Practical Uncertainty Quantification in Orbital Mechanics

The chapter provides an overview of methods to quantify uncertainty in orbital mechanics. It also provides an initial classification of these methods with particular attention to whether the quantification method requires a knowledge of the system model or not. For some methods the chapter provides applications examples and numerical comparisons on selected test cases.

[1]  Massimiliano Vasile,et al.  An intrusive approach to uncertainty propagation in orbital mechanics based on Tchebycheff polynomial algebra , 2015 .

[2]  Martin Berz,et al.  Verified Integration of ODEs and Flows Using Differential Algebraic Methods on High-Order Taylor Models , 1998, Reliab. Comput..

[3]  A. Doostan,et al.  Nonlinear Propagation of Orbit Uncertainty Using Non-Intrusive Polynomial Chaos , 2013 .

[4]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[5]  M. Vasile,et al.  Asteroid rotation and orbit control via laser ablation , 2016 .

[6]  Puneet Singla,et al.  An Approach for Nonlinear Uncertainty Propagation: Application to Orbital Mechanics , 2009 .

[7]  Gary Tang,et al.  Mixed aleatory-epistemic uncertainty quantification with stochastic expansions and optimization-based interval estimation , 2011, Reliab. Eng. Syst. Saf..

[8]  Roger G. Ghanem,et al.  On the construction and analysis of stochastic models: Characterization and propagation of the errors associated with limited data , 2006, J. Comput. Phys..

[9]  M. Berz,et al.  Asteroid close encounters characterization using differential algebra: the case of Apophis , 2010 .

[10]  Kiyosi Itô 109. Stochastic Integral , 1944 .

[11]  Terence Soule,et al.  Genetic Programming: Theory and Practice , 2003 .

[12]  Massimiliano Vasile,et al.  On the Use of Positive Polynomials for the Estimation of Upper and Lower Expectations in Orbital Dynamics , 2018 .

[13]  Edmondo Minisci,et al.  HIGH DIMENSIONAL SENSITIVITY ANALYSIS USING SURROGATE MODELING AND HIGH DIMENSIONAL MODEL REPRESENTATION , 2015 .

[14]  Massimiliano Vasile,et al.  Comparison of non-intrusive approaches to uncertainty propagation in orbital mechanics , 2015 .

[15]  A. Genz,et al.  Fully symmetric interpolatory rules for multiple integrals over infinite regions with Gaussian weight , 1996 .

[16]  Aubrey B. Poore,et al.  Nonlinear Uncertainty Propagation in Orbital Elements and Transformation to Cartesian Space Without Loss of Realism , 2014 .

[17]  Angel Jorba,et al.  A Software Package for the Numerical Integration of ODEs by Means of High-Order Taylor Methods , 2005, Exp. Math..

[18]  M. Berz,et al.  TAYLOR MODELS AND OTHER VALIDATED FUNCTIONAL INCLUSION METHODS , 2003 .

[19]  Peter Walley,et al.  Towards a unified theory of imprecise probability , 2000, Int. J. Approx. Reason..

[20]  Edmondo Minisci,et al.  Uncertainty treatment in the GOCE re-entry , 2017 .

[21]  S. Ghosal Convergence rates for density estimation with Bernstein polynomials , 2001 .

[22]  Massimiliano Vasile,et al.  Collision and re-entry analysis under aleatory and epistemic uncertainty , 2016 .

[23]  H. Montag Non-gravitational Perturbations and Satellite Geodesy , 1987 .

[24]  D. Drob,et al.  Nrlmsise-00 Empirical Model of the Atmosphere: Statistical Comparisons and Scientific Issues , 2002 .

[25]  Pol D. Spanos,et al.  Spectral Stochastic Finite-Element Formulation for Reliability Analysis , 1991 .

[26]  R. Park,et al.  Nonlinear Mapping of Gaussian Statistics: Theory and Applications to Spacecraft Trajectory Design , 2006 .

[27]  Dongbin Xiu,et al.  The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations , 2002, SIAM J. Sci. Comput..

[28]  Hugh G. Lewis,et al.  Multidimensional extension of the continuity equation method for debris clouds evolution , 2016 .

[29]  J. C Mason,et al.  Near-best multivariate approximation by Fourier series, Chebyshev series and Chebyshev interpolation , 1980 .

[30]  Jack P. C. Kleijnen,et al.  Kriging Metamodeling in Simulation: A Review , 2007, Eur. J. Oper. Res..

[31]  Jeffrey K. Uhlmann,et al.  New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.

[32]  Massimiliano Vasile,et al.  Autonomous navigation of a spacecraft formation in the proximity of an asteroid , 2016 .

[33]  Takao Fujiwara,et al.  Integration of the collisionless Boltzmann equation for spherical stellar systems , 1983 .

[34]  Thomas Stützle,et al.  Ant colony optimization: artificial ants as a computational intelligence technique , 2006 .

[35]  Roger Ghanem,et al.  Stochastic Finite Element Analysis for Multiphase Flow in Heterogeneous Porous Media , 1998 .

[36]  A. Celletti,et al.  Four Classical Methods for Determining Planetary Elliptic Elements: A Comparison , 2005 .

[37]  T. Singh,et al.  Uncertainty Propagation for Nonlinear Dynamic Systems Using Gaussian Mixture Models , 2008 .

[38]  Lilia Maliar,et al.  Smolyak Method for Solving Dynamic Economic Models: Lagrange Interpolation, Anisotropic Grid and Adaptive Domain , 2013 .

[39]  Massimiliano Vasile,et al.  Analysis of spacecraft disposal solutions from LPO to the Moon with high order polynomial expansions , 2017 .

[40]  Kyle J. DeMars,et al.  Probabilistic Initial Orbit Determination Using Gaussian Mixture Models , 2013 .

[41]  A. Milani,et al.  Theory of Orbit Determination , 2009 .

[42]  I. Sobola,et al.  Global sensitivity indices for nonlinear mathematical models and their Monte Carlo estimates , 2001 .

[43]  Massimiliano Vasile,et al.  De-orbiting and re-entry analysis with generalised intrusive polynomial expansions , 2016 .

[44]  H. H. Selim,et al.  Final state predictions for J2 gravity perturbed motion of the Earth’s artificial satellites using Bispherical coordinates , 2013 .

[45]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.

[46]  Marco Dorigo,et al.  Ant colony optimization , 2006, IEEE Computational Intelligence Magazine.