Control and Modeling of Complex Systems pp 45-62 | Cite as

# Time-Domain FIR Filters for Stochastic and Deterministic Systems

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## Abstract

In this paper, several FIR filters based on the time-domain are proposed for stochastic and deterministic systems. For state space signal models, FIR filters with linear structure are required to be independent of the initial state and to minimize the given optimal criteria subject to being unbiased for stochastic systems and quasi-deadbeat for deterministic systems. The concept of FIR filter design is shown to be applicable to parameter estimation problems.

## Keywords

Time domain Finite Impulse Response Initial state independence Unbiased Quasi-deadbeat## Preview

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## References

- [1]E.-W. Bai and Y. Ye, “Constrained logarithmic least squares in parameter estimation,”
*IEEE Transactions on Automatic Control*vol. 44, pp. 182–186, 1999.MathSciNetzbMATHCrossRefGoogle Scholar - [2]A. M. Bruckstein and T. Kailath, “Recursive limited memory filtering and scattering theory,”
*IEEE Transactions on Information Theory*vol. 31, pp. 440–443, 1985.MathSciNetCrossRefGoogle Scholar - [3]F. Carravetta and G. Mavelli, “Minimax quadratic filtering of uncertain linear stochastic systems with partial fourth-order information,”
*IEEE Transactions on Automatic Control*vol. 44, no. 6, 1999.MathSciNetGoogle Scholar - [4]B.-S. Chen and W.-S. Hou, “Deconvolution filter design for fractal signal transmission systems: A multiscale Kalman filter bank approach,”
*IEEE Transactions on Signal Processing*vol. 45, no. 5, pp. 1359–1364, 1997.CrossRefGoogle Scholar - [5]Y.-M. Cheng, B.-S. Chen, and L.-M. Chen, “Minimax deconvolution design of multirate systems with channel noises: A unified approach,”
*IEEE Transactions on Signal Processing*vol. 47, no. 11, 1999.Google Scholar - [6]L. Dai, “Filtering and LQG problems for discrete-time stochastic singular systems,”
*IEEE Transactions on Automatic Control*vol. 34, no. 10, pp. 1105–1108, 1989.zbMATHCrossRefGoogle Scholar - [7]L. Danyang and L. Xuanhuang, “Optimal state estimation without the requirement of a priori statistics information of the initial state,”
*IEEE Transactions on Automatic Control*vol. 39, no. 10, pp. 2087–2091, 1994.zbMATHCrossRefGoogle Scholar - [8]J. C. Darragh and D. P. Looze, “Noncausal minimax linear state estimation for systems with uncertain second-order statistics,”
*IEEE Transactions on Automatic Control*vol. 29, no. 6, 1984.Google Scholar - [9]C. E. de Souza, R. M. Palhares, and P. L. D. Peres, “Robust
*H*_{oc}filtering for uncertain linear systems with multiple time-varying state delays,“*IEEE Transactions on Signal Processing*vol. 49, no. 3, pp. 569–576, 2001.MathSciNetCrossRefGoogle Scholar - [10]D. Z. Feng, Z. Bao, and X. D. Zhang, “Modified RLS algorithm for unbiased estimation of FIR system with input and output noise,”
*Electronics Letters*vol. 36, no. 3, pp. 273–274, 2000.CrossRefGoogle Scholar - [11]M. Fu, C. E. de Souza, and Z. Q. Luo, “Finite horizon robust Kalman filter design,” in Proceedings of the 38th
*IEEE Conference on Decision and Control*1999, pp. 4555–4560.Google Scholar - [12]J. C. Geromel, “Optimal linear filtering under parameter uncertainty,”
*IEEE Transactions on Signal Processing*vol. 47, no. 1, pp. 168–175, 1999.MathSciNetCrossRefGoogle Scholar - [13]
