Effect of Faults on Kalman Filter of State Vectors in Linear Systems

He Song; Shaolin Hu

doi:doi:10.11648/j.ijdst.20190502.13

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Effect of Faults on Kalman Filter of State Vectors in Linear Systems

He Song, Shaolin Hu

Received: 25 July 2019 Accepted: 14 August 2019 Published: 28 August 2019

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Abstract

Kalman filter (KF) is composed of a set of recursion algorithms which can be used to estimate the optimal state of the linear system, and widely used in the control system, signal processing and other fields. In the practical application of the KF, it is an unavoidable problem that how faults or anomalies are infectious to the estimation value of state vectors in the linear system, which must be paid much attention to and solved down. In this paper, the effect of sensor faults and control input anomalies on the Kalman filtering values of state vectors is discussed, the transmission relationship is established to analyze the estimation deviation of state vectors which comes from pulse or step faults/anomalies, and a sufficient condition is deduced for the convergence of the estimation deviation of state vectors; Four different system models with 3-dimension state vector and 2-dimension observation vector are selected for simulation calculation and comparative analysis, simulation results show that sensor faults and control input anomalies in linear systems may cause significant deviations in the estimation value of state vectors for a long time, and there are distinct differences in the estimation value of state vectors. The research results provide a certain theoretical reference for us to analyze system fault types and to identify fault.

DOI	10.11648/j.ijdst.20190502.13
Published in	International Journal on Data Science and Technology (Volume 5, Issue 2, June 2019)
Page(s)	45-56
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

