18 September 2014 Statistical bounds and maximum likelihood performance for shot noise limited knife-edge modeled stellar occultation
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Abstract
Applications of stellar occultation by solar system objects have a long history for determining universal time, detecting binary stars, and providing estimates of sizes of asteroids and minor planets. More recently, extension of this last application has been proposed as a technique to provide information (if not complete shadow images) of geosynchronous satellites. Diffraction has long been recognized as a source of distortion for such occultation measurements, and models subsequently developed to compensate for this degradation. Typically these models employ a knife-edge assumption for the obscuring body. In this preliminary study, we report on the fundamental limitations of knife-edge position estimates due to shot noise in an otherwise idealized measurement. In particular, we address the statistical bounds, both Cramér- Rao and Hammersley-Chapman-Robbins, on the uncertainty in the knife-edge position measurement, as well as the performance of the maximum-likelihood estimator. Results are presented as a function of both stellar magnitude and sensor passband; the limiting case of infinite resolving power is also explored.
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Patrick J. McNicholl, Patrick J. McNicholl, Peter N. Crabtree, Peter N. Crabtree, } "Statistical bounds and maximum likelihood performance for shot noise limited knife-edge modeled stellar occultation", Proc. SPIE 9227, Unconventional Imaging and Wavefront Sensing 2014, 922707 (18 September 2014); doi: 10.1117/12.2059317; https://doi.org/10.1117/12.2059317
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