Bernese GPS Software Version 5.0 - Bernese GNSS Software

9. Combination of Solutions
9.1 Motivation
The increasing number of permanent GPS stations all over the world and the associated
big number of observations to be processed ask for sequential processing methods. A conventional
processing of all observations in one step using, e.g., GPSEST may be appropriate
for small campaigns (a few days with 24 hour sessions of about 20-30 sites). The computing
power available today does not allow to go far beyond this limit.
The program ADDNEQ2 (”Menu>Processing>Normal equation stacking”) was developed to compute
multi-session solutions from the (statistically correct) combination of a set of single-session
solutions. It replaces the program ADDNEQ that was distributed up to Version 4.2 of
the Bernese GPS Software. The theory of combining sequential solutions is well-known in
geodesy since [Helmert, 1872]. Sequential adjustment techniques are in general independent
of the observation types of the individual solutions. This implies, e.g., that even results from
different techniques (terrestrial geodetic techniques or space techniques GNSS, SLR, VLBI,
DORIS) might be combined. Here, we focus on the combination of GNSS results, only.
Normal equations may be stored by the programs GPSEST and ADDNEQ2 for a sequence
of solutions including a large number of parameter types (coordinates, troposphere, orbit
parameters, etc.). The parameters supported by ADDNEQ2 are listed in Table 1.1. GPSEST
is in general used to process individual sessions while combination of different sessions is
done with ADDNEQ2.
The special features of normal equation stacking methods allow for an extremely rapid and
flexible computation of many solution types, without going back to the original observations.
These features include a new definition of the geodetic datum, the setup of station velocities
as unknowns, the modification of a priori sigmas for different parameters types, the change
of physical models such as the number of troposphere parameters, and different parameter
pre-elimination options. Some unique options are offered only by ADDNEQ2 and are not
available in GPSEST such as a sophisticated definition of the geodetic datum or estimation
of site velocities.
This chapter first presents the basics of sequential least-squares estimation (Section 9.2) and
normal equation manipulations (Section 9.3). Section 9.4 describes the use of ADDNEQ2
and Section 9.5 suggests a few typical applications.
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