GPS Receiver Test. Conducted by the Department of Mathematical Geodesy and Positioning Delft University of Technology

Transcription

1 GPS Receiver Test Conducted by the Department of Mathematical Geodesy and Positioning Delft University of Technology A. Amiri-Simkooei R. Kremers C. Tiberius May 24

2 Preface For the purpose of a receiver test, to be carried out by the Mathematical Geodesy and Positioning (MGP) section of TU Delft, under contract with Leica Geosystems AG based in Switzerland, two of Leica s latest GPS/GNSS receivers were provided, the Leica System GPS2. The receivers were tested, early Winter 23/24, in a typical reference station set up, at the GNSS observatory of the Department in Delft, and in a typical survey environment with both a zero and a short baseline to assess measurement performance. The results of these tests are documented in this report. AliReza Amiri-Simkooei Rien Kremers Christian Tiberius May 3rd, 24 Section of Mathematical Geodesy and Positioning (MGP) Delft University of Technology (TU Delft) Kluyverweg NL-2629 HS Delft The Netherlands 2

3 Table of Contents INTRODUCTION...4 DATA QUALITY Baseline Processing Least-Squares Residuals Time-Correlation of Phase Residuals Residual Statistics...7 DATA QUANTITY Integrity Monitoring Observation, Outlier and Slip Counts Code Standard Deviation Standard Deviation Versus Elevation and Azimuth...29 SUMMARY AND CONCLUSION...3 BIBLIOGRAPHY

4 Chapter Introduction The Leica System GPS2 is a new high-end dual-frequency GPS/GNSS receiver. In the sequel, for the sake of convenience, the receiver is simply called Leica GPS2. In order to obtain an impression of data quality and quantity about this new receiver, the section of Mathematical Geodesy and Positioning (MGP) has carried out a test at the end of December, 23 and in the beginning of January, 24. The Leica SR53 and Trimble 57 high-end GPS receivers were involved in the test for the purpose of benchmark. The equipment used in the test is displayed in figure.. All GPS receivers used in the test are dual-frequency GPS receivers with 2 channels. They provide code (pseudorange) and (carrier) phase observations both on L and L2 frequency, also under Anti-Spoofing. The observations on the second frequency are then obtained by so-called semi-codeless measurement techniques. The observation types will be indicated by the Rinex designation according to [Gurtner, 994]. They are C, P2, L and L2, for respectively the code and phase, on both frequencies. For each receiver the collected measurements have been converted into Rinex format, using manufactures proprietary converters. Figure.: From left to right, Leica SR53 receiver (top) and AT52 antenna (bottom), Trimble 57 receiver (top) and Zephyr antenna (bottom), and Leica GPS2 receiver (top) and AX22 antenna (bottom) involved in the test. The Leica GPS2 receiver has been tested on two aspects. The experiments and the results will be discussed in the following two chapters. The quality of the Leica GPS2 receiver observations is assessed in a field test with a comparison with the Leica SR53 and Trimble 57 receivers. Chapter 2 on data quality gives the results in terms of measurement precision. Chapter 3 is titled data quantity, and keywords are signal tracking and multipath-susceptibility. A long duration session was measured to infer how long and how well the receiver is capable of tracking the GPS satellites. 4

5 Chapter 2 Data Quality Zero and short baselines have been measured in the field, a flat meadow just outside the built-up area of Delft, 2.5 km southwest of the Geodesy building. Two receivers from each manufacturer (Leica SR53, Trimble 57 and Leica GPS2) were used to measure a zero and a -meter baseline. These measurements took place simultaneously for the three receiver-pairs, see figure 2.. The simultaneous time span of the short baseline test for the three receiver-pairs was from 2:25: to 3:44:59 (GPS time), Thursday, January 5 th, 24, and, from 2:25: to 3:44:59 (GPS time), Friday, January 6 th, 24, for the zero baseline test. Those data were collected at a -second interval with an elevation cut-off angle of 5 degrees. In a zero baseline test, two receivers are connected to the same antenna and low noise amplifier (LNA) with the help of a signal splitter. The test is conducted to examine receiver performance and give an impression of the observations noise characteristics, since all common errors, like those due to multipath, atmosphere, satellite orbits and clocks are eliminated in the GPS baseline processing. In the short baseline test, the receivers are operated with individual antennae like in a typical high accuracy GPS survey application, but the baseline is just meters long. Because the distance is extremely short, the atmospheric and orbits effects will cancel when processing the baseline data. Multipath effects will not be eliminated, however. These tests address the performance of the full system, antennas and receivers. They give us an impression of overall system performance including observation noise plus mitigation of multipath effects. Per manufacturer only receiver s own equipment was used. The purpose of this test is to achieve -- under favorable (but though operational) circumstances -- optimal measurement performance per receiver, independent from other equipment or existing infrastructure. Two receivers per manufacturer were employed to enable precise relative positioning, and to assess the quality of the precise phase observations. Figure 2.: The short baseline measurement set up in the field: three -meter baselines were set out 5 meters apart (three configurations). 5

