GPS Antenna Calibration at the National Geodetic = Survey

Gerald L. Mader

National Geodetic Survey

NOS, NOAA

Silver Spring, MD

 

Abstract

The precise point whose position is being = measured when a GPS baseline is determined is generally assumed to be = the phase center of the GPS antenna. However, the phase center of a GPS = antenna is neither a physical point nor a stable point. For any given = GPS antenna, the phase center will change with the changing direction of = the signal from a satellite. Ideally, most of this phase center = variation depends on satellite elevation. Azimuthal effects are only = introduced by the local environment around each individual antenna site. = These phase center variations affect the antenna offsets that are needed = to connect GPS measurements to physical monuments. Ignoring these phase = center variations can lead to serious (up to 10cm) vertical errors. This = paper will describe the procedure by which NGS is calibrating GPS = antennas and how this information may be obtained and used to avoid = problems from these antenna variations.

 

Introduction

 

Differential GPS solutions are used = routinely to provide geodetic positions with precisions that are often = as good as a few millimeters. These positions are typically obtained = from a baseline vector that extends from a station whose position is = known and constrained to a station whose position is being determined. = With increasing frequency, the constrained station may be part of a = continuously operating reference network operated as a service to users = by a variety of agencies around the world. Consequently, GPS users will = often find they are using different antenna types within a single = baseline as well as within a given network. The use of different antenna = types demands that the contribution of the antennas themselves to the = geodetic solution be examined.

A GPS geodetic solution for a baseline provides the = vector between the phase centers of the antennas at either end of the = baseline. However, a real antenna does not have a single well-defined = phase center. Instead, the location of the phase center is a function of = the direction from which the antenna receives a signal. If this = variation is ignored, the measured baseline will be between the average = phase centers of the two antennas. These average phase center locations = are a weighted average of all the individual phase centers for each of = the measurements included in the solution. When the antennas at opposite = ends of relatively short baselines are identical, these variations = should cancel out and no effect is seen. However, different antenna = types exhibit different phase variations and baselines with different = antenna types will show increasing sensitivity to such things as = elevation cutoff angle and the distribution of observations within a = solution.

In addition, the phase center is not a physical = point that can be accessed with a tape measure by a user who needs to = know the connection between a GPS 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 = center and an external antenna reference point (ARP) on the antenna be = known.

To illustrate these problems, consider some test = data taken between two different antenna types in fairly common usage. = The reference antenna for these examples is a Dorne/Margolin antenna = element mounted on a choke ring designed by the Jet Propulsion = Laboratory and designated as type T (hereafter referred to as JPL = D/M+crT). The test antenna is a Trimble compact L1/L2 with groundplane = (hereafter referred to as TRM 22020.00). Table 1 shows the vector = components (North, East, and Up) for three different solutions over this = baseline, L1 only, L2 only, and the ionosphere-free L1/L2 combination, = hereafter called L3.

 

Table 1. TRM 22020.00 - JPL D/M+crT Vector = Components

No Phase Center Offsets or Variations = Applied

Frequency North (cm) East = (cm) Up (cm)

L1 497.12 7.36 3.71

L2 497.24 6.94 5.62

L3 496.93 8.02 0.74

 

The vector components shown in Table 1 are = between the average L1 phase centers of the two antennas, the average L2 = phase centers, and the average L3 phase centers. No phase center antenna = offsets or phase center variations have been applied. The solutions used = the same 24-hour data set and no tropospheric unknowns were solved for. =

Table 1 shows that the vector components are not = the same for each solution frequency. The difference in the north = component are about 1mm and are essentially negligible. The east = component differences from the average are about 5mm and probably do = reflect real systematic differences in this component of the phase = centers of the two antennas. The largest differences, several cm, are in = the up component. These differences are due to the different L1 and L2 = average phase centers in these two antennas. Clearly, a lack of = knowledge of these phase center locations can lead to significant = vertical errors.

The National Geodetic Survey (NGS) has measured the = average L1 and L2 phase center offsets from these ARPs by a technique = that will be described shortly. Table 2 shows the results when these = offsets are used to reference the baseline determinations to a physical = point on the antenna rather than to the previously ill-defined phase = centers.

