RU2165595C1 - System to conduct topographic survey of roadbed ( versions ) and method of conducting of topographic survey - Google Patents

Abstract

FIELD: measurement technology employed in topographic survey which data can be used in repair and reconstruction of roads, runways, and so on. SUBSTANCE: system includes constellations of GPS and GLONASS satellites, mobile GPS receiver and fixture carrying its antenna moved with the aid of motor vehicle, second stationary GPS receiver located at point with known coordinates and stationary computer for data processing. Unit carrying antenna is manufactured in the form of single wheel that carries aid to anchor antenna in the form of stake put into socket anchored on wheel. In correspondence with second version fixture carrying antenna of mobile GPS receiver is placed on top of motor vehicle and is manufactured in the form of rotary suspension of cranked shape. Method of conducting of topographic survey includes initialization of measurement hardware, survey of points of structural lines of surface in coordinates X, Y, H by way of discrete reading of information from GPS and GLONASS satellites when at least 5 satellites determining position of phase center of antenna of GPS receiver are observed, transmission of primary information into stationary computer which also receives data from stationary GPS receiver located at point with known coordinates and differential processing of information by stationary computer with the help of software into which sub-programs of corrections taking account of displacement of phase center of antenna in process of survey both in plan coordinates X, Y and in height coordinates H are entered. Output information comes in electronic form with precision ± 5 cm in plan and ±0.25 cm in height. EFFECT: simplified design of system for topographic survey ensuring high- precision survey in coordinates X, Y, H. 13 cl, 5 dwg

Description

 The invention relates to measuring equipment for topographic surveying using GPS signals, the data of which can be used in the reconstruction and repair of roads, runways, etc., and can also be used for certification, inventory or compilation of a cadastre of roads.

 Until recently, mechanical instruments, such as surveying instruments, were used to perform topographic surveys of road surfaces. To determine the plan and the longitudinal profile of the route, topographic surveys and leveling of surfaces were used. The data obtained using this technique are based on visual measurements and therefore have low accuracy. In addition, they are laborious and require a lot of time to complete.

 Known for more advanced - automated methods for surveying the roadway. For example, in US patent N 5075772, H 04 N 007/18, H 04 N 005/84, publ. 12.24.91, a method is described in which spots of paint or metal marks are discretely uniformly applied to the roadway, relative to which the surface is then shot using a field installation - a shooting car, on which shooting equipment, including video cameras, is fixed in certain positions measuring devices based on infrared or ultraviolet radiation (depending on the type of paint stains), or electromagnetic sensors for detecting metal stains. The measured data is stored digitally or in the form of monitor images on magnetic tapes. However, shooting with such instruments on spots cannot give the centimeter accuracy of measurements necessary for microprofiling of road surfaces.

 With the establishment by the United States of America a series of satellites of the Global Positioning System (GPS), which allows you to determine the location of a specific point on the earth with relatively high accuracy (a standard GPS receiver is able to determine position with an accuracy of less than 1 m), topographic devices have been identified that determine the longitudinal and transverse profiles of roads in X-U-Z coordinates using satellite signals (for example, US patent N 5721685, publ. 24.02.98, G 01 11/30, E 01 C 19/00). The device according to this patent is a field installation in the form of a car, on which a touch panel with two GPS receivers mounted on it, installed at the ends of the panel, as well as several sensors (ultrasonic or infrared) are mounted at the front or back at a height of 1 meter from the surface, installed between GPS receivers to measure the distance to the road surface at right angles to it. The installation also contains an on-board computer connected to GPS-receivers and sensors by wired communication, installed in the car, where a video camera and a distance measuring device that initializes are also placed. Digital information is transmitted from GPS receivers and sensors to the on-board computer at regular intervals. The primary survey data is transferred to the office computer for post-processing and transfer to the software product - X, Y, Z-files. In this device, improving the accuracy of measurements is achieved through the use of a large number of ultrasonic or other sensors (from 4 to 9 sensors in different use cases), which cannot but affect the cost of installation.