6 2. Baseline Processing Both sessions of the three configurations in this experiment were static, but we processed the data by using a single epoch kinematic model [de Jong, 999; Tiberius, 999], which means that each epoch will have one baseline result calculated only from those observations of the epoch. Baseline components and differential receiver clock biases along with integer double difference ambiguities were estimated by least squares, in which the integer double difference ambiguities are determined by the LAMBDA method (LAMBDA, the Least-squares AMBiguity Decorrelation Adjustment, refer to [Teunissen, 993], [de Jonge and Tiberius, 996]). Per baseline, both L and L2 data were used in one straight combined processing. Figures 2.2 and 2.3 display the time series of kinematic positioning results for Leica GPS2 and Trimble 57, for zero and short baselines, respectively. Table 2. displays statistics to compare the data quality of all three types of receivers, for example, the standard deviations of short and zero baseline components and the means of the zero baseline components for the Leica SR53, Trimble 57 and Leica GPS2 receivers. Accordingly, the maximum and the minimum values of both zero and short baseline components are given in table 2.2. From these figures and tables 2. and 2.2, it is very clear that there is no significant difference on the mean value (bias) between all three receiver types, but there is a significant difference between Leica GPS2 and Trimble 57 on the zero baselines in the noise level. The noise level of the Leica GPS 2 sensor could have been reduced by introducing an automatically adaptive Phase Lock Loop bandwidth regulation. All three sensors can reach mm-level positioning precision even in the short baseline case, but the standard deviations of the Trimble 57 baselines both for the zero and for the short baselines are larger than those of the Leica GPS2 by.94 times to 2.2 times and by.9 times to.66 times, respectively. The standard deviations for the short baseline reflect the final coordinate precision of the systems neglecting atmospheric influences. Receiver Mean (mm) Standard Deviation (mm) Session East North Up East North Up Short Leica SR Baseline Trimble Leica GPS Leica SR Zero Trimble Baseline Leica GPS Table 2.: Mean and standard deviation statistic for two sessions (the mean of short baseline is excluded from the table, since the true values are not known) in local East, North and Up coordinate system. Receiver Max (mm) Min (mm) Session East North Up East North Up Short Leica SR Baseline Trimble Leica GPS Leica SR Zero Trimble Baseline Leica GPS Table 2.2: Maximum and minimum statistic for two sessions in local East, North and Up coordinate system (for short baseline they refer to their individual averages). 6

7 East Component (mm) North Component (mm) Up Component (mm) Epochs Epochs Epochs Figure 2.2: Time series of three components of Trimble 57 (in blue) and of Leica GPS2 (in red) zero baselines. East Component (mm) North Component (mm) Up Component (mm) Epochs Epochs Epochs Figure 2.3: Time series of three components of Trimble 57 (in blue) and of Leica GPS2 (in red) short baselines (offset by their individual averages). 7

8 2.2 Least-Squares Residuals For the processing of the residuals, in-house software, namely the RELRES program, was used [de Jong, 999]. The processing of the data is done epoch-by-epoch. We will analyze the least-squares single difference residuals of the adjustments. Under the working mathematical model, the residuals of the single difference observations are expected to have zero mean. The residuals represent the measurements noise and they show biases and anomalies when present. A similar analysis was made in [Bona and Tiberius, 2]. Note that in our analysis the a-priori standard deviation of the least-squares residual is constant and the same for all epochs and all channels (satellites), so that time-series of residuals later on can be mutually compared. In discussing the figures 2.4 through 2. we consider biases, trends and variations in the time series, and, apart from these, we make an attempt to quantify the width of the noise band, in order to present an indication on the nominal receiver noise. Before doing so, we address the issue of time correction. It should be kept in mind throughout this chapter, that in general, filtering or smoothing brings down the noise level, at the price of time correlation. Additionally, multipath in the short baseline may introduce time-correlation to the observations. 8

9 Zero Baseline, Leica SR53, PRN2, L 2 Zero Baseline, Leica SR53, PRN, L 2 Residual [mm] Residual [mm] Zero Baseline, Leica GPS2, PRN2, L Zero Baseline, Leica GPS2, PRN, L 2 Residual [mm] Residual [mm] Figure 2.4: Time series of least-squares residuals in zero baseline, for L phase, Leica SR53 (top), Leica GPS2 (bottom); high elevation satellite PRN2 (left) and low elevation satellite PRN (right). Zero Baseline, Trimble 57, PRN2, L 2 Zero Baseline, Trimble 57, PRN, L 2 Residual [mm] Residual [mm] Figure 2.5: Time series of least-squares residuals in zero baseline, for L phase, Trimble 57; high elevation satellite PRN2 (left) and low elevation satellite PRN (right). Figures show the time series of L and L2 phase residuals in zero baseline tests for a low elevation satellite (PRN) at right and a high elevation satellite (PRN2) at left, for the Leica SR53, GPS2 and Trimble 57 receivers. A simple comparison shows that the residuals (both for L and L2) of a low elevation satellite are generally noisier than those of a high elevation satellite. However, for Trimble 57, the difference is not very significant for L phase residuals. It is also obvious that the residuals of the L2 phase are noisier than those of the L phase, independent of the type of receivers used. 9

10 Zero Baseline, Leica SR53, PRN2, L2 2 Zero Baseline, Leica SR53, PRN, L2 2 Residual [mm] Residual [mm] Zero Baseline, Leica GPS2, PRN2, L Zero Baseline, Leica 2, PRN, L2 2 Residual [mm] Residual [mm] Figure 2.6: Time series of least-squares residuals in zero baseline, for L2 phase, Leica SR53 (top), Leica GPS2 (bottom); high elevation satellite PRN2 (left) and low elevation satellite PRN (right). Zero Baseline, Trimble 57, PRN2, L2 2 Zero Baseline, Trimble 57, PRN, L2 2 Residual [mm] Residual [mm] Figure 2.7: Time series of least-squares residuals in zero baseline, for L2 phase, Trimble 57; high elevation satellite PRN2 (left) and low elevation satellite PRN (right). The residuals of the Leica GPS2 receiver, on the zero baseline, (at both low and high elevation and for both L and L2 phase) seem to be less noisy than those of the Leica SR53 and the Trimble 57 receivers. Given the antenna, this is a good indication of the noise of the receiver.

