After RTK - Part 1

Will advances in Precise Point Positioning succeed base-rover and network RTK?
By Gavin Schrock, PLS
“Always do whatever’s next”—George Carlin
 Note: this is an expanded version of the article of the same name in the June issue of Professional Surveyor Magazine; the expanded version gave us an opportunity to elaborate on some of the geekier elements of the subject and to add a suggested reading list. The PPP-RTK subject continues in the July print issue in “Taking Cues from the Other Fieldwork,” an examination of the development of PPP-RTK solutions for precision agriculture and how these developments will likely inform similar solutions for surveying.

Improving on What Is Already Pretty Amazing

No matter how new or amazing a technological tool is that we use while surveying out in the field, our thoughts often turn to the apparent shortcomings of that tool, and we start imagining faster, better, and more cost-effective tools: always setting our sights higher. I’m reminded of the classic Calvin and Hobbes comic where Calvin is reading the instructions on the back of a microwave popcorn packet exclaiming, "It takes 6 minutes to microwave this. Who’s got that kind of time?" GNSS, almost without argument (among those who use it), is one of the most amazing technological developments ever, but is no exception to this dynamic.
Imagine being able to turn on a GNSS rover anywhere in the world and being able to achieve centimeter precisions in real-time, without having to set up a base and without having to connect with a network. That scenario is not necessarily on some distant horizon, and a recent symposium on the subject, held in Frankfurt in February of 2012, yielded some great insights into just how close were are to those capabilities. The future of high precision real-time GNSS is here, sort of … 
Welcome to “GNSS Next,” an ongoing series of articles exploring the next stages in high-precision GNSS, with a specific emphasis on how these developments will serve surveying and related industries. The first few installments will be dedicated to PPP-RTK, what many see as the most-likely viable successor (or complement) to RTK and Network RTK (RTN): current state of the technology, how it works, possible timelines for productization for surveying use, and some practical and perhaps legal considerations when adopted. GNSS Next installments in the print version of PSM will be supplemented with expanded online versions; the online versions like this will include the geekier elements and reference links.  Subsequent installments will also look at such subjects as constellation upgrades, the impacts of the new signals, jamming mitigation, and communications options for transmission of corrections, other challenges to GNSS, and new GNSS product types and applications on the near horizon.
So, back to the likely successor to RTK/RTN, Precise Point Positioning (PPP) and related approaches like PPP-RTK and States Space Representation (SSR). These ideas are not new—they’ve been available in one form or another almost as long as RTK—but now they’re nearly ready to hit prime time. Some reading suggestions will be referenced throughout this article to a reading list to follow, and as PPP is now moving out of purely academic circles it will soon (most likely) greatly benefit surveying in the near future; it is good idea that we surveyors read up on it. A really informative intro into PPP (see Reading List[1]) was put together by Dr. Richard Langley (of the University of New Brunswick and host of the Canspace geodesy forum). Though a bit techie, it is a good starting point to learn about legacy PPP.
Before we examine these concepts and initials, let’s back up to look at the evolution of high-precision GNSS to understand how PPP came about and more importantly why.  