 Closest to the proposed invention is a system including a GPS satellite system, a mobile rover device made in the form of a two-wheeled trolley with a platform mounted on it at a height of 3 m, on which the antenna is placed and under which are installed: 12-channel GPS receiver, number system paths (including wheel encoders, an orientation sensor and a rotation potentiometer), a system of digital video cameras for front, side and rear viewing (7 cameras in total) and an on-board computer. The rover device is connected by a barbell to a tractor, which performs the movement of the device on the roadway. The system also includes a second GPS-receiver, placed stationary at a point with known coordinates. Data is read with the simultaneous observation of 4 satellites, while the relative position data (i.e., the plan) is read from three satellites and the time base data from the fourth. During the shooting phase information is read, supplemented by dead reckoning information and digital video review information. Information is transferred to the post-processing unit on a stationary computer, which converts the output information into electronic form (floppy disks, files). The accuracy of the definitions of this system is up to 1 cm for a stationary GPS-receiver and up to 5 cm for a mobile GPS-receiver [1].

 However, in this system, phase information is read with the simultaneous observation of only 4 satellites. This means that this system can only take planned (in X, Y coordinates) information and cannot bind to measuring heights (H). In addition, the phase information in this system is only additional to the calculated data, therefore, the measurement of one phase information will not be able to provide the specified accuracy.

 To obtain complete calculated data, the shooting device has a complex hardware design. In addition, the placement of all measuring equipment on a two-wheeled trolley of the rover device creates the possibility of mechanical and weather influences on it.

 Thus, the objective of the invention is to significantly simplify the device used in the system for conducting topographic surveys using GPS signals, while at the same time maintaining high accuracy during phase measurements in the coordinates X, Y, H.

 The problem is achieved in that in the system for conducting topographic surveys of the road surface, comprising: a constellation of GPS satellites; mobile GPS receiver; a device that carries the antenna of a mobile GPS receiver; a vehicle for moving the GPS receiver and the device carrying the antenna; means for attaching the device carrying the antenna to the vehicle; a second GPS receiver stationary at a point with known coordinates; and the post-processing unit of the shooting data, including a stationary computer, it is proposed that the device carrying the antenna be made in the form of a single wheel on which the antenna mount means are placed, which allows the antenna to be placed in a vertical position at the initialization point; Place the mobile GPS receiver in the vehicle, and with the constellation of GPS satellites additionally use the constellation of GLONASS satellites (Global Navigation Satellite System).

 In this case, the antenna mounting means is made in the form of a pole located in a socket fixed to a wheel. And the device that carries the antenna of the mobile GPS-receiver is made with the possibility of fixing it on the left or right side of the vehicle within up to 0.5 m behind its size, to ensure the possibility of combining the phase center of the antenna with the structural line of the road surface.

 In addition, the means of attaching the device carrying the antenna to the vehicle is made in the form of a rod system mounted on the vehicle and connected to the rod system of the mounting frame in the form of a triangle, one of the ends of which is extended to the left or right up to 0.5 m beyond the size of the vehicle and is the mounting location of the device carrying the antenna.

 In a second embodiment of the system, also comprising: a constellation of GPS satellites; mobile GPS receiver; a device that carries the antenna of a mobile GPS receiver; a vehicle for moving the GPS receiver and the device carrying the antenna; means for attaching the device carrying the antenna to the vehicle; a second GPS receiver stationary at a point with known coordinates; and a post-processing unit for shooting data, including a stationary computer, it is proposed: the means for attaching the device carrying the antenna to the vehicle to be placed on the vehicle cover, and the device carrying the antenna can be made in the form of a knee-shaped swivel suspension, the end of one knee of which is rotatably mounted on the roof on the mounting device of this device, and the end of the other knee which carries the antenna; place the mobile GPS-receiver in the vehicle, and with the constellation of GPS satellites additionally use the constellation of GLONASS satellites.

 At the same time, the swivel suspension is made with the possibility of extension within 0.5 m to the left or right beyond the vehicle’s overall dimension in order to ensure the possibility of combining the phase center of the antenna and the structural line to be removed.

 It is also characteristic of both options that a vehicle is used as a vehicle and an additional controller is placed in it, as well as that each GPS receiver additionally has GLONASS channels.

