Wgs 84 coordinate system as it looks. Conversion issues between different coordinate systems
However, it is expected that during national emergencies, the US Department of Defense may use its control over GPS, i.e. prevent civilian users from accessing the signal or reduce the signal so that the navigation system cannot provide civil aviation.
Advantages and disadvantages of SNA
Satellite navigation systems have a number of advantages over existing radio navigation systems (RTS). The main advantages of satellite navigation include the provision of accurate and reliable 4-dimensional navigation in all areas and at all aircraft flight altitudes and, as a result:
reducing the risk of catastrophes associated with the inaccuracy of information about the location of the aircraft, especially in those areas (altitudes) of the flight of the aircraft, where the use operating funds impossible or economically impractical;
use of a single navigation aid to support all stages of aircraft flight, including precision landing approaches to unequipped airfields;
the possibility of implementing automatic dependent monitoring, will provide an increase bandwidth when reducing the longitudinal and lateral separation intervals of the aircraft in those areas where the organization of observation using radar stations is impossible or economically unreasonable;
increasing the flexibility and efficiency of aircraft flights with high precision of aircraft navigation and the use of area navigation by reducing flight time and saving fuel;
reducing the cost of servicing air traffic when decommissioning the fleet of existing navigation and landing aids and for the operation of the aircraft by replacing various types of on-board equipment with single means.
However, the long-term operation of GPS and GLONASS has shown that satellite navigation systems have the following disadvantages:
sensitivity to unintentional interference caused by atmospheric effects;
blocking the signal when the antenna is obscured by aircraft structural elements during evolutions;
sensitivity to intentional interference that may limit the service area;
insufficient accuracy when used for precision approach purposes.
The above disadvantages can be eliminated by using various kinds of functional additions. There are three categories of add-ons: airborne, terrestrial and satellite.
ICAO strategy in the field developmentair navigation using SNA
In recent years, there has been an active introduction of satellite navigation systems to solve the problems of area navigation on various stages flight. In the future, the SNS will gradually replace all terrestrial navigation systems and become the only means of providing navigation throughout the route.
ICAO has now developed Required Navigation Performance (RNP), which defines the requirements for the accuracy of maintaining navigation parameters within a particular airspace. This indicator is not associated with a specific type of navigation equipment, which makes it general character and makes it applicable to satellite navigation systems. The RNP value is determined by the retention value, which characterizes the size of the area centered at the point of the given aircraft location, within which it will be during 95% of the flight time (Fig. 2.1) .
Rice. 2.1. RNP area
The holding value is expressed in nautical miles. To facilitate the use of RNP in airspace planning, the elliptical shape of this area is being replaced by a circular one. Therefore, for example, RNP type 1 means that at an arbitrary point in time, with a probability of 0.95, an aircraft must be within a radius of one nautical mile from a point indicated by the air traffic authority.
RNP types define the minimum navigation performance accuracy in a given area of airspace. They are set taking into account the accuracy of onboard navigation equipment, as well as piloting errors.
In order to ensure the required level of accuracy at various stages of flight, the following types of RNP have been developed: en-route and airfield.
For example, in flight conditions along the route, where the traffic density is not so high, the RNP value will be in the range from 20 to 1, and when maneuvering in the airfield area in landing approach conditions, from 0.5 to 0.3.
Route RNP types are presented in Table. 2.2. .
Table 2.2
RNP Route Types
Type RNP 1 is envisaged to provide the most efficient flights on ATS routes as a result of using the most accurate information about the VAM, as well as to apply the area navigation method, which allows for the greatest flexibility in organizing routes, changing routes and making necessary adjustments in real time in accordance with the needs airspace structures. This type of RNP provides for the most efficient provision of flights, the use of flight rules and airspace organization during the transition from the aerodrome area to the flight along the ATS route and vice versa, i.e. when performing SID and STAR.
Type RNP 4 is intended for ATS routes based on limited distance between navaids. This type of RNP is typically used in airspace over a continent. This type RNP is intended to reduce lateral and longitudinal separation minima and improve operational efficiency in oceanic airspace and areas where the use of ground-based navigation aids is limited.
The RNP 10 type provides reduced lateral and longitudinal separation minima and improves operational efficiency in oceanic airspace and certain areas where the capability of air navigation aids is limited.
The RNP 12.6 type provides limited route optimization in areas with a reduced level of navigation aids.
The RNP 20 type characterizes the minimum capabilities for the accuracy of determining the VAM, which are considered acceptable for ensuring flights on ATS routes by any aircraft in any controlled airspace at any time.
An analysis of the types of RNPs proposed by ICAO shows that in order to ensure the continued use of existing navigation equipment without changing the existing structure of ATS routes in some areas or regions, an RNP value of 5 (9.3 km) can be set. Evidence of this is the introduction of RNP5 type area navigation (B-RNAV) in the European Region in 1998.
Aerodrome RNP types are presented in Table. 2.3.
Table 2.3
Types of RNP when maneuvering in the aerodrome area
|
Sample operation(s) |
Accuracy in the horizontal plane 95% |
Accuracy vertical 95% | ||
|
initial entry, intermediate entry, Inaccurate entry, departure |
220 m (720 ft) |
Not assigned |
0.5 to 0.3 |
|
|
220 m (720 ft) |
20 m (66 ft) | |||
|
Approach with vertical control |
16.0 m (52 ft) |
8.0 m (26 ft) | ||
|
Precise approach to |
From 6.0 m to 4.0 m (20 -13 ft) | |||
*) According to .
Notes:
1) A planned operation at the lowest altitude above the runway threshold requires 95% of the position error value usingGNSS.
2) Accuracy and alarm delay requirements include the performance rating of the fail-safe receiver.
The use of SNS at the landing approach stage will allow, in combination with the wide area coverage augmentation system (WAAS), to increase its accuracy to submeter and, as a result, ensure the implementation of an inaccurate landing approach (without glide path guidance).
The use of SNS at the landing approach stage in combination with a limited area augmentation system (LAAS) will improve its accuracy to centimeter and ensure the performance of a precision approach (with glide path guidance).
