From Kalman to Particle Filtering for solving Signal Processing Problems with Neural Networks

September 4, 2002, 8:30-9:20

Many nonlinear signal processing problems are best solved by sequential algorithms. The inherent sequential arrival of data and possible nonstationarities in the underlying process necessitate this. The simple, and well known, approach to sequential learning and inference is to cast the problem in a state space formulation and apply the Extended Kalman Filter (EKF). This works by local linearisations of the state space equations and consequently approximating the induced probability densities by Gaussian distributions. Several enhancements to the basic EKF approach exist including the framework to handle multiple models, iterative refinements of the local approximations about the operating point and a technique known as the Unscented Kalman Filter (UKF). Other, more sophisticated nonparametric, ways of representing the modelling uncertainties via sampling methods fall under the class of algorithms known as Particle Filters. These are more suitable for problems where linear approximations often fail, inducing multi-modal probability densities of the underlying uncertainties. Hence they are better approaches in models such as Neural Networks which are used as function approximators in problems containing high nonlinearities. This talk will partly be of a tutorial nature, reviewing and motivating recent developments in sequential modelling with nonlinear models. I will also illustrate my recent work on two interesting applications: A data-driven approach to modelling air-pollution and tracking rapidly changing resonances in speech signals.