## 6 Conclusions  
In this paper, a VFLL-assisted PLL for global navigation satellite system (GNSS) receivers based on maximum likelihood estimation was proposed. The loop makes full use of the advantages of the VFLL and PLL and can realize a trade-off between dynamic robustness and tracking accuracy in the loop. Compared with the traditional VFAPLL, the loop performance is improved. The new architecture not only takes advantage of the vector tracking loop but also achieves a very low tracking threshold through ML estimation. In the process of ML estimation, the discriminator is removed, and the coherent integration result of the signal is directly used as the input of the navigation filter. The problem of the limited tracking range of the discriminator is avoided, and the tracking sensitivity of the loop is improved. The method proposed in this paper improves the performance of carrier tracking loop in high dynamic weak signal environments. The proposed loop structure improves the tracking accuracy and robustness of the loop.  
Deficiencies in the Paper and Prospects for Future Work  
The test signals used in the paper are all from the GNSS simulator or the high dynamic motion model of the JPL laboratory in the United States. If we can find in the future an external environment where the navigation signal strength and carrier motion meet the test conditions, it will be more helpful to combine theory with practice.  
In addition, although the MLE algorithm shows better robustness and faster response speed in high dynamic scenarios, its computing load is greater than that of traditional algorithms. Because the computing load of the MLE (LM) algorithm increases almost linearly with the increase in the number of iterations, so we need to further optimize the MLE algorithm based on LM algorithm.  
Conceptualization, N.L. and S.Z.; methodology, N.L.; software, N.L.; validation, N.L., Y.J. and S.Z.; writing--original draft preparation, N.L.; writing--review and editing, N.L.; supervision, S.Z. All authors have read and agreed to the published version of the manuscript.  
This research received no external funding.  
The authors declare no conflict of interest.  
List of Symbols  
\begin{tabular}{l l} \(f_{0}\) & represents the Doppler frequency, corresponding to the relative motion speed \\  & of the satellite and the receiver \\  & represents the first-order rate of change of the Doppler frequency, corresponding \\  & to the relative motion acceleration of the satellite and the receiver \\  & represents the second-order rate of change of the Doppler frequency, corresponding \\  & to the relative motion jerk of the satellite and the receiver \\  & Sampling interval for discretization of continuous time state equation \\  & state, 'k' represents the time epoch of the data sample \\  & state noise \\  & the covariance matrix of the prediction error \\  & the random jitter of the third derivative of the carrier frequency. \\  & coherent integration processed output of the integral eliminator of the VFLL \\  & Assisted PLL loop \\  & represents the C/A code autocorrelation function \\  & the phase difference between the copied C/A code and the received C/A code \\  & Coherent integration time \\ \end{tabular}