## 2 Quality Control Algorithms for GPS Observations
### Ionospheric Effects  
The delay of GPS signals occurs through the ionosphere, which is a shell of electrons and electrically charged atoms and molecules that surrounds the earth, stretching from a height of approximately 50 km to more than 1,000 km. Ionospheric delay is one of the largest sources of error in GPS positioning and navigation and it can vary from a few meters to more than twenty meters within one day [13]. The delay is proportional to the number of electrons and is inversely proportional to \(\hat{f}\). Thus, the effect is dispersive, and depends on the frequency \(f\). If the delay was not accounted for, the range errors on the L\({}_{1}\) frequency in the zenith direction could reach 30 m [14]. The magnitude of ionospheric range errors is related to the Total Electron Content (TEC) along the signal path from a GPS satellite to the receiver and is dependent on the signal frequency and the level of ionospheric activity. The TEC is defined as the total number of electrons that are contained in a vertical column with a cross-sectional area of 1 m\({}^{2}\) along the signal path between the satellite and the receiver. GPS users with dual-frequency P-code receivers can correct the ionospheric range error through an appropriate combination of the pseudo-ranges observed on L\({}_{1}\) and L\({}_{2}\). Single-frequency users with C/A-code receivers do not have that correction. They either have to persevere with the reduced measurement accuracy or employ a model for the correction of ionospheric range errors. Several electron density models such as Bent [15] and International Reference Ionosphere (IRI) [16] are available for the study of electron density profiles at different altitudes from the ionosphere [17,18]. The Klobuchar model [19] is the only model available for estimating the ionospheric time delay for single frequency GPS users. The Klobuchar model is a simple computational model with an ideal description for the ionosphere's average behavior. In dual frequency receivers, the ionospheric delay can be estimated precisely by taking advantage of the dispersive nature of the ionosphere. The delay is estimated by measuring the difference in arrival times of the two GPS frequencies. In this study, we calculated the ionospheric delay (\(ion_{dual}\)) of dual-frequency receiving data using carrier-phase observations in L\({}_{1}\) and L\({}_{2}\). We also used the broadcast message containing the ionospheric model coefficients for computing the ionospheric group delay along the signal path to obtain a single-frequency delay in the ionosphere (\(ion_{1:1}\), \(ion_{1:2}\)). The ionospheric delay (\(ion_{dual}\)) at one epoch using a dual frequency receiver is  
\[ion_{dual}=\alpha(\Phi_{2}-\Phi_{1})-\alpha(\lambda_{2}N_{2}-\lambda_{4}N_{ 1}) \tag{10}\]  
where \(N_{2}\) and \(N_{l}\) are L\({}_{1}\) and L\({}_{2}\) carrier-phase ambiguity, respectively. Because we are only interested in changes of \(ion_{dual}\) over time for the individual \(PRN\) (_Pseudo Random Noise_), Equation (10) can be written as follows;  
\[ion_{dual}=\alpha(\Phi_{2}-\Phi_{1}) \tag{11}\]  
Additionally, the ionospheric delay (\(ion_{1:1}\), \(ion_{1:2}\)) for a single frequency receiver is calculated with an algorithm developed by [PERSON] [19]. The ionospheric delay of L\({}_{1}\) frequency can be computed by the Klobuchar model using the eight ionospheric model coefficient in the navigation file and quality control parameters (\(\alpha\), \(\beta\), \(\varphi_{R}\) and \(\lambda_{R}\)). The Klobuchar algorithm is based on the shell model or single layer model of the ionosphere. The implicit assumption is that the TEC is concentrated in an infinitesimally thin spherical layer at a certainheight, e.g., 350 km [9]. The algorithm is known to be compensated for 50\(\sim\)60% of the actual group delay. The ionospheric delay of L\({}_{1}\) frequency (\(ion_{\text{L1}}\)) is  
\[ion_{\text{L}_{1}}=