Probabilistic Analysis of Light Curves

Abstract

To date, most light curve analyses take place using time and frequency domain analyses that generally lack in their ability to quantify the information content of the data. In this paper, we examine the information content of light curves using information theoretic and functional data approaches to characterize physical and dynamic attributes of space objects from non-resolved photometric observations. The information content is examined in a probabilistic context where a set of simulated light curves for a diverse set of object shapes, sizes and dynamics are used to demonstrate the application and value of Functional Data Analysis, data clustering and information theory. The results confirm the value of these approaches by correctly categorizing independent sets of light curve measurements and quantifying the likelihood of a given light curve being associated with a specific object. These analytical tools can also be applied to better understand how well a given set of observations characterize an object and, hence, guide the necessity of future observations. In this paper, we also comment on how the proposed ideas can enable the use of light curves, treated as a functional observation, for joint object tracking and characterization within a multi-hypothesis testing framework such as Finite Set Statistics.