On the GNSS integer ambiguity success rate
prof.dr.ir. P.J.G. Teunissen1
Introduction
Global Navigation Satellite System (GNSS) ambiguity resolution is the process of
effectively accounting for the integerness of the unknown cycle ambiguities of the
double-difference (DD) carrier phase data. It applies to a great variety of GNSS
models. This holds true not only for the current Global Positioning System (GPS),
but also for the future modernized GPS and the European Galileo system. The
GNSS models range from sinale-baseline models used for kinematic positioning
to multi-baseline models used as a tool for monitoring and studying geodynamic
phenomena. The models may have the relative receiver-sate I lite geometry included
(referred to as geometry-based) or excluded (referred to as geometry-free). The
geometry is included through the unit direction vectors in the design matrix When
the geometry is excluded, the baseline components are not involved as unknowns
in the model, but instead the receiver-satellite ranges themselves. The models
may also be discriminated as to whether the slave receiver(s) are in motion or
not. When the receivers are in motion, one solves for one or more trajectories,
because with the receiver-satellite geometry included, one will have new coordinate
unknowns for each new epoch. One may also discriminate as to whether the
differential atmospheric delays are included as unknowns or not. In case of
sufficiently short baselines these delays are often neglected.
Despite the differences in application of the various GNSS models, their ambiguity-
resolution problems are intrinsically the same. In all cases the aim is to incorporate
the integerness of the ambiguities into the adjustment so as to improve the precision
of the results. Once the integer ambiguities are known, the corresponding carrier
phase measurements will act as if they are high precision pseudo-range
measurements, thereby allowing the remaining parameters, such as baseline
coordinates, to be estimated with a comparable high precision.
For the purpose of ambiguity resolution, GNSS data processing is usually carried
out in three different steps (see figure 1). In the first step no distinction is made
between ambiguities and other parameters, like baseline coordinates and
atmospheric delays. The parameter estimation problem is solved without taking
into account the special integer nature of the ambiguities. The result so obtained
is often referred to as the 'float solution'.
In the second step, the float solution of the ambiguities is used to estimate the
integer ambiguity values. Here one could chooseTrom a wide variety of integer
estimation methods. These methods range from simple rounding schemes to
more advanced methods based on integer searches. One popular method is the
LAMBDA method, developed at the Department of Mathematical Geodesy of the
Delft University of Technology [4]. With this method, the ambiguities are estimated
by means of integer least-squares using a very efficient search procedure (For
details on the method consult nttp://www.geo.tudelft.nl/map/Available on request
are a FORTRAN and a Matlab implementation of the LAMB DA-method. Directly
available for download is an extensive description of the method and its
implementation in the report [1]. The Matlab-implementation comes with a
separate guide and also includes a user-friendly demo-application which can be
used for solving small problems interactively.)
1 Peter Teunissen is associated as professor with the Department of Mathematical Geodesy and
Positioning, Faculty of Civil Engineering and Geosciences, Delft University of Technology
