H-infinity filtering for a class of nonlinear discrete-time systems based on unscented transform. (English) Zbl 1197.94075

Summary: This paper is concerned with the \(H_{\infty }\) filtering for a class of nonlinear discrete-time systems. By embedding the unscented transform technique into the extended \(H_{\infty }\) filter structure, the unscented \(H_{\infty }\) filtering can be carried out using the statistical linear error propagation approach. Moreover, the unscented \(H_{\infty }\) information form filter has been developed for decentralized fusion by defining appropriate information state vectors and matrices. The novel filter achieves not only higher accuracy, but also robustness against model uncertainty. Simulation results for the frequency modulation demodulation and bearings-only tracking are presented to illustrate the effectiveness of the proposed method.


94A12 Signal theory (characterization, reconstruction, filtering, etc.)
Full Text: DOI


[1] Shen, B.; Wang, Z. D.; Shu, H. S.; Wei, G. L.: H\(\infty \) filtering for nonlinear discrete-time stochastic systems with randomly varying sensor delays, Automatica 45, No. 4, 1032-1037 (2009) · Zbl 1162.93039
[2] Wang, Z. D.; Liu, Y. R.; Liu, X. H.: H\(\infty \) filtering for uncertain stochastic time-delay systems with sector-bounded nonlinearities, Automatica 44, No. 5, 1268-1277 (2008) · Zbl 1283.93284
[3] Zhang, J. H.; Xia, Y. Q.; Shi, P.: Parameter-dependent robust H\(\infty \) filtering for uncertain discrete-time systems, Automatica 45, No. 2, 560-565 (2009) · Zbl 1158.93406
[4] Shi, P.; Mahmoud, M.; Nguang, S. K.; Ismail, A.: Robust filtering for jumping systems with mode-dependent delays, Signal processing 86, No. 1, 140-152 (2006) · Zbl 1163.94387
[5] Shen, X. M.; Deng, L.: A dynamic system approach to speech enhancement using the H\(\infty \) filtering algorithm, IEEE transactions on speech and audio processing 7, No. 4, 391-399 (1999)
[6] Labarre, D.; Grivel, E.; Najim, M.; Christov, N.: Dual H\(\infty \) algorithms for signal processing–application to speech enhancement, IEEE transactions on signal processing 55, No. 11, 5195-5208 (2007) · Zbl 1390.94257
[7] Vikalo, H.; Hassibi, B.; Erdogan, A. T.; Kailath, T.: On robust signal reconstruction in noisy filter banks, Signal processing 85, No. 1, 1-14 (2005) · Zbl 1148.94375
[8] Kulatunga, H.; Kadirkamanathan, V.: Multiple H\(\infty \) filter-based deterministic sequence estimation in non-Gaussian channels, IEEE signal processing letters 13, No. 4, 185-188 (2006)
[9] Grimble, M. J.; Sayed, A. E.: Solution of the H\(\infty \) optimal linear filtering problem for discrete-time systems, IEEE transactions on acoustics, speech and signal processing 38, No. 7, 1092-1104 (1990) · Zbl 0712.93053
[10] Hassibi, B.; Sayed, A. H.; Kailath, T.: Indefinite-quadratic estimation and control: A unified approach to H2 and H\(\infty \) theories, (1999) · Zbl 0997.93506
[11] Hassibi, B.; Sayed, A. H.; Kailath, T.: Linear estimation in Krein spaces–part II: Applications, IEEE transactions on automatic control 41, No. 1, 34-49 (1996) · Zbl 0862.93056
[12] Shen, X. M.; Deng, L.: Game theory approach to discrete H\(\infty \) filter design, IEEE transactions on signal processing 45, No. 4, 1092-1095 (1997)
[13] Simon, D.: Optimal state estimation: Kalman, H\(\infty \) and nonlinear approaches, (2006)
[14] Shaked, U.; Berman, N.: H\(\infty \) nonlinear filtering of discrete-time processes, IEEE transactions on signal processing 43, No. 9, 2205-2209 (1995)
[15] Einicke, G. A.; White, L. B.: Robust extended Kalman filtering, IEEE transactions on signal processing 47, No. 9, 2596-2599 (1999) · Zbl 1006.93588
[16] Seo, J.; Yu, M. J.; Park, C. G.; Lee, J. G.: An extended robust H\(\infty \) filter for nonlinear constrained uncertain systems, IEEE transactions on signal processing 54, No. 11, 4471-4475 (2006) · Zbl 1373.93110
[17] Julier, S. J.; Uhlmann, J. K.; Durrant-Whyte, H. F.: A new method for nonlinear transformation of means and covariances in filters and estimators, IEEE transactions on automatic control 45, No. 3, 477-482 (2000) · Zbl 0973.93053
[18] Ito, K.; Xiong, K.: Gaussian filters for nonlinear filtering problems, IEEE transactions on automatic control 45, No. 5, 910-927 (2000) · Zbl 0976.93079
[19] Arulampalam, M. S.; Maskell, S.; Gordon, N.; Clapp, T.: A tutorial on particle filters for online nonlinear non-Gaussian Bayesian tracking, IEEE transactions on signal processing 50, No. 2, 174-188 (2002)
[20] G. Sibley, G.S. Sukhatme, L. Matthies, The iterated sigma point Kalman filter with applications to long range stereo, in: Proceedings of the Second Robotics: Science and Systems Conference, Philadelphia, PA, 2006, pp. 16–19.
[21] Zhou, K.; Doyle, J. C.; Glover, K.: Robust and optimal control, (1996) · Zbl 0999.49500
[22] Song, T. L.: Observability of target tracking with bearings-only measurements, IEEE transactions on aerospace and electronic systems 32, No. 4, 1468-1472 (1996)
[23] Kirubarajan, T.; Bar-Shalom, Y.; Lerro, D.: Bearings-only tracking of maneuvering targets using a batch-recursive estimator, IEEE transactions on aerospace and electronic systems 37, No. 3, 770-780 (2001)
[24] Arulampalam, M. S.; Ristic, B.; Gordon, N.; Mansell, T.: Bearings-only tracking of maneuvering targets using particle filters, EURASIP journal on applied signal processing 15, 2351-2365 (2004) · Zbl 1076.93039
[25] R. Olfati-Saber, Distributed Kalman filter with embedded consensus filters, in: Proceedings of the 44th IEEE Conference on Decision and Control, and the European Control Conference, Seville, Spain, 2005, pp. 8179–8184.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.