# Comparison of Enhanced Noise Model Performance Based on Analysis of Civilian GPS Data
## 2 Description of the Data Collection Process  
Data were collected from civilian L1-band GPS units at multiple locations. At each location, data were collect from four units with a Telit Jupiter-F2 integrated GPS module, as well as a single standard USB-connected GPS receiver--GlobalSat BU-353S4. The first- and second-order statistics of the location data showed no significant difference between the two devices. For brevity, we present our findings using the data obtained only with the GlobalSat BU-353S4.  
The location of satellites is a major factor of GPS accuracy degradation. Devices function well when the satellites are widely distributed [21]; hence, the altitude errors in measurements are typically much larger than those in latitude or longitude. The GPS satellites operate at an inclination of around \(55^{\circ}\); consequently, for devices at higher latitudes, the GPS satellite positions are biased strongly towards the equator.  
To ensure that our analysis was not biased due to specifics of the GPS satellite constellation geometry, we carried out measurements at four locations with latitudes between \(45^{\circ}\) and \(10^{\circ}\) South (see Table 1). Data were recorded at each site for approximately \(48\) h. The decimated latitude and longitude errors (deviations from time average) are shown in Figure 1. Disregarding the initialisation period (typically \(\sim\)1 min), the data resemble a random walk.  
While this cursory look seems suggestive, calculating the residuals defined as \(r_{t}=X_{t}-\xi_{0}\) (here, \(\xi_{0}\) denotes the long-time average, or the 'true' position) and creating a QQ-plot [22] reveals the non-Gaussian nature of \(r_{t}\) (for technical details see Appendix A).  
In Figure 2 the QQ-plot of the latitude data collected in Dunedin is depicted. In order to support the graphical findings, we have also calculated two more normality tests [23], one based on [PERSON] and [PERSON]'s work [24; 25], and another one suggested by [PERSON] [26]. The latter is the most suitable for our use, as it does not assume the knowledge of mean and standard deviation of the normal distribution, but estimates these from the sample. The null hypothesis of both tests is that the data come from a normal distribution. Since both tests return \(p\)-values much smaller than 0.01, we can thus conclude at a 99% confidence level that latitude data do not support the assumption of normal distribution. Similar conclusions can be drawn for longitude and altitude data at all locations.  
\begin{table}
\begin{tabular}{l c c c} \hline
**Measurement Site** & **Latitude (South)** & **Longitude (East)** & **Dates** \\ \hline North Stradbroke Island & 27\({}^{\circ}\)25\({}^{\prime}\)14\({}^{\prime\prime}\) & 153\({}^{\circ}\)30\({}^{\prime}\)52\({}^{\prime\prime}\) & 14 September 2014 \\ Port Douglas & 16\({}^{\circ}\)29\({}^{\prime}\)07\({}^{\prime\prime}\) & 145\({}^{\circ}\)27\({}^{\prime}\)59\({}^{\prime\prime}\) & 17 September 2014 \\ Thursday Island & 10\({}^{\circ}\)34\({}^{\prime}\)79\({}^{\prime\prime}\) & 142\({}^{\circ}\)13\({}^{\prime}\)47\({}^{\prime\prime}\) & 21 September 2014 \\ \hline Dunedin & 45\({}^{\circ}\)51\({}^{\prime}\)50\({}^{\prime\prime}\) & 170\({}^{\circ}\)30\({}^{\prime}\)48\({}^{\prime\prime}\) & 6 August 2014 \\  & & & 7 August 2014 \\  & & & 15 August 2014 \\  & & & 27 September 2014 \\  & & & 5 October 2014 \\  & & & 22 October 2014 \\ \hline \end{tabular}
\end{table}
Table 1: Measurement sites and dates of observations.  
Figure 1: The longitude and latitude errors at each location. Due to the large number of observations, the data have been decimated.