Introduction
To date, the use of global navigation satellite systems (GNSS) allows a number of applications for both technical and scientific contexts. Several techniques enable all users to measure three-dimensional coordinates with different associated precisions. For technical applications, real-time kinematic (RTK) (
Wang 1999;
Langley 1998) and network-RTK (NRTK) (
Hofmann-Wellenhof et al. 2007;
Cina et al. 2014) modes have become a standard and can be very useful because they provide centimetric precisions in real time, but they both require the availability of ground-based infrastructures (geodetic networks) for the corrections definition and for their transfer to users (radio or internet). Especially in the offshore or mountain areas, RTK and NRTK can be affected by several problems, such as the lack of internet coverage or control points. Moreover, in vast nonurbanized areas, the implementation of a dense geodetic network for positioning could become uneconomical.
A first attempt to overcome the need for ground-based infrastructures and provide corrections for GNSS positioning has been done implementing satellite-based augmentation systems (SBAS), which provide coverage of wider areas and broadcast GNSS corrections to a large number of users through the use of geostationary satellites coupled with a continuously operating reference stations (CORS) network for the corrections estimation (
Li et al. 2020;
Walter et al. 2010;
Choy et al. 2017;
Wang et al. 2018). Several countries have implemented their public SBAS based on code-observables corrections. Earlier examples are the US wide area augmentation system (WAAS) and the European geostationary navigation overlay system (EGNOS), but several other services are now available or under development as reported in the map in
GSA (2020a, p. 14) or their table (
GSA 2020a, p. 97). However, these services typically use code observables and provide only a metric precision, which fails to achieve the centimeter-level positioning accuracy necessary for most demanding technical applications.
The last
have seen the development and the spread of several global services for real-time positioning with centimeter level precision as well as acquisition of phase corrections (
Anantakarn and Witchayangkoon 2019). These commercial services, mainly developed for offshore applications, use the precise point positioning (PPP) approach (
Bisnath and Gao 2009;
Kouba and Heroux 2001;
Zumberge et al. 1997), supported by the computing of corrections from global CORS networks. The use of permanent stations of known coordinates allows modeling of spatial-correlated source of errors and defining a correction model suitable in the area covered by the GNSS network. These corrections can be finally sent to users from geostationary satellites through L-band signals (
Rizos et al. 2012;
Gumilar et al. 2019). These augmentation systems deliver corrections for accurate positioning to wide areas with theoretical precisions a little lower than the ones of NRTK, maintaining errors in the order of a few centimeters (
Anantakarn and Witchayangkoon 2019;
Hemisphere 2020). Using these services, it is possible to obtain a homogeneous positioning quality using a single receiver also without the need of an internet connection (
Choy et al. 2017;
Boylan 2016). Nevertheless, signals from commercial SBAS services cannot be implemented by all the GNSS receivers because it is necessary to have specific hardware and purchase a subscription (
Choy et al. 2017).
Currently, different companies provide similar positioning services, a list of which has been given in table format by GSA (
2020a, p. 98) together with the declared accuracies and the used constellations. For some of those, it is also possible to receive corrections via internet connection. Moreover, the European Union is developing an open service, also based on PPP corrections, for the Galileo constellation, named the High Accuracy Service (HAS), which should provide real-time accuracies smaller than 20 and
(95%) for the horizontal and vertical components, respectively, promising a convergence time shorter than 300 s for the global service and 100 s over the European area (
GSA 2020b). In this case, corrections will be sent to users directly by GNSS satellites using the Galileo E6b band or by internet, without the use of geostationary satellites. The service will be fully operational after 2025. Furthermore, also the Chinese BeiDou is about to implement a high-accuracy correction service based on PPP in its BeiDou satellite based augmentation system (BDSBAS) (
BeiDou 2019), which should provide horizontal accuracies within
and vertical accuracies within
at 95%, with convergence time shorter than
.
