The GPS equations and the Problem of Apollonius

Author

Hoshen, Joseph

Author_Institution

Lucent Technol. Bell Lab., Naperville, IL, USA

Volume

32

Issue

3

fYear

1996

fDate

7/1/1996 12:00:00 AM

Firstpage

1116

Lastpage

1124

Abstract

By relating the Global Positioning System (GPS) problem of location to the ancient Problem of Apollonius, this work presents a closed solution to the pseudorange positioning problem for two and three dimensions The positioning problem, given by a set of nonlinear equations, has been reduced to the solution of a quadratic equation. The resulting expressions yield either two or one physically meaningful solutions for both the two- and three-dimensional problems. Expressions for the boundary curves and surfaces that separate the one-solution domain from the two-solution domains are also given. Asymptotic lines and planes for the boundary curves and surfaces have also been derived.

Keywords

Global Positioning System; boundary-value problems; nonlinear equations; GPS equations; Problem of Apollonius; asymptotic lines; asymptotic planes; boundary curves; closed solution; location; nonlinear equations; one-solution domain; quadratic equation; three-dimensional problems; two-dimensional problems; two-solution domains; Application software; Earth; Global Positioning System; Military computing; Nonlinear equations; Radio frequency; Satellite broadcasting; Time measurement; Timing; Vehicles;

fLanguage

English

Journal_Title

Aerospace and Electronic Systems, IEEE Transactions on

Publisher

ieee

ISSN

0018-9251

Type

jour

DOI

10.1109/7.532270

Filename

532270