Keywords

1 Introduction

Over the last 10 years, a number of on-line positioning services have been developed to allow the public to submit GPS data from user stations and receive coordinates usually by email (Ghoddousi-Fard and Dare 2006). These include the OPUS service operated by the US National Geodetic Survey (Snay and Soler 2008) using NGS’s PAGES softwareFootnote 1 and the CRS-PPP operated by Natural Resources Canada using Precise Point Positioning technique.Footnote 2 Currently AUSPOSFootnote 3 run by Geoscience Australia is the only Southern Hemisphere service. AUSPOS has limitations for New Zealand users as it produces coordinates at the epoch of observation in the ITRF2008 reference frame and not in NZGD2000, New Zealand’s national datum, and does not incorporate all of the PositioNZ CORS network.

This paper describes progress in the development of a GPS processing engine for New Zealand (NZ) using the PositioNZ CORS network. PositioNZ-PP is under development by LINZ (Palmer 2010). It is an on-line GPS processing application that processes NZ user supplied GPS data observed in ‘static’ mode using reference stations of the PositioNZ CORS network (Collett 2010). While PositioNZ stations record both GPS and GLONASS, PositioNZ-PP currently only uses the GPS. We hope to incorporate other GNSS data later. When fully deployed, the data will be processed automatically using Bernese GPS software (Dach et al 2007) and the coordinates will be transformed into NZGD2000 datum. Development of the GPS processing engine is basically complete, the user interface is under development and the Station Coordinate Prediction Model and the New Zealand Deformation Model (each of which corrects coordinates for crustal deformation) are currently being upgraded to incorporate recent earthquakes in New Zealand. It is planned that the system will be ready for deployment during 2014.

2 Description of the GPS Processing Procedure

The process starts with a RINEX file submitted by a user through the LINZ web page. The antenna type and height are taken initially from the RINEX file header but the web interface allows users to check the values and ensure that these are accurate. The program then performs some quality assurance tests on the data, determines rough initial coordinates for the stations and identifies three suitable PositioNZ reference stations to use as control stations. It then uses a mathematical model to predict ITRF coordinates for the reference stations at the time the user submitted RINEX file was observed. These coordinates are used as a priori coordinates for the GPS processing and as control for the ITRF coordinates for the user station that are determined in a network adjustment. Once the processing is complete, the final ITRF coordinates are converted to NZGD 2000. Key steps in this process are described in more detail below.

3 Pre-processing User File

The user file is checked by the UNAVCO supported GPS RINEXing and quality assurance program TEQCFootnote 4 (Estey and Meertens 1999). During this step the program determines the time interval spanned by the observations and performs some quality assurance tests to confirm that the observation ratio is at least 95% and the maximum multipath index is less than 2. In addition this step confirms that the file contains at least 120 epochs (i.e. at least 1 h of data at a 30-s rate) of observations and that the maximum duration of the file is less than 48 h. If any of these requirements are not met, the file is rejected. The approximate position is also extracted from the RINEX file at this stage and is used for the PositioNZ reference station ranking procedure discussed below. The next step is to identify and acquire the best available precise orbit files. The program will use the final, rapid or ultra-rapid orbit depending on file availability when the job is processed.

4 Selection of Reference Stations

The next step in the PositioNZ-PP workflow is to identify three reference stations among the 38 PositioNZ sites (see Fig. 1 for a map showing the location of the sites). Normally GPS on-line positioning services select reference stations based on minimizing the distance to the user’s station (Ghoddousi-Fard and Dare 2006). PositioNZ-PP uses two parameters. The first, and most important, is the length of the baseline between the user’s station (the coordinate associated from the submitted RINEX file) and the candidate reference station. The length is the distance between the two positions calculated from the difference in their geocentric coordinates; however, the parameter that goes into the weighting is a percentage value (Dfactor) depending on the interval within which the calculated length falls. The second ranking function is one minus the dot product of the user station (us)-reference station baseline for the candidate reference station (cs) baseline (X cs -X us ) and the previously selected reference station (ps) baseline (X ps -X us ) divided by the product of the baseline lengths for the previously selected and candidate stations. This function (Eq. 1) is designed to identify a group of candidate reference stations that (as much as possible) surround the user station.

$$ {\it dot}=1-\frac{\left({\mathbf{X}}_{ps}-{\mathbf{X}}_{us}\right)\bullet \left({\mathbf{X}}_{cs}-{\mathbf{X}}_{us}\right)}{{\it BaselineLengt{h}}_{ps} {\it BaselineLengt{h}}_{cs}} $$
(1)
Fig. 1
figure 1

New Zealand PositioNZ network. The stations in the LINZ PositioNZ network that were used to provide test data sets are ploted as blue triangles while all others are plotted as red

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The final ranking involves the Dfactor and dot criterion combined, with the former and later having 65% and 35% respective weighting. Our experience shows that the number of intervals in the Dfactor table was the key step in optimizing reference station selection. Currently the Dfactor table has 50 intervals with a 1 km distance step for the first interval, followed by 10 km for the next 40 intervals beyond which steps become increasingly course until a maximum of 5,000 km is reached. The Dfactor table extends to very large distances to support users in New Zealand’s remote Sub-Antarctic and Kermadec Islands.