System Faults, Kalman Filter, Control Input Anomalies, Sensors Faults

References

[1]	R. E. Kalman. “A new approach to linear filtering and prediction problems”, J. Basic Eng. Trans., vol. 82, no. 1, pp. 35-45, 1960.
[2]	G. R. Chen. “Problems and Challenges in Control Theory under Complex Dynamical Network Environments”, Acta Autom. Sin, vol. 39, no. 4, pp. 312-321, 2013.
[3]	T. T. Hong, S. L. Hu. “Effect of initial deviation on Kalman filter of state vectors in linear system”, Acta Autom. Sin, vol. 43, no. 5, pp. 789-794, 2017.
[4]	L. Qing, Y. M. Zhang. “Adaptive integral-type sliding mode control for spacecraft attitude maneuvering under actuator stuck failures”, Chin. J. Aeronaut., vol. 24, no. 1, pp. 32-45, 2011.
[5]	X. Wei, M. Verhaegen. “Sensor and actuator fault diagnosis for wind turbine systems by using robust observer and filter”, Wind Energy, vol. 14, no. 4, pp. 491-516, 2011.
[6]	B. Gou, X. Ge. “An open-switch fault diagnosis method for single-phase PWM rectifier using a model-based approach in high-speed railway electrical traction drive system”, IEEE Trans. Power Electron., vol. 31, no. 5, pp. 3816-3826, 2016.
[7]	G. H. B. Foo, X. Zhang, D. M. Vilathgamuwa. “A sensor fault detection and isolation method in interior permanent-magnet synchronous motor drives based on an extended Kalman filter”, IEEE Trans. Ind. Electron., vol. 60, no. 8, pp. 3485-3495, 2013.
[8]	Q. Hu, B. Li, A. Zhang. “Robust finite-time control allocation in spacecraft attitude stabilization under actuator misalignment”, Nonlinear Dyn., vol. 73, no. 1-2, pp. 53-71, 2013.
[9]	Y. L. Zhang, W. M. Chen. “Overview on sensor fault diagnosis technology”, Transducer Microsyst. Technol., vol. 28, no. 1, pp. 4-6+12, 2009.
[10]	A. J. Volponi, H. DePold, R. Ganguli. “The use of Kalman filter and neural network methodologies in gas turbine performance diagnostics: a comparative study”, J. Eng. Gas Turbines Power, vol. 125, no. 4, pp. 917-924, 2003.
[11]	D. Mattern, L. Jaw, T. H. Guo. “Using neural networks for sensor validation”, 34th AIAA/ASME/SAE/ASEE Joint Propuls. Conf. Exhib., pp. 3547, 1998.
[12]	S. O. T. Ogaji, R. Singh, S. D. Probert.“Multiple-sensor fault-diagnoses for a 2-shaft stationary gas-turbine”, Appl. Energy, vol. 71, no. 4, pp. 321-339, 2002.
[13]	N. Aretakis, K. Mathioudakis, A. Stamatis.“Identification of sensor faults on turbofan engines using pattern recognition techniques”, Control Eng. Pract., vol. 12, no. 7, pp. 827-836, 2004.
[14]	B. Yuksek, N. K. Ure, F. Caliskan. “Fault tolerant heading control system design for Turac unmanned aerial vehicle”, Trans. Inst. Meas. Control, vol. 39, no. 3, pp. 267-276, 2017.
[15]	T. Wang, W. Xue, L. V. Huaibei. “Study on sensor fault diagnosis simulation for aircraft engine control system”, Comput. Simul, vol. 33, no. 2, pp. 56 – 60, 2016.
[16]	J. Zhang, J. Xiong, M. Ren. “Filter-based fault diagnosis of wind energy conversion systems subject to sensor faults”, J. Dyn. Syst. Meas. Control, vol. 138, no. 6, pp. 061008, 2016.
[17]	L. Li, Z. Wang, Y. Shen. “Fault diagnosis for attitude sensors via a bank of extended Kalman filters”, Control Conf., IEEE, pp. 6634-6638, 2016.
[18]	J. Ma, S. H. Ni. “Deterministic sampling strong tracking ﬁltering algorithms: fast detection and isolation for aircraft actuator fault”, Control Theory Appl., vol. 32, no. 6, pp. 734-743, 2015.
[19]	X. Chen, R. Sun, W. Jiang. “A novel two-stage extended Kalman filter algorithm for reaction flywheels fault estimation”, Chin. J. Aeronaut., vol. 29, no. 2, pp. 462-469, 2016.
[20]	F. B. Hmida, K. Khémiri, J. Ragot. “Three-stage Kalman filter for state and fault estimation of linear stochastic systems with unknown inputs”, J. Franklin Inst., vol. 349, no. 7, pp. 2369-2388, 2012.
[21]	M. Zhou, Z. H. Wang. “Unknown input filter based fault diagnosis method for over-actuated systems”, Syst. Eng. Electron., vol. 38, no. 12, pp. 2842-2848, 2016.
[22]	B. Friedland. “Treatment of bias in recursive filtering”, IEEE Trans. Autom. Control, vol. 14, no. 4, pp. 359-367, 1969.
[23]	P. K. Kitanidis. “Unbiased minimum-variance linear state estimation”, Automatica, vol. 23, no. 6, pp. 775-778, 1987.
[24]	M. Darouach, M. Zasadzinski. “Unbiased minimum variance estimation for systems with unknown exogenous inputs”, Automatica, vol. 33, no. 4, pp. 717-719, 1997.
[25]	C. S. Hsieh. “Robust two-stage Kalman filters for systems with unknown inputs”, IEEE Trans. Autom. Control, vol. 45, no. 12, pp. 2374-2378, 2000.
[26]	S. Gillijns, B. D. Moor. “Unbiased minimum-variance input and state estimation for linear discrete-time systems”, Automatica, vol. 43, no. 1, pp. 111-116, 2007.
[27]	X. P. Huang, Y. Wang. Kalman Filter Principle and its Application--MATLAB Simulation, Beijing: Publishing House of Electronics Industry, 2015.
[28]	J. Z. Di. Matrix Theory, Beijing: Science Press, 2016.

