## Vladimir Dobrushkin

https://math.uri.edu/~dobrush/

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the appendix entitled GNU Free Documentation License.

# Global Positioning System

The basic static navigational solution of the Global Positioning System (GPS) is based upon the simultaneous
measurement of the pseudoranges between a set of GPS satellites and a user's receiver. Each pseudorange measurement
represents a sphere of position for the receiver centered on the corresponding GPS satellite. The intersection of
four or more spheres allows an estimate of the receiver's position and the receiver's clock o€set to be formed.
This scenario is referred to as a spherical navigation solution. The GPS static positioning problem is defined as
follows:
a set of *n* simultaneous pseudorange measurements as well as the positions &
R
i
) of the
corresponding GPS satellites from which the pseudorange
measurements are made;
®nd
the solution for the receiver's position

Traditionally, the approach taken to solve this basic navigational problem is to use a gradient solution approach by linearizing the measurements about an initial estimate of the state parameters,