In the context of space situational awareness tasks, traditional admissible region (AR) methods face significant computational complexity challenges due to excessively large calculation ranges. This paper proposes an innovative minimum admissible region (MAR) theoretical framework that achieves a lower-bound approximation of the admissible domain range by systematically decoupling the uncertainty propagation mechanisms in observational data. Specifically, the MAR method ensures a 99.73% true orbit state inclusion probability during initial orbit determination and achieves an orders-of-magnitude reduction in domain volume compared to the original AR in simulation validations. The reduction in computational complexity provides robust technical support for real-time data processing in space situational awareness systems.