Nonlinear gaussian filtering with missing and delayed measurements

Abstract

The state variables are a set of variables that completely describe a system’s behavior, i.e., their temporal evolution results from the system dynamics. Thus, the knowledge of the state variables is crucial to study the behavior of any dynamic system. These variables are generally referred to as hidden (latent) states due to the unavailability of any direct information. Mostly, the latent states are inferred from the measurements (data) which are typically acquired from surveys, sensors, etc. The received measurements inherently involve some degree of uncertainty (due to imperfect sensors, mishandled data in surveys, or unknown measuring environments), giving an erroneous and unreliable knowledge of states. Such scenarios oblige one to settle for the best feasible estimate, in some sense (e.g., minimum mean square error), of the states. Estimation, or more broadly filtering (a recursive process of estimation), facilitates a tool to determine the latent states of a dynamical system from the available system information and noisy measurements. It finds applications in numerous real-life problems—target tracking, biomedical, financial prediction, weather forecasting, industrial diagnosis etc. For linear filtering problems, the Kalman filter (KF) provides an optimal solution. However, its performance deteriorates for nonlinear filtering problems. Subsequently, several nonlinear variants of the KF were reported in literature, referred to as nonlinear Gaussian filters; these filters approximate all the probability density functions (PDFs) as Gaussian during the filtering process. They involve intractable integrals which are numerically approximated during the filtering. Apart from Gaussian filtering, there is another class of nonlinear filters, named particle filtering, which is mostly beyond the scope of the contributions of this thesis.