ProStar Holdings is partnering with Tersus GNSS, a global manufacturer of patented GNSS technologies. ProStar is the developer of PointMan Precision Mapping Solutions and the LinQD enterprise integration platform.
The collaboration will deliver a complete precision mapping solution to the utility and critical infrastructure industries worldwide, the companies announced.
The partnership is designed to integrate Tersus’s survey-grade GNSS receivers with ProStar’s PointMan, providing an affordable, field-ready solution available through Tersus’s international distribution network. Tersus GNSS has operations in China, the United States, and Australia, and is recognized for its innovation in GNSS receiver and base station technology for high-precision positioning applications.
The collaboration represents the latest step in ProStar’s strategy to expand its partnerships through the LinQD open API integration platform, delivering its technologies in one connected precision mapping solution.
ProStar’s LinQD platform is designed to enable seamless interoperability between emerging technologies and legacy systems, creating a robust global ecosystem for geospatial intelligence. By uniting equipment manufacturers and service providers under this initiative, ProStar continues to strengthen PointMan’s position as a premier mapping solution for the critical infrastructure industry worldwide.
For decades, survey-grade GNSS rovers have been essential tools for precision applications, but high costs and complex configurations have limited access to survey-grade GNSS rovers to large firms and specialized professionals. GEO-MEASURE is an affordable fully equipped RTK rover integrating robust hardware, a dedicated mobile app, and a preloaded RTK corrections service into a single turnkey package.
GEO-MEASURE is engineered for professional reliability with quad-frequency support across GPS, GLONASS, Galileo and BeiDou, Its 1,040 tracking channels provide resilience under canopy or in urban environments. Its rugged, waterproof housing is built for daily use, while a 24-hour rechargeable battery and USB-C charging make it as convenient as a consumer device while still delivering survey-grade performance.
Available for both iOS and Android, a free companion app simplifies setup, the company said. Once paired via Bluetooth, users can:
visualize survey points on maps
capture field notes
manage multiple projects
export data in standard formats (CSV, KML, GPX, GeoJSON) for integration with GIS platforms, CAD workflows, or drone mission software.
By making centimeter-level accuracy affordable, accessible and scalable, GEO-MEASURE opens professional-grade GNSS workflows to new audiences in construction, GIS, drone operations, agriculture and environmental monitoring.
Tallysman Wireless has added the housed SSL990XF full-band survey-grade GNSS antenna to its line of GNSS products.
The SSL990XF uses a derivative of Tallysman’s patented VeroStar antenna element to provide full GNSS + L-band corrections frequency coverage.
The SSL990XF is 63 mm in diameter and 28 mm tall and weighs ~50 grams, making it a very small and light housed full-band precision antenna. It has a very tight average phase-center variation of 4 mm or lower for all frequencies and overall azimuths and elevation angles.
The full-band SSL990XF antenna supports GPS/QZSS L1/L2/L5, QZSS L6, GLONASS G1/G2/G3, Galileo E1/E5ab/E6 and BeiDou B1/B2ab/B3, as well as L-band correction services. Also supported in the region of operation are satellite-based augmentation systems: WAAS (North America), EGNOS (Europe), MSAS (Japan), or GAGAN (India).
The SSL990XF is housed in a weatherproof (IP67) enclosure and is mounted using either adhesive tape or a mounting collar that includes a waterproofing O-ring. Two antenna cable connector options are available. The first is a female SMA, and the second is an MCX. It is an ideal antenna for precision UAV and all applications where light weight and precision matter.
The radio-frequency spectrum has become congested worldwide as many new LTE bands have been activated, and their signals or harmonic frequencies can affect GNSS antennas and receivers.
In North America, the planned Ligado service, which will broadcast in the frequency range of 1526 to 1536 MHz, can affect GNSS signals. Similarly, new LTE signals in Europe [Band 32 (1452–1496 MHz)] and Japan [Bands 11 and 21 (1476–1511 MHz)] have also affected GNSS signals. Tallyman’s new SSL990XF with eXtended Filtering (XF) technology mitigates the interference effects of these new signals.
“Nothing can remain immense if it can be measured,” Hannah Arendt wrote in 1958 in The Human Condition. This could be the guiding inspiration for any geodesist or surveyor throughout history. In about 240 B.C., Eratosthenes became the father of geodesy by ingeniously measuring Earth’s circumference using the Sun, a well, a vertical column, the distance a camel caravan traveled from Syene to Alexandria and some basic mathematics. His estimate of 46,000 kilometers was 16% too large but remarkably close considering that he lacked any modern measuring tool. (For a great account of this epic feat, see John Noble Wilford’s The Mapmakers.)
Geodesy, a branch of applied mathematics, is concerned with accurately measuring and understanding three of Earth’s fundamental properties: its geometric shape, its orientation in space, and its gravity field. Earth’s true shape varies from the mathematically smooth surface of an ellipsoid due to local differences in its density that cause variations in the strength of the gravitational pull, in turn causing regions to dip below or bulge above a reference ellipsoid.
This undulating shape is the geoid, which geodesists have defined as the three-dimensional surface along which the pull of gravity is a specific constant. It serves as the zero-level surface for height measurements globally, and all GNSS are pegged to it. It is a hypothetical surface that essentially represents an extension of the idealized mean sea level over (actually, mostly under) Earth’s land surface. Unlike the surface of the oceans, however, it is unaffected by wind, waves, the Moon, or forces other than Earth’s gravity.
