×

zbMATH — the first resource for mathematics

Gaussian sum approximation filter for nonlinear dynamic time-delay system. (English) Zbl 1348.94016
Summary: This paper focuses on designing Gaussian sum approximation filter for both accurately and rapidly estimating the state of a class of nonlinear dynamic time-delay systems. Firstly, a novel nonaugmented Gaussian filter (GF) is derived, whose superiority in computation efficiency is theoretically analyzed as compared to the standard augmented GF. Secondly, a nonaugmented Gaussian sum filter (GSF) is proposed to accurately capture the state estimates by a weight sum of the above-proposed GF. In GSF, each GF component is independent from the others and can be performed in a parallel manner so that GSF is conducive to high-performance computing across many compute nodes. Finally, the performance of the proposed GSF is demonstrated by a vehicle suspension system with time delay, where the GSF achieves higher accuracy than the single GF and is computationally much more efficient than the particle filter with the almost same accuracy.
MSC:
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Lee, S; Jeon, M; Shin, V, Distributed estimation fusion with application to a multisensory vehicle suspension system with time delays, IEEE Trans. Ind. Electron., 59, 4475-4482, (2012)
[2] Capisani, L.M., Ferrara, A., de Loza, A.F., Fridman, L.M.: manipulator fault diagnosis via higher order sliding-mode observers. IEEE Trans. Ind. Electron. 59(10), 3979-3986 (2012) · Zbl 1388.65025
[3] Dong, HL; Wang, ZD; Gao, HJ, Robust H-infinity filtering for a class of nonlinear networked systems with multiple stochastic communication delays and packet dropouts, IEEE Trans. Signal Process., 58, 1957-1966, (2010) · Zbl 1392.94183
[4] Wang, ZD; Lam, J; Liu, XH, Filtering for a class of nonlinear discrete-time stochastic systems with state delays, Int. J. Comput. Appl. Math., 201, 153-163, (2007) · Zbl 1152.93053
[5] Kahlil, M; Sarkar, A; Adhikari, S, Nonlinear filters for chaotic oscillatory systems, Nonlinear Dyn., 55, 113-137, (2009) · Zbl 1248.70022
[6] Xu, Y; Vedula, P, A moment-based approach for nonlinear stochastic tracking control, Nonlinear Dyn., 67, 119-128, (2012) · Zbl 1242.93125
[7] Li, HP; Shi, P, Robust H-infinity filtering for nonlinear stochastic systems with uncertainties and Markov delays, Automatica, 48, 159-166, (2012) · Zbl 1244.93158
[8] Murray, L; Storkey, A, Particle smoothing in continuous time: a fast approach via density estimation, IEEE Trans. Signal Process., 59, 1017-1026, (2011) · Zbl 1391.65022
[9] Wang, XX; Liang, Y; Pan, Q; Yang, F, A Gaussian approximation recursive filter for nonlinear systems with correlated noises, Automatica, 48, 2290-2297, (2012) · Zbl 1257.93102
[10] Wang, XX; Liang, Y; Pan, Q; Zhao, CH; Yang, F, Nonlinear Gaussian smoothers with colored measurement noise, IEEE Trans. Autom. Control, 60, 870-876, (2015) · Zbl 1360.93681
[11] Ito, K; Xiong, K, Gaussian filters for nonlinear filtering problems, IEEE Trans. Autom. Control, 45, 910-927, (2000) · Zbl 0976.93079
[12] Horwood, JT; Poore, AB, Adaptive Gaussian sum filters for space surveillance, IEEE Trans. Autom. Control, 56, 1777-1790, (2011) · Zbl 1368.93715
[13] Subrahmanya, N; Shin, YC, Adaptive divided difference filtering for simultaneous state and parameter estimation, Automatica, 45, 1686-1693, (2009) · Zbl 1184.93110
[14] Terejanu, G; Singla, P; Singh, T; Scott, PD, Adaptive gaussian sum filter for nonlinear Bayesian estimation, IEEE Trans. Autom. Control, 56, 2151-2156, (2011) · Zbl 1368.93730
[15] Wu, YX; Hu, DW; Wu, MP; Hu, XP, A numerical-integration perspective on Gaussian filters, IEEE Trans. Signal Process., 54, 2910-2921, (2006) · Zbl 1388.65025
[16] Julier, S; Uhlmann, JK; Durrant-Whyte, HF, A new method for the nonlinear transformation of means and covariances in filters and estimators, IEEE Trans. Autom. Control, 45, 477-482, (2000) · Zbl 0973.93053
[17] Nørgaard, M; Poulsen, NK; Ravn, O, New developments in state estimation for nonlinear systems, Automatica, 36, 1627-1638, (2000) · Zbl 0973.93050
