The global positioning system (GPS) uses satellites and computers to determine the location of a GPS receiver on or near earth. This is done by computing the time difference for signals (from various satellites) to arrive at the GPS receiver. The US government developed the system, sustains it, and makes it reachable in a free manner to anybody with a GPS receiver. However, it also has the capability to selectively inhibit access to the system. Initially, GPS was restricted for US military use; however, it became freely available for civilian use after a civilian aircraft was shot down for flying over prohibited airspace of the erstwhile Union of Soviet Socialist Republics (USSR) in 1983. Apart from GPS, there are other systems either in use or under development for providing geolocation information, such as Russia’s Global Navigation Satellite System (GLONASS), the European Union’s Galileo positioning system, China’s BeiDou Navigation Satellite System, and India’s Regional Navigation Satellite System NAVIC. This book, published in 2016, is in its third edition; it focuses on the theory, algorithms, and applications of GPS. The two earlier editions were published in 2003 and 2007, respectively.

The book, which is highly technical, has 13 chapters. The authors begin by introducing some of the navigational systems. They then study coordinate and time systems, satellite orbits, GPS measurements, and factors that can have an impact on GPS measurements, such as the ionosphere, the troposphere, Einstein’s relativity theory, tides, and clock errors. They then focus on mathematical models of GPS observations and equivalence of various algorithms, and important “adjustment and filtering algorithms for statistical and kinematic as well as dynamic GPS data.” Ambiguity “can arise during phase measurement when the receiver loses its lock on the signal and phase measurement must be reinitiated.” So a cycle slip happens, hence the cycle count has to begin again. Thus, the authors concentrate on mechanisms for cycle slip detection and ambiguity resolution. They also look at parametrization of the GPS observation model, algorithms for processing GPS data, and applications of GPS theory and algorithms with focus on software development.

The movement of satellites is affected not only by the force of the earth, but also the sun and the moon, the atmospheric drag, solar radiation, tides, general relativity effects, and so on. So the authors focus on perturbed orbits of satellite motion and their determination. They place emphasis on orbit theory when there are no singularities. Chapter 13 concludes the book; it is very brief and includes the authors’ comments on some important topics and discussions on unfinished problems related to GPS.

The book contains many illustrations, some of which are in color, references at the end of chapters and also at the end of the book, two appendices, and a handy index. The book is extremely mathematically oriented with a plethora of equations, integrals, and derivatives. This third edition has seen many revisions since the first edition appeared in 2003. In the preface to the third edition, the authors list out clearly all the revisions made by them since then. This book will be useful for those interested in studying or working with navigational systems such as GPS. However, the reader should be mathematically sophisticated.