Optimized distributed fusion filtering for singular systems with fading measurements and stochastic nonlinearity

Chen Wang; Jun Hu; Hui Yu; Dongyan Chen; Chen Wang; Jun Hu; Hui Yu; Dongyan Chen

doi:10.3934/math.2022143

AIMS Mathematics

2022, Volume 7, Issue 2: 2543-2567. doi: 10.3934/math.2022143

Previous Article Next Article

Research article

Optimized distributed fusion filtering for singular systems with fading measurements and stochastic nonlinearity

1.
Department of Mathematics, Harbin University of Science and Technology, Harbin 150080, China
2.
School of Automation, Harbin University of Science and Technology, Harbin 150080, China

Received: 21 August 2021 Accepted: 14 October 2021 Published: 17 November 2021
MSC : 93A14, 93E11

In this paper, the problem of optimized distributed fusion filtering is considered for a class of multi-sensor singular systems in the presence of fading measurements and stochastic nonlinearity. By utilizing the standard singular value decomposition, the multi-sensor stochastic singular systems are simplified to two reduced-order nonsingular subsystems (RONSs). The local filters (LFs) with corresponding error covariance matrices are proposed for RONSs via the innovation analysis approach. Then, on the basis of the matrix-weighted fusion estimation algorithm, the distributed fusion filters (DFFs) are designed for RONSs with multiple sensors in the linear minimum variance sense. Moreover, the DFFs are obtained by utilizing the state transformation for original singular systems. It can be observed that the DFFs have better accuracy in contrast with the LFs. Finally, an illustrate example is put forward to verify the feasibility of the proposed fusion filtering scheme.
- singular systems,
- distributed fusion filter,
- innovation analysis approach,
- singular value decomposition,
- multi-sensors
Citation: Chen Wang, Jun Hu, Hui Yu, Dongyan Chen. Optimized distributed fusion filtering for singular systems with fading measurements and stochastic nonlinearity[J]. AIMS Mathematics, 2022, 7(2): 2543-2567. doi: 10.3934/math.2022143

Related Papers:

Abstract

In this paper, the problem of optimized distributed fusion filtering is considered for a class of multi-sensor singular systems in the presence of fading measurements and stochastic nonlinearity. By utilizing the standard singular value decomposition, the multi-sensor stochastic singular systems are simplified to two reduced-order nonsingular subsystems (RONSs). The local filters (LFs) with corresponding error covariance matrices are proposed for RONSs via the innovation analysis approach. Then, on the basis of the matrix-weighted fusion estimation algorithm, the distributed fusion filters (DFFs) are designed for RONSs with multiple sensors in the linear minimum variance sense. Moreover, the DFFs are obtained by utilizing the state transformation for original singular systems. It can be observed that the DFFs have better accuracy in contrast with the LFs. Finally, an illustrate example is put forward to verify the feasibility of the proposed fusion filtering scheme.