The current air traffic management system is based on the concept of predetermined route separation. Such a system guarantees flight safety by reducing throughput. The use of the SNA will make it possible to change the existing route structure by reducing the separation norms (minimums). This will increase the capacity of the global transport system, increase its efficiency and profitability due to route optimization. The first steps in this direction have already been taken. For example, firstly, the width of routes (tracks) in the Pacific Ocean for aircraft equipped with SNA equipment has been changed from 60 NM (111 km) to 30 NM (55.5 km). Secondly, since 1997, a reduced vertical separation has been introduced in the North Atlantic region from 600 m (2000 ft) to 300 m (1000 ft) between flight levels 290 (8840m) and 410 (12500m). In the European Region, the phased introduction of reduced vertical separation standards, between the above levels, began in 2001.
SNS and new technology capabilities in the field of communication, navigation and surveillance systems will allow the idea of free flight to be realized in the future. The idea of free flight means the optimization of the route in flight dynamics at any given moment of time based on the knowledge of the exact location of the aircraft and the velocity vector in the given region. In this case, the flight plan becomes a simple preliminary statement of intent.
This idea is the ultimate goal of a future air navigation system.
In free flight, the onboard systems of the aircraft calculate and transmit information about the location and short-term intentions to air traffic control services. Dispatch services monitor satisfactory separation aircraft and intervene briefly in the flight process in the presence of a dangerous approach or collision.
Thus, satellite navigation systems are considered as a necessary tool for en-route flights, non-precision approaches, airspace separation, route optimization and the implementation of the idea of free flight.
test questions
What SNAs are included in GNSS?
What is the configuration of the location of satellites in GPS and GLONASS systems?
What are the main segments of a satellite navigation system?
What values correspond to the accuracy characteristics of GPS and GLONASS?
In which case can the US Department of Defense use its control over GPS?
What is the abbreviation RNP?
What values correspond to en-route and aerodrome RNP types?
Which augmentation system, together with the SNS, will allow for the implementation of a precision approach?
How will the application of the SNA change the existing route structure?
What does the idea of free flight mean?
COORDINATE SYSTEMS
Coordinate systems used in geodesy
Geodesy uses three coordinate systems:
geocentric (tied to the Earth);
ellipsoidal.
In some countries, when processing geodetic measurements, ellipsoids are used, derived from the results of geodetic work covering the territory of a given country or several countries. Such “working” ellipsoids are called reference ellipsoids. The coordinate system defined on such an ellipsoid is called local.
The reference ellipsoid differs from the general earth ellipsoid in size, and its center does not coincide with the center of the Earth. Due to the mismatch between the centers of the reference ellipsoids and the real Earth, the minor axis of the reference ellipsoid does not coincide with the axis of rotation of the Earth (Fig. 3.1).
ellipsoid
Global
ellipsoid
Fig.3.1. Differences between the general earth ellipsoid
and reference ellipsoid
As the main earth coordinate system, a geocentric, earth-bound, spatial rectangular system (X, Y, Z) is adopted, the beginning of which is the center of mass of the Earth S (geocenter, i.e. the center of mass, including the mass of the atmosphere) (Fig. 3.2) . The Z axis will coincide with the Earth's rotation axis.
Rice. 3.2. Geocentric Cartesian Coordinate System (X, Y, Z)
The geocentric coordinate system is used in determining the position of the aircraft when solving the corresponding system of equations. The Earth's surface can be accurately approximated by an ellipsoid of revolution with oblate poles. In this case, the deviation of the ellipsoid surface in height from the geoid does not exceed 100 m.
An ellipsoid of revolution is obtained by rotating a meridian ellipse about its minor axis. Therefore, the shape of the ellipsoid is described by two geometric parameters: the semi-major axis a and minor semiaxis b . Usually b is replaced by the compression (oblateness) parameter of the ellipsoid:
To spatially determine the position of a point on the physical surface of the Earth (or in space) with respect to the ellipsoid of revolution, geodetic coordinates are used: φ - latitude and λ - longitude, h- height from the surface of the ellipsoid. The height h above the ellipsoid is measured along the normal (perpendicular) to its surface (Fig. 3.3).
Rice. 3.3. Geodetic coordinate system and height
It can be noted that in navigation, the concept of geographical coordinates is usually used instead of geodetic coordinates. The reason for this is that before the advent of the CNS, the accuracy of determining the MVS was such that there was no need to make distinctions between these coordinate systems.
Coordinate systemsWGS-84 and PZ-90
Navigation is impossible without the use of coordinate systems. When using SNA for air navigation purposes, a geocentric coordinate system is used.
In 1994, ICAO recommended as a standard for all ICAO member states from January 1, 1998 to use the WGS-84 global geodetic coordinate system, because in this coordinate system, the position of the aircraft is determined using the GPS system. The reason for this is that the use of local geodetic coordinates on the territory of various states, and there are more than 200 such coordinate systems, would lead to an additional error in determining the MAM due to the fact that the waypoints entered into the SNS receiver-indicator belong to a coordinate system that differs from WGS-84.
The center of the WGS-84 global coordinate system coincides with the Earth's center of mass. The Z-axis corresponds to the direction of the usual earth's pole, which moves due to the oscillatory rotation of the earth. The X-axis lies in the plane of the equator at the intersection with the plane of the zero (Greenwich) meridian. The Y-axis lies in the equatorial plane and is 90° away from the X-axis (Fig. 3.4).
Rice. 3.4. Defining the WGS-84 Coordinate System
IN Russian Federation, in order to provide geodetic support for orbital flights and solve navigation problems when using GLONASS, the geocentric coordinate system "Parameters of the Earth 1990" is used. (PZ-90). For the implementation of geodetic and cartographic work, starting from May 1, 2002, the system of geodetic coordinates of 1995 (SK-95) is used. The transition from the geodetic coordinate system of 1942 (SK-42) to SK-95 will take a certain period of time before all navigation points on the territory of Russia will be transferred to the new coordinate system.
The main parameters of the coordinate systems discussed above are presented in Table. 3.1.