Surveyors are content with measuring much smaller portions of Earth’s surface, from single lots to national boundaries. Unlike Eratosthenes, they work with the latest fruit of modern science and technology — including GNSS receivers, robotic total stations, inertial measurement units, lidar, other sensors and unmanned aerial vehicles — and can measure distances with millimeter precision.
When I started in this business a little more than 20 years ago, we used to group GPS receivers by accuracy into three buckets: consumer grade, resource/mapping grade and survey grade. As accuracy has increased for all GNSS receivers, the boundaries between those categories, especially between mapping and surveying, have blurred. Additionally, we now have way more GNSS satellites — in some parts of the world, as many as 70 are in view at one time — and a panoply of public and private, ground-based and satellite-based corrections services.
So, surveyors have a growing set of tools, and they are constantly getting more accurate and more user-friendly.
Now, let me throw another number in the mix: 66. That is the average age of surveyors in the United States. In the short run, employment for surveyors hinges in part on the vagaries of the economy. In the long run, however, population growth and climate change will force large investments in infrastructure. On most construction sites, the first to arrive and the last to leave are the surveyors. We know what their tools are, but who will they be?
Mobile mapping using an OxTS xNAV650 INS and lidar sensor. Photo: OxTS
We discussed mobile mapping with Jacob Amacker, application engineer, OxTS.
How do you define “mobile mapping” as opposed to “surveying”?
We use the two terms interchangeably. Each one has a different connotation depending on where you are in the world and both can be useful. We use them to cover a broad range of use cases, but “mobile mapping” is used more specifically for land-based mapping of the environment. A typical application might be a van equipped with an INS [inertial navigation system] and lidar sensors.
“Surveying” can be used a bit more generally, applying to aerial or pedestrian-based mapping, but it does have the connotation of static mapping, which we do not typically handle.
What are your main markets for mobile mapping?
It is very hard to say. The world of mobile mapping is so diverse. However, lidar mapping could be seen as both the largest and the fastest-growing market in the surveying world as lidar has become widely affordable. Although our technology can be used with any surveying devices, at OxTS we particularly like to use lidar and are focusing on getting the best results from lidar data. This has included making our own point-cloud georeferencing software to maximize the potential of our navigation data in making point clouds.
What are the main differences between your devices for aerial mapping and for ground-based mapping?
We use the same INS device for both ground and aerial mapping. For use on manned aircraft, we would always recommend our highest accuracy system with the best IMU, the Survey+. The main source of inaccuracy in survey data will come from the IMU error over the range to the objects. Because most of this range is the aircraft’s altitude, this error is quite significant. For land-based mapping work, the measurements provided by the lighter and smaller xNAV650 are still suitable for many high-precision applications.
GNSS-INS integration has been done for decades. What is new and what are the remaining challenges?
It is now much more affordable to have very high-grade IMUs and GNSS receivers. Nevertheless, there will always be further improvements to be made to how the data streams are combined. On a similar note, other navigation aiding sources are increasingly being considered to supplement the IMU and the GNSS receiver — such as wheel speed sensors, lidar, camera odometry and others that can also be integrated to stabilize and improve the navigation data. Overall, it is very exciting what is yet to come out of INS technology. In recent years, it has become so good that people expect more and more from it, and this demand must be met. What happens when GNSS drops out? We are seeing increasing development to make the navigation data robust against challenges of any environment.
Given the IMU’s drift, for how long can your system function at an acceptable level in case of a GNSS outage?
It is difficult to put a number on what kind of drift is acceptable, as it depends on the application and the end-user requirements. Typically, half a meter of drift in one minute of GNSS-outage might be the goal for some of the higher-grade surveyors. Still others might only be satisfied with negligible drift.
What keeps the INS and the lidar unit synchronized during a GNSS outage?
The INS has an internal clock to keep the timing during a GNSS outage. Of course, this will not be as accurate as the atomic clocks on the satellites, but it is quite adequate to maintain survey-grade accuracy during GNSS outages. GNSS is still necessary to get the timing information in the first place, and this is a reliance that INS devices will want to remove in the future.
SBG Systems has announced a new inertial navigation system (INS) named Quanta Micro, completing its Quanta product line.
The Quanta Micro GNSS-aided INS offers a unique combination of navigation performance and low size, weight, power and cost (SWAP-C).
Quanta Micro leverages a survey-grade inertial measurement unit (IMU) for optimal heading performance in single antenna applications, and high immunity to vibrating environments. An optional secondary antenna enables fast heading initialization in low dynamic applications.
Main Features
Accuracy: 0.015° roll/pitch, 0.035° heading, 1 cm position (PPK)
Integrates a survey-grade IMU: 0.8°/h gyro bias instability
Versatile INS/GNSS to suit land, air or marine applications
Highly tested and calibrated from -40°C to 85°C
Robust to vibrating environments
Quad-constellation multi-band RTK GNSS receiver
Smooth post-processing workflow with Qinertia software
Major size reduction with no compromise on performance.