All these correction services are roughly similar in their functioning principle, providing slightly different accuracies and different spatial coverages, regional or global. In this paper, we will focus on the Atlas service managed by Hemisphere GNSS. This infrastructure is composed of 200 permanent stations distributed on a global scale, and it provides corrections for global positioning system (GPS), global navigation satellite system (GLONASS), Galileo, and BeiDou constellations, allowing a submeter positioning accuracy. Three geostationary satellites cover almost all the Earth, thus making Atlas solutions very flexible. The Atlas correction service is available on single- and dual-frequency GNSS receivers at three different levels:
•
Atlas Basic: 95% [ root mean square (RMS)],
•
H30: 95% ( RMS), and
•
H10: 95% ( RMS).
In general, the precision related to each level of the service can be reached only after a period of convergence, which is declared to be depending on the selected service.
The aim of this paper is to assess the performance of the Atlas correction system in the best operating conditions, meaning the absence of obstacles to sky visibility, that could occur at midlatitudes (about 45° north) where the elevation of the geostationary satellite is quite low (about 30°). Furthermore, a test was carried out in order to verify if this technology can actually be an effective alternative to the classical RTK technique in case of land applications. The analysis was possible thanks to the availability of a Stonex S900A receiver (Monza, Italy), which implements the Atlas service for the standalone positioning. This receiver can track all carrier signals sent by the modern GNSS satellites (GPS, GLONASS, BeiDou, and Galileo) using 600 channels, with a frequency up to 20 Hz. It integrates a high-accuracy antenna together with an internal multipath suppressive board. A subscription is needed to benefit from the full Atlas service, allowing one to receive L-band corrections without any time restrictions.
Different aspects have been investigated: the convergence time needed for the measures to initialize, the congruence with the declared reference system, the measures’ repeatability, and the reliability of the formal error estimated in real time. Data have been acquired in two different contexts, one representing ideal conditions of sky visibility and with long sessions on a fixed point, and the other concerning a real survey located along the Adriatic coast. In both cases, the same analysis approach has been followed, and the corresponding results have been compared in order to evaluate the impact of the environmental conditions.
Data Sets
Two different data sets were acquired for testing the Atlas performance in different contexts, both following the idea to record 1-Hz solutions on a reference point for a time span long enough to allow a statistical analysis of the solutions. In particular, the first data set was acquired in ideal conditions and for a sufficient time span in order to assess the performance of the system. In the following sections, we will refer to this data set as the lab test.
Differently, a second data set, hereafter called the field test, was acquired in order to verify which performance can be expected in certain operational conditions. In particular, we used as reference some benchmarks belonging to an already existing geodetic network along the Adriatic coast. The location of all the test benchmarks is shown in Fig.
1. The same S900A receiver was used for all the acquisitions acquiring all the available constellations.
For the GNSS constellations, at the test time (2019), besides the 32 GPS satellites and the 23 GLONASS ones, about 24 and 10 satellites were actually available for the Galileo and BeiDou constellations, respectively. These have been improving in the last years, and thus the number of satellites available is now higher.
Lab Test
The first data set consists of 135 h of GNSS data acquired in June 2019 over the roof of the Engineering Department of the University of Bologna at the sampling frequency of 1 Hz, thus providing a representative statistical sample for a general assessment about the Atlas global correction service during a standalone positioning. The absence of significant obstacles that could obstruct the proper satellites view from the receiver guaranteed ideal conditions. Data were acquired using all the available constellations in 41 sessions with a time span ranging from about 1–5 h. The receiver was switched off and restarted after each session with the aim to simulate a number of surveys in the most similar conditions and allowing a statistical evaluation of the convergence time the system needs to provide the declared performances. The upper-bound limit of about 5 h was not a choice but a technical limit of the instrument controller coupled with the S900A, which was not designed for acquiring autonomously real-time positions for very long sessions. Moreover, in some cases, we shortened the observing sessions to obtain a higher number of new converging phases and better evaluate this parameter. Once the instrument had converged, the acquisition continued in order to evaluate repeatability of the solutions, also on long acquisition times.
In three cases, the raw GNSS observables (codes and phases) were recorded too, in order to calculate the postelaborated coordinates with a PPP approach by using GIPSY-OASIS II version 6.4 software. This was done by continuously acquiring data for about 12 h because the record of raw data does not undergo the limitations occurring to Atlas real-time solutions, and it allowed us to have a reference position for the chosen point.
