Surface subsidence induced by coal mining poses severe threats to global ecosystems and infrastructure. A critical challenge in subsidence prediction lies in the sensitivity of existing probabilistic integral parameter inversion methods to gross errors, leading to unstable predictions and compromised reliability. To address this limitation, we propose the IGGIII-BFGS algorithm that integrates robust estimation with unconstrained optimization method, enhancing resistance to gross errors during parameter inversion. Through systematic comparison of four robust estimation methods (Huber, L1, Geman–McClure, IGGIII) fused with BFGS, the IGGIII-BFGS method demonstrated superior stability and accuracy, reducing relative errors in key parameters (subsidence factor q, horizontal displacement coefficient b, and tangent of major influence angle tan β) to near-zero levels. Validation on the Huainan mining case study showed that the IGGIII-BFGS method achieved a 25.8% reduction in subsidence RMSE compared to standard BFGS, with predicted curves exhibiting strong agreement with field measurements. This advancement enables precise forecasting of subsidence and horizontal displacement, which hold significant value for the sustainable development of the surface ecological environment and social stability.