A proposed simplified technique for confirming high precision GNSS antenna offsets/Supaprastintas metodas auksto tikslumo globalines navigacines palydovines sistemos antenos nukrypimams aprobuoti.1. Introduction
The consistency of the phase centre offsets (PCO) of antennas is important when trying to achieve geodetic measurements, which are accurate at the millimetre level. The precise point whose position is being measured when a GNSS baseline is determined is generally assumed to be the phase centre of the GNSS antenna.
However, the phase centre of a GNSS antenna is neither a physical point nor a stable point. For any given antenna, the phase centre will change with the changing direction of the signal from the satellite. Ideally, most of this phase centre movement depends on satellite elevation (Leick 1995).
The phase centre movements affect the antenna offsets that are needed to connect GNSS measurements to physical monuments (Geo 2000). Ignoring these phase centre movements can lead to serious (up to 20 cm) vertical errors.
In addition, the phase centre is not a physical point that can be accessed with a tape measure by a user who needs to know the connection between a GNSS solution and a monument embedded in the ground. However, this kind of connection must be known if a site is ever to be occupied by different antenna types and continuity of positioning is expected. This requires that the vector between the phase centre and an external antenna reference point (ARP) on the antenna be known (Menge et al. 1998).
The function of antennas is to convert electromagnetic waves into electrical currents and vice versa. A GPS/GNSS position therefore refers to the phase centre of the receiver antenna. In reality the phase measurement, and as a consequence the determined signal path length depends on azimuth and elevation of the incoming signal. The purpose of antenna calibration is thus to describe these deviations from an ideal single set of offset parameters for a specific antenna.
Calibration procedures can be classified as absolute or relative and as field or laboratory procedures. Field procedures use GNSS signals from satellites in view; thus an operable navigation system is an essential condition for the calibration. Relative field calibration procedures use differential GNSS measurements to determine the calibration results of a test antenna with respect to a reference antenna. Relative calibration parameters are published and it is made clear that these are by comparison with a named antenna type and model (Mader 1999, Rothacher 2001).
Absolute antenna calibration in an anechoic chamber is a standard technique in radio-frequency engineering (Kraus et al. 2003). Originally, antenna calibration-to find out where satellite receiver antennas measure from--was done in the relative mode, as explained above.
With time and the arrival of new technology, it became possible to calibrate the benchmark antenna using much improved laboratory methods. At this stage, the imperfections in the benchmark itself were determined. These imperfections could then be added to the relative calibrations previously performed to develop what became known as absolute calibration. However, in a philosophical sense, there is no such thing as an absolute value for a measurable quantity. It is only possible to approach that indeterminable absolute truth by using methods that will serve to minimize residual errors (Schmid et al. 2003). However, as a matter of convenience, it is often comfortable to think of a measured value determined by a much better system as being absolutely accurate--even though it is not.
2. Calibration of modified theodolite
A theodolite (Wild T2) has been fitted with a spacer so that a GNSS antenna can be mounted directly onto the telescope (Figs 1, 2). The telescope can then be set horizontally or at an elevation angle to simulate incoming signals at different elevations. Naturally, the spacer itself needs to be calibrated.
[FIGURE 1 OMITTED]
[FIGURE 2 OMITTED]
To find out the offset between the spacer bolt and the intersection of the theodolite axes, measurements were carried out using a CE Johansson AB (CEJ) Topaz 15-6-6 CNC measuring machine. This machine is programmable and can measure the actual dimensions of different geometries and is particularly labour-saving when several similar products are to be measured. This high precision measuring machine measures dimensions down to thousandths of millimetres.
At first, the spacer thickness was measured without it being fitted to the theodolite. Six points in millimetres were measured and averaged (Tab 1).
The side lengths of the spacer were got by measuring four points on each side (Tab 2).
Figure 2 shows the GNSS antenna mounted directly on the spacer on top of the telescope so that the antenna can be rotated out of the horizontal without interfering with the body of the theodolite. Four points on the centre of the spacer were measured (Tab 3). These points were taken on diameters inside the spacer bolt and the crossing of these diameters was accepted as the centre of the spacer.
Measuring the distance between the top surface of the spacer and the intersection of the theodolite's three axes was carried out, and then the theodolite telescope was set up exactly vertically. Four points were measured at the telescope eyepiece a and on the cylindered surface surrounding the objective lens b (Fig 3, Tab 4).
[FIGURE 3 OMITTED]
The height of the top surface of the spacer above the centre line of the telescope was measured seven times independently (Tab 5).
