Definition & Development
of Galileo

Signal Structure

Galileo Test Bed GATE

ESA Galileo Test Bed GSTB_V1

GNSS Software
Simulation

C-Nav Study

Tropospheric Correction Models and "Blind" Meteorological Parameters

GNSS microwave signals suffer from tropospheric propagation delays due to the refractive index N of the earth's neutral atmosphere (N>1). These tropospheric propagation delays mainly depend on atmospheric pressure, temperature and relative humidity (or water vapour pressure). The tropospheric propagation delay can be divided into a hydrostatic and a wet component. The total (slant) delay can be modelled in zenith direction with help of mapping functions.

The zenith hydrostatic delay can easily be modelled depending on the total pressure at the antenna site. One of the best fitting hydrostatic models is the model of Saastamoinen.

It is much more difficult to model the wet component of the tropospheric delay: this delay depends on the temperature and the water vapour pressure (or, equivalently, on the relative humidity). In comparison to the hydrostatic delay, a knowledge of the wet refractivity profile throughout the troposphere is needed in order to obtain a high accuracy for this tropospheric delay component. It is possible to derive the zenith wet delay with surface measurements and thereby assuming a certain distribution of the water vapour in the troposphere.

To improve "conventional" zenith wet delay models there are two new approaches:

• an entirely empirical approach that depends on the surface pressure p, partial water vapour pressure e and the temperature t(T):

  the coefficients k have not fixed values but every coefficient is modelled by a mean value and an amplitude, that means the coefficients depend on the day of the year.

• the second model is based on physical principles and does not use empirical model functions; this model depends on the mean temperature, surface water vapour pressure and the water vapour lapse rate.

 

Modelling Meteorological Parameters (and the Coefficients of the Empirical Model) as Harmonic Functions For users with no access to meteorological measurements "harmonic" functions can be provided which model the parameteres by a seasonal and - if reasonable - additionally a diurnal variation. As depicted in the formula below, for example the temperature is modelled by a seasonal variation (temperature is higher in summer than in winter) and a diurnal variation (whose amplitude is smaller in winter than in summer); DOYW means the day of "maximum winter". All the coefficients of the harmonic functions of the meteorological parameters (as well as the coefficients of the empirical ZWD model) are determined from a least square adjustment using input data of GDAS NWM data of 3.5 years. Using the ZHD model of Saastamoinen with "blind" surface pressure as input and the physical ZWD model with "blind" meteorological parameters yields the "blind model" for the user with no access to meteorological measurements. The figure below depicts the RMS of the tropospheric zenith total delay (ZPD) compared by integrated zenith total delays of the GDAS NWM.

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