 1329–1333.
[15] W. Foy, “Position-location solutions by Taylor-series estimation,” IEEE Trans-
actions on Aerospace and Electronic Systems, vol. AES-12, no. 2, pp. 187–194,
1976.
[16] Y. Chan and K. Ho, “A simple and efficient estimator for hyperbolic location,”
IEEE Transactions on Signal Processing, vol. 42, no. 8, pp. 1905–1915, 1994.
[17] H. Schau and A. Robinson, “Passive source localization employing intersect-
ing spherical surfaces from time-of-arrival differences,” IEEE Transactions on
Acoustics, Speech, and Signal Processing, vol. 35, no. 8, pp. 1223–1225, August
1987.
[18] J. Smith and J. Abel, “Closed-form least-squares source location estima-
tion from range-difference measurements,” IEEE Transactions on Acoustics,
Speech, and Signal Processing, vol. 35, no. 12, pp. 1661–1669, December 1987.
[19] H. Qasem and L. Reindl, “Unscented and extended Kalman estimators for non
linear indoor tracking using distance measurements,” in Proceedings of the 4th
Workshop on Positioning, Navigation and Communication, 2007, pp. 177–181.
[20] M. Forti and A. Tesi, “New conditions for global stability of neural networks
with application to linear and quadratic programming problems,” IEEE Trans-
actions on Circuits and Systems I: Fundamental Theory and Applications,
vol. 42, no. 7, pp. 354–366, 1995.
[21] J. Parker, A. Khoogar, and D. Goldberg, “Inverse kinematics of redundant
robots using genetic algorithms,” in Proceedings of the IEEE International
Conference on Robotics and Automation, 1989, pp. 271–276 vol.1.
[22] N. Metropolis, A. W. Rosenbluth, M. N. Rosenbluth, and A. H. Teller, “Equa-
tions of calculation by fast computing machines,” Journal of Chemical Physics,
pp. 1087–1092, 1953.
[23] S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, “Optimization by simulated
annealing,” Science, vol. 220, no. 4598, pp. 671–680, May 1983.
[24] C. Warren, “A technique for autonomous underwater vehicle route planning,”
IEEE Journal of Oceanic Engineering, vol. 15, no. 3, pp. 199–204, 1990.
[25] T.-C. Liang and J.-S. Liu, “An improved trajectory planner for redundant ma-
nipulators in constrained workspace,” in Proceedings of the IEEE International
Conference on Robotics and Automatio, vol. 4, 1999, pp. 3153–3158 vol.4.
[26] M. Jaryani, “An effective manipulator trajectory planning with obstacles us-
ing virtual potential field method,” in Proceedings of the IEEE International
Conference on Systems, Man and Cybernetics, 2007, pp. 1573–1578.