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Strong Tracking Tobit Kalman Filter with Model Uncertainties

  • Zhan-long DuEmail author
  • Xiao-min Li
Regular Papers Control Theory and Applications
  • 35 Downloads

Abstract

The Tobit Kalman filter (TKF) is a good choice for applications of discrete time-varying systems with censored measurements. The traditional TKF is usually designed under the assumption of exactly knowing system state and measurement functions, which can not guarantee the good performance and is even unsuitable for system with model mismatch. To ensure the performance, this paper proposes a novel TKF algorithm in the presence of both censored measurements and model uncertainties. Our proposed algorithm, called strong tracking TKF (STTKF), adopts the orthogonal principle as an additional criterion to overcome model mismatch problem. By introducing fading factor into a priori error covariance, STTKF adaptively adjust gain matrix according to different model mismatch degree. Firstly the recursive fading factor formulation is deduced based on orthogonal principle. Then the designed STTKF process is given in a recursive manner. Finally the effectiveness of STTKF is verified by two examples of oscillator system and unmanned aerial vehicle (UAV) transmitter.

Keywords

Censored measurement fading factor Kalman filter model mismatch orthogonal principle strong tracking filter Tobit model 

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References

  1. [1]
    T. Lu and M. Wang, “Nonlinear mixed–effects HIV dynamic models with considering left–censored measurements,” Journal of Statistical Distributions & Applications, vol. 1, no. 1, pp. 1–14, January, 2014.MathSciNetCrossRefzbMATHGoogle Scholar
  2. [2]
    R. A. Martin and P. Wild, “Bivariate left–censored measurements in biomonitoring: a Bayesian model for the determination of biological limit values based on occupational exposure limits,” Annals of Work Exposures & Health, vol. 61, no. 5, pp. 1–5, May, 2017.Google Scholar
  3. [3]
    O. Usoltseva, “A consistent estimator in the accelerated failure time model with censored observations and measurement errors,” Theory of Probability & Mathematical Statistics, vol. 82, no. 1, pp. 161–169, January, 2011.MathSciNetCrossRefGoogle Scholar
  4. [4]
    F. Xaver, “Mixed discrete–continuous Bayesian inference: censored measurements of sparse signals,” IEEE Transactions on Signal Processing, vol. 63, no. 21, pp. 5609–5620, June, 2015.MathSciNetCrossRefzbMATHGoogle Scholar
  5. [5]
    B. Ibarz–Gabardos and P. J Zufiria, “A Kalman filter with censored data,” IEEE International Workshop on Intelligent Signal Processing, pp. 74–79, October, 2005.CrossRefGoogle Scholar
  6. [6]
    J. Arthur, A. Attarian, F. Hamilton, and H. Tran, “Nonlinear Kalman filtering for censored observations,” vol. 316, pp. 155–166, September, 2017.Google Scholar
  7. [7]
    M. Yu, C. J. Liu, B. B. Li, and W. H. Chen, “An enhanced particle filtering method for GMTI radar tracking,” IEEE Transactions on Aerospace & Electronic Systems, vol. 52, no. 3, pp. 1408–1420, June, 2016.CrossRefGoogle Scholar
  8. [8]
    B. Allik, C. Miller, M. J. Piovoso, and R. Zurakowski, “Estimation of saturated data using the Tobit Kalman filter,” Proc. of American Control Conference, pp. 4151–4156, June 2014.Google Scholar
  9. [9]
    B. Allik, C. Miller, M. J. Piovoso, and R. Zurakowski, “The Tobit Kalman filter: an estimator for censored measurements,” IEEE Transactions on Control Systems Technology, vol. 24, no. 1, pp. 365–371, June, 2015.CrossRefGoogle Scholar
  10. [10]
    B. Allik, C. Miller, M. J Piovoso, and R. Zurakowski, “Nonlinear estimators for censored data: a comparison of the EKF, the UKF and the Tobit Kalman filter,” Proc. of American Control Conference, pp. 5146–5151, July, 2015.Google Scholar
  11. [11]
    B. Allik, M. J. Piovoso, and R. Zurakowski, “Recursive estimation with quantized and censored measurements,” Proc. of American Control Conference, pp. 5130–5135, July, 2016.Google Scholar
  12. [12]
