Abstract
This paper studies the optimal and suboptimal deconvolution problems over a network subject to random packet losses, which are modeled by an independent identically distributed Bernoulli process. By the projection formula, an optimal input white noise estimator is first presented with a stochastic Kalman filter. We show that this obtained deconvolution estimator is time-varying, stochastic, and it does not converge to a steady value. Then an alternative suboptimal input white-noise estimator with deterministic gains is developed under a new criterion. The estimator gain and its respective error covariance-matrix information are derived based on a new suboptimal state estimator. It can be shown that the suboptimal input white-noise estimator converges to a steady-state one under appropriate assumptions.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. M. Mendel, “White-noise estimators for seismic data processing in oil exploration,” IEEE Trans. on Automatic Control, vol. 22, no. 5, pp. 694–706, October 1977.
J. M. Mendel, “Minimum-variance deconvolution,” IEEE Trans. Geosci. Remote Sensing, vol. 19, no. 3, pp. 161–171, January 1981.
S. Sun, “Multi-sensor information fusion white noise filter weighted by scalars based on Kalman predictor,” Automatica, vol. 40, no. 8, pp. 1447–1453, January 2004.
X. Sun, Y. Gao, Z. Deng, C. Li, and J. Wang, “Multi-model information fusion Kalman filtering and white noise deconvolution,” Information Fusion, vol. 11, no. 2, pp. 163–173, 2010.
X. Sun and G. Yan, “Self-tuning weighted measurement fusion white noise deconvolution estimator and its convergence analysis,” Digital Signal Processing, vol. 23, no.1, pp. 38–48, 2013.
Z. Deng, H. Zhang, S. Liu, and L. Zhou, “Optimal and self-tuning white noise estimators with applications to deconvolution and filtering problems,” Automatica, vol. 32, no. 2, pp. 199–216, February 1996.
L. Chisci and E. Mosca, “Polynomial equations for the linear MMSE state estimation,” IEEE Trans. on Automatic Control, vol. 37, no. 5, pp. 623–626, 1992.
H. Zhang, L. Xie, and Y. C. Soh, “Optimal and self-tuning deconvolution in time domain,” IEEE Trans. on Signal Processing, vol. 47, no. 8, pp. 2253–2261, 1999.
H. Zhang, L. Xie, and Y. C. Soh, “H ∞ deconvolution filtering, prediction, and smoothing: a Krein space polynomial approach,” IEEE Trans. on Automatic Control, vol. 48, no. 3, pp. 888–892, 2000.
B. Zhang, J. Lam, and S. Xu, “Deconvolution filtering for stochastic systems via homogeneous polynomial Lyapunov functions,” Signal Processing, vol. 89, no. 4, pp. 605–614, 2009.
X. Lu, H. Zhang, and J. Yan, “On the H ∞ deconvolution fixed-lag smoothing,” International Journal of Control, Automation, and Systems, vol. 8, no. 4, pp. 896–902, 2010.
B. Chen and J. Hung, “Fixed-order H 2 and H ∞ optimal deconvolution filter designs,” Signal Processing, vol. 80, no. 2, pp. 311–331, 2000.
A. Cuenca, J. Salt, V. Casanova, and R. Pizá, “An approach based on an adaptive multi-rate smith predictor and gain scheduling for a networked control system: implementation over profibus-DP,” International Journal of Control, Automation, and Systems, vol. 8, no. 2, pp. 473–481, 2010.
A. Cuenca, P. García, P. Albertos, and J. Salt, “A non-uniform predictor-observer for a networked control system,” International Journal of Control, Automation, and Systems, vol. 9, no. 6, pp. 1194–1202, 2011.
B. Sinopoli, L. Schenato, M. Franceschetti, K. Poolla, M. I. Jordan, and S. S. Sastry, “Kalman filtering with intermittent observations,” IEEE Trans. on Automatic Control, vol. 49, no. 9, pp. 1453–1464, September 2004.
