## Abstract

This paper presents a derivative-free method for computing approximate solutions to the uncertain Lambert problem (ULP) and the reachability set problem (RSP) while utilizing higher-order sensitivity matrices. These sensitivities are analogous to the coefficients of a Taylor series expansion of the deterministic solution to the ULP and RSP, and are computed in a derivative-free and computationally tractable manner. The coefficients are computed by minimizing least squared error over the domain of the input probability density function (PDF), and represent the nonlinear mapping of the input PDF to the output PDF. A non-product quadrature method known as the conjugate unscented transform is used to compute the multidimensional expectation values necessary to determine these coefficients with the minimal number of full model propagations. Numerical simulations for both the ULP and the RSP are provided to validate the developed methodology and illustrate potential applications. The benefits and limitations of the presented method are discussed.

Original language | English (US) |
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Article number | 50 |

Journal | Celestial Mechanics and Dynamical Astronomy |

Volume | 132 |

Issue number | 10 |

DOIs | |

State | Published - Oct 1 2020 |

## All Science Journal Classification (ASJC) codes

- Modeling and Simulation
- Mathematical Physics
- Astronomy and Astrophysics
- Space and Planetary Science
- Computational Mathematics
- Applied Mathematics