Optimal State Estimation for Partially Observed Boolean Dynamical Systems in the Presence of Correlated Observation Noise

Abstract

Recently, state space signal models have been proposed to characterize the behavior of discrete-time boolean dynamical systems. The current system model is one in which the system is observed in the presence of noise. The existing algorithms, however, rely on an assumption of independent and identically distributed (i.i.d.) white noise processes. The existing recursive MMSE process of estimating a Boolean dynamical system (in the presence of i.i.d. noise) is called the Boolean Kalman Filter (BKF). Here we address a different sort of noise, one that is correlated in time to other observation noise, specifically through an AR(1) time series process. In this thesis, we propose modifications to the state-space model that will allow the existing Boolean Kalman Filtering recursive process to adapt to handle time-correlated noise. Additionally, we will propose a modification to the Boolean Particle Filtering approximation to compensate for the same correlated noise AR(1) process.

In addition, this document will address a new software package created in the R programming language that will allow the scientific community easier (and free) access to the algorithms created by the Genomic Signal Processing Lab at Texas A&M University. These algorithms will be explained in this document, with results of the algorithms derived from the use of the package.