(Last updated: June 2015)
 

A space debris removal tour optimized via a genetic algorithm.

A space debris removal tour optimized via a genetic algorithm.

The field of astrodynamics is integral to the analysis and operation of space systems, providing a platform for engi-neers to handle data efficiently, whether they are ranging measurements between two spacecraft or optical observations of space debris.   In my lab, I intend to conduct research in astrodynamics that will enable future space systems to be smart, efficient, and autonomous.  Below are some specific topics I am working on:
 

The Too-Short Arc Problem

A conceptual schematic of the direct Bayesian admissible region concept.

A conceptual schematic of the direct Bayesian admissible region concept.

The difficulty in cataloging active satellites, space debris, and other RSOs is two-fold.  First, in order to maintain a 22,000-object catalog as well as add to it approximately 700,000 objects of at least 1 cm in diameter expected to exist in low Earth orbit alone, sensors must be tasked to track objects for only several seconds at a time to ensure adequate coverage.  Consequently, there is insufficient information to obtain the full state of the observed object based upon a single track.  The need to autonomously associate multiple observations to a common object gives rise to the second difficulty: the dependency of the initial orbit determination (IOD) accuracy on the association result and vice versa.  Conventional approaches of testing association hypotheses based upon IOD quality can often fail since sparse measurements lead to poor, if not divergent, estimates.

I am approaching this problem, known as the too-short arc (TSA) problem, with an integrative approach encompassing both hardware and software research.  I plan to install an optical telescope for the lab so that new association algorithms may be devised, implemented, and tested under one roof.  The telescope will also benefit the broader SSA research community through data sharing with other academic institutions.  In my previously published work, I proposed a method to associate optical tracks using probability density functions defined in range / range-rate space called admissible regions.  The method was validated with actual data, where, in addition to track association, I identified error sources, designed an observation campaign, and extracted astrometric data from telescope images.
 

Advanced Navigation Methods

Results of a simulated navigation study of a LiAISON constellation between GEO and an Earth-Moon system LPO.

Results of a simulated navigation study of a LiAISON constellation between GEO and an Earth-Moon system LPO.

Many spacecraft beyond low Earth orbit currently rely on ground-based navigation techniques that require persistent human interaction.  These techniques, however, tend to be expensive: e.g., NASA’s Deep Space Network (DSN) quotes over $1000 per hour for its tracking services.  In addition, the orbit determination accuracy may be limited due to the chronic oversubscription of the DSN, or, especially for GEO satellites, poor observation geometry.  Breakthrough research in navigation can not only alleviate these problems but also bring about a completely new class of space utilization.  For instance, on-board GPS sensors made cost-effective tracking possible for nanosatellites.  Similar capabilities in high Earth orbit and above will have an equally large impact on commercial and military satellite operation in GEO as well as on deep space science missions.

My primary research interest this realm has been to leverage distinctive features of dynamics experienced in outer space and to fuse non-traditional measurement types into the navigation solution.  At the University of Colorado, I was involved in research on the Linked Autonomous Interplanetary Satellite Orbit Navigation (LiAISON) concept, in which absolute states of multiple spacecraft are computed based on relative measurements amongst them, combined with information from the asymmetry of the force field.  Simulations suggest that LiAISON improves state estimates for assets in GEO, interplanetary transfer, and on the lunar surface, just to name a few examples.
 

Uncertainty Quantification

Analytically propagated uncertainty expressed via a Gaussian mixture model.

Analytically propagated uncertainty expressed via a Gaussian mixture model.

A precise understanding of the state uncertainty of a given spacecraft is important in several day-to-day tasks in SSA including observation association and conjunction assessment (CA).  Especially for the latter, conventional linear uncertainty propagation has been shown to produce grossly optimistic results.  It is also a critical aspect of navigation, allowing for improved state estimates over longer propagation arcs.  Non-Gaussian descriptions of uncertainty, however, tend to be computationally intractable and thus hard to transfer over to real-world scenarios.

I am investigating efficient methods for uncertainty quantification in astronautics with a focus on analytic solutions.  Orbital dynamics are particularly amenable to such an approach as many forces encountered by RSOs have a dominant deterministic component whose uncertainty is sufficiently modeled via parametric errors.  Analytic methods, then, are not only academically interesting but also operationally preferable for their unrivaled speed advantage over numerical integration.  In my recent work, I applied to SSA the idea that, for a deterministic force model, a probability density function (PDF) may be expressed analytically for all time if an analytic expression exists for both the dynamical solution flow and the initial value of the PDF.  The propagated PDF may be expressed as a Gaussian mixture model in order to make subsequent applications of the PDF tractable in tasks like CA.