### 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 |

State | 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).

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*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.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - An adaptive Gaussian sum filtering approach for orbit uncertainty estimation

AU - Giza, Dan

AU - Singla, Puneet

AU - Jah, Moriba

PY - 2010/12/1

Y1 - 2010/12/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=80053418735&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=80053418735&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:80053418735

SN - 9780877035602

T3 - Advances in the Astronautical Sciences

SP - 475

EP - 488

BT - Spaceflight Mechanics 2010 - Advances in the Astronautical Sciences

ER -