Saturated Power Control Scheme for Kalman Filtering via Wireless Sensor Networks


We investigate the Kalman filtering problem via wireless sensor networks over fading channels. When part or all of the observation measurements are lost in a random fashion, we obtain the conclusion that the packet dropout probabilities depend upon the time-varying channel gains and the transmission power levels used by the sensors. We develop a satu- rated power controller which trades off sensor energy expenditure versus state estimation accuracy. The latter is measured by the expected value of the future covariance matrices provided by the associated time-varying Kalman filter. We study the statistical convergence properties of the error covariance matrix and pointed out the existence of the admissible packet arrival probability bound.

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D. Zhang, Z. Miao and X. Wang, "Saturated Power Control Scheme for Kalman Filtering via Wireless Sensor Networks," Wireless Sensor Network, Vol. 5 No. 10, 2013, pp. 203-207. doi: 10.4236/wsn.2013.510023.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] H. Gharavi and S. P. Kumar, “Special Section on Sensor Networks Andapplications,” Proceedings of the IEEE, Vol. 91, No. 8, 2003, pp. 1151-1152.
[2] P. Havinga, J. C. Hou and F. Zhao, “Wireless Sensor Net- works,” IEEE Wireless Communications, Vol. 11, No. 12, 2004, pp. 4-5.
[3] M. Ilyas, I. Mahgoub and L. Kelly, “Handbook of Sensor Networks: Compact Wireless and Wired Sensing Systems,” CRC-Press, Boca Raton, 2004.
[4] X. Shen, Q. Zhang and Q. M. Cai, “Wireless Sensor Networking,” IEEE Wireless Communications, Vol. 14, No. 6, 2007, pp. 4-5.
[5] J. P. Hespanha, P. Naghshtabrizi and Y. Xu, “A Survey of Recent Results in Networked Control Systems,” Proceedings of the IEEE, Vol. 1, No. 95, 2007, pp. 138-162.
[6] J. G. Proakis, “Digital Communications,” McGraw-Hill, New York, 1995.
[7] L. Schenato, B. Sinopoli, M. Franceschetti, K. Poolla and S. S. Sastry, “Foundations of Control and Estimation over Lossy Networks,” Proceedings of the IEEE, Vol. 95, No. 1, 2007, pp. 163-187.
[8] D. M. Zhang and X. G. Wang, “Static Output Feedback Control of Networked Control Systems with Packet Dropout,” International Journal of Systems Science, Vol. 43, No. 4, 2012, pp. 665-672.
[9] R. Buche and H. J. Kushner, “Control of Mobile Com- munications with Time Varying Channels in Heavy Traffic,” IEEE Transactions on Automatic Control, Vol. 47, No. 6, 2002, pp. 992-1003.
[10] C. D. Charalambous, S. M. Djouadi and S. Z. Denic, “Stochastic Power Control for Wireless Networks via SDEs: Probabilistic QoS Measures,” IEEE Transactions on Automatic Control, Vol. 51, No. 12, 2005, pp. 4396-4401.
[11] F. Gunnarsson and F. Gustafsson, “Control Theory Aspects of Power Control in UMTS,” Control Engineering Practice, Vol. 11, No. 10, 2003, pp. 1113-1125.
[12] S. V. Hanly and D.-N. Tse, “Power Control and Capacity of Spread Spectrum Wireless Networks,” Automatica, Vol. 35, No. 12, 1999, pp. 1987-2012.
[13] M. Huang, P. E. Caines and R. P. Malham, “Uplink Po- wer Adjustment in Wireless Communication Systems: A Stochastic Control Analysis,” IEEE Transactions on Automatic Control, Vol. 49, No. 10, 2004, pp. 1693-1708.
[14] G. Caire, G. Taricco and E. Biglieri, “Optimum Power Control over Fading Channels,” Institute of Electrical and Electronics Engineers, Transactions on Information Theory, Vol. 45, No. 5, 1999, pp. 1468-1489.
[15] N. A. Pantazis and D. D. Vergados, “A Survey on Power Control Issues in Wireless Sensor Networks,” IEEE Communication Surveys and Tutorials, Vol. 9, No. 4, 2007, pp. 86-107.
[16] P. G. Park, C. Fischione and K. H. Johansson, “Experi- mental Evaluation of Power Control Algorithms for Wireless Sensor Networks,” Proceedings of the IFAC World Congress, Seoul, 2008.
[17] J.-J. Xiao, S. Cui, Z.-Q. Luo and A. J. Goldsmith, “Power Scheduling of Universal Decentralized Estimation in Sensor Networks,” IEEE Transactions on Signal Processing, Vol. 54, No. 2, 2006, pp. 413-422.
[18] X. Zhang, H. V. Poor and M. Chiang, “Optimal Power Allocation for Distributed Detection over MIMO Channels in Wireless Sensor Networks,” IEEE Transactions on Signal Processing, Vol. 56, No. 9, 2008, pp. 4124- 4140.
[19] D. M. Zhang, X. G. Wang and J. Liu, “Robust Power Control Method for Wireless Sensor Networks with Static Output Feedback,” Journal of Control Theory and Application, Vol. 10, No. 1, 2012, pp. 44-49.
[20] B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. I. Jordan and S. S. Sastry, “Kalman Filtering with Intermittent Observations,” IEEE Transactions on Automatic Control, Vol. 49, No. 9, 2004, pp. 1453-1464.
[21] X. H. Liu and G. Andrea, “Kalman Filtering with Partial Observation Losses,” Proceedings of 43rd IEEE CDC, Bahamas, 14-17 December 2004, pp. 4180-4186.
[22] K. Plarre and F. Bullo, “On Kalman Filtering for Detectable Systems with Intermittent Observations,” IEEE Trans- actions on Automatic Control, Vol. 54, No. 2, 2009, pp. 386-390.
[23] M. Huang and S. Dey, “Stability of Kalman Filtering with Markovian Packet Losses,” Automatica, Vol. 43, No. 4, 2007, pp. 598-607.
[24] Z. Jin, V. Gupta and R. Murray, “State Estimation over Packet Dropping Networks Using Multiple Description Coding,” Automatica, Vol. 42, No. 9, 2006, pp. 1441- 1452.
[25] L. Shi, M. Epstein and R. M. Murray, “Kalman Filtering over a Packet-Dropping Network: A Probabilistic Perspective,” IEEE Transactions on Automatic Control, Vol. 55, No. 3, 2010, pp. 594-604.
[26] W. A. Zhang, G. Feng and L. Yu, “Multi-Rate Distributed Fusion Estimation for Sensor Networks with Packet Losses,” Automatica, Vol. 48, No. 9, 2012, pp. 2016-2028.
[27] E. D. Quevedo, A. Anders, S. L. Alex and D. Subhrakanti, “On Kalman Filtering over Fading Wireless Channels with Controlled Transmission Powers,” Automatica, Vol. 48, No. 7, 2012, pp. 1306-1316.

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