We used to divide GPS receivers into consumer grade, resource grade and survey grade. Have these categories been replaced by a continuum of GNSS capabilities?
Clem Driscoll
“In the U.S. commercial telematics market, GPS remains the primary source of location data, with very little reliance on other GNSS networks. A bigger issue is the generation of cellular networks used to transmit GPS data, with 3G network sunsets pending and 5G on the horizon. As autonomous commercial vehicles become closer to a reality, multiple GNSS networks and differential techniques will become essential. These solutions are currently in development.” Clem Driscoll
C.J. Driscoll & Associates
Greg Turetzky
“No. These categories still define important hardware distinctions (such as antenna) and required correction services that define the achievable specifications. Although they all have correlators, they have very different architectures; however, resource and survey have a blurrier line.” Greg Turetzky
Consultant
Members of the EAB
Tony Agresta Nearmap
Miguel Amor Hexagon Positioning Intelligence
Thibault Bonnevie SBG Systems
Alison Brown NAVSYS Corporation
Ismael Colomina GeoNumerics
Clem Driscoll C.J. Driscoll & Associates
John Fischer Orolia
Ellen Hall Spirent Federal Systems
Jules McNeff Overlook Systems Technologies, Inc.
Terry Moore University of Nottingham
Bradford W. Parkinson Stanford Center for Position, Navigation and Time
Orthometric height support (survey-grade elevations) enables Arrow GNSS receivers to collect high-accuracy, survey-grade vertical data with any data-collection software.
Eos Positioning Systems Inc. has added support for GEOID height models within its Arrow Series GNSS receivers. Eos manufactures high-accuracy GNSS receivers for any app running on iOS/Android/Windows devices and using the Eos Arrow Series.
“You can use Arrow Series receivers with any data-collection software in the world, and benefit from accurate orthometric heights,” Eos CTO Jean-Yves Lauture said. “Our Arrow receivers will output accurate GNSS elevations no matter which data-collection software you use to capture it.”
Image: Eos Positioning
With support for GEOID models, Arrow receivers automatically output survey-grade elevations to all iOS and Android data collection software. Support will also soon be available for Windows devices.
The Arrow receivers now support the entire United States to provide survey-grade elevation in NAVD88 orthometric heights through the GEOID12B (US) model. The Arrow receivers also support the Canadian CGG2013a and HTv2.0 GEOID models for the CGVD2013 and CGVD28 vertical datums, respectively. Additional GEOID models for other countries are planned.
“Eos is intensely focused on supporting high-accuracy GIS, engineering, surveying and construction users by supporting the latest GEOID elevation models within our GNSS monitoring software,” Lauture said. “Our roadmap remains focused on high-accuracy BYOD users by supporting all iOS, Android and Windows users with this capability.”
The problem is that typical Bluetooth GNSS receivers usually provide inaccurate, built-in elevation models. This inaccuracy is reflected in the Mean Sea Level elevation output by those receivers. By outputting orthometric height, the Arrow now solves this problem and turns any smartphone or tablet into a 3D, survey-grade accurate data collection device, the company said.
Eos has designed this new feature so that users will easily be able to update to new GEOID models as they become available.
Field technicians in pipeline, construction, engineering, architecture, water and any other industry are finally able to enjoy GNSS location with survey-grade vertical accuracy on their iOS and Android devices, with the data-collection app of their choice and their Eos Arrow receivers.
Skycatch has announced an on-premise data processing and GNSS base station, the Skycatch Edge1, manufactured in partnership with DJI and now available worldwide.
Edge1 base station. (Photo: Skycatch)
Tested and optimized for the Skycatch Explore1 and DJI Phantom 4 RTK drones, the self-positioning Edge1 allows commercial drone users the ability to process and receive data without the need for internet or cellular connectivity, the company said.
Field teams can fly their drone, process the data and receive centimeter-level data outputs in 30 minutes or less, directly to a tablet. 2D maps and 3D point clouds are available for viewing and sharing directly from the tablet.
The Edge1 concept began as a companion to the Skycatch Explore 1 drone. Now, a new generation of the Edge1 will support all DJI drones, including the recently released DJI Phantom 4 RTK, and will process any 2D geotagged images.
In addition to a survey-grade GNSS base station, the Edge1 includes built-in WiFi, LTE, reliable sub-5-centimeter accuracy, and delivers high-quality data outputs, the company added. Built around a state-of-the-art compute module, the Edge1 is also capable of running deep learning algorithms to extract more insights from collected data in near real time.
“It’s truly a revolutionary product that we’re excited to make available to the DJI community, and the construction and mining industry at large,” said Christian Sanz, founder & CEO of Skycatch. “With the partnership and support of DJI, the Edge1 will be assembled with precision execution in their world-class manufacturing facility, and will be available faster to the customer.”
“As the commercial drone industry has grown, the amount of data collected by our enterprise users is unprecedented,” said Jan Gasparic, director of strategic partnerships at DJI. “We are glad to work with Skycatch to manufacture the Skycatch Edge1 GNSS base receiver, enabling enterprise customers, especially those in the construction industry, to process data from their DJI drones on-site and in real-time.”
Skycatch is an industrial data collection and analytics company focused on indexing and extracting critical information from the physical world, using a combination of hardware, software and artificial intelligence. Built for enterprise, its turnkey solutions are deployed across global project sites with largest construction, mining and energy companies.