The length of the telescope was found to be 15.178 cm. The distance from the eyepiece to the theodolite trunnion axis was measured by making measurements to both sides of the theodolite casing at both faces (Fig 4). Additional measurements along the length of the telescope gave offsets as shown in figures 5 and 6.
[FIGURE 4 OMITTED]
[FIGURE 5 OMITTED]
[FIGURE 6 OMITTED]
3. Field observation to determine vertical offsets
Geodetic and precise GNSS measurements require an exact knowledge of the reception characteristics of the GNSS antennas used, and therefore a calibration is necessary.
An attempt was made to independently arrive at calibration parameters, which might be compared with numbers obtained from other sources. For this purpose, having in mind that many points were inaccessible due to snow cover we decided to use the pillars marked G3, G4, G5, and Topcon (Fig 7).
[FIGURE 7 OMITTED]
The precise positions of these pillars have been measured and the 'true' coordinates are known (Tab 6). These coordinates were developed by network adjustment, which were computed using Leica Geo Office software, version 7. These coordinates were measured by geodetic techniques that are more precise than those used for the actual calibration methods, that is by a preplanned static GNSS campaign using both frequencies on phase measurements, with post processing of vectors and thereafter network adjustment including standard statistical analyses testing for mistakes and internal consistency in the network.
A GPS receiver calibration base can consist of several points, and their number can be varied (Skeivalas et al. 2006). In this case, the analysis calibration base consists of four stations. The test antennas on pillars G4 and G5 were Leica GS15 GNSS receivers, and the test antenna on pillar G3-a Leica GS15 GNSS receiver--was on a tripod. The fourth pillar, named Topcon, was chosen as the reference antenna, with parameters from the GPS antenna calibrations at the National Geodetic Survey (NGS) (Mader 1999).
4. Antenna calibration test results
As already noted, the precise point whose position is being measured by satellite techniques is generally assumed to be the phase centre of the antenna. The phase centre is, however, neither a physical point nor necessarily a stable point. For any given type of GNSS antenna, the phase position will change with the changing direction of the signal from a satellite. Ideally, most of this phase centre variation depends on the elevation of the satellite. The National Geodetic Survey (NGS) has developed a procedure for calibrating GPS antennas to allow the phase centre variation with satellite motion to be observed.
The calibration procedure normally involves placing a reference antenna in one location and the test antenna at another location close by and differencing the data to determine the phase centre offsets. This procedure is carried out under somewhat perfect circumstances. For best results, every antenna should ideally be calibrated at the site of intended use. To do this, it is necessary to have a reference antenna with characteristics.
The antenna calibration procedure uses field measurements to determine the relative phase centre position and phase centre variations of a series of test antennas with respect to a reference antenna (Schmitz, et al. 2002). As was mention above, for this experiment Topcon (type AT2775-42) was chosen as the reference antenna. The test antennas were Leica GS15 GNSS receivers which are set to track to an elevation mask of 15[degrees]. This test did not provide the absolute phase calibration for each antenna, but rather the relative calibrations with respect to this reference antenna. Since the reference antenna was the same for all tests, the antenna calibration for all test antennas could be used in any combination to find out the antenna phase centres.
The aim of this first field trial was to test a procedure for getting the vertical antenna phase centre offset. Conditions were less than ideal due to continuing snow cover, with the result that existing pillars that were further apart than considered optimal had to be used. The actual observing procedure was simply to establish the receivers on the pillars as already noted, and then to record approximately 1 hour's worth of observations at 1 second intervals using both L1 and L2 frequencies. Great care, meanwhile, was taken to measure and record the height of the various antennas over their points. Measurements were subsequently made to connect the physical height measuring point to the conventional antenna reference point (ARP), which is the lower surface of the standard bolt at the base of all surveying antenna.
These observations were then extracted from the respective receivers, converted into RINEX format using the respective manufacturers' conversion systems, and imported to the LGO software system. The aim here was to process the observations to obtain vector positional differences between Topcon and the pillar-mounted Leica antenna.
In detail, and with the use of the menu language of LGO, all the antenna, including Topcon, were designated as unknown--in other words having zero antenna phase centre offsets. Then, at the Topcon pillar, the published offset values for L1 and L2 (Mader 2001) were used to compute the Cartesian coordinates of those phase centres. Next, using only the GPS observations, the vectors were processed, giving the Cartesian coordinates of the phase centres at the Leica antenna. Vectors were computed separately for the two frequencies.
Finally, the previously adjusted coordinates of the pillars at the Leica stations and the processed vector results were converted into UTM zone 32 coordinates based on the GRS80 Ellipsoid. The difference between these end results thus produced the desired offset estimates as listed in table 7.