*J.*C. Geromel and M. C. de Oliveira, “H_{2}and H robust filtering for convex bounded uncertain systems,”*IEEE Transactions on Automatic Control*vol. 46, no. 1, pp. 100–107, 2001.zbMATHCrossRefGoogle Scholar - [14]S. Gollamudi and Y.-F. Huang, “Adaptive minimax filtering via recursive optimal quadratic approximations,”
*Circuits and Systems*vol. 3, pp. 142–145, 1999.Google Scholar - [15]S. H. Han, P. S. Kim, and W. H. Kwon, “Receding horizon state estimation with estimated horizon initial state and its application to aircraft engine systems,” in
*Proceedings of the 8th IEEE International Conference on Control Applications*Hawai’i, HW, 1999.Google Scholar - [16]S. H. Han, W. H. Kwon, and P. S. Kim, “Receding horizon unbiased FIR filters for continuous-time state space models without a priori initial state information,”
*IEEE Transactions on Automatic Control*vol. 46, no. 5, pp. 766–770, 2001.MathSciNetzbMATHCrossRefGoogle Scholar - [17]S. H. Han, W. H. Kwon, and P. S. Kim, “New deadbeat minimax filters for deterministic state space models without the requirement of a priori initial state information,”
*IEEE Transactions on Automatic Con*trol, to appear, 2002.Google Scholar - [18]B. Hassibi and T. Kaliath
*“H*_{09}bounds for least-squares estimators,“*IEEE Transactions on Automatic Control*vol. 46, no. 2, pp. 309–314, 2001.MathSciNetCrossRefGoogle Scholar - [19]G. A. Hirchoren and C. E. D’Attellis, “Estimation of fractional Brownian motion with multiresolution Kalman filter banks,”
*IEEE Transactions on Signal Processing*vol. 47, no. 5, pp. 1431–1434, 1999.MathSciNetzbMATHCrossRefGoogle Scholar - [20]L. Hong, G. Cheng, and C. K. Chui, “A filter-bank-based Kalman filtering technique for wavelet estimation and decomposition of random signals
*” IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing*vol. 45, no. 2, pp. 237–241, 1998.CrossRefGoogle Scholar - [21]A. H. Jazwinski, “Limited memory optimal filtering,”
*IEEE Transactions on Automatic Control*vol. 13, pp. 558–563, 1968.CrossRefGoogle Scholar - [22]A. J. Krener, “Kalman-Bucy and minimax filtering,”
*IEEE Transactions on Automatic Control*vol. 25, no. 2, 1980.MathSciNetCrossRefGoogle Scholar - [23]O. K. Kwon, C. E. de Souza, and H. S. Ryu, “Robust
*110„ filter for discrete-time uncertain systems,” in Proceedings of the 35th IEEE Conference on Decision and Control*1996, pp. 4819–4824.Google Scholar - [24]W. H. Kwon, P. S. Kim, and S. H. Han, “A receding horizon unbiased FIR filters for discrete-time state space models,”
*Automatica*vol. 38, no. 3, pp. 545–551, 2002.zbMATHCrossRefGoogle Scholar - [25]W. H. Kwon, P. S. Kim, and P. Park, “A receding horizon Kalman FIR filter for discrete time-invariant systems,”
*IEEE Transactions on Automatic Control*vol. 44, no. 9, pp. 1787–1791, 1999.MathSciNetzbMATHCrossRefGoogle Scholar - [26]W. H. Kwon, P. S. Kim, and P. Park, “A receding horizon Kalman FIR filter for linear continuous-time systems,”
*IEEE Transactions on Automatic Control*vol. 44, no. 11, pp. 2115–2120, 1999.MathSciNetzbMATHCrossRefGoogle Scholar - [27]W. H. Kwon and O. K. Kwon, “FIR filters and recursive forms for continuous time-invariant state-space models,”
*IEEE Transactions on Automatic Control*vol. 32, pp. 352–356, 1987.zbMATHCrossRefGoogle Scholar - [28]W. H. Kwon, K. H. Lee, and S. H. Han, “Quasi-deadbeat Hoo parameter estimation,” in
*Proceedings of the Asian Control Conference*2002.Google Scholar - [29]H. Li and M. Fu, “A linear matrix inequality approach to robust Hco filtering,”
*IEEE Transactions on Signal Processing*vol. 45, no. 9, pp. 2338–2350, 1997.CrossRefGoogle Scholar - [30]X. R. Li and C. He, “Optimal initialization of linear recursive filters,” in Proceedings of the 37th
