مکان‌یابی بر اساس تفاضل توان سیگنال دریافتی با به کارگیری بهینه‌سازی محدب در شبکه حسگر بی‌سیم
محورهای موضوعی : مهندسی برق و کامپیوترحسن نظری 1 * , میثم رئیس دانایی 2 , مرتضی سپه‌وند 3
1 - دانشگاه جامع امام حسین (ع)
2 - دانشگاه جامع امام حسین (ع)
3 - دانشگاه جامع امام حسین (ع)
چکیده مقاله :
برای انجام مکان‌یابی بر اساس تفاضل توان سیگنال دریافتی در شبکه حسگر بی‌سیم می‌بایست توان دریافتی آلوده به نویز را توسط تعدادی حسگر مرجع جمع‌آوری نمود. به دلیل مشخص‌بودن تابع چگالی احتمال نویز استفاده از تخمین‌گر حداکثر درست‌نمایی بهترین انتخاب خواهد بود. تابع هزینه این تخمین‌گر غیر خطی و غیر محدب است و تا کنون برای آن جواب تحلیلی ارائه نشده است. یکی از راه‌حل‌ها برای غلبه بر این مشکل استفاده از روش‌های بهینه‌سازی محدب است. در این مقاله برای غلبه بر این مشکل تابع هزینه تخمین‌گر حداکثر درست‌نمایی را به دست می‌آوریم و آن را با روش آزادسازی نیمه‌معین حل می‌کنیم. شبیه‌سازی‌های کامپیوتری نشان می‌دهد در شرایطی که حسگرهای شبکه به صورت غیر منظم در محیط پخش شوند تخمین‌گر جدید نسبت به سایر تخمین‌گرها جذر متوسط انرژی خطای مکان‌یابی کمتری را نشان می‌دهد، یعنی دقت مکان‌یابی بالاتری دارد. در روش جدید دقت مکان‌یابی نسبت به سایر روش‌ها تا 20% افزایش می‌یابد و پیچیدگی محاسباتی آن نیز نسبت به روش‌های بهینه‌سازی محدب 30% کمتر است.
Localization with differential received signal strength measurement in recent years has been very much considered. Due to the fact that the probability density function is known for given observations, the maximum likelihood estimator is used. This estimator can be asymptotically represented the optimal estimation of the location. After the formation of this estimator, it is observed that the corresponding cost function is highly nonlinear and non-convex and has a lot of minima, so there is no possibility of achieving the global minimum with Newton method and the localization error will be high. There is no analytical solution for this cost function. To overcome this problem, two methods are existed. First, the cost function is approximated by a linear estimator. But this estimator has poor accuracy. The second method is to replace the non-convex cost function with a convex one with the aid of convex optimization methods, in which case the global minimum is obtained. In this paper, we proposed new convex estimator to solve cost function of maximum likelihood estimator. The results of the simulations show that the proposed estimator has up to 20 percent performance improvement compared with existing estimators, moreover, the execution time of proposed estimator is 30 percent faster than other convex estimators.
[1] N. Patwari, Location Estimation in Sensor Networks, Ph.D. Disseration, University of Michigan, Ann Arbor, USA, 2005.
[2] X. Fang and J. Li, "Frame theory for optimal sensor augmentation problem of AOA localization," IEEE Signal Process. Lett., vol. 25, no. 9, pp. 1310-1314, Sept. 2018.
[3] Y. Kang, Q. Wang, J. Wang, and R. Chen, "A high-accuracy TOA-based localization method without time synchronization in 3D space," IEEE Trans. Ind. Informat., vol. 15, no. 1, pp. 173-182, Jan. 2019.
[4] S. Salari, F. Chan, Y. T. Chan, and W. Read, "TDOA estimation with compressive sensing measurements and hadamard matrix," IEEE Trans. Aerosp. Electron. Syst., vol. 54, no. 6, pp. 3137-3142, Dec. 2018.
[5] X. Tian, et al., "Improve accuracy of fingerprinting localization with temporal correlation of the RSS," IEEE Trans. Mob. Comput., vol. 17, no. 1, pp. 113-126, Jan. 2018.
[6] Y. Y. Li, G. Q. Qi, and A. D. Sheng, "Performance metric on the best achievable accuracy for hybrid TOA/AOA target localization," IEEE Commun. Lett., vol. 22, no. 7, pp. 1474-1477, Jul. 2018.
[7] R. Sari and H. Zayyani, "RSS localization using unknown statistical path loss exponent model," IEEE Commun. Lett., vol. 22, no. 9, pp. 1830-1833, Sep. 2018.
[8] C. Li, Y. Li, Z. Tian, S. L. Weekes, and K. Pahlavan, "Design and performance evaluation of a localization system to locate unwanted drones by using wireless signals," in Proc. IEEE Inte Conf. on Consumer Electronics, ICCE’16, 6 pp., Las Vegas, NV, USA, 12-14 Jan. 2018.
