Statistical Inference in Modeling the Orbital Debris Environment
- Paper number
IAC-06-B6.2.03
- Author
Dr. Yu-lin Xu, Jacobs Sverdrup, United States
- Year
2006
- Abstract
Reliable information on orbital debris (OD) populations, such as the spatial density, flux, size, and shape distributions, is important for satellite impact risk assessments. Research concerning the characterization of the OD environment often deals with problems of a statistical nature. For example, the NASA Orbital Debris Engineering Model, ORDEM2000, is based on OD populations derived statistically from ground-based and in situ measurements through a maximum likelihood estimator. Also, the size distribution of the OD objects detected by Haystack radar is estimated by a statistical size estimation model from the measured radar cross section (RCS) distributions. This paper reviews three statistical approaches that have been used for the statistical inference of the Haystack radar OD data, and discusses their respective pros and cons. These include: (1) the standard Generalized Linear Model, (2) the expectation maximization algorithm for solving linear inverse problems with positive constraints, which was used in the development of ORDEM2000, and (3) a Bayesian approach that is a simple application of the multiplicative rule of probability and Bayes’ theorem. Common to all three statistical inference processes mentioned above, the key quantity required is the probability density function (PDF) specifying the contribution of a given model parameter to a given observed quantity, which can be either empirical or theoretically calculated. The estimation of the Haystack debris populations requires the probability of an object in an orbit of given orbital elements to be detected in a given bin of radar measured range and range-rate values. The inference of a size distribution from an observed RCS distribution requires a similar but different type of distribution density function. In addition to the discussion on statistical algorithms, this paper also discusses the procedure for the construction of the conditional PDF, using the RCS density function as an example. Practical examples on the RCS analysis are included in the paper.
- Abstract document
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