High-degree cubature Kalman filter for nonlinear state estimation with missing measurements. (English) Zbl 07887051
Summary: This paper proposes high-degree cubature Kalman filter for nonlinear systems with missing measurements. We derive out the explicit formulas for the prediction and update in the filtering. To fulfill the numerical computation, especially the numerical integrals, of these formulas, the fifth-degree spherical-radial cubature rule is adopted to give a high-degree cubature Kalman filtering algorithm. Through numerical example, it is shown that the fifth-degree cubature Kalman filter has better precision and stability than the extended Kalman filter, the unscented Kalman filter, and the fifth-degree unscented Kalman filter.
© 2021 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd
© 2021 Chinese Automatic Control Society and John Wiley & Sons Australia, Ltd
MSC:
| 93-XX | Systems theory; control |
Keywords:
fifth-degree cubature Kalman filter; nonlinear discrete systems; spherical-radial cubature ruleReferences:
| [1] | R.Radhakrishnan, S.Bhaumik, and N. K.Tomar, Continuous‐discrete filters for bearings‐only underwater target tracking problems, Asian J. Control21 (2019), no. 4, 1576-1586. · Zbl 1432.93352 |
| [2] | F.Qu and S.Tong, Observer‐based fuzzy adaptive quantized control for uncertain nonlinear multiagent systems, Int. J. Adapt. Control Signal Process.33 (2019), no. 4, 567-585. · Zbl 1417.93193 |
| [3] | D.Cilden‐Guler and C.Hajiyev, SVD‐aided EKF attitude estimation with UD factorized measurement noise covariance, Asian J. Control21 (2019), no. 4, 1423-1432. · Zbl 1432.93338 |
| [4] | X.Xie, D.Yue, and J. H.Park, Observer‐based state estimation of discrete‐time fuzzy systems based on a joint switching mechanism for adjacent instants, IEEE Trans. Cybernetics50 (2020), no. 8, 3545-3555. |
| [5] | R.He et al., Robust maneuver strategy of observer for bearings‐only tracking, Asian J. Control21 (2019), no. 4, 1719-1731. · Zbl 1432.93074 |
| [6] | S. V.Bordonaro et al., Converted measurement sigma point Kalman filter for bistatic sonar and radar tracking, IEEE Trans. Aerosp. Electron. Syst.55 (2019), no. 1, 147-159. |
| [7] | A.Shaghaghian and P.Karimaghaee, Improving GPS/INS integration using FIKF‐filtered innovation Kalman filter, Asian J. Control21 (2019), no. 4, 1671-1680. · Zbl 1432.93354 |
| [8] | K.Xiong and C.Wei, Adaptive iterated extended Kalman filter for relative spacecraft attitude and position estimation, Asian J. Control20 (2018), no. 4, 1595-1610. · Zbl 1397.93209 |
| [9] | P.Shi, X.Su, and F.Li, Dissipativity‐based filtering for fuzzy switched systems with stochastic perturbation, IEEE Trans. Autom. Control61 (2016), no. 6, 1694-1699. · Zbl 1359.93493 |
| [10] | A.Gelb (ed.) Ed., Applied optimal estimationEdited byA.Gelb (ed.), MA: M.I.T Press, Cambridge, 1974. |
| [11] | S.Julier, J.Uhlmann, and H. F.Durrant‐Whyte, A new method for the nonlinear transformation of means and covariances in filters and estimators, IEEE Trans. Autom. Control45 (2000), no. 3, 477-482. · Zbl 0973.93053 |
| [12] | E.Wan and R.Van der Merwe, The unscented Kalman filter, Kalman Filtering and Neural Networks, John Wiley & Sons Inc., New York, 2001, pp. 221-280. |
| [13] | I.Arasaratnam and S.Haykin, Cubature Kalman filters, IEEE Trans. Autom. Control54(2009), no. 6, 1254-1269. · Zbl 1367.93637 |
| [14] | I.Arasaratnam, S.Haykin, and T. R.Hurd, Cubature Kalman filtering for continuous‐discrete systems: theory and simulations, IEEE Trans. Signal Process.58 (2010), no. 10, 4977-4993. · Zbl 1391.93223 |
| [15] | K.Ito and K. Q.Xiong, Gaussian filters for nonlinear filtering problems, IEEE Trans. Autom. Control45 (2000), no. 5, 910-927. · Zbl 0976.93079 |
| [16] | S. J.Julier and J. K.Uhlmann, Unscented filtering and nonlinear estimation, Proc. IEEE92 (2004), no. 3, 401-422. |
| [17] | H.Menegaz et al., A systematization of the unscented Kalman filter theory, IEEE Trans. Autom. Control60 (2015), no. 10, 2583-2598. · Zbl 1360.93705 |
| [18] | Y.Wu et al., A numerical‐integration perspective on Gaussian filters, IEEE Trans. Signal Process.54 (2006), no. 8, 2910-2921. · Zbl 1388.65025 |
| [19] | B.Jia, M.Xin, and Y.Cheng, High‐degree Cubature Kalman filter, Automatica49(2013), no. 2, 510-518. · Zbl 1259.93118 |
| [20] | D.Meng et al., A seventh‐degree Cubature Kalman filter, Asian J. Control20 (2018), no. 1, 250-262. · Zbl 1391.93251 |
| [21] | T.Zhang et al., Application of improved fifth‐degree cubature Kalman filter in the nonlinear initial alignment of strapdown inertial navigation system, Rev. Sci. Instrum90 (2019), no. 1, 015111. |
| [22] | C.Wei et al., Fifth‐degree Cubature Kalman filter estimation of seeker line‐of‐sight rate using augmented‐dimensional model, J. Guid. Control Dynam.40 (2017), no. 9, 2355-2362. |
| [23] | Z. M.Li et al., A novel fifth‐degree Cubature Kalman filter approaching the lower bound on the number of Cubature points, Circuits Syst. Signal Process.37 (2018), no. 9, 4090-4108. · Zbl 1428.62414 |
| [24] | Z.Li et al., A novel fifth‐degree Cubature Kalman filter for real‐time orbit determination by radar, Math. Problems Eng2017 (2017), 8526804. · Zbl 1426.93338 |
| [25] | E.Santos‐Diaz, S.Haykin, and T. R.Hurd, Fifth‐degree continuous‐discrete Cubature Kalman filter for radar, IET Radar Sonar Navig.12 (2018), no. 11, 1225-1232. |
| [26] | M. V.Kulikova and G. Y.Kulikov, Square‐rooting approaches to accurate mixed‐type continuous‐discrete extended and fifth‐degree Cubature Kalman filters, IET Radar Sonar Navig.14 (2020), no. 11, 1671-1680. |
| [27] | Z.Wang et al., Robust H∞ filtering for stochastic time‐delay systems with missing measurements, IEEE Trans. Signal Process.54(2006), no. 7, 2579-2587. · Zbl 1373.94729 |
| [28] | S.Arunagirinathan, P.Muthukumar, and Y. H.Joo, Robust reliable H∞ control design for networked control systems with nonlinear ctuator faults and randomly missing measurements, Int. J. Robust Nonlinear Countrol29 (2019), no. 12, 4168-4190. · Zbl 1426.93078 |
| [29] | J.Hu et al., Event‐based filtering for time‐varying nonlinear systems subject to multiple missing measurements with uncertain missing probabilities, Inform Fusion38 (2017), 74-83. |
| [30] | M. M.Rana, L.Li, and S. W.Su, Distributed state estimation of smart grids with packet losses, Asian J. Control19 (2017), no. 4, 1306-1315. · Zbl 1370.93261 |
| [31] | M.Li and Y.Chen, Wide‐area stabiliser on sliding mode control for cross‐area power systems with random delay and packet dropouts, Asian J. Control20 (2018), no. 6, 2130-2142. · Zbl 1407.93087 |
| [32] | M.Atitallah, M.Davoodi, and N.Meskin, Event‐triggered fault detection for networked control systems subject to packet dropout, Asian J. Control20 (2018), no. 6, 2195-2206. · Zbl 1407.93225 |
| [33] | J.Liu and X.Ruan, Networked iterative learning control design for nonlinear systems with stochastic output packet dropouts, Asian J. Control20 (2018), no. 3, 1077-1087. · Zbl 1398.93367 |
| [34] | W. Q.Liu et al., Robust fusion steady‐state filtering for multisensor networked systems with one‐step random delay, missing measurements, and uncertain‐variance multiplicative and additive white noises, Int. J. Robust Nonlinear Countrol29 (2019), no. 14, 4716-4754. · Zbl 1426.93336 |
| [35] | A.Hermoso‐Carazo and J.Linares‐Perez, Different approaches for state filtering in nonlinear systems with uncertain observations, Appl. Math. Comput.187 (2007), no. 2, 708-724. · Zbl 1114.93102 |
| [36] | J.Hu et al., A variance‐constrained approach to recursive state estimation for time‐varying complex networks with missing measurements, Automatica64 (2016), 155-162. · Zbl 1329.93135 |
| [37] | L.Xu, K.Ma, and H.Fan, Unscented Kalman filtering for nonlinear state estimation with correlated noises and missing measurements, Int. J. Control, Autom. Syst.16 (2018), no. 3, 1011-1020. |
| [38] | L.Li and Y.Xia, UKF‐based nonlinear filtering over sensor networks with wireless fading channel, Inform Sciences316 (2015), 132-147. · Zbl 1441.94048 |
| [39] | L.Li and Y.Xia, Unscented kalman filter over unreliable communication networks with markovian packet dropouts, IEEE Trans. Autom. Control58 (2013), no. 12, 3224-3230. |
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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