 

Table 2. TRM 22020.00 - JPL D/M+crT Vector = Components

Phase Center Offsets Applied

Frequency North (cm) East = (cm) Up (cm)

L1 497.27 7.24 .22

=

L2 497.14 7.10 .26

=

L3 497.48 7.45 .95

=

 

Table 2 shows that the discrepancies between the = solutions has significantly improved in the up component and the east = component. The offsets for these solutions used values for the TRM = 22020.00 antenna that averaged calibrations for 4 different antennas of = this particular model. The deviation of individual antennas from the = average calibration values can sometimes be several mm. Using standard = calibrations to find an L1 and L2 average phase center is essential not = only for reconciling the differences between solutions made with = different frequencies or frequency combinations, but also for baselines = using different antennas over the same monuments.

While the above example shows the utility of = calibrating the average L1 and L2 phase centers with respect to the ARP, = it does not illustrate the problems encountered by ignoring the = variation of the phase center location with direction to the signal. = Fortunately, almost all GPS antennas currently in use are azimuthally = symmetric and the dominant phase variation occurs with elevation. = However, the local environment around the antenna can introduce both = azimuth and elevation variations from the ideally measured phase = patterns. These local variations will be ignored for the sake of these = calibrations. One effect of these phase center variations (PCV) can be = illustrated by varying the elevation cutoff angle. This dependence is = shown in Table 3 for the same data used above. Only the L3 solutions are = shown.

 

Table 3. TRM 22020.00 - JPL D/M+crT Vector = Components

L3 Solutions as Function of Elevation Cutoff With = Phase Center Offsets Only

Cutoff (deg) North (cm) East = (cm) Up (cm)

10 497.41 7.41 1.22

15 497.48 7.45 0.95

20 497.53 7.35 0.64

25 497.63 7.31 0.25

Table 3 shows that the up-component of the = baseline varies by about 1cm as the elevation cutoff changes from 10 to = 25 degrees for these L3 solutions. The horizontal components of this = baseline change by only 1-2mm. If the information that describes the = change in phase center location as a function of elevation is included, = the results shown in Table 4 are obtained. The horizontal components = have systematically shifted by about 1mm and the excursion of the = up-component with elevation cutoff angle is now reduced to only about = 3mm.

 

Table 4. TRM 22020.00 - JPL = D/M+crT Vector Components

L3 Solutions as Function of Elevation Cutoff With = Phase Center Offsets and Variations

Cutoff (deg) North (cm) East = (cm) Up (cm)

10 497.36 7.54 -0.01

15 497.43 7.59 -0.14

20 497.45 7.48 = 0.03

25 497.54 7.45 = 0.15

Elevation-dependent PCV can also affect a = baseline solution in which a tropospheric scale factor is being = adjusted. GPS solutions usually include an estimate of the phase delay = to the signals as they travel through the troposphere to each antenna. = Different propagation path delays may seriously affect the baseline = components, particularly the vertical, if left uncorrected. Because the = estimates of these propagation delays computed by the model in the = software may be inaccurate, the GPS data themselves can be used to = estimate the remaining differential path delays by including in the GPS = solution an adjustment for a tropospheric scale factor. Simply = expressed, this scale factor adjustment is a constant multiplicative = factor for each tropospheric delay computed by the model used in the = solution software. For this technique to work properly, the phase delay = contained in the GPS data as a function of elevation must be due solely = to the troposphere. An additional phase change, introduced by the = antennas and superimposed on the GPS data, will still be interpreted by = the software as being due to the troposphere alone. The result will be = incorrect tropospheric scale factor adjustments and incorrect baseline = height components. Table 5 illustrates the magnitude of the problems = that can result. This Table repeats the L3 result from Table 2, where = only the phase center offsets were applied to the solution (+OFF). The = next line shows the baseline components when the tropospheric scale = factor is adjusted (+OFF, +T). The up components changes by over 3cm. = The Table also shows the result when the offsets and PCV are applied = (+PCV) and when the tropospheric scale factor adjustment is included = along with these calibrations (+PCV, +T). The last 2 lines of Table 5 = show only a 1mm height change when the tropospheric scale factor is = included. The correct up-component for this baseline, based on leveling = data, is =960.3cm. The solutions using the full calibration data = (offsets and PCV) give results closest to this value.

Table 5. TRM 22020-00 - JPL D/M+crT = Vector Components

Effect of PCV on L3 Solutions With and Without = Troposphere

North (cm) East (cm) Up = (cm)

+OFF 497.48 7.45 0.95

+OFF,+T 497.49 7.45 -2.74

<= /DIR>

+PCV 497.43 7.59 -0.14=

+PCV,+T 497.42 7.54 -0.04<= /P>

Having demonstrated the importance of using = antenna calibrations for GPS baseline solutions, the techniques by which = NGS determines these calibrations will now be examined.

