title: ÐÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ²Ð¸Ð½Ð½ÑÑ Ð°ÑÐ¸ÑÐ¼ÐµÑÐ¸Ðº Ð² Ð°Ð½Ð°Ð»Ð¸Ð·Ðµ Ð´Ð°Ð½Ð½ÑÑ Ñ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ Ð½ÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÑÑ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¼Ð°Ð³Ð¸ÑÑÑÐ°
titleType: Subtitle
title: The use of twin arithmetic in the analysis of data with interval uncertainty
Creators: name: ÐÐ¸ ÐÑÐ¹ÑÐ¸
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2023
Subjects: ÐÐ½ÑÐµÑÐ²Ð°Ð»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· (Ð¼Ð°Ñ.)
Ð Ð¾Ð±Ð¾ÑÑ Ð¿ÑÐ¾Ð¼ÑÑÐ»ÐµÐ½Ð½ÑÐµ
Ð·Ð°Ð´Ð°ÑÐ° Ð¾Ð±ÑÐ°ÑÐµÐ½Ð¸Ñ Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ²Ð°
Ð½ÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÑÐ½Ð½Ð¾ÑÑÑ
Ð·Ð¾Ð½Ð° Ð¾Ð±ÑÐµÐ½Ð¸Ðµ
Ð»Ð¾ÐºÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ
set inversion problem
uncertainty
communication zone
localization

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ ÑÐ²Ð¸Ð½Ð½ÑÑ Ð°ÑÐ¸ÑÐ¼ÐµÑÐ¸Ðº Ð¸ ÑÐµÑÐµÐ½Ð¸Ðµ Ð·Ð°Ð´Ð°Ñ Ð¾Ð±Ð»Ð°ÑÑÐ¸ ÑÐ²ÑÐ·Ð¸ Ð¸ Ð»Ð¾ÐºÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð¿Ð¾Ð´Ð²Ð¾Ð´Ð½ÑÑ ÑÐ¾Ð±Ð¾ÑÐ¾Ð² Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ SIVIA. ÐÐ°Ð´Ð°ÑÐ¸, ÐºÐ¾ÑÐ¾ÑÑÐµ ÑÐµÑÐ°Ð»Ð¸ÑÑ Ð² ÑÐ¾Ð´Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ: ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²Ð¾Ð¿ÑÐ¾ÑÑ ÐºÐ¾Ð¼Ð¿ÑÑÑÐµÑÐ½Ð¾Ð¹ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ ÑÐ²Ð¸Ð½Ð½ÑÑ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð¾Ð² Ð½Ð° ÑÐ¾Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ð¼ Ð¿Ð¾Ð¿ÑÐ»ÑÑÐ½Ð¾Ð¼ ÑÐ·ÑÐºÐµ, Ð¿Ð¾Ð»ÑÑÐ¸Ð¼ Ð²Ð½ÑÑÑÐµÐ½Ð½Ð¸Ðµ Ð¸ Ð²Ð½ÐµÑÐ½Ð¸Ðµ Ð¾ÑÐµÐ½ÐºÐ¸ ÑÑÐ½ÐºÑÐ¸Ð¹. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ ÑÐ²Ð¸Ð½Ð½ÑÑ Ð°ÑÐ¸ÑÐ¼ÐµÑÐ¸ÐºÐ¾Ð² ÑÑÐ°Ð½ÑÑÐ·ÑÐºÐ¸Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÐºÐ¾Ð². ÐÐ·ÑÑÐµÐ½Ð¸Ðµ Ð¸ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ñ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° Ð¾Ð±ÑÐ°ÑÐµÐ½Ð¸Ñ Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ²Ð°, ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Â«Ð¾Ð±ÑÐ°ÑÐ½Ð¾Ð¹Â» Ð·Ð°Ð´Ð°ÑÐ¸ - Ð²Ð¾ÑÑÑÐ°Ð½Ð¾Ð²Ð»ÐµÐ½Ð¸Ðµ ÑÐ½ÑÑÐ° ÑÐ¾ÐºÐ° Ð¿Ð¾ Ð´Ð°Ð½Ð½ÑÐ¼ Ð´Ð°ÑÑÐ¸ÐºÐ¾Ð². ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð¿ÑÐ¾Ð±Ð»ÐµÐ¼ Ð¿Ð¾Ð´Ð²Ð¾Ð´Ð½ÑÑ ÑÐ¾Ð±Ð¾ÑÐ¾Ð², Ð² ÑÐ¾Ð¼ ÑÐ¸ÑÐ»Ðµ Ð·Ð¾Ð½Ð° Ð¾Ð±ÑÐµÐ½Ð¸Ñ Ð¸ Ð»Ð¾ÐºÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸. Ð ÑÑÐ¾Ð¹ ÑÑÐ°ÑÑÐµ Ð² Ð¾ÑÐ½Ð¾Ð²Ð½Ð¾Ð¼ Ð¸Ð·ÑÑÐ°ÐµÑÑÑ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° ÑÐ²Ð¸Ð½Ð½ÑÑ Ð¿ÑÐ¸ Ð°Ð½Ð°Ð»Ð¸Ð·Ðµ Ð´Ð°Ð½Ð½ÑÑ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»ÑÐ½Ð¾Ð¹ Ð½ÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÐ¸. ÐÑ ÑÐµÐ°Ð»Ð¸Ð·ÑÐµÐ¼ Ð±Ð°Ð·Ð¾Ð²ÑÐ¹ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ ÑÐ²Ð¸Ð½Ð½ÑÑ Ð² python Ð¸ Ð¾Ð´Ð½Ð¾Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾ Ð²Ð²Ð¾Ð´Ð¸Ð¼ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼ Ð¾Ð±ÑÐ°ÑÐµÐ½Ð¸Ñ Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ²Ð°. Ð Ð·Ð°Ð´Ð°ÑÐµ Ð¾Ð±ÑÐ°ÑÐµÐ½Ð¸Ñ Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ², Ñ. Ðµ. IXI = f^(-1) (Y), f Ð¸ Y ÑÐ²Ð»ÑÑÑÑÑ Ð½ÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½ÑÐ¼Ð¸.