GPS Solutions

, Volume 17, Issue 3, pp 309–326

Analytical 2D GNSS PVT solutions from a hyperbolic positioning approach

Original Article

DOI: 10.1007/s10291-012-0280-x

Cite this article as:
Dambeck, J. & Braun, B. GPS Solut (2013) 17: 309. doi:10.1007/s10291-012-0280-x


GNSS receivers estimate 3D antenna position and receiver clock bias when at least four satellites are tracked. If only three satellites are available, a 2D antenna position solution is still possible. We derive an almost exact algorithm for the determination of two possible antenna positions and the corresponding receiver clock biases based on pseudorange measurements to three GNSS satellites and a height measurement. The two ambiguous solutions exactly reflect the same height measurement. One of the solutions can be eliminated if some prior knowledge of the user position, for example, near the Earth, is available. In general, a less accurate height measurement gives a less accurate 2D GNSS solution, and vice versa. The determination of the receiver antenna position is based upon the intersection of two confocal hyperboloid sheets and the ellipsoid, resulting in a hyperbola along which the user is located. The algorithm is verified by numerical computations.


2D GNSS PVT solutionHyperbolic positioningAltitude measurementPseudorange differencesHyperboloid sheets

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Institute of Flight System DynamicsTechnische Universität MünchenGarchingGermany