 The goal is also achieved by the fact that when carrying out a method of topographic survey, which includes operations: initializing a mobile GPS receiver and taking points of structural lines of the surface in the coordinates of the X, Y plan by discrete reading information from GPS satellites that determine the position of the phase center of the GPS receiver antenna, accumulating primary information, its transmission for post-processing to a stationary computer, which also sends data from a stationary GPS-receiver from a point with known coordinates, and differential image information processing in a stationary computer using software with output information output in electronic form, a method is proposed to be performed using the above-described device, while shooting is also carried out taking into account the heights of H points of structural lines, the information is additionally read from GLONASS satellites, while simultaneously observing at least 5 satellites, as well as with longitudinal and transverse tilts of the antenna, due to the surface profile, and the corresponding displacements of its phase center in the software the software introduces the subroutines for taking into account the displacement of the antenna phase center in two stages: at one stage, determine the longitudinal surface slope for each point of the structural line, take into account that the longitudinal antenna tilt is equal to the longitudinal surface slope, and introduce the correction subroutine in determining the heights H of the points taken, at another determine the transverse slope of the surface for each point of the structural line, compare it with the slope at the initialization point, take into account that the algebraic difference of the compared and initial slopes surface is the angle of the antenna at a given point, and introduce the correction subroutine in determining the X, Y coordinates of the points taken.

 When shooting phase information through a satellite system in the kinematic mode, it is necessary to save the phase of the carrier frequency, i.e. you need to “see” as many satellites as possible. If during shooting there is a loss of phase of the carrier frequency, the measurement stops. To continue work, you must turn off the equipment and again initialize. In order to prevent loss of phase of the carrier frequency according to this invention, not only the constellation of the American satellite system - GPS, but also the Russian satellite system GLONASS is used, which doubles the total number of satellites. And in the hardware version, the GPS receivers used have 12 GPS channels with a code and a carrier phase at a frequency of L1 and 12 GLONASS channels with a code and a carrier phase at a frequency of L1, which makes it possible to “see” at least 5 satellites at the same time and take measurements in X coordinates , Y, H continuously (in the absence of obstacles).

 The implementation of the device carrying the antenna, with the placement of the pole with the antenna directly on a separate wheel (the so-called "fifth" wheel of the car) is intended for shooting mainly fixed (coated) surfaces. In this case, the wheel carrying the antenna acts as a tracing wheel on the removed structural line. When placing the axis of the trailing wheel on the structural line at the initialization point, the pole with the antenna is installed in a vertical position and allows you to direct the phase center of the antenna directly to the structural line, which makes it possible to more accurately read surface points during shooting using a GPS receiver and satellite system.

 The fastening of the wheel that carries the antenna, both on the left and on the right side of the vehicle (car) makes it possible to shoot both the edge and the axis of the coatings when the car is moving in accordance with the Rules of the road: on the right lane.

 The second embodiment of the device with the placement of a pole with an antenna on a suspension bracket mounted on the roof of a car is intended for surveying predominantly unfixed surfaces (top of the subgrade, edges, edges of highways with a transitional type of coating, etc.), while the antenna suspension allows you to install it so that the phase center of the antenna is located directly above the removable structural line of the surface. The car suspension during shooting averages the surface being removed and gives a more accurate representation of it. The extension of the antenna suspension beyond the vehicle’s dimensions allows you to increase the width of the surface to be removed, and turning it beyond any vehicle’s dimensions allows shooting from both sides of the car. T.O. the design of the device carrying the antenna, in both versions, allows you to place the antenna directly above the removed structural line and precisely point its phase center to this line, which makes it possible to carry out measurements not only in the X, Y coordinates (i.e., fix the planned position), but and take the heights H of the points of the structural lines. In combination with the ability to read information from more than 5 satellites, a more accurate representation of the recorded structural line in coordinates X, Y, N. is simultaneously obtained.

 The placement of measuring equipment in the car eliminates the influence of mechanical and weather influences on it, which also affects the increase in measurement accuracy. And the use of a controller (for example, of the Hushy type) as part of the equipment that controls the shooting process and sets the mode of its conduct: the length of the measurement era, naming the surveyed points, etc., allows you to automate the shooting process and increase the accuracy of measurements.

 The implementation of the method, including the transfer of survey data from a mobile GPS-receiver to a stationary computer and their cameral processing (taking into account the data of a stationary GPS-receiver) using the standard WinPrizm software, into which correction subroutines are introduced that take into account the influence of the longitudinal and transverse tilts of the antenna when calculating the planned coordinates X, Y and heights H are also aimed at improving the accuracy of measurements.