    W. L. Li, Y. M. Jia, and J. P. Du, “Tobit Kalman filter with time–correlated multiplicative measurement noise,” IET Control Theory & Applications, vol. 11, no. 1, pp. 122–128, September, 2016.MathSciNetCrossRefGoogle Scholar
  13. [13]
    H. Geng, Z. Z. Wang, and Y. Liang, “Tobit Kalman filter with fading measurements,” Signal Processing, vol. 140, no. 1, pp. 60–68, January, 2017.CrossRefGoogle Scholar
  14. [14]
    C. Miller, B. Allik, M. Piovoso, and R. Zurakowski, “Estimation of mobile vehicle range & position using the tobit Kalman filter,” Decision and Control, pp. 5001–5007, February, 2015.Google Scholar
  15. [15]
    J. Huang and X. He, “Detection of intermittent fault for discrete–time systems with output dead–zone,” Journal of Control Science and Engineering, vol. 2017, no. 10, pp. 1–10, February, 2017.zbMATHGoogle Scholar
  16. [16]
    K. Loumponias, N. Vretos, P. Daras, and G. Tsaklidis, “Using Tobit Kalman filtering in order to improve the motion recorded by Microsoft Kinect,” Proc. of 8th International Workshop on Applied Probabilities, 2016.Google Scholar
  17. [17]
    D. H. Zhou and P. M. Frank, “Strong tracking filtering of nonlinear time–varying stochastic systems with coloured noise: application to parameter estimation and empirical robustness analysis,” International Journal of Control, vol. 65, no. 2, pp. 295–307, September, 1996.MathSciNetCrossRefzbMATHGoogle Scholar
  18. [18]
    M. Narasimhappa, S. L. Sabat, and J. Nayak, “Adaptive sampling strong tracking scaled unscented Kalman filter for denoising the fibre optic gyroscope drift signal,” Science Measurement & Technology IET, vol. 9, no. 3, pp. 241–249, May, 2014.CrossRefGoogle Scholar
  19. [19]
    M. Narasimhappa, S. L. Sabat, and J. Nayak, “Adaptive sampling strong tracking scaled unscented Kalman filter for denoising the fibre optic gyroscope drift signal,” Science Measurement & Technology IET, vol. 9, no. 3, pp. 241–249, May, 2014.CrossRefGoogle Scholar
  20. [20]
    X. J. Li, Z. G. Xu, and D. H. Zhou, “Chaotic secure communication based on strong tracking filtering,” Physics Letters A, vol. 372, no. 44, pp. 6627–6632, October, 2008.CrossRefzbMATHGoogle Scholar
  21. [21]
    D. Wang, D. H. Zhou, Y. H. Jin, and S. J. Qin, “A strong tracking predictor for nonlinear processes with input time delay,” Computers & Chemical Engineering, vol. 28, no. 12, pp. 2523–2540, November, 2004.CrossRefGoogle Scholar
  22. [22]
    X. L. Deng, W. Z. Guo, J. Y. Xie, and J. Liu, “Particle filter based on strong tracking filter,” International Conference on Machine Learning and Cybernetics, pp. 658–661, September, 2005.Google Scholar
  23. [23]
    X. X. Wang, L. Zhao, Q. X. Xia, and Y. Hao, “Strong tracking filter based on unscented transformation,” Control & Decision, vol. 25, no. 7, pp. 1063–1068, July, 2010.MathSciNetGoogle Scholar
  24. [24]
    X. X. Wang, Z. Lin, and H. X. Xue, “Strong tracking CDKF and application for integrated navigation,” Control & Decision, vol. 25, no. 12, pp. 1837–1842, December 2010.MathSciNetGoogle Scholar
  25. [25]
    Z. L. Du, X. M. Li, Z. G. Zheng, and Q. Mao, “Fault prediction with combination of strong tracking square–root cubature Kalman filter and autoregressive model,” Control Theory & Applications, vol. 31, no. 8, pp. 1047–1052, August 2014.Google Scholar
  26. [26]
    Q. B. Ge, T. Shao, S. D. Chen, and C. L. Wen, “Carrier tracking estimation analysis by using the extended strong tracking filtering,” IEEE Transactions on Industrial Electronics, vol. 64, no. 2, pp. 1415–1424, February 2017.CrossRefGoogle Scholar
  27. [27]
    Q. C. Yang, S. Y. Li, and Y. P. Cao, “A strong tracking filter based multiple model approach for gas turbine fault diagnosis,” Journal of Mechanical Science & Technology, vol. 32, no. 1, pp. 465–479, January 2018.CrossRefGoogle Scholar

Copyright information

© Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Baicheng Test CenterBaichengChina
  2. 2.College of Electrical and Electronics EngineeringShijiazhuang Tiedao UniversityShijiazhuangChina

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