References

[1]	L. Dai, Singular control systems, Springer-Verlag, 1989. doi: 10.1007/BFb0002475.
[2]	I. Dassios, Optimal solutions for non-consistent singular linear systems of fractional nabla difference equations, Circuits Syst. Signal Process., 34 (2015), 1969–1797. doi: 10.1007/s00034-014-9930-2. doi: 10.1007/s00034-014-9930-2
[3]	I. Dassios, G. Kalogeropoulos, On a non-homogeneous singular linear discrete time system with a singular matrix pencil, Circuits Syst. Signal Process., 32 (2013), 1615–1635. doi: 10.1007/s00034-012-9541-8. doi: 10.1007/s00034-012-9541-8
[4]	I. Dassios, On non homogeneous linear generalized linear discrete time systems, Circuits Syst. Signal Process., 31 (2012), 1699–1712. doi: 10.1007/s00034-012-9400-7. doi: 10.1007/s00034-012-9400-7
[5]	Z. Feng, Z. Jiang, W. Zheng, Reachable set synthesis of singular Markovian jump systems, J. Frankl. Inst. Eng. Appl. Math., 357 (2020), 13785–13799. doi: 10.1016/j.jfranklin.2020.09.042. doi: 10.1016/j.jfranklin.2020.09.042
[6]	Q. Wu, Q. Song, Z. Zhao, Y. Liu, F. E. Alsaadi, Stabilization of T-S fuzzy fractional rectangular descriptor time-delay system, Int. J. Syst. Sci., 52 (2021), 2268–2282. doi: 10.1080/00207721.2021.1882613. doi: 10.1080/00207721.2021.1882613
[7]	S. Sun, J. Ma, Optimal filtering and smoothing for discrete-time stochastic singular systems, Signal Process., 87 (2007), 189–201. doi: 10.1016/j.sigpro.2006.05.007. doi: 10.1016/j.sigpro.2006.05.007
[8]	X. Yu, J. Li, Optimal filtering and a smoothing algorithm for a singular system with a complex stochastic uncertain parameter matrix, IEEE Trans. Circuits Syst. Ⅱ-Express Briefs, 67 (2020), 780–784. doi: 10.1109/TCSII.2019.2922010. doi: 10.1109/TCSII.2019.2922010
[9]	S. Sun, J. Ma, Distributed reduced-order optimal fusion Kalman filters for stochastic singular systems, ACTA Automatica Sinica, 32 (2006), 286–290. doi: 10.16383/j.aas.2006.02.017. doi: 10.16383/j.aas.2006.02.017
[10]	S. Sun, Y. Shen, J. Ma, Optimal fusion reduced-order Kalman estimators for discrete-time stochastic singular systems, Control Intell. Syst., 36 (2008), 1–9. doi: 10.2316/Journal.201.2008.1.201-1614. doi: 10.2316/Journal.201.2008.1.201-1614
[11]	J. Feng, M. Zeng, Descriptor recursive estimation for multiple sensors with different delay rates, Int. J. Control, 84 (2011), 584–596. doi: 10.1080/00207179.2011.563321. doi: 10.1080/00207179.2011.563321
[12]	Y. Dou, C. Ran, Y. Gao, Weighted measurement fusion Kalman estimator for multisensor descriptor system, Int. J. Syst. Sci., 47 (2016), 2722–2732. doi: 10.1080/00207721.2015.1018368. doi: 10.1080/00207721.2015.1018368
[13]	M. M. Fahmy, J. O'Reilly, Observers for descriptor systems, Int. J. Control, 49 (1989), 2013–2028. doi: 10.1080/00207178908559759. doi: 10.1080/00207178908559759
[14]	V. L. Syrmos, F. L. Lewis, Robust eigenvalue assignment for generalized systems, Automatica, 28 (1992), 1223–1228. doi: 10.1016/0005-1098(92)90064-M. doi: 10.1016/0005-1098(92)90064-M
[15]	J. Sun, C. Zhang, J. Gu, Decentralized optimal fusion filtering for multi-sensor multi-delay singular systems, Circuits Syst. Signal Process., 31 (2012), 163–176. doi: 10.1007/s00034-011-9313-x. doi: 10.1007/s00034-011-9313-x
[16]	C. Zhu, Y. Xia, L. Xie, L. Yan, Optimal linear estimation for systems with transmission delays and packet dropouts, IET Signal Process., 7 (2013), 814–823. doi: 10.1049/iet-spr.2012.0348. doi: 10.1049/iet-spr.2012.0348
