Global Navigation Satellite System, Datums and Mapping Accuracy

Version	Summary	Created by	Modification	Content Size	Created at	Operation
1		Hari Krishna Dhonju	--	3759	2023-10-10 12:57:26	\|
2	layout	Jessie Wu	+ 3 word(s)	3762	2023-10-11 03:26:50	\| \|
3	layout	Jessie Wu	-14 word(s)	3748	2023-10-12 08:53:09	\|

This entry is adapted from the peer-reviewed paper 10.3390/agronomy13102563

Current Global Navigation Satellite System (GNSS)-based geodetic techniques allow up to millimeter accuracy in positioning to be achieved globally, and high-precision mass-market positioning is becoming available to an accuracy of 5–10 cm.

tectonic shift visualization web imagery GNSS datum

1. A Primer on the Global Navigation Satellite System

The Global Positioning System (GPS) was first operationalized by the U.S. Department of Defense in 1978, although its satellite constellation was not fully complete until 1995. The Russian GLONASS, European Galileo, and Chinese BeiDou systems achieved full operational capability in 1995, 2021, and 2020, respectively, albeit functioning at a range of position accuracies and levels of global coverage. The four systems are collectively referred to as Global Navigation Satellite Systems (GNSS). The GPS system was originally restricted to military use until the Reagan administration allowed degraded civilian use following the destruction of a Korean Airlines passenger plane that strayed into Russian airspace in 1983. The Clinton administration allowed civilian access to un-degraded GPS signals in 2000, and this commitment was made permanent in 2007 ^[1]. Civilian access to data from GLONASS and BeiDou geo-positioning systems has followed. Galileo access was always open, as it was the only non-military system.

The data sampling rate (also known as the update rate) of a GNSS module is the rate at which the position is calculated and reported. This is determined by both the satellite constellation accessed and the receiver chipset quality, with the primary limitation being the computing power of the receiver ^[2]. The GPS constellation outputs data at 1000 Hz. However, many receivers support only a 1 Hz rate, although receivers with update rates of 5, 10, and 20 Hz are available. A 1 Hz rate is adequate for non-moving applications. This specification is important to agricultural applications involving moving vehicles. For example, the orchard imaging system described by Anderson et al. ^[3] captures geolocated images at 10 fps from a ground vehicle moving at 7 km/h, i.e., 1.9 m/s. The matching of frame capture time to location data collected at this rate or higher will require interpolation of GNSS data.

A single point receiver (also referred to as a standalone receiver) of GNSS data has a positioning error of 5–10 m because of fluctuations in the GNSS signal due to variations in the layers of the atmosphere, multipath signals, and receiver electrical noise, in addition to errors in satellite clocks and imperfect satellite orbits. In differential GNSS (DGNSS), data are collected from a reference (base) station(s) at a known location, with the estimated position error on the reference station used to adjust the estimated rover position. Real-time kinematics (RTKs) also use base station data but employ more sophisticated algorithms, correcting ionospheric changes and satellite clock errors. Position accuracies of DGNSS and RTK are approx. 0.5 m and 0.02 m, respectively. In Australian surveying practice, the use of DGPS supported by local base stations has been largely replaced by the use of RTK based on a public/private network of Continuously Operating Reference Stations (CORS). However, a data link is required to access the CORS-RTK service in real time, and internet or 4G cellular service has been limited in agricultural areas.

The satellite-based augmentation system (SBAS, also known as wide-area differential GNSS) is an alternative that is widely adopted in Australian broadacre agriculture. In SBAS, a satellite signal is used to provide correction for satellite orbits and clocks, and information on the signal delay incurred in passes through the ionosphere that is calculated from multiple base stations. Such systems achieve a horizontal position 1 sigma accuracy below 1 m. Major agricultural technology providers such as John Deere (Moline, Illinois, United States), Case (Turin, Italy), Ag Leader (Ames, Iowa, United States), and Trimble (Westminister, Colorado, United States) have relied on the Inmarsat-4 constellation of three high-orbit satellites to deliver the correction data. However, the F-1 satellite that services Australasia has had several outages since its launch in 2005, including in March 2023 when two-thirds of the Australian winter wheat seeding program was reported to be impacted ^[4].