Table 3.1
Coordinate systems used in navigation
|
Parameter | ||||||
|
Major axis, m | ||||||
|
Minor axis, m | ||||||
|
Offset from center of mass Earth on the axis, m | ||||||
|
Orientation relatively axes, angles. sec. |
ω X | |||||
|
ω at | ||||||
Note. Values ∆х, ∆у, ∆zAndω X , ω at , ωz for PZ-90 are given relative to WGS-84, and for SK-95 and SK-42 relative to PZ-90.
From Table. 3.1 it can be seen that the WGS-84 and PZ-90 coordinate systems are almost the same. It follows from this that when flying along the route and in the area of the aerodrome, with the existing accuracy of determining the MAM, it does not matter in what coordinate system the navigation points will be determined.
In the PZ-90 coordinate system, the center (S’) relative to the WGS-84 center (S) has an offset along the X, Y, Z axes:
ΔX = 2 m, ΔY = 6 m, ΔZ = - 4.5 m,
and, in addition, the Y’ and Z’ axes are also shifted relative to the WGS-84 axes (Y, Z) by angular values:
ω Y = - 0.35'', ω Z = - 0.11''.
The X axis in WGS-84 and the X’ axis in PZ-90 are the same.
The angular displacement of the Y' axis of PZ-90 relative to the Y axis of WGS-84 of 0.35'' leads to a linear displacement on the surface of the ellipsoid at the equator of 10.8 m, and the offset of the Z' axis with respect to the Z axis in 0.11'' - 3.4 m. These displacements can lead to a general (radial) displacement of a point located on the PZ-90 surface relative to WGS-84 by 11,3 m.
test questions
What is the definition of a reference ellipsoid?
For what purposes is the geocentric coordinate system used when using the SNA?
What geometric parameters describe an ellipsoid of revolution?
What coordinate system is adopted by ICAO as a standard?
What coordinate system is used in GLONASS?
What are the main parameters that characterize WGS-84 and PZ-90?
Is it fundamental in what coordinate system WGS-84 or PZ-90, navigation points will be measured during the flight along the route?
What is the radial displacement of a point on the surface of an ellipsoid in the PZ-90 coordinate system relative to WGS-84?
PRINCIPLES FOR DETERMINING AIRCRAFT NAVIGATION PARAMETERS IN SNA
General principles of the functioning of the SNA
The principles of operation of GNSS are relatively simple, but advanced achievements of science and technology are used for their implementation.
All GPS or GLONASS satellites are equal in their system. Each satellite emits a coded signal at two carrier frequencies (L1; L2) through the transmitting antenna, which can be received by the corresponding user receiver located in the satellite coverage area. The transmitted signal contains the following information:
satellite ephemeris;
ionospheric modeling coefficients;
satellite status information;
system time and satellite clock drift;
satellite drift information.
In the receiver of the onboard equipment of the aircraft, a code is generated that is identical to that received from the satellite. When comparing two codes, a time shift is determined, which is proportional to the distance to the satellite. By simultaneously receiving signals from several satellites, you can determine the location of the receiver with high accuracy. Obviously, for the functioning of the system, the exact synchronization of the codes generated on the satellites and in the receivers is necessary.
A key factor in determining the accuracy of the system is that all components of the satellite signal are precisely controlled by atomic clocks. Each satellite has four quantum generators, which are high-precision frequency standards with a stability of 10 -13 . The receiver clock is less accurate, but its code is constantly compared with the satellite clock and an offset is generated to compensate for drift.
The ground segment controls the satellites, performs control functions and determines the navigation parameters of the satellites. Data on the results of measurements made by each control station is processed at the main control station and used to predict the satellite ephemeris. In the same place, at the main control station, signals are generated to correct the satellite clock.
The position of an aircraft using GPS and GLONASS is determined in geodetic coordinate systems, which may differ from the geodetic coordinates used in on-board navigation systems.
Physical and technical principles of functioning of the SNS.
The WGS84 Global Earth Ellipsoid is a geodesic ellipsoid with a fixed geocentric Global Earth coordinate system. The WGS84 ellipsoid is defined by a set of constants and ellipsoid model parameters that describe the dimensions and shape of the Earth, gravitational and magnetic fields. WGS84 is the standard global ellipsoid adopted as the global coordinate system by the US Department of Defense, as well as the coordinate system for the global positioning system (GPS). It is compatible with the International Terrestrial Coordinate System (ITRS). Currently, WGS84 (G1674) follows the criteria described in Technical Note 21 (TN 21) of the International Earth Rotation Service (IERS). The responsible organization is the US National Geospatial-Intelligence Administration (NGA). The NGA plans to make adjustments to the WGS84 coordinate system in 2013 to align with the rules of the 2010 IERS Convention Technical Note 36 (TN 36).
- Origin (Origin of coordinates): The center of mass of the Earth, including the oceans and atmosphere, is taken as the origin of the coordinate system.
- Z-Axis (Z axis): Points at the reference pole defined by the International Earth Rotation Service (IERS Reference Pole). This direction corresponds to the direction to the conventional pole of the Earth (BIH Conventional Terrestrial Pole) (for the period 1984.0) with an error of 0.005".
- X-Axis (X-Axis): The X-axis lies in the plane of the reference meridian (IERS Reference Meridian) and passes through the origin along the normal to the Z-axis.
- Y-Axis (Y axis): Pads the Earth-Centered Earth-Fixed (ECEF) orthogonal coordinate system to the right.
- Scale (Scale): Its scale - the scale of the Earth's structure is consistent with the alternative theory of gravity (relativistic theory of gravitation). Combined with ITRS.
- Orientation: Presented by the International Bureau of Time (Bureau International de l'Heure) for the period 1984.0.
- Time Evolution (Temporary development): The change in time will not create any global rotation residuals relative to the earth's crust.
