Application of a Fuzzy Model to the Task of Filtering in Nonlinear Dynamic Systems

In this paper, we consider various approaches to the problem of filtering in nonlinear dynamic systems and their algorithms. The Strong Tracking Unscented Kalman Filter, based on the combination of Unscented Kalman Filter and Strong Tracking Kalman Filter, provides stability to the uncertainty of the process model directly using a suboptimal scaling factor (SSF). The softening coefficient is part of the SSF and it improves the smoothness of the system state assessment. The coefficient is determined empirically and is included in the entire filtering process, which leads to a loss of accuracy in the time segments in which the process model is defined. The paper explores the use of Takagi --- Sugeno fuzzy model (T-S model) to adjust in real time the softening coefficient when the object's dynamics changes. As a result of a comparative analysis of the accuracy of the studied filters for the nonlinear model, it was found that the new filter using a fuzzy logical adaptive system possesses good smoothness of assessment and the greatest accuracy

References

[1] Kulikova M.V., Kulikov G.Yu. Numerical methods for nonlinear filtering of signals and measurements. Vychislitel’nye tekhnologii [Computational Technologies], 2016, vol. 21, no. 4, pp. 64--98 (in Russ.).

[2] Al Bitar N., Gavrilov A.I. Comparative analysis of integration algorithms in a loosely coupled inertial-satellite system based on real data processing. Giroskopy Navig., 2019, vol. 27, no. 3 (106), pp. 31--52 (in Russ.). DOI: https://doi.org/10.17285/0869-7035.0004

[3] Kudryavtseva I.A. Efficiency analysis of extended Kalman filtering, unscented Kalman filtering and unscented particle filtering. Nauchnyy vestnik MGTU GA [Civil Aviation High Technologies], 2016, no. 224 (2), pp. 43--51 (in Russ.).

[4] Kulikov R.S. Comparing of accuracy of nonlinear filtering in extended Kalman filter and in unscented filter. Radiotekhnika [Radioengineering], 2016, no. 9, pp. 135--140 (in Russ.).

[5] Shavrin V.V., Tislenko V.I., Lebedev V.Yu., et al. Quasioptimal estimation of GNSS signal parameters in coherent reception mode using sigma-point Kalman filter. Gyroscopy Navig., 2017, vol. 8, iss. 1, pp. 24--30. DOI: https://doi.org/10.1134/S2075108717010060

[6] Sudheesh P., Jayakumar M. Nonlinear tracking using unscented. Proc. SIRS-2017, 2018, vol. 678, pp. 38--46.

[7] Xu L., Ma K., Fan H. Unscented Kalman filtering for nonlinear state estimation with correlated noises and missing measurements. Int. J. Control Autom. Syst., 2018, vol. 16, iss. 3, pp. 1011--1020. DOI: https://doi.org/10.1007/s12555-017-0495-2

[8] Hu G., Gao S., Zhong Y., et al. Modified strong tracking unscented Kalman filter for nonlinear state estimation with process model uncertainty. Int. J. Adapt. Control Signal Process, 2015, vol. 29, iss. 12, pp. 1561--1577. DOI: https://doi.org/10.1002/acs.2572

[9] Narasimhappa M., Sabat S.L., Nayak J. Adaptive sampling strong tracking scaled unscented Kalman filter for denoising the fibre optic gyroscope drift signal. IET Sci. Meas. Technol., 2015, vol. 9, iss. 3, pp. 241--249. DOI: https://doi.org/10.1049/iet-smt.2014.0001

[10] Jwo D.-J., Lai S.-Y. Navigation integration using the fuzzy Strong Tracking Unscented Kalman. J. Navigation, 2009, vol. 62, iss. 2, pp. 303--322. DOI: https://doi.org/10.1017/S037346330800516X

