scholarly journals A Gravity Assist Mapping Based on Gaussian Process Regression

2021 ◽  
Vol 68 (1) ◽  
pp. 248-272
Author(s):  
Yuxin Liu ◽  
Ron Noomen ◽  
Pieter Visser
Keyword(s):  
Gaussian Process ◽  
Gaussian Process Regression ◽  
Space Mission ◽  
Mission Design ◽  
Gravity Assist ◽  
Arbitrary Initial Condition ◽  
Space Mission Design ◽  
Training Samples ◽  
Three Body ◽  
The Hill

AbstractWe develop a Gravity Assist Mapping to quantify the effects of a flyby in a two-dimensional circular restricted three-body situation based on Gaussian Process Regression (GPR). This work is inspired by the Keplerian Map and Flyby Map. The flyby is allowed to occur anywhere above 300 km altitude at the Earth in the system of Sun-(Earth+Moon)-spacecraft, whereas the Keplerian map is typically restricted to the cases outside the Hill sphere only. The performance of the GPR model and the influence of training samples (number and distribution) on the quality of the prediction of post-flyby orbital states are investigated. The information provided by this training set is used to optimize the hyper-parameters in the GPR model. The trained model can make predictions of the post-flyby state of an object with an arbitrary initial condition and is demonstrated to be efficient and accurate when evaluated against the results of numerical integration. The method can be attractive for space mission design.

scholarly journals Dynamical Systems, the Three-Body Problem and Space Mission Design

Equadiff 99 ◽  
2000 ◽  
pp. 1167-1181 ◽  
Author(s):  
Wang Sang Koon ◽  
Martin W. Lo ◽  
Jerrold E. Marsden ◽  
Shane D. Ross
Keyword(s):  
Dynamical Systems ◽  
Body Problem ◽  
Space Mission ◽  
Mission Design ◽  
Three Body Problem ◽  
Space Mission Design ◽  
Three Body

Topographic Kernels for Gaussian Process Regression in Digital Soil Mapping

2021 ◽  
Author(s):  
Thomas Gläßle ◽  
Kerstin Rau ◽  
Thomas Scholten ◽  
Philipp Hennig
Keyword(s):  
Gaussian Process ◽  
Domain Knowledge ◽  
Gaussian Process Regression ◽  
Kernel Functions ◽  
Soil Mapping ◽  
Digital Soil Mapping ◽  
Base Case ◽  
Training Samples ◽  
Additive Regression Model ◽  
Additive Regression

<p>Gaussian Processes provide a theoretically well-understood regression framework that is widely used in the context of Digital Soil Mapping. Among the reasons to use Gaussian Process Regression (GPR) are its interpretability, its builtin support for uncertainty quantification, and its ability to handle unevenly spaced and correlated training samples through a user-specified covariance kernel. The base case of GPR is performed with covariance models that are specified functions of Euclidean distance. In order to incorporate information other than the relative positions, regression-kriging extends GPR by an additive regression model of choice, and co-kriging considers a covariance model between covariates and the target variable. In this work, we use the alternative approach of incorporating topographic information directly into the kernel function by use of a non-Euclidean, non-stationary distance function. In particular, we devise kernels based on a path of least effort, where <em>effort</em> is locally specified as a function constructed from prior knowledge. It can e.g. be derived from local topographic variables. We demonstrate that our candidate models improve prediction accuracy over the base model. This shows that domain knowledge can be integrated into the model by means of handcrafted kernel functions. The approach is not per se restricted to topographic variables, but could be used for any covariate quantity that is available at output resolution.</p>

scholarly journals Hyperbolic normal forms and invariant manifolds: Astronomical applications

2012 ◽  
pp. 1-12 ◽  
Author(s):  
C. Efthymiopoulos
Keyword(s):  
Normal Form ◽  
Invariant Manifolds ◽  
Continuation Method ◽  
Space Mission ◽  
Mission Design ◽  
Unstable Periodic Orbits ◽  
Space Mission Design ◽  
Dynamical Astronomy ◽  
Initial Domain ◽  
Asymptotic Orbits

In recent years, the study of the dynamics induced by the invariant manifolds of unstable periodic orbits in nonlinear Hamiltonian dynamical systems has led to a number of applications in celestial mechanics and dynamical astronomy. Two applications of main current interest are i) space manifold dynamics, i.e. the use of the manifolds in space mission design, and, in a quite different context, ii) the study of spiral structure in galaxies. At present, most approaches to the computation of orbits associated with manifold dynamics (i.e. periodic or asymptotic orbits) rely either on the use of the so-called Poincar? - Lindstedt method, or on purely numerical methods. In the present article we briefly review an analytic method of computation of invariant manifolds, first introduced by Moser (1958), and developed in the canonical framework by Giorgilli (2001). We use a simple example to demonstrate how hyperbolic normal form computations can be performed, and we refer to the analytic continuation method of Ozorio de Almeida and co-workers, by which we can considerably extend the initial domain of convergence of Moser?s normal form.

Risk-based technology portfolio optimization for early space mission design

2006 ◽  
Vol 42 (1) ◽  
pp. 22-36 ◽  
Author(s):  
A. Elfes ◽  
W.P. Lincoln ◽  
G. Rodriguez ◽  
C.R. Weisbin ◽  
J.A. Wertz
Keyword(s):  
Portfolio Optimization ◽  
Space Mission ◽  
Mission Design ◽  
Space Mission Design
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