Uncertainty propagation and conjunction assessment for resident space objects

vii

[1]  N. Wiener.  The Homogeneous Chaos , 1938 .

[2]  William Feller,et al.  The fundamental limit theorems in probability , 1945 .

[3]  R. A. Leibler,et al.  On Information and Sufficiency , 1951 .

[4]  C. W. Clenshaw,et al.  A method for numerical integration on an automatic computer , 1960 .

[5]  T. W. Anderson.  On the Distribution of the Two-Sample Cramer-von Mises Criterion , 1962 .

[6]  J. Vinti.  Inclusion of the third zonal harmonic in an accurate reference orbit of an artificial satellite. , 1966 .

[7]  A. G. Azpeitia,et al.  Introduction to Numerical Analysis. , 1968 .

[8]  A. T. Fuller,et al.  Analysis of nonlinear stochastic systems by means of the Fokker–Planck equation† , 1969 .

[9]  H. Sorenson,et al.  Nonlinear Bayesian estimation using Gaussian sum approximations , 1972 .

[10]  John R. Rice,et al.  A Metalgorithm for Adaptive Quadrature , 1975, JACM.

[11]  D. Siegmund.  Importance Sampling in the Monte Carlo Study of Sequential Tests , 1976 .

[12]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[13]  Jorge J. Moré,et al.  Computing a Trust Region Step , 1983 .

[14]  Linda L. Crawford,et al.  An analytic method to determine future close approaches between satellites , 1984 .

[15]  Alan Genz,et al.  Fully symmetric interpolatory rules for multiple integrals , 1986 .

[16]  Ivo Babuška,et al.  The h, p and h-p version of the finite element method: basis theory and applications , 1992 .

[17]  David J. Nauer,et al.  History of on-orbit satellite fragmentations , 1992 .

[18]  Salvatore Alfano,et al.  Determining satellite close approaches , 1992 .

[19]  Liam M. Healy,et al.  Close conjunction detection on parallel computer , 1995 .

[20]  Richard M. Karp,et al.  An optimal algorithm for Monte Carlo estimation , 1995, Proceedings of IEEE 36th Annual Foundations of Computer Science.

[21]  John L. Junkins,et al.  Non-Gaussian error propagation in orbital mechanics , 1996 .

[22]  George Trapp,et al.  Using Complex Variables to Estimate Derivatives of Real Functions , 1998, SIAM Rev..

[23]  Deok-Jin Lee,et al.  Probability of Collision Error Analysis , 1999 .

[24]  V. Lebedev,et al.  A QUADRATURE FORMULA FOR THE SPHERE OF THE 131ST ALGEBRAIC ORDER OF ACCURACY , 1999 .

[25]  Gianfranco Corradi,et al.  A trust region algorithm for constrained optimization , 2000, Int. J. Comput. Math..

[26]  Maruthi R. Akella,et al.  Probability of Collision Between Space Objects , 2000 .

[27]  Subhash Challa,et al.  Nonlinear filtering via generalized Edgeworth series and Gauss-Hermite quadrature , 2000, IEEE Trans. Signal Process..

[28]  Niels Kjølstad Poulsen,et al.  New developments in state estimation for nonlinear systems , 2000, Autom..

[29]  Gene H. Golub,et al.  Computation of Gauss-Kronrod quadrature rules , 2000, Math. Comput..

[30]  B. Rozovskii,et al.  Fourier--Hermite Expansions for Nonlinear Filtering , 2000 .

[31]  Nicholas I. M. Gould,et al.  Trust Region Methods , 2000, MOS-SIAM Series on Optimization.

[32]  Shannon L. Coffey,et al.  Uncorrelated observations processing at Naval Space Command , 2002 .

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

[34]  Russell P. Patera,et al.  Satellite Collision Probability for Nonlinear Relative Motion , 2002 .

[35]  Collision Risk Assessment with a `Smart Sieve' Method , 2002 .

[36]  Dominik Endres,et al.  A new metric for probability distributions , 2003, IEEE Transactions on Information Theory.

[37]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[38]  B. Tapley,et al.  Statistical Orbit Determination , 2004 .

[39]  G. Karniadakis,et al.  An adaptive multi-element generalized polynomial chaos method for stochastic differential equations , 2005 .

[40]  Russell P. Patera,et al.  Calculating Collision Probability for Arbitrary Space Vehicle Shapes via Numerical Quadrature , 2005 .

[41]  Salvatore Alfanol,et al.  A Numerical Implementation of Spherical Object Collision Probability , 2005 .

