Examining the Kalman filter in the field of noise and interference with the non-Gaussian distribution

Authors

DOI:

https://doi.org/10.15587/1729-4061.2018.140649

Keywords:

Kalman filter, recursive algorithm, Python, non-Gaussian noise, distribution law

Abstract

We have developed a sequential recursive Kalman Filter algorithm to filter data in the field of the non-Gaussian noise distribution to be used in measurement instruments. A special feature of the constructed Kalman Filter algorithm to filter data with the non-Gaussian noises is the absence of a need to determine a priori the statistical characteristics of noise.

The applicability of the developed Kalman filtering procedure was tested by processing different distribution laws: the Cauchy, Pareto noises, normal and logistic distributions. The effectiveness of the devised filtering procedure is confirmed by applying the filter when processing experimental data with different laws of noise distribution. We have conducted approbation of the developed procedure for the Kalman filtering based on data obtained experimentally, with respect to the superposition of noise distribution laws. The a priori estimate for a filtering error when the number of iterations exceeds 30 tends to zero.

The devised filtering procedure employing the Kalman filter could be used when performing the metrological certification of measuring instruments under industrial conditions. Under such circumstances, measuring information could become noisy due to various noises, including those that are not governed by the Gaussian distribution law. The filter could be used when processing data from control systems over state parameters, implemented on the principle of a magnitude threshold control.

The applied aspect of the scientific result obtained implies the possibility of extending the scope of application of the classic Kalman filter in measurement instruments. This is a prerequisite for the development of a generic filtering algorithm using the Kalman filter. 

Author Biographies

Olga Oliynyk, Ukrainian State University of Chemical Technology Gagarina ave., 8, Dnipro, Ukraine, 49005

PhD, Associate Professor

Department of Computer-integrated Technologies and Metrology

Yuri Taranenko, Ukrainian State University of Chemical Technology Gagarina ave., 8, Dnipro, Ukraine, 49005

Doctor of Technical Sciences, Professor, Head of Department

Department of Computer-integrated Technologies and Metrology

Dmitriy Losikhin, Ukrainian State University of Chemical Technology Gagarina ave., 8, Dnipro, Ukraine, 49005

Senior Lecturer

Department of Computer-integrated Technologies and Metrology

Alexander Shvachka, Ukrainian State University of Chemical Technology Gagarina ave., 8, Dnipro, Ukraine, 49005