Precise Point Positioning in the Evolution of GNSS

Single frequency post-processing came about in the years following the launch of the U.S. GPS constellation in 1978. This allowed amazing feats of positioning, even far from civilization and control marks, plus positioning on the seas and in the air. Early commercial receivers began to hit the geodesy and surveying communities for post processing around 1982, followed by early real-time systems like differential services for marine applications. Commercial dual-frequency hit about 1988. Even then, many thought we had reached the pinnacle of GPS capabilities, but development did not stand still.
Post processing of the day enabled high precisions, and it still does, widely held as a “gold standard.”  Arguably the ultimate in GNSS positioning, post-processing has its own drawbacks for certain applications; it requires temporary or permanent infrastructure (bases or CORS), takes many hours and a lot of skill to do properly—it’s good, but not fast or cheap. Differential real-time of the day required less infrastructure, but it was not very precise—fast, but not good or very cheap. For many applications like surveying and construction, there was a need for higher precision real-time, and in 1992 the first commercial Real-Time Kinematic (RTK) solutions hit the market. 
By utilizing dual-frequencies, and differential methods (read up on “double differencing” and “ambiguity fixing”) RTK could yield precisions comparable to that of full post-processing (over short baselines), but in real time. This was good, fast, but not exactly cheap (a base and often someone to watch was needed). A new twist on RTK was added in the late 90s: network RTK (RTN). RTN allowed for longer baselines, not having to set up a base, geodetic reference, and some other elements could be added (that feature quite prominently in PPP), like improved orbit and geodynamic model data. Fast and good, but again, not exactly cheap as there still needed to be infrastructure.
While DGPS was fast enough, good enough, and cheap enough for marine navigation, some agricultural uses, and some mapping uses, it was not good enough for surveying. RTK and post-processing is definitely good enough for surveying, fast enough (depending on the application), and arguably cheap enough. But within academic and scientific circles, as well as industries like marine construction and others in remote or offshore locations without infrastructure, none of these tools suited their needs for affordable high precision.
It is generally accepted among academics that the concept of Precise Point Positioning (PPP) was introduced in a 1995 paper (see Reading List[2]) by Pierre Héroux and Jan Kouba of Natural Resources (NRcan) Canada. The idea was to utilize very precise clock and orbit products and observations of a single rover to resolve the distance from multiple satellites to said rover. This differs from post-processing, DGPS, RTK, and RTN as those methods rely on comparing observations from the rover with those of one or more external receivers—in short, differencing. While it may seem like an oversimplification, it essentially is a contrast between relying wholly on “observations” and relying on “error states” products (i.e. clock, orbit, ionospheric, and tropospheric models).  Some refer to these two as Observation Space Representation (OSR) and States Space Representation (SSR). You’ll be hearing much more about SSR in the near future; the RTCM committee (the international body that establishes data transmission standards such as GNSS correction flavors like RTCM3.1 et al) has already established a standard for transmission of these SSR (see Reading List[3][4]) error states messages.
That such developments would come from academia, science, and natural resources interests like Natural Resources Canada (NRCan) would invest in the development of PPP speaks to their needs. Canada is mind-boggling huge with sparsely populated areas of rich natural resources and very sparse geodetic references. It’s not cost effective to set up tens of thousands of CORS or establish enough marks to set your base up on, so no wonder much PPP development comes out of Canada. The same kind of motivations came from academia worldwide; studies of plate tectonics (earthquakes, volcanoes) and resource management in remote areas (and in reality most of the earth and its oceans are remote) do not lend themselves well to precision/speed/cost trade-offs of the other methods. A new method, PPP was born of these needs.

PPP Parts, Products, Processing, and Performance

To make PPP work, like other GNSS positioning methods, you have to determine with great certainty the distance from the phase center of your rover to that of multiple satellites. To do this you need to know a few things: where was the satellite when the signal left it, what time was it when it left, and what time was it when you received it. PPP, as opposed to RTK and other relative/differential methods, relies almost exclusively on really tightly tracked satellites and very tight clock offset data (products), and this requires very well coordinated tracking and clock-orbit product realizations worldwide. These clock/orbit products need to be derived from a worldwide array of CORS stations of the highest order tied to global reference frameworks. And this is where an amalgam of scientific agencies, academic institutions, space agencies, governments, and private industries collaborated on voluntary and self-governed cooperative arrays like that of the International GNSS Service for Geodynamics (IGS see Reading List[5]), begun in 1993.
The IGS pools resources of over 200 entities worldwide. These resources include GNSS tracking stations, CORS, data centers, and analysis centers. Various partners, like NASA’s Jet Propulsion Laboratory, produce clock and orbit products that are freely available for public use. There are also private tracking networks operated by the likes of Navcom (a John Deere Company), and Fugro (an infrastructure and geodynamics monitoring company), Trimble, and Veripos (a marine and land construction resources company), that generate clock and orbit products for their customers within precision agriculture, marine construction, monitoring, and geodynamics data needs that may not be met by conventional relative GNSS methods.
You may already be using the same types of clock and orbit products PPP uses without realizing it; a number of the Satellite Based Augmentation Services (SBAS) like the Federal Aviation Administration’s (FAA) Wide Area Augmentation System (WAAS) and Navcom’s Starfire services (mainly for agriculture) rely heavily on clock/orbit. Some surveying rovers have even been designed to utilize SBAS transmissions to augment conventional differential approaches, like the Ashtech PM100, a single-frequency unit that adds SBAS and can work in a base-rover pair and can yield centimeter precisions post-processed; solutions like this are ways that manufacturers can deliver high precision with lower-cost hardware (but not necessarily very precise in real-time mode). RTN software developers typically apply orbit products directly in the solutions, with some applying PPP-like methods and products as part of the process and then converting outputs to standard correction type’s standard RTK/RTN rover use. The latter is how the Geo++ GNSMART system is used on many RTN works.
Some surveyors and geodesists may already be familiar with PPP, and there are existing resources and solutions for both single frequency and dual-frequency applications. Indeed, there are already some existing free services you might want to take for a spin, though you should note the reference framework of the outputs (NRcan’s service outputs in ITRF or NAD83-CSRS, which is handy if you are working in Canada). You can upload the observations from your receiver to a free portal hosted by Natural Resources Canada’s PPP service (see Reading List[6]), or try NASA/JPL’s Automated Precise Positioning Service (see Reading List[7]). 
These services work a lot like the National Geodetic Survey’s (NGS) online services where you upload your observation files and the service spits out a resolved position, but the similarity ends there. OPUS and OPUS-RS rely on a relatively dense network of CORS and their observations for traditional baseline processing. But like OPUS, the resultant precisions of these PPP services are a direct function of the length of observations.  
For PPP this “convergence,” or time needed to achieve the best possible position from a set of rover observations, has in the past been the biggest hurdle to overcome for PPP developers and those who wish to implement PPP more broadly into applications for surveying, construction, and precision agriculture. The pioneers of PPP yearned for real time as well; science and academia also realize that post-processed PPP has limited utility. Last year’s earthquake and tsunami in Japan have accelerated research into real-time detection and warning systems, indicating that PPP is better suited to monitoring offshore, far from CORS infrastructure.