*IEEE Conference on Decision and Control*1998, pp. 2335–2340.Google Scholar - [31]K. V. Ling and K. W. Lim, “Receding horizon recursive state estimation,”
*IEEE Transactions on Automatic Control*vol. 44, no. 9, pp. 1750–1753, 1999.MathSciNetzbMATHCrossRefGoogle Scholar - [32]D. Liu, “Minimum-time filter for discrete linear time-varying system,” in
*Proceedings of the 31st IEEE Conference on Decision and Control*1992, pp. 2222–2223.Google Scholar - [33]D. P. Looze, H. V. Poor, K. S. Vastola, and J. C. Darragh, “Minimax control of linear stochastic systems with noise uncertainty,”
*IEEE Transactions on Automatic Control*vol. 28, no. 9, 1983.MathSciNetCrossRefGoogle Scholar - [34]M. S. Mahmoud, N. F. Al-Muthairi, and S. Bingulac, “Robust Kalman filtering for continuous time-lag systems,”
*Systems and Control Letters*vol. 38, pp. 309–319, 1999.MathSciNetzbMATHCrossRefGoogle Scholar - [35]M. S. Mahmoud, L. Xie, and Y. C. Soh, “Robust Kalman filtering for discrete state-delay systems,”
*IEE Proceedings on Control Theory and Applications*vol. 147, no. 6, pp. 613–618, 2000.CrossRefGoogle Scholar - [36]N. C. Martins and M. Athans, “Time-invariant Kalman filtering, a minimax approach,” in
*Proceedings of the 37th IEEE Conference on Decision and Control*vol. 3, pp. 2896–2901, 1998.Google Scholar - [37]A. V. Medvedev and T. Toivonen, “Feedforward time-delay structures in state estimation: Finite memory smoothing and continuous deadbeat observers,” in
*Proceedings of IEE Conference on Control Theory and Applications*1994, pp. 121–129.Google Scholar - [38]R. Nikoukhah, S. L. Campbell, and F. Delebecque, “Kalman filtering for general discrete-time linear systems,”
*IEEE Transactions on Automatic Control*vol. 44, no. 10, 1999.MathSciNetCrossRefGoogle Scholar - [39]R. M. Palhares, C. E. de Souza, and P. L. D. Peres, “Robust
*H*_{oc}filter design for uncertain discrete-time state-delayed systems: An LMI approach,“ in*Proceedings of the 38th IEEE Conference on Decision and Control*1999, pp. 2347–2352.Google Scholar - [40]I. R. Petersen and D. C. McFarlane, “Optimal guaranteed cost control and filtering for uncertain linear systems,”
*IEEE Transactions on Automatic Control*vol. 39, no. 9, pp. 1971–1977, 1994.MathSciNetzbMATHCrossRefGoogle Scholar - [41]A. P. Petrovic and A. J. Zejak, “Minimax approach to envelope constrained filter design,”
*Electronics Letters*vol. 34, no. 25, 1998.CrossRefGoogle Scholar - [42]Y. A Phillis, “Estimation and control of systems with unknown covariance and multiplicative noise,”
*IEEE Transactions on Automatic Control*vol. 34, no. 10, 1989.MathSciNetCrossRefGoogle Scholar - [43]V. Poor and D. P. Looze, “Minimax state estimation for linear stochastic systems with noise uncertainty,” IEEE
*Transactions on Automatic Control*vol. 26, no. 4, pp. 902–906, 1981.MathSciNetzbMATHCrossRefGoogle Scholar - [44]R. G. Reynolds, “Robust estimation with unknown noise statistics,”
*IEEE Transactions on Automatic Control*vol. 35, no. 9, 1990.Google Scholar - [45]B. Sayyarrodsari, J. P. How, B. Hassibi, and A. Carrier, “An LMI formulation for the estimation-based approach to the design of adaptive filters,” in
*Proceedings of the 37th IEEE Conference on Decision and Control*1998.Google Scholar - [46]B. Sayyarrodsari, J. P. How, B. Hassibi, and A. Carrier, “Estimation-based synthesis of H
_{om}-optimal adaptive FIR filters for filtered-LMS problems,”*IEEE Transactions on Signal Processing*vol. 49, no. 1, pp. 164–178, 2001.CrossRefGoogle Scholar - [47]F. C. Schweppe
