### Abstract

This focus of this paper is the application of the polynomial approximation method to obtain satellite reachability sets for Space Situational Awareness (SSA) applications. Least squares coefficients for the approximation of the final state solution are calculated in a Jacobian free and computationally tractable manner. The numerical integration method used in the polynomial approximation technique exploits the symmetric structure of the input variable probability density functions (pdf’s) to compute the density function for the solution space. The Conjugate Unscented Transformation (CUT) method is utilized for this purpose, and is used to calculate the coefficients with a minimal number of full model propagations. Numerical simulation results are given to validate the approach.

Original language | English (US) |
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Title of host publication | Spaceflight Mechanics 2019 |

Editors | Francesco Topputo, Andrew J. Sinclair, Matthew P. Wilkins, Renato Zanetti |

Publisher | Univelt Inc. |

Pages | 3001-3020 |

Number of pages | 20 |

ISBN (Print) | 9780877036593 |

State | Published - Jan 1 2019 |

Event | 29th AAS/AIAA Space Flight Mechanics Meeting, 2019 - Maui, United States Duration: Jan 13 2019 → Jan 17 2019 |

### Publication series

Name | Advances in the Astronautical Sciences |
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Volume | 168 |

ISSN (Print) | 0065-3438 |

### Conference

Conference | 29th AAS/AIAA Space Flight Mechanics Meeting, 2019 |
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Country | United States |

City | Maui |

Period | 1/13/19 → 1/17/19 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Aerospace Engineering
- Space and Planetary Science

### Cite this

*Spaceflight Mechanics 2019*(pp. 3001-3020). [AAS 19-437] (Advances in the Astronautical Sciences; Vol. 168). Univelt Inc..

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*Spaceflight Mechanics 2019.*, AAS 19-437, Advances in the Astronautical Sciences, vol. 168, Univelt Inc., pp. 3001-3020, 29th AAS/AIAA Space Flight Mechanics Meeting, 2019, Maui, United States, 1/13/19.

**A probabilistic approach for reachability set computation for efficient space situational awareness.** / Hall, Zach; Singla, Puneet.

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

TY - GEN

T1 - A probabilistic approach for reachability set computation for efficient space situational awareness

AU - Hall, Zach

AU - Singla, Puneet

PY - 2019/1/1

Y1 - 2019/1/1

N2 - This focus of this paper is the application of the polynomial approximation method to obtain satellite reachability sets for Space Situational Awareness (SSA) applications. Least squares coefficients for the approximation of the final state solution are calculated in a Jacobian free and computationally tractable manner. The numerical integration method used in the polynomial approximation technique exploits the symmetric structure of the input variable probability density functions (pdf’s) to compute the density function for the solution space. The Conjugate Unscented Transformation (CUT) method is utilized for this purpose, and is used to calculate the coefficients with a minimal number of full model propagations. Numerical simulation results are given to validate the approach.

AB - This focus of this paper is the application of the polynomial approximation method to obtain satellite reachability sets for Space Situational Awareness (SSA) applications. Least squares coefficients for the approximation of the final state solution are calculated in a Jacobian free and computationally tractable manner. The numerical integration method used in the polynomial approximation technique exploits the symmetric structure of the input variable probability density functions (pdf’s) to compute the density function for the solution space. The Conjugate Unscented Transformation (CUT) method is utilized for this purpose, and is used to calculate the coefficients with a minimal number of full model propagations. Numerical simulation results are given to validate the approach.

UR - http://www.scopus.com/inward/record.url?scp=85072987366&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072987366&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:85072987366

SN - 9780877036593

T3 - Advances in the Astronautical Sciences

SP - 3001

EP - 3020

BT - Spaceflight Mechanics 2019

A2 - Topputo, Francesco

A2 - Sinclair, Andrew J.

A2 - Wilkins, Matthew P.

A2 - Zanetti, Renato

PB - Univelt Inc.

ER -