## 5 Conclusions and Future Work  
This study developed a real-time loosely-coupled 3 DMA GNSS with a Doppler measurements positioning system via FGO, and skymask context-based candidate sampling. Our approach distributes the candidates more effectively and mitigates local minima issues. Based on the experimental results, the positioning RMSE of loosely-coupled 3 DMA GNSS with Doppler measurements via FGO is around 21 m with STD 15 m (on average). Performance can be further improved when optimizing in a combined direction with RMSE reduced to about 16 m with a STD of 13 m. The FGO can provide a lower standard deviation error than the candidate-based 3 DMA GNSS, which means that it can provide a smoother and more robust solution.  
However, the performance of LC-FGO still has space to be improved. The results show that candidate-based 3 DMA GNSS intermittently outperforms LC-FGO. The reason is the positioning error of 3 DMA GNSS keeps contributing to the integration with Doppler measurements. Accumulated error results affect future batch optimization. An adaptive scheme should be developed to select the high confidence information in the sliding window. Moreover, tighter integration of the 3 DMA GNSS with Doppler measurements should be effected to improve the performance.  
Furthermore, bad Doppler measurements result in wrongly estimated velocity. This will degrade the FGO performance. Doppler measurements error mitigation or correction is the key to improving the positioning. In future research, we will explore how 3 DMA  
Figure 11: Zoom-in map plot of positioning error caused by badly estimated velocity.  
GNSS can more tightly integrate with Doppler measurements to provide a more robust positioning in the urban canyons for smart health applications and beyond.  
Conceptualization, L.-T.H.; Data curation, M.J.L.L., J.F., T.N. and M.B.; Formal analysis, H.-F.N.; Funding acquisition, J.-R.R.; Investigation, L.-T.H., T.N., M.B. and J.-R.R.; Methodology, H.-F.N.; Project administration, L.-T.H., T.N., M.B. and J.-R.R.; Resources, T.N., M.B. and J.-R.R.; Software, H.-F.N., M.J.L.L. and J.F.; Supervision, L.-T.H. and J.-R.R.; Validation, H.-F.N. and J.F.; Visualization, M.J.L.L.; Writing--original draft, H.-F.N.; Writing--review and editing, L.-T.H., M.B. and J.-R.R. All authors have read and agreed to the published version of the manuscript.  
Research reported in this publication was supported in part by the NSF grant 1952180 under the Smart and Connected Community program, as well as by NSF Grant ECCS-1928614, the National Eye Institute of the National Institutes of Health under Award Number R21 FY033689, and DoD grant VR200130 under the \"Delivering Sensory and Semantic Visual Information via Auditory Feedback on Mobile Technology\". The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health and NSF, and DoD.  
Not applicable.  
New York University (NYU) and John-Ross Rizzo (J.-R.R.) have financial interests in related intellectual property. NYU owns a patent licensed to Tactile Navigation Tools. NYU, J.-R.R. are equity holders and advisors of said company.