KRATOS: KOLLISION RISK ASSESSMENT TOOL
IN ORBITAL ELEMENT SPACES
Joshua T. Horwood, Navraj Singh, and Jeffrey M. Aristoff
Numerica Corporation, 5042 Technology Parkway, Suite 100, Fort Collins, CO 80528
Apoorva Bhopale
Air Force Research Laboratory, 3550 Aberdeen Avenue SE, Kirtland AFB, NM 87117
ABSTRACT
KRATOS provides an innovative approach to computing the probability of collision (PC) between resident space
objects that reduces misdetection and false alarms rates and supports the mission’s goal of performing conjunction
assessment screening further out into the future. Although applicable to all regimes of space, KRATOS was
designed to treat objects in the challenging non-linear and non-Gaussian regimes. KRATOS rivals the accuracy
of Monte-Carlo methods but with little added computational cost relative to the traditional linearization (Foster)
method. This paper provides an overview of the KRATOS algorithm and demonstrates its efficacy using real
and simulated data. Scenarios are presented in which use of the Foster method would produce false alarms or
misdetections, and hence would misinform the analyst. Use of KRATOS in these scenarios provides a reliable
PC, as verified using Monte-Carlo simulation, and hence would better inform the analyst.
1. INTRODUCTION
Traditional methodologies for assessing collision risk between resident space objects (RSOs) can produce misde-
tections and false alarms. The resulting probabilities of collision (PCs) can be too high, implying a high false
alarm rate and the need to perform costly and unnecessary evasive maneuvers, or too low, meaning that some
potential collisions go undetected, which could have dire consequences. The desire to perform conjunction as-
sessment (CA) screening further out into the future, up to one week for Low Earth Objects (LEOs), for example,
adds to the challenge of providing reliable space situational awareness (SSA). Thus, what is needed are new
methodologies that reduce these false alarm and misdetection rates, and hence better inform courses of action.
As the PC calculation is far too expensive to perform on all possible pairs of objects, one first employs
techniques called conjunction filtering that aim to quickly rule out infeasible conjunctions at a computational
cost less than that of a full PC calculation. After a filter or set of filters returns all feasible conjunction pairs,
one then proceeds to quantify the collision risk by computing the PC on each remaining pair. Linearization
techniques based on the Foster method [1] make several simplifying assumptions in the PC calculation including
that of a realistic Gaussian covariance in position-velocity space of the two approaching objects at the time-of-
closest approach (TCA). With the desire to do CA further out into the future and uncorrelated tracks (UCTs)
generated from the new Space Fence that will inevitably possess large covariances, non-linear effects will become
more pronounced, resulting in a breakdown of covariance realism and rendering the Gaussian assumption in
Foster’s method invalid. Methods that relax the Gaussian assumption will be needed in the future; some
preliminary research on computing the PC using Gaussian mixtures models has been considered by DeMars,
Cheng, and Jah [2] as part of the Adaptive Entropy Gaussian Information Synthesis (AEGIS) algorithm [3].
Alternatively, Monte-Carlo simulation can be used, but it is too computationally demanding to apply on all high
risk events.
The Kollision Risk Assessment Tool in Orbital Element Spaces (KRATOS) provides a new approach to
computing the PC between RSOs that supports the mission’s goal of performing CA screening further out into
the future. Although applicable to all regimes of space, KRATOS was designed to treat objects in the challenging
non-linear and non-Gaussian regimes by relaxing the Gaussian assumptions present in the traditional Foster
method. In such challenging regimes, KRATOS is able to efficiently compute the PC over much longer screening
intervals than what is currently possible, by leveraging the Numerica’s prior work in Gaussian mixture filters
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