Even a GNSS receiver that can supply raw pseudorange and carrier-phase measurements now costs only a few hundred dollars, and in this month’s column, a couple of researchers from Down Under pit a couple of these receivers up against a couple of survey-grade receivers. Did this cheap receiver turn out to be a good thing?
By Robert Odolinski and Peter J.G. Teunissen
ALL GOOD THINGS ARE CHEAP; ALL BAD ARE VERY DEAR. That’s what the famous American essayist (and surveyor) Henry David Thoreau wrote in his diary on March 3, 1841. He was likely referring, in part, to the cheapness of the things he came across in nature such as birdsong or the plants and trees on the shores of Walden Pond and the dearness of some luxuries and comforts of civilization, which he tended to eschew. But what has that got to do with GPS, you might ask?
When they were first introduced in the late 1970s and early 1980s, GPS receivers were very dear. Many of them sold for anywhere from $50,000 to $250,000, which would be equivalent to about twice those amounts in today’s dollars. The first civilian receivers were large bulky affairs. As I documented in this column in April 1990 (“Smaller and Smaller: The Evolution of the GPS Receiver”), the “first commercially available GPS receiver was the STI-5010 built by Stanford Telecommunications Inc. It was a dual-frequency, C/A- and P-code, slow-sequencing receiver. Cycling through four satellites took about five minutes, and the receiver unit alone required about 30 centimeters of rack space. External counters, also requiring rack space, made pseudorange measurements. An external computer controlled the receiver and computed positions.” While it could be transported in a small truck (and some were), it was not designed for portability and ease of use by surveyors or geodesists.
Then, in 1982, Texas Instruments introduced the first relatively compact civil GPS receiver, the TI 4100, also known as the Navstar Navigator. And as I also noted in that column more than 15 years ago, this “receiver could make both C/A- and P-code measurements along with carrier-phase measurements on both L1 and L2 frequencies. Its single hardware channel could track four satellites simultaneously through a multiplexing arrangement. The 37 × 45 × 21-centimeter receiver/processor had a handheld control and display unit and an optional dual-cassette data recorder for saving measurements for post-processing. The unit, although portable, weighed 25 kilograms and consumed 110 watts of power (the receiver doubled as a hand warmer). Field operation required a supply of automobile batteries.”
My, how things have changed. Beginning around 1990, receivers steadily got smaller and smaller and cheaper and cheaper. Survey-grade GNSS (not just GPS) receivers can now be purchased for well under $10,000 and consumer-grade units sell for as little as a hundred dollars or less. And, of course, the GNSS modules inside smartphones and other devices cost manufacturers only a couple of dollars or so.
But even a GNSS receiver that can supply raw pseudorange and carrier-phase measurements now costs only a few hundred dollars, and in this month’s column, a couple of researchers from Down Under pit a couple of these receivers up against a couple of survey-grade receivers. Did this cheap receiver turn out to be a good thing?
Read on to find out.
GPS has been the number-one positioning tool for a range of applications during the past few decades. The integration of the emerging global navigation satellite systems, such as the Chinese BeiDou Navigation Satellite System (BDS), can give improved precise (millimeter- to centimeter-level) real-time kinematic (RTK) positioning. When BDS is combined with GPS, about double the number of satellites are visible in the Asia-Pacific region, which can make single-frequency RTK and low-cost receiver RTK positioning possible.
In this article, we will analyze the performance of L1 GPS + B1 BDS in Dunedin, New Zealand, using low-cost receivers. We compare their performance to that of L1+L2 GPS survey-grade receivers.
First, we describe the GPS+BDS functional and stochastic models and the data used for our evaluations. Least-squares variance component estimation (LS-VCE) is used as a means to determine the code and phase (co)variances to formulate a realistic stochastic model. (An incorrect stochastic model will deteriorate the ambiguity resolution and consequently the achievable positioning precisions.)
Having correctly defined the stochastic model, we focus on the positioning performance. We investigated the ambiguity resolution and positioning performance, both formally and empirically, for customary and high-elevation cut-off angles. The high cut-off angles are used to mimic situations when low-elevation multipath is to be avoided. Lastly, we compared all our results between using low-cost and survey-grade antennas.
GPS+BDS POSITIONING MODEL
The model that we used for positioning is given as follows. Assume that sG + 1 GPS satellites are tracked on fG frequencies and sB + 1 BDS satellites on fB frequencies. As we apply system-specific double-differencing (DD), one pivot satellite is used per system. The total number of DD phase and code observations per epoch then equals 2 fGsG + 2 fBsB. We assume for now that cross-correlation between frequencies as well as code and phase is absent. The combined multi-frequency short-baseline GPS+BDS model is then defined as follows.
The system-specific DD phase and code observation vectors are denoted as φ* and p*, respectively, with * = {G, B} where G = GPS and B = BDS. The single-epoch GNSS model of the combined system is given as
(1)
and
(2)
in which
is the combined phase vector,
is the combined code vector,
is the combined integer ambiguity vector,
is the real-valued baseline vector,
is the combined phase random observation noise vector,
is the combined code random observation noise vector, and
D[.] denotes the dispersion operator.