11 Zero Baseline, Leica SR53, PRN2, C Zero Baseline, Leica SR53, PRN, C Residual [cm] 5 5 Residual [cm] Zero Baseline, Leica GPS2, PRN2, C Zero Baseline, Leica GPS2, PRN, C Residual [cm] 5 5 Residual [cm] Figure 2.8: Time series of least-squares residuals in zero baseline, for C code, Leica SR53 (top), Leica GPS2 (bottom); high elevation satellite PRN2 (left) and low elevation satellite PRN (right). Zero Baseline, Trimble 57, PRN2, C Zero Baseline, Trimble 57, PRN, C Residual [cm] 5 5 Residual [cm] Figure 2.9: Time series of least-squares residuals in zero baseline, for C code, Trimble 57; high elevation satellite PRN2 (left) and low elevation satellite PRN (right). Figures show the time series of C and P2 code residuals in the zero baseline test, for the low elevation satellite PRN (5º-º) and the high elevation satellite PRN2 (5º-7º), for the Leica SR53, GPS2 and Trimble 57 receivers. At epoch 2:29:3 (epoch 27 in figure at which we have a loss of lock), a small glitch in the residuals of the C and P2 (both at low and high elevation) can be seen for the Leica SR53 receiver. A simple comparison shows that the residuals (both for C and P2 codes) of a low elevation satellite are generally noisier than those of a high elevation satellite. As can be seen, the residuals of the P2 code are noisier than those of the C code, independent of the type of receivers used.

12 Zero Baseline, Leica SR53, PRN2, P2 Zero Baseline, Leica SR53, PRN, P2 Residual [cm] 5 5 Residual [cm] Zero Baseline, Leica GPS2, PRN2, P Zero Baseline, Leica GPS2, PRN, P2 Residual [cm] 5 5 Residual [cm] Figure 2.:Time series of least-squares residuals in zero baseline, for P2 code, Leica SR53 (top), Leica GPS2 (bottom); high elevation satellite PRN2 (left) and low elevation satellite PRN (right). Zero Baseline, Trimble 57, PRN2, P2 Zero Baseline, Trimble 57, PRN, P2 Residual [cm] 5 5 Residual [cm] Figure 2.:Time series of least-squares residuals in zero baseline, for P2 code, Trimble 57; high elevation satellite PRN2 (left) and low elevation satellite PRN (right). The residuals on code of the Trimble 57 receiver, (at both low and high elevation), to a large extent, seem to be (much) noisier than those of the Leica SR53 and the Leica GPS2 receivers. On the other hand, the residuals of the Trimble 57 show a more white-noise characteristic than those of the Leica SR53 and the Leica GPS2 for which a kind of smoothing and hence time correlation can be seen. Smoothing brings down the noise level at the price of time correlation. Thus, the noise level cannot be assessed without taking time correlation into account. 2

13 Satellite PRN2 Satellite PRN Type Receiver Std. (mm) Max. (mm) Min. (mm) Std. (mm) Max. (mm) Min. (mm) Leica SR L Trimble Leica GPS Leica SR L2 Trimble Leica GPS Leica SR C Trimble Leica GPS Leica SR P2 Trimble Leica GPS Table 2.3 : Standard deviation (std), maximum (max) and minimum (min) values of residuals (L, L2 C and P2) for a high (PRN2) and a low (PRN) elevation satellite, zero baseline, all in millimeters. Satellite PRN2 Satellite PRN Type Receiver Std. (mm) Max. (mm) Min. (mm) Std. (mm) Max. (mm) Min. (mm) Leica SR L Trimble Leica GPS Leica SR L2 Trimble Leica GPS Leica SR C Trimble Leica GPS Leica SR P2 Trimble Leica GPS Table 2.4 : Standard deviation (std), maximum (max) and minimum (min) values of residuals (L, L2, C and P2) for a high (PRN2) and a low (PRN) elevation satellite, short baseline, all in millimeters. The tables 2.3 and 2.4 present the minimum and maximum value of the least-squares residuals over the full hour 2 minutes period, for a high elevation satellite (PRN2) and a low elevation satellite (PRN), for each observation type. Also the standard deviation is given. From figures 2.4 to 2., we can obtain some comparative impressions not only on the Leica SR53, Leica GPS2 and the Trimble 57 receivers, but also different behavior on high elevation and low elevation satellites. These figures allow us to see the details, from which we can conclude at least: 3

14 ) The residuals of a high elevation satellite are generally less noisy than those of a low elevation satellite no matter which type of receivers, however, this conclusion is not very distinct in the case of the zero baseline. The reason has been given in the beginning of this chapter. 2) The residuals of the L phase observations are less noisy when compared to those of the L2 phase. 3) The residuals of the L and L2 phase for the Leica GPS2 receiver seem to be less noisy than those of the Leica SR53 and Trimble 57 receivers both on the short baseline and the zero baseline. Further numerical values for statistics on the residuals as mean, median and standard deviation per satellite (and hence elevation) are presented in section Time-Correlation of Phase Residuals Here we will investigate the common assumption with data processing, of observations possessing only white noise. That is, they are not correlated from epoch to epoch. We consider a correlogram of the time-series of the least-squares residual. The correlogram gives the auto-correlation coefficient versus lag (the interval between two samples). The coefficient at lag equals by definition. If the residual would be a white noise process, then all other coefficients should be about zero, otherwise, the residuals probably show the behavior of time correlation. Two aspects may cause time-correlation for the least-squares residuals: one is that the observations are quite noisy (e.g. because of the anti-spoofing encryption) so that some smoothing or filtering may be applied, while, the other one is that some time-correlation error resources, such as multipath effects, atmospheric delays, remain in the residuals after data processing. The latter (external) cause can generally be ruled out on zero baseline data. 4

