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In this paper, we develop a robust hybrid estimation algorithm for the Stochastic Linear Hybrid System (SLHS) with unknown continuous fault inputs. Most existing estimation algorithms for hybrid systems with fault inputs are designed such that every faulty mode is modeled as a discrete state, which incurs a large number of the discrete states in the estimation model. The proposed algorithm overcomes this problem by decoupling the unknown fault inputs from the estimation error dynamics and has the same number of the discrete states as the original hybrid system. The proposed algorithm is validated with a vertical take-off and landing (VTOL) aircraft application.