State estimation for discrete linear systems with observation time-delayed noise

Previous Article
Cluster synchronization for linearly coupled complex networks
JIMO Home
This Issue
Next Article
Global optimality conditions for some classes of polynomial integer programming problems

January 2011, 7(1): 79-85. doi: 10.3934/jimo.2011.7.79

State estimation for discrete linear systems with observation time-delayed noise

Peng Cui ^1, , Hongguo Zhao ^2, and Jun-e Feng ^3,

1.	School of Control Science and Engineering, Shandong University, Jinan 250000, China
2.	Department of Information Science and Technology, Taishan University, Taian 271021, China
3.	School of Mathematics, Shandong University, Jinan 250000, China

Received July 2010 Revised September 2010 Published January 2011

Abstract
Related Papers

State estimation problem is discussed for discrete-time systems with delays in measurement noise sequence, which is usually seen in network control and geophysical prospecting systems. An optimal recursive filter is derived via state augmentation. Dimensions of the optimal filter just are the sum of dimensions of state and observation vector. Therefore, they are not related to the size of delay. Besides, a sub-optimal recursive filter with same dimension as the original state is designed. The sub-optimal filter realizes instant optimization at current time. One example shows the effectiveness of the proposed approach.

Keywords: Kalman filtering., optimal estimation, sub-optimal estimation, Time-delayed noise.

Mathematics Subject Classification: Primary: 93E11; Secondary: 62M2.

Citation: Peng Cui, Hongguo Zhao, Jun-e Feng. State estimation for discrete linear systems with observation time-delayed noise. Journal of Industrial and Management Optimization, 2011, 7 (1) : 79-85. doi: 10.3934/jimo.2011.7.79

References:

[1]	B. D. O. Anderson and J. B. Moore, "Optimal Filtering," Prentice-Hall, Englewood Cliffs, New Jersey, 1979.
[2]	M. Basin, J. Rodriguez-Gonzalez and R. Martinez Zúniga, Optimal filtering for linear state delay systems, IEEE Trans. on Automatic Control, 50 (2005), 684-690. doi: 10.1109/TAC.2005.846599.
[3]	A. Calzolari, P. Florchinger and G. Nappo, Nonlinear filtering for markov systems with delayed observations, Int. J. Appl. Math. Comput. Sci., 19 (2009), 49-57. doi: 10.2478/v10006-009-0004-8.
[4]	Y. Chocheyras, Near field three dimensional time delay and doppler target motion analysis, in "International Conference on Acoustics, Speech, and Signal Processing," (1989), 2649-2652. doi: 10.1109/ICASSP.1989.267012.
[5]	T. Kailath, A. H. Sayed, and B. Hassibi, "Linear Estimation", Prentice-Hall, Englewood Cliffs, New Jersey, 1999.
[6]	R. E. Kalman, A new approach to linear filtering and prediction problems, Trans. ASME, Series D, Journal of Basic Engineering, 82 (1960), 35-45.
[7]	R. E. Kalman and R. S. Bucy, New results in linear filtering and prediction theory, Transactions of the ASME-Journal of Basic Engineering, 83 (1961), 95-108.
[8]	H. Kwakernaak, Optimal filtering in linear systems with time delays, IEEE Trans. on Automatic Control, 12 (1967), 169-173. doi: 10.1109/TAC.1967.1098541.
[9]	X. Lu, H. S. Zhang, W. Wang and K. L. Teo, Kalman filtering for multiple time-delay systems, Automatica, 41 (2005), 1455-1461. doi: 10.1016/j.automatica.2005.03.018.
[10]	D. MacMillan, J. Bohm, M. Gipson, R. Haas, A. Niell, T. Nilsson, A. Pany, B. Petrachenko and J. Wresnik, Simulation analysis of the geodetic performance of the future IVS VLBI2010 system, in "American Geophysical Union Fall Meeting," San Francisco, (2008), G33A-0667.
[11]	G. A. Medrano-Cerda, Filtering for linear system involving time delays in the noise process, IEEE Trans. on Automatic Control, 28 (1983), 801-803. doi: 10.1109/TAC.1983.1103318.
[12]	C. L. Su and C. N. Lu, Interconnected network state estimation using randomly delayed measurements, IEEE Trans. on Power Systems, 16 (2001), 870-878. doi: 10.1109/59.962439.
[13]	A. Subramanian and A. H. Sayed, Multiobjective filter design for uncertain stochastic time-delay systems, IEEE Trans. on Automatic Control, 49 (2004), 149-154. doi: 10.1109/TAC.2003.821422.
[14]	S. L. Sun, Linear minimum variance estimators for systems with bounded random measurement delays and packet dropouts, Signal Processing, 89 (2009), 1457-1466. doi: 10.1016/j.sigpro.2009.02.002.
[15]	Z. Wang, D. W. C. Ho and X. Liu, Robust filtering underrandomly varying sensor delay with variance constraints, IEEE Trans. on Circuits and Systtems II: Express Briefs, 51 (2004), 320-326. doi: 10.1109/TCSII.2004.829572.
[16]	E. Yaz and A. Ray, Linear unbiased state estimation under randomly varying bounded sensor delay, Applied Mathematics Letters, 11 (1998), 27-32. doi: 10.1016/S0893-9659(98)00051-2.
[17]	H. S. Zhang, X. Lu, and D. Z. Cheng, Optimal estimation for continuous-time systems with delayed measurements, IEEE Trans. on Automatic Control, 51 (2006), 823-827. doi: 10.1109/TAC.2006.874983.
[18]	H. G. Zhao, H. S. Zhang and C. H. Zhang, Optimal filtering for linear discrete-time systems with single delayed measurement, Int. J. of Control, Automation, and Systems, 6 (2008), 378-385.