PhD, Associate Professor

Department of Computer-integrated Technologies and Metrology

References

  1. Grewal, M. S. (2011). Kalman Filtering. International Encyclopedia of Statistical Science, 705–708. doi: https://doi.org/10.1007/978-3-642-04898-2_321
  2. Daum, F. (2005). Nonlinear filters: beyond the Kalman filter. IEEE Aerospace and Electronic Systems Magazine, 20 (8), 57–69. doi: https://doi.org/10.1109/maes.2005.1499276
  3. Wan, E. A., Van Der Merwe, R. (2000). The unscented Kalman filter for nonlinear estimation. Proceedings of the IEEE 2000 Adaptive Systems for Signal Processing, Communications, and Control Symposium (Cat. No.00EX373). doi: https://doi.org/10.1109/asspcc.2000.882463
  4. Su, W., Huang, C., Liu, Р., Ma, М. (2010). Application of adaptive Kalman filter technique in initial alignment of inertial navigation system. Journal of Chinese Inertial Technology, 18 (1), 44–47.
  5. Babikir, A., Mwambi, H. (2016). Factor Augmented Artificial Neural Network Model. Neural Processing Letters, 45 (2), 507–521. doi: https://doi.org/10.1007/s11063-016-9538-6
  6. Doz, C., Giannone, D., Reichlin, L. (2011). A two-step estimator for large approximate dynamic factor models based on Kalman filtering. Journal of Econometrics, 164 (1), 188–205. doi: https://doi.org/10.1016/j.jeconom.2011.02.012
  7. Obidin, M. V., Serebrovskiy, A. P. (2013). Ochistka signala ot shumov s ispol'zovaniem veyvlet preobrazovaniya i fil'tra Kalmana. Informacionnye process, 13 (3), 198–205.
  8. Sarkka, S., Nummenmaa, A. (2009). Recursive Noise Adaptive Kalman Filtering by Variational Bayesian Approximations. IEEE Transactions on Automatic Control, 54 (3), 596–600. doi: https://doi.org/10.1109/tac.2008.2008348
  9. Sun, X.-J., Gao, Y., Deng, Z.-L., Li, C., Wang, J.-W. (2010). Multi-model information fusion Kalman filtering and white noise deconvolution. Information Fusion, 11 (2), 163–173. doi: https://doi.org/10.1016/j.inffus.2009.06.004
  10. Nikitin, A. P., Chernavskaya, O. D., Chernavskii, D. S. (2009). Pareto distribution in dynamical systems subjected to noise perturbation. Physics of Wave Phenomena, 17 (3), 207–217. doi: https://doi.org/10.3103/s1541308x09030054
  11. Arasaratnam, I., Haykin, S. (2009). Cubature Kalman Filters. IEEE Transactions on Automatic Control, 54 (6), 1254–1269. doi: https://doi.org/10.1109/tac.2009.2019800
  12. Stano, P., Lendek, Z., Braaksma, J., Babuska, R., de Keizer, C., den Dekker, A. J. (2013). Parametric Bayesian Filters for Nonlinear Stochastic Dynamical Systems: A Survey. IEEE Transactions on Cybernetics, 43 (6), 1607–1624. doi: https://doi.org/10.1109/tsmcc.2012.2230254
  13. Gavrilov, A. V. (2015). Ispol'zovanie fil'tra Kalmana dlya resheniya zadach utochneniya koordinat BPLA. Sovremennye problemy nauki i obrazovaniya, 1-1, 1784.
  14. Rudenko, E. A. (2010). A optimal discrete nonlinear arbitrary-order filter. Journal of Computer and Systems Sciences International, 49 (4), 548–559. doi: https://doi.org/10.1134/s1064230710040052
  15. Kaladze, V. A. (2011). Fil'truyushchie modeli statisticheskoy dinamiki. Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Sistemniy analiz i informacionnye tekhnologii, 1, 22–28.
  16. Wu, M., Smyth, A. W. (2007). Application of the unscented Kalman filter for real-time nonlinear structural system identification. Structural Control and Health Monitoring, 14 (7), 971–990. doi: https://doi.org/10.1002/stc.186
  17. Taranenko, Yu. K., Oleynik, O. Yu. (2017). Model' adaptivnogo fil'tra Kalmana. Tekhnologiya priborostroeniya, 1, 9–11.
  18. Cover, T. M., Thomas, J. A. (2012). Elements of information theory. John Wiley & Sons, 36.
  19. Rossum, G. (2001). Yazyk programmirovaniya Python. 454. Available at: http://rus-linux.net/MyLDP/BOOKS/python.pdf
  20. Degtyarev, A. A., Tayl', Sh. (2003). Elementy teorii adaptivnogo rasshirennogo fil'tra Kalmana. Preprinty Instituta prikladnoy matematiki im. M. V. Keldysha RAN, 26–36.
  21. Chernavskiy, D. S., Nikitin, A. P., Chernavskaya, O. D. (2007). O mekhanizmah vozniknoveniya raspredeleniya Pareto v slozhnyh sistemah. Moscow: Fizicheskiy in-t im. P. N. Lebedeva, 17.

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Published

2018-08-16

How to Cite

Oliynyk, O., Taranenko, Y., Losikhin, D., & Shvachka, A. (2018). Examining the Kalman filter in the field of noise and interference with the non-Gaussian distribution. Eastern-European Journal of Enterprise Technologies, 4(4 (94), 36–42. https://doi.org/10.15587/1729-4061.2018.140649

Issue

Vol. 4 No. 4 (94) (2018): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

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Copyright (c) 2018 Olga Oliynyk, Yuri Taranenko, Dmitriy Losikhin, Alexander Shvachka

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