Precise point positioning (PPP) uses the ‘direct observables’ of dual frequencies broadcast by satellites (L1 and L2 in the case of GPS) to estimate ionospheric change and ‘ephemerides’ data, which are precise estimates of satellite orbits estimated using data from a global network of ground stations. Post-processing solutions have been available to implement corrections based on such estimates, but recently improved ephemerides data have become available with low latency over the internet. For example, an open-source toolkit (‘Ginan’) has recently been released for the creation of precise point positioning (PPP) positions and analysis products in Australia ^[5]. This free resource can be used in local applications with 4 or 5G service or an internet connection to deliver position correction data, providing positioning accuracy to 3 to 5 cm across Australia ^[5]. It is anticipated that in the future, consumer-level devices will access this service to deliver a highly accurate positioning capability. However, PPP requires more processing power than conventional methods and connectivity for access to an ephemeris correction stream, and it can take longer (minutes to hour) to converge to full accuracy.

The recent development of the Starlink communication satellite constellation (Starlink, Redmond, Washington, USA) is dramatically changing connectivity, offering (Australian) continent-wide coverage in a reliable, low-cost solution. This resource currently consists of 3580, of a planned 12,000, low-orbit satellites. This capacity can underpin the delivery of SBAS, RTK, or PPP services.

2. A Primer on GNSS Datums

Location data collected across a site over time could be referenced to a local reference point or datum. Such data would be internally consistent, avoiding the need to consider continental drift, but would not allow for the import of external datasets based on other data.

The different GNSS positioning systems use different ‘datums’, i.e., GPS WGS84 (World Geodetic System 1984), GLONASS PZ-90, Galileo GTRF, and the BeiDou Coordinate System (BDC). These datums provide an ‘absolute’ (also referred to as ‘dynamic’, ‘time dependent’, or ‘earth-centric’) position of any point on Earth’s surface. In these datums, a given measurement will appear to shift on a map with time due to continental drift. In practice, these data do not continuously accommodate continental plate movement, but provide yearly step changes (benchmarking to ground control point positions on the 1st of July each year). These reference frames are based on an estimate of Earth’s center of mass, a reference ellipsoid used to represent the shape of the Earth, and a geoid, which is the equipotential surface of the Earth’s gravity field and is estimated using an earth gravitational model. The geoid is used to determine the height/elevation of a given point on the surface of the Earth and is generally expressed as elevation relative to mean sea level (MSL). The various data differ in their accuracy of fit to Earth’s surface; they are optimized in terms of representing the whole globe or a part of the globe. Transformation parameters are used for the transformation of coordinates between different reference frames. There are, however, several versions (‘realizations’) of each of these reference frames, and attention to the realization in use is important for sub-meter spatial measurements.

An international consortium has maintained the International Terrestrial Reference System (ITRS) since 1991. The ITRS consists of procedures for creating reference frames, such as a series of implementations of this system, known as the International Terrestrial Reference Frames (ITRFs), the latest of which is ITRF2020. Navigation systems, as used by the various GNSS, are generally referenced to an ITRF solution.

For example, the latest update of the GLONASS reference system was in December 2013 (PZ-90.11) ^[6]. The transformation from PZ-90.11 to ITRF2008 involves only a shift, without rotation or scale. The Galileo navigation system utilizes the Galileo Terrestrial Reference Frame, which is aligned to new ITRF realizations, with (2σ) differences of less than 3 cm ^[7]. The China Terrestrial Reference Frame (CGCS) 2000 is referred to as ITRF97 with the epoch of 2000.0.

As the foundation system, the WGS84 coordinate system is widely used. WGS84 was implemented in 1987 with six successive refinements, each using more accurate coordinates of the reference stations. However, Kelly et al. ^[8] note the changes in WG84 are ‘not well known in the geospatial community’, with many users failing to record which realization data have been captured in WGS84 (G1762), introduced in October 2013, which was reported to have an accuracy (1σ) of 0.5 cm relative to ITRF2008. The latest WGS84 realization, G2139 (released on 3 January 2021), aligned with ITRF2020. The difference between WGS84 and ITRF realizations is mainly due to the use of a different set of base stations by the two systems ^[8]^[9].

If the WGS84 realization used in data capture is not recorded, the data are said to be captured in the ‘WGS ensemble’. If the date of data collection is not recorded, no correction can be made for tectonic motion, which is required for a comparison of the measurements made in other years. Geosciences Australia reports the accuracy of the WGS84 ensemble to be between 2–5 m in Australia ^[10], with uncertainty to increase with time given tectonic movement.

