CISE Seminar: Dr. Girish N. Nair, University of Melbourne, Australia

Pulling Back from Infinity: Asymptotically Optimal Sampling of Infinite-Dimensional Measurements

Vision-based sensors are widely used in autonomous localisation and navigation, and yield rich, high-dimensional measurements. Inspired by statistical mechanics, recent work has proposed going to the continuum limit, and treating such measurements as infinite-dimensional objects on a continuous pixel domain. While this can simplify the analysis, in practical implementations the resulting filter must be reduced to a finite-dimensional model, ideally with minimal degradation. In this talk, we propose a novel approach for performing this reduction. Assuming linear scalar states with Gaussian process and measurement noise, we seek to sample the infinite-dimensional measurement at N points, in order to minimize the mean-squared filtering error. We show that for large N, this problem can be expressed using the notion of an asymptotic point density function from the field of high-resolution quantization. This leads to a nonlinear Urysohn integral equation, which may be solved numerically to yield an asymptotically optimal N-point filter. The mean-square approximation error decays like N^{-4}, which is faster than the typical N^{-2} decay of high-resolution quantization, suggesting that this method will be efficient even at moderate or small N. These properties are verified by simulations based on a linearized pinhole camera measurement model. (In collaboration with Max Varley and Tim Molloy)

Girish N. Nair was born in Malaysia and is a Professor at the Dept. of Electrical and Electronic Engineering at the University of Melbourne, Australia. He is a Fellow of the IEEE (2018) and has received several prizes, including the CSS George S. Axelby Outstanding Paper Award in 2014, a SIAM Outstanding Paper Prize in 2006, and the Best Theory Paper Prize at the UKACC Int. Conf. on Control, Cambridge Uni., in 2000. From 2015 – 2019 he was an Australian Research Council Future Fellow, and since 2019 he has been the Principal Australian Investigator of an Australia-US Multidisciplinary University Research Initiative project, involving four Australian universities collaborating with Boston University and MIT. He has served as an Associate Editor for the IEEE Trans. Automatic Control from 2011-1015, and for the SIAM Journal on Control & Optimization from 2006 – 2011. His interests are in classical and nonclassical information theory as applied to problems in control and estimation.

Faculty Hosts: Yannis Paschalidis & John Baillieul

Student Host: Nguyen Nguyen