[9] S. Tomic, M. Beko, M. Tuba, and V. M. F. Correia, "Target localization in NLOS environments using RSS and TOA measurements," IEEE Wirel. Commun. Lett., vol. 7, no. 6, pp. 1062-1065, Dec. 2018.
[10] S. M. Kay, Fundamentals of Statistical Signal Processing, volume i: Estimation Theory, PTR Prentice-Hall, Englewood Cliffs, 1993.
[11] H. Lohrasbipeydeh, T. A. Gulliver, and H. Amindavar, "Unknown transmit power RSSD based source localization with sensor position uncertainty," IEEE Trans. on Communications, vol. 63, no. 5, pp. 1784-1797, May 2015.
[12] A. Beck, P. Stoica, and J. Li, "Exact and approximate solutions of source localization problems," IEEE Trans. Signal Process., vol. 56, no. 5, pp. 1770-1778, May 2008.
[13] R. W. Ouyang, A. K. S. Wong, and C. T. Lea, "Received signal strength-based wireless localization via semidefinite programming: noncooperative and cooperative schemes," IEEE Trans. Veh. Technol., vol. 59, no. 3, pp. 1307-1318, Mar. 2010.
[14] R. M. Vaghefi, M. R. Gholami, R. M. Buehrer, and E. G. Strom, "Cooperative received signal strength-based sensor localization with unknown transmit powers," IEEE Trans. Signal Process., vol. 61, no. 6, pp. 1389-1403, Mar. 2013.
[15] Y. Hu and G. Leus, "Robust differential received signal strength-based localization," IEEE Trans. Signal Process., vol. 65, no. 12, pp. 3261-3276, Jun. 2017.
[16] S. Tomic, M. Beko, R. Dinis, and V. Lipovac, "RSS-based localization in wireless sensor networks using SOCP relaxation," IEEE 14th Workshop on Signal Processing Advances in Wireless Communications, SPAWC’13, pp. 749-753, Darmstadt, Germany, 16-19 Jun. 2013.
[17] CVX Research, Inc., CVX: MATLAB Software for Disciplined Convex Programming [Online]. Available: http://cvxr.com/cvx/. [Accessed: 17-Dec-2010].
[18] J. H. Lee and R. M. Buehrer, "Location estimation using differential RSS with spatially correlated shadowing," in Proc. IEEE Glob. Telecommun. Conf., pp. 4613-4618, Honolulu, HI, USA, 30 Nov.- 4 Dec. 2009.
[19] N. Salman, Y. J. Guo, A. H. Kemp, and M. Ghogho, "Analysis of linear least square solution for RSS based localization," in Proc. Int. Symp. on Communications and Information Technologies, ISCIT’12, pp. 1051-1054, Gold Coast, QLD, Australia, 2-5 Oct. 2012.
[20] M. R. Gholami, R. M. Vaghefi, and E. G. Strom, "RSS-based sensor localization in the presence of unknown channel parameters," IEEE Trans. Signal Process., vol. 61, no. 15, pp. 3752-3759, Aug. 2013.
[21] S. Tomic, M. Beko, R. Dinis, M. Tuba, and N. Bacanin, "Bayesian methodology for target tracking using combined RSS and AoA measurements," Phys. Commun., vol. 25, no. 1, pp. 158-166, Dec. 2017.
[22] N. Patwari, et al., "Locating the nodes," IEEE Signal Processing Mag., vol. 22, no. 4, pp. 54-69, Jul. 2005.
[23] S. Tomic, M. Beko, and R. Dinis, "RSS-based localization in wireless sensor networks using convex relaxation: noncooperative and cooperative schemes," IEEE Trans. Veh. Technol., vol. 64, no. 5, pp. 2037-2050, May 2015.
[24] G. Rahimi, M. R. Danaee, and S. Bayat, "A generalized total least squares algorithm for RSS-based localization with unknown path-loss model parameters," in Proc. 24th Iran. Conf. Elec. Eng. ICEE’16, pp. 521-524, Shiraz, Iran, 10-12 May 2016.
[25] T. S. Rappaport, Wireless Communications Principles and Practice, vol. 2, Prentice Hall PTR New Jersey, 1996.
[26] Z. Li, X. Zhong, and J. Wei, "A novel geometry-based model for localization based on received signal strength," in Proc. IEEE 87th Vehicular Technology Conf., VTC Spring’18, 5 pp., Porto, Portugal, 3-6 Jun. 2018.
[27] R. M. Vaghefi and R. M. Buehrer, "Received signal strength-based sensor localization in spatially correlated shadowing," in Proc. IEEE ICASSP’13, pp. 4076-4080, Vancouver, BC, Canada, 26-31 May 2013.
[28] S. Boyd and L. Vandenberghe, Convex Optimization, Cambridge University Press, 2004.