Sequential Estimation in Nonlinear and Nonstationary Signal Processing

Many modern signal processing problems involve systems that are nonlinear and nonstationary. Data-driven models that are based on powerful function approximation methods such as neural networks have been applied with demonstrable success to these problems. Nonstationarity imposes a particular difficulty in these settings because regularisation techniques such as cross validation can be inapplicable. This tutorial will address sequential estimation techniques that are useful in nonlinear and nonstationary environments. It will use a Bayesian dynamical systems approach and will introduce concepts and algorithms involving the extended Kalman filter (EKF) and powerful variants of it. Starting from the EKF, we will review more recent developments in sequential Markov Chain Monte Carlo (Particle Filters), and explore their application in a number of practical examples taken from speech signal processing and an image processing problem in microarray gene expression analysis.