Bernese GPS Software Version 5.0 - Bernese GNSS Software

11.3 Theory
Table 11.1: Correlation of height estimation and troposphere parameter estimation and ratio
between formal accuracy of height estimation with (σ1) and without (σ2)
estimation of troposphere parameters as a function of cutoff angle. Homogeneous
distribution of satellites above the elevation cutoff angle is assumed. See
[Rothacher and Beutler, 1998].
Elevation cutoff angle 30 25 20 15 10 5
Correlation -0.985 -0.976 -0.964 -0.943 -0.907 -0.830
σ1/σ2 31.2 20.6 13.8 9.2 6.1 3.9
numbers for the correlation between troposphere zenith delay and station height estimates
assuming a uniform distribution of the GNSS satellites over the sky above the cutoff angle.
If this is not the case (e.g., due to presence of the “northern hole” resulting from the
satellite’s orbital inclination of 55 o ) the numbers are even more dramatic [Rothacher and
Beutler, 1998].
Table 11.1 impressively shows that, if troposphere parameters and station height are estimated
together (clock parameters have to be estimated in any case, in the double-difference
processing mode they are estimated implicitly), the situation may be considerably improved
by lowering the elevation cutoff angle, that is, by observing satellites close to the horizon.
The correlations are decreased further by estimating one set of station coordinates over a
longer time interval, e.g., several days by combining several sessions on the normal equation
level (see Section 9.5).
In summary, we may state that troposphere biases are orders of magnitude above the noise
level of the phase observable. Their influence thus must be reduced to make full use of the
accuracy of the observable by either of the following two methods:
• Model tropospheric refraction without using the GNSS observable (e.g., by using
ground meteorological measurements or water vapor radiometers).
• Estimate troposphere parameters (e.g., zenith path delays) in the general GNSS parameter
estimation process.
Both methods are used today depending on the circumstances; for both methods there are
options in the Bernese GPS Software Version 5.0 . Before discussing the options available,
we briefly review some aspects of the theory.
11.3 Theory
Tropospheric refraction is the path delay caused by the neutral (non-ionized) part of the
Earth’s atmosphere. The troposphere is a non-dispersive medium for radio waves up to
frequencies of about 15 GHz (see, e.g., [Bauerˇsíma, 1983]). Tropospheric refraction is thus
identical for both GNSS carriers, L1 and L2 (and both phase and code measurements – see
Eqn. (2.34)). The tropospheric path delay ∆̺ is defined by
∆̺ = (n − 1) ds = 10 −6
N trop ds , (11.3)
Bernese GPS Software Version 5.0 Page 241