15 Zero Baseline, Leica SR53, PRN2, L Zero Baseline, Leica SR53, PRN, L Correlation.5 Correlation Lags [s] Zero Baseline, Leica GPS2, PRN2, L Lags [s] Zero Baseline, Leica GPS2, PRN, L Correlation.5 Correlation Lags [s] Lags [s] Figure 2.2:Auto-correlation coefficient for L phase in zero baseline, Leica SR53 (top), Leica GPS2 (bottom); high elevation satellite PRN2 (left) and low elevation satellite PRN (right). Zero Baseline, Trimble 57, PRN2, L Zero Baseline, Trimble 57, PRN, L Correlation.5 Correlation Lags [s] Lags [s] Figure 2.3:Auto-correlation coefficient for L phase in zero baseline, Trimble 57, high elevation satellite PRN2 (left) and low elevation satellite PRN (right). Figures give the correlograms for L and L2 phase in the zero baseline case. It is very clear that the receiver noise of the Leica SR53 and the Trimble 57 L and L2 phase is all white noise, the conclusion can only be made for the Leica GPS2 L phase. The L2 phase shows some slight time correlation over a few (4-8) seconds. 5

16 Zero Baseline, Leica SR53, PRN2, L2 Zero Baseline, Leica SR53, PRN, L2 Correlation.5 Correlation Lags [s] Zero Baseline, Leica GPS2, PRN2, L Lags [s] Zero Baseline, Leica GPS2, PRN, L2 Correlation.5 Correlation Lags [s] Lags [s] Figure 2.4:Auto-correlation coefficient for L2 phase in zero baseline, Leica SR53 (top), Leica GPS2 (bottom); high elevation satellite PRN2 (left) and low elevation satellite PRN (right). Zero Baseline, Trimble 57, PRN2, L2 Zero Baseline, Trimble 57, PRN, L2 Correlation.5 Correlation Lags [s] Lags [s] Figure 2.5:Auto-correlation coefficient for L2 phase in zero baseline, Trimble 57, high elevation satellite PRN2 (left) and low elevation satellite PRN (right). 6

17 2.4 Residual Statistics Figures give us chances to investigate the details of the residual behavior. Here we need some general impression of those residuals. Figures 2.6 and 2.7 show the phase and code residual statistics for the Trimble 57 configuration, and figures 2.8 and 2.9 show those for the Leica GPS2 configuration, of respectively the zero and the short baseline. One type of observation residuals of all satellites during the measuring period is presented in one graph versus the individual means of the elevations. It is noted that the results presented pertain to single difference observations. Since not all satellites are available for the full 48 seconds time span, at least epochs have been used for each estimate. The statistics include the standard deviation (red circle), mean (blue plus) and median (black cross) per satellite. Mind that for some low elevation satellites, the actual marker may incidentally fall outside the graph (i.e. be beyond the range of the vertical axis). The mean of the residuals gives the central value of the probability distribution and identifies the long-term trend, and the standard deviation gives the variability of the distribution around the mean, while the difference of mean and median indicates that some outliers may hide in the data. It should be noted that the difference between the mean and the median can also occur because of some systematic effect in the observations (e.g. multipath). From figures , we would like to give the following summaries: ) The statistics of the residuals show further elevation dependence of the measurement noise. The figures may suggest a direct relation between elevation and measurement precision. The behavior can however be very different for different observation types and for different equipment. 2) Multipath, as a systematic effect, makes the precision of the measurements worse. This can simply be verified by comparing the residual statistics of the zero baseline with those of the short baseline. 3) The L-phase standard deviations seem to be better than those of the L2-phase, at both low and high elevation, for both the zero and the short baselines, and independent of the type of the receivers used. Also, in the zero baseline, L2-phase displays stronger elevation dependence than L. 4) It is very clear that the zero baseline shows a very good mean characteristic, the means of the residuals are close to zero. However, this conclusion cannot be made for the short baseline, since multipath introduces some systematic errors into the observations, especially those satellites at low elevation. The L and L2 phase of some low elevation satellites (below 2 degrees) for all short baseline sessions display a poor mean characteristic. 5) In general, there is no large difference between the mean and median above 2 degrees elevation; differences occur in particular for L- and L2-phase residuals of satellites PRN (elevation 9 degrees; azimuth 3 degrees), PRN (elevation 5 degrees; azimuth 37 degrees) and PRN8 (elevation 4 degrees; azimuth 35 degrees), for different receivers (short baseline session), which indicates that there may be some outliers in the observations; or there may be a serious multipath effect for these satellites. 6) For the zero baseline, the L and L2 phase observations of the Leica GPS2 configuration are generally better than those of the Trimble 57, especially at high elevation. That is, compared to the Trimble 57 zero baseline test, the Leica GPS2 shows lower receiver noise. 7) For the short baseline, the L and L2 phase observations of the Leica GPS2 and of the Trimble 57 behave more or less alike (see Table 2.4 for details). Differences are mainly due to the statistics of the residuals for satellites PRN, PRN and PRN8 (see item 5). 7

