Bernese GPS Software Version 5.0 - Bernese GNSS Software

8. Initial Phase Ambiguities and Ambiguity
Resolution
8.1 Motivation
Basically, the initial phase ambiguity parameters in the original observation equations are
integer numbers of cycles. Unfortunately, they contain several additional linear terms which
cannot be separated unambiguously: receiver and satellite clock corrections, their hardware
delays, and an initial phase shift between receiver and satellite. These numerous linear terms
prevent access to the integer character of the carrier phase ambiguities.
The equations (2.34c) and (2.34d) are simplified since the ambiguity term contains all these
linear parameters. Consequently, the ni Fk are not integer anymore. As the implementation
of the zero-difference processing follows exactly these equations, ambiguity resolution in the
zero-difference case is not possible in the Bernese GPS Software.
After differencing the observations between two stations and two satellites (double differenced
observation) the clock corrections, hardware delays for receiver and satellite as well
as the initial phase shift term have canceled out or may be neglected. We then have again
access to the integer nature of the initial phase ambiguities.
Technically two steps are necessary: The initial phase ambiguity parameters have to be
estimated as real-valued parameters in a first step. In a second step the ambiguities are
resolved. This means that (in our terminology) the correct integer numbers are assigned to
the real-valued estimates. Let us introduce the following notation:
p 1 is the column array containing all non-ambiguity parameters,
p 0 1 are the corresponding a priori values,
p 2 is the column array containing all ambiguity parameters,
p 0 2 are the corresponding a priori values, and
¯p 0 2 are the corresponding known true (integer) numbers. Moreover
Ψ is the array containing the terms “computed” (model function),
l is the array containing all measurements (terms “observed”),
y,y ′ are the arrays of reduced measurements (terms “observed – computed”),
v,v ′ are the arrays containing the residuals.
Bernese GPS Software Version 5.0 Page 167