Parameters
WGS84 can be identified using four parameters: the semi-major axis WGS84, the flattening factor of the Earth, the nominal mean angular velocity of the Earth, and the geocentric gravitational constant. Parameter values are presented in the table below.
| Parameter | Designation | Meaning |
|---|---|---|
Large axle (Semi-major Axis) |
a | |
Flattening Factor of the Earth |
1/f | |
Nominal Mean Angular Velocity |
ω | 7292115 10 -11 radians/sec |
Geocentric Gravitational Constant |
GM | 3986004.418 10 8 m 3 /sec 2 |
The GM value includes the mass of the Earth's atmosphere. Global Positioning System (GPS) users should remember the original WGS84 GM value of 3986005.0 10 8 m3/sec 2 as defined in the GPS control document (ICD-GPS-200) and NIMA Technical Report 8350.2 (Technical Report).
Implementations of WGS84
The EPSG database and the NGS website use a space between "WGS" and "84" in the name "WGS 84". The EPSG database does not contain any specific implementations of the WGS84 ellipsoid.
| Geog 2D Code | Ellipsoid Code | Short name | Ellipsoid Epoch | District code | District name | Note | Bias |
|---|---|---|---|---|---|---|---|
| 4326 | 6326 | WGS84 | 1984 | 1262 | World (World) | First implementation established by the US Department of Defense in 1987 using Doppler observations. |
No |
| WGS84 (G730) | 1994.0 | Implementation submitted by the US Department of Defense on June 29, 1994 based on GPS observations. The letter G stands for "GPS" and 730 is the GPS week number. Based on ITRF91. |
0.70 m | ||||
| WGS84 (G873) | 1997.0 | Implementation submitted by the US Department of Defense on January 29, 1997 based on GPS observations. |
0.20 m | ||||
| WGS84 (G1150) | 2001.0 | Implementation submitted by the US Department of Defense on January 20, 2002 based on GPS observations. The letter G stands for "GPS" and 1150 is the GPS week number. Based on ITRF2000. |
0.06 m | ||||
| WGS84 (G1674) | 2005.0 | Implementation submitted by the US Department of Defense on February 08, 2012 based on GPS observations. The letter G stands for "GPS" and 1674 is the GPS week number. Based on ITRF2008. |
0.01 m |
Transform Options
Below are the transition parameters between WGS84 (G1674) and previous WGS84 implementations, as well as some ITRF implementations.
Transition parameters between different ITRF implementations can be found in the .
| Transfer from | Transition to | Epoch | T1 m |
T2 m |
T3 m |
D ppb |
R1 mas |
R2 mas |
R3 mas |
Accuracy m |
|---|---|---|---|---|---|---|---|---|---|---|
| 2001.0 | -0.0047 | +0.0119 | +0.0156 | +4.72 | +0.52 | +0.01 | +0.19 | 0.0059 | ||
| ITRF2008 | WGS84 (G1674) | 2005.0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.10 |
| ITRF2000 | WGS84 (G1150) | 2001.0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.10 |
| ITRF94 | WGS84 (G873) | 1997.0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.10 |
| ITRF91 | WGS84 (G730) | 1994.0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0.10 |
| ITRF90 | WGS84 (original) | 1984.0 | +0.060 | -0.517 | -0.223 | -11.0 | +18.3 | -0.3 | +7.0 | 0.01 |
The direction of rotation of the coordinate system is clockwise. Units: m (meters), mas (milliseconds of arc) and ppb (parts per billion).
1 mas = 0.001 " = 2.77778 e -7 degrees = 4.84814 e -9 radians. 0.001" is approximately equal to 0.030 m on the Earth's surface.
WGS84 and ITRF
In general, ITRS (and its ITRFyy implementations) are identical to WGS84 within one meter. There are two types of implementation of WGS84.
- An older implementation based on the US Naval Navigation Satellite System, also known as the Doppler Transit system, providing station positions with an accuracy of approximately one meter.
Regarding this implementation, the International Earth Rotation Service has published the transformation parameters between ITRF90 and this Doppler system in the file: WGS84.TXT . - Updated implementations of WGS84 based on GPS data such as G730, G873 and G1150. These updated implementations of WGS84 match ITRF to 10 cm accuracy level.
There are no officially published transformation parameters for these implementations. This means that ITRF coordinates can also be expressed in WGS84 with an accuracy level of 10 cm.
The OGP Surveying & Positioning Committee recommends in its explanatory note No. 4 (Guidance note 4): "Use the international terrestrial reference system (ITRF) as a reference geodetic system for the purposes of surveying and positioning in real time", in the case when the published values of the transition parameters allow transforming coordinates with an accuracy of less than one meter - stick to the old formulation "local datum to WGS84", and use the new formulation "local datum to ITRFyy at epoch yyyy.y" when published transition parameter values provide sub-meter accuracy.
WGS84, ITRF and NAD83
The original implementation of WGS84 is largely consistent with NAD83 (1986). Subsequent implementations of WGS84, however, roughly coincide with those of ITRS.
The 1983 North American Datum (NAD83) is used throughout North America except Mexico. This coordinate system is implemented across the US and Alaska (North American Plate) through the National Reference Stations (National CORS), which provide the basis for obtaining strict transition parameters between ITRF and NAD83 implementations, as well as for countless scientific papers.
Since November 2011, the Network of Reference Stations (CORS) has over 1,800 stations, employing over 200 different organizations, and the network continues to expand. The most recent implementation of the NAD83 system is technically named NAD83 (2011/PA11/MA11) epoch 2010.00, and forms the framework for defining the National Spatial Reference System (NSRS). In Canada, the NAD83 system is also controlled through the Canadian Active Control System. Thus, the control and maintenance of the NAD83 system is the responsibility of two organizations, the US National Geodetic Survey (NGS), http://www.ngs.noaa.gov, and the Department of natural resources Canada (NRCan), http://www.nrcan.gc.ca.
Mexican Datum of 1993 (Mexican Datum of 1993)
National Institute Statistics and Geography of Mexico (INEGI), http://www.inegi.org.mx , the federal agency responsible for geodesy and cartography in the country, has adopted the ITRF92 geocentric coordinate system, for epoch 1988.0, as its geodetic base. The implementation of this system is achieved through a network of 14 stations of stationary GPS receivers of the National Geodetic Network (RGNA). Recently, the ITRF2008 system, for epoch 2010.0, was adopted as the new basis for the Mexican coordinate system.
