# Ionospheric Error Models for Satellite-Based Navigation--Paving the Road towards LEO-PNT Solutions
## 4 Results
### Ionospheric Delay Results
#### 4.2.2 Data from Android Devices--Dynamic Conditions  
Due to the rapid development of GNSS chipsets, Android devices have been extensively used in positioning-related studies in recent years. In 2016, GNSS-equipped Android  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**AVG [m]** & **No Correction** & **Klobuchar** & **IRI** & **IAMM (Proposed)** \\ \hline Mean & 5.390 & 3.244 & 3.159 & 1.976 \\  & – & (\(-\)39.7\%) & (\(-\)41.4\%) & (\(-\)63.3\%) \\ \hline StD (1-\(\sigma\)) & 1.277 & 1.051 & 1.0682 & 0.848 \\  & – & (\(-\)17.7\%) & (\(-\)16.4\%) & (\(-\)33.6\%) \\ \hline \hline \multicolumn{5}{c}{**a** Using observations from Tampere University (high-grade)} \\ \hline
**AVG [m]** & **No Correction** & **Klobuchar** & **IRI** & **IAMM (Proposed)** \\ \hline Mean & 6.209 & 4.252 & 4.397 & 4.1708 \\  & – & (\(-\)31.5\%) & (\(-\)29.2\%) & (\(-\)32.8\%) \\ \hline StD (1-\(\sigma\)) & 3.470 & 3.219 & 3.141 & 3.164 \\  & – & (\(-\)7.2\%) & (\(-\)9.5\%) & (\(-\)8.8\%) \\ \hline \hline \multicolumn{5}{c}{**b** Using observations from the FinnRef network (high-grade)} \\ \hline
**AVG [m]** & **No Correction** & **Klobuchar** & **IRI** & **IAMM (Proposed)** \\ \hline Mean & 42.815 & 34.052 & 38.884 & 36.388 \\  & – & (\(-\)20.5\%) & (\(-\)9.2\%) & (\(-\)15\%) \\ \hline StD (1-\(\sigma\)) & 18.710 & 18.103 & 18.397 & 18.211 \\  & – & (\(-\)3.2\%) & (\(-\)1.7\%) & (\(-\)2.7\%) \\ \hline \hline \end{tabular}
\end{table}
Table 4: 3D positioning errors from GNSS receivers using different ionospheric correction models.  
sartphones made GNSS raw observations available to the public; such raw data can be used to study and interpret positioning accuracy and atmospheric effects. As previously, we collected RINEX observations from these phones in dynamic conditions (phone placed in a moving car, mostly on highways) at various locations (8 locations in Europe) and calculated the resulting positioning errors by applying the same Equations (10) and (12). However, since the exact ground-truth location is no longer available in dynamic conditions, the reference coordinates \(x_{ij},y_{i,j}\), _and_\(z_{ij}\) from Equation (11) were taken from National Marine Electronics Association (NMEA) data. NMEA data are estimates produced by the smartphone using its own proprietary algorithms and typically based on GNSS, cellular, and sensor-aided data to generate the best available estimate of the phone's true position. The statistics were calculated for 8 scenarios collected via the GNSSlogger app from a Nokia XR20 phone in Poland (5 scenarios) and Latvia (2 scenarios) and from a Xiaomi Redmi phone in France (1 scenario).  
As shown in Table 4c, the results based on the Android measurements differ from the results based on fixed reference stations, and they show that the Klobuchar model has the best performance, followed by our IAMM model and then the IRI model. The Klobuchar model decreased the positioning error mean and standard deviation by 20.5% and 3.2%, respectively. Our model came next in reducing the error mean by 15% and error standard deviation by 2.7%. Finally, the IRI model reduced the error mean and standard deviation by 9.2% and 1.7%, respectively, with respect to the no-correction case.  
It is evident that the positioning errors of Android devices from all models are considerably worse than those obtained from GNSS reference stations (Table 4a,b). Several things can explain this increased inaccuracy. First of all, there are many fluctuations and biases in the smartphone's components [38]. Secondly, dynamic conditions of Android-based measurements may suffer more errors compared to static acquisition. Finally,) the ground-truth position was not available in Android phones; the reference track in there was the NMEA track, which is itself prone to errors (see additional explanations concerning Figure 7 in the next section). We remark that when it comes to positioning, a device explicitly designed for GNSS monitoring will provide much greater accuracy than a smartphone.