Ice loads significantly challenge ocean structures, making their inversion on vertical offshore platforms based on acceleration responses essential for effective design, maintenance and risk assessment in icy conditions. To enhance accuracy and stability in ice load monitoring, we propose a method that combines state space model and regularization techniques. First, we establish a dynamic model of the ice-structure interaction using the state space method, simplifying the multi-degree-of-freedom offshore platform to a two-degree-of-freedom model. The dynamic response is simulated using the Newmark method for ice force inversion. Second, we address potential noise and uncertainty in observed data through regularization, which significantly improves accuracy and stability compared to traditional methods. Simulation analyses confirm the method's universality and effectiveness across various ice conditions.