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The control programs of complex autonomous systems that have conditional branching can be modeled as linear hybrid systems. When the state knowledge is perfect, linear hybrid systems with state-based transition conditions can be verified against a specified unsafe set using existing model checking software. This paper introduces a formal method for calculating the failure probability due to state estimation uncertainty of these sensor-driven hybrid systems. Problem complexity is described and some reduction techniques for the failure probability calculation are given. An example goal-based control program is given and the failure probability for that system is calculated.