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