Drivers for Use and Development

More than a few of your fellow surveyors have been using PPP for many years: surveyors who take up contracts in developing countries with little or no CORS infrastructure, or sites in Oceania or otherwise-remote locales have found that PPP can be utilized with great reliance. But, you have to be patient. PPP is used by surveyors even inside the United States; it is a post-processing alternative that does not require fixed or temporary CORS, and some use it to establish primary control or as a redundant check for OPUS. It’s not a tool to be used casually unless you become fully aware of its limitations.
Academia and science have been using PPP for tectonic plate movement studies since PPP first hit the scene. There are numerous research outfits like the geodesy Lab of Central Washington University (CWU) who have hosted a CORS array known as PANGA (Pacific Northwest Geodetic Array, see Reading List[8]) for more than 15 years. PANGA includes hundreds of science CORS and pulls data from several state’s RTNs. CWU utilizes not only an array of PPP tools like NASA/JPL’s Gipsy for long-period post-processed time series, but has also integrated the rapid/high-precision motion engines of Trimble VRSNet into their analyses.
As with the efforts in Japan to improve earthquake/tsunami/volcanic detection and warning systems, these common goals and drivers have prompted science and academia worldwide to further develop PPP and overcome the sloooowness of legacy PPP solutions. Like the developments in real-time PPP for precision agriculture, we surveyors will eventually benefit from such research. Read more about the real-time PPP developments in agriculture in “Taking Cues from the Other Fieldwork” in the July 2012 issue of Professional Surveyor Magazine.   
On the subject of the 2011 Japan earthquakes and tsunamis, a very compelling presentation was given at the recent Frankfurt PPP Symposium by the Hitachi Zosen company, prime contractor on the offshore GNSS buoys that hold such promise in improving tsunami warning systems (see Reading List[9]). There are several challenges for offshore tsunami detection and warning buoys: they need to be far offshore (a hundred kilometers or more), they have to withstand rough seas, and they need to be able to return high-precision sea-rise data in real time.
Japan has the largest homogenous CORS array in the world; the baseline lengths to the desired buoy locations are too long for conventional RTK or RTN solutions and the convergence times would be too long for legacy PPP methods. These 30+ ton buoys are designed for brutal sea conditions, far offshore and in deep water, and, while the existing buoys responded admirably during the 2011 events, true functionality will only be realized by having more bouys, farther offshore. And the key to success will be in coming up with a hybrid PPP solution that responds with high precisions—and rapidly. Promising results have come from leveraging the iono and tropo data from the existing onshore CORS array and enabling ambiguity resolution, which the research team refers to as PPP-AR. Such methods, adding ambiguity resolution to PPP, feature prominently in nearly every one of the advanced PPP solutions presented at the same symposium: parallel development among many academic and commercial research entities worldwide. 
PPP can be most certainly cheap, and even good, but the challenge lies in the realm of fast. To have viable real-time PPP these issues need to be overcome. There have been some great strides in overcoming the convergence time challenge, and there are currently some successful real-time PPP applications both academic and commercial.

