Filtering Techniques for Stochastic Hybrid Systems

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.