1. The results of the fieldwork, which was performed under less than ideal conditions, are nevertheless within approximately 15 % of the vertical antenna offset values given in the Leica Viva GNSS controller firmware. At the time of writing, the NGS has not yet published its values on its web site. Further, it is interesting to note that, again at the time of writing, the offset parameters released by Leica (hard wired into LGO) do not include variations due to satellite elevations. These elevation values are of course available for the older Topcon antenna.
2. It therefore follows that it would be advantageous to carry out additional field tests. Intuitively, it would be better to have the test pillars much closer together, and tests need to be completed with different satellite geometry configurations as well as using both GPS and GLONASS together, and indeed separately.
3. At the same time, the relative success of the field trial thus far suggests that using the theodolite as an antenna mounting can also develop confirmatory results. However, two aspects here will need to be resolved:
For the fieldwork, it will be necessary to know the azimuth in which the telescope is pointing, so that the antenna phase centres can be adjusted with respect to the pillar coordinates.
Similarly, the geometric procedures for that 'movement' will need to be identified.
4. Meanwhile, reference is made to the use of a high precision industrial measuring device for calibrating the theodolite spacer. This was the first attempt at using this machine for any purpose at Gj0vik University College since its recent installation. The results can only be described as impressive, with measurement repeatability better than one hundredth of a millimetre. The availability of this device needs further evaluation concerning the controls that are normally expected on optical instruments.
This study describes an experiment that was undertaken as part of the Doctorate of Geomatic programme between Vilnius Gediminas Technical University (VGTU) in Lithuania and Gj0vik University College (GUC) in Norway.
In particular, we would like to thank Hans Pedersveen (Gjovik University College, Norway) for constructing the spacer for the theodolite and Kenneth Kalvag (Gjovik University College, Norway) for helping measure the theodolite with the high precision CE Johansson Topaz 15-6-6 measuring machine.
Received 05 May 2010, accepted 23 August 2010
Geo. GNPCVDB. GNSS phase variations database [online] 2000. [cited 23 April 2010]. Available from Internet: <http://www.gnpcvdb.geopp.de>.
Kraus, J. D.; Marhefka, R. J. 2003. Antennas: for all Applications. 3rd ed. New York: McGraw-Hill. 14-27.
Leick, A. 1995. GPS Satellite Surveying. New York, Chichester, Brisbance, Toronto, Singapore: John Wiley and Sons. 352 p.
Mader, G. L. 1999. GPS Antenna calibration at the national geodetic survey, GPS Solutions 3(1): 50-58.
Mader, G. L. 2001. A comparison of absolute and relative GPS antenna calibration, GPS Solutions 4(4): 37-40.
Menge, F.; Seeber, G.; Volksen, C. et al. 1998. Results of absolute field calibration of GPS antenna PCV, in Proceedings of the 11th International Technical Meeting of the Satellite Division of the Institute of Navigation, ION GPS. Nashville, Tennessee, USA, September 15-18, 1998. 31.
Rothacher, M. 2001. Comparision of absolute and relative antenna phase center variations, GPS Solutions 4(4): 55-60.
Schmid, M.; Rothacer, M. 2003. Estimation of elevation dependent satellite antenna phase center variations of GPS satellites, Journal Geodesy 77: 440-446.
Schmitz, M.; Wubbena, G.; Boettcher, G. 2002. Test of phase center variations of various GPS antennas, and some results, GPS Solutions 6(1-2): 18-27.
Skeivalas, J.; Putrimas, R. 2006. The calibration of GPS receivers applying the calibration bases, Geodesy and Cartpgraphy [Geodezija ir kartografija]. Vilnius: Technika, 32(2): 29-32. (in Lithuanian).
Wubbena, G.; Schmitz, M.; Menge, F. et al. 1997. A new approach for field calibration of absolute GPS antenna phase center variations, Navigation: Journal of the Institute of Navigation 44(2).
Vilma Zubinaite (1), George Preiss (2)
(1) PhD Student, (2) Assistant Professor, 1 Vilnius Gediminas Technical University, (2) Gjovik University College
E-mail: (1) firstname.lastname@example.org, (2) email@example.com
Vilma ZUBINAITE (1), PhD
Date and place of birth: 1982, Mazeikiai, Lithuania.
Education: Vilnius Gediminas Technical University, Department of Geodesy and Cadastre.
Research interests: calibration of GNSS antennas, investigation into solar storm effects to ground position, satellite movement theory.
Publication: three articles and research reports.
George PREISS, Asst Prof
Date and place of birth: 1942, Beaconsfield, England.