[18] Arasaratnam, I; Haykin, S, Cubature Kalman filter, IEEE Trans. Autom. Control, 54, 1254-1269, (2009) · Zbl 1367.93637
[19] Jia, B; Xin, M; Cheng, Y, Sparse-grid quadrature nonlinear filtering, Automatica, 48, 327-341, (2012) · Zbl 1260.93161
[20] Jia, B; Xin, M; Cheng, Y, Relations between sparse-grid quadrature rule and spherical-radial cubature rule in nonlinear Gaussian estimation, IEEE Trans. Autom. Control, 60, 199-204, (2015) · Zbl 1360.93698
[21] Wang, XX; Pan, Q; Liang, Y; Yang, F, Gaussian smoothers for nonlinear systems with one-step randomly delayed measurements, IEEE Trans. Autom. Control, 58, 1828-1835, (2013) · Zbl 1369.93680
[22] Simo, S, Unscented rauch-tung-striebel smoother, IEEE Trans. Autom. Control, 53, 845-849, (2008) · Zbl 1367.93691
[23] Arasaratnam, I; Haykin, S, Cubature Kalman smoother, Automatica, 47, 2245-2250, (2011) · Zbl 1226.93123
[24] Jia, B; Xin, M; Cheng, Y, High-degree cubature Kalman filter, Automatica, 49, 510-518, (2013) · Zbl 1259.93118
[25] Xiong, K; Zhang, HY; Chan, CW, Performance evaluation of UKF-based nonlinear filtering, Automatica, 42, 261-270, (2006) · Zbl 1103.93045
[26] Xiong, K; Zhang, HY; Chan, CW, Author’s reply to comments on performance evaluation of UKF-based nonlinear filtering, Automatica, 43, 569-570, (2007) · Zbl 1137.93418
[27] Wu, YX; Hu, DW; Hu, XP, Comments on performance evaluation of UKF-based nonlinear filtering, Automatica, 43, 567-568, (2007) · Zbl 1137.93417
[28] Wang, SY; Feng, JC; Tse, CK, A class of stable square-root nonlinear information filters, IEEE Trans. Autom. Control, 59, 1893-1898, (2014) · Zbl 1360.93716
[29] Straka, O; Duník, J; Šimandl, M, Truncation nonlinear filters for state estimation with nonlinear inequality constraints, Automatica, 48, 273-286, (2012) · Zbl 1260.93156
[30] Bruno, OST; Leonardo, ABT; Luis, AA; Denni, SB, On unscented Kalman filtering with state interval constraints, J. Process Control, 20, 45-57, (2010)
[31] Forbes, JRJ; Ruiter, AH; Zlotnik, DE, Continuous-time norm-constrained Kalman filtering, Automatica, 50, 2546-2554, (2014) · Zbl 1301.93154
[32] Chung, K.L.: A Course in Probability Theory. Academic Press, Nwew York (2001) · Zbl 1248.70022
[33] Fan, J.Q., Yao, Q.W.: Nonlinear Time Series. Springer, German (2005)
[34] Shi, P; Luan, XL; Liu, F, H\(∞ \) filtering for discrete-time systems with stochastic incomplete measurement and mixed delays, IEEE Trans. Ind. Electr., 59, 2732-2739, (2012)
[35] Ho, YC; Lee, RCK, A Bayesian approach to problems in stochastic estimation and control, IEEE Trans. Autom. Control, 9, 333-339, (1964)
[36] Priemer, R., Vacroux, A.G.: Estimation in linear systems with multiple time delays. IEEE Trans. Autom. Control 13(4), 384-387 (1969) · Zbl 1119.74435
[37] Golub, G.H., Van Loan, C.F.: Matrix Computations, Fourth edn. The Johns Hopkins University Press, Baltimore (2013) · Zbl 1268.65037
[38] Plataniotis, KN; Androutsos, D; Venetsanopoulos, AN, Nonlinear filtering of non-Gaussian noise, J. Intell. Robot. Syst., 19, 207-231, (1997)
[39] Wu, H; Chen, G, Suboptimal Kalman filtering for linear systems with Gaussian-sum type of noise, Math. Comput. Model., 29, 101-125, (1999) · Zbl 0994.93061
[40] Zia, A; Kirubarajan, T; Reilly, JP; Yee, D; Punithakumar, K; Shirani, S, An EM algorithm for non-linear state estimation with model uncertainties, IEEE Trans. Signal Process., 56, 921-936, (2008) · Zbl 1390.94516
[41] Arasaratnam, I; Haykin, S, Discrete-time nonlinear filtering algorithms using Gauss-Hermite quadrature, Proc. IEEE, 95, 953-977, (2007)
[42] Yagiz, N; Hacioglu, Y, Backstepping control of a vehicle with active suspensions, Control Eng. Pract., 16, 1457-1467, (2008) · Zbl 1157.90449
[43] Zhu, Q; Ishitobi, M, Chaotic vibration of a nonlinear full-vehicle model, Int. J. Solids Struct., 43, 747-759, (2006) · Zbl 1119.74435
[44] Dai, L; Wu, J, Stability and vibrations of an all-terrain vehicle subjected to nonlinear structural deformation and resistance, Commun. Nonlinear Sci. Numer. Simul., 12, 72-82, (2007) · Zbl 1111.34037
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.