 

NGS Antenna Calibration Procedure

The NGS antenna calibration procedure uses = field measurements to determine the relative phase center position and = phase center variations of a series of test antennas with respect to a = reference antenna. Relative antenna calibrations are used because these = calibrations are easy to perform in a consistent manner and absolute = antenna calibrations have not yet been satisfactorily demonstrated. = There is no practical difference to using relative or absolute antenna = calibrations until the baseline lengths approach several thousand km in = length. As the baseline length increases, the curvature of the earth=92s = surface causes the same satellites to appear at increasingly different = elevations at the ends of the baseline. These situations would require = an absolute calibration in order to remove the direct contribution of = possible errors in the defined calibrations for the reference antenna to = the scale of the baselines. For almost all other situations short of a = global network, relative antenna calibrations should be = satisfactory.

To perform these antenna calibrations, a test range = has been established at NGS=92s Instrumentation and Methodologies Branch = in Corbin, VA. This test range, pictured in Figure 1, consists of two = stable 6 in. diameter concrete piers rising about 1.8m above ground. On = the tops of these piers, antenna-mounting plates are permanently = attached. The piers, separated by 5m, are located in a flat grassy field = and lie along a north-south line. Leveling data show that the south = (test antenna) pier is 3.4mm taller than the north (reference antenna) = pier. The reference and test antennas are connected to Ashtech Z12 = receivers which are set to track to an elevation mask of 10=B0. A = Rubidium oscillator is used as an external frequency standard for both = of these receivers.

Figure 1. The NGS antenna = calibration test facility at Corbin, VA uses a JPL D/M+crT as a = reference antenna. The test antennas are located 5m away at = approximately the same height. Both antennas are connected to Ashtech = Z-12 receivers which use a Rubidium oscillator as an external frequency = standard.

 

The reference antenna used for these calibration = measurements is a Dorne/Margolin choke ring antenna, type T originally = designed by the Jet Propulsion Laboratory and designated JPL D/M+crT. = These tests do not provide the absolute phase calibration for each = antenna tested, but rather the relative calibrations with respect to = this reference antenna. Since the reference antenna is the same for all = tests, the antenna calibrations for all test antennas may be used in any = combination to find the antenna phase centers and PCV.

Beginning several years ago, and at intervals since = then, additional JPL D/M+crT antennas have been placed on the test pier = in order to determine the location of this antenna=92s L1 and L2 phase = centers on this pier. As illustrated in Figure 2, these positions are = then used as the a priori positions for the L1 and L2 phase centers of = the test antennas. The displacements that are found from the test = antenna solutions then give these test antenna phase center locations = relative to the reference antenna. Since the average L1 and L2 phase = center offsets of the JPL D/M+crT are defined to be 11.0cm and 12.8cm = respectively, the average L1 and L2 phase center offsets of the test = antennas can be easily found.

Figure 2. This Figure shows how the average phase = center offsets are found. Multiple measurements of several JPL D/M+crT = reference antennas were made on the test pier to establish a priori L1 = and L2 positions for all antennas tested on this pier. The offsets from = these a priori positions are combined with the defined offsets for the = reference antenna to find the L1 & L2 phase center offsets from the = test antennas ARP.

 

As shown earlier, the average phase center position = is a function of the elevation cutoff angle. For the NGS antenna = calibrations, a standard elevation cutoff angle of 15 degrees has been = defined for the determination of the test antenna=92s L1 and L2 average = phase center locations. These single frequency solutions use no PCV = corrections or tropospheric scale factor estimation and are done using = the NGS PAGES software. This software uses double-difference phase = observations, which are free of any differential tropospheric or = ionospheric effects for this extremely short baseline. The solutions use = 24 hours of data to determine these L1 and L2 offsets. Once these L1 and = L2 offsets have been found, the test antennas PCV can be determined.

The variation of the phase center as a function of = elevation is determined separately for L1 and L2. No azimuth dependence = is estimated in these PCV solutions. The PCV is determined using L1 or = L2 single differences rather than double differences in order to = determine the relative PCV directly rather than from different = satellites at different elevations. The PCV is essentially a curve and = this curve is better determined from direct measurements of points on = this curve rather than differences along this curve.

Since single differences are being used as the = observable, the clock differences between the two GPS receivers do not = cancel out as they do with double differences. Therefore, a Rubidium = oscillator is used as an external frequency standard to remove most of = the variation due to clock differences and time delays from the a priori = single difference phase residuals. With these a priori phase residuals = now relatively flat as a function of time, editing cycle slips and = outlying data points is easily accomplished.