As a result, taking into account the fact that the nameplate accuracy of the set of two GG24 Ashtech receivers (GPS + GLONASS) used for shooting when determining the coordinates of the antenna phase center is the mean square error:
in static - distances ± (10 mm + 1 ppm · d),
excess ± (17 mm + 1.7 ppm · d),
in kinematics - distances ± (15 mm + 1 ppm · d),
excess ± (22 mm + 1.7 ppm · d),
where d is the measured distance in km, ppm = 1 · 10 ^-6 , the accuracy of the proposed system and method, which mainly depends on the accuracy of pointing the antenna phase center to the structural line, is ± 5 cm in plan and ± 25 mm in height, which significantly exceeds the requirements of SNiP in terms of topographic surveys of roads at the survey stage for a working draft; ± 20 cm in plan and ± 6 cm in height.

The invention is illustrated by the accompanying drawings:
FIG. 1 is a block diagram of a proposed system;
FIG. 2 is a side view of a device carrying an antenna attached to a car;
FIG. 3 is a top view of a device carrying an antenna attached to a car;
FIG. 4 is an end view of a suspension mounting device with an antenna on a car roof;
FIG. 5 is a top view of a suspension mounting device with an antenna on a car roof.

 A general diagram of a system for performing topographic surveys is shown in FIG. 1. The system has a constellation of satellites 1, including satellites of the GPS system and the GLONASS system, the signals from which are fed to the antenna 2 connected to the GPS receiver 3, which in turn is connected to the controller 4. The change data of the GPS receiver 3 is fed to the post-processing unit to a stationary computer 5, which also receives data from a GPS receiver 6, installed stationary at the base station and having information with known coordinate data X, Y, H from the State Geodetic Station. The antenna of the GPS receiver 6 of the base station also communicates with satellites 1.

 A device for performing topographic surveys as an exemplary embodiment is shown in FIG. 2 and 3. The mobile device carrying the antenna 2 of the mobile GPS receiver 3 is made in the form of a single wheel 7, on the holder of which there is mounted antenna fastening means in the form of a connecting device 8 for fixing the sleeve 9, which acts as a socket in which it is placed and tuned in the vertical position of the pole 10 with the antenna. The device that carries the antenna, through the connecting device 8, is attached to one end of the triangular mounting frame 11, which is configured to install this end (and, therefore, the device that carries the antenna) in the left or right position for the size of the vehicle. One fixed side 12 of the mounting frame 11 is rigidly attached to two vertical rods 13, connected at right angles to the upper horizontal rods 14, mounted on the mounting device 15 on the car cover. The vertical rods 13 below are removably attached to the towing hinges of the car. Antenna 2 has a wired connection with a GPS receiver 3 located in the car and connected to the controller 4. This shooting device is made collapsible. After disassembling, all its components are placed in the same car that is used for shooting, for transportation to a new site of work. The assembly time of the device is about 20 minutes.

 In FIG. 4 and 5 show a second embodiment of the design and mounting of the device carrying the antenna of the GPS receiver 3, on the roof of the car. The mounting device 15, mounted in the transverse direction on the roof of the car, for example, on its gutters, contains two pairs of mounting brackets 16, mounted on opposite sides of the roof. Each pair of brackets 16 is mounted on two sides to one of two guides 17 using clamping couplings 18, which allows you to change the distance between the pair of brackets 16. On each of the guides 17 between the couplings 18 is a clamping coupling 19. Between the couplings 19, in the transverse direction from the rails 17, a rigid plate 20 is placed on which a sleeve 21 is vertically fixed, serving as a socket for accommodating one end of the articulated suspension 22. At the second end of the swivel suspension, in a vertically upward position, a sleeve 23 is placed that serves as a socket for accommodating a pole 24 with an antenna. The antenna has a wired connection with the GPS receiver 3, connected to the controller 4, placed in the car. This version of the shooting device is also made collapsible and is placed in the car when moving to the object of work and back. Assembly time ≈ 10 min.

 Topographic survey is performed as follows.

 For shooting, a set of autonomous satellite coordinates determination X, Y, H - GG24 Ashtech is used, which works with two satellite systems: GPS and GLONASS. A vehicle was used as a vehicle.

 When shooting fixed surfaces (cement concrete, asphalt concrete coatings of roads and airfields), a device with an antenna mount on the "fifth" wheel of the car is used. At the initialization point selected on a surface with a longitudinal slope close to zero, the longitudinal axis of the trailing wheel is mounted on a structural line (edge, coating axis), the pole with the antenna is aligned vertically at a height of ≈ 3 m to avoid interference from moving vehicles. The transverse slope of the coating on which the vehicle is currently located is measured.

