Granular filtration model and algorithms in the mobile robot global localization problem

Keywords: state estimation, dynamic system, digital filtration, optimal filtration, non-systematic error, robot positioning.


Methods for estimating the parameters and states of dynamic systems are an urgent task, the results of which are used in various fields, including processes in technical systems, cosmological and physical research, medical diagnostic systems, economics, finance, biotechnology, ecology and others. Despite significant scientific and practical advances in this area, researchers in many countries around the world continue to search for new methods for estimating the parameters and condition of the studied objects and improving existing ones. An example of such methods is digital and optimal filtering, which have been widely used in technical systems since the middle of the last century, in particular, in the processing of financial and economic data, physical experiments and other information technologies for various purposes. The model and algorithms of granular filtration are considered on a practical example - a variant of the problem of global localization of a mobile robot (global localization for mobile robots) or the problem of a hijacked robot problem. In the General embodiment, it is to determine the position of the robot according to the data from the sensor. This problem was generally solved by a number of probabilistic methods in the late 1990s and early 2000s. The task is important and finds application in mobile robotics and industry. The tasks of positioning submarines, aircraft, cars, etc. are essentially similar. The problem of robot positioning is also considered. Let the robot turn on in the dark maze. It has a maze map and a compass. In the labyrinth at some points there are stations marked on the map, which can receive and reflect the signal. The robot does not know where the maze is, but it can send a signal at any time and with some error know the distance to the nearest station. The robot begins to wander the maze, taking each step in a new randomly chosen direction, but his compass also gives some unsystematic error. At each step, the robot determines the distance to the nearest station. The goal is to find out the coordinates of the robot in the maze in the frame of reference entered on the map.


1. Anderson B.D.O., Moore J.B., Optimal Filtering. – Englewood Cliffs, NJ: Prentice Hall, Inc., 1979. – 367 p.
2. Бідюк П.І., Романенко В.Д., Тимощук О.Л. – Аналіз часових рядів. – Київ: Політехніка, 2011. – 608 с.
3. Kay S.M., Fundamentals of Statistical Signal Processing: Estimation Theory. – Upper Saddle River, NJ: Prentice Hall, 1993, 595 p.
4. Chui C.K., Chen G., Kalman Filtering with Real-Time Applications. – Berlin: Springer, 2009. – 239 p.
5. Haykin S., Adaptive Filtering Theory. – Upper Saddle River NJ: Prentice Hall, 2007, 920 p.
6. Згуровский М.З., Подладчиков В.Н. Аналитические методы калмановской фильтрации. – Киев: Наукова думка, 1997. – 320 с.
7. Press S.J., Subjective and Objective Bayesian Statistics. – Hoboken, NJ: John Wiley & Sons, Inc., 2003. – 558 p.
8. Pole A., West M., Harrison J., Applied Bayesian Forecasting and Time Series Analysis. – Boca Raton, FL: Chapman & Hall/CRC, 2000. – 410 p.
9. Liu D., Wang Z. Recursive filtering for stochastic parameter systems with measurement quantizations and packet disorders. – Elsevier, Applied Mathematics and Computation, Vol. 398, 2021. DOI:
10. Tan L., Li C. Output feedback leader-following consensus for nonlinear stochastic multiagent systems: The event-triggered method. - Elsevier, Applied Mathematics and Computation, Vol. 395, 2021. DOI:
11. Chaparro L.F., Akan A. Signals and Systems Using MATLAB (Third edition). – Academic Press, 2019. DOI:
12. Yilmaz V. Automated ground filtering of LiDAR and UAS point clouds with metaheuristics. – Elsevier, Optics & Laser Technology, Vol. 138, 2021. DOI:
13. Acciaio B., Backhoff-Veraguas J. Causal optimal transport and its links to enlargement of filtrations and continuous-time stochastic optimization. – Elsevier, Stochastic Processes and their Applications, Vol. 130, 2020. DOI:
14. Coutin L., Lejay A. Sensitivity of rough differential equations: An approach through the Omega lemma. – Elsevier, Journal of Differential Equations, Vol. 264, 2018. DOI:
15. Weidong Z., Guanhua Li. Positioning error compensation on two-dimensional manifold for robotic machining. – Elsevier, Robotics and Computer-Integrated Manufacturing, Vol. 59, 2019. DOI:
16. Klimchik A., Pashkevich A. CAD-based approach for identification of elasto-static parameters of robotic manipulators. – Elsevier, Finite Elements in Analysis and Design, Vol. 75, 2013. DOI:
17. Zargarbashi S.H.H., Khan W. Posture optimization in robot-assisted machining operations. – Elsevier, Mechanism and Machine Theory, Vol. 51, 2012. DOI:
18. Klecker S., Hichri B. Robotic trajectory tracking: Bio-inspired position and torque control. – Elsevier, Procedia CIRP, Vol. 88, 2020. DOI:
19. Pérez-Rubio M.C., Losada-Gutiérrez C., Espinosa F. A realistic evaluation of indoor robot position tracking systems: The IPIN 2016 competition experience. – Elsevier, Measurement, Vol. 135, 2019. DOI:
20. Sun S., Zhao J. Path planning for multiple mobile anchor nodes assisted localization in wireless sensor networks. – Elsevier, Measurement, Vol. 141, 2019. DOI:
How to Cite
Pantyeyev, R., & Bidyuk, P. (2020). Granular filtration model and algorithms in the mobile robot global localization problem. Herald of Kyiv Institute of Business and Technology, 45(3), 41-46.