The Effect of TLS Radome on GNSS Precise Positioning

This article presents the results of a test carried out to check the usability of spherical TLS targets as GNSS antenna radomes (herein called TLS radomes). On different days, the survey was conducted using two GNSS antennas, one of them with a TLS radome. Measurements were made using 2 roof pillars on the rooftop as base-rover pillars with little obstruction. The measurements were carried out for approximately 1 hour in every scenario. The software used for data processing is MATLAB-based software and the raw data were processed using the double difference (DD) strategy to obtain optimal results. The results of the data processing indicated that the TLS radome has no significant influence on availability and accuracy of estimated position. The signals are slightly attenuated by the radome (1-2 dBHz) and the noise level is slightly increased but both effects are negligible for practical purposes. However, we found that the antenna should be calibrated with the TLS radome to clarify apparent minor phase center eccentricities (1-2 mm) and to reduce systematic effects with long periods (few minutes) and amplitudes up to about 5 mm which are likely due to phase center variations.


Introduction
Use The use of TLS targets is required for absolute orientation of point clouds obtained by laser scanning. It is particularly important for change monitoring where such targets can be used to establish the connection to a well-defined datum. The experiment presented herein is based on the idea of mounting a GNSS antenna inside a TLS target so that its position can be determined precisely while scanning. The spherical TLS target resembles an antenna radome. Therefore we will call it"TLS radome" within this report. The experiments were carried out at the rooftop for collecting the data. The purpose of the observations is to determine the effects of the TLS radome on the positioning. In particular we want to clarify 1. whether GNSS positioning is possible using the TLS radome (signal reception sufficient); 2. whether the TLS radome increases the noise level of the raw observations and the computed positions (P3 and P5), and lastly, 3. whether there are any systematic effects on the antenna phase center and phase center variation requiring calibration.
Two pillars were selected for use because they have little obstruction (P3, P5). Observations were carried out on 4 days and during periods with approximately equal satellite geometry.
For scenario 1 of the experiment, we used two NovAtel 702GG antennas, one without any modification and one mounted inside the TLS radome but without the top half of the radome. We put the GNSS antenna with the half open TLS radome on pillar P5 as a rover and the other one as base on pillar P3. Then, for scenario 2, data were collected using a closed TLS radome on P5 and the same antenna as before on P3. For scenario 3, we swapped the position of both devices such that the closed TLS radome was now on the base pillar located with fixed coordinates and the antenna without TLS radome is the rover. And lastly, we measured without any TLS radome and compared the results to those of the other scenarios.
The processing was carried out using in Matlab and the measurement data were taken from download in the rinex form. Satellite orbits were retrieved from the IGS server. Antenna phase center data were retrieved from NGS. In this article it is assumed that the reader has a basic understanding of GNSS and GNSS data processing.

Measurement Equipment
Measurements were made using the same equipment and sites in the four scenarios with four days of measurement, as outlined below in table 2.1 and figure 2.1   The measurement data and the required auxiliary data are as given in table 2.2. This article investigates the relative positioning performance. In general, the observed data from satellites can be defined as follows [1]: (2) where Pi and Li are pseudorange and carrier phase range on selected frequency (i =1,2), ρ is related to geometrical range from receiver to satellite, dρ is the orbital error, dtrop and dion are troposphere and ionosphere biases, c is the speed of light (299,729,458 m/s), dt and dT are time error of receiver and satellites, MPi and MLi are related to multipath error of pseudorange and carrier phase range, λi and Ni are related to wavelength and ambiguity number, while ϑPi and ϑLi are related to noise error.

Relative Positioning
The performance of relative positioning were analyzed by using double difference (DD) positioning using carrier phase range that constructed by differencing two single difference (SD) observation. SD can be described as follows: where Δ is the difference between receivers A and B. The superscript -j is the observed satellite. The satellite clock error is eliminated by taking single difference between receivers that observed the same satellite, while the atmospheric biases like tropospheric and ionospheric may be eliminated depending to the length of the baseline. Multipath would be considered as a noise error that could not be eliminated.
The remaining receiver clock error is then eliminated by subtracting two single difference observation. Mathematically, a DD is defined as follows [2] [6]: (4) where the two satellites are denoted as he superscript-j and k. The atmospheric biases are negligible in Eq. 3, however the noise error is multiplied up to two times with respect to SD. The processing strategy was designed as follow:  The following calculations were carried out using data from observation, i.e. 1 hour of observation Rinex data 1 second sampling rate.
Calculations were also carried out with Glonass signals (if available) during similar observation periods in equal satellite geometry. Integer ambiguities are estimated and resolved on an epoch-by-epoch basis in kinematic positioning mode.
 The initial scenario assumes all the observations are processed in difference mode. Hence, the atmospheric errors and clock errors are almost canceling. To create a scenario with different radome, the data were sorted out by the stations to arrange the conditions required. As the local time and the location of the test are essentially affecting the results due to variations in the ionosphere and troposphere activity, calculations of the measurement effect on same time window sessions were performed.
 Mask angles of ten degrees were selected. The receiver noise level was neglected, and when required, IGS precise orbit corrections were used. Tropospheric effects are also independent of frequency. Hence a Saastamoinen model was used as the standard model correction [3].
 Furthermore, the observations were grouped in short-term observations (less than and equal to 60 minutes) for positioning in particular to study with the impact of temporal variability for static and kinematic positioning.
 Additionally, since most observation data covers satellites with low elevation angles, observation to satellites which are below 10 degrees are removed to minimize the influence of errors in the data processing.
 The distance between base and rover was under 50 meters. By using this short baseline, the atmospheric errors are assumed to be eliminated.
 The LAMBDA ambiguity resolution search was used to estimate the carrier phase ambiguities [8]. The final solution was the combined (Forward + Backward filter).  The figure shows that there is slightly more high-frequency noise with closed TLS radome than using the half-open one. However, when computing the standard deviation of the kinematic coordinates, the lowfrequency noise which is the effect of multipath interference and phase center variations dominates [5], [7], [9]. The level of these low-frequency components is not changed when the TLS radome is closed, see table 3.1. We conclude that there is no significant effect of the top half of the TLS target on the quality of the estimated position in case the position is determined from static processing of several minutes of data.

