我們研究了無線感測器網路(Wireless Sensor Network, WSN) 在混合直視(Line Of Sight, LOS) 與非直視(Non-Line Of Sight, NLOS) 訊號環境中的目標物定位，由於非直視訊號的影響，會使得原本的定位方法準確度下降，加上考量到感測器資源有限，是以接收訊號強度(Received Signal Strength, RSS) 等數據對其做量化(quantization)，融合中心以此量化訊號進行目標物定位。
由於非直視訊號的效應，我們透過建立雙模式高斯混合分佈的測量誤
差，並且假設其混合模型參數是完全未知，因此採用最大期望(Expectation Maximization, EM) 方法來近似目標物位置和混合模型參數的最大似然估計(Maximum Likelihood Estimation, MLE)，而我們所提出的方法修正了最小平方法(Least Squares Estimation, LSE) 在測量誤差屬於高斯混合分佈的狀況。

We studied the target localization method for quantized wireless sensor networks(WSN) in the mixed Line Of Sight (LOS) and Non-Line Of Sight (NLOS) signal environments. Owing to the influence of NLOS signals, the accuracy of conventional localization methods are degraded. And, considering limited power resources of sensors,
the Received Signal Strength (RSS) data is usually quantized to several bits. The fusion center can only employ the quantized signals to localize the target position. Due to the effect of non-line of sight signals, we model the measurement noise as a Gaussian mixture distribution and assume that the mixture model parameters are completely unknown. Therefore, the Expectation Maximization (EM) method is used to approximate the Maximum Likelihood Estimation (MLE) target position and the mixed model parameters. The proposed method modifies the Least Squares Estimation (LSE) condition in which the measurement error belongs to a Gaussian mixture distribution.

[1] S. Borman, “The expectation maximization algorithm-a short tutorial,” Submitted
for publication, vol. 41, 2004.
[2] S. Prince, Computer Vision: Models Learning and Inference. Cambridge University
Press, 2012.
[3] I. F. Akyildiz, W. Su, Y. Sankarasubramaniam, and E. Cayirci, “Wireless sensor
networks: a survey,” Computer networks, vol. 38, no. 4, pp. 393–422, 2002.
[4] R. Niu and P. K. Varshney, “Performance analysis of distributed detection in a
random sensor field,” IEEE Transactions on Signal Processing, vol. 56, no. 1, pp.
339–349, Jan 2008.
[5] N. Patwari, J. N. Ash, S. Kyperountas, A. O. Hero, R. L. Moses, and N. S. Correal,
“Locating the nodes: cooperative localization in wireless sensor networks,” IEEE
Signal Processing Magazine, vol. 22, no. 4, pp. 54–69, July 2005.
[6] T. He, P. Vicaire, T. Yan, Q. Cao, G. Zhou, L. Gu, L. Luo, R. Stoleru, J. A.
Stankovic, and T. F. Abdelzaher, “Achieving long-term surveillance in vigilnet,”
in Proceedings IEEE INFOCOM 2006. 25TH IEEE International Conference on
Computer Communications, April 2006, pp. 1–12.
[7] A. D. Wood, J. A. Stankovic, G. Virone, L. Selavo, Z. He, Q. Cao, T. Doan, Y. Wu,
L. Fang, and R. Stoleru, “Context-aware wireless sensor networks for assisted living
and residential monitoring,” IEEE Network, vol. 22, no. 4, pp. 26–33, July
2008.
[8] R. Mittal and M. P. S. Bhatia, “Wireless sensor networks for monitoring the environmental
activities,” in 2010 IEEE International Conference on Computational
Intelligence and Computing Research, Dec 2010, pp. 1–5.
[9] H. Lee, A. Banerjee, Y. Fang, B. Lee, and C. King, “Design of a multifunctional
wireless sensor for in-situ monitoring of debris flows,” IEEE Transactions on Instrumentation
and Measurement, vol. 59, no. 11, pp. 2958–2967, Nov 2010.
[10] J. Liberti and T. Rappaport, Smart antennas for wireless communications: IS-95
and third generation CDMA applications, ser. Prentice Hall communications engineering
and emerging technologies series. Prentice Hall, 1999, includes bibliographical
references (pages 345-365) and index.
[11] K. Yang, G. Wang, and Z. Luo, “Efficient convex relaxation methods for robust
target localization by a sensor network using time differences of arrivals,” IEEE
Transactions on Signal Processing, vol. 57, no. 7, pp. 2775–2784, July 2009.
[12] R. P and M. L. Sichitiu, “Angle of arrival localization for wireless sensor networks,”
in 2006 3rd Annual IEEE Communications Society on Sensor and Ad Hoc
Communications and Networks, vol. 1, Sep. 2006, pp. 374–382.
[13] X. Li, “Rss-based location estimation with unknown pathloss model,” IEEE Transactions
on Wireless Communications, vol. 5, no. 12, pp. 3626–3633, December
2006.
[14] G. Wang and K. Yang, “A new approach to sensor node localization using rss
measurements in wireless sensor networks,” IEEE Transactions on Wireless Communications,
vol. 10, no. 5, pp. 1389–1395, May 2011.
[15] R. Niu and P. Varshney, “Target location estimation in wireless sensor networks
using binary data,” in 38th Annual Conference on Information Sciences and Systems,
2004.