show all references

References:

[1]	B. D. O. Anderson and J. B. Moore, "Optimal Filtering," Prentice-Hall, Englewood Cliffs, New Jersey, 1979.
[2]	M. Basin, J. Rodriguez-Gonzalez and R. Martinez Zúniga, Optimal filtering for linear state delay systems, IEEE Trans. on Automatic Control, 50 (2005), 684-690. doi: 10.1109/TAC.2005.846599.
[3]	A. Calzolari, P. Florchinger and G. Nappo, Nonlinear filtering for markov systems with delayed observations, Int. J. Appl. Math. Comput. Sci., 19 (2009), 49-57. doi: 10.2478/v10006-009-0004-8.
[4]	Y. Chocheyras, Near field three dimensional time delay and doppler target motion analysis, in "International Conference on Acoustics, Speech, and Signal Processing," (1989), 2649-2652. doi: 10.1109/ICASSP.1989.267012.
[5]	T. Kailath, A. H. Sayed, and B. Hassibi, "Linear Estimation", Prentice-Hall, Englewood Cliffs, New Jersey, 1999.
[6]	R. E. Kalman, A new approach to linear filtering and prediction problems, Trans. ASME, Series D, Journal of Basic Engineering, 82 (1960), 35-45.
[7]	R. E. Kalman and R. S. Bucy, New results in linear filtering and prediction theory, Transactions of the ASME-Journal of Basic Engineering, 83 (1961), 95-108.
[8]	H. Kwakernaak, Optimal filtering in linear systems with time delays, IEEE Trans. on Automatic Control, 12 (1967), 169-173. doi: 10.1109/TAC.1967.1098541.
[9]	X. Lu, H. S. Zhang, W. Wang and K. L. Teo, Kalman filtering for multiple time-delay systems, Automatica, 41 (2005), 1455-1461. doi: 10.1016/j.automatica.2005.03.018.
[10]	D. MacMillan, J. Bohm, M. Gipson, R. Haas, A. Niell, T. Nilsson, A. Pany, B. Petrachenko and J. Wresnik, Simulation analysis of the geodetic performance of the future IVS VLBI2010 system, in "American Geophysical Union Fall Meeting," San Francisco, (2008), G33A-0667.
[11]	G. A. Medrano-Cerda, Filtering for linear system involving time delays in the noise process, IEEE Trans. on Automatic Control, 28 (1983), 801-803. doi: 10.1109/TAC.1983.1103318.
[12]	C. L. Su and C. N. Lu, Interconnected network state estimation using randomly delayed measurements, IEEE Trans. on Power Systems, 16 (2001), 870-878. doi: 10.1109/59.962439.
[13]	A. Subramanian and A. H. Sayed, Multiobjective filter design for uncertain stochastic time-delay systems, IEEE Trans. on Automatic Control, 49 (2004), 149-154. doi: 10.1109/TAC.2003.821422.
[14]	S. L. Sun, Linear minimum variance estimators for systems with bounded random measurement delays and packet dropouts, Signal Processing, 89 (2009), 1457-1466. doi: 10.1016/j.sigpro.2009.02.002.
[15]	Z. Wang, D. W. C. Ho and X. Liu, Robust filtering underrandomly varying sensor delay with variance constraints, IEEE Trans. on Circuits and Systtems II: Express Briefs, 51 (2004), 320-326. doi: 10.1109/TCSII.2004.829572.
[16]	E. Yaz and A. Ray, Linear unbiased state estimation under randomly varying bounded sensor delay, Applied Mathematics Letters, 11 (1998), 27-32. doi: 10.1016/S0893-9659(98)00051-2.
[17]	H. S. Zhang, X. Lu, and D. Z. Cheng, Optimal estimation for continuous-time systems with delayed measurements, IEEE Trans. on Automatic Control, 51 (2006), 823-827. doi: 10.1109/TAC.2006.874983.
[18]	H. G. Zhao, H. S. Zhang and C. H. Zhang, Optimal filtering for linear discrete-time systems with single delayed measurement, Int. J. of Control, Automation, and Systems, 6 (2008), 378-385.