Results
On the other hand, the time series exhibit equal noise level of both high-and low-frequency contributions before and after swapping the antennas i.e., for scenarios 2 and 3. This is expected. However, we also note that there is a mirrored systematic error pattern ( figure 3.2). This is an indication of systematic errors due to unmodelled phase center variations. Since phase center variations of the employed Novatel GPS antennas were used we interpret this as an effect of the TLS radome on the phase center variations. From figure 3.2, we discovered that scenario 2 and 3 yield equal noise levels and but opposite sign of the systematic pattern. Any mean phase center difference ∆p between antenna w/ and w/o TLS radome would cause a difference of magnitude 2|∆p| of the estimated coordinates before and after antenna swap. In this experiment (see table 3.2) the median values only differ by 1.6 mm (N), 3.5 mm (E), and 1.1 mm (U). So, the phase center eccentricity is most likely affected by less than 2 mm by the TLS radome.    figure 3.2 that the precision is approximately equal for all different scenarios. In particular, is the standard deviation is 1.6 mm (N), 1.0 mm (E), and 1.5 mm (Up). However, the coordinates differ by up to 3.5 mm between the scenarios. Based on the respective empirical standard deviations, these differences are not significant. The duration of the test measurements is too short in order to clarify whether these differences are actually random deviations or are due to phase center eccentricities and systematic effects caused by the TLS radome. Even if they are systematic and due to the TLS radome the effects are small (less than 2 mm in mean phase center) and may be negligible for the intended application (if the effects are equal for all TLS radomes used within the network). However, it would be appropriate to carry out a proper antenna calibration using a TLS radome in order to further clarify this point.

Conclusion
The use of the TLS radome for GPS measurements slightly attenuates the signals (approximately 1-2 dBHz). However, this effect is small and does not impair the availability of GPS position solutions. GPS positioning is possible using this TLS radome and standard GPS data processing.
The precision obtained for kinematic positions in the different scenarios is about 1.6 mm (N), 1.0 mm (E), 1.5 mm (U) for all scenarios. Using the TLS radome does not significantly increase the noise level of the coordinates when processing data in static or short-term static mode (at least a few minutes of data).
We found mirrored systematic error patterns when swapping the antennas with and without TLS radome. The error patterns have a magnitude of up to 5 mm. The median coordinates over 1 hour changed by less than 4 mm between the scenarios. All this indicates that there may be a systematic effect of the TLS radome on mean phase center and on phase center variation on the mmlevel. Given this order of magnitude, these effects would be negligible for the proposed application if the same TLS radome/GPS antenna were always used on the same network sites, the GPS antennas and radomes were always oriented equally, and GPS positions were derived from static or short-term static sessions only.
However, this may not be feasible from a practical point of view, and it is not possible to predict whether or not different TLS radomes would cause the same phase center eccentricities and variations as the radome used herein. Thus, we propose to calibrate 2-3 GPS antennas with TLS radome in oder to find out, whether these effects are actually systematic and predictable across different samples or not. The results of such a calibration (in particular: repeatability of parameters for the same antenna/radome, repeatability across antennas/radomes, order of magnitude of parameters) will allow selecting an appropriate site setup and data processing scheme.
Should the design of the TLS radome be changed, e.g. by selecting a different TLS target shape/size or material, or by coating the target for modified optical reflectivity, a test resembling scenario 2 and 3 of the experiments covered herein (i.e., static processing with antenna swap) should be carried out to quickly assess the impact. The corresponding data processing can be carried out using standard GPS post-processing software like Leica GeoOffice, Trimble Business Center, or others.