The entries of the baseline design and wavelength matrices are given as
where is the x 1 vector of 1s, is the differencing matrix, is the unit matrix, the geometry-matrices GG and GB contain the undifferenced receiver-satellite unit direction vectors for GPS and BDS, respectively, is the wavelength of frequency , denotes the Kronecker product, and “diag” and “blkdiag” indicate diagonal and block diagonal matrices, respectively. The entries of the positive definite variance matrices are given as
(3)
where , denote the phase and code standard deviation, respectively, and the satellite elevation-angle-dependent weight.
The model in Equation 1 applies to short baselines, and thus the ionospheric and tropospheric delays are assumed absent. The broadcast ephemerides are used to obtain the satellite coordinates. Further, the Least-squares AMBiguity Decorrelation Adjustment (LAMBDA) technique is used to estimate the integer ambiguities a. The observation noise vectors εand e, respectively, are zero-mean vectors, provided that no multipath is present in Equation 1.
EXPERIMENT SETUP
The GNSS receivers we used are depicted in FIGURE 1. Firstly, two low-cost single-frequency receivers were set up to collect L1+B1 GPS+BDS data for two days. These receivers cost a few hundred U.S. dollars. Since the patch antennas we used have been shown to have less effective signal reception and multipath suppression in comparison to survey-grade antennas, the receivers that collected data for two days were additionally connected to such antennas. These antennas have a cost of slightly more than US$1,000 per antenna. To compare the low-cost solution to a survey-grade receiver-solution, two such receivers (which cost several thousand U.S. dollars) were connected to the same survey-grade antennas through splitters and collected L1+L2 GPS data. A detection, identification and adaption procedure was used to eliminate any outliers.
FIGURE 1. Low-cost single-frequency receivers collecting GPS+BDS data for single-baseline RTK, with patch antennas (left) and survey-grade antennas (right) on Jan. 4–6 and Jan. 6–8, 2016, respectively. Survey-grade dual- frequency GPS receivers were connected to the same survey-grade antennas simultaneously to truly track the same GPS constellation.
FIGURE 2 depicts the corresponding redundancy of the two receiver models (that is, the number of observations minus the number of estimated unknowns) together with the number of satellites over 48 hours (30-second epoch interval). The number of BDS satellites (magenta lines) is overall smaller than when compared to GPS (blue lines) in Dunedin. However, Figure 2 also shows that the model strength of L1+B1 GPS+BDS, as measured by its redundancy, is almost similar to that of L1+L2 GPS except for some hours at the middle of the two days. This implies that the two receiver models can potentially give competitive RTK ambiguity resolution and positioning performance. This is however only true if the receiver code and phase observation noise would be of similar magnitude between the receivers used, hence the need for an analysis of the receiver observation precision.
FIGURE 2. Redundancy (left) and number of satellites (right) of L1+B1 GPS+BDS and L1+L2 GPS during Jan. 6–8, 2016, (48 hours) for an elevation cut-off angle of 10°.
In our receiver evaluations, we determined a set of reference ambiguities by using a known baseline and treating them as time-constant parameters over the two days in a dynamic model.
LOW-COST RTK POSITIONING
The code and phase variances were estimated by LS-VCE using data independent from the data used for the following positioning analysis. The variances are needed to formulate a realistic stochastic model, whereas an incorrect stochastic model will deteriorate the ambiguity resolution and consequently the achievable positioning precisions. TABLE 1 depicts the corresponding estimated standard deviations (STDs) used for our positioning models.
TAB LE 1. Zenith-referenced undifferenced code and phase standard deviations estimated by least-squares variance component estimation.
Table 1 shows that the code precision of L1 GPS and B1 BDS improves significantly when the survey-grade antennas are used instead of patch antennas (49 centimeters STD for L1/B1 that decreases to about 30 centimeters), due to their better signal reception and multipath suppression abilities. For testing our stochastic model, we used data that is independent from the data used to estimate the code/phase precision.
Positioning Performance. The single-epoch (instantaneous) RTK positioning results for 24 hours data are shown in FIGURE 3, with ambiguity-float solutions shown at the top and ambiguity-fixed solutions at the bottom. Only the correctly fixed solutions are depicted as determined by comparing the instantaneously estimated ambiguities to the set of reference ambiguities. The 95% empirical and formal confidence ellipses and intervals are shown in green and red, respectively. They were computed from the empirical and formal position variance matrices. The empirical variance matrix was estimated from the positioning errors as obtained from comparing the estimated positions to precise benchmark coordinates. The formal variance matrix used was determined from the mean of all single-epoch formal variance matrices.
FIGURE 3. Horizontal (north (N), east (E)) position scatter and corresponding vertical (U) time series of the float (top) and correctly fixed (bottom) L1+B1 GPS+BDS single-epoch RTK solutions for an elevation cut-off angle of 10°. The 95% empirical and formal confidence ellipses and intervals are shown in green and red, respectively. The 24 hour (30 second) period is 22:00-22:00 UTC Jan. 5-6, 2016, for patch antennas in (a) and 21:48-21:48 UTC Jan. 8-9, 2016, for survey-grade antennas in (b), which are periods independent of the periods used to determine the stochastic model through the code/phase STDs in Table 1.
