Multivariate Normality of Cartesian-Framed Covariances: Evaluation and Operational Significance

Lechtenberg, Travis F

关键词: CARTESIAN COORDINATES;    COLLISION AVOIDANCE;    COVARIANCE;    DRAG;    ERROR ANALYSIS;    MANEUVERABILITY;    MATRICES (MATHEMATICS);    MONTE CARLO METHOD;    MULTIVARIATE STATISTICAL ANALYSIS;    NORMALITY;    PROBABILITY THEORY;    RISK ASSESSMENT;    SATELLITE ORBITS;   

RP-ID  :  GSFC-E-DAA-TN71120-1

美国|英语

来源: NASA Technical Reports Server

【 摘 要 】

Collision avoidance relies on representative Cartesian uncertainty volumes in order to calculate probabilities of collision. Among the potential shortcomings of a covariance matrix representation of state errors, the most worrisome is the coordinate mismatch between the Cartesian framework in which these matrices are distributed and the curvilinear path that satellite orbits actually follow. The present study compares curvilinear-based and Cartesian covariance representations for ~50,000 conjunctions to determine the frequency in which significant deviations from Gaussianity are observed, then compares the 2-D Pc result from the Cartesian covariance to a Monte Carlo Pc conducted in element space to assess operational significance.