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# Uncertainties in GPS Positioning: A Mathematical Discourse

In 2014, I read in *Mathematics Today* about a competition that was taking place called the Mathematical Competitive Game 2014-2015. It concerned GPS positioning and one had to try to estimate the uncertainty in the position of a GPS receiver from actual data. In due course, I submitted an entry called “Uncertainties in GPS Positioning.”

The intended readership for the entry was individuals interested in GPS, such as university students. The reader will benefit from being able to: understand how a GPS receiver calculates its position; understand why the calculated position is only an approximation to the true position; gain some appreciation of the factors which contribute to the difficulties in calculating an approximation of the true position; gain some appreciation of the mathematical steps that are employed in order to reduce errors in the approximation.

I was fortunate enough to achieve some success by winning the Joint First prize, Individual Category.

As a result of my research into the topic of GPS positioning, I submitted a book proposal to Elsevier called *Uncertainties in GPS Positioning: A Mathematical Discourse**, *it was accepted, and the book published in January, 2017.

Today, we all know what a GPS receiver is: it communicates with a satellite system and lets you know where you are on a map. A receiver receives signals from several orbiting satellites and processes them. The receiver has a built-in map. Uncertainties in GPS Positioning: A Mathematical Discourse describes the calculations performed by a GPS receiver and describes the problem associated with making sure that the estimated location is in close agreement with the actual location.

** Uncertainties in GPS Positioning: A Mathematical Discourse** provides a brief introduction to positioning and navigation systems, followed by the main topics that cover an introduction to GPS, basic GPS principles, signals from satellites to receiver for GPS, GPS modernization, signals from satellites to receiver for other satellite navigation systems, the solution of an idealized problem, and sources of inaccuracy. An example positioning problem with estimated inaccuracies is presented in detail, including a step-by-step mathematical solution. For each topic, background information is provided to aid the reader comprehend the subject matter. The future of satellite navigation systems is also discussed.

Dr. Alan Oxley is a tutor in the Faculty of Engineering, Design, and Information & Communications Technology (EDICT) at Bahrain Polytechnic, Kingdom of Bahrain. He and his former postgraduate students have published a number of researcher papers. In 2014-2015 the Mathematical Competitive Game took place with the topic ‘Uncertainties in GPS Positioning.’ Dr. Oxley’s entry received First Prize ex-aequo. His research interests are wide-ranging in both mathematics and computer science.

We are pleased to offer a free chapter of his book, “*Introduction to GPS.”*

If you would like to view more chapters, you can access the book on ScienceDirect. If you prefer a print or e-copy, visit the Elsevier Store. Apply discount code **STC317** for up to 30% off the list price and free global shipping.

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