Estimation and detection of nonlinear/chaotic signals: A Bayesian-based approach

Nonlinear systems are an important field of study in several disciplines. Engineering, science, mathematics, finance and medicine are examples of fields where nonlinear systems play a crucial role in research development. Unfortunately, most of the methods in the literature that pertain to nonlinear systems do not take full advantage of the nonlinear structure. In fact, most methods perform some type of linearization to the nonlinear process, potentially disregarding useful information.;This thesis develops a true nonlinear model-based approach to estimation and detection of nonlinear systems in high noise environments. We show that by using all past measurements one can update the conditional density function of the system state to perform optimal estimation and detection.;Here we provide the necessary theory to develop the Bayesian-based nonlinear estimation and detection schemes along with several examples. These examples include using known dynamical systems, such as Henon and Duffing-Ueda maps, as well as real-world data sets to demonstrate the capabilities of the proposed methods.