18 Zero Baseline, Trimble 57, L Zero Baseline, Trimble 57, L2 [mm] 5 [mm] Zero Baseline, Trimble 57, C Zero Baseline, Trimble 57, P [cm] 2 [cm] Figure 2.6:Residual statistics of zero baseline versus elevation for Trimble 57; o stands for standard deviation, + for mean and x for median. Short Baseline, Trimble 57, L Short Baseline, Trimble 57, L2 [mm] 5 [mm] Short Baseline, Trimble 57, C Short Baseline, Trimble 57, P [cm] 2 [cm] Figure 2.7:Residual statistics of short baseline versus elevation for Trimble 57; o stands for standard deviation, + for mean and x for median. 8

19 Zero Baseline, Leica GPS2, L Zero Baseline, Leica GPS2, L2 [mm] 5 [mm] Zero Baseline, Leica GPS2, C Zero Baseline, Leica GPS2, P [cm] 2 [cm] Figure 2.8:Residual statistics of zero baseline versus elevation for Leica GPS2; o stands for standard deviation, + for mean and x for median. Short Baseline, Leica GPS2, L Short Baseline, Leica GPS2, L2 [mm] 5 [mm] Short Baseline, Leica GPS2, C Short Baseline, Leica GPS2, P [cm] 2 [cm] Figure 2.9:Residual statistics of short baseline versus elevation for Leica GPS2; o stands for standard deviation, + for mean and x for median. 9

20 We have investigated the details of the residual behavior, the estimated statistics of observations per satellite and the time-correlation of the observation residuals as well. Here we focus on the non-diagonal elements of the single difference observations variance-covariance, the covariances between different GPS observation types. From the variances and covariances, one can compute the empirical correlation coefficient, which can explore the crosscorrelation relationship between different GPS observation types [Tiberius and Kenselaar, 23]. To be allowed to use only one single variance value for all channels / satellites, we here restrict our computations to the residuals of only two satellites PRN2 and PRN6, both with elevations larger than 45 in the case of the zero baseline. Tables 2.5, 2.6 and 2.7 give on the diagonal the standard deviation in terms of the single differenced code and phase observation, and the correlation coefficients as the off-diagonal elements for Leica SR53, Trimble 57 and Leica GPS2, respectively. From the tables, it can be seen that the estimated standard deviations quite well agree with those obtained in the preceding of this section for the higher elevation satellites (Fig. 2.6 and Fig. 2.8). Moreover, there is a significant correlation between the observations on the frequencies, i.e., between the L and L2 phase for all receivers. The values are comparable between the SR53 and the GPS2 (.4 and.47, respectively). The correlation for the Trimble 57 is larger (.68), demonstrating a larger dependence between the two carrier phases. The structure of the variance-covariance matrix for the cross-correlation measurement technique, employed by the receiver to get around the Anti-Spoofing encryption, was suggested in Teunissen et al. (998). Code / Phase L L2 C P2 L.7 mm L mm C cm -. P cm Table 2.5: Estimated variances and covariances in terms of standard deviation per observation type and of correlation coefficient between observation types for Leica SR53 in the case of zero baseline. Code / Phase L L2 C P2 L.3 mm L mm C cm.6 P cm Table 2.6: Estimated variances and covariances in terms of standard deviation per observation type and of correlation coefficient between observation types for Trimble 57 in the case of zero baseline. Code / Phase L L2 C P2 L.4 mm.47.. L mm..3 C cm.7 P cm Table 2.7: Estimated variances and covariances in terms of standard deviation per observation type and of correlation coefficient between observation types for Leica GPS2 in the case of zero baseline. 2

21 Chapter 3 Data Quantity A Leica GPS2 high-end GPS/GNSS receiver was set up to measure for a full 24 hours period on the roof of the Geodesy building, see figure 3.. The antenna was installed at point 23. The measurements were collected at a second interval and with a satellite elevation cut-off angle. The purpose is to collect as many as possible observations, to all visible satellites, in principle from horizon to horizon. The results will be compared to those obtained for a Leica SR53 receiver as well as a Trimble 57 receiver at exactly the same location. To keep approximately the same configuration for the satellites geometry, the observations have been collected 3 minutes and 56 seconds earlier each day. Table 3. gives the types of receivers and the types of antenna as well as the starting time for each experiment. Receiver Type Antenna Type Date Start Time Duration Unusable Sat. Leica SR53 AT52 6 Dec. 23 5:5: 24 hour PRN 22 Trimble 57 Zephyr 3 Dec. 23 4:9:56 24 hour PRN 22 Leica GPS2 AX22 Jan. 24 3:32:44 24 hour PRN 22, 23 Table 3. List of high-end receivers and antennas used in experiment as well as the date, starting time and duration of data collection. High-end GPS receivers may be used as permanent reference station, so continuity of operation is important (i.e. operation without any interruption by malfunctioning). In this test, only a first very preliminary impression is obtained, since 24 hours is quite a limited period of time. During the test, as indicated in table 3., one (and sometimes two) satellite(s), namely PRN 22 and PRN 23, were unusable, according to the USNO (United States Naval Observatory) notice. We did not collect any observations of these unusable satellites, though the navigation messages were present in the data files. That is, for Leica SR53 and Trimble 57 receivers the data were collected to 28 satellites and for the Leica GPS2 to 27 satellites. Figure 3.: The sites on the roof of the Geodesy building; point 23 is the mast (triangle) next to the stairs 2

