## 5 Conclusions  
In this paper we provide an introduction about how to use the Allan variance algorithm to model the time-correlated error present in the local clock estimation data due to the VT feedback process. We applied the preliminary stationary field tests in two open-sky situations, and the estimated clock drift residual curves in terms of the Allan deviation are plot based on these static statistic data. A distinctive segment has been discovered in the curve shape related to the VT loop which can be differentiated from the one produced by the ST loop. The separate segment marks that the Markov noise is present in the clock drift estimated from the GNSS SDR using the VT technique instead of the ST architecture. In this work, the 1 st-order Gauss-Markov process is adopted to model such noise source. Then, an improved A-VTTCES-KF algorithm is proposed to suppress the biased error in the PVT solutions caused by such VT-induced time-correlated error in the tracking loop. The state vector and the process covariance matrix can be improved with the given time-correlated model. Once the time-correlated error is estimated through the A-VTTCES-KF, the performance of the clock drift estimations can be enhanced by removing the known error source. In other words, the carrier NCO updates, i.e., Equation (24), can end up with obtaining a more accurate value, and the code NCO updates, which are aided by the carrier NCO, will accordingly be improved as well. A Matlab-based GNSS SDR designed by the author is used to process the GPS L1 C/A signals in the field test to verify the proposed algorithms. The respective SDR using ordinary adaptive KF algorithm and the commercial low-cost U-Blox receiver are used for calculating the positioning solutions, relied on an open-source package program, RTKLIB, as the comparisons. The coherent integration time is chosen as 5 ms in this work, so the loop rate of the PLL and DLL updates is 200 Hz in the GNSS SDR. The experimental results have demonstrated that, when the LR of the VT architecture is set to 5 Hz, the GNSS SDR using the proposed A-VTTCES-KF can embrace the improvements of 14.17% and 21.40% in terms of the RTK positioning when compared with the VT SDR with the ordinary adaptive KF method and the U-Blox receiver, respectively. In addition, the DGPS positioning solutions produced by the proposed VT SDR also outperform the ones obtained from the SDR using the ordinary method method at a percentage of 9.73%. Towards the case of increasing the performance based on the code-based positioning algorithms, the receiver design methods, e.g., the discriminator applied for the code error estimation, the DLL bandwidth, could dramatically make a difference on the navigation solutions. Since the multipath interference has a higher influence on the pseudo-range measurement than the carrier phase measurement. Under this circumstance, it is acceptable that the DGPS positioning results estimated from the U-Blox receiver performed better than the proposed SDR architecture. It should also be noted that the proposed approach seems to work more efficiently in areas where the VT LR is lower. For example, the enhanced GNSS SDR was proved to provide higher improvements when the VT LR is chosen as 5 Hz rather than the case of the VT LR being set to 10 Hz. An approach using the Allan variance to account for the time-correlated error present in the typical VT loop has been proposed in this work, and the idea to compensate such error towards the VT-based receiver design has seldom been mentioned in previous researches. The time-correlated error would add extra biases to the GNSS measurements such that the code-based and carrier-phase-based positioning results can be intimately affected, and the related accuracies will be accordingly decreased. Under this circumstance, two major improvements have been made through the proposed A-VTTCES-KF.