Field Test
The second data set was acquired during September 2019 to consider the heterogeneous conditions of a real situation. In this case, the surveyed test points were those of the Coastal Geodetic Network (RGC), realized in 2016 thanks to the collaboration between the Coastal Monitoring Unit of regional agency for prevention, environment and energy of emilia-romagna (ARPAE) and the Department of Civil, Chemical and Environmental Engineering (DICAM) of the University of Bologna (
Vecchi et al. 2020). These benchmarks, located along the Adriatic coast, are used for local monitoring surveys and their coordinates are aligned to the official national reference system ETRS89-ETRF2000 (2008.0 epoch) (
Gandolfi et al. 2017a;
Vecchi et al. 2020). RGC monographs available on the ARPAE Cartographic Portal (
ARPAE 2021), have been used as a reference for the following analysis. These measures involved 15 RGC benchmarks, and for each one, a 10-min-long observing session was performed acquiring data at a 1-Hz frequency. Also in this case, signals of all the constellations were used.
The campaign involved three distinct days, surveying five points each. The time spent between the instrument turn on and when it reached converged condition (CONV marked on the screen) was accounted for, but no data were acquired in the meanwhile. Moving from a point to another, the receiver was not powered off in order to avoid new initializations of the system, in the perspective of a time optimization required by operational conditions. In several cases, the convergence was lost when moving, and the time necessary to reach it again was accounted for after having reached the next RGC benchmark. In only one case (RICE0300), it was impossible to perform the Atlas positioning because of an obstruction of the sky visibility in the direction of the geostationary satellite.
Methods
On the basis of the described data sets, the following analysis has been performed to evaluate different aspects:
•
accuracy: the coherence between the Atlas coordinates and the reference positions,
•
convergence time: the time needed by the system to work at the declared accuracy,
•
repeatability/precision: the inherent agreement between coordinates obtained by measuring the same point after a certain time span, and
•
reliability of the formal errors: the representativity of the formal horizontal and vertical errors [horizontal root mean square (HRMS)/vertical root mean square (VRMS)] value compared with the real errors.
Henceforth, RMS will refer to the instrument formal errors because the interface uses HRMS/VRMS to indicate the a priori estimation of the positioning errors. Differently, the sample standard deviation (STD) will denote the sample standard deviation calculated a posteriori in the coordinate analysis.
Accuracy
Assessment of the Atlas system’s accuracy required a set of reference coordinates expressed in the same reference system stated by Hemisphere, which is the ITRF2008. By comparing these reference coordinates with the ones obtained by the survey, it is possible to describe the agreement of the observed values with their true values. In order to compute the most representative ITRF2008 coordinates of the lab test benchmark estimated using the Atlas service, we averaged the values of all the coordinates acquired under the condition of having a formal horizontal error (HRMS) less than . Because the system is declared converged when the HRMS goes under , this should allow us to consider only positions recorded in best operating conditions. The number of such positions actually used was 254,376, meaning more than 70 h of observations.
The reference position for the same point was estimated by computing three different PPP solutions using the GIPSY-OASIS II software [developed by jet propulsion laboratory (JPL)]. These solutions were calculated starting from raw data acquired during long observing sessions (about 12 h), and they should guarantee an accuracy within
(
Gandolfi et al. 2017b). The formal reference frame to which the PPP solutions are aligned is IGb08, a coherent update of the ITRF2008, therefore fully comparable with the Atlas reference. The three independent PPP solutions were averaged, obtaining the reference position with which to compare the one estimated using Atlas. The comparison between the postprocessed PPP coordinates and the ones obtained from Atlas is given in Table
1, where positions are expressed in the universal transverse mercator (UTM) system. The agreement of the mean Atlas position with the reference one (IGb08) is at the centimeter level, thus proving the correct realization of the Atlas reference system. In light of this, the averaged Atlas coordinates will be used a reference for all the following evaluations.