PPP-RTK’s “Show and Tell”

In February of 2012, a symposium on PPP-RTK and open standards was hosted by the BKG (Germany’s federal agency for cartography and geodesy) in Frankfurt. Over 180 GNSS positioning developers, pioneers, manufacturers, practitioners and academics participated in this PPP “show-and-tell” that may very well be remembered as an unofficial coming-of-age event for real-time PPP. This was an event of some of the “deepest geekage” I could have imagined, but I was not the only one scratching his head over how far the research into real-time PPP has come through the efforts of so many scientific and commercial teams, both collaboratively and independently. 
Getting over my apprehension as one of the few relatively geek-challenged attendees, I found these genius types to be quite affable and willing to de-geek such heady concepts for outsiders. And, while quite respectful of their scientific peers, and all presenting with great depth and candor, we have to remember that there is still an element of competition even among academic institutions, so some of their best cards were held understandably close to the chest.
So, what are the differences between the legacy PPP solutions and those for real-time PPP that these fine minds have been working on? Starting with the fundamentals of legacy PPP: how does it work anywhere in the world and without having to connect to a network? The key is in the external products, developed from worldwide resources like the IGS or commercial networks. The basics are the clock and orbit products: these have to be the best possible. Orbit products have improved dramatically over the three decades of GPS/GNSS. Surveyors are familiar with the after-the-fact orbit products like Precise Orbits that they apply to post-processing sessions. What some may not realize is that some of the predicted orbit products (from NASA et al) like Ultra-Rapid Orbits are now so tight that if used in post-processing they can yield nearly the same results. Some surveyors may also not realize that products like Ultra-Rapid Orbits are already applied to their RTN solutions (as opposed to base-rover RTK that relies on broadcast orbits). The same applies to clocks; incredibly tight clock offset products are now available freely and frequently enough to enable near-real-time PPP. Some commercial providers have improved on the free products for their customers. Additional error state products desired for advanced PPP applications include elements of space weather like Total Electron Content (TEC) in both the vertical (VTEC) and slant versions (STEC).
Another huge bonus of this error-state-product-centric method is that the “products” are very small data files in comparison to full GNSS observation files; this is a key to the delivery methods that can be employed. These various “error states” products are a representation of a current state of an error source (like clock and orbit). There is a term called “States Space Representation” (SSR) which is contrasted by another term “Observation Space Representation” OSR, which refers to the observation-centric methods of post-processing, RTK, and RTN. To send the observations from one receiver or CORS can run 500 bytes per second or more; now multiply that by an entire network. A combined transmission of all of the “states”-type products needed to broadcast, let’s say by single satellite channel, for an entire region, state, or country could be less than one set of real-time observations. Some of the commercial providers are doing just that. More efficient and cheaper communications are afoot. 
One presenter at the symposium is currently testing the transmission of these relatively tiny SSR type messages via television signals (see Reading List[10]), and there is talk of regions leasing channels on satellites, or perhaps channels on satellite radio—so many more options that we currently have.
But even with the advances in clocks and orbits, there is still a trade-off in precision and time convergence. With legacy clock and orbit solutions alone, it can take 10-90 minutes to get even 10cm: good and cheap but not fast. Or you can have a rapid solution, but not at all precise: fast and cheap, but not good. Innovations presented at the recent symposium to overcome the challenges of fast mostly rely on adding several more “error states” products, mainly regional or localized ionospheric models (a lot like RTN derive and apply to their solutions).  This enables good and fast, but veering into the territory of not cheap as you have to rely on some CORS infrastructure.
These issues too will likely be overcome in the near future, and perhaps, as many speculate, this may enable less-dense networks and most certainly alternative communications methods. One option is to do variations on a kind of hybrid of PPP and RTK (leveraging regional RTN), dubbed PPP-RTK, and applying elements of certain legacy solutions, like doing full or partial ambiguity fixes. Again, this relies on CORS infrastructure, and that eats into the territory of cheap.
Among the developers of real-time PPP there are many approaches. There is talk of PPP with ambiguity fix, with partial ambiguity fix, without ambiguity fix, with de-coupled clocks, etc.  OK, I’ll drop the pretense of really knowing how these work, and besides putting you to sleep, I would probably get taken to task by the science guys for misrepresenting their approaches. Suffice it to say that there are many innovative approaches nearing the same improved thresholds for precision and convergence time.