For applications requiring higher accuracy, it is critical that the WGS84 realization epoch and date of data capture (‘coordinate epoch’) be recorded as metadata to allow for correct transformation to other coordinate systems. The metadata for the transformed dataset should also record the transformation method and parameters used. This ensures other users of the data are aware of the accuracy and lineage of the data. Epochs are recorded as year and decimal year, e.g., 1 January 2020 is 2020.000. Unfortunately, recording formats such as XML or JSON do not provide for such metadata. ISO19115, which defines the schema required for an enhanced description of the acquisition and processing of geographic information, including images ^[11]^[12], should be updated to accommodate such a requirement.

The geodetic datum used in China (GCJ-02) is based on WGS-84 but with the use of an obfuscation algorithm that adds random offsets to both the latitude and longitude. A GCJ-02 map will correctly display the location of a point with GCJ-02 coordinates, but a WGS-84 marker will be randomly offset between 100 and 700 m from the expected location on a GCJ-02 map. As required by Chinese law, there is no official API for conversion between GCJ-02 and WGS-84 ^[13].

As an alternative to the use of a global reference frame, such as WGS84 or ITRF, a local reference frame can be used to provide a better model of the shape of Earth’s surface in a portion of the globe. For example, Australia has implemented the Australian Terrestrial Reference Frame 2014 (ATRF2014) as a dynamic local datum. National data are often mandated for use in activities, such as national mapping and cadastral surveying.

However, ‘static’ objects are changing in global position due to continental drift. Australia is the world’s fastest-moving continent, drifting to the northeast at approximately 7 cm per year, with a much smaller intercontinental movement ^[14]. Thus, the position of a feature such as an orchard boundary will have shifted by approximately 2 m in 30 years. For operational convenience, location data can be reported in terms of position at a set date using a ‘static’ (also known as ‘time independent’ or ‘plate centric’) datum. For example, Australia operated on the Geocentric Datum of Australia 1994, or GDA94 (with epoch 1999.000), until 2017, when GDA2020 became available ^[15]. GDA2020 represents locations on the Australian continent as of 2020.000, using the ITRF 2014 at epoch 2020.000.

Thus, high-resolution GNSS measurements are made in terms of a global reference frame, such as WGS84 (G1762), but the data can be presented in a product, e.g., for use in FMIS, in the national geodetic datum. In Australia, both the static datum of GDA2020 and the dynamic datum of ATRF are recognized by the Australian National Measurement Act as standards for measurement of position ^[16]. Australia supports both dynamic and static data (ATRF and GDA2020, respectively) to cater to the needs of both plate- and global-centric users. A number of countries for which continent drift is not as great an issue have implemented only a local and not a static datum ^[9].

The parameters for transformation between a given pair of reference frames, e.g., realizations of GDA94, GDA2020, ARTF2014, and WGS84, are described by an ‘EPSG’ number ^[17]. There are over 6000 EPSG parameter sets, reflecting the myriad of reference frames used globally ^[18]. The use of an inappropriate transformation in moving between reference frames will introduce spatial error.

For example, if a position reported in a static datum, such as GDA94, is transformed to a dynamic datum, such as WGS84, the point will be represented by its position in the dynamic datum as of 1994.000, unless an additional correction for the date of data collection and continental shift is made. In another example, data captured on WGS 84 with a handheld receiver on 25 April 2023 is likely to have been observed using the latest WGS 84 revision and should be labeled with the coordinate epoch (date of data collection) as WGS 84 (G1762)@2023.315. However, if an augmentation service (RTK, PPP) has been used, it is likely that the data will have been collected in another datum, even though the system software may indicate the use of WGS84. For example, the Australian CORS RTK outputs data in the GDA2020 datum. Transformation of these data to the latest realization of WGS84 will produce WGS 84 (G1762)@2020.000.

For emphasis, geolocation data should be reported in terms of the reference datum and any transformation methods used for data records requiring sub-meter resolution. If a dynamic datum is used, the date of data capture (coordinate epoch) should also be recorded. Further, the uncertainty resulting from the transformation of data should be documented for applications requiring <1 m accuracy ^[19].