WGS84, ITRF and SIRGAS
The Geocentric Reference System of the Americas 1995 (SIRGAS 1995) has been approved for use throughout the South American continent for geodesy and cartography. Most of the countries in South America and the Caribbean participated in this venture, using 58 reference stations, which were later extended to Central and North America. ITRF94 was taken as the initial coordinate system, for the epoch 1995.42. America's Geocentric Reference System 2000 (SIRGAS 2000) was implemented through observations at a network of 184 stations in 2000 and the ITRF2000 system was set to epoch 2000.40. The SIRGAS 2000 coordinate system includes reference to level posts and replaces the previous SIRGAS 1995 system used only in South America to the SIRGAS coordinate system, which also covers Central America. The name was changed in 2001 for use throughout Latin America. There are several pages on the Internet with information about the SIRGAS coordinate system, for example: http://www.ibge.gov.br/home/geociencias/geodesia/sirgas .
WGS84, ITRF and ETRS89
The European Terrestrial Reference System ETRS89 is based on the International Reference System ITRF89, at epoch 1989.0 and is tracked by a network of approximately 250 permanent Global Navigation Satellite System (GNSS) stations known as the European Permanent Reference Network (EPN). The maintenance of the European Terrestrial Reference System (ETRS89) is the responsibility of a subcommittee of the International Geodetic Association of the European Reference System (IAG Sub-commission EUREF). More information about this system can be found on the Internet at: http://www.euref.eu . The Central Bureau of the Reference Network (EPN) is located at the Royal Observatory of Belgium, http://www.epncb.oma.be .
WGS84, ITRF and GDA94
The 1994 geocentric coordinate system of Australia (GDA94) was originally assigned to the international geodetic coordinate system ITRF92, at epoch 1994.0. The GDA94 system is controlled by the Australian Regional GNSS Network (ARGN), which includes 15 permanent GPS stations throughout Australia, as well as 8 stations in Australia, known as the Australian Core Network (AFN). The responsible organization for monitoring the GDA94 system is Geoscience Australia, http://www.auslig.gov.au .
Links
- WGS84 (G730), (G873) and (G1150) - http://www.ngs.noaa.gov/CORS/Articles
- ITRF94, ITRF96, ITRF97, ITRF2000, ITRF2005 and ITRF2008 -
Abbreviation for World Geodetic System, which in translation corresponds to the concept of global support system, adopted at the time of 1984 with the aim of providing geodetic orientation in world space: space, air, sea and land navigation.
Such a unified world system counting appeared not in one year. Since the late fifties of the last century, when the formation of space age both in the USSR and in the USA, a need arose for accurate conduct and support of space launches and flights. To ensure this activity, it was necessary to create a unified planetary geodetic network, with the help of which it was possible to conduct geodetic, gravimetric and astronomical observations.
With periodic constancy every six years, since 1960, all-terrestrial geodetic systems wgs60, wgs66, wgs72 were created in the USA. The last of the listed systems, wgs, was considered the geodetic basis of the first Transit navigation satellite system.
In 1980, the International Union for Geodesy adopted a new geodetic reference system GRS80. It presented a combination of models: geoid, terrestrial ellipsoid and the gravitational model of the Earth. In the USA in 1983 they adopted their geodetic system NAD83.
And yet, in 1984, within the framework of the Department of Defense, the United States of America made a decision to build for its own purposes, as a military department and navigation satellite tasks, a new WGS with an annual numbering of 84. For this, by that time, the GPS Navstar navigation satellite system, which received subsequently global distribution and is used throughout the world to date. WGS84 was introduced in 1987 and is close in its parameters to NAD83.
Main parameters WGS 84
The WGS-84 world system is an astronomical-geodesic-gravimetric reference system inscribed in the figure of the Earth. For any such system, the establishment of certain parameters is characteristic. These parameters in the wgs 84 reference system include:
- geocentric rectangular coordinate system with the origin at the point of the geometric center of mass of the Earth (shown in Fig. 1);
- mathematical basis, for which the shape of an ellipsoid of revolution with specific geometric and physical quantities is taken;
- gravitational model of the Earth, with values and their values determined for a specific date.
Orientation of the 0Z axis of the rectangular coordinate system is presented in the direction of the conventional pole direction, established in accordance with the data of the International Time Bureau (BIH) for the date 1984. At the intersection of the plane of the prime meridian (Greenwich) with a deviation of 5.31 seconds to the east and the equatorial plane, the 0X axis is oriented. Right-handed and perpendicular to the 0X axis in the equatorial plane, so to speak, the second planning axis 0Y, completes the formation of the geometry of the reference system. To eliminate the floating effect due to the movement of the earth's crust, tectonic plates, the orientation of the X, Y, Z axes remains unchanged.
Fig.1. Geocentric World Geodetic System 84.
The physical orientation of the X, Y, Z axes in WGS84 was determined by the coordinates at five control stations of the GPS Transit navigation satellite system on the date 1984 (see Fig. 2).
Fig.2. Physical orientation at points WGS84.
Subsequently, the number of reference points increased to seventeen and was redefined twice already using the existing GPS Navstar navigation satellite system. In 2002 it was adopted latest version WGS84, which achieved high accuracy in determining rectangular coordinates (X, Y, Z), geodetic coordinates (B, L) and geodetic heights above the spheroid level (H). Thus, the ellipsoid was tied physically to the earth's surface.
International Geodetic Coordinate System
Simultaneously with the start of WGS84 in 1987, the foundations of a new world geodetic system were laid within the framework of the International Earth Rotation Service (IERS). Other than others functional tasks This service used the international terrestrial reference system (ITRS) and the reference frame (ITRF) to estimate the parameters of the Earth. In short, the differences between them are as follows. The reference system (ITRS) defines and sets the parameters of geodetic, mathematical, physical (gravimetric) Earth models. In the reference basis (ITRF) there is a physical construction and fixing of a kind of framework in the form of reference stations with their actual coordinates, through which an almost global geodetic system is implemented.
