Abstract
Inspired by the robust student t-distribution based nonlinear filter (RSTNF), a student t-distribution and unscented transform (UT) based filter for state estimation of heavy-tailed nonlinear dynamic systems, a modified RSTNF for intermittent observations is derived. The fusion estimation for nonlinear multisensor systems with intermittent observations and heavy-tailed measurement and process noises is studied. In this work, the centralized fusion, the sequential fusion, and the naïve distributed fusion algorithms are presented, respectively. Theoretical analysis shows that the presented algorithms are effective, which are the efficient extension of the classical unscented Kalman filter (UKF) or the cubature Kalman filter (CKF) based algorithms with Gaussian noises. Simulation results show that the presented algorithms are effective and feasible.
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Piché R, Särkkä S, Hartikainen J. Recursive outlier-robust filtering and smoothing for nonlinear systems using the multivariate student-t distribution. In: Proceedings of IEEE International Workshop on Machine Learning for Signal Processing, Santander, 2012. 1–6
Huang Y L, Zhang Y G, Shi P, et al. Robust Kalman filters based on gaussian scale mixture distributions with application to target tracking. IEEE Trans Syst Man Cybern Syst, 2019, 49: 2082–2096
Yan L P, Di C Y, Wu Q M J, et al. Sequential fusion estimation for multisensor systems with non-Gaussian noises. Sci China Inf Sci, 2020, 63: 222202
Yan L P, Di C Y, Wu Q M J, et al. Sequential fusion for multirate multisensor systems with heavy-tailed noises and unreliable measurements. IEEE Trans Syst Man Cybern Syst, 2022, 52: 523–532
Chan S C, Zou Y X. A recursive least m-estimate algorithm for robust adaptive filtering in impulsive noise: fast algorithm and convergence performance analysis. IEEE Trans Signal Process, 2004, 52: 975–991
Kovačević B, Durović Z, Glavaški S. On robust Kalman filtering. Int J Control, 1992, 56: 547–562
Durović Z, Kovacevic B D. Robust estimation with unknown noise statistics. IEEE Trans Autom Control, 1999, 44: 1292–1296
Gandhi M A, Mili L. Robust Kalman filter based on a generalized maximum-likelihood-type estimator. IEEE Trans Signal Process, 2010, 58: 2509–2520
Ge Q B, Wei Z L, Liu M X, et al. Adaptive quantized estimation fusion using strong tracking filtering and variational Bayesian. IEEE Trans Syst Man Cybern Syst, 2020, 50: 899–910
Yin L, Shen Y. Robust filtering of discrete-time linear systems with correlated process and measurement noises. IEEE Trans Circ Syst I, 2020, 67: 1008–1020
Alessandri A, Awawdeh M. Moving-horizon estimation with guaranteed robustness for discrete-time linear systems and measurements subject to outliers. Automatica, 2016, 67: 85–93
Huang Y L, Zhang Y G, Li N, et al. Robust student’s t based nonlinear filter and smoother. IEEE Trans Aerosp Electron Syst, 2016, 52: 2586–2596
Huang Y L, Zhang Y G, Li N, et al. A robust gaussian approximate filter for nonlinear systems with heavy tailed measurement noises. In: Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2016. 4209–4213
Zhang L, Lan J, Li X R. A normal-Gamma filter for linear systems with heavy-tailed measurement noise. In: Proceedings of International Conference on Information Fusion (FUSION), Xi’an, 2018. 2552–2559
Agamennoni G, Nieto J I, Nebot E M. Approximate inference in state-space models with heavy-tailed noise. IEEE Trans Signal Process, 2012, 60: 5024–5037
Zhu H, Leung H, He Z S. A variational Bayesian approach to robust sensor fusion based on Student-t distribution. Inf Sci, 2013, 221: 201–214
Roth M, Ożkan E, Gustafsson F. A student’s filter for heavy tailed process and measurement noise. In: Proceedings of International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2013. 5770–5774
Nurminen H, Ardeshiri T, Piche R, et al. Robust inference for state-space models with skewed measurement noise. IEEE Signal Process Lett, 2015, 22: 1898–1902
Liu X, Ren Z G, Lyu H Q, et al. Linear and nonlinear regression-based maximum correntropy extended Kalman filtering. IEEE Trans Syst Man Cybern Syst, 2021, 51: 3093–3102
Huang Y L, Zhang Y G, Li N, et al. A robust student’s t based cubature filter. In: Proceedings of the 19th International Conference on Information Fusion, Heidelberg, 2016. 9–16
Amor N, Kahlaoui S, Chebbi S. Unscented particle filter using student-t distribution with non-Gaussian measurement noise. In: Proceedings of International Conference on Advanced Systems and Electric Technologies, 2018. 34–38
