Model-based estimation of probabilistic hybrid automata

The ability to monitor and diagnose complex physical systems is critical for constructing highly autonomous artifacts that can function robustly in harsh environments over a long period of time. To accomplish this, we need to use high fidelity models that describe both the discrete stochastic behavior and the continuous dynamics of these complex systems. These models are used by a hybrid monitoring and diaj~nosis capability that tracks a system's dynamics as it moves between distinctive behavioral modes. In this thesis, we address the challenge of learning these hybrid discrete/continuous models. We introduce a Hybrid Parameter Estimation System that extracts parameter estimates from sensor data. First, we review a method for Hybrid Modeling based on Probabilistic Hybrid Automata (PHA) [Hofbaur and Williams, 2002]. Second, we introduce Hybrid Parameter Estimation as a technique for learning the parameters of a PHA, by unifying standard nonlinear estimation techniques with classical probabilistic estimation techniques. Finally, we introduce the Hybrid Expectation Maximizatio