As for the field test, the reference coordinates of each benchmark were compared with the averaged value of the coordinates surveyed in the related session performed using Atlas in converged conditions. Because the RGC reference coordinates are expressed in the ETRF2000 (2008.0)-UTM32 frame, a transformation was performed to align the Atlas solutions and allow the comparison. In order to compare coherently the field test results with those of lab test, for the latter, we also evaluated the accuracy by considering the mean coordinates recorded in the first after convergence for each of the 41 sessions.
Convergence Time
The evaluation of the convergence time of the solutions is a very significant aspect, especially for the practical point of view, because it is the time that a surveyor has to wait before starting to work, and it could depend on several elements, such as the satellites view and the multipath effect (
Seepersad and Bisnath 2015;
Abou Galala et al. 2018). When the receiver is turned on, the system needs some time to provide the declared precision. The used H10 service fixes a threshold of
for the HRMS value to consider a solution as converged. The controller displays a mark CONV to state the converged status of the system, and a surveyor should use this information to start operating expecting the performance declared by Hemisphere. The manufacturers declare a convergence time ranging from 10 to
(
Hemisphere 2020). Because all the solutions with a HRMS value equal or smaller to
are considered as converged, we computed the time necessary to reach this condition for each measuring session.
Repeatability
Coordinate repeatability is the parameter that can be used to evaluate the positioning precision. It refers to the agreement between results obtained by measuring the same point in the same conditions in relation to a certain range of time. In the analysis, we distinguish between two different concepts: precision and pass-to-pass repeatability.
Precision has been evaluated by computing the STD of the coordinates acquired during the same session in converged conditions. This evaluation followed the same procedure for both the data sets, with sessions of different length: a few hours for the lab test and for the field test. The precision aspect can be analyzed in deeper detail by observing the histogram showing the distribution of the residuals, or in other words the probability of occurrence of a certain value. The histogram of the horizontal residuals was obtained by considering the Euclidean distance of the coordinates with respect to the real value, choosing classes of . The histogram of the height residuals have been defined using classes of . Both the described graphs have been obtained by considering only the residuals related to converged solutions for all the acquired sessions.
The pass-to-pass repeatability has been defined for agricultural applications (
ISO 2012;
Hemisphere 2018), and it represents the capability of the system to provide coherent coordinates within a short time range. Therefore, we simulated a test comparing each couple of observations spaced out by
to obtain a distribution of these biases. We calculated their standard deviation, which actually represents the pass-to-pass precision, and the maximum bias between these couples of coordinates. The declared pass-to-pass repeatability for the Atlas service is about
(
) (
Hemisphere 2018).
Another analysis focused on the precision, which could be obtained from static surveys with different acquisition times (1, 5, 10, 15, and ). The result of a static survey is typically the average value of the coordinates acquired during the observing session; therefore, we used moving averages to simulate several of these surveys. The STD of the time series of averaged coordinates was computed to define the precision of the measuring sessions performed using different time spans. This computation concerned only the time series with at least of data in converged conditions, and the standard deviation has been calculated for each time duration.
Reliability of Formal Errors
During a real-time positioning, users can have feedback on the coordinate quality thanks to two statistical parameters: the formal horizontal and vertical errors (HRMS and VRMS). Therefore, these values should be reliable to avoid accepting solutions that are actually less precise or waiting too long to record the coordinates. In particular, the formal error should be reliable, especially after reaching the convergence; otherwise, the user might not realize they were working without the expected precision.
The lab test allowed the evaluation of the reliability of the formal errors, thanks to the availability of a reference position to calculate the real errors of the coordinates. For each of the 41 sessions, a time series of the residuals between Atlas coordinates and the reference position was calculated. The value of each residual has been compared with its related formal error, expressed in terms of RMS (), multiplied by a scalar in order to define a certain confidence level.
A reliability parameter
was calculated for any epoch
by using
where
,
, and
components;
= reference coordinates; and
= measured ones. The formal error RMS is the HRMS in case of northing and easting, whereas it is the VRMS for the height. We used
to define the 95% confidence level or
for the 99.73% one. If the absolute value of the residual is higher than the threshold (
) this means that the formal error has been underestimated at the considered confidence level. The percentages of solutions affected by an underestimation of the formal error have been evaluated through
where
= number of observations of the session used to weight the value.