 Prior to this, a stationary GPS-receiver is installed at a point having coordinates X, Y, H in a given coordinate system. After measuring the height of the phase center of the antenna and initializing the measuring equipment, the car begins to move in such a way that the axis of the trailing wheel is above the structural line to be taken. Shooting is performed discretely in kinematic mode. Depending on the required discreteness, the length of the era of kinematic measurements and the speed of the car are selected. So, with a length of the measurement era of 2 seconds and a speed of 40 km / h, the resolution is 20 m.

 If it is necessary to fix the meeting elements of the situation (the beginning and end of the fences, road signs, picket, etc.), a stop is performed, the antenna is accurately guided. The name of the structural lines in the elements of the situation is set from the controller.

 After completing the survey of one structural line, the position of the antenna, if necessary, is rebuilt to take the next line.

 In the process of shooting from the controller, it is necessary to ensure that at least five satellites are simultaneously in the antenna’s visibility range, otherwise the carrier phase will be lost, after which it is necessary to turn off the receiver and re-initialize. Kinematic observations at a static point are completed.

 Another variation of the implementation of the device on the wheel is the placement of a pole with an antenna on a field curvimeter, manually moved nearby. Such a device is used to shoot structural lines of a complex configuration, for example, the edges of asphalt concrete pavement in an urban area, which has 90-degree turns without rounding, or in cases where a resolution of 1-3 m is required.

 Topographic surveying of non-fixed surfaces (subsoil brow edges, edges and axis of gravel or sand and gravel road surfaces) is performed as follows: the device’s antenna on the suspension mounted on the car roof at a height of ≈ 3 m from the road surface is installed so that its phase center was above the removable structural line. Further measurements are performed similarly to shooting fixed surfaces.

 Processing of the measurement results is carried out in the standard WinPrizm software, where the measurement files are copied from the base and mobile receiver. The result of the processing is a file of coordinates and heights of kinematic and static points, which is exported to one of the CAD systems, where a digital model of the removed surface is built and evaluated.

 In the process of movement, due to the inconsistency of the longitudinal and transverse slopes of the coating, the antenna receives longitudinal and transverse slopes. The longitudinal slope does not affect the planned position, since the phase center shifts along the structural line, but gives a significant increase in the antenna height. The transverse slope shifts the phase center in plan and has almost no effect on the height of the antenna. In this regard, the discrete coordinates and heights of the structural lines obtained in WinPrizm are corrected in the created GPS correction software, which at the first stage analyzes the longitudinal surface slope for each point of a particular structural line, assumes that the longitudinal antenna slope is equal to the longitudinal surface slope, and makes corrections in the heights of the determined points. At the second stage, for each point, the transverse slope of the surface is determined. The initial data for calculating the transverse slope are the results of WinPrizm on adjacent structural lines. The calculated lateral slope is compared with that measured at the initialization point at which the antenna was positioned vertically. It is assumed that the algebraic difference between the current and initial surface slopes is the angle of the antenna at a given point, after which corresponding corrections are introduced into the coordinates.

 Corrected coordinates and point heights of all captured structural lines are transmitted to CAD. The obtained rectangular coordinates are converted into the well-known CREDO-DIALOGUE software package, where a digital terrain model is constructed based on the existing coverage, tracing is performed, the coordinates of the rotation angles of the route, the radii of vertical and horizontal curves and their appearance (circular, circular with transitional, clothoid ), the picket is broken, the route plan, longitudinal and transverse profiles are evaluated, microprofiling is carried out - measures to correct the longitudinal and transverse coating profiles, the volumes of the leveling layers are calculated.

 In the future, after repair or reconstruction of the road is completed, an executive survey is carried out similarly, the quality of construction work is assessed, including the evenness of the coating, the actual volume of layers laid - as the space between two surfaces. Survey materials and project data can be converted into a geographic information system, for example, MapInfo.

 The application of this method allows to increase labor productivity depending on specific conditions by 20-30 times in comparison with traditional instrumental methods.

 Used Books.