Figure 3 shows a good fit between the formal and empirical confidence ellipses/intervals, which thus illustrates realistic LS-VCE STDs in Table 1 that were used in the stochastic model. Note also the two-order of magnitude improvement when going from float to fixed solutions, and that the low-cost receiver plus survey-grade antenna has the most precise ambiguity-float positioning solutions.
Ambiguity Resolution and Positioning Performance for Higher Cut-Off Angles. We subsequently investigated the low-cost L1+B1 GPS+BDS performance for high elevation cut-off angles, so as to mimic situations in urban canyon environments or when low-elevation-angle multipath is present and is to be avoided. We have made comparisons to the survey-grade L1+L2 GPS results. It has been shown that a good ambiguity resolution performance does not necessarily imply a good positioning performance, so we investigated what effect this has on our positioning models.
The following integer least-squares (ILS) success rates (SRs) are thus computed based on epochs with the condition of positional dilution of precision (PDOP) ≤ 10 and averaged over all epochs over two days of data. By including and excluding epochs with large PDOPs, we can show how the positioning performance of the different models is affected by poor receiver-satellite geometries. To better understand how this exclusion of epochs with large PDOPs also influenced the empirical ambiguity-correctly-fixed positioning performance, we constructed TABLE 2, which shows the corresponding positioning STDs for two days of data. These STDs were computed by comparing the estimated positions to precise benchmark coordinates. In addition to the positioning performance, we depict in Table 2 the corresponding empirical ILS SR for full ambiguity-resolution, which is given by the ratio of the number of correctly fixed epochs to the total number of epochs.
TABLE 2. Single-epoch empirical STDs (N, E, U) of correctly fixed positions for the three positioning models together with their ILS SR for four elevation cut-off angles and 48 hours of data (Jan. 4–6 and Jan. 6–8, 2016). The empirical STDs and ILS SRs are also shown when conditioned on PDOP ≤ 10.
Table 2 shows that the L1+B1 low-cost receiver plus patch antenna combination has (as expected) smaller SRs in comparison to those when the survey-grade antenna is used. This latter combination has comparable SRs to the (PDOP-conditioned) SRs of the survey-grade L1+L2 GPS receiver for cut-off angles up to 25°.
In support of better understanding Table 2, FIGURE 4 shows typical positioning results for the different receiver and antenna combinations with elevation cut-off angles of 10° (top two rows) and 25° (bottom two rows). The first and third rows show the local horizontal (N, E) positioning scatterplots and the second and fourth rows the vertical (U) time series over two days of data. The float solutions are depicted in gray, and incorrectly and correctly fixed solutions in red and green, respectively. The zoom-in is given to better show the spread of the correctly fixed solutions with millimeter-centimeter level precisions. The formal ambiguity-float STDs are also shown under the up time series to reflect consistency between the empirical and formal positioning results.
FIGURE 4. Horizontal (N, E) scatterplots and vertical (U) time series for L1+B1 low-cost receiver with patch antenna (first column) with 99.5% (89.8%) ILS SR, L1+B1 low-cost receiver with survey-grade antenna (second column) with 100% (97.8%) ILS SR, and survey-grade L1+L2 GPS (third column) with 100% (94.1%) ILS SR, using 10° (top two rows) and 25° (bottom two rows) cut-off angles respectively (Jan. 4–6, 2016, for low-cost receiver with patch antenna and Jan. 7–8, 2016, for the low-cost and survey-grade receivers with survey-grade antennas). The SRs are conditioned on PDOP ≤ 10 and computed based on all epochs. Below the vertical time series, the ADOP is depicted in blue color, the 0.12-cycles level as red, and ambiguity-float vertical formal STDs are shown in gray.
We also depict in Figure 4 the ambiguity dilution of precision (ADOP) as an easy-to-compute scalar diagnostic to measure the intrinsic model strength for successful ambiguity resolution. The ADOP is defined as
(cycles) (4)
with n being the dimension of the ambiguity vector, the ambiguity variance matrix, and |.| denoting the determinant. ADOP gives a good approximation to the average precision of the ambiguities, and it also provides for a good approximation to the ILS SR. The rule-of-thumb is that an ADOP smaller than about 0.12 cycles corresponds to an ambiguity SR larger than 99.9%.
Figure 4 shows that more solutions are incorrectly fixed (red dots) when the ADOPs (blue lines) are larger than the 0.12 cycle level (red dashed lines). The figure also reveals that the L1+B1 low-cost receiver plus patch antenna combination achieves an ILS SR (99.5%) similar to that of the survey-grade L1+L2 GPS receiver (SR of 100%) for the cut-off angle of 10°. This ILS SR corresponds to the availability of correctly fixed solutions (green dots) with millimeter-centimeter level positioning precision over the two days. The L1+L2 GPS receiver has, moreover, large ambiguity-fixed positioning excursions at the same time as the formal STDs are large for the cut-off angle of 25° due the poor GPS-only receiver-satellite geometry for this high cut-off angle. This is also reflected by the corresponding relatively large ambiguity-fixed STDs depicted in Table 2 that are improved from decimeter- to millimeter-level when the PDOP ≤ 10 condition is applied. Figure 4 also shows that the L1+B1 low-cost receiver with the survey-grade antenna has a larger SR of 97.8% when compared to the PDOP-conditioned SR for L1+L2 GPS of 94.1% for the cut-off angle of 25° (see also Table 2), owing to the use of BDS that significantly improves the receiver-satellite geometry.