There are varied approaches known as the “French method” (see Reading List[11]), the “GFZ method” from the German Research Center for Geosciences (see Reading List[12]), the “Canada DNR method” (see Reading List[13]), and many more.  There are solutions developed by commercial entities like Deere Inc. and Trimble (initially developed for precision agriculture, see July 2012 issue of Professional Surveyor Magazine and Reading List[14] [15]), Fugro and Veripos for worldwide monitoring, energy, and marine construction (see Reading List[16] [17]), and GPS Solutions Inc. (see Reading List[18]) for a wide variety of applications. The reason I have loaded you down with references to these respective presentations is that a quick review will give you an idea of how far along these solutions have come as well as the challenges facing implementation for many surveying applications—great progress but still a ways to go.
The search for a “sweet spot” in the trade-offs between precision and convergence time, at least in terms of something that would be viable for typical surveying (something like 1cm-3cm in 3D in a few seconds, perhaps after an initial convergence of a few minutes or less) has been achieved by these and other developers and researchers. In most cases the best results have had to include additional error states data from local networks (CORS spaced at around 100km).
Japan has been a particularly interesting “petri-dish” for such solutions to grow: this from having the 1,200+ CORS national network available and the new quasi-orbit QZSS satellites coming online. A neat thing about the QZSS constellation (though the final build out will be only three or four satellites) is that they follow a figure-8 orbit over Japan, Australia, and areas in between: this orbit designed to have at least two of the satellites in high-sky view at all times—great for urban canyon and canopy-challenged GNSS applications. In addition to some signals to be interoperable with other constellations, QZSS has some test bandwidth set aside for research, and there have been tests adding QZSS into the PPP mix (see Reading List[19] [20]). The possibility that such regional augmentations systems may also be able to deliver the combined error states messages via satellite-QZSS may very well be delivering this double benefit soon.
There is certainly competition among commercial developers of the PPP solutions, but this is also true of academic institutions; there is a lot of patent activity with regards to various PPP approaches. We all benefit from such healthy competition. And there are also elements of open-source developments. One such element is RTKLIB (see Reading List[21]). Some recent experiments in real-time PPP by the same team who developed much of RTKLIB yielded some astounding results (see Reading List[22]).
A great summation of the current state of real-time PPP and how these developments might impact RTN (see Reading List[23]) came in the presentation at the symposium by Tamás Horváth, operator of the public RTN in Hungary. He pointed out that despite the success of many of these scientific and commercial innovations to overcome the fast/good/cheap trade-off, the current state of PPP is still not yet suited for high-precision real-time uses like surveying. But he noted we are perhaps close enough to viability that RTN operators should begin partnering with the PPP community as likely providers of “error states” products, in particular the ionospheric model products that seem to be the key to PPP overcoming the fast challenges. 

How Soon for Surveying?

How close are we to seeing this as viable for surveyors? Will we need new rover equipment? Will multiple constellations and new signals bring this any sooner? Will the need for RTN infrastructure go away? The short answer (from an informal question posed to a number of the developers at the symposium) was that we are looking at almost immediately a PPP-RTK hybrid (which indeed already exists in some forms), but that PPP free of dense networks is about five years out.
There would likely not be any need for new rovers to take advantage of PPP-RTK. Some manufacturers already have experience in developing SBAS receivers and receivers that can use PPP-like solutions for aviation and agriculture. A number of developers at the symposium, like Dimitry Kolosov of Topcon’s Moscow Technology Center, said that adapting current rovers is more of a software consideration than one of hardware.
RTN, as arrays of CORS, serve also geodetic reference framework infrastructure and would likely be valued for that reason, even if they were not necessarily needed in the same density required to produce legacy RTN corrections. And there seems to be no avoiding the need for locally generated “error state” products in future PPP solutions—RTN will need to be around for a very long time.
But how would such a technology change the way surveyors do their job? What would be the repercussions of the possibility that such high precision real-time positioning could be faster and cheaper and useable anywhere, with little or no infrastructure, and by potentially anyone, even non-surveyors? Those are some pretty big issues to examine—we’ll have to leave those to another installment.  For now, let’s just suffice it to say that there is something cool on a near horizon, and it would behoove us surveyors to learn more about it. 