It can be more simply explained by the following example. The task is to build a rectangular coordinate system on the plane of a paper sheet, for example, A-1 format, with the origin in the center of this sheet, and the 0X and 0Y axes should be parallel to the edges of the format.
This problem can be solved in two ways. In the first of them, the center is obtained by connecting the diagonals to each other. The second way is to find all four centers of the sides of a rectangle, which is the paper size. By connecting the centers of the sides, the center of the sheet is obtained. Ideally, the two points should match. But most likely this will not happen due to errors in determining the middle of the sides. Further, the graphic accuracy of drawing diagonals from the corners will also introduce its inaccuracies. Not ideal, perhaps, and a rectangular sheet of paper, its edges may not be parallel. At graphic construction instrumental errors of a ruler, pencil, protractor arise directly from the point of the center of the coordinate axes.
Obviously, two slightly different coordinate systems with different centers and small rotations of the axes can turn out. So the sheet itself, the coordinate system, its center can be conditionally attributed to the ITRS reference system. But the reference marks, for example, the midpoints of the sides of the format, fix the coordinate system on paper and, by analogy, conditionally refer to the ITRF reference basis.
With regard to the figure of the Earth and the definition, for example, of its center of mass as the origin of the geocentric coordinate system, it is much more difficult. You can't physically draw it with a pencil. As reference marks for WGS84 in Fig. 2, control stations laid along the equator line act. The coordinate system in WGS84 and the reference system in ITRS are theoretically the same. However, the accuracy of reference to the origin in the center of mass of our planet is higher due to the fact that hundreds of such reference marks are in the ITRF reference base.
To date, ITRF, as the physical embodiment of the global geodetic network, has about 800 stations with Navstar GPS receivers. Updates, clarifications, correction of initial coordinates occur periodically both at stations in WGS84, which can be considered an integral part of the ITRF, and in the entire terrestrial geodetic basis.
To form a complete and rather complex physical and mathematical picture under the name of the Earth, the main and auxiliary parameters indicated in the table below are taken as the parameters of the transition from the geoid to the triaxial ellipsoid of rotation in WGS84.
All sizes and parameters of an ellipsoid calculated and accepted for use in the geodetic environment of a particular country or a global network, such as WGS84, have their own values, time (date) of calculation and the name "datum". The ITRF parameters (datum) are considered to be the most accurate, which are monitored daily by satellite methods for measuring coordinates at reference stations and are published annually with the date.
In global systems other than WGS84, which in recent years have been used in the leading countries of the world, including Russia (PZ90, PZ90.02, PZ90.11), if it is necessary to solve certain problems, it is possible to link different datums, determine the conversion coefficients and perform the actual recalculation of coordinates in different systems. In the Russian Federation, such recalculations are regulated by the state standard 51794-2001.
The coordinate system of 1995 (SK-95) was established by Decree of the Government of the Russian Federation of July 28, 2002 No. 586 “On the establishment of unified state coordinate systems”. Used in the implementation of geodetic and cartographic work, starting from July 1, 2002.
Before the completion of the transition to the use of the SC, the government of the Russian Federation decided to use the unified system of geodetic coordinates of 1942, introduced by the Decree of the Council of Ministers of the USSR of 04/07/1996 No. 760.
The expediency of introducing SK-95 is to increase the accuracy, efficiency and economic efficiency of solving the problems of geodetic support that meets the modern requirements of the economy, science and defense of the country. Obtained as a result of joint adjustment of the coordinates of the points of the state space network (SGS), the Doppler geodetic network (DGS) and the astronomical geodetic network (AGS) for the 1995 epoch, the 1995 coordinate system is fixed by the points of the state geodetic network.
SK-95 is strictly coordinated with the unified state geocentric coordinate system, which is called "Parameters of the Earth 1990." (PZ-90). SK-95 is installed under the condition that its axes are parallel to the spatial axes of SK PZ-90.
Reference ellipsoid is taken as reference surface in SK-95.
The accuracy of SK-95 is characterized by the following root-mean-square errors of the mutual position of points for each of the planned coordinates: 2-4 cm for adjacent AGS points, 30-80 cm at distances from 1 to 9 thousand km between points.
The accuracy of determining normal heights, depending on the method of their determination, is characterized by the following mean square errors:
· 6-10 cm on average across the country from the level of leveling networks of 1 and 2 classes;
· 20-30 cm from astronomical and geodetic determinations during the creation of the AGS.
The accuracy of determining the excess heights of the quasi-geoid by the astronomical gravimetric method is characterized by the following root mean square errors:
· from 6 to 9 cm at a distance of 10-20 km;
30-50 cm at a distance of 1000 km.
SK-95 is different from SK-42
1) increasing the accuracy of transmitting coordinates over a distance of more than 1000 km by 10-15 times and the accuracy of the relative position of adjacent points in the state geodetic network by an average of 2-3 times;
2) the same distance accuracy of the coordinate system for the entire territory of the Russian Federation;
3) the absence of regional deformations of the state geodetic network, reaching several meters in SK-42;
4) the possibility of creating a highly efficient system of geodetic support based on the use of global navigation satellite systems: Glonass, GPS, Navstar.
The development of the astronomical and geodetic network for the entire territory of the USSR was completed by the beginning of the 80s. By this time, it became obvious that the general adjustment of the AGS was performed without dividing it into series of triangulation of the 1st class and continuous networks of the 2nd class, since a separate adjustment led to significant deformations of the AGS.
In May 1991, the general adjustment of the AGS was completed. Based on the results of the adjustment, the following AGS accuracy characteristics were established:
1) root mean square error of directions 0.7 seconds;
2) the root mean square error of the measured azimuth is 1.3 seconds;
3) relative root-mean-square error of measurement of basic sides 1/200000;
4) the mean square error of adjacent points is 2-4 cm;
5) root-mean-square error of transmitting the coordinates of the source point to points at the edges of the network for each coordinate of 1 m.
