title: ÐÑÑÐ¾ÐºÐ¾ÑÐ¾ÑÐ½Ð¾Ðµ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ Ð¾ÑÐ½Ð¾ÑÐ¸ÑÐµÐ»ÑÐ½ÑÑ ÐºÐ¾Ð¾ÑÐ´Ð¸Ð½Ð°Ñ Ð¿Ð¾ ÑÐ¸Ð³Ð½Ð°Ð»Ð°Ð¼ ÐÐÐ¡Ð¡ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ RTK
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: Precise relative positioning with RTK using GNSS signals
Creators: name: ÐÐµÑÑÐ¾Ð², ÐÐ³Ð¾ÑÑ
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: 2021
Subjects: ÐÑÑÐ¸ÑÐ»Ð¸ÑÐµÐ»ÑÐ½ÑÐµ Ð¼Ð°ÑÐ¸Ð½Ñ ÑÐ»ÐµÐºÑÑÐ¾Ð½Ð½ÑÐµ
Ð¡Ð¿ÑÑÐ½Ð¸ÐºÐ¾Ð²Ð°Ñ Ð½Ð°Ð²Ð¸Ð³Ð°ÑÐ¸Ñ
Ð Ð°Ð´Ð¸Ð¾ÑÐ¸Ð³Ð½Ð°Ð»Ñ
ÑÐ¸Ð»ÑÑÑ ÐÐ°Ð»Ð¼Ð°Ð½Ð°
Ð½ÐµÐ¾Ð´Ð½Ð¾Ð·Ð½Ð°ÑÐ½Ð¾ÑÑÑ ÑÐ°Ð·Ð¾Ð²ÑÑ Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ð¹
Kalman filtering
carrier-phase ambiguities

description: Ð¢ÐµÐ¼Ð° Ð²ÑÐ¿ÑÑÐºÐ½Ð¾Ð¹ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ: Â«ÐÑÑÐ¾ÐºÐ¾ÑÐ¾ÑÐ½Ð¾Ðµ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ðµ Ð¾ÑÐ½Ð¾ÑÐ¸ÑÐµÐ»ÑÐ½ÑÑ ÐºÐ¾Ð¾ÑÐ´Ð¸Ð½Ð°Ñ Ð¿Ð¾ ÑÐ¸Ð³Ð½Ð°Ð»Ð°Ð¼ ÐÐÐ¡Ð¡ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ RTKÂ». ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¾ÑÐ¾Ð±ÐµÐ½Ð½Ð¾ÑÑÐµÐ¹ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð¾Ð±ÑÐ°Ð±Ð¾ÑÐºÐ¸ Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ð¹ Ð ÐÐ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ RTK, Ð° ÑÐ°ÐºÐ¶Ðµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð²Ð»Ð¸ÑÐ½Ð¸Ñ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð¼ÐµÑÐ¾Ð´Ð° Ð½Ð° ÑÐ¾ÑÐ½Ð¾ÑÑÑ Ð¾Ð¿ÑÐµÐ´ÐµÐ»ÐµÐ½Ð¸Ñ Ð¾ÑÐ½Ð¾ÑÐ¸ÑÐµÐ»ÑÐ½ÑÑ ÐºÐ¾Ð¾ÑÐ´Ð¸Ð½Ð°Ñ. Ð ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ»Ð° ÑÐµÐ°Ð»Ð¸Ð·Ð¾Ð²Ð°Ð½Ð° Ð¼Ð¾Ð´ÐµÐ»Ñ Ð¾Ð±ÑÐ°Ð±Ð¾ÑÐºÐ¸ Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ð¹ Ð ÐÐ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ RTK Ð² ÑÑÐµÐ´Ðµ MATLAB. Ð ÐºÐ°ÑÐµÑÑÐ²Ðµ Ð²ÑÐ¾Ð´Ð½ÑÑ Ð´Ð°Ð½Ð½ÑÑ Ð´Ð»Ñ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð½Ð¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð±ÑÐ»Ð¸ Ð²Ð·ÑÑÑ Ð¿Ð°ÑÑ Ð·Ð°Ð¿Ð¸ÑÐµÐ¹ Ñ Ð¿ÑÐ¸ÐµÐ¼Ð½ÑÑ Ð¼Ð¾Ð´ÑÐ»ÐµÐ¹ NV08-CSM ÑÐ¸ÑÐ¼Ñ âÐÐÐ¡ ÐÐ°Ð²Ð¸Ð³Ð°ÑÐ¸Ð¾Ð½Ð½ÑÐµ ÑÐµÑÐ½Ð¾Ð»Ð¾Ð³Ð¸Ð¸â, ÑÐ¾Ð´ÐµÑÐ¶Ð°ÑÐ¸Ðµ Ð² ÑÐµÐ±Ðµ ÑÐ¾Ð¾Ð±ÑÐµÐ½Ð¸Ñ Ñ Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð½ÑÐ¼Ð¸ Ð ÐÐ ÑÐ¸Ð³Ð½Ð°Ð»Ð¾Ð² ÐÐÐ¡Ð¡, Ð° ÑÐ°ÐºÐ¶Ðµ ÑÑÐµÐ¼ÐµÑÐ¸Ð´Ñ Ð¸ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÑ Ð²ÑÐµÐ¼ÐµÐ½Ð¸ Ð²Ð¸Ð´Ð¸Ð¼ÑÑ ÑÐ¿ÑÑÐ½Ð¸ÐºÐ¾Ð² ÐÐÐ¡Ð¡. ÐÐ±Ð° Ð¿ÑÐ¸ÐµÐ¼Ð½Ð¸ÐºÐ°, ÐºÐ°Ðº Ð¸ Ð±Ð°Ð·Ð¾Ð²Ð°Ñ Ð»Ð¸Ð½Ð¸Ñ, Ð²Ð¾ Ð²ÑÐµÐ¼Ñ Ð¿ÑÐ¸ÐµÐ¼Ð° ÑÐ¸Ð³Ð½Ð°Ð»Ð¾Ð² ÐÐÐ¡Ð¡ Ð±ÑÐ»Ð¸ ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½Ñ. Ð ÐºÐ°ÑÐµÑÑÐ²Ðµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² ÑÐ°Ð±Ð¾ÑÑ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½Ñ Ð³ÑÐ°ÑÐ¸ÐºÐ¸ ÑÐ³Ð»Ð¾Ð² Ð¾ÑÐ¸ÐµÐ½ÑÐ°ÑÐ¸Ð¸ Ð¸ Ð´Ð»Ð¸Ð½Ñ Ð±Ð°Ð·Ð¾Ð²Ð¾Ð¹ Ð»Ð¸Ð½Ð¸Ð¸ Ñ ÑÐµÑÐµÐ½Ð¸ÐµÐ¼ Ð²ÑÐµÐ¼ÐµÐ½Ð¸ Ð±ÐµÐ· Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ Ð¼ÐµÑÐ¾Ð´Ð° RTK Ð¸ Ñ ÐµÐ³Ð¾ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸ÐµÐ¼, Ð° ÑÐ°ÐºÐ¶Ðµ ÑÐ¾ÑÑÐ°Ð²Ð»ÐµÐ½Ñ ÑÐ°Ð±Ð»Ð¸ÑÑ, ÑÐ¾Ð´ÐµÑÐ¶Ð°ÑÐ¸Ðµ Ð´Ð¸ÑÐ¿ÐµÑÑÐ¸Ñ Ð¸ ÑÑÐµÐ´Ð½ÐµÐµ Ð¾ÑÐºÐ»Ð¾Ð½ÐµÐ½Ð¸Ðµ Ð¾Ñ Ð¸ÑÑÐ¸Ð½Ð½Ð¾Ð³Ð¾ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ñ ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²ÑÑÑÐ¸Ñ Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ð¹. ÐÑÑÐ¾Ð´Ñ Ð¸Ð· Ð°Ð½Ð°Ð»Ð¸Ð·Ð¾Ð² Ð´Ð°Ð½Ð½ÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð±ÑÐ» ÑÐ´ÐµÐ»Ð°Ð½ Ð²ÑÐ²Ð¾Ð´ Ð¾ ÑÐ¾Ð¼, ÑÑÐ¾ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ð¼ÐµÑÐ¾Ð´Ð° RTK Ð´Ð»Ñ Ð¾ÑÐ½Ð¾ÑÐ¸ÑÐµÐ»ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð·Ð¸ÑÐ¸Ð¾Ð½Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ ÑÑÑÐµÑÑÐ²ÐµÐ½Ð½Ð¾ ÑÐ²ÐµÐ»Ð¸ÑÐ¸Ð²Ð°ÐµÑ ÐµÐ³Ð¾ ÑÐ¾ÑÐ½Ð¾ÑÑÑ Ð¿Ð¾ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ñ Ð¾ÑÐ½Ð¾ÑÐ¸ÑÐµÐ»ÑÐ½ÑÐ¼Ð¸ ÐºÐ¾Ð¾ÑÐ´Ð¸Ð½Ð°ÑÐ°Ð¼Ð¸, Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÐ¼Ð¸ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ ÑÐ°Ð·Ð½Ð¾ÑÑÐ¸ SPP Ð¸Ð»Ð¸ Ð¼ÐµÑÐ¾Ð´Ð¾Ð¼ ÑÐ³Ð»Ð°Ð¶ÐµÐ½Ð½ÑÑ ÐºÐ¾Ð´Ð¾Ð²ÑÑ Ð²ÑÐ¾ÑÑÑ ÑÐ°Ð·Ð½Ð¾ÑÑÐµÐ¹. Ð¢Ð°ÐºÐ¶Ðµ Ð±ÑÐ»Ð¸ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½Ñ Ð°Ð½Ð°Ð»Ð¾Ð³Ð¸ÑÐ½ÑÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð´Ð»Ñ Ð¼ÐµÑÐ¾Ð´Ð° RTK Ð¿ÑÐ¸ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ð¸ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð² Ð¾Ð±ÑÐ°Ð±Ð¾ÑÐºÐ¸. ÐÑÑÐ¾Ð´Ñ Ð¸Ð· Ð°Ð½Ð°Ð»Ð¸Ð·Ð¾Ð² Ð´Ð°Ð½Ð½ÑÑ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð² Ð±ÑÐ» ÑÐ´ÐµÐ»Ð°Ð½ Ð²ÑÐ²Ð¾Ð´ Ð¾ ÑÐ¾Ð¼, ÑÑÐ¾ ÑÐ²ÐµÐ»Ð¸ÑÐµÐ½Ð¸Ðµ Ð¾Ð±ÑÐµÐ¼Ð° Ð²ÑÐ±Ð¾ÑÐºÐ¸ Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ð¹ ÐºÐ¾Ð´Ð¾Ð²ÑÑ Ð²ÑÐ¾ÑÑÑ ÑÐ°Ð·Ð½Ð¾ÑÑÐµÐ¹ Ð´Ð»Ñ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ñ ÐºÐ¾Ð²Ð°ÑÐ¸Ð°ÑÐ¸Ð¾Ð½Ð½Ð¾Ð¹ Ð¼Ð°ÑÑÐ¸ÑÑ Ð¸Ð·Ð¼ÐµÑÐµÐ½Ð¸Ð¹, Ð° ÑÐ°ÐºÐ¶Ðµ ÑÐ²ÐµÐ»Ð¸ÑÐµÐ½Ð¸Ðµ Ð¾Ð±ÑÐµÐ¼Ð° Ð²ÑÐ±Ð¾ÑÐºÐ¸ Ð¿ÑÐ¸Ð±Ð»Ð¸Ð¶ÐµÐ½Ð½ÑÑ ÑÐ°Ð·Ð¾Ð²ÑÑ Ð½ÐµÐ¾Ð´Ð½Ð¾Ð·Ð½Ð°ÑÐ½Ð¾ÑÑÐµÐ¹ Ð´Ð»Ñ Ð¸Ñ ÑÑÑÐµÐ´Ð½ÐµÐ½Ð¸Ñ, Ð²ÐµÐ´ÐµÑ Ðº ÑÐ²ÐµÐ»Ð¸ÑÐµÐ½Ð¸Ñ ÑÐ¾ÑÐ½Ð¾ÑÑÐ¸ Ð¾ÑÐ½Ð¾ÑÐ¸ÑÐµÐ»ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾Ð·Ð¸ÑÐ¸Ð¾Ð½Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ. ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¼Ð¾Ð³ÑÑ Ð±ÑÑÑ Ð¿ÑÐ¸Ð¼ÐµÐ½ÐµÐ½Ñ ÐºÐ°Ðº Ð¾Ð¿Ð¾ÑÐ½ÑÐ¹ Ð¼Ð°ÑÐµÑÐ¸Ð°Ð» Ð´Ð»Ñ Ð¾Ð·Ð½Ð°ÐºÐ¾Ð¼Ð»ÐµÐ½Ð¸Ñ Ñ ÑÐµÑÐ½Ð¾Ð»Ð¾Ð³Ð¸ÐµÐ¹ RTK, ÑÐ°Ðº Ð¸ Ð´Ð»Ñ ÐµÐµ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð¸ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸ Ð² ÑÐµÐ°Ð»ÑÐ½Ð¾Ð¼ Ð¾Ð±Ð¾ÑÑÐ´Ð¾Ð²Ð°Ð½Ð¸Ð¸, Ð¸ÑÑÐ¾Ð´Ñ Ð¸Ð· ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð½Ð¾Ð¹ Ð² MATLAB Ð¼Ð¾Ð´ÐµÐ»Ð¸.
description: The subject of the graduate qualification work is âPrecise relative positioning by GNSS signals using RTK methodâ. This work is devoted to the study of the execution of the processing of raw navigation measurements by the RTK method. In the course of the work, a model for processing raw measurements by the RTK method in MATLAB was implemented. As input data for the developed model, we took pairs of records from the NV08-CSM receiving modules of the âNVS Navigation Technologiesâ company, containing messages with the measured raw measurements of GNSS signals, as well as ephemeris and time parameters of visible GNSS satellites. Both receivers, as well as the baseline, were stationary while receiving GNSS signals. As a results of the work are presented graphs of orientation angles and baseline length during processing time. The graphs are plotted without taking into account RTK technology and with it. In addition, it was compiled tables containing the variance and mean deviation from the true value of the corresponding measurements. Based on the analysis of the results, it was concluded that the application of the RTK method for relative positioning increases its accuracy in comparison with the relative coordinates obtained by the SPP difference method or the smoothed code double difference method. Similar results were also presented for the RTK method with changing processing parameters. Based on the results of data analysis, it was concluded that an increase in the sample size of measurements of the code double differences for calculating the covariance matrix, as well as an increase in the sample size of approximate phase ambiguities for their averaging, increases the accuracy of relative positioning. The obtained results can be used as a reference material for acquaintance with the RTK technology, and for its study and implementation in real equipment, based on the developed MATLAB model.