[17]	S. Sun, J. Ma, Linear estimation for networked control systems with random transmission delays and packet dropouts, Inf. Sci., 269 (2014), 349–365. doi: 10.1016/j.ins.2013.12.055. doi: 10.1016/j.ins.2013.12.055
[18]	J. Linares-Pérez, R. Caballero-Águila, I. García-Garrido, Optimal linear filter design for systems with correlation in the measurement matrices and noises: recursive algorithm and applications, Int. J. Syst. Sci., 45 (2014), 1548–1562. doi: 10.1080/00207721.2014.909093. doi: 10.1080/00207721.2014.909093
[19]	S. Wang, Z. Wang, H. Dong, F. E. Alsaadi, Recursive state estimation for linear systems with lossy measurements under time-correlated multiplicative noises, J. Frankl. Inst. Eng. Appl. Math., 357 (2020), 1887–1908. doi: 10.1016/j.jfranklin.2019.11.031. doi: 10.1016/j.jfranklin.2019.11.031
[20]	B. D. O. Anderson, J. B. Moore, Optimal filtering, New Jersey: Prentice-Hall, 1979. doi: 10.1007/978-94-011-4691-3.
[21]	Y. Li, H. Li, Optimal state estimation for finite-field networks with stochastic disturbances, Neurocomputing, 414 (2020), 238–244. doi: 10.1016/j.neucom.2020.07.065. doi: 10.1016/j.neucom.2020.07.065
[22]	Y. Dou, C. Ran, WMF self-tuning Kalman estimators for multisensor singular system, Int. J. Syst. Sci., 50 (2019), 1873–1888. doi: 10.1080/00207721.2019.1645234. doi: 10.1080/00207721.2019.1645234
[23]	Q. Gan, C. J. Harris, Comparison of two measurement fusion methods for Kalman-filter-based multisensor data fusion, IEEE Trans. Aerosp. Electron. Syst., 37 (2001), 273–279. doi: 10.1109/7.913685. doi: 10.1109/7.913685
[24]	S. Sun, Multi-sensor optimal information fusion Kalman filter with application, Aerosp. Sci. Technol., 8 (2003), 57–62. doi: 10.1016/j.ast.2003.08.003. doi: 10.1016/j.ast.2003.08.003
[25]	S. Sun, Multi-sensor information fusion white noise filter weighted by scalars based on Kalman predictor, Automatica, 40 (2004), 1447–1453. doi: 10.1016/j.automatica.2004.03.012. doi: 10.1016/j.automatica.2004.03.012
[26]	S. Sun, Z. Deng, Multi-sensor optimal information fusion Kalman filter, Automatica, 40 (2004), 1017–1023. doi: 10.1016/j.automatica.2004.01.014. doi: 10.1016/j.automatica.2004.01.014
[27]	J. Ma, S. Sun, Information fusion estimators for systems with multiple sensors of different packet dropout rates, Inf. Fusion, 12 (2011), 213–222. doi: 10.1016/j.inffus.2010.11.003. doi: 10.1016/j.inffus.2010.11.003
[28]	H. Tan, B. Shen, K. Peng, H. Liu, Robust recursive filtering for uncertain stochastic systems with amplify-and-forward relays, Int. J. Syst. Sci., 51 (2020), 1188–1199. doi: 10.1080/00207721.2020.1754960. doi: 10.1080/00207721.2020.1754960
[29]	L. Liu, L. Ma, J. Zhang, Y. Bo, Distributed non-fragile set-membership filtering for nonlinear systems under fading channels and bias injection attacks, Int. J. Syst. Sci., 52 (2021), 1192–1205. doi: 10.1080/00207721.2021.1872118. doi: 10.1080/00207721.2021.1872118
[30]	Y. Liu, F. Han, N. Hou, H. Dong, H. Liu, Set-membership filtering for piecewise linear systems with censored measurements under Round-Robin protocol, Int. J. Syst. Sci., 51 (2020), 1578–1588. doi: 10.1080/00207721.2020.1768453. doi: 10.1080/00207721.2020.1768453
[31]	C. Ran, S. Sun, Y. Dou, WMF reduced-order robust estimators for multisensor descriptor systems, IET Contr. Theory Appl., 12 (2018), 2232–2244. doi: 10.1049/iet-cta.2018.5498. doi: 10.1049/iet-cta.2018.5498
[32]	Y. Tang, W. Sun, D. Liu, X. Li, Finite-time simultaneous stabilization for stochastic port-controlled Hamiltonian systems over delayed and fading channels, Complexity, 2020 (2020), 1–12. doi: 10.1155/2020/6387025. doi: 10.1155/2020/6387025