Finally, we also tested the low-cost receiver-solution (with survey-grade antennas) for a baseline length of 7 kilometers, where (small) residual slant ionospheric delays are present. It was shown that this combination still has the potential to achieve ambiguity resolution and positioning performance competitive with the survey-grade receiver-solution.
CONCLUSIONS
In this article, we evaluated a low-cost L1+B1 GPS+BDS RTK setup and compared its ambiguity resolution and positioning performance to a survey-grade L1+L2 GPS solution in Dunedin, New Zealand. The LS-VCE procedure was used to determine the variances of the low-cost receivers. The estimated variances are needed so as to formulate a realistic stochastic model, otherwise the ambiguity resolution and hence the achievable positioning precisions would deteriorate.
Since we analyzed a short baseline, the LS-VCE variances were shown to likely be affected by multipath. To mitigate multipath we connected the low-cost receivers to survey-grade antennas with better signal reception and multipath suppression abilities. It was shown that the survey-grade antennas can significantly improve the performance for the low-cost receivers so that the code/phase noise estimates more resemble that of survey-grade receivers. The LS-VCE STDs were furthermore shown to be realistically estimated for an independent time period.
We also demonstrated that the low-cost receivers can give competitive instantaneous ambiguity resolution and positioning performance to that of the survey-grade receivers. This is particularly true when the low-cost receivers are connected to survey-grade antennas.
ACKNOWLEDGMENTS
This article is based on the paper “On the Performance of a Low-cost Single-frequency GPS+BDS RTK Positioning Model” presented at the 2017 International Technical Meeting of The Institute of Navigation held Jan. 30-Feb. 1, 2017, in Monterey, California.
Ryan Cambridge at the School of Surveying, University of Otago, collected the low-cost receiver data. Author Peter J.G. Teunissen was supported by an Australian Research Council Federation Fellowship. All of this support is gratefully acknowledged.
MANUFACTURERS
The low-cost receivers used in the research were u-blox EVK-M8T receivers. The survey-grade receivers were Trimble NetRS receivers. The patch antennas were u-blox ANN-MS antennas, while the survey-grade antennas were Trimble Zephyr 2 GNSS antennas.
ROBERT ODOLINSKI conducted his Ph.D. studies at Curtin University, Perth, Australia, from 2011 to 2014. His research focus is next-generation multi-GNSS integer ambiguity resolution enabled precise positioning. In 2015, Odolinski started his position as a lecturer/research fellow in geodesy/GNSS at the School of Surveying, University of Otago, New Zealand.
PETER J.G. TEUNISSEN is a professor of geodesy and navigation and the head of the Curtin GNSS Research Centre, Curtin University. He is also with the Department of Geoscience and Remote Sensing, Delft University of Technology, Delft, The Netherlands. His research interests include multiple GNSS and the modeling of next-generation GNSS for high-precision positioning, navigation and timing applications.
FURTHER READING
• Authors’ Conference Paper
“On the Performance of a Low-cost Single-frequency GPS+BDS RTK Positioning Model” by R. Odolinski and P.J.G. Teunissen in Proceedings of the 2017 International Technical Meeting of The Institute of Navigation, Monterey, California, Jan. 30 – 1 Feb., 2017, pp. 745–753.
• Authors’ Related Work
“Single-Frequency, Dual-GNSS Versus Dual-frequency, Single-GNSS: A Low-cost and High-grade Receivers GPS-BDS RTK Analysis” by R. Odolinski and P.J.G. Teunissen in Journal of Geodesy, Vol. 90, No. 11, 2016, pp. 1255–1278, doi:10.1007/s00190-016-0921-x.
“Combined BDS, Galileo, QZSS and GPS Single-frequency RTK” by R. Odolinski, P.J.G. Teunissen and D. Odijk in GPS Solutions, Vol. 19, No. 1, 2015, pp. 151–163, doi:10.1007/s10291-014-0376-6.
“Instantaneous BeiDou+GPS RTK Positioning With High Cut-off Elevation Angles” by P.J.G. Teunissen, R. Odolinski and D. Odijk in Journal of Geodesy, Vol. 88, No. 4, 2014, pp. 335–350, doi: 10.1007/s00190-013-0686-4.
“The Future of Single-Frequency Integer Ambiguity Resolution” by S. Verhagen, P.J.G. Teunissen and D. Odijk in Proceedings of the VII Hotine-Marussi Symposium on Mathematical Geodesy, Rome, June 6–10, 2009, edited by N. Sneeuw, P. Novák, M. Crespi and F. Sanso, International Association of Geodesy Symposia, Vol. 137, 2012, pp. 33–38, doi:10.1007/978-3-642-22078-4 5.
“Centimeter-Level Positioning for UAVs and Other Mass-Market Applications” by C. Mongredien, J.-P. Doyen, M. Strom and D. Ammann in Proceedings of ION GNSS+ 2016, the 29th International Technical Meeting of the Satellite Division of The Institute of Navigation, Portland, Oregon, Sept. 12–16, 2016, pp. 1441–1454.
