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Stochastic Hybrid Systems (SHS) blend continuous and discrete dynamics, relevant to communication, vehicle control, finance, and tracking. Our research focuses on state estimation for linear and non-linear SHS, emphasizing solutions for missing measurements. Historically, SHS state estimation leaned towards deterministic models, overlooking issues like measurement loss. Researchers now explore probabilistic and guard condition-based state transitions. For example, in flying objects, SHS captures discrete flight modes and continuous dynamics. We introduce the Data Loss Detection Kalman Filter for linear SHS, bolstered by Chi-square statistics for measurement loss. In non-linear SHS, the Reallocation Resample Particle Filter and Systematic Resample Particle Filter excel in handling missing measurements. Our research illuminates state estimation intricacies, offering practical solutions.