Education: University of Cambridge, University of Oxford.
Affiliation and functions: Lieutenant Colonel, Royal Engineers, retired. Later GPS Consultant and Chair of International Committee of US Civil GPS Service Interface Committee (CGSIC). Since 1998, Geomatics Group, Faculty of Technology, Economy and Management, Gj0vik University College. Lecturer/student supervisor in advanced land surveying specializing in GNSS, accuracy and precision, and BuildingSMART.
Research interests: examining GNSS error sources, calibrating GNSS systems, building intelligent modeling (BIM). Publications: numerous technical reports, research reports, and conference papers.
Table 1. Thickness of the spacer Point Thickness mm 1 34.427 2 34.407 3 34.384 4 34.461 5 34.346 6 34.584 Average 34.435 Table 2. Side lengths of the spacer Point Side #1 mm Side #2 mm 1 50.783 50669 2 50.941 50.673 3 50.896 50.647 4 50.842 50.577 Average 50.866 50.642 Table 3. Measurements of the spacer centre Point X mm Y mm Z mm 1 -25.352 -13.464 -24.953 2 -25.348 -13.500 -24.939 3 -25.348 -13.523 -24.950 4 -25.348 -13.544 -24.961 Average -25.350 -13.508 -24.951 Table 4. Theodolite telescope sections centres Telescope section Trial Centre a Centre b 1 X: -26.988 X: -24.411 Y: +57.236 Y: +57.395 Z: +56.364 Z: -84.057 2 X: -26.992 X: -24.404 Y: +57.229 Y: +57.387 Z: +56.437 Z: -84.055 3 X: -26.988 X: -24.409 Y: +57.227 Y: +57.397 Z: +56.438 Z: -84.057 4 X: -26.991 X: -24.408 Y: +57.229 Y: +57.391 Z: +56.438 Z: -84.056 Average X: -26.990 X: -24.408 Y: +57.230 Y: +57.393 Z: +56.419 Z: -84.056 Table 5. Height of the top surface of the spacer above the centre line of the telescope Trial Height cm 1 5.8140 2 5.8476 3 5.7440 4 5.8000 5 5.6940 6 5.8500 7 5.7000 Average 5.7785 Table 6. Coordinates of points Cartesian Coordinates Station X m Y m Z m G3 3066692.7092 578391.5633 5544112.9459 G4 3066690.3503 578391.2773 5544114.3169 G5 3066664.7974 578350.8902 5544132.5828 Topcon 3066794.3904 578320.0022 5544065.9730 UTM Zone 32 Coordinates Point North m East m Height m G3 6740481.797 591500.621 222.917 G4 6740484.538 591500.707 222.957 G5 6740520.983 591464.823 222.993 Topcon 6740381.020 591414.036 224.210 Table 7. Calculation of phase centre measurements of frequencies L1 and L2 (North, East and Height are in UTM Zone 32 on the GRS80 Ellipsoid) X m Y m Z m Frequency L1 Station G4 By vector 3066690.4708 578391.3054 5544114.5318 Network 3066690.3503 578391.2773 5544114.3169 adjustment Difference 0.1205 0.0281 0.2149 Station G5 By vector 3066664.9185 578350.9124 5544132.8056 Network 3066664.7974 578350.8902 5544132.5828 adjustment Difference 0.1211 0.0222 0.2228 Frequency L2 Station G4 By vector 3066690.4709 578391.3043 5544114.5325 Network 3066690.3503 578391.2773 5544114.3169 adjustment Difference 0.1206 0.0270 0.2156 Station G5 By vector 3066664.9228 578350.9207 5544132.8149 Network 3066664.7974 578350.8902 5544132.5828 adjustment Difference 0.1254 0.0305 0.2311 North m East m Height m Ant. over point cm Frequency L1 6740484.5350 591500.7130 223.2050 6740484.5380 591500.7070 222.9570 -0.0030 0.0060 0.2480 0.2320 6740520.850 591464.8220 223.2470 6740520.9830 591464.8230 222.9930 0.0020 -0.0010 0.2540 0.2345 Frequency L2 6740484.5360 591500.7120 223.2050 6740484.5380 591500.7070 222.9570 -0.0020 0.0050 0.2480 0.2320 6740520.9840 591464.8290 223.2580 6740520.9830 591464.8230 222.9930 0.0010 0.0060 0.2650 0.2345 Ant. over Phase ARP cm centre cm Frequency L1 0.1575 0.1735 0.1575 0.1770 Frequency L2 0.1575 0.1735 0.1575 0.1880