Bernese GPS Software Version 5.0 - Bernese GNSS Software

16.2 Antenna Phase Center Corrections in the Bernese GPS Software
mean antenna phase center
∆r
antenna reference point
surface of the
function
∆φ ′ (α,z)
Figure 16.1: Representation of an azimuth-zenith angle-dependent antenna phase center
variation model in the Bernese GPS Software.
The antenna reference points for different antenna types are defined in
RINEX and IGS standards. For most antenna types the reference points are
given in file ftp://ftp.igs.org/igscb/station/general/antenna.gra.
e ... denotes the unit vector in the direction from the receiver antenna to the
satellite, and
∆φ ′ (α,z) ... is the function modeling the phase center variations. Two different model
functions may be used in the Bernese GPS Software:
1) Piece-wise linear function in elevation (and optionally in the azimuth):
polygon approach.
2) Spherical harmonic function of maximum degree nmax and maximum
order mmax ≤ nmax :
∆φ ′ (α,z) =
nmax
n
n=1 m=0
˜Pnm(cos z) (anm cos mα + bnm sinmα) , (16.2)
where ˜ Pnm are normalized associated Legendre functions of degree n
and order m, and anm,bnm are the coefficients of the harmonic series
development.
The representation based on a series of spherical harmonics is physically
more meaningful, in particular for azimuth-dependent variations, but the
polygon model may be introduced more easily into other software packages
(linear interpolation between tabular values).
Eqn. (16.1) can be used to represent the phase center correction ∆φk(αi k ,zi k ) for the receiver
antenna k in the direction to the satellite i. The same representation can also be used to
) for the satellite antenna as a function of
describe the phase center corrections ∆φi (αk i ,nki nadir angle n and azimuth α (measured in the satellite-fixed reference frame). The geometrical
distance ̺i k between station k and satellite i is corrected for both effects, ∆φk(αi k ,zi k )
and ∆φi (αk i ,nki ).
Bernese GPS Software Version 5.0 Page 329