3. A Primer on Web Mapping

Veenendaal et al. ^[20] reviewed trends in web mapping. Briefly, the use of web map services provides an ‘easy’ path for the introduction of a mapping capability within a given service, which is supported by easily available training resources, e.g., Beeflamb ^[21]. ESRI reports a trend for clients to deliver data to customers using WebGIS (such as ArcGIS Online, arcgis.com accessed on 30 September 2023) rather than by the supply of datasets or production of PDFs, providing ‘live data in the hands of field operators’ ^[22]. This trend is also true for FMIS, e.g., Zhang et al. ^[23] discuss design principles for the integration of Google Maps into FMIS. Example applications include the use of Google Maps to visualize locations of tens of thousands of small gardens ^[24] and locations of animal ‘exploitation farms’ ^[25]. In non-agricultural examples, GE imagery was used in the display of meteorological satellite data ^[26], bird species distribution ^[27], and geochemical data ^[28]. However, web mapping has several limitations that should be understood in the context of use with FMIS.

The default coordinate system for geolocation data is geographic (longitude and latitude, generally in WGS84), measured in degrees for a given earth model. This geographic data are projected for visualization, e.g., for the display of data in FMIS as a two-dimensional view of Earth’s surface. This process involves a conversion of geographic data to projected coordinates for a given map type and datum. The commonly used Mercator projection involves a cylindrical projection, distorting the pole regions (such that Greenland appears larger than Africa).

A variant of the Mercator projection system that is used in web mapping applications has the official identifier of EPSG:3857 and is known as Web Mercator, ESRI Web Mercator, Google Web Mercator, Spherical Mercator, WGS 84 Web Mercator, and WGS 84/Pseudo-Mercator. The Web Mercator achieved prominence when it was adopted by Google Maps in 2005. Its advantage lies in the use of a spherical (a sphere with a radius of 6,378,137.0 m is assumed) over an ellipsoidal model for the Earth, which requires simpler calculations for the projection of points and thus lower computing resources. However, Web Mercator is not a recognized geodetic system due to the error involved in the projection of latitudes and longitudes from the WGS84 ellipsoid onto a sphere ^[29]. Distances and angles should not be estimated from Web Mercator maps. Battersby et al. ^[29] provide details on the implications of using Web Mercator in various online map services.

The most common standards used in serving pre-rendered or on-the-fly computed map tiles over the internet are the Web Map Service (WMS) and the Web Map Tile Service (WTMS) protocols. The OpenLayers library ^[30] is a commonly used open-source JavaScript library for interfacing web map services in web applications. OpenLayers requires input of data in WGS84 datum by default ^[31]. To display data on a web mapping application, the typical workflow involves (i) the transformation of data to WGS84, (ii) the transformation of WGS84 data to the Web Mercator (spherical) projection, and (iii) the display of a map.

A number of widely available web map services with global coverage layers are available, including Google Maps, ESRI, Mapbox, Bing Maps, AppleMaps, OpenStreetMap, and Mapquest. Goodchild et al. ^[32] reviewed the technical specifications of Google Earth, while Lesiv et al. ^[33] reported on the spatial and temporal availability of imagery in Google Earth and Bing Maps. As mentioned earlier, Chinese web map service providers are required to use obfuscated GCJ02 ^[13]. The popular provider Beiduo Maps adds a further obfuscation to GCJ-02, termed BD-09, to prevent competitors from accessing Beiduo’s data ^[34].

The Google Maps service is particularly popular, including in scientific and technical applications ^[35] due to its availability at higher resolutions (to 15 cm where aerial imagery has been used) and relatively higher currency (imaging dates). The image scale and regularity of image updating of these resources varies by location and is related to population density. Satellite-based imagery is typically used, although input from other platforms is used, e.g., aerial imagery, when available, e.g., from local national mapping agencies ^[33]. When higher resolution imagery is not available, Landsat imagery (spatial resolution of 15 m) is used ^[36]. Under their fair use policy, Google Earth (GE) imagery is free for use for websites with less than a certain number of tiles/visits per day.

Local map resources may also be available. For example, the Queensland Government maintains Queensland imagery as an online map service ^[37]. The resource contains imagery collected on multiple dates from 1930 to 2019 and is a mosaic of ortho-rectified aerial imagery of high spatial resolution (0.5–50 cm) from remotely piloted aircraft, piloted aircraft, and satellites ^[37]. UAV imagery can also be locally acquired ^[38]^[39].

