## 2 Materials and Methods
### A-VTTCES-KF Algorithm
#### 2.1.5 Introduction of the Proposed A-VTTCES-KF  
An introduction related to the process of presenting the A-VTTCES-KF in this work is summarized in Figure 8, where the blocks associated with the dashed lines correspond to the preliminary work to build the system model of the A-VTTCES-KF; the solid lines correspond to the real-time field test process with the proposed GNSS SDR using the A-VTTCES-KF. At first, two groups of the stationary field tests in terms of Situation #1 and Situation #2, based on the WNLS method, are implemented to estimate the local clock drift. Then, the Allan variance results using the clock drift estimations are computed and plot as shown in Figures 5 and 6. Based on the computation results, we conclude that there is the GM process random noise or time-correlated error being present in the VT loop. The 1 st-order GM process is chosen in this research to model the time-correlated error, and the corresponding parameters can be read by the Allan variance plots. Furthermore, the stationary data through the field test of Situation #3 are also exploited to plot the Allan variance curves, by which \(S_{f}\) and \(S_{g}\) could be obtained and they are essential for the receiver clock modelling. Besides, the innovation sequence is adopted in the KF to adaptively adjust the process covariance matrix. The purpose of using such adaptive algorithm is to improve the performance of the state vector driving processes and enhance the robustness of the GNSS SDR. Finally, the proposed A-VTTCES-KF is applied in the GNSS SDR, which will be used for a thorough field test in this research.  
It should be noticed that the GM parameters are estimated in Situations #1 and Situation #2, and the estimated results will be subsequently used for the model of the time-correlated error applied  
Figure 8: Introduction about the process of presenting the A-VTTCES-KF.  
to the A-VTTCES-KF. Then, the positioning performance of the GNSS SDR using the A-VTTCES-KF will be tested in Situation #3. In order to verify that the estimated GM parameters are commonly available for different cases from Situation #1 and Situation #2 to extend the application scope of the estimating results in Tables 1 and 2, so these values are not directly obtained through Situation #3. In other words, if the other researchers would like to apply the GM model to their own experiments in the future, it can be exploited to prove that the GM parameters listed in this work can be directly used and no more stationary field tests are required for estimating the GM parameters. As mentioned earlier, the estimated results through Situation #1 and Situation #2 are very close to each other, so it is reasonable that these parameters can be used for the other cases. Furthermore, if more precision GM parameters are required for other experiments, the stationary field tests can still be implemented for obtaining an accurate positioning solution as well as possible. On the other hand, how to improve the estimation performance in terms of \(S_{f}\) and \(S_{g}\) is not our main contribution in this work. These two parameters are estimated through the stationary field test in Situation #3 instead of the other two situations to remove as many factors, e.g., temperature, long-term effects, as possible, since these factors may influence the difference between the estimations and the real values. It is worth mentioning that all the GM parameters, \(S_{f}\) and \(S_{g}\) are feasible to be estimated through one single stationary test.