Geospatial data statistics involve the aggregation and analysis of location data to derive the distribution of clients within geospatial. The need for privacy protection in geospatial data analysis has become paramount due to concerns over the misuse or unauthorized access of client location information. However, existing private geospatial data statistics mainly rely on privacy computing techniques such as cryptographic tools and differential privacy, which leads to significant overhead and inaccurate results. In practical applications, geospatial data is frequently generated by mobile devices such as smartphones and IoT sensors. The continuous mobility of clients and the need for real-time updates introduce additional complexity. To address these issues, we first design \textit{spatially distributed point functions (SDPF)}, which combines a quad-tree structure with distributed point functions, allowing clients to succinctly secret-share values on the nodes of an exponentially large quad-tree. Then, we use Gray code to partition the region and combine SDPF with it to propose $\mathtt{EPSpatial}$, a scheme for accurate, efficient, and private statistical analytics of geospatial data. Moreover, considering clients' frequent movement requires continuous location updates, we leverage the region encoding property to present an efficient update algorithm.Security analysis shows that $\mathtt{EPSpatial}$ effectively protects client location privacy. Theoretical analysis and experimental results on real datasets demonstrate that $\mathtt{EPSpatial}$ reduces computational and communication overhead by at least $50\%$ compared to existing statistical schemes.