Bernese GPS Software Version 5.0 - Bernese GNSS Software

7.5 Parameterization
EVERY SESSION: The parameters are pre-eliminated after each session (or after each file if
baseline-wise correlation is enabled). They neither appear in the result files nor in
the output normal equation.
PRIOR TO NEQ SAVING: The parameters are pre-eliminated before saving the normal equation.
The parameters remain, however, in the solution provided by GPSEST, i.e.,
output files containing the parameters may be written.
EVERY EPOCH: This option is only available for epoch parameters, i.e., for clock corrections,
kinematic coordinates, and stochastic ionosphere parameters.
AS SOON AS POSSIBLE: This option allows for pre-elimination of ambiguity parameters as
soon as they are no longer used.
We refer also to the flow diagram of GPSEST in Figure 7.3 where the different pre-elimination
options are included.
7.5.6 Back-Substitution of Epoch-Parameters
Epoch-parameters are generally set up and pre-eliminated epoch-wise due to their potentially
large number. In order to obtain a solution for these parameters a back-substitution
step is necessary. This procedure is implemented in GPSEST of the Bernese GPS Software
Version 5.0 for clock parameters and kinematic station coordinates. After solving the main
normal equation the resulting non-epoch parameters are inserted back into the observation
equations which are successively solved for each epoch. To this purpose, parts of the
observation equation are stored in a scratch file as soon as clock parameters or kinematic
coordinates are to be estimated. Depending on the number of stations and the sampling
rate this binary scratch file may become large. It is stored by default in the user-specific
directory ${U}/WORK where enough disk space should be available.
Program GPSEST offers two options for recovering the variance-covariance information concerning
epoch parameters, see option “Var-covar wrt epoch parameters” in panel “GPSEST 3.2:
General Options 2” (see Figure 8.5). With option CORRECT the variance-covariance information
is correctly recovered by including the corresponding information for the non-epoch
parameters.
The normal equation for the parameter vectors p i with i = 1,... ,n may be written in the
following way if p 1 denotes the non-epoch parameters and p i denotes the parameters valid
for epochs i = 2,... ,n:
⎛
⎜
N = ⎜
⎝
N11 N12 N13 ... N1n
N21 N22 0 ... 0
N31 0 N33 ... 0
... ... ... ... ...
Nn1 0 0 ... Nnn
⎞
⎟
⎠
. (7.36)
Taking advantage of the fact that all off-diagonal matrix blocks referring to two epoch
parameters are zero, the block Q ii referring to epoch parameters p i in the inverted normal
equation can be written as
Q ii = N −1
ii
+ N −1
ii Ni1Q 11N1iN −1
ii for i = 2,... ,n (7.37)
Bernese GPS Software Version 5.0 Page 153