### 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 language | English (US) |
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Title of host publication | Spaceflight Mechanics 2010 - Advances in the Astronautical Sciences |

Subtitle of host publication | Proceedings of the AAS/AIAA Space Flight Mechanics Meeting |

Pages | 475-488 |

Number of pages | 14 |

Publication status | Published - Dec 1 2010 |

Event | AAS/AIAA Space Flight Mechanics Meeting - San Diego, CA, United States Duration: Feb 14 2010 → Feb 17 2010 |

### Publication series

Name | Advances in the Astronautical Sciences |
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Volume | 136 |

ISSN (Print) | 0065-3438 |

### Other

Other | AAS/AIAA Space Flight Mechanics Meeting |
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Country | United States |

City | San Diego, CA |

Period | 2/14/10 → 2/17/10 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*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).