Bernese GPS Software Version 5.0 - Bernese GNSS Software

9. Combination of Solutions
We may apply this transformation to the a priori coordinates in the ITRF97-normal equations,
in matrix notation
X 0 00 = R X097 − ∆ . (9.19)
Only the a priori coordinates are changed. The matrices N and b remain untouched which
means that the estimated coordinate corrections are unaffected by the transformation. This
is allowed if rotation angles α,β,γ and scale parameter µ are small.
Because fixing reference station coordinates for datum definition is not recommended, the
importance of the a priori coordinate transformation may be seen in the handling of small
rotations between reference frames caused by introduced orbits given in different reference
frames.
9.3.4 Parameter Transformations
Program ADDNEQ2 allows for parameter transformations of various kinds. A priori information
may be changed or parameter representation may be converted to another representation.
Examples will be given below.
At normal equation level only linear transformations are possible. Let us write a general
transformation of the parameter improvement from p to ˜p by
p = C˜p + c . (9.20)
Substituting this expression into the normal equation Np = b, Eqn. (7.4) leads to a transformed
normal equation of the form
i.e.,
Changing A Priori Parameter Values
C ⊤ NC˜p = C ⊤ b − C ⊤ Nc , (9.21)
Ñ = C ⊤ NC , ˜ b = C ⊤ b − C ⊤ Nc . (9.22)
Changing the a priori values of parameters is based on the following relation between old
and new parameters:
p = ˜p + (x 0 new − x0old ) (9.23)
which is a special case of the transformation equation (Eqn. (9.20)). A priori values do
not have any influence on the normal equation matrix N, but change the vector b on the
right-hand side of the normal equation system, see Eqn. (9.22):
˜b = b − N(x 0 new − x0old ) . (9.24)
The transformation of a priori values is performed immediately after reading each normal
equation file. A priori values are changed, if different values are provided as input (this is,
e.g., always true for the station coordinates). If the system contains drift parameters (e.g.,
Earth orientation parameters from GPSEST), the a priori values of all drift parameters are
automatically transformed to zero.
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