The L1 and L2 single difference phase residuals are = formed by constraining the test antenna to its L1 or L2 position using = the previously determined average phase center offsets. These residuals = now contain only variation due to residual time delay differences and to = the PCV. A least squares solution is used to solve for a clock offset = for each measurement epoch and for a 4th order polynomial in = elevation. The observation equation is expressed as:

D (F obs - F = calc)i =3D t i = + a 1 q i + a 2 = q i 2 + a 3 q i 3 + a 4 q i 4

where D (F obs - F = calc) i is the single difference phase residuals, = q is the elevation angle in degrees, a i is the polynomial coefficient and = t i is the remaining relative = time delay. This procedure has been coded into a FORTRAN program call = ANTCAL.

Separate polynomials are estimated for L1 and L2. A = constant term for the polynomial is not estimated since it is not = readily separable from the clock values and would be lost in any case = during double difference data processing. An elevation cutoff of 10 = degrees is now used to extend the coverage of these corrections to lower = elevations. These coefficients define the PCV for this antenna.

Figure 3. This figure shows a sample = from the antenna calibration file ant_info.002. The file contains a = format explanation followed by the results for each antenna tested. The = antennas are identified by an unambiguous and machine-readable standard = name.

 

In order to accommodate other calibration = techniques using different methods, the PCV is expressed in a tabular = format rather than as the coefficients defined above, which are unique = to NGS. This allows GPS solution software to adapt to a standard format = without regard to the source of these data. An example of this format is = shown in Figure 3. All the NGS antenna calibrations are contained in a = file designated as ant_info.002. The first line of this file contains = the file name and a version designation. The version gives the initials = of the person to last modify the file, the date of this modification, = and the current number of antennas in the file. This allows users to = easily monitor changes to the file, which most commonly are due to the = addition of new antenna models. More significant changes to the format = or to previously published information will cause a change to the = extension of the ant_info file name.

The first few lines of the ant_info.002 file are a = header, which explains the format for the data. The antenna calibration = for any antenna begins with the antenna identification code. This is a = standard name for each model antenna, which consists of a 3-character = designation for the manufacturer followed by the antenna model number = which is found stamped on each antenna. This model number may be = followed by a suffix that indicates if certain options are included with = this antenna model (e.g. if an optional groundplane is attached or not, = +gp or =96gp or a radome is included or not, +rd or =96rd). The = remainder of this line may include a description of the antenna or an = alias by which the antenna is also known. The agency providing this = data, the number of measurements, and the date entered into this file = are also included on this line.

The north, east, and up L1 antenna offset from the = ARP, are given in mm on the next line. This is followed by the L1 PCV on = the next 2 lines. The PCV is expressed in mm also and is given in 5=B0 = elevation increments beginning with 90=B0 and going down to 0=B0. Since = the NGS PCV measurements extend to only 10=B0 elevation, the last 2 PCV = entries (5=B0 and 0=B0) and left at 0.0. The lines containing the same = data for L2 immediately follow the L1 data. If a particular antenna is = an L1 only antenna, the L2 data fields will contain all 0.0=92s.

As mentioned previously, the solution for the PCV = coefficients does not include a constant term. Consequently, the initial = computation of the PCV tabular values includes an arbitrary constant = value with no particular physical meaning. Since the essential = information from the PCV is its curvature, a constant is subtracted from = each tabular entry so that the PCV value at 90=B0 is always 0.0. This is = done by convention to keep all the PCV values for the various antennas = within a similar range and to facilitate comparisons. It has no effect = on the results obtained with these PCVs.

The PCV for the JPL D/M+crT is defined to be 0.0 = over the entire elevation range. In reality this is certainly not the = case. The phase center meanders with elevation for these antennas just = as it does for any other antenna. These adopted PCV values only reflect = the fact that an absolute PCV for this antenna has not been = satisfactorily measured and that this is the adopted reference antenna. =

The PCV data are used to correct the observed GPS = phase data as it is obtained from a RINEX file. Each L1 and L2 phase = observation is corrected. This is done by using the elevation of a = satellite at the time of each measurement to linearly interpolate the L1 = and L2 PCV value from the PCV table. This interpolated value is = converted to the appropriate units (meters or L1 or L2 cycles) and added = to the observed phase. This procedure effectively removes each change in = phase introduced by the antenna as the satellites move across the = sky.