Â ÐÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÑ ÑÑÐ°ÐºÑÑÐµÑÑÑ Ð² Ð²Ð¸Ð´Ðµ Ð¸Ð½ÑÐµÑÐ²Ð°Ð»Ð°, ÐÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ²Ð¾ Y ÑÐ¾ÑÑÐ¾Ð¸Ñ Ð¸Ð· Ð²Ð½ÑÑÑÐµÐ½Ð½ÐµÐ³Ð¾ Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ²Ð° Y^â Ð¸ Ð²Ð½ÐµÑÐ½ÐµÐµ Ð¼Ð½Ð¾Ð¶ÐµÑÑÐ²Ð¾ Y^â. ÐÐ¾ÑÑÐµÐ´ÑÑÐ²Ð¾Ð¼ Ð°Ð»Ð³Ð¾ÑÐ¸ÑÐ¼Ð° SIVIA, Ð¼Ñ Ð¼Ð¾Ð¶ÐµÐ¼ Ð¸Ð½ÑÑÐ¸ÑÐ¸Ð²Ð½Ð¾ ÑÐ²Ð¸Ð´ÐµÑÑ Ð²Ð½ÐµÑÐ½ÑÑ, Ð²Ð½ÑÑÑÐµÐ½Ð½ÑÑ Ð¸ Ð½ÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½ÑÑ Ð¾Ð±Ð»Ð°ÑÑÐ¸. ÐÐ¾Ð´Ð²Ð¾Ð´Ð½Ð°Ñ ÑÑÐµÐ´Ð° ÑÐ°ÐºÐ¶Ðµ Ð¸Ð¼ÐµÐµÑ Ð½ÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÐ¸, Ð¸ Ð¼Ñ Ð¼Ð¾Ð¶ÐµÐ¼ Ð»ÑÑÑÐµ Ð¾ÑÐ»Ð¸ÑÐ¸ÑÑ Ð½ÐµÐ¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÐ¸, Ð²ÑÐ·Ð²Ð°Ð½Ð½ÑÐµ ÑÐ°ÑÑÐµÑÐ°Ð¼Ð¸, Ð¾Ñ Ð²Ð½ÑÑÑÐµÐ½Ð½ÐµÐ³Ð¾ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¸. ÐÑÑÐ¾Ð´Ñ Ð¸Ð· ÑÑÐ¾Ð³Ð¾, Ð¼Ñ Ð¿ÑÐ¸Ð¼ÐµÐ½ÑÐµÐ¼ ÐµÐ³Ð¾ Ð´Ð»Ñ Ð¾Ð±Ð½Ð°ÑÑÐ¶ÐµÐ½Ð¸Ñ, ÑÑÐ¾ Ð¸Ð³ÑÐ°ÐµÑ Ð±Ð¾Ð»ÑÑÑÑ ÑÐ¾Ð»Ñ Ð² ÑÐ°Ð±Ð¾ÑÐµ Ñ Ð·Ð¾Ð½Ð¾Ð¹ ÑÐ²ÑÐ·Ð¸ Ð¸ Ð¿Ð¾Ð·Ð¸ÑÐ¸Ð¾Ð½Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÑÐ¾Ð±Ð¾ÑÐ¾Ð².
description: The given work is devoted to the study of twin arithmetic and the solution of problems in the field of communication and localization of underwater robots using SIVIA. The research set the following goals: Researching the issues of computer implementation of twin algorithms in a modern popular language, we obtain internal and external function estimates. Study of twin arithmetic of French mathematicians. Study and implementation of the set inversion algorithm, Study of the "inverse" problem - the restoration of the current cord according to the sensor data. Study and implementation of the set inversion algorithm, Study of the "inverse" problem - the restoration of the current cord according to the sensor data. Study of the problems of underwater robots, including the zone of communication and localization. This article mainly studies the application of the twin algorithm in the analysis of interval uncertainty data. We are implementing a basic twin algorithm in python and introducing a set reversal algorithm at the same time. In the set inversion problem, IXI = f^(-1) (Y), f and Y are indefinite. Uncertainty is treated as an interval. The indefinite set Y consists of the inner set Y^â and the outer set Y^â. Through the SIVIA algorithm, we can intuitively see the outer, inner, and undefined areas. The underwater environment also has uncertainties, and we can better distinguish the uncertainties caused by the calculations from the internal representation of the penumbra. Based on this, we use it for detection, which plays a big role in working with the communication zone and positioning of robots.