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APA Style

He Song, Shaolin Hu. (2019). Effect of Faults on Kalman Filter of State Vectors in Linear Systems. International Journal on Data Science and Technology, 5(2), 45-56. https://doi.org/10.11648/j.ijdst.20190502.13

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ACS Style

He Song; Shaolin Hu. Effect of Faults on Kalman Filter of State Vectors in Linear Systems. Int. J. Data Sci. Technol. 2019, 5(2), 45-56. doi: 10.11648/j.ijdst.20190502.13

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AMA Style

He Song, Shaolin Hu. Effect of Faults on Kalman Filter of State Vectors in Linear Systems. Int J Data Sci Technol. 2019;5(2):45-56. doi: 10.11648/j.ijdst.20190502.13

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@article{10.11648/j.ijdst.20190502.13,
  author = {He Song and Shaolin Hu},
  title = {Effect of Faults on Kalman Filter of State Vectors in Linear Systems},
  journal = {International Journal on Data Science and Technology},
  volume = {5},
  number = {2},
  pages = {45-56},
  doi = {10.11648/j.ijdst.20190502.13},
  url = {https://doi.org/10.11648/j.ijdst.20190502.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdst.20190502.13},
  abstract = {Kalman filter (KF) is composed of a set of recursion algorithms which can be used to estimate the optimal state of the linear system, and widely used in the control system, signal processing and other fields. In the practical application of the KF, it is an unavoidable problem that how faults or anomalies are infectious to the estimation value of state vectors in the linear system, which must be paid much attention to and solved down. In this paper, the effect of sensor faults and control input anomalies on the Kalman filtering values of state vectors is discussed, the transmission relationship is established to analyze the estimation deviation of state vectors which comes from pulse or step faults/anomalies, and a sufficient condition is deduced for the convergence of the estimation deviation of state vectors; Four different system models with 3-dimension state vector and 2-dimension observation vector are selected for simulation calculation and comparative analysis, simulation results show that sensor faults and control input anomalies in linear systems may cause significant deviations in the estimation value of state vectors for a long time, and there are distinct differences in the estimation value of state vectors. The research results provide a certain theoretical reference for us to analyze system fault types and to identify fault.},
 year = {2019}
}

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TY  - JOUR
T1  - Effect of Faults on Kalman Filter of State Vectors in Linear Systems
AU  - He Song
AU  - Shaolin Hu
Y1  - 2019/08/28
PY  - 2019
N1  - https://doi.org/10.11648/j.ijdst.20190502.13
DO  - 10.11648/j.ijdst.20190502.13
T2  - International Journal on Data Science and Technology
JF  - International Journal on Data Science and Technology
JO  - International Journal on Data Science and Technology
SP  - 45
EP  - 56
PB  - Science Publishing Group
SN  - 2472-2235
UR  - https://doi.org/10.11648/j.ijdst.20190502.13
AB  - Kalman filter (KF) is composed of a set of recursion algorithms which can be used to estimate the optimal state of the linear system, and widely used in the control system, signal processing and other fields. In the practical application of the KF, it is an unavoidable problem that how faults or anomalies are infectious to the estimation value of state vectors in the linear system, which must be paid much attention to and solved down. In this paper, the effect of sensor faults and control input anomalies on the Kalman filtering values of state vectors is discussed, the transmission relationship is established to analyze the estimation deviation of state vectors which comes from pulse or step faults/anomalies, and a sufficient condition is deduced for the convergence of the estimation deviation of state vectors; Four different system models with 3-dimension state vector and 2-dimension observation vector are selected for simulation calculation and comparative analysis, simulation results show that sensor faults and control input anomalies in linear systems may cause significant deviations in the estimation value of state vectors for a long time, and there are distinct differences in the estimation value of state vectors. The research results provide a certain theoretical reference for us to analyze system fault types and to identify fault.
VL  - 5
IS  - 2
ER  -

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Author Information

He Song

School of Automation and Information Engineering, Xi’an University of Technology, Xi’an, China
Shaolin Hu

School of Automation and Information Engineering, Xi’an University of Technology, Xi’an, China; Automation School, Guangdong University of Petrochemical Technology, Maoming, China