*Uncertain Dynamic Systems.*Englewood Cliffs, NJ: Prentice-Hall, 1973.Google Scholar - [48]U. Shaked and C. E. de Souza, “Robust minimum variance filtering,”
*IEEE Transactions on Signal Processing*vol. 43, no. 11, pp. 2474–2483, 1995.CrossRefGoogle Scholar - [49]T. Soderstrom, W. X. Zheng, and P. Stoica, “Comments on `On a least-squares-based algorithm for identification of stochastic linear systems,’”
*IEEE Transactions on Signal Processing*vol. 47, no. 5, pp. 1395–1396, 1999.CrossRefGoogle Scholar - [50]Y. S. Suh and J. W. Choi, “Continuous-time deadbeat fault detection and isolation filter design,” in Proceedings of the 38th IEEE Conference on Decision and Control, 1999, pp. 3130–3131.Google Scholar
- [51]Y. Theodor and U. Shaked, “Robust discrete-time minimum-variance filtering,”
*IEEE Transactions on Signal Processing*vol. 44, no. 2, pp. 181–189, 1996.MathSciNetCrossRefGoogle Scholar - [52]Y. Theodor, U. Shaked, and C. E. de Souza, “A game theory approach to robust discrete-time H
_{oe}-estimation,”*IEEE Transactions on Signal Processing*vol. 42, no. 6, pp. 1486–1495, 1994.CrossRefGoogle Scholar - [53]M. E. Valcher“State observers for discrete-time linear systems with unknown inputs,”
*IEEE Transactions on Automatic Control*vol. 44, pp. 397–401, 1999.MathSciNetzbMATHCrossRefGoogle Scholar - [54]S. Verdú and H. V. Poor, “Minimax linear observers and regulators for stochastic systems with uncertain second-order statistics,”
*IEEE Transactions on Automatic Control*vol. 29, no. 6, pp. 499–511, 1984.zbMATHCrossRefGoogle Scholar - [55]Z. Wang, B. Huang, and H. Unbehauen, “Robust
*H*_{oo}observer design of linear time-delay systems with parametric uncertainty,“*Systems and Control Letters*vol. 42, pp. 303–312, 2001.MathSciNetzbMATHCrossRefGoogle Scholar - [56]Z. Wang, J. Zhu, and H. Unbehauen, “Robust filter design with time-varying parameter uncertainty and error variance constraints,”
*International Journal of Control*vol. 72, no. 1, pp. 30–38, 1999.MathSciNetzbMATHCrossRefGoogle Scholar - [57]J. T. Watson, Jr. and K. M. Grigoriadis, “Optimal unbiased filtering via linear matrix inequalities,”
*Systems and Control Letters*vol. 35, pp. 111–118, 1998.MathSciNetzbMATHCrossRefGoogle Scholar - [58]L. Xie, Y. C. Soh, and C. E. de Souza, “Robust Kalman filtering for uncertain discrete-time systems,”
*IEEE Transactions on Automatic Control*vol. 39, no. 6, pp. 1310–1314, 1994.zbMATHCrossRefGoogle Scholar - [59]G.-H. Yang and J. L. Wang, “Robust nonfragile Kalman filtering for uncertain linear systems with estimator gain uncertainty,”
*IEEE Transactions on Automatic Control*vol. 46, no. 2, pp. 343–348, 2001.zbMATHCrossRefGoogle Scholar - [60]Y. Zhang, C. Wen, and Y. C. Soh, “Unbiased LMS filtering in the presence of white measurement noise with unknown power,”
*IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing*vol. 47, pp. 968–972, 2000.zbMATHCrossRefGoogle Scholar - [61]W.-X. Zheng, “Estimation of the parameters of autoregressive signals from colored noise-corrupted measurements,”
*IEEE Signal Processing Letters*vol. 7, no. 7, pp. 201–204, 2000.CrossRefGoogle Scholar - [62]W. X. Zheng, “A fast convergent algorithm for identification of noisy autoregressive signals,” in
*Proceedings of the 2000 IEEE International Symposium on Circuits and Systems*Geneva, Switzerland, 2000, pp. 497–500.Google Scholar - [63]Y. Zhu, “Efficient recursive state estimator for dynamic systems without knowledge of noise covariances,”
*IEEE Transactions on Aerospace and Electronic Systems*vol. 35, pp. 102–114, 1999.CrossRefGoogle Scholar

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