The adjusted network included:
· 164306 items of 1st and 2nd class;
· 3.6 thousand geodetic azimuths determined from astronomical observations;
· 2.8 thousand basic sides in 170-200 km.
The Doppler astronomical-geodesic network and the CGS were subjected to joint adjustment.
The volume of astronomical and geodetic information processed during joint adjustment to establish SK-95 exceeds the volume of measurement information by an order of magnitude.
In 1999, the Federal Service for Geodesy and Cartography (FSGiK) of the SGS of a qualitatively new level based on satellite navigation systems: Glonass, GPS, Navstar. The new GHS includes geodetic constructions of various accuracy classes:
1) FAGS (fundamental)
2) High precision WGS
3) Satellite geodetic network class 1 (SGS 1)
4) Astronomical geodesic network and geodesic networks of condensation.
WGS-84 has now become an international navigation system. All airports in the world, in accordance with the requirements of ICAO, define their aeronautical landmarks in WGS-84. Russia is no exception. Since 1999, orders have been issued on its use in the system of our civil aviation (Last orders of the Ministry of Transport No. HA-165-r dated May 20, 2002 “On the performance of work on geodetic survey of aeronautical landmarks of civil airfields and airways of Russia” and No. HA- 21-r dated February 4, 2003 “On the introduction of recommendations for preparing ... for flights in the precision area navigation system ...”, see www.szrcai.ru), but there is still no clarity on the main thing - whether this information is open (otherwise it loses its meaning), and this depends on completely different departments that are not inclined to openness. For comparison: the coordinates of the ends of the runway of the airfield with a resolution of 0.01 ”(0.3 m) are currently issued by Kazakhstan, Moldova and the countries of the former Baltic states; 0.1” (3 m) - Ukraine and the countries of Transcaucasia; and only Russia, Belarus and all middle Asia reveal these vital data for navigation with an accuracy of 0.1" (180 m).
We also have our own global coordinate system, an alternative to WGS-84, which is used in GLONASS. It is called PZ-90, developed by our military, and besides them, by and large, no one is interested, although it has been elevated to the rank of state.
Our state coordinate system - the "Coordinate System of 1942", or SK-42, (like the recently replaced SK-95) differs in that, firstly, it is based on the Krasovsky ellipsoid, somewhat larger than the WGS-84 ellipsoid, and secondly, "our" ellipsoid is shifted (by about 150 m) and slightly turned relative to the general earth. This is because our geodetic network covered a sixth of the land even before the advent of any satellites. These differences lead to a GPS error on our maps of the order of 0.2 km. After taking into account the transition parameters (they are available in any Garmin "e), these errors are eliminated for navigation accuracy. But, alas, not for the geodesic: there are no exact unified coordinate connection parameters, and this is due to local mismatches within the state network. Surveyors have to for each individual the district itself to look for the parameters of transformation into the local system.
Geodetic coordinates, methods of their transformation. ITRF, WGS-84, PZ-90, SK-42, SK-95 systems. Coordinate transformation according to the method of Helmert and Molodensky
3.1. Reference systems of coordinates and time
The unified state system of geodetic coordinates of 1995 was obtained as a result of joint adjustment of three independent, but interconnected, geodetic constructions of various accuracy classes: KGS, DGS, as of their status for the period 1991-93.
The amount of measuring astronomical and geodetic information processed to introduce the 1995 coordinate system exceeds by an order of magnitude the corresponding amount of information used to establish the 1942 coordinate system (SK-42).
Space geodetic network is designed to set the geocentric coordinate system, the Doppler geodetic network - to propagate the geocentric coordinate system, the astronomical-geodetic network - to set the geodetic coordinate system and to maintain the coordinate system to consumers.
In joint adjustment AGS is represented as a spatial construction. The heights of the AGS points relative to the Krasovsky reference ellipsoid are determined as the sum of their normal heights and the heights of the quasigeoid obtained from astronomical gravimetric leveling.
In the process of several approximations of the joint adjustment of the quasi-geoid height for the territory of remote eastern regions were additionally refined taking into account the adjustment results. In order to control the geocentricity of the coordinate system, the joint adjustment includes independently determined geocentric radius-vectors of 35 KGS and DGS points, located at a distance of about 1000 km from each other, for which the heights of the quasi-geoid above the common Earth ellipsoid were obtained by the gravimetric method; and normal heights - from leveling.
As a result of the joint adjustment of the CGS, DGS, AGS and the values of the radius vectors of the points, a network of 134 GGS control points was built, covering the entire territory with an average distance between adjacent points of 400...500 km.
The accuracy of determining the mutual position of these points for each of the three spatial coordinates is characterized by mean square errors of 0.25 ... 0.80 m at distances from 500 to 9000 km.
The absolute errors of referring the positions of points to the center of mass of the Earth do not exceed 1 m along each of the three axes of spatial coordinates.
These points were used as initial points in the final general adjustment of the AGS.
The accuracy of determining the mutual planned position of the points, obtained as a result of the final adjustment of the AGS as of 1995, is characterized by mean square errors: 0.02 ... 0.04 m for adjacent points, 0.25 ... 0.80 m at distances from 1 to 9 thousand km.
Between the unified state system of geodetic coordinates of 1995 (SK-95) and the unified state geocentric coordinate system “Parameters of the Earth 1990” (PZ-90), a connection is established, determined by the parameters of the mutual transition (orientation elements). Directions of coordinate axes X, Y, 2 the geocentric coordinate system used is determined by the coordinates of the KGS points; the origin of coordinates of this system is set under the condition of coincidence with the center of mass of the Earth.
The reference surface in the state geocentric coordinate system (PZ-90) is a common earth ellipsoid with the following geometric parameters:
semi-major axis 6378 136 m;
compression 1:298.257839.
The geometrical parameters of the common earth ellipsoid are assumed to be equal to the corresponding parameters of the level ellipsoid of revolution. In this case, the level ellipsoid of revolution is taken outer surface the normal Earth, whose mass and angular velocity of rotation are set equal to the mass and angular velocity of the Earth's rotation.