22 3. Integrity Monitoring The 24-hour data are processed and analysed with the integrity monitoring software [de Jong, 997] developed at the Department. Data analysis is possible on the observations of a single receiver to a single satellite. The integrity monitoring software aims at detecting in real-time outliers and slips in dual frequency data. For the present analysis, a post-processing version of the software is used. The integrity monitoring software can provide the following statistics per satellite counts of the number of complete observation epochs an epoch is complete if all code (C and P2) and phase (L and L2) observations to a satellite are available counts of the number of incomplete observation epochs an epoch is incomplete if some or all of the code and phase observations to a satellite are missing (or when a full observation epoch is missing) counts of the number of outliers in the C and P2 code observations theoretically the software is able to detect outliers of approximately 4 times the a-priori code standard deviation, which is fixed at.75 m counts of the number of slips in the L and L2 phase observations theoretically the software is able to detect slips of even cycle estimates of the standard deviation of the C and P2 code observations the standard deviations are estimated from linear combinations of code and phase observations The linear combinations, Mc and Mp2, of observations read + α 2 = C+ L α α M C L 2α + α = P2 + L α α M P 2 L 2 2 with α = f f 2 the ratio of the two GPS carrier frequencies, squared, and all observations C, P2, L and L2 have been expressed in meters. The geometric range to the satellite, the atmospheric delays and the clock errors are absent in these combinations. Present are the carrier phase ambiguities (of L and L2), but they are constants. These so-called multipath combinations are free from time-varying effects and should thus be constants, apart from noise on the observations. The noise of the code (pseudorange) will thereby dominate. The combinations Mc and Mp2 give an impression of the measurement precision of the code (C or P2) and possibly of multipath effects. In the sequel, three analyses are performed, based on the statistics provided by the integrity monitoring software: counts of observation epochs, and of outliers and slips code standard deviation, as function of elevation code standard deviation, as function of elevation and azimuth

23 3.2 Observation, Outlier and Slip Counts In this section we consider the counts of observation epochs, both complete and incomplete, and of outliers and slips. The counts are accumulated over the full 24 hours period and over all available GPS satellites for each experiment. A relation will be laid with the satellite elevation, as receivers performances are known to depend on this parameter; the counts are binned over 5 degrees elevation intervals. Table 3.2 presents the observation counts. In theory, the total number of expected observations can be computed from the satellites visible (above the horizon). In the Netherlands, on average, a satellite is visible for about 9 hours. The expected numbers are thus computed using simple geometry and based on the available almanac files at U.S. Coast Guard navigation center website. The expected total would be 2492 or if all 28 or 27 satellites would be permanently visible: (28 or 27) It should be noted that the three receivers used in this study have 2 channels to track the satellites. But for some special time-spans it is possible to observe more satellites than 2 in the Netherlands with the present overpopulated GPS constellation. Thus, the expected values presented in Table 3.2 have been corrected for extra satellites. Receiver Type Count Percentage Expected Complete Incomplete Complete Incomplete Leica SR Trimble Leica GPS Table 3.2. Data availability: counts in terms of complete and incomplete observation epochs accumulated over 24 hours and all 27 or 28 satellites; absolute figures and relative, as percentages. The counts realized are presented as absolute figures and relative as percentages. The counts on complete epochs are referred to the expected total, those on incomplete epochs to the total of observed epochs (thus the sum of complete and incomplete epochs together). A late start and an early ending of the tracking primarily cause the difference between expected and complete observation epochs; the satellite first has to rise somewhat from the horizon in order to pick up the signal, and the signal is already lost before the satellite reaches the horizon. The incomplete epochs are caused by tracking interruptions (on one or both frequencies; during a satellite pass). The number of complete epochs (percentage) for Trimble 57 and Leica GPS2 are 98.77% and 98.63%, which are quite comparable. On the other hand, the Leica GPS2 receiver when compared to its previous version, i.e. Leica SR53, is improved for data collection (about.%). In addition to table 3.2, the numbers of complete and incomplete epochs deserve some elaboration. These numbers, as function of the elevation angle, are given in figures 3.2 and 3.3. The vertical axes in these figures (top) range from to %. It can be seen that the receivers fail to track the satellites in particular in the first interval from to 5 degrees elevation. Satellite tracking above degrees seems to be no problem (all complete epochs). A comparison between these two figures shows that the Leica GPS2 and Trimble 57 receivers behave more or less similarly for the complete epochs. The difference in between -5 degrees elevation angle is mainly due to the fact that for the Leica receiver we have 27 satellites whereas for Trimble 28. When 28 satellites are available, the chance to have more satellites than 2 is larger than when we have only 27 satellites. Because it is not possible to allocate the additional observations to specific satellite(s) and/or elevation angles, the expected values used to plot Figures 3.2 and 3.3 are not accounted for this effect. On the other hand, since the satellite tracking above degrees seems to be no problem, one can allocate the number of missed epochs to the interval of - degrees and especially to the interval of -5 degrees. Actually for the Trimble receiver (with 28 satellites), 839 observation epochs were missed, whereas for the Leica (with 27 satellites) 432 epochs. 23

