Nonlinear filtering with various irregularities in measurement data

Abstract

Estimation is a popular computational tool for determining the internal states of a dynami cal system from noisy measurements. A recursive process of estimation is called filtering. The conceptual filtering solution is obtained in terms of 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, while an optimal nonlinear filter is still a future scope. This thesis is particularly concerned with suboptimal nonlinear filtering. There are two popular nonlinear filtering methods, namely Gaussian filtering and particle fil tering. The Gaussian filtering approximates the unknown PDFs as well as the unknown noises as Gaussian. The particle filtering characterizes the unknown PDFs as a weighted summation of particles. The literature beholds many variants of the Gaussian filtering as well as the particle fil tering, availing an impressive trade-off between accuracy and computational demand. Therefore, if an adequate computational budget is available, under the general problem scenarios, the accu racy may not be a serious concern despite the suboptimality of nonlinear filtering. Although the practical problems often perceive complicated scenarios, where the existing nonlinear filters fail or underperform.