 1. US patent N 5517419, IPC CL C 01 C 7/04, dated 05/14/96.

Claims (13)

 1. A system for performing topographic surveys of a roadway comprising a constellation of GPS satellites, a mobile GPS receiver, a device that carries the antenna of a mobile GPS receiver, a vehicle for moving the GPS receiver and device that carries the antenna, means for attaching the device that carries the antenna to a vehicle, a second GPS receiver, stationary at a point with known coordinates, and a post-processing unit of survey data, including a stationary computer, characterized in that the device carrying the antenna The GPS mobile receiver is made in the form of a single wheel on which the antenna mount means supporting the antenna is placed, the GPS mobile receiver is placed in the vehicle, and the constellation of GLONASS satellites is additionally used with the constellation of GPS satellites.  2. The system according to claim 1, characterized in that the antenna mounting means is made in the form of a pole located in a socket mounted on a wheel.  3. The system according to claim 1 or 2, characterized in that the device carrying the antenna of the mobile GPS receiver is configured to be mounted on the left or right side of the vehicle within 0.5 m of its size.  4. The system according to claims 1, 2 or 3, characterized in that the means of fastening the device carrying the antenna of the mobile GPS receiver to the vehicle is made in the form of a boom system mounted on the vehicle and a mounting frame connected to the boom system, made in the shape of a triangle, one of the ends of which, which is the mounting location of the device carrying the antenna, is extended to the left or right up to 0.5 m beyond the vehicle’s overall dimensions.  5. The system of claims. 1, 2, 3 or 4, characterized in that the vehicle is additionally placed controller.  6. The system of claims. 1, 2, 3, 4 or 5, characterized in that a vehicle is used as a vehicle.  7. The system of claims. 1, 2, 3, 4, 5 or 6, characterized in that each GPS receiver has additional GLONASS channels.  8. A system for performing topographic surveys of a roadway comprising a constellation of GPS satellites, a mobile GPS receiver, a device carrying an antenna of a GPS receiver, a vehicle for moving a GPS receiver and a device carrying an antenna, means for attaching a device carrying an antenna to a vehicle means, a second GPS-receiver, placed stationary at a point with known coordinates, a post-processing unit of survey data, including a stationary computer, characterized in that the fastening means of the device carrying the antenna nnu of the mobile GPS-receiver, to the vehicle is located on the roof of this vehicle and is made in the form of an articulated swivel suspension, the end of one knee of which is placed on the roof on the vehicle attachment means, and the end of the other knee which carries an antenna, a mobile GPS-receiver placed in a vehicle, and with the constellation of GPS satellites, the constellation of GLONASS satellites is additionally used.  9. The system of claim 8, characterized in that the swivel suspension is made with the possibility of extension within up to 0.5 m to the left or to the right beyond the size of the vehicle.  10. The system of claim 8 or 9, characterized in that the controller is additionally placed in the vehicle.  11. The system according to claims 8, 9 or 10, characterized in that a vehicle is used as a vehicle.  12. The system according to claims 8, 9, 10 or 11, characterized in that each GPS receiver has additional GLONASS channels.  13. A method for performing a topographic survey, including initializing the measuring equipment, including a mobile GPS receiver, and taking points of the structural lines of the surface in the coordinates of the X, Y plan by discrete reading information from GPS satellites that determine the position of the phase center of the GPS receiver antenna, transmitting primary information for post-processing to a stationary computer, which also sends data from a stationary GPS-receiver located at a point with known coordinates, and differential processing of inf formations in a stationary computer using software with output information output in electronic form, characterized in that the topographic survey is performed using the system according to items l - 9, while the survey is also performed taking into account the heights H of the points of the structural lines, the information is additionally read from GLONASS satellites, at the same time at least 5 satellites are simultaneously observed, as well as with longitudinal and transverse tilts of the antenna due to the surface profile and the corresponding displacements of its phase center in the program mm software, the phase center offset accounting subroutines are introduced in two stages: at one stage, the longitudinal surface slope for each point of the structural line is determined, the antenna longitudinal slope is taken into account the surface longitudinal slope, and the correction subprogram is introduced in determining the heights H of the removed points, at another stage determine the transverse slope of the surface for each point of the structural line, the transverse slope of the surface is compared with the slope at the initialization point, take into account that the algebraic difference is compared and the source of surface slope is the inclination angle of the antenna at a given point, and the subroutine is introduced corrections in determining the coordinates X, Y of points filmed.

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