music Hello! My name is Tyurin Sergey. I am an Associate Professor at SPbU. Today we start the module about geodetic control of the survey. The module includes two lessons. In the first one, I will tell you about coordinate systems used in surveying and geodetic networks. In the second lesson, my colleague Artem will talk about a geodetic control using Global Satellite Positioning Systems. So, let's begin. In geodetic applications, terrestrial (global) and reference (regional) coordinate systems, as well as local coordinate systems, are used. Reference coordinate systems include national geodetic coordinate systems. The Global coordinate system is a geocentric spatial coordinate system with a beginning at the mass center of the Earth. The Z axis is directed to the conditional Earth pole, as defined by the recommendations of the International Earth Rotation and Reference Systems Service (IERS), the X axis is directed to the point of intersection of the equator plane and the Reference meridian, the Y axis complements the system to the right-handed coordinate system. The Global coordinate system rotates with the Earth. In a geocentric coordinate system, the position of a point in space is determined by the values of the X, Y, Z coordinates. In geodetic applications, the geodetic coordinates B, L, H are used for the same purpose, referring to a common earth ellipsoid - - an ellipsoid of revolution (spheroid) whose geometric center coincides with the center of the global coordinate system. The Z axis is the axis of rotation of the ellipsoid. The geodetic latitude B is defined as the angle between the perpendicular to the ellipsoid passing through the given point and the plane of the equator; geodetic longitude L is the dihedral angle between the plane of the initial meridian and the plane of the meridian passing through a given point; the geodetic height H is the section of the perpendicular to the common terrestrial ellipsoid from its surface to a given point. Usually an ellipsoid is characterized by the value of the semimajor axis or semiminor axis. However, there is another way of doing it - using the semimajor axis and the flattening value. Flattening is connected with the dimensions of the semiaxes through the ratio you can see on the slide. The slide shows the sizes of the main Earth ellipsoids. The implementation of global coordinates is a complex scientific task. An implementation of such a coordinate system for GPS is the WGS-84 system. The Russian GLONASS uses the PZ-90 coordinate system. An analogue of the geocentric coordinate systems PZ-90 and WGS-84 is the International Earth Support System ITRS, maintained and regularly updated by the International Earth Rotation Service. The practical embodiment of ITRS is International Terrestrial Reference Frame (ITRF), with more than 500 stations worldwide. ITRF is the most accurate embodiment of the Earth coordinate system. Let's consider in more detail the Russian coordinate system PZ-90. “Earth Parameters of 1990” and its latest version PZ-90.11, established by Decree of the Government of the Russian Federation N1240 dated November 24, 2016 are a system of geodetic parameters, including fundamental geodetic constants, parameters of the Earth ellipsoid, parameters of the Earth’s gravitational field, geocentric coordinate system and parameters of its relationship with other coordinate systems. When refining the geocentric coordinate system, the data on the establishment of terrestrial coordinate systems obtained by domestic and international scientific organizations were used to the maximum. In PZ-90.11, the orientation of the coordinate axes, the linear scale and the position of the coordinate system origin converge with similar parameters of the International Earth Reference Frame ITRF in centimeters. Now let us duscuss the reference system. The reference surface in geodetic reference coordinate systems, as well as in the terrestrial coordinate system, is a spheroid. The difference is that the position of the coordinates origin in these systems and the orientation of their axes may not coincide. Thus, these systems are associated with local reference ellipsoids used in a single country or group of countries. It should be noted that it is possible to use the sizes and shapes of the same ellipsoid in various coordinate systems that differ in their orientation (initial geodetic dates). In reference systems, geodetic coordinates are usually used: geodetic latitude, geodetic longitude, and height above an ellipsoid. By the Decree of the Government of the Russian Federation N 1240 November 24, 2016, GSK-2011 geodetic coordinate system was established as the state CS for use in the implementation of geodetic and cartographic works. Since 1946, the reference coordinate system of 1942 (SK-42) was used in Russia. Decree of the Government of the Russian Federation of July 28, 2000 No. 568 dated July 1, 2002 introduced the geodetic reference coordinate system of 1995 (SK-95). According to the same decree No. 1240, these coordinate systems can be applied in individual cases until January 1, 2021. Let me tell you in more detail about these two systems. In the SK-42 coordinate system, the Krasovsky ellipsoid was used as a reference surface. When this sistem was established, 2 conditions had to be implemented. First: parallelism of the Z axis of the reference coordinate system to the middle axis of rotation of the Earth and parallelism of the initial astronomical and geodesic meridians planes. Due to measurement errors and limited processing (adjustment) capabilities, these conditions at that time could not be reliably controlled, which led to the rotation of the reference coordinate system axes, which was first reliably estimated in the early 80s using satellite data. The reference surface in the 1995 coordinate system, as well as in SK-42, is the Krasovsky ellipsoid. The axes of the SK-95 coordinate system are set under the condition of parallelism to the axes of the terrestrial coordinate system PZ-90. With the transition to GSK-2011, we moved away from using a reference ellipsoid. GSK-2011 geodetic coordinate system is a practical implementation of the terrestrial spatial coordinate system with the origin at the Earth mass center.