An adaptive Gaussian sum filtering approach for orbit uncertainty estimation

Dan Giza, Puneet Singla, Moriba Jah

Research output: Chapter in Book/Report/Conference proceedingConference contribution

4 Citations (Scopus)

Abstract

An approach for nonlinear filtering when measurements are sparse is discussed which makes use of the Fokker-Planck-Kolmogorov Equation (FPKE). The central idea is to replace the evolution of initial state estimates for a dynamical system with the evolution of a probability density function (pdf) for state variables. The transition pdf corresponding to a dynamical system state vector is approximated by using a finite Gaussian mixture model. The mean and covariance of each Gaussian mixture model component are propagated through the use of an Unscented Kalman Filter (UKF), and the unknown amplitudes are found by minimizing the FPKE error over the entire volume of interest. This leads to a convex quadratic minimization problem guaranteed to have a unique solution. The two-body problem with non-conservative atmospheric drag forces and initial condition uncertainty will be used to show the efficacy of the ideas developed in this paper.

Original languageEnglish (US)
Title of host publicationSpaceflight Mechanics 2010 - Advances in the Astronautical Sciences
Subtitle of host publicationProceedings of the AAS/AIAA Space Flight Mechanics Meeting
Pages475-488
Number of pages14
StatePublished - Dec 1 2010
EventAAS/AIAA Space Flight Mechanics Meeting - San Diego, CA, United States
Duration: Feb 14 2010Feb 17 2010

Publication series

NameAdvances in the Astronautical Sciences
Volume136
ISSN (Print)0065-3438

Other

OtherAAS/AIAA Space Flight Mechanics Meeting
CountryUnited States
CitySan Diego, CA
Period2/14/102/17/10

Fingerprint

Fokker Planck equation
probability density function
probability density functions
dynamical systems
Probability density function
Dynamical systems
Orbits
orbits
two body problem
Nonlinear filtering
state vectors
Kalman filters
Kalman filter
transition probabilities
drag
Drag
optimization
estimates
Uncertainty

All Science Journal Classification (ASJC) codes

  • Aerospace Engineering
  • Space and Planetary Science

Cite this

Giza, D., Singla, P., & Jah, M. (2010). An adaptive Gaussian sum filtering approach for orbit uncertainty estimation. In Spaceflight Mechanics 2010 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Space Flight Mechanics Meeting (pp. 475-488). (Advances in the Astronautical Sciences; Vol. 136).
Giza, Dan ; Singla, Puneet ; Jah, Moriba. / An adaptive Gaussian sum filtering approach for orbit uncertainty estimation. Spaceflight Mechanics 2010 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Space Flight Mechanics Meeting. 2010. pp. 475-488 (Advances in the Astronautical Sciences).
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Giza, D, Singla, P & Jah, M 2010, An adaptive Gaussian sum filtering approach for orbit uncertainty estimation. in Spaceflight Mechanics 2010 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Space Flight Mechanics Meeting. Advances in the Astronautical Sciences, vol. 136, pp. 475-488, AAS/AIAA Space Flight Mechanics Meeting, San Diego, CA, United States, 2/14/10.

An adaptive Gaussian sum filtering approach for orbit uncertainty estimation. / Giza, Dan; Singla, Puneet; Jah, Moriba.

Spaceflight Mechanics 2010 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Space Flight Mechanics Meeting. 2010. p. 475-488 (Advances in the Astronautical Sciences; Vol. 136).

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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Giza D, Singla P, Jah M. An adaptive Gaussian sum filtering approach for orbit uncertainty estimation. In Spaceflight Mechanics 2010 - Advances in the Astronautical Sciences: Proceedings of the AAS/AIAA Space Flight Mechanics Meeting. 2010. p. 475-488. (Advances in the Astronautical Sciences).