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

Date: Wednesday, June 7, 2023
Time: 12:00pm – 1:00pm
Location: 665 Commonwealth Ave, Room 1101

Girish N. Nair
Professor
University of Melbourne, Australia

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

Vision-based sensors are widely used in autonomous localization 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 with the Department of Electrical and Electronic Engineering, University of Melbourne, Australia. He has been an IEEE Fellow since 2018 and was an Australian Research Council Future Fellow from 2015 – 2019. His research interests are in information-theoretic methods for filtering and control, including in autonomous navigation and localisation. Prof. Nair is a recipient of several prizes, including the IEEE CSS Axelby Outstanding Paper Award in 2014 and a SIAM Outstanding Paper Prize in 2006.

Faculty Hosts: Yannis Paschalidis & John Baillieul
Student Host: Nguyen Nguyen