文章基本信息

标题：Analysis of the Bayesian Cramér-Rao lower bound in astrometry - Studying the impact of prior information in the location of an object
其他标题：Studying the impact of prior information in the location of an object
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作者：Alex Echeverria ; Alex Echeverria ; Jorge F. Silva 等
期刊名称：Astronomy & Astrophysics
印刷版ISSN：0004-6361
电子版ISSN：1432-0746
出版年度：