Particle Filter Methods for Space Object Tracking

An approach for space object tracking utilizing particle filters is presented. New methods are developed and used to construct a robust constrained admissible region given a set of angles-only measurements, which is then approximated by a finite mixture distribution. This probabilistic initial orbit solution is refined using subsequent measurements through a particle filter approach. A proposal density is constructed based on an approximate Bayesian update and samples, or particles, are drawn from this proposed probability density to assign and correct weights, which form the basis for a more accurate Bayesian update. A finite mixture distribution is then fit to these weighted samples to reinitialize the cycle. This approach is compared to methods that approximate all probability densities as finite mixtures and process them as such. Both approaches utilize recursive estimation based on Bayesian statistics, but the benefits of densely sampling the support probability based on incoming measurements is weighed against remaining solely within the finite mixture approximation and performing measurement corrections there.

[1]  Arthur Cayley,et al.  I. A second memoir upon quantics , 1856, Proceedings of the Royal Society of London.

[2]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[3]  Rudolph van der Merwe,et al.  Sigma-point kalman filters for probabilistic inference in dynamic state-space models , 2004 .

[4]  E. Jury,et al.  Positivity and nonnegativity conditions of a quartic equation and related problems , 1981 .

[5]  Arthur Cayley.  The Collected Mathematical Papers: A Discussion of the Sturmian Constants for cubic and quartic Equations , 2009 .

[6]  Par C. Sturm.  Mémoire sur la résolution des équations numériques , 2009 .

[7]  P. R. Escobal,et al.  Methods of orbit determination , 1976 .

[8]  R. Broucke,et al.  On the equinoctial orbit elements , 1972 .

[9]  H. Sorenson,et al.  Nonlinear Bayesian estimation using Gaussian sum approximations , 1972 .

[10]  Branko Ristic,et al.  Beyond the Kalman Filter: Particle Filters for Tracking Applications , 2004 .

[11]  A. Milani,et al.  Orbit determination with very short arcs. I admissible regions , 2004 .

[12]  M. Kaplan.  Modern spacecraft dynamics & control , 1976 .

[13]  Alessandro Rossi,et al.  Orbit determination of space debris: admissible regions , 2007 .

[14]  Stephen A. Vavasis,et al.  Solving Polynomials with Small Leading Coefficients , 2005, SIAM J. Matrix Anal. Appl..

[15]  Kyle J. DeMars,et al.  Probabilistic Initial Orbit Determination Using Gaussian Mixture Models , 2013 .

[16]  R. H. Gooding.  A New Procedure for Orbit Determination Based on Three Lines of Sight (Angles Only) , 1993 .