Conclusions
The aim of the proposed study is to analyze Atlas global correction service, examining its performance in standalone positioning conditions. Several tests have been performed using a S900A Stonex receiver in two different contexts. A first data set consists of repeated measures on a fixed point located on the rooftop of the Engineering Department of the University of Bologna, and the second one involved 15 different points belonging to the RGC of Emilia Romagna. In both cases, we simulated a situation where there is no availability of network coverage for NRTK corrections or benchmarks for RTK positioning. These conditions are usual in offshore surveying or in remote areas outside of NRTK network boundaries. Several time series of 1-Hz solutions were acquired and used to evaluate different parameters: accuracy, convergence time, reliability of the formal errors, coordinate precision, and repeatability.
Atlas reference frame has shown to be coherent with what the company declares (ITRF2008) at the centimeter level. This was assessed by comparing Atlas solutions to a reference position estimated using GIPSY software and the same GNSS observables. Considering the first after the convergence of the solutions, the positioning accuracy is about in the plan, with some value up to several decimeters, in both lab conditions and the field surveying.
A significant aspect from the practical point of view concerns the convergence time that is required before starting the survey. In the lab test, the convergence time was assessed after restarting the instrument at the beginning of each session, and its average value is about , characterized by a large variability (). On the other hand, in the field test, the average convergence time is about , obtained by operating without switching off the instrument but losing the converges conditions because of the transfers from one point to another.
We evaluated the reliability of the formal errors (HRMS and VRMS) displayed by the instrument, which should provide an estimation of the positioning precision, helping users to be aware of the survey quality in real time. An underestimation of these errors may lead the users to accept solutions that are not complying the survey standards. Therefore, we checked the percentage of cases in which this could occur. Considering a 95% confidence level, the formal errors have shown to be reliable for the northing, whereas they result in underestimated values in about the 10% of the cases for easting and height components. Similar results were found considering 3σ confidence interval. Nevertheless, by excluding some anomalous sessions from the statistics, the formal errors were found fully reliable for all the coordinate components.
As for the precision, the lab test showed that the 87% of the solutions are distributed within
in the plan, a percentage slightly lower than the declared 95%. In terms of STD, the coordinates acquire an overall precision of about 3.1, 6.8, and
considering the northing, easting, and height components, respectively. On the other hand, the system provides better precisions considering short time spans: in terms of pass-to-pass (measures spaced by
in time) the STD values are 2.0, 2.6, and 4.7, whereas considering 1-Hz acquisition over
, the precision values become 1.5, 2.4, and 2.3. Finally, we investigated the possibility to improve the precision by acquiring data with static sessions, testing time spans ranging from 1 to
. Using Atlas, differently from other techniques, the precision is not significantly improved by performing static positioning. This fact can be interpreted as a consequence of the slow drift occurring to the position solutions over time, which is shown in Fig.
3.
Despite the fact that 2019 data have been considered for this work, we are confident that the increased number of available satellites does not change dramatically the system performances and this contribution can be a reliable picture of the Atlas functioning at the time. Furthermore, it will be a benchmark for evaluations on the progresses of the technique in the future, when both Galileo and BeiDou will be fully operational and implemented in the updated Atlas network. Summarizing, the coordinates obtained using the Atlas correction system are well aligned to the ITRF2008 reference frame and can be considered accurate at the level in the plan when the system reaches convergence, with only few exceptions. For coordinates measured within a short period (), the service provides precisions at the level, whereas the difference between coordinates measured after long periods may be over in a significant percentage of cases.
From the practical point of view, the viability of the Atlas positioning in land surveys is strongly affected by the presence of obstacles to the sky visibility, especially in the direction of the geostationary satellite that sends the corrections. On the other hand, compared with other GNSS techniques, the Atlas positioning is independent of the presence of a stable internet connection, and it provides just slightly poorer accuracies. The time required by the system to start the survey is still much higher for the Atlas with respect to a classical network RTK. Therefore, the tested technology can be suitable for land surveys where the presence of obstacles to the sky visibility is minimal and the system does not require being frequently reinitialized.