[42]  Salvatore Alfano.  Addressing Nonlinear Relative Motion For Spacecraft Collision Probability , 2006 .

[43]  Jared M. Maruskin,et al.  Fundamental limits on spacecraft orbit uncertainty and distribution propagation , 2006 .

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

[45]  Heikki Haario,et al.  DRAM: Efficient adaptive MCMC , 2006, Stat. Comput..

[46]  James G. Miller,et al.  A New Sensor Allocation Algorithm for the Space Surveillance Network , 2007 .

[47]  John R. Hershey,et al.  Approximating the Kullback Leibler Divergence Between Gaussian Mixture Models , 2007, 2007 IEEE International Conference on Acoustics, Speech and Signal Processing - ICASSP '07.

[48]  Richard I. Abbot,et al.  Decision Support in Space Situational Awareness , 2007 .

[49]  Oliver E. Drummond,et al.  Metrics for evaluating track covariance consistency , 2007, SPIE Optical Engineering + Applications.

[50]  Neculai Andrei,et al.  An Unconstrained Optimization Test Functions Collection , 2008 .

[51]  Thomas A. Zang,et al.  Stochastic approaches to uncertainty quantification in CFD simulations , 2005, Numerical Algorithms.

[52]  D. Richmond.  Space Situational Awareness (SSA) research findings , 2008 .

[53]  B. Carlin,et al.  Markov Chain Monte Carlo conver-gence diagnostics: a comparative review , 1996 .

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

[55]  Lance A. M. Benner,et al.  Predicting the Earth encounters of (99942) Apophis , 2008 .

[56]  Hugh F. Durrant-Whyte,et al.  On entropy approximation for Gaussian mixture random vectors , 2008, 2008 IEEE International Conference on Multisensor Fusion and Integration for Intelligent Systems.

[57]  F. Kenneth Chan,et al.  Spacecraft Collision Probability , 2008 .

[58]  Stephen P. Boyd,et al.  Graph Implementations for Nonsmooth Convex Programs , 2008, Recent Advances in Learning and Control.

[59]  S. Alfano,et al.  Satellite Conjunction Monte Carlo Analysis , 2009 .

[60]  S. Haykin,et al.  Cubature Kalman Filters , 2009, IEEE Transactions on Automatic Control.

[61]  Suman Chakravorty,et al.  The partition of unity finite element approach with hp-refinement for the stationary Fokker–Planck equation , 2009 .

[62]  Geoffrey T. Parks,et al.  Robust Aerodynamic Design Optimization Using Polynomial Chaos , 2009 .

[63]  N. Johnson,et al.  THE KESSLER SYNDROME: IMPLICATIONS TO FUTURE SPACE OPERATIONS , 2010 .

[64]  Chris Sabol,et al.  Linearized Orbit Covariance Generation and Propagation Analysis via Simple Monte Carlo Simulations (Preprint) , 2010 .

[65]  Scot S. Olivier,et al.  Intelligent sensor tasking for space collision mitigation , 2010, Defense + Commercial Sensing.

[66]  Aubrey B. Poore,et al.  Gaussian Sum Filters for Space Surveillance: Theory and Simulations , 2011 .

[67]  Yang Cheng,et al.  Sparse Gauss-Hermite Quadrature Filter with Application to Spacecraft Attitude Estimation , 2011 .

[68]  Puneet Singla,et al.  The Conjugate Unscented Transform — An approach to evaluate multi-dimensional expectation integrals , 2012, 2012 American Control Conference (ACC).

[69]  Eliminating Assumptions Regarding Satellite Conjunction Analysis , 2012 .

[70]  Chris Sabol,et al.  Comparison of Covariance Based Track Association Approaches Using Simulated Radar Data , 2012 .

[71]  Nitin Arora,et al.  Global Point Mascon Models for Simple, Accurate, and Parallel Geopotential Computation , 2012 .

[72]  Suman Chakravorty,et al.  Nonlinear Filter Based on the Fokker-Planck Equation , 2012 .

[73]  Vincent Agi Coppola,et al.  Including Velocity Uncertainty in the Probability of Collision Between Space Objects , 2012 .

[74]  Sergey Oladyshkin,et al.  Data-driven uncertainty quantification using the arbitrary polynomial chaos expansion , 2012, Reliab. Eng. Syst. Saf..

[75]  M. Nayak.  Impact of National Space Policy on Orbital Debris Mitigation and US Air Force End of Life Satellite Operations , 2012 .

[76]  Thierry Dargent,et al.  Using Multicomplex Variables for Automatic Computation of High-Order Derivatives , 2010, TOMS.

