Chapter 1
Introduction
Estimation and tracking of dynamic systems has been the research focus of many a mathematician since the dawn of statistical mathematics. Many estimation methods have been developed over the past 50 years that allow statistical inference (estimation) for dynamic systems that are linear and Gaussian. In addition, at the cost of increased computational complexity, several methods have shown success in estimation when applied to nonlinear Gaussian systems. However, real-world dynamic systems, both linear and nonlinear, usually exhibit behavior that results in an excess of outliers, indicative of non-Gaussian behavior. The toolbox of standard Gaussian estimation methods have proven inadequate for these problems resulting in divergence of the estimation filters when applied to such real-world data.
With the advent of high-speed desktop computing, over the past decade the emphasis in mathematics has shifted to the study of dynamic systems that are non-Gaussian in nature. Much of the literature related to performing inference for non-Gaussian systems is highly mathematical in nature and is lacking in practical methodology that the average engineer can utilize without a lot of effort. In addition, several of the Gaussian methods related to estimation for nonlinear systems are presented ad hoc, without a cohesive derivation. Finally, there is a lack of continuity in the conceptual development to date between the Gaussian methods and their non-Gaussian counterparts. ...