[1]	Z. G. Feng, Kok Lay Teo, N. U. Ahmed, Yulin Zhao, W. Y. Yan. Optimal fusion of sensor data for Kalman filtering. Discrete and Continuous Dynamical Systems, 2006, 14 (3) : 483-503. doi: 10.3934/dcds.2006.14.483
[2]	Hanqing Jin, Shige Peng. Optimal unbiased estimation for maximal distribution. Probability, Uncertainty and Quantitative Risk, 2021, 6 (3) : 189-198. doi: 10.3934/puqr.2021009
[3]	Matthieu Canaud, Lyudmila Mihaylova, Jacques Sau, Nour-Eddin El Faouzi. Probability hypothesis density filtering for real-time traffic state estimation and prediction. Networks and Heterogeneous Media, 2013, 8 (3) : 825-842. doi: 10.3934/nhm.2013.8.825
[4]	Claude Stolz. On estimation of internal state by an optimal control approach for elastoplastic material. Discrete and Continuous Dynamical Systems - S, 2016, 9 (2) : 599-611. doi: 10.3934/dcdss.2016014
[5]	Jiangqi Wu, Linjie Wen, Jinglai Li. Resampled ensemble Kalman inversion for Bayesian parameter estimation with sequential data. Discrete and Continuous Dynamical Systems - S, 2022, 15 (4) : 837-850. doi: 10.3934/dcdss.2021045
[6]	Dominique Chapelle, Philippe Moireau, Patrick Le Tallec. Robust filtering for joint state-parameter estimation in distributed mechanical systems. Discrete and Continuous Dynamical Systems, 2009, 23 (1&2) : 65-84. doi: 10.3934/dcds.2009.23.65
[7]	Hui Huang, Eldad Haber, Lior Horesh. Optimal estimation of $\ell_1$-regularization prior from a regularized empirical Bayesian risk standpoint. Inverse Problems and Imaging, 2012, 6 (3) : 447-464. doi: 10.3934/ipi.2012.6.447
[8]	H. T. Banks, D. Rubio, N. Saintier, M. I. Troparevsky. Optimal design for parameter estimation in EEG problems in a 3D multilayered domain. Mathematical Biosciences & Engineering, 2015, 12 (4) : 739-760. doi: 10.3934/mbe.2015.12.739
[9]	Sie Long Kek, Kok Lay Teo, Mohd Ismail Abd Aziz. Filtering solution of nonlinear stochastic optimal control problem in discrete-time with model-reality differences. Numerical Algebra, Control and Optimization, 2012, 2 (1) : 207-222. doi: 10.3934/naco.2012.2.207
[10]	Robert J. Elliott, Tak Kuen Siu. Stochastic volatility with regime switching and uncertain noise: Filtering with sub-linear expectations. Discrete and Continuous Dynamical Systems - B, 2017, 22 (1) : 59-81. doi: 10.3934/dcdsb.2017003
