Simon J. Julier, University College London, United Kingdom
Tractable Estimation in Nonlinear Systems
An awkward fact of life is that almost all systems of interest are nonlinear. Nonlinearities introduce many challenges for estimation systems, including biases, coupling through higher order dependencies, and restrict estimates to lie on nonlinear manifolds. Although these problems can be solved in theory, it is well-known that, in practice, the theoretical solutions are intractable and suboptimal approximations must be used. Historically, linear minimum mean squared error estimators such as the Kalman filter were developed. Given the limitations of these algorithms, many other approaches—such as particle filters, Gaussian mixture models, grids and kernel density estimators have been proposed.
In this talk, we revisit the problem of how to develop tractable methods which will improve the performance of least squares estimators in nonlinear systems. There are two reasons for this. First, some methods (such as mixture models) build upon linear estimators, and improving the performance of these improves the performance of the entire system. Second, approaches such as particle filters suffer from problems such as the curse of dimensionality, and cannot be applied in practice. In particular, this talk will review the sigma point approaches, such as the Unscented Kalman Filter (UKF), the Cubature Kalman Flter (CKF). We will show how these approaches lead to a framework which is naturally scalable. We will also discuss the strengths and limitations of these approaches.
Simon J. Julier is a Senior Lecturer at the Vision, Imaging and Virtual Environments Group, in the Computer Science Department at UCL. Before joining UCL, Dr. Julier worked for nine years at the 3D Mixed and Virtual Environments Laboratory at the Naval Research Laboratory in Washington DC. There he was PI of the Battlefield Augmented Reality System (BARS), a research effort to develop man-wearable systems for providing situation awareness information. He served as the Associate Director of the 3DMVEL from 2005–2006. His research interests include user interfaces, distributed data fusion, nonlinear estimation, and simultaneous localisation and mapping.