Advanced Kalman filtering with applications to power system and epidemiological data analysis

Abstract

Estimation is a popular computational tool for determining the internal states of a dynamical system from noisy measurements. A recursive process of estimation is called filtering. The conceptual filtering solution is obtained using unknown probability density functions (PDF). Several analytical filtering solutions have been presented in the literature by characterizing the unknown PDFs differently. The popularly known Kalman filter is an optimal analytical filter for linear dynamical systems. However, there is still a scope for exploring the development of an optimal nonlinear filter in the future. Thankfully, the popularly known Gaussian filtering provides a widely accepted suboptimal solution for nonlinear filtering problems. Some of the popular Gaussian filters are the extended Kalman filter (EKF), unscented Kalman filter (UKF), cubature Kalman filter (CKF), and cubature quadrature Kalman filter (CQKF). This thesis mainly focuses on two directions: i) developing advanced filtering methods for handling various practical irregularities and ii) developing advanced power system state estimation (PSSE) methods for improving the PSSE accuracy in the monitoring of real-life power system networks. However, in the middle of the thesis work, the Covid-19 outbreak was witnessed, which was soon proved to be one of the deadliest pandemics of the last several centuries. Therefore, in the interest of scientific responsibility, a new research direction was chosen to develop an advanced algorithm for epidemiological state estimator (ESE) method.