Monte Carlo Filters for Nonlinear and Non-Gaussian Dynamic Systems

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9982846This research is concerned with Monte Carlo methods for nonlinear and non-Gaussian dynamic systems. The basic idea of the Monte Carlo filter is to sequentially generate random samples from the distribution of the current state of the system. Compared with traditional filtering methods, simple, flexible, yet powerful Monte Carlo techniques provide effective means to deal with complex dynamic systems. The investigator studies four specific topics in this research. Topic (I) studies a special Monte Carlo filter called Mixture Kalman filter for the conditional dynamic linear models, a class of widely encountered systems in practice. This filter utilizes the `marginalization' operation to improve efficiency. Topic (II) studies a partial rejection control operation, an operation aimed to generate more efficient random samples in Monte Carlo filters. Topic (III) studies methods to deal with dynamic systems with unknown system coefficients, an important but difficult problem. Topic (IV) is devoted to several applications of Monte Carlo filters, including tracking multiple maneuvering targets in a clutter environment; Bayesian receivers in digital wireless communications; on-line estimation of the market volatility in financial time series analysis; and stochastic system control with non-Gaussian innovations.Dynamic systems are widely used in almost all fields of applications. Examples abound in radar or sonar surveillance systems, in mobile telecommunications, in economic and financial data analysis, in computer vision, in medical diagnostics, in speech recognition, in feed-back control and guidance systems, and in Internet traffic monitoring and control, just to name a few. Most of them are nonlinear and non-Gaussian. One of the main challenges in dealing with dynamic systems is that they usually require on-line (in real time) estimation and prediction (filtering) of the ever-changing system characteristics, given the continuous flow of observations and information from the system. The investigator studies and develops Monte Carlo filters for nonlinear and non-Gaussian dynamic systems. The basic idea of the Monte Carlo filter is to sequentially generate random samples to represent the status (distribution) of the current state of the system. Modern computing power has made it feasible to use Monte Carlo methods as filtering methods in application. Compared with traditional filtering methods, simple, flexible, yet powerful Monte Carlo techniques provide effective means to deal with complex dynamic systems. This research enriches the toolkit of on-line filtering for nonlinear and non-Gaussian dynamic systems. Faster and more effective filtering techniques will certainly have significant impact on a wide range of important applications in real life and make significant contributions to advancing science and technology. It also promotes the interdisciplinary research between engineering and statistics.