Gavin Schrock, PLS is a surveyor, technology writer, and operator of an RTN. He’s also on our editorial board.
Reading List:

  1. “Innovation: Precise Point Positioning, A Powerful Technique with a Promising Future.” Sunil B. Bisnath, Yang Gao, GPS World.
  2. GPS Precise Point Positioning with a Difference. Pierre Héroux and Jan Kouba of Natural Resources (NRcan) Canada 1995.
  3. RTCM State Space Representation (SSR) Overall Concepts Toward PPP-RTK. Gerhard Wübbena, Geo++ GmbH 2012.
  4. RTCM State Space Representation Messages, Status and Plans. Martin Schmidt Geo++ GmbH. RTK2012/06_Schmitz_Martin.pdf
  5. IGS – International GNSS Service, reference links page:
  6. Natural Resources Canada, NRCan's PPP  (Precise Point Positioning) is a free online post-processing service that allows GPS users in Canada (and abroad) to compute better-accuracy positions from their GPS raw observation data.
  7. APPS accepts GPS measurement files and applies the most advanced GPS positioning technology from NASA's Jet Propulsion Laboratory to estimate the position of your GPS receivers, whether they are static, in motion, on the ground, or in the air.
  8. The Pacific Northwest Geodetic Array (PANGA) uses real-time GPS measurements to monitor crustal deformation and mitigate natural hazards throughout the Pacific Northwest. These hazards arise from earthquakes, volcanic eruptions, landslides, and coastal sea-level encroachment.
  9. Development of Japanese Disaster Mitigation System Using Real-time PPP with Ambiguity Resolution for Tsunami Buoys and Ground Network. Masayuki Kanzaki, Yasuhiro Matsushita, Hitoyoshi Nishimura, Akira Wada, Hideshi Kakimoto, Minoru Hayashi of Hitachi Zosen Corporation, Tokyo, Japan.
  10. Lossless RTCM data compression for broadcasting via TV satellite links. Rafa Mielniczuk, Andreas Engstler, Harald Gebhard, Univ. of Applied Sciences, Konstanz &AGH Univ. of Science and Technology, Kraków.
  11. Phase Biases Estimation for Undifferenced Ambiguity Resolution. D. Laurichesse, Centre National d’Etudes Spatiales Toulouse, France.
  12. Augmenting Global Real-Time PPP Service With Regional Network For Instantaneous cm-Level Positioning. Maorong Ge, Xingxing Li, Hongping Zhang, Thomas Nischan, Markus Ramatschi, Soeren Klose, Jens Wickert, German Research Centre for Geosciences.
  13. Undifferenced GPS Ambiguity Resolution using the Decoupled Clock Model and Ambiguity Datum Fixing. Paul Collins ,York University, Toronto, Natural Resources Canada, Sunil Bisnath York University, Toronto,  François Lahaye and Pierre Héroux, Natural Resources Canada.
  14. NavCom Global StarFire Service. Chaochao Wang, John Deere Company.
  15. Worldwide Centimeter-Accurate GNSS Positioning using Trimble RTX Technology. Herbert Landau, Trimble Navigation. RTK2012/17_Landau_Herbert.pdf
  16. Fugro’s Precise (Point) Positioning Services. Kees de Jong & Xianglin Liu.
  17. Providing GNSS Augmentation Data: A Commercial Service Provider’s Perspective. Pieter Toor, Research & Innovation Manager, Veripos.
  18. Processing GNSS Data in Real-time: Algorithms, Issues, and Challenges, Leoš Mervart, Christian Rocken, Zdeněk Lukeš, GPS Solutions Inc. & Institute of Geodesy, TU Prague.
  19. Centimeter-class Positioning Augmentation Utilizing Quasi-Zenith Satellite System. Y. Sato, M. Saito, M. Miya, M. Shima, Y. Omura, J. Takiguchi, Mitsubishi Electric Corporation, K. Asari Satellite Positioning Research and Application Center (SPAC).
  20. JAXA’s PPP experiment  via QZSS.  Japan Aerospace Exploration Agency, M. Miyoshi, K. Kawate, S. Kogure, and H. Noda, H. Soga, Y. Hirahara, T. Sawamura,  A. Yasuda, Tokyo University of Marine Science and Technology.
  21. RTKLIB is an open source program package for standard and precise positioning with GNSS. RTKLIB consists of a portable program library and several application programs utilizing the library. There are tools and algorithms for PPP, DPOGS, RTK, and more.
  22. PPP Ambiguity Resolution Implementation in RTKLIB v 2.4.2. Tomoji Takasu, Tokyo University of Marine Science and Technology.
  23. PPP-RTK: Friend or Foe? from the network RTK  service providers’ point of view.

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