Chapter 1
Introduction

Over the last decade, the development and application of GNSS (global navigation satellite system) has been unabatedly progressing. Not only is the modernization of the U.S. GPS (global positioning system) in full swing, the Russian GLONASS (Global'naya Navigatsionnaya Sputnikovaya Sistema) system has undergone a remarkable recovery since its decline in the late 1990s to be now fully operational. The first static and kinematic surveys with the Chinese Beidou system are being published, and the signals of the European Galileo system are being evaluated. While many individuals might look back on the exciting times they were fortunate to experience since the launch of the first GPS satellite in 1978, there are many more enthusiastic individuals gearing up for an even more exciting future of surveying and navigation with GNSS. Yes, it seems like a long time has passed since sunset admirers on top of Mount Wachusett, seeing a GPS antenna with cables connected to a big “machine” in a station wagon were wondering if it would “take off,” or if you were “on their side,” or regular folks in a parking lot approaching a car with a “GPS” license plate were wondering if you had “such a thing.”

Much has been published on the subject of GNSS, primarily about GPS because of its long history. Admirably efficient search engines uncover enormous amounts of resources on the Internet to make an author wonder what else is there to write about. We took the opportunity of updating GPS Satellite Surveying to add strength by including two additional authors, while looking at rearranging the material in a way that reflects the maturity and permanency of the subject and de-emphasizes the news of the day or minor things that may have gotten the early pioneers of GPS excited.

Perhaps the most visible outcome of the rearrangement of the material for this edition is that GNSS in earnest starts only in Chapter 5, which may come as a surprise to the unexpected reader. However, if was determined that first presenting the geodetic and statistical foundations for GPS Satellite Surveying would be more efficient, and then focusing on GNSS, thus taking advantage of having the prerequisites available and not being side-tracked by explaining essential fill-in material. Therefore, there are two chapters devoted to least-squares estimation, followed by a chapter on geodesy. These three chapters clearly identify the traditional clientele this book tries to serve, i.e., those who are interested in using GNSS for high-accuracy applications. The other chapters cover GNSS systems, GNSS positioning, RTK (real-time kinematic), troposphere and ionosphere, and GNSS user antennas. There are nine appendices.

Chapter 2, least-squares adjustment, contains enough material to easily fill a regular 3-credit-hour college course on adjustments. The focus is on estimating parameters that do not depend on time. The material is presented in a very general form independently of specific applications, although the classical adjustment of a geodetic or surveying network comes to mind as an example. The approach to the material is fairly unique as compared to a regular course on least squares because it starts with the mixed model in which the observations and the parameters are implicitly related. This general approach allows for an efficient derivation of various other adjustment models simply by appropriate specifications of certain matrices. Similarly, the general linear hypothesis testing is a natural part of the approach. Of particular interest to surveying applications are the sections on minimal and inner constraints, internal and external reliability, and blunder detection.

Chapter 3, recursive least squares, represents new material that has been added to this fourth revision. In particular in view of RTK application where the position of the rover changes with time, it was deemed appropriate to add a dedicated chapter in which the estimation of time-dependent parameters is the focus. Consequently, we changed the notation using the argument of time consistently to emphasize the time dependency. A strength of this chapter is that it explicitly deals with patterned matrices as they occur in RTK and many other applications. Apart from the term “recursive least squares,” other terms might be “first-order partitioning regression” or “Helmert blocking,” that express the technique applied to these patterned matrices. Although Chapters 2 and 3 are related since there is only one least-squares method, Chapter 3 stands on its own. It also could serve easily as a text for a regular 3-credit-hour college course.

Chapter 4 is dedicated to geodesy. It provides details on reference frames, such as the ITRF (international terrestrial reference frame), as well as the transformation between such frames. The geodetic datum is a key element in this chapter, which is defined as an ellipsoid of defined location, orientation, and size and an associated set of deflection of the vertical and geoid undulations. Establishing the datum, in particular measuring gravity to compute geoid undulations, is traditionally done by geodesists. The fact that here it is assumed that all this foundational material is given indicates that geodesy is treated not as a science by itself in this book but rather as an enabling element that supports accurate GNSS applications. As the “model for all,” we present the three-dimensional (3D) geodetic model, which is applicable to networks of any size and assumes that the geodetic datum is available. In addressing the needs of surveying, the topic of conformal mapping of the ellipsoidal surface is treated in great detail. This includes, as a transitional product encountered along the way, computations on the ellipsoidal surface. It is well known that computing on the conformal mapping plane is limited by the area covered by the network since distortions increase with area. Additionally, the respective computations require the geodesic line, which is mathematically complicated, and the respective expressions are a result of lengthy but unattractive series expansions. Clearly, an attempt is made to point out the preference of the 3D geodetic model when there is the opportunity to do so.

Chapter 5, finally, introduces the various GNSS systems. In order to provide background information on satellite motions, the chapter begins with an elementary discussion of satellite motions, the Kepler elements that describe such motions, and the particularly simple theory of normal orbits, i.e., motion in a central gravity field. The disturbing forces that cause satellites to deviate from normal orbits are discussed as well. However, the material is not presented at the level of detail needed for accurate satellite orbit determination. We assume that orbit determination will continue to be handled by existing expert groups and that respective products will be available either through the broadcast navigation message or the International GNSS Service (IGS) and other agencies in the form of precise and/or ultra-rapid ephemeris and satellite clock data. This chapter includes new material on GPS modernization and on the GLONASS, Galileo, and Beidou systems. In the meantime, interface control documents are available for all these GNSS systems and posted on the Internet. The reader is advised to consult these documents and similar publications that expertly address the space segment.

Chapter 6 discusses in detail the various GNSS positioning approaches conveniently in “one place.” It begins with specifying the fundamental pseudorange and carrier phase equations. All relevant functions of these observables are then grouped and listed without much additional explanation. These functions are all well known; exceptions might be the triple-frequency functions. We introduce the “across” terminology in order to more easily identify the specific differencing. As such, we have the across-receiver, across-satellite, and across-time observation (single) differences, and then the traditional double-difference and triple-difference functions. A separate section is dedicated to operational details. That section includes everything one needs to know when carrying out high-accuracy positioning with GNSS. We especially stress the “GNSS infrastructure” that has established itself to support users. By this, we mean the totality of GNSS services provided by government agencies, user groups, universities, and above all the IGS and the (mostly) free online computing services. IGS provides products of interest to the sophisticated high-end GNSS user, while the computation services are of most interest to those responsible for processing field data. This is indeed a marvelous GNSS infrastructure that is of tremendous utility.

As to the actual GNSS positioning approaches, Chapter 6 is concerned with three types of approaches, each having been assigned a separate section. The first section deals with navigation solution, which uses the broadcast ephemeris, and the traditional double-differencing technique with ambiguity fixing for accurate positioning. The double differences are formed on the basis of the base station and base satellite concept to conveniently identify the linear dependent double differences. We note that the reason for the popularity of the double-difference functions is the cancelation of common mode errors, such as receiver and satellite clock errors and hardware delays, as well as the tropospheric and ionospheric impacts on the carrier phases in...