[16] R. Niu and P. K. Varshney, “Target location estimation in sensor networks with
quantized data,” IEEE Transactions on Signal Processing, vol. 54, no. 12, pp.
4519–4528, Dec 2006.
[17] F. Gustafsson and F. Gunnarsson, “Mobile positioning using wireless networks:
possibilities and fundamental limitations based on available wireless network measurements,”
IEEE Signal Processing Magazine, vol. 22, no. 4, pp. 41–53, July
2005.
[18] H. Wymeersch, J. Lien, and M. Z. Win, “Cooperative localization in wireless networks,”
Proceedings of the IEEE, vol. 97, no. 2, pp. 427–450, Feb 2009.
[19] L. Cheng, Q. Qi, X. Wu, Y. Shao, and Y. Wang, “A nlos selection based localization
method for wireless sensor network,” in 2017 7th IEEE International Conference
on Electronics Information and Emergency Communication (ICEIEC), July 2017,
pp. 340–343.
[20] S. Tomic, M. Beko, R. Dinis, and P. Montezuma, “A robust bisection-based estimator
for toa-based target localization in nlos environments,” IEEE Communications
Letters, vol. 21, no. 11, pp. 2488–2491, Nov 2017.
[21] Y. Wang, L. Cheng, and N. Hu, “Bayes sequential test based nlos localization
method for wireless sensor network,” in The 27th Chinese Control and Decision
Conference (2015 CCDC), May 2015, pp. 5230–5234.
[22] Y. Huang, S. Zhang, and Y. Jing, “An indoor mobile localization strategy based on
particle filter in nlos environment,” in 2016 Chinese Control and Decision Conference
(CCDC), May 2016, pp. 6518–6522.
[23] S. Korkmaz and A. van der Veen, “Robust localization in sensor networkswith iterative
majorization techniques,” in 2009 IEEE International Conference on Acoustics,
Speech and Signal Processing, April 2009, pp. 2049–2052.
[24] J. N. Ash and R. L. Moses, “Outlier compensation in sensor network selflocalization
via the em algorithm,” in Acoustics, Speech, and Signal Processing,
2005. Proceedings.(ICASSP’05). IEEE International Conference on, vol. 4.
IEEE, 2005, pp. iv–749.
[25] A. P. Dempster, N. M. Laird, and D. B. Rubin, “Maximum likelihood from incomplete
data via the em algorithm,” JOURNAL OF THE ROYAL STATISTICAL
SOCIETY, SERIES B, vol. 39, no. 1, pp. 1–38, 1977.
[26] G. V. Reklaitis, A. Ravindran, and K. M. Ragsdell, Engineering optimization:
Methods and applications. Wiley New York, 1983.
[27] E. C. Ifeachor and B. W. Jervis, Digital signal processing: a practical approach.
Pearson Education, 2002.
[28] F. Yin, A. M. Zoubir, C. Fritsche, and F. Gustafsson, “Robust cooperative sensor
network localization via the em criterion in los/nlos environments,” in 2013
IEEE 14th Workshop on Signal Processing Advances in Wireless Communications
(SPAWC), June 2013, pp. 505–509.
[29] F. Yin, C. Fritsche, D. Jin, F. Gustafsson, and A. M. Zoubir, “Cooperative localization
in wsns using gaussian mixture modeling: Distributed ecm algorithms,”
IEEE Transactions on Signal Processing, vol. 63, no. 6, pp. 1448–1463, March
2015.
[30] and, “Energy based collaborative source localization using acoustic micro-sensor
array,” in 2002 IEEE Workshop on Multimedia Signal Processing., Dec 2002, pp.
371–375.
[31] O. Ozdemir, R. Niu, and P. K. Varshney, “Channel aware target localization with
quantized data in wireless sensor networks,” IEEE Transactions on Signal Processing,
vol. 57, no. 3, pp. 1190–1202, March 2009.
[32] S. M. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory.
Upper Saddle River, NJ, USA: Prentice-Hall, Inc., 1993.
[33] A. Mezghani, M. Khoufi, and J. A. Nossek, “Maximum likelihood detection for
quantized mimo systems,” in 2008 International ITG Workshop on Smart Antennas,
Feb 2008, pp. 278–284.
[34] S. B. V. and, “Likelihood-based statistical estimation from quantized data,” IEEE
Transactions on Instrumentation and Measurement, vol. 54, no. 1, pp. 409–414,
Feb 2005.
[35] S. Schlupkothen, G. Dartmann, and G. Ascheid, “A novel low-complexity numerical
localization method for dynamic wireless sensor networks,” IEEE Transactions
on Signal Processing, vol. 63, no. 15, pp. 4102–4114, Aug 2015.
[36] J. Bilmes, “A gentle tutorial of the em algorithm and its application to parameter
estimation for gaussian mixture and hidden markov models,” Tech. Rep., 1998.
[37] J. Nocedal and S. J. Wright, Numerical Optimization, 2nd ed. New York, NY,
USA: Springer, 2006.
[38] W. Spendley, G. R. Hext, and F. R. Himsworth, “Sequential application of simplex
designs in optimisation and evolutionary operation,” Technometrics, vol. 4, no. 4,
pp. 441–461, 1962. [Online]. Available: http://www.jstor.org/stable/1266283