[11]	Ming Mei. Stability of traveling wavefronts for time-delayed reaction-diffusion equations. Conference Publications, 2009, 2009 (Special) : 526-535. doi: 10.3934/proc.2009.2009.526
[12]	Martin Gugat, Markus Dick. Time-delayed boundary feedback stabilization of the isothermal Euler equations with friction. Mathematical Control and Related Fields, 2011, 1 (4) : 469-491. doi: 10.3934/mcrf.2011.1.469
[13]	Lizhong Qiang, Bin-Guo Wang. An almost periodic malaria transmission model with time-delayed input of vector. Discrete and Continuous Dynamical Systems - B, 2017, 22 (4) : 1525-1546. doi: 10.3934/dcdsb.2017073
[14]	Edward Hooton, Pavel Kravetc, Dmitrii Rachinskii. Restrictions to the use of time-delayed feedback control in symmetric settings. Discrete and Continuous Dynamical Systems - B, 2018, 23 (2) : 543-556. doi: 10.3934/dcdsb.2017207
[15]	Weijiu Liu. Asymptotic behavior of solutions of time-delayed Burgers' equation. Discrete and Continuous Dynamical Systems - B, 2002, 2 (1) : 47-56. doi: 10.3934/dcdsb.2002.2.47
[16]	Jérôme Fehrenbach, Jacek Narski, Jiale Hua, Samuel Lemercier, Asja Jelić, Cécile Appert-Rolland, Stéphane Donikian, Julien Pettré, Pierre Degond. Time-delayed follow-the-leader model for pedestrians walking in line. Networks and Heterogeneous Media, 2015, 10 (3) : 579-608. doi: 10.3934/nhm.2015.10.579
[17]	Isabelle Schneider, Matthias Bosewitz. Eliminating restrictions of time-delayed feedback control using equivariance. Discrete and Continuous Dynamical Systems, 2016, 36 (1) : 451-467. doi: 10.3934/dcds.2016.36.451
[18]	Yanbin Tang, Ming Wang. A remark on exponential stability of time-delayed Burgers equation. Discrete and Continuous Dynamical Systems - B, 2009, 12 (1) : 219-225. doi: 10.3934/dcdsb.2009.12.219
[19]	Yijun Lou, Xiao-Qiang Zhao. Threshold dynamics in a time-delayed periodic SIS epidemic model. Discrete and Continuous Dynamical Systems - B, 2009, 12 (1) : 169-186. doi: 10.3934/dcdsb.2009.12.169
[20]	Chongyang Liu, Meijia Han, Zhaohua Gong, Kok Lay Teo. Robust parameter estimation for constrained time-delay systems with inexact measurements. Journal of Industrial and Management Optimization, 2021, 17 (1) : 317-337. doi: 10.3934/jimo.2019113

2020 Impact Factor: 1.801

Tools

Metrics

Other articles
by authors

on AIMS
Peng Cui Hongguo Zhao Jun-e Feng
on Google Scholar
Peng Cui Hongguo Zhao Jun-e Feng

[Back to Top]