K. Plarre and F. Bullo, “On Kalman filtering for detectable systems with intermittent observations,” IEEE Trans. on Automatic Control, vol. 54, no. 2, pp. 386–390, 2009.
K. You, M. Fu, and L. Xie, “Mean square stability for Kalman filtering with Markovian packet losses,” Automatica, vol. 47, no. 12, pp. 2647–2657, 2011.
M. Sahebsara, T. Chen, and S. L. Shah, “Optimal H 2 filtering in networked control systems with multiple packet dropout,” IEEE Trans. on Automatic Control, vol. 52, no. 8, pp. 1508–1513, 2007.
S. Sun, L. Xie, W. Xiao, and Y. C. Soh, “Optimal linear estimation for systems with multiple packet dropouts,” Automatica, vol. 44, no. 5, pp. 1333–1342, 2008.
G. Wei, Z. Wang, and H. Shu, “Robust filtering with stochastic nonlinearities and multiple missing measurements,” Automatica, vol. 45, no. 3, pp. 836–841, 2009.
B. Shen, Z. Wang, H. Shu, and G. Wei, “On nonlinear H ∞ filtering for discrete-time stochastic systems with missing measurement,” IEEE Trans. on Automatic Control, vol. 53, no. 9, pp. 2170–2180, 2008.
J. Ma, L. Liu, and S. Sun, “White noise filters for systems with multiple packet dropouts,” Proc. of the 30th Chinese Control Conference, Yantai, China, pp. 1586–1590, July 22–24, 2011.
C. Yu, N. Xiao, C. Zhang, and L. Xie, “An optimal deconvolution smoother for systems with random parametric uncertainty and its application to semiblind deconvolution,” Signal Processing, vol. 92, no. 10, pp. 2497–2508, 2012.
H. Zhang, X. Song, and L. Shi, “Convergence and mean square stability of optimal estimators for systems with measurement packet dropping,” IEEE Trans. on Automatic Control, vol. 57, no. 5, pp. 1248–1253, 2012.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Editorial Board member Young Soo Suh under the direction of Editor Zengqi Sun.
This journal was supported by the National Nature Science Foundation of China (61104050, 61203029), the Natural Science Foundation of Shandong Province (ZR2011FQ020), the Research Fund for the Doctoral Program of Higher Education of China (20120131120058), and the Project of Shandong Province Higher Educational Science and Technology Program (J12LN18).
Chunyan Han received her Ph.D. degree in Control Theory and Control Engineering from Shandong University in 2010. She is currently a lecturer at the School of Electrical Engineering, University of Jinan. Her research interest covers optimal control and estimation, time delay systems, and Markov jump linear systems.
Wei Wang received his Ph.D. degree in Control Science and Engineering from Shenzhen Graduate School, Harbin Institute of Technology, in 2010. He is currently a Lecturer at Shandong University, Jinan Shandong, China. His research interests include optimal control and estimation for delayed systems, distributed control and estimation.
Yuan Zhang is currently working as an Associate Professor at University of Jinan, China. He received his M.Sc. degree in Communication Systems and Ph.D. in Control Theory & Engineering both from Shandong University, China, in 2003 and 2012 respectively. As the first author or corresponding author he has published more than 20 peer reviewed technical papers in archival journals and conference proceedings, including IEEE Communications Letters, Elsevier Ad Hoc Networks, etc. He has served as Corresponding Guest Editor for a special issue of International Journal of Ad Hoc and Ubiquitous Computing. His research interests are in wireless networks and optimal estimation, currently focusing on wireless sensor networks and smartphone sensing. He is a member of IEEE.
Rights and permissions
About this article
Cite this article
Han, C., Wang, W. & Zhang, Y. White noise estimators for networked systems with packet dropouts. Int. J. Control Autom. Syst. 11, 1187–1195 (2013). https://doi.org/10.1007/s12555-012-0451-0
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12555-012-0451-0