## 5 Conclusions  
This paper focuses on monitoring the surface settlement of the Banji 110,801 working face from 10 April 2021 to 28 June 2022, utilizing a synergistic monitoring approach combining InSAR and UAV technologies. The reliability of the inversion of the probability integration method parameters was verified using the BFGS algorithm. The results obtained led to the following conclusions:  
Under the condition of a 10 cm error, the BFGS algorithm can still effectively invert the parameters of the probability integration method, and the inversion results are relatively stable. The D-InSAR technique is applicable for monitoring small deformations at the edges of subsidence basins. However, it faces challenges when dealing with significant deformation gradients, leading to incoherence in the interferometric image pairs. As a result, it becomes impractical to monitor regions with large-gradient deformations at the center of the subsidence basins. Additionally, relying solely on D-InSAR data for monitoring is insufficient to invert the parameters associated with mining subsidence. UAV oblique photogrammetry technology enables the monitoring of settlement in both the central and the edge areas of subsidence basins, meeting the accuracy requirements for predicting parameter inversion in mining subsidence. However, its accuracy in monitoring the edge of subsidence basins is significantly inferior to that of D-InSAR technology. The two sets of monitoring data were combined using fusion techniques. The fusion data met the error requirements for inverting the parameters of the probability integration method through the BFGS algorithm. As a result, the collaborative monitoring of mine subsidence, utilizing InSAR and UAV technology, and employing the BFGS algorithm for probability integration method parameter inversion, was not only feasible but also superior to the singular application of UAV oblique photogrammetry. This approach introduces a novel idea and method for unmanned mine subsidence monitoring.  
In this study, there are certain limitations associated with the inversion of probabilistic integral model parameters using the BFGS algorithm. These include a lack of global convergence; sensitivity to initial guesses; variable convergence rates, particularly when dealing with ill-conditioned functions; and limited applicability to non-smooth or discontinuous objective functions. In future research endeavors, we intend to address and rectify these shortcomings by making improvements to the algorithm.  
Conceptualization, M.Z.; data curation, H.T. and M.Z.; formal analysis, M.Z. and H.T.; investigation, X.Y. ([PERSON]), S.X. and Y.H.; methodology, X.Y. ([PERSON]) and M.Z.; supervision, H.T.; validation, X.Y. ([PERSON]), H.T. and M.Z.; visualization, H.T.; writing--original draft, M.Z. and H.T.; writing--review and editing, M.Z. and H.T. All authors have read and agreed to the published version of the manuscript.  
**Funding:** The work was funded in part by the Research on Essential Technologies and Implementation Methods for Unmanned Monitoring in Mining Areas (No. 2022 yjrc26), the Key Research and Development Program of Anhui Province under Grant 202104a07020014, the Major science and technology projects of Anhui Province under Grant 202103a05020026, Open Foundation of the Key Laboratory of Universities in Anhui Province for Prevention of Mine Geological Disasters (No. 2022-MGDP-08), Key Laboratory of Aviation-Aerospace-Ground Cooperative Monitoring and Early Warning of Coal Mining-induced Disasters of Anhui Higher Education Institutes (Anhui University of Science and Technology) (No. KLAHEI202204).  
**Institutional Review Board Statement:** Not applicable.  
**Informed Consent Statement:** Not applicable.  
**Data Availability Statement:** Not applicable.  
**Conflicts of Interest:** The authors declare no conflict of interest.