Bernese GPS Software Version 5.0 - Bernese GNSS Software

9.3 Manipulation of Normal Equations
ADDNEQ2 this manipulation is performed based on the information contained in the station
information file (see Section 9.4.6). Changes are notified to the user in the program output
file.
The station information file allows a consistent change of station and equipment names as
well as of antenna eccentricities which may be very useful, e.g., for reprocessing. A change
in the antenna position is taken into account by transforming the a priori station position
information (see Section 9.3.4). On the other hand, when changing the antenna name only
the antenna name is changed. It is not possible to consider an alternative antenna phase
center variation model on this level of analysis. Some auxiliary parameter information can,
however, not be changed at normal equation level. Examples are tropospheric mapping
function or satellite antenna group definition (see Section 9.3.11).
9.3.2 Rescaling the Normal Equation Matrices
Rescaling of normal equations is important, e.g., if two or more normal equation systems
have to be combined, where each of them stems from a different processing software or
strategy. A typical example is given by the use of different sampling rates for GNSS observations.
Due to the time-correlations of GNSS observations, the results remain (almost) the
same, but the variance-covariance matrices change if different sampling rates are used.
The problem is solved by the following transformation: assuming the original normal equation
system
N p = b , (9.15)
the new system reads as
κ N p = κ b , (9.16)
where κ is the a priori scale factor. Its statistical meaning is the ratio of the variances:
κ = σ2 old
σ 2 new
. (9.17)
In program ADDNEQ2 the rescaling is performed if the a priori information on the scale
factor is provided in a WGT file (option “Variance rescaling factors” see Section 22.10.5).
9.3.3 A Priori Transformation of Coordinates into a Different Reference Frame
A parameter transformation must be used for the transition between two reference frames.
Let us assume that we want to combine normal equations stemming from solutions with
fixed coordinates in, e.g., ITRF97 (denoted by index “97”) with a second set of normal
equations where the ITRF2000 (denoted further by index “00”) was used. Both reference
frames are related by the 7-parameter transformation (rates neglected)
⎛
⎜
⎝
Xi
Yi
Zi
⎞
⎟
⎠
00
= (1 + µ)
⎛
⎜
⎝
1 γ −β
−γ 1 α
β −α 1
⎞
⎟
⎠
R
⎛
⎜
⎝
Xi
Yi
Zi
⎞
⎟
⎠
97
⎛ ⎞
∆X
⎜ ⎟
+ ⎝ ∆Y ⎠
∆Z
∆
. (9.18)
Bernese GPS Software Version 5.0 Page 187