Modelling studies show that the PositioNZ stations are well configured to act as base stations within mainland New Zealand. Figure 2 shows contour plots of baseline distance averaged over the top three reference station choices. The figure shows that the average baseline distance for the three base stations selected using the algorithm discussed above is nearly always less than 100 km and always less than 150 km except for a limited area in the far north of North Island and the southern end of Stewart Island where the average distance increases to nearly 200 km. The effect of Eq. (1) on the reference station selections is shown in Fig. 3. Figure 3a shows a contour plot of the minimum azimuth difference of baselines to the top three reference stations for our preferred reference station ranking while Fig. 3b shows a similar plot where the ranking is just based on distance. A comparison of these two plots demonstrates our preferred algorithm selects reference stations with a greater diversity of azimuths than can simple distance based ranking.

Fig. 2
figure 2

Contour plot showing average distances using the top three PositioNZ stations identified by the reference station ranking algorithm

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Fig. 3
figure 3

Contour plot showing minimum angles formed between the three reference station- user station baselines as a function of the rover location for the North Island of New Zealand. (a) Is calculated using both the distance ranking function and the dot function in Eq. (1) with a 65% and 35% weighting respectively while (b) just uses the distance ranking function

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Once a candidate reference station is identified the program attempts to acquire the RINEX data. If the file is not available or the time coverage between the user station and the reference station is not at least 95%, PositioNZ-PP will go to the next station on the list.

5 Station Coordinate Prediction Model

Before a GPS processing session is started, the code develops accurate a priori coordinates of the reference stations at the epoch of observation using LINZ’s Station Coordinate Prediction Model. While a priori coordinates are always required by GPS processing, this step is particularly important because the GPS processing algorithm used by PositioNZ-PP determines the final coordinates using the network adjustment step in Bernese, which holds the a priori coordinates fixed. As a result, the a priori coordinates must be highly accurate because they in effect are the control for the final NZGD2000 coordinates that are given to the users. This model incorporates the measured velocity for each station and the effect of annual seasonal variation in the coordinates, any offsets caused by equipment changes or earthquakes events. The model also includes a function for decaying exponential post-seismic signals, which are caused by major earthquakes and slow-slip events. Slow slip events, which are common in central New Zealand (Wallace and Beavan 2010; Wallace et al. 2012), are important in modeling the time series for PositioNZ stations along the east coast of North Island and the northern end of South Island. This model, which is based on a prototype developed by GNS Science (Beavan 2008), was recently updated to include the effects of the 2009 Dusky Sound Earthquake (Beavan et al. 2010) and 2010–2011 Christchurch earthquake sequence (Beavan et al. 2012) along with all slow slip events that have occurred since 27 June 2008 (Pearson 2013). The model needs to be continuously monitored and maintained to respond to new slow slip events, as well as other influences such as GNSS equipment changes.

6 GPS Processing Engine

The next step is to initiate GPS processing using a Bernese Processing Engine (BPE) script. This first imports reference station RINEX files and performs some checks to identify and remove any bad data. Next the process forms baselines between the reference and user stations in a star pattern centered on the user station. Each baseline is checked to identify and fix cycle slips as well as outlier observations. The next step is to resolve the carrier phase ambiguities for each baseline using the quasi-ionosphere-free (QIF) strategy (Dach et al. 2007). This stratagem, which is only available using high end GPS processing software such as the Bernese suite, is optimized for longer baselines (up to approximately 2,000 km) and fairly long observing sessions. While most users will not require such long baselines, users in New Zealand’s remote offshore islands and the Ross Dependency probably will because the average distance to reference stations increases rapidly away from the main islands of New Zealand (see Fig. 2). The last step is the network solution where the carrier phase ambiguities are fixed at their values from the QIF step and the reference station coordinates are held fixed at the observation epoch which are determined by the Station Coordinate Prediction Model discussed above. During this step the final coordinates are determined in the ITRF datum and at the epoch of observation.

7 Determination of NZGD2000 Coordinates

The GPS processing discussed above produces ITRF2008 coordinates at the epoch of observation. To convert them to NZGD2000, the coordinates are first transformed to ITRF96 coordinates at the epoch of observation using the ITRF2008 and ITRF96 transformation (Pearson 2013). These ITRF96 coordinates are then transformed between the epoch of observation and epoch 2000.0 using the New Zealand deformation model. The model is currently being updated by Crook et al. (2013) to include models of the 2009 Dusky Sound earthquake (Beavan et al. 2010) and the 2010–2011 Christchurch earthquake sequence (Beavan et al. 2012). This model has grids specifying the horizontal velocities and displacements associated with the Dusky Sound earthquake and Christchurch earthquakes. Using these grids, the total displacement between the epoch of observation and 2000.0 can be calculated by multiplying the velocities by the time interval between the observation and reference epochs and adding any seismic displacements. The NZGD2000 coordinates are calculated by applying the displacement vector to the ITRF96 coordinates at the epoch of observation (Blick and Grant 2010).