[33]	J. Hu, Z. Wang, D. Chen, F. E. Alsaadi, Estimation, filtering and fusion for networked systems with network-induced phenomena: New progress and prospects, Inf. Fusion, 31 (2016), 65–75. doi: 10.1016/j.inffus.2016.01.001. doi: 10.1016/j.inffus.2016.01.001
[34]	S. Sun, H. Lin, J. Ma, X. Li, Multi-sensor distributed fusion estimation with applications in networked systems: a review paper, Inf. Fusion, 38 (2017), 122–134. doi: 10.1016/j.inffus.2017.03.006. doi: 10.1016/j.inffus.2017.03.006
[35]	Z. Wang, F. Yang, D. Ho, X. Liu, Robust finite-horizon filtering for stochastic systems with missing measurements, IEEE Signal Process. Lett., 12 (2005), 437–440. doi: 10.1109/LSP.2005.847890. doi: 10.1109/LSP.2005.847890
[36]	J. Hu, Z. Wang, S. Liu, H. Gao, A variance-constrained approach to recursive state estimation for time-varying complex networks with missing measurements, Automatica, 64 (2016), 155–162. doi: 10.1016/j.automatica.2015.11.008. doi: 10.1016/j.automatica.2015.11.008
[37]	J. Hu, Z. Wang, H. Gao, Recursive filtering with random parameter matrices, multiple fading measurements and correlated noises, Automatica, 49 (2013), 3440–3448. doi: 10.1016/j.automatica.2013.08.021. doi: 10.1016/j.automatica.2013.08.021
[38]	C. Pang, S. Sun, Fusion predictors for multisensor stochastic uncertain systems with missing measurements and unknown measurement disturbances, IEEE Sens. J., 15 (2015), 4346–4354. doi: 10.1109/JSEN.2015.2416511. doi: 10.1109/JSEN.2015.2416511
[39]	X. Li, X. Fu, R. Rakkiyappan, Delay-dependent stability analysis for a class of dynamical systems with leakage delay and nonlinear perturbations, Appl. Math. Comput., 226 (2014), 10–19. doi: 10.1016/j.amc.2013.10.004. doi: 10.1016/j.amc.2013.10.004
[40]	X. Lu, H. Li, An improved stability theorem for nonlinear systems on time scales with application to multi-agent systems, IEEE Trans. Circuits Syst. Ⅱ-Express Briefs, 67 (2020), 3277–3281. doi: 10.1109/TCSII.2020.2983180. doi: 10.1109/TCSII.2020.2983180
[41]	X. Lu, H. Li, Prescribed finite-time $H_{\infty}$ control for nonlinear descriptor systems, IEEE Trans. Circuits Syst. Ⅱ-Express Briefs, 68 (2021), 2917–2921. doi: 10.1109/TCSII.2021.3060550. doi: 10.1109/TCSII.2021.3060550
[42]	S. Wang, H. Fang, X. Tian, Recursive estimation for nonlinear stochastic systems with multi-step transmission delays, multiple packet dropouts and correlated noises, Signal Process., 115 (2015), 164–175. doi: 10.1016/j.sigpro.2015.03.022. doi: 10.1016/j.sigpro.2015.03.022
[43]	S. Wang, H. Fang, X. Liu, Distributed state estimation for stochastic non-linear systems with random delays and packet dropouts, IET Contr. Theory Appl., 9 (2015), 2657–2665. doi: 10.1049/iet-cta.2015.0257. doi: 10.1049/iet-cta.2015.0257
[44]	R. A. Horn, C. R. Johnson, Topics in matrix analysis, New York: Cambridge University Press, 1991. doi: 10.1017/CBO9780511840371.
[45]	L. Dai, Observers for discrete singular systems, IEEE Trans. Autom. Control, 33 (1988), 187–191. doi: 10.1109/9.387. doi: 10.1109/9.387
[46]	S. Sun, T. Tian, H. Lin, State estimators for systems with random parameter matrices, stochastic nonlinearities, fading measurements and correlated noises, Inf. Sci., 397 (2017), 118–136. doi: 10.1016/j.ins.2017.02.048. doi: 10.1016/j.ins.2017.02.048
[47]	P. C. Müller, Some aspects of the optimal control of non-linear descriptor systems, J. Appl. Math. Mech., 65 (2001), 769–776. doi: 10.1016/S0021-8928(01)00082-X. doi: 10.1016/S0021-8928(01)00082-X

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)