[77]  J. Skelton.  Data Handling and Protection of Need-to-Know Data in a Need-to-Share Netcentric Enterprise , 2012 .

[78]  Aubrey B. Poore,et al.  Orbital State Uncertainty Realism , 2012 .

[79]  Simo Särkkä,et al.  Fourier-Hermite Kalman Filter , 2012, IEEE Transactions on Automatic Control.

[80]  Volkan Y. Senyurek,et al.  Performance Comparison of Artificial Neural Network and Gaussian Mixture Model in Classifying Hand Motions by Using sEMG Signals , 2013 .

[81]  Shovan Bhaumik,et al.  Cubature quadrature Kalman filter , 2013, IET Signal Process..

[82]  Brandon A. Jones,et al.  Satellite Collision Probability Estimation Using Polynomial Chaos , 2013 .

[83]  Kyle J. DeMars,et al.  Entropy-Based Approach for Uncertainty Propagation of Nonlinear Dynamical Systems , 2013 .

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

[85]  Hyochoong Bang,et al.  Adaptive sparse grid quadrature filter for spacecraft relative navigation , 2013 .

[86]  Jason Tichy,et al.  GPU Accelerated Conjunction Assessment with Applications to Formation Flight and Space Debris Tracking , 2013 .

[87]  Carolyn Kalender,et al.  Sparse Grid-Based Nonlinear Filtering , 2013, IEEE Transactions on Aerospace and Electronic Systems.

[88]  Vivek Vittaldev,et al.  Collision probability for space objects using Gaussian mixture models , 2013 .

[89]  Ming Xin,et al.  High-degree cubature Kalman filter , 2013, Autom..

[90]  Christopher D. Karlgaard,et al.  Parallelized sigma point and particle filters for navigation problems , 2013 .

[91]  Salvatore Cssi Alfano.  Operating characteristic approach to effective satellite conjunction filtering , 2013 .

[92]  James E. Fowler,et al.  Hyperspectral Image Classification Using Gaussian Mixture Models and Markov Random Fields , 2014, IEEE Geoscience and Remote Sensing Letters.

[93]  Kyle J. DeMars,et al.  Collision Probability with Gaussian Mixture Orbit Uncertainty , 2014 .

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

[95]  Steven L. Brunton,et al.  Long-time uncertainty propagation using generalized polynomial chaos and flow map composition , 2014, J. Comput. Phys..

[96]  M. Holzinger,et al.  Probabilistic Tracklet Characterization and Prioritization Using Admissible Regions , 2014 .

[97]  P. Nair,et al.  Aircraft Robust Trajectory Optimization Using Nonintrusive Polynomial Chaos , 2014 .

[98]  Puneet Singla,et al.  Nonlinear uncertainty propagation for perturbed two-body orbits , 2014 .

[99]  Aubrey B. Poore,et al.  Gauss von Mises Distribution for Improved Uncertainty Realism in Space Situational Awareness , 2014, SIAM/ASA J. Uncertain. Quantification.

[100]  R. Armellin,et al.  A high order method for orbital conjunctions analysis: Monte Carlo collision probability computation , 2015 .

[101]  Nitin Arora,et al.  Parallel Computation of Trajectories Using Graphics Processing Units and Interpolated Gravity Models , 2015 .

[102]  D. Scheeres,et al.  Tractable Expressions for Nonlinearly Propagated Uncertainties , 2015 .

[103]  Mark Rutten,et al.  Dynamic Steering for Improved Sensor Autonomy and Catalogue Maintenance , 2015 .

[104]  Mark L. Psiaki,et al.  Gaussian Sum Reapproximation for Use in a Nonlinear Filter , 2015 .

[105]  Henrique Marra Menegaz,et al.  A Systematization of the Unscented Kalman Filter Theory , 2015, IEEE Transactions on Automatic Control.

[106]  Aubrey B. Poore,et al.  Implicit-Runge–Kutta-based methods for fast, precise, and scalable uncertainty propagation , 2015 .

[107]  Puneet Singla,et al.  Conjugate Unscented Transformation-Based Approach for Accurate Conjunction Analysis , 2015 .

[108]  J. Crassidis,et al.  AAS 15-423 GENERALIZED GAUSSIAN CUBATURE FOR NONLINEAR FILTERING , 2015 .

[109]  Brandon A. Jones,et al.  Postmaneuver Collision Probability Estimation Using Sparse Polynomial Chaos Expansions , 2015 .

[110]  Frank Mueller,et al.  Languages and Compilers for Parallel Computing , 2015, Lecture Notes in Computer Science.