Matthew P. Wilkins, Applied Defense Solutions, Eamonn J. Moyer, Applied Defense Solutions, Islam I. Hussein, Applied Defense Solutions, Paul W. Schumacher, Jr, Air Force Research Laboratory
Keywords: Uncorrelated Observations, Optical and Radar Observations, Space Situational Awareness, Probabilistic Admissible Region, Constrained Admissible Region, Orbital Debris
Abstract:
Correlating new detections back to a large catalog of resident space objects (RSOs) requires solving one of three types of data association problems: observation-to-track, track-to-track, or observation-to-observation. The authors previous work has explored the use of various information divergence metrics for solving these problems: Kullback-Leibler (KL) divergence, mutual information, and Bhattacharrya distance. In addition to approaching the data association problem strictly from the metric tracking aspect, we have explored fusing metric and photometric data using Bayesian probabilistic reasoning for RSO identification to aid in our ability to correlate data to specific RS Os. In this work, we will focus our attention on the KL Divergence, which is a measure of the information gained when new evidence causes the observer to revise their beliefs. We can apply the Principle of Minimum Discrimination Information such that new data produces as small an information gain as possible and this information change is bounded by ε. Choosing an appropriate value for ε for both convergence and change detection is a function of your risk tolerance. Small ε for change detection increases alarm rates while larger ε for convergence means that new evidence need not be identical in information content. We need to understand what this change detection metric implies for Type I α and Type II β errors when we are forced to make a decision on whether new evidence represents a true change in characterization of an object or is merely within the bounds of our measurement uncertainty. This is unclear for the case of fusing multiple kinds and qualities of characterization evidence that may exist in different metric spaces or are even semantic statements. To this end, we explore the use of Sequential Probability Ratio Testing where we suppose that we may need to collect additional evidence before accepting or rejecting the null hypothesis that a change has occurred. In this work, we will explore the effects of choosing ε as a function of α and β. Our intent is that this work will help bridge understanding between the well-trodden grounds of Type I and Type II errors and changes in information theoretic content.
Date of Conference: September 19-22, 2017
Track: Astrodynamics