## 5 Conclusions  
In terms of the timeliness and accuracy of RTK in harsh environments, both the measurement quality and the filter robustness need to improve, especially with the presence of non-Gaussian noise. This paper focus on multi-GNSS DF applications and a new nonlinear filter strategy is proposed. It consists of the DF data-aided AR method and the AMC-KF based on MCC and adaptive KBW. The superiorities are verified through tests with various baselines. First of all, ionosphere-free and wide-lane measurements are used for the DF data-aided AR method. The ambiguities on each frequency are directly converted without searching. Then, the corrected carrier measurements are used for the float solution by the proposed AMC-KF. The AMC-KF is robust to non-Gaussian noise and sparking noise as it employs MCC and adaptive KBW to measure the similarity between the input and output. Compared to the conventional DD-KF, the proposed strategy achieves higher accuracy and efficiency. The following conclusions are obtained:  
1. For the positioning accuracy of short baselines, the RMS and STD of positioning error improved by more than 30%, 30%, and 60% on the E, N, and U components, respectively. The applicability and flexibility of the proposed AMC-KF are validated significantly. 2. For the proposed adaptive KBW, the efficiency and accuracy are compared and validated with fixed KBW [1, 5, 25, 30]. The results show that large KBWs increase the computational load, while the small KBWs gain a worse positioning accuracy. The proposed optimization strategy can change the KBW adaptively according to the measurements and is validated to be effective as it considers both efficiency and accuracy. 3. A total of 29 satellites were involved in the ambiguity resolution test with long baselines. It validates that the proposed DF data-aided AR method achieves a success rate of more than 93%. The results are expected to be further improved with stringent data synchronization and cycle-slip detection. 4. For the long baseline test, the proposed filter strategy obtains an improvement of more than 40% in all directions as the noise is effectively suppressed. For the longer baseline BONE-WBEE, the RMS of positioning error is reduced by more than 75% on E, N, and U, which shows that the proposed method plays a better role in long baseline RTK when the multi-GNSS multi-frequency data is stably available. Our future work focuses on deriving the sequential form of the proposed nonlinear filter strategy and applying it to smartphone RTK applications. To improve the precision and reliability of dynamic navigation in urban environments, the integration of the proposed method with vector-tracking GNSS receivers will also be explored. Conceptualization, J.L. ; methodology, J.L. ; software, J.L. and T.L. ; investigation, Y.J., B.X., and Z.L. ; data curation, J.L., M.S. and T.L. ; writing--original draft preparation, J.L. ; writing--review and editing, B.X., M.S., M.L., Z.L. and G.X. ; supervision, Y.J., B.X., Z.L., and G.X. All authors have read and agreed to the published version of the manuscript. This study is supported by the Guangdong Basic and Applied Basic Research Foundation (No. 2021A1515012600); the Opening Project of Guangxi Wireless Broadband Communication and Signal Processing Key Laboratory (No. GXKL06200217); the Open Fund of Key Laboratory of Urban Land Resources Monitoring and Simulation, Ministry of Natural Resources (No. KF-2021-06-104).