Sequential Bayesian modeling of non-stationary non-Gaussian processes

Abstract

This thesis brings a unifying approach for modeling non-stationary non-Gaussian signals which are widely encountered in many multidisciplinary research fields. In the literature, different approaches have been used to model non-stationary signals. However, they could not fulfill the increasing needs where non-Gaussian processes are involved until the development of Sequential Monte Carlo techniques (particle filters). In general particle filtering, the problem is expressed in terms of nonlinear and/or non-Gaussian state-space equations and we need information about the functional form of the state variations. In this thesis, we bring a general solution for cases where these variations are unknown and the process distributions cannot be expressed by a closed form probability density function. We propose a novel modeling scheme which is as unified as possible to cover these problems. First, a novel technique is proposed to model Time-Varying Autoregressive Alpha Stable processes where unknown, time-varying autoregressive coefficients and distribution parameters can be estimated. Successful performances have been supported by posterior Cramer Rao Lower Bound values. Next, we extend our methodology to model cross-correlated signals where vector autoregressive processes with non-Gaussian driving signals can also be modeled. Later, this extension is used as a building block to provide a more unifying solution where both mixing matrix and latent processes are modeled from their mixtures. This can be interpreted as a solution for non-stationary Dependent Component Analysis. Successful simulation results verify that our methodology is very flexible and provides a unifying solution for the modeling of non-stationary processes in all cases described above.