4. Positional Accuracy of Web Imagery

Web mapping thus provides an easy-to-use display of geographic information but not a precise geographic information system (GIS). Data collected using the standard WGS84 ellipsoid model is converted on the fly to the Web Mercator spherical model. There is no error at the equator in this conversion, but error increases at higher latitudes, and points can be offset by up to 43 km near the poles. This ‘georeferencing’ error is significant for high-resolution applications, even in near-equatorial positions. Therefore, Web Mercator is not recommended for use in navigation or relative positioning in official use by United States government agencies ^[40].

Another source of misalignment between WGS84 coordinates of GE imagery and GNSS survey lies in the registration of remotely sensed images to ground control points (GCP) and the compositing/mosaicking of these images, i.e., ‘georeferencing (horizontal distortion)’ and ‘orthorectification (vertical distortion)’ errors. Web tile images are an ortho-mosaic of images from different data sources and spatiotemporal resolutions. Web map providers rely on the image registration undertaken by the image providers. Ideally, this process involves stretching and warping of the image to achieve registration to ground control points (GCPs), e.g., if the camera view is oblique to the ground. However, the satellite imagery consumed by web map providers, such as GE, will not have been registered to GCPs. For example, the positional accuracy (RMSE) of GeoEye-1 images was documented to be 6.0 m on average, ranging from 2 to 9 m for panchromatic images of seven image sets ^[41]. Further, the mosaicking of images to produce a single image involves automated routines using feature matching, with the translating, stretching, and rotation of images used to match features. The process is not perfect, with positional errors remaining, particularly at high resolutions. The web map providers do not use mosaic images from different sources but rather ‘composite’ them (without feature matching). The merger of images is often visibly noticeable in web imagery. Positional accuracies (horizontal and vertical) and spatial resolution of web map tile images will, therefore, vary temporally (given image updating) with geographic location ^[42].

Web imagery providers do not provide information on the photogrammetric accuracy of their maps. Various researchers have reported that the positional accuracy of GE imagery varies by location ^[42]^[43]^[44]^[45]. In these studies, the position of a number of ‘ground control points’ (GCPs) of known (WGS84) geolocations is compared to the location given for that point on Google Maps. For example, a horizontal positional accuracy (RMSE) of 1.73 m was documented in Khartoum across 16 checkpoints ^[43], while a horizontal positional accuracy (95% confidence level interval) of close to 1 m was documented in Rome from GE imagery across 41 checkpoints ^[44], and a horizontal positional accuracy (mean absolute error) of 0.13 m in the south and 2.3 m in the northeast of Montreal, Canada, with an overall RMSE of 1.08 m, was estimated using 10 checkpoints ^[42]. In Addis Ababa, Ethiopia, Mulu et al. ^[45] reported horizontal positional accuracy (RMSE) of GE imagery at 4.58 m with an error range of between 0.0125 and 5.0 m between GCPs. The RMSE on checkpoint coordinates from Google Maps and corresponding points on Orthophotos (1:4000 scale) in Thailand was reported as 3.3 m (a minimum error of 0.0 m and a maximum error of 28.6 m) ^[46].

In these examples, a higher error is not associated with a higher latitude, indicating that the Web Mercator projection is not the primary issue in these cases. It is likely that the results relate to the resolution of the available Google Map and the ability of the user to find a checkpoint on the Google Map. For example, as of 13 April 2023, Google Maps provides satellite imagery with maximum resolution that is similar to both Montreal and Rome but lower for Khartoum.

The uncertainty in positional accuracy due to georeferencing and orthorectification errors can limit the use of web maps. If positional accuracy better than 1.5 m is required in the display of geolocated data on a web map, an empirical correction could be made based on an assessment of the positional accuracy of the GE imagery. For local mapping, a 2D conformation transformation can be used for transformation between grid coordinate systems using a four-parameter transformation (also known as a similarity or Helmert’s transformation) based on the parameters of scale, rotation, and translation in both x and y directions. These four parameters can be estimated when two horizontal control points are known in both Universal Transverse Mercator (UTM) coordinate systems. In this conformal transformation, straight lines remain straight, and orthogonal angles are preserved. This procedure is illustrated in the following case study.

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