Bernese GPS Software Version 5.0 - Bernese GNSS Software

7.5 Parameterization
is often used for station coordinates and it is “almost mandatory” for UT1-UTC estimates
at the starting epoch (see Chapter 15).
The situation is slightly more complicated when ellipsoidal coordinates are to be constrained.
The reason for constraining ellipsoidal coordinates rather than rectangular coordinates
might be, e.g., different accuracy of the a priori horizontal and vertical positions. The
ellipsoidal coordinates may be fixed using the fictitious observation
Hp = 0 , (7.28)
where H is the Jacobi matrix of the transformation between a rectangular and ellipsoidal
coordinate system:
⎛
⎞
⎜
H = ⎜
⎝
∂ϕ
∂x
∂λ
∂x
∂h
∂x
∂ϕ
∂y
∂λ
∂y
∂h
∂y
∂ϕ
∂z
∂λ
∂z
∂h
∂z
⎟ . (7.29)
⎠
For the computation of the matrix H the spherical approximation is sufficient.
7.5.4.2 Relative Constraining
It is also possible to constrain (the improvements of) two parameters with respect to each
other (relative constraints) using the fictitious observation
pi − pj = 0 . (7.30)
Ellipsoidal coordinates of two stations may be constrained as well:
Hi p i − Hj p j = 0 . (7.31)
Relative constraining is possible in GPSEST for troposphere zenith path delay and gradient
parameters as well as for stochastic ionosphere parameters. Program ADDNEQ2 allows, in
addition, for relative constraining of station coordinates and velocities (see Section 9.3.9).
7.5.4.3 Zero-Mean Condition
Another type of constraints that are available in the Bernese GPS Software is the zero-mean
condition of the estimated corrections for a group (m ... n) of parameters:
n
pi = 0 . (7.32)
i=m
Zero-mean conditions may be selected by the user, e.g., in GPSEST for realizing an ensemble
of reference clocks (see Section 14.2.2). In some cases a zero-mean condition is applied automatically
by the program (e.g., for differential code biases in ADDNEQ2, see Chapter 13).
Bernese GPS Software Version 5.0 Page 151