Mass of the Earth M , including the mass of its atmosphere multiplied by the gravitational constant f, is the geocentric gravitational constant fM = 39860044 x 10 7 m 3 / s 2, the angular velocity of the Earth's rotation w taken equal to 7292115 x10 11 rad/s, the harmonic coefficient of the geopotential of the second degree J 2 , which determines the compression of the common earth ellipsoid, is taken equal to 108263x10 8 .
The 1995 coordinate system is set so that its axes are parallel to the axes of the geocentric coordinate system. The position of the beginning of SK-95 is set in such a way that the values of the coordinates of the GGS Pulkovo point in the SK-95 and SK-42 systems coincide.
The transition from the geocentric coordinate system to SK-95 is carried out according to the formulas:
X SK-95 = X PZ-90 - DX 0
Y SK-95 = Y PZ-90 - DY 0
Z SK-95 = Z PZ-90 - DZ 0
where ДХ 0 , ДН 0 , ДZ 0 - linear elements of orientation., setting the coordinates of the origin of the coordinate system of 1995 relative to the geocentric coordinate system PZ-90, are DKh = +25.90 m; DN 0 \u003d -130.94 m, Jho \u003d -81.76 m.
The reference surface in SK-95 is the Krasovsky ellipsoid with the following parameters:
semi-major axis 6378 245 m;
compression 1:298.3.
The position of the GHS points in the adopted systems is given by the following coordinates:
spatial rectangular coordinates X, Y, Z;
geodesic (ellipsoidal) coordinates B, L, H;
flat rectangular coordinates x and y, calculated in the Gauss-Kruger projection.
Geodetic heights of GGS points are determined as the sum of the normal height and the height of the quasi-geoid above the reference ellipsoid, either directly by space geodesy methods, or by referencing points with known geocentric coordinates.
The normal heights of the GGS points are determined in the Baltic system of heights of 1977, the initial beginning of which is the zero of the Kronstadt footstock.
Height maps of the quasi-geoid above the common earth ellipsoid and Krasovsky's reference ellipsoid on the territory of the Russian Federation are published Federal Service geodesy and cartography of Russia and the Topographic Service of the Armed Forces of the Russian Federation.
The scale of the GTS is set by the Unified State Standard of Time-Frequency-Length. The length of a meter is taken in accordance with the resolution of the MAS General Conference on Weights and Measures (October 1983) as the distance traveled by light in vacuum in 1:299,792,458th of a second.
In the work on the development of the GGS, the atomic TA (813) and coordinated UTC (SU) time scales are used, set by the existing reference base of the Russian Federation, as well as the parameters of the Earth's rotation and corrections for the transition to international time scales, periodically published by the State Standard of Russia in special bulletins public service time and frequency (GSVCH).
Astronomical latitudes and longitudes, astronomical and geodetic azimuths, determined from observations of stars, are reduced to the system of the fundamental star catalog, to the system of the mean pole and to the system of astronomical longitudes adopted for the epoch of the GGS adjustment.
Metrological support of geodetic works is carried out in accordance with the requirements of the state system for ensuring the uniformity of measurements.
Post-glacial recoil, observed predominantly in northern latitudes as a consequence of the Ice Age. The influence can reach up to several millimeters per year in height;
Pole tide, which is the reaction of the elastic crust of the Earth to displacements of the pole of rotation. With polar motion components of the order of 10 m, the maximum displacement will be 10–20 mm.
The models of the listed corrections are given in . Other corrections are added if they are greater than 1 mm and can be calculated according to some model.
The speed of tectonic movements can reach 10 cm/year. If for some station the speed in ITRF has not yet been determined from observations, then the speed vector should be determined as the sum of the speeds:
, (3.47)
where is the horizontal plate velocity calculated from the NNR NUVEL1A tectonic plate motion model, and epncb.
oma.
be]. A basic network of 93 fundamental points was measured via GPS during May 1989. This was later expanded to 150 permanent GPS observing stations. Finally, EUREF is a single system for the whole of Europe, which is harmonized with the WGS-84 and ITRF systems. The resulting datum is known as ETRF-89 (or ETRS89), and for many purposes it can be considered an implementation of WGS-84 in Europe. Many countries adopt EUREF points as a "zero" class network from which they extend national networks.
South America has implemented a similar reference frame SIRGAS ( Sistema de Referência Geocêntrico para as Américas), in Australia - GDA94 (Geocentric Datum of Australia), in the USA and Canada - NAD83(CORS96) .
3.3. Reference coordinate systems
These earth systems are associated with local reference ellipsoids. The centers of reference ellipsoids, as a rule, do not coincide with the center of mass of the Earth due to orientation errors. Therefore, these systems are sometimes also called quasi-geocentric.
The main plane in the reference system is the plane of the equator of the reference ellipsoid. Axis Z directed along the normal to the equator, along the minor axis of the ellipsoid. Axis X is directed in the plane of the initial meridian of the geodetic system, that is, it passes through the point B=0, L=0. Axis Y complements the two previous axes to the right (or left) coordinate system. It is possible to use the sizes and shapes of the same ellipsoid in different coordinate systems that differ in their orientation (initial geodetic dates).
In reference systems, geodetic (spheroid) coordinates are usually used (Fig. 3.6): geodetic latitude B, geodetic longitude L and the height above the ellipsoid H.
Due to the observational limitations imposed earlier by the conventions of geodesy, two different types of geodetic systems have historically been performed:
Two-dimensional continental planned geodetic systems fixed by points of geodetic networks with coordinates , , for example, coordinate systems 1942 (CK-42), North American system NAD-27,
Completely independent continental height systems, which are essentially physical geodetic bases, independent of the ellipsoid, and are built on the basis of equalization of leveling observations. Such systems include the Baltic height system of 1942 adopted in Russia and the National Geodetic Vertical Datum of 1929 (National Geodetic Vertical Datum, NGVD29) adopted in the USA. In these systems, point heights are given relative to the geoid (quasi-geoid). Global height systems have not yet been defined and adopted by NAD-27