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Plain Text BibTeX RIS

APA Style

He Song, Shaolin Hu. (2019). Effect of Faults on Kalman Filter of State Vectors in Linear Systems. International Journal on Data Science and Technology, 5(2), 45-56. https://doi.org/10.11648/j.ijdst.20190502.13

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ACS Style

He Song; Shaolin Hu. Effect of Faults on Kalman Filter of State Vectors in Linear Systems. Int. J. Data Sci. Technol. 2019, 5(2), 45-56. doi: 10.11648/j.ijdst.20190502.13

Copy | Download

AMA Style

He Song, Shaolin Hu. Effect of Faults on Kalman Filter of State Vectors in Linear Systems. Int J Data Sci Technol. 2019;5(2):45-56. doi: 10.11648/j.ijdst.20190502.13

Copy | Download

@article{10.11648/j.ijdst.20190502.13,
  author = {He Song and Shaolin Hu},
  title = {Effect of Faults on Kalman Filter of State Vectors in Linear Systems},
  journal = {International Journal on Data Science and Technology},
  volume = {5},
  number = {2},
  pages = {45-56},
  doi = {10.11648/j.ijdst.20190502.13},
  url = {https://doi.org/10.11648/j.ijdst.20190502.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijdst.20190502.13},
  abstract = {Kalman filter (KF) is composed of a set of recursion algorithms which can be used to estimate the optimal state of the linear system, and widely used in the control system, signal processing and other fields. In the practical application of the KF, it is an unavoidable problem that how faults or anomalies are infectious to the estimation value of state vectors in the linear system, which must be paid much attention to and solved down. In this paper, the effect of sensor faults and control input anomalies on the Kalman filtering values of state vectors is discussed, the transmission relationship is established to analyze the estimation deviation of state vectors which comes from pulse or step faults/anomalies, and a sufficient condition is deduced for the convergence of the estimation deviation of state vectors; Four different system models with 3-dimension state vector and 2-dimension observation vector are selected for simulation calculation and comparative analysis, simulation results show that sensor faults and control input anomalies in linear systems may cause significant deviations in the estimation value of state vectors for a long time, and there are distinct differences in the estimation value of state vectors. The research results provide a certain theoretical reference for us to analyze system fault types and to identify fault.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Effect of Faults on Kalman Filter of State Vectors in Linear Systems
AU  - He Song
AU  - Shaolin Hu
Y1  - 2019/08/28
PY  - 2019
N1  - https://doi.org/10.11648/j.ijdst.20190502.13
DO  - 10.11648/j.ijdst.20190502.13
T2  - International Journal on Data Science and Technology
JF  - International Journal on Data Science and Technology
JO  - International Journal on Data Science and Technology
SP  - 45
EP  - 56
PB  - Science Publishing Group
SN  - 2472-2235
UR  - https://doi.org/10.11648/j.ijdst.20190502.13
AB  - Kalman filter (KF) is composed of a set of recursion algorithms which can be used to estimate the optimal state of the linear system, and widely used in the control system, signal processing and other fields. In the practical application of the KF, it is an unavoidable problem that how faults or anomalies are infectious to the estimation value of state vectors in the linear system, which must be paid much attention to and solved down. In this paper, the effect of sensor faults and control input anomalies on the Kalman filtering values of state vectors is discussed, the transmission relationship is established to analyze the estimation deviation of state vectors which comes from pulse or step faults/anomalies, and a sufficient condition is deduced for the convergence of the estimation deviation of state vectors; Four different system models with 3-dimension state vector and 2-dimension observation vector are selected for simulation calculation and comparative analysis, simulation results show that sensor faults and control input anomalies in linear systems may cause significant deviations in the estimation value of state vectors for a long time, and there are distinct differences in the estimation value of state vectors. The research results provide a certain theoretical reference for us to analyze system fault types and to identify fault.
VL  - 5
IS  - 2
ER  -

Copy | Download