One of the key problems in the implementation of closed-loop control systems is to measure all states of a dynamic system, especially, when there are severe environmental conditions. Consequently, the use of certain types of sensors is impossible for technical or economic reasons. Also, in electromechanical systems, there are a lot of values that cannot be directly measured by physical sensors. Thus, mathematical algorithms named as observers and estimators are in use to calculate the states of the dynamic system utilizing math model and available set of sensors. One of the widespread observation algorithms, which are in use in electromechanical systems, is a particle filter which allows to determine the coordinates of the state vector of a nonlinear system with a non-Gaussian law of state distribution and measurements. Also, the practical value of the algorithm is due to the high sensitivity to sensor noise and convergence at large initial deviations of the estimated state values from the real values. However, the implementation of the algorithm requires considerable computational cost, which is caused by the calculation of a large number of state points that may have dynamic systems. In order to reduce the computational complexity, the paper proposes a modification of the particle filter, which was named as fuzzy particle filter. The modified algorithm involves switching the number of particles during the estimation process of the state vector using fuzzy logic with only one fuzzy input. The novel observer was applied to wheel electrical drive to estimate state vector. Mathematical modelling of the dynamics of the wheel electrical drive system when a vehicle is travelling on different surfaces proves the adequacy of the fuzzy particle filter. The proposed algorithm showed similar accuracy and lower computational cost compared to the classical particle filter. The modified observer was also found to have a little effect on the dynamics and static characteristics of a closed-loop control system with a full-state feedback controller while the fuzzy particle filter defines the coordinates of the state vector.

- Smetana I.V., Lozynsʹkyy A.O. Metody identyfikatsiyi koordynat stanu. Analiz problem ta shlyakhy yikh vyrishennya. Visnyk Natsionalʹnoho universytetu «Lʹvivsʹka politekhnika».2003. No. 485 : Elektroenerhetychni ta elektromekhanichni systemy. S. 118–125.
- Marushchak, Ya. Yu., Kushnir, A. P. Eksperymentalʹni doslidzhennya dvomasovykh elektromekhanichnykh system z urakhuvannyam syl dysypatsiyi. Elektrotekhnichni ta kompʺyuterni systemy. 2011. No. 3. S. 98–100.
- Gordon, N. J., Salmond, D. J., & Smith, A. F. Novel approach to nonlinear/non-Gaussian Bayesian state estimation. In IEE Proceedings F-radar and signal processing. 1993. Vol. 140, No. 2, pp. 107–113.
- Del Moral, Pierre. "Non Linear Filtering: Interacting Particle Solution" (PDF). Markov Processes and Related Fields. 1996. № 2 (4). pp. 555–580.
- Cheng, Q., Victorino, A.C., and Charara, A. Nonlinear observer of sideslip angle using a particle filter estimation methodology. IFAC Proceedings Volumes. 2011. No. 44(1), pp. 6266–6271.
- Dandach, H., Abdallah, F., De Miras, J. and Charara, A. Vehicle dynamics estimation using box particle filter. In 2012 12th International Conference on Control Automation Robotics & Vision (ICARCV) . 2012. pp. 118– 123.
- Ma, J. and Zhao, Q. Robot Visual Servo with Fuzzy Particle Filter. JCP, 2012. No. 7(4), pp. 842–845.
- Vantsevich, V., Gorsich, D., Lozynskyy, A., Demkiv, L. and Borovets, T. State Observers for Terrain Mobility Controls: A Technical Analysis. In IFToMM World Congress on Mechanism and Machine Science (Springer, Cham). 2019. pp. 3681–3690.
- Fox, D., Thrun, S., & Burgard, W. Probabilistic robotics. MIT Press. 2005.
- Gray, J. P., Vantsevich, V. V., Opeiko, A. F., & Hudas, G. R. A Method for Unmanned Ground Wheeled Vehicle Mobility Estimation in Stochastic Terrain Conditions. In Proc. of the 7th Americas Regional Conference of the ISTVS, Tampa, Florida, USA. 2013.
- Belousov, B., Ksenevich, T. I., Vantsevich, V., & Naumov, S.. An active long-travel, two performance loop control suspension of an open-link locomotion module for off-road applications. SAE Technical Paper. 2014. No. 2014-01-2288.