[11] Crassidis J.L. Sigma-point Kalman filtering for integrated GPS and inertial navigation. IEEE Trans. Aerosp. Electron. Syst., 2006, vol. 42, iss. 2, pp. 750--756. DOI: https://doi.org/10.1109/TAES.2006.1642588

[12] Julier S.J., Uhlmann J.K. Unscented filtering and nonlinear estimation. Proc. IEEE, 2004, vol. 92, iss. 3, pp. 401--422. DOI: https://doi.org/10.1109/JPROC.2003.823141

[13] Hu G., Wang W., Zhong Y., et al. A new direct filtering approach to INS/GNSS integration. Aerospace Sci. Technol., 2018, vol. 77, pp. 755--764. DOI: https://doi.org/10.1016/j.ast.2018.03.040

[14] Feng Y., Li X., Zhang X. An adaptive compensation algorithm for temperature drift of micro-electro-mechanical systems gyroscopes using a Strong Tracking Kalman filter. Sensors, 2015, vol. 15, pp. 11222--11238. DOI: https://doi.org/10.3390/s150511222

[15] Arghavani N., Almobaied M., Guzelkaya M., et al. On-line rule weighting for PID-type fuzzy logic controllers using Extended Kalman filter. IFAC-PapersOnLine, 2017, vol. 50, iss. 1, pp. 6946--6951. DOI: https://doi.org/10.1016/j.ifacol.2017.08.1221

[16] Tehrani M., Nariman-zadeh N., Masoumnezhad M. Adaptive fuzzy hybrid un-scented/H-infinity filter for state estimation of nonlinear dynamics problems. Trans. Inst. Meas. Control, 2018, vol. 41, iss. 6. DOI: https://doi.org/10.1177/0142331218787607

[17] Jwo D.-J., Chung F.-C. Fuzzy adaptive unscented Kalman filter for ultra-tight GPS/INS integration. IEEE Int. Symp. Comp. Intel. Design, 2010, pp. 229--235. DOI: https://doi.org/10.1109/ISCID.2010.148

[18] An J., Yu Y., Tang J., et al. Fuzzy-based hybrid location algorithm for vehicle position in VANETs via fuzzy Kalman filtering approach. Adv. Fuzzy Syst., 2019, vol. 2019, art. 5142937. DOI: https://doi.org/10.1155/2019/5142937

[19] Tseng C.-H., Chang C.-W., Jwo D.-J. Fuzzy adaptive interacting multiple model nonlinear filter for integrated navigation sensor fusion. Sensors, 2011, vol. 11, iss. 2, pp. 2090--2111. DOI: https://doi.org/10.3390/s110202090

[20] Yazdkhasti S., Sasiadek S.Z., Ulrich S. Performance enhancement for GPS/INS fusion by using a fuzzy adaptive unscented Kalman filter. 21st MMAR, 2016, pp. 1194--1199. DOI: https://doi.org/10.1109/MMAR.2016.7575308

[21] Pires D.S., Serra G.L.d.O. Methodology for evolving fuzzy Kalman filter identification. Int. J. Control Autom. Syst., 2019, vol. 17, iss. 3, pp. 793--800. DOI: https://doi.org/10.1007/s12555-017-0503-6

[22] Piegat A. Fuzzy modeling and control. Heidelberg, Physica-Verlag, 2001.

[23] Barragan A.J., Al-Hadithi B.M., Jimenez A., et al. A general methodology for online TS fuzzy modeling by the extended Kalman filter. Appl. Soft Comput., 2014, vol. 18, pp. 277--289. DOI: https://doi.org/10.1016/j.asoc.2013.09.005

[24] Matveev V.V., Raspopov V.Ya. Osnovy postroeniya besplatformennykh inertsial’nykh navigatsionnykh system [Basics of engineering strapdown inertial navigation systems]. St. Petersburg, Kontsern "TsNII "Elektropribor" Publ., 2009.

[25] Salychev O.S. Verified approaches to inertial navigation. Moscow, BMSTU Publ., 2017.