Editing Global Positioning System (section)

=== User-satellite geometry ===
{{further|#Geometric interpretation}}

Although usually not formed explicitly in the receiver processing, the conceptual time differences of arrival (TDOAs) define the measurement geometry. Each TDOA corresponds to a [[hyperboloid]] of revolution (see [[Multilateration]]). The line connecting the two satellites involved (and its extensions) forms the axis of the hyperboloid. The receiver is located at the point where three hyperboloids intersect.<ref name="Abel1">{{cite journal |last1=Abel |first1=J. S. |last2=Chaffee |first2=J. W. |year=1991 |title=Existence and uniqueness of GPS solutions |journal=IEEE Transactions on Aerospace and Electronic Systems |publisher=Institute of Electrical and Electronics Engineers (IEEE) |volume=27 |issue=6 |pages=952–956 |bibcode=1991ITAES..27..952A |doi=10.1109/7.104271 |issn=0018-9251}}</ref><ref name="Fang">{{cite journal |last=Fang |first=B. T. |year=1992 |title=Comments on "Existence and uniqueness of GPS solutions" by J.S. Abel and J.W. Chaffee |journal=IEEE Transactions on Aerospace and Electronic Systems |publisher=Institute of Electrical and Electronics Engineers (IEEE) |volume=28 |issue=4 |page=1163 |bibcode= |doi=10.1109/7.165379 |issn=0018-9251}}</ref>

It is sometimes incorrectly said that the user location is at the intersection of three spheres. While simpler to visualize, this is the case only if the receiver has a clock synchronized with the satellite clocks (i.e., the receiver measures true ranges to the satellites rather than range differences). There are marked performance benefits to the user carrying a clock synchronized with the satellites. Foremost is that only three satellites are needed to compute a position solution. If it were an essential part of the GPS concept that all users needed to carry a synchronized clock, a smaller number of satellites could be deployed, but the cost and complexity of the user equipment would increase.