The PCV of an antenna is inseparable from the = offset for that antenna. Using a different average phase center offset = will cause ANTCAL to produce a different set of PCV values. However, = when the PCV are applied to observed phase data (and provided the = appropriate set of PCV values are used), different average phase center = offsets will give the same position for the ARP. The fact that GPS = measures the location of the phase center and that different phase = center heights above the ARP can yield the same position for the ARP may = seem strange. However, this fact emphasizes the arbitrary location of = the phase center and the importance of always using the PCV and the = offsets that were determined together.

Figure 4 shows the data used to determine the PCV = for one particular test antenna. The points shown in Figure 4 are = essentially the a priori single difference phase residuals with the = epoch-by-epoch time delays removed. The phase variation with elevation = is clearly evident. Figure 4 also shows the polynomial fit to these data = and the location of the tabular PCV values (before the normalizing = constant has been subtracted). Careful examination of Figure 4 also = shows the effect of multipath due to reflections from the ground. These = multipath signals are at a much higher frequency than the overall PCV = and hence do not influence the low order polynomial used to estimate the = PCV. Plots like that shown in Figure 4 are maintained by NGS as a = quality control for each individual antenna calibration.NGS ordinarily = tries to calibrate at least 3 different members of each antenna species = in order to get even a rough idea of the repeatability of the = calibrations. The numbers reported in the ant_info.002 file are an = average of each of these individual calibrations. An example of this rms = repeatability is shown in Figure 5 for the 4 separate calibrations that = went into the averages for the TRM 22020.00 that was shown earlier. The = RMS repeatabilities of several mm in the up-offset and the PCV are = typical of most of the antennas that have been calibrated. NGS has also = calibrated 5 separate JPL D/M+crT antennas for comparison to the single = member of this model that is used as a reference for all calibrations. = These results are shown in Figure 6. Except for the north offset, the = average offsets and PCV for this group is within a fraction of a mm of = the reference antenna. The north offset is larger than the other offsets = but is on the order of the RMS. While this offset and RMS is comparable = to what is seen for most other antennas, it does seem large for what is = otherwise a very repeatable set of measurements for this class of = antenna.

Figure 4. This figure shows the = phase residuals for an antenna calibration as a function of elevation. = The phase variation is clearly evident. The solid curve is the = polynomial fit to these data and the dots indicate the elevation = increments used in the summary file.

 

Figure 5. The average calibration results = for the TRM 22020.00 are shown along with the rms repeatability for the = four measurements of this antenna that went into the average.

Figure 6. The average calibrations = for 5 separate JPL D/M+crT antennas relative to the JPL D/M+crT antenna = chosen as the reference antenna are shown.

 

Summary

 

GPS antennas are calibrated under somewhat = ideal conditions. These NGS in situ calibrations are performed at the = same site, at a consistent height, and on flat terrain with no = reflectors, other than the ground, that may cause unwanted multipath = reflections leading to azimuthal asymmetries. Users should always = remember that the conditions under which these calibrations were = determined are, hopefully, a reasonable approximation to the unique = circumstances for the antennas to which they are applied. Under ideal = circumstances, every antenna would be individually calibrated at its own = site. While this is possible and might be accomplished for permanent GPS = tracking sites, it is impractical for sites that are only infrequently = and briefly occupied.

An antenna calibration is an essential part of = doing the most precise GPS surveying possible. However, an antenna = calibration by itself is not a statement about the relative merits of = any particular model of antenna. All antennas have an average phase = center offset and a PCV with respect to an antenna reference point. It = is essential to know what these are, but knowing them says nothing about = whether an antenna is =91good=92 or =91bad=92 for any particular = application. This sort of evaluation would be the subject of a different = series of measurements. The most significant contribution of antenna = calibrations is ensuring interoperability within the growing community = of GPS antenna types.

All NGS antenna calibrations are performed relative = to a specific antenna and have been done under identical conditions. = These calibrations are a consistent set of measurements and it would not = be advisable to use the results from another source of calibrations with = these NGS or yet another source of calibrations. While calibrations may = be internally consistent within any given measurements scheme, different = calibration techniques have different sources of systematic error that = may not cancel out when using results from different schemes.

NGS, along with numerous other groups, has been = using these calibrations in its software and GPS processing for several = years already. These calibrations are available to other GPS users via = the world wide web at httpd://www.ngs.noaa.gov/GRD/GPS/Projects/ANTCAL/. The = web site contains the complete summary of all calibration results as = well as additional information about the antennas, including photographs = and engineering drawings to aid in identifying the correct antenna = offsets and the antenna reference points to which they refer. NGS will = continue its antenna calibration program to provide a consistent set of = reliable calibrations for all geodetic-quality GPS antennas.