## 6 Conclusions  
In this paper, in order to improve the tracking performance of the vector receiver in the high dynamic and weak signal environment, the adaptive square root cubature Kalman filter algorithm is applied to the navigation filter in the vector tracking loop, which improves the stability and numerical accuracy of the filter, realizes the real-time measurement of the observed noise covariance matrix, and reduces the adverse effects caused by high dynamics and weak signal channels. The algorithm in this paper is compared with the vector loop based on SRCKF and the scalar loop based on ASRCKF. The test results show that when the number of signal channels is three or fewer, or even when the carrier performs high dynamic motion on that basis, compared with the SRCKF VLL and the ASRCKF SLL, the ASRCKF VLL shows lower position error and speed error and higher filtering accuracy. When the number of channels with signals is restored to four or more, the vector loop based on ASRCKF or SRCKF can achieve rapid retracking, while the scalar loop based on ASRCKF is only greatly improved compared to the highly dynamic weak signal. Compared with the other two vector loops, its tracking performance still has a gap. Additionally, through quantitative evaluation, the tracking performance of the ASRCKF algorithm in the vector tracking loop is about 18% higher than that of the SRCKF. Under the same conditions, the computational complexity of the two algorithms is similar. Therefore, in vector tracking loop, compared with the SRCKF algorithm, the ASRCKF algorithm can improve the tracking accuracy and tracking performance under the premise of the same computational complexity. In summary, the ASRCKF-based vector loop among the three loops has the most accurate estimation and tracking performance.  
[PERSON] is responsible for algorithm derivation, simulation experiment, and drafting manuscripts. [PERSON] gave important suggestions on the derivation part of the algorithm. [PERSON] was responsible for guiding the writing of the paper, participating in the writing, and checking for errors in the paper. All authors have read and agreed to the published version of the manuscript.  
This research was supported by the National Natural Science Foundation of China (No. 61231006, No. 61501078).  
Not applicable.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Carrier-to-Noise Ratio** & \begin{tabular}{c} **Average Consumption** \\ **Time of ASRCKF** \\ **(N/N\({}_{0}\), dB/Hz)** \\ \end{tabular} & \begin{tabular}{c} **Average Consumption** \\ **Time of ASRCKF** \\ **(s)** \\ \end{tabular} & \
\begin{tabular}{c} **Average Value of RMSE\({}_{total}\)** \\ **of ASRCKF** \\ **(s)** \\ \end{tabular} &
\begin{tabular}{c} **Average Value of RMSE\({}_{total}\)** \\ **of SRCKF** \\ **(s)** \\ \end{tabular} \\ \hline
25 & 0.0122 & 0.0123 & 0.0125 & 0.025 \\
23 & 0.015 & 0.015 & 0.019 & 0.026 \\
21 & 0.019 & 0.021 & 0.022 & 0.03 \\
20 & 0.022 & 0.025 & 0.025 & 0.039 \\
19 & 0.025 & 0.025 & 0.029 & 0.05 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The average time consumption and filtering performance of the two algorithms of ASRCKF and SRCKF when the C/N\({}_{0}\) is 25, 23, 21, 20, and 19 dB-Hz, respectively.  
**Acknowledgments:** The authors would like to thank the editor-in-chief and the anonymous reviewer for their constructive suggestions and improve the quality of the paper.