| Many real-world systems are dynamic systems that operate in a sequential manner, producing sequential data. These data are either time-series data or sequence data over some types of relationships. Dynamic Bayesian Networks (DBNs) are important and widely used to model these sequential data, revealing inherent correlations between data of the systems. Under DBNs, Bayesian inference provides an optimal framework for sequential data analysis and produces solutions potentially better than other non Bayesian-based methods. Yet, intricate computations required by Bayesian inference are barrier to its application. To this end, various Bayesian computational methods have been proposed especially for dynamic systems to alleviate the difficulty, making Bayesian analysis possible. Loosely speaking, deterministic and stochastic methods are two basic categories of Bayesian computations. Although stochastic methods are more powerful and multi-purpose than deterministic methods, the computational complexity often forbids them from performing online inference. This dissertation investigates the theory of a new deterministic approach: expectation propagation (EP).; EP is an extension to the sequential Assumed Density Filter (ADF). It can provide more accurate inference than other deterministic methods as it can refine the posterior approximation of each state in a recursive manner. EP has comparable performance and yet higher efficiency than the stochastic methods, which need a sufficient large number of samples to approximate the posterior distributions for a desired accuracy.; In this dissertation, we investigate the EP solutions to two important nonlinear dynamic systems, namely, the conditional linear systems and hybrid nonlinear systems. We demonstrate how different nonlinear inference methods, such as extended Kalman filter, unscented Kalman filter, unscented Kalman smoother, can be incorporated into the EP solution for solving these nonlinear dynamic problems. We detail the derivations of EP algorithms for the two systems and show their accuracy and efficiency over other exiting deterministic and stochastic methods. The subsequent tasks for the remaining dissertation will be to: (1) Continue on the work of engine health monitoring problems, including gas pass tracking and engine modeling; (2) Investigate a general solution for EP on hybrid nonlinear model; (3) Discover more advantages of EP in my current Telematics project. |