8 Preliminary Estimate of Accuracy Achievable by PositioNZ-PP Processing Engine

We use seven PositioNZ sites as test stations. These were selected to avoid areas affected by recent earthquakes in New Zealand. The location of the test stations are shown in Fig. 1. Since PositioNZ-PP will reject reference stations whose name is the same as that of the user station and the distance is less than 10 m, the test station will not also be used as a reference station.

Table 1 Summary test data
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9 Method

All tests were conducted between day of year (DOY) 348 and 365 in 2011 (19 days) and DOY 027 to 029 in 2012 (3 days). The standard 24 h RINEX files were acquired for each of the 21 days and processed using the PositionNZ-PP algorithm. In addition, we took 47 non-overlapping 4 h samples and 130 non-overlapping 2 h samples for each station using the windowing capability of TEQC to divide the 24 h RINEX files into shorter sessions. In order to average out the effect of changes in the satellite constellation, the 2 and 4 h samples were selected so that the sampled time intervals are spread evenly over the day. Each data set was processed using a slightly modified PositioNZ-PP processing algorithm that saved the geocentric Cartesian coordinates at the epoch of observation for each test station. The epoch of observation was used since the models used to convert coordinates to (or from) epoch 2000.0 have not yet been updated for the combined effects of the co-seismic and post seismic displacements from the Christchurch earthquake sequence and Dusky Sound earthquake of 2009. This means that the projected coordinates for the reference stations may be slightly displaced from their true positions but all of the test stations were selected so that they were located outside of the regions undergoing significant co-seismic displacements. All of the test data sets ran normally. In total, at each of the seven test stations the number of test solutions included:

  • twenty-one × 24 h solutions;

  • forty-seven × 4 h solutions, and;

  • one hundred and thirty × 2 h.

Because the updated Station Coordinate Prediction Model was not available for these tests, our best estimate of the position of each station is to average the twenty-one 24 h test solutions so we used this as a point of comparison for the coordinates produced by the individual solutions. This procedure assumes that the lack of information on crustal deformation has a minimal effect on the results of the test because the measurements and final coordinates refer to very similar epoch times. As a result the reduction of the coordinates to NZGD2000 is unnecessary. The results for all of the test stations were then combined into a single estimate of the RMS. The results (summarized in Table 1) suggest that the PositioNZ-PP processing engine can produce standard deviations of ±11 mm in the East direction, ±8 mm in the North direction and ±19 mm in the up direction for 2 h observing sessions. These results are comparable to those achieved by the National Geodetic Surveys OPUS service (Soler et al. 2006). Analysis of the 2 h tests suggests that small, but significant changes in accuracy can be expected as a function of the time of the day due to the combined effect of changes in satellite geometry and atmospheric conditions.

All of our tests used final IGS orbits, however many users will submit datasets to PositioNZ-PP before the about 2 weeks latency period for the final orbits has elapsed. In this case PositioNZ-PP will default to use the best available orbit (which will usually be the IGS Rapid orbit). To quantify the effect that rapid orbits might have on the precision of the estimated coordinate, we repeated the analysis described above for two sites using the same datasets used in the original test and version of the GPS engine modified to use only rapid orbits. The maximum difference between coordinates developed using rapid and final orbits was less than 0.1 mm suggesting that the use of rapid orbits is unlikely to have any significant effect on the accuracy of PositioNZ-PP coordinates. To quantify the effect of sessions incorporating more than one GMT day, we tested a total of forty 2 h sessions that started 1 h before GMT midnight. These sessions were spread over 7 days and used six PositioNZ sites. The resulting accuracies (shown on the bottom row of Table 1) are comparable to the results for sessions that do not include more than one GMT day.

10 Conclusions

The GPS processing part of PositioNZ-PP online GPS processing tool is almost complete. It is hoped that the system will be ready for deployment during 2014. Results of preliminary testing using the IGS final orbits suggest that the PositioNZ-PP processing engine can produce standard deviations of ±11 mm in the East component, ±8 mm in the North component and ±19 mm in the up component for 2 h samples. These results are comparable to those achieved by the National Geodetic Surveys OPUS service (Soler etal. 2006). The standard deviations improve to ±6 mm in the East and North and ±16 mm in the up component for the 4 h samples. For the 24 h data sets, the RMS values were ±2 mm in the North and East and ±6 mm in the up components respectively. The results were not significantly degraded using the IGS rapid orbits rather than the final orbits.