“Initial Assessment of the COMPASS/BeiDou-2 Regional Navigation Satellite System” by O. Montenbruck, A. Hauschild, P. Steigenberger, U. Hugentobler, P.J.G. Teunissen and S. Nakamura in GPS Solutions, Vol. 17, No. 2, 2013, pp. 211–222, doi:10.1007/s10291-012-0272-x.
• LAMBDA
“On the Reliability of Integer Ambiguity Resolution” by S. Verhagen in Navigation, Vol. 52, No. 2, Summer 2005, pp. 99–110, doi: 10.1002/j.2161-4296.2005.tb01736.x.
“ADOP in Closed Form for a Hierarchy of Multi-frequency Single-baseline GNSS Models” by D. Odijk and P.J.G. Teunissen in Journal of Geodesy, Vol. 82, 2008, pp. 473–492, doi: 10.1007/s00190-007-0197-2.
Components easily pack into a baseball-style case. Photo: Nicholas DiGruttolo
By Nicholas DiGruttolo
When asked to do a small survey job overseas, we were concerned about shipping bulky and expensive survey equipment. Shipping costs are not trivial. Add to that the real possibility that your survey equipment may be confiscated by the local authorities, as ours was in Djibouti, and the cost of shipping equipment becomes a substantial part of the overall job. There should be alternatives, especially if accuracy requirements are not stringent.
Faced with this problem for a second time, we considered a new receiver system that has many advantages over conventional survey-grade GNSS receivers: It is small, lightweight and low-cost without sacrificing performance, making it ideal for precision surveying in remote areas of the world and for traveling to the job site by commercial airline. All the components, including the tripods, rods and batteries, are constructed from commercial off-the-shelf (COTS) components. A complete base and rover kit fits in a baseball bag and weighs less than 10 kilograms. The kit is sized and approved as carry-on luggage.
The system is scalable from a simple single-frequency semi-mobile receiver for control networks and some semi-kinematic mapping applications, to a dual-frequency network RTK solution.
The system comes with free processing software that supports carrier-phase relative positioning in real time and post mission, as well as precise-point positioning (PPP) and CA-code differential correction. The software is designed with a simple user interface for easy selection of base and rover data or automatic data download of the closest Continuously Operating Reference Station (CORS) from the U.S. National Geodetic Survey database.
Complete survey set including GNSS receiver, antenna, battery and cables, fits in a small handheld plastic case. Photo: Nicholas DiGruttolo
The system fills a gap between survey applications, where centimeter-level precision is an absolute necessity, and mapping applications, where meter-level is tolerable. The product offers sub-foot precision in most cases and centimeter precision in ideal situations.
Our team recently performed topographic mapping of an oil refinery site in Saudi Arabia and surveyed a precise-elevation network in Sarasota, Fla., to research the effects of sea-level rise. The small size of the COTS components simplified transport to Saudi Arabia, eliminating additional airline baggage fees and easing import through customs. Researchers performing the sea-level study reduced field time by increasing the number of receivers needed to observe a robust vertical control network.
Oil Refinery. The oil refinery project entailed mounting a GNSS antenna on the roof of an off-road vehicle and driving multiple transects around the 18-kilometer perimeter of the site to record the elevation of the terrain. Kinematic data was recorded at 1 Hz using a GPS-only version of the single-frequency receiver. Baseline length to the local reference station varied from less than 1 kilometer to about 10 kilometers. The site was open desert with no overhead obstructions or sources of multipath other than the roof of the vehicle on which the antenna was mounted. Post-processing and comparison to simultaneously collected data from a high-precision survey-grade receiver revealed positional accuracy of about 5 centimeters horizontal and 10 centimeters vertical, when the system’s trajectory was compared to the truth trajectory provided by the survey-grade receiver. Figure 1 shows the difference between the two trajectories. The system’s antenna was 2 feet away from the survey-grade antenna along the driving direction of the vehicle; the trajectory was mostly in the north-south direction and hence the 0.6-m offset in the plot!
Figure 1. Antenna location difference in the sub-decimeter range between the survey-grade system and the compact low-cost system. Note: A 0.6-m offset is to be removed from the difference, as the two antennas were mounted 0.6 m apart in the vehicle driving direction.
Sea Level. The sea-level-rise study required a high-accuracy vertical control network to cover a 2,500 hectare area. The purpose of the network is to determine the shortest term effects of sea-level rise with a rate of 1.8 millimeter/year in the affected area. Ten benchmarks were established throughout the area of interest, and a robust network of static observations was performed with a combination of two dual-frequency and two single-frequency receivers. The single-frequency receivers were GPS-only units where two standard 4-inch patch antennas were mounted on rods adjusted to a 0.9-meter height. The addition of two receivers provided greater redundancy and a stronger network solution in much less time than would have been possible with only one pair of survey-grade receivers. Figure 2 shows the addition of several loop ties to the network as a result of adding the two roving, lightweight receivers.
Figure 2. Sea-level rise monitoring network showing increased tie points and redundancy as a result of adding the extra lightweight precision receivers to the survey-grade receivers.
Nicholas DiGruttolo works as a field surveying manager for JBrown Professional Group Inc., Northrop Grumman Corporation, and has recently become vice president of surveying.