Bar-Shalom Y, Li X R, Kirubarajan T. Estimation with Applications to Tracking and Navigation: Theory Algorithm and Software. Hoboken: Wiley, 2001
Yan L, Li X R, Xia Y, et al. Optimal sequential and distributed fusion for state estimation in cross-correlated noise. Automatica, 2013, 49: 3607–3612
Yan L, Li X R, Xia Y, et al. Modeling and estimation of asynchronous multirate multisensor system with unreliable measurements. IEEE Trans Aerosp Electron Syst, 2015, 51: 2012–2026
Hu J, Wang Z D, Chen D Y, et al. Estimation, filtering and fusion for networked systems with network-induced phenomena: new progress and prospects. Inf Fusion, 2016, 31: 65–75
Ge Q B, Shao T, Yang Q M, et al. Multisensor nonlinear fusion methods based on adaptive ensemble fifth-degree iterated cubature information filter for biomechatronics. IEEE Trans Syst Man Cybern Syst, 2016, 46: 912–925
Xu J, Li J X, Xu S. Data fusion for target tracking in wireless sensor networks using quantized innovations and Kalman filtering. Sci China Inf Sci, 2012, 55: 530–544
Yan L P, Xia Y Q, Fu M Y. Optimal fusion estimation for stochastic systems with cross-correlated sensor noises. Sci China Inf Sci, 2017, 60: 120205
Shen C, Li J, Huang W. Robust centralized multi-sensor fusion using cubature information filter. In: Proceedings of the 30th Chinese Control and Decision Conference, 2018. 3297–3302
Yan L P, Di C Y, Wu Q M J, et al. Distributed fusion estimation for multisensor systems with non-Gaussian but heavy-tailed noises. ISA Trans, 2020, 101: 160–169
Dong P, Jing Z L, Leung H, et al. Robust consensus nonlinear information filter for distributed sensor networks with measurement outliers. IEEE Trans Cybern, 2019, 49: 3731–3743
Wang Z D, Ho D W C, Liu X H. Variance-constrained filtering for uncertain stochastic systems with missing measurements. IEEE Trans Autom Control, 2003, 48: 1254–1258
Sinopoli B, Schenato L, Franceschetti M, et al. Kalman filtering with intermittent observations. IEEE Trans Autom Control, 2004, 49: 1453–1464
Kar S, Sinopoli B, Moura J M F. Kalman filtering with intermittent observations: weak convergence to a stationary distribution. IEEE Trans Autom Control, 2012, 57: 405–420
Xia Y Q, Shang J Z, Chen J, et al. Networked data fusion with packet losses and variable delays. IEEE Trans Syst Man Cybern B, 2009, 39: 1107–1120
Sun S L. Optimal linear filters for discrete-time systems with randomly delayed and lost measurements with/without time stamps. IEEE Trans Autom Control, 2013, 58: 1551–1556
Yan L P, Xiao B, Xia Y Q, et al. State estimation for asynchronous multirate multisensor nonlinear dynamic systems with missing measurements. Int J Adapt Control Signal Process, 2012, 26: 516–529
Han C Y, Wang W. Linear state estimation for Markov jump linear system with multi-channel observation delays and packet dropouts. Int J Syst Sci, 2019, 50: 163–177
Song J H, Ding D R, Liu H J, et al. Non-fragile distributed state estimation over sensor networks subject to DoS attacks: the almost sure stability. Int J Syst Sci, 2020, 51: 1119–1132
Kotz S, Nadarajah S. Multivariate t-Distributions and Their Applications. Cambridge: Cambridge University Press, 2004
Roth M. On the Multivariate t Distribution. Technical Report LiTH-ISY-R-3059, 2013
Sun S L, Deng Z L. Multi-sensor optimal information fusion Kalman filter. Automatica, 2004, 40: 1017–1023
Ma H B, Yan L P, Xia Y Q, et al. Kalman Filtering and Information Fusion. Berlin: Springer, 2020
Julier S J, Uhlmann J K. Unscented filtering and nonlinear estimation. Proc IEEE, 2004, 92: 401–422
Arasaratnam I, Haykin S. Cubature Kalman filters. IEEE Trans Autom Control, 2009, 54: 1254–1269
Lin H L, Sun S L. Optimal sequential fusion estimation with stochastic parameter perturbations, fading measurements, and correlated noises. IEEE Trans Signal Process, 2018, 66: 3571–3583
Kailath T, Sayed A H, Hassibi B. Linear Estimation. Englewood Cliffs: Prentice Hall, 2000
Ding D R, Wang Z D, Han Q L. A set-membership approach to event-triggered filtering for general nonlinear systems over sensor networks. IEEE Trans Autom Control, 2020, 65: 1792–1799
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This work was supported by the National Natural Science Foundation of China (Grant Nos. 62076031, 62073036) and Beijing Natural Science Foundation (Grant No. 4202071).
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Xiao, B., Wu, Q.M.J. & Yan, L. Multisensor fusion estimation of nonlinear systems with intermittent observations and heavy-tailed noises. Sci. China Inf. Sci. 65, 192203 (2022). https://doi.org/10.1007/s11432-020-3223-6
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DOI: https://doi.org/10.1007/s11432-020-3223-6