24 The graphs at bottom on incomplete epochs reveal some data loss at low elevations. Note that the vertical axes range here from to %, so the rate of incomplete data is rather small. The incomplete epochs are caused at low elevation angles (mainly between -5 degrees). A comparison between Figures 3.2 and 3.3 shows that the Trimble 57 and the Leica GPS2 receivers lose approximately 2% and 5% of the data (as incomplete ones) in the -5 degrees elevation angle interval. Since the total number of complete epochs for both receivers in this interval looks the same, this may mean that the total number of observed (both complete and incomplete) epochs for the Leica receiver is larger than for the Trimble receiver. This can also be verified from the results presented in Table 3.2. Tables 3.3 and 3.4 give the number of outliers, for the C and P2 code observations with a degree and degrees satellite elevation cut-off angle, respectively. As can be seen from table 3.3, the outlier percentages of code observations, in general, are quite low. The C code has approximately outliers, which is negligible. A little bit larger number for the P2 code is explained by the fact that the a-priori standard deviation for the code was set to.75 m, and the P2 code shows a somewhat larger standard deviation at low elevation, which can also be seen from figures 3.4 and 3.5. Table 3.4 implies that most of the outliers (perhaps more than 9%) on C and P2 code happen in the low elevation range (- degrees). However, this conclusion is not very distinct on P2 code for Trimble 57. Tables 3.5 and 3.6 present the number of slips, for both the L and L2 phase observations with a -degree and - degrees satellite elevation cut-off angle, respectively. As can be seen from table 3.5, the number of L cycle slips almost equals the number of L2 cycle slips; it turns out that cycle slips on L and L2 occur usually simultaneously with these receivers. In general the number of cycle slips is rather limited. Table 3.6 implies that most of the slips on L and L2 phase happens in the low elevation range (- degrees). The numbers of outliers and slips under the header percentage both in table 3.3 and table 3.5 have been referenced each time to the number of complete epochs (in table 3.2). For tables 3.4 and 3.6, the number of complete epochs has been adapted to reflect the -degrees elevation cut-off angle. The number of complete epochs for Trimble 57 and Leica GPS2 is and It should be concluded that with larger data availability (i.e., in particular at low elevation) outlier and slips become more likely to occur. Receiver Type Count Percentage C Code P2 Code C Code P2 Code Trimble Leica GPS Table 3.3: Outlier counts on C and P2 code, absolute figures and relative, as percentages of the number of complete epochs, with degree elevation cut-off angle. Receiver Type Count Percentage C Code P2 Code C Code P2 Code Trimble Leica GPS Table 3.4 Outlier counts on C and P2 code, absolute figures and relative, as percentages of the number of complete epochs, with degrees elevation cut-off angle. 24

25 Number of complete epochs as % number of expected epochs 8 Percent Elevation of satellites (5 deg interval) Number of incomplete epochs as % number of observed epochs 8 Percent Elevation of satellites (5 deg interval) Figure 3.2: Data collection by receiver Trimble 57; number of complete epochs as percentage of the number of expected epochs, binned after elevation (top); number of incomplete epochs as percentage of the number of observed epochs, binned after elevation (bottom). Number of complete epochs as % number of expected epochs 8 Percent Elevation of satellites (5 deg interval) Number of incomplete epochs as % number of observed epochs 8 Percent Elevation of satellites (5 deg interval) Figure 3.3: Data collection by receiver Leica GPS2; number of complete epochs as percentage of the number of expected epochs, binned after elevation (top); number of incomplete epochs as percentage of the number of observed epochs, binned after elevation (bottom). 25

26 Receiver Type Count Percentage L Phase L2 Phase L Phase L2 Phase Trimble Leica GPS Table 3.5: Slip counts on L and L2 phase, absolute figures and relative, as percentages of the complete epochs, with degree elevation cut-off angle. Receiver Type Count Percentage L Phase L2 Phase L Phase L2 Phase Trimble Leica GPS Table 3.6 Slip counts on L and L2 phase, absolute figures and relative, as percentages of the complete epochs, with degrees elevation cut-off angle. 3.3 Code Standard Deviation This section presents estimates of the standard deviation of the code observation (undifferenced), as function of the satellite elevation. Observation noise is known to depend strongly on the satellite elevation. By the antenna gain pattern, the atmospheric path length and multipath, the quality of the observations will generally degrade with decreasing elevation. Figures 3.4 and 3.5 give the estimates for the standard deviation of the C and P2 code observations of the Trimble 57 and Leica GPS2 receivers. The standard deviations for the code observations are computed for 5 minutes time intervals, per satellite. They are plotted as a function of the elevation angle (mean value over the 5 minutes period). The dependence of the noise on the satellite elevation is evident for all code observations. And at the lowest elevation angles, the standard deviation estimates are, in most cases, suddenly smaller than that of neighboring low elevation angles. This is probably related to the data loss below 5 degrees. For the Trimble 57 receiver, the standard deviation of multipath combinations for C and P2 code observations comes down to.-.2 m at high elevations. For C code, it hardly exceeds.8 m at low elevation and it does not get better than.4 m. The general standard deviation estimated from all multipath combinations is.32 m. For P2 code, the standard deviation of multipath combination hardly exceeds. m at low elevation and it does not get better than.3 m. The general standard deviation estimated from all multipath combinations is.33 m. 26

27 .8 C code standard deviation estimates vs. elevation.8 P2 code standard deviation estimates vs. elevation Standard deviation [m] Standard deviation [m] Figure 3.4: Estimated standard deviation in meter for multipath combinations MC (left) and MP2 (right); Trimble 57 receiver..8 C code standard deviation estimates vs. elevation.8 P2 code standard deviation estimates vs. elevation Standard deviation [m] Standard deviation [m] Figure 3.5: Estimated standard deviation in meter for multipath combinations MC (left) and MP2 (right); Leica GPS2 receiver. For the Leica GPS2, the standard deviation of multipath combinations for C and P2 code observations comes down to.5 m at high elevations and it hardly exceeds.2 m at low elevation. It can get better than.2 m and.3 m at low elevation for C and P2, respectively. The general standard deviation estimated from all multipath combinations is.7 m and.2 m for C and P2 code, respectively. In the following we consider time series of the multipath combinations themselves. Figures 3.6 and 3.7 show the multipath combinations for one pass of satellite PRN 3. The horizontal axes represent 6 hours and 27 minutes. The solid green lines give the elevation angle, with the scale along the vertical axes at right. As can be seen from the figures, the C codes in blue are nearly as noisy as P2 codes in red for all receivers. Figure 3.6 shows the multipath combinations for the Trimble 57 receiver. The variation for both C and P2 covers 2 m at low elevation, and just within m at high elevation. As we mentioned before, the C and P2 code behave similarly, however, the P2 code (in red) seems to be a little bit noisier than the C code (in green). Both of them, to some extent, are stable at the high elevation. The two multipath combinations give the impression that the time series are more or less like a random series, which may imply independence of neighboring observations. It seems that both receiver noise and multipath errors exist in this time series and the former plays the main role in this combination. 27

28 Figure 3.7 shows the multipath combinations for the Leica GPS2 receiver. The variation for both C and P2 is within m at low elevation, and within.5 m at high elevation. The P2 code seems to be a little bit noisier than the C code. Both of them are quite stable at the high elevation. The time series of the multipath combination here cannot be interpreted as a random series from one sample to the next. A kind of smoothing and hence correlation between the observation epochs can be observed. As long as the receiver can bring down the noise level well, this correlation can be expected because of multipath. That is, for the Leica receiver, it seems also that both receiver noise and multipath error exist in this multipath combination, but the latter plays the main role. 2 Multipath combination for a single pass satellite (c) 9 MP2 [m] MC [m] Elevation angle [deg] Time [sec] Figure 3.6. Multipath combinations MC (top, offset by the mean) and MP2 (bottom, offset by the mean with adding 3 m) as a function of time for a single pass of satellite PRN 3; Trimble 57 receiver. x 4 2 Multipath combination for a single pass satellite (a) 9 MP2 [m] MC [m] Elevation angle [deg] Time [sec] x 4 Figure 3.7. Multipath combinations MC (top, offset by the mean) and MP2 (bottom, offset by the mean with adding 3 m) as functions of time for a single pass of satellite PRN 3; Leica GPS2 receiver. 28

29 3.4 Standard Deviation Versus Elevation and Azimuth Multipath effects depend on the receiver-satellite geometry. These effects may induce both an elevation and azimuth dependence on the statistics. The test location, point 23 on the mast is depicted in figure 3.8. The observation platform is to the left of this mast (mainly North). In figure 3. point 23 is the mast (triangle) in the middle, next to the stairs. In order to get an impression of the severity of the multipath conditions on the test location, standard deviations for the code observations are computed for fixed 5 minutes time intervals and plot as a function of both satellite azimuth and elevation, for C and P2 code observations for three experiments. In other words, we have plotted Figures 3.4 and 3.5 not only in terms of elevation angles but now also in terms of azimuth for each satellite. Figures 3.9 and 3. show the results. The same color bar, for both sky plots, has been used to make the comparison simple. These graphs require careful inspection, as the differences are small. If little or no multipath effects are present at a site, the estimates can be expected to be scattered more or less random over the skyplot (at least for similar elevation angles). If, on the other hand, multipath is playing a significant role, the best and worst estimates will show an uneven distribution, i.e. a dependence on azimuth. This is the case for both C and P2 code observations in Figures 3.9 and 3.. Figure 3.8: The AX22 antenna on the top of the mast (point 23) on the roof of the Geodesy building; X = m, Y = m, Z = m (ITRF 2 at epoch 24.). The site is at 52 degrees latitude North. 29

30 North.4.3 North West East.7.6 West East South. South. Figure 3.9: Code standard deviation estimates versus elevation and azimuth for C (left) and P2 (right). Trimble 57 receiver. North.4.3 North West East.7.6 West East South. South. Figure 3.: Code standard deviation estimates versus elevation and azimuth for C (left) and P2 (right); Leica GPS2. The worst estimates, the red, yellow, and probably green dots, are mainly concentrated in the North-East, i.e., the direction to the roof of the observatory, see Figure 3.. The North-West direction yields observations with relatively less noise than that in the North-East direction. As such, the experiment turned out to be highly repeatable, and the azimuth-elevation multipath plots give a multipath footprint of the site on the Geodesy building. This analysis can serve as a multipath source locator. For the Trimble 57 receiver, Figure 3.9 shows the results. The worst estimates for both C and P2 are concentrated in the North-East direction. In this direction, the standard deviation of C code seems to be a little bit better than that of P2 code. As can be seen, for both code observations, in general, the standard deviation estimates get larger at low elevation. For the Leica GPS2 receiver, Figure 3. shows the results. The worst estimates for both C and P2 are again concentrated in the North-East direction. In this direction, the standard deviation of C and P2 codes seems to be more or less the same. As can be seen, for both code observations, in general, the standard deviation estimates do not get very much larger at low elevation (cf. Figure 3.9). That is, from this standpoint, at lower elevation angle, the Leica GPS2 receiver has a better performance than the Trimble 57 receiver. 3