# A Proposal of a Troposphere Model in a GNSS Simulator for VANET Applications
## 5 Tropospheric Model Solution
### Tropospheric Collins Model  
In this work the Troposphere Collins model [14] has been chosen for the implementation. This model is also used by Satellite-Based Augmentation System (SBAS) for maximum precision differential corrections, with the aim of increasing the accuracy and integrity of the GPS system data, such as the Wide Area Augmentation System (WAAS) and European Geostationary Navigation Overlay System (EGNOS), that are air navigation aids developed to augment the GPS, with the goal of improving its accuracy, integrity, and availability. The model provides an estimate of the zenith total tropospheric delay that is dependent on empirical estimates of five meteorological parameters at a receiver--namely, pressure, \begin{table}
\begin{tabular}{c c} \hline \hline
**Value** & **Description** \\ \hline GPGGA & GP: GPS-GGA: type of message \\ \hline Time format & hhhmmss.ss (h: hours, m: minutes, s: seconds \\
090000.00 & 09 (h): 00 (m): 00.00 (s) \\ \hline
3921.28520559,N & 39\({}^{\circ}\) 21.28520559\({}^{\prime}\) North (latitude) \\
01613.51936448,E & 16\({}^{\circ}\) 13.51936448\({}^{\prime}\) East (longitude) \\ \hline GPS Quality indicator & 0 = Invalid \\  & 1 = GPS fix \\  & 2 = DGPS fix \\
1 & 3 = Fix GPS PPS \\
4 = RTK (Real Time Kinematic) entire \\
5 = RTK float & 5 = RTK float \\  & 6 = Navigazione Stimata (dead reckoning) \\  & 7 = Input Manual \\  & 8 = Simulation \\ \hline
05 & number of satellites \\ \hline  & Horizontal Dilution of Precision (HDOP) \\
2.87 & (This is a unitless number indicating \\  & how accurate the horizontal position is. \\  & Lower is better). \\ \hline
160.0,M & Altitude (meters above mean-sea-level) \\ \hline \multirow{4}{*}{\(-\)21.3213,M} & Geoidal Separation, meteres: the difference between the \\  & \(WGS84^{*}\) earth ellipsoid surface and mean-sea-level (geoid) \\ \cline{1-1}  & surface, “-” = mean-sea-level surface below WGS-84 ellipsoid \\ \cline{1-1}  & surface (\({}^{*}\) World Geodetic System 1984) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: NMEA GGA string description. temperature, water vapour pressure, temperature lapse rate and water vapour lapse rate. These estimates of the meteorological parameters are dependent on the receiver's height, latitude and day-of-year, and are interpolated from reference values for the yearly averages of the parameters and their associated seasonal variations. The total tropospheric delay (indicated with \(T(E)\)) at a given elevation angle can be expressed as the sum of two different components of delay due to 'wet' and 'dry' delay:  
\[T(E)=(T_{z,dry}+T_{z,wet})\cdot M(E), \tag{2}\]  
where \(T_{z,dry}\) is the zenith 'dry' delay, \(T_{z,wet}\) is the zenith 'wet' delay and \(M(E)\) is a mapping function that maps the zenith total delay to the appropriate receiver to satellite elevation angle and it is defined as follows:  
\[M(E)=\frac{1.001}{\sqrt{0.002001+sin^{2}(E)}}, \tag{3}\]  
where \(E\) represents the satellite elevation with respect to the receiver, in degrees. The most difficult part of the model regards the estimation of the values of \(T_{z,dry}\) and \(T_{z,wet}\). These two values depend on meteorological parameters such as:  
* Atmospheric pressure [\(P\) (mbar)]. * Temperature [\(T\) (K)]. * Water vapor pressure [\(e\) (mbar)]. * Lapse rate temperature [\(\beta\) (K/m)]. * Lapse rate of water vapor [\(\lambda\) (adimensional)]  
Since these data are not available in the simulator, a formula was used to estimate them, based on various factors, such as: receiver latitude and day of the year:  
\[\xi(\phi,D)=\xi_{0}(\phi)-\Delta\xi(\phi)cos\left[\frac{2\pi(D-D_{min})}{365,2 5},\right] \tag{4}\]  
where \(D_{min}\) assumes the value of 211 for the southern latitudes and the value of 28 for the northern latitudes. Values of \(\xi_{0}(\phi)\) and \(\Delta\xi(\phi)\) represent the average seasonal variations at latitude (\(\phi\)) and day of the year (\(D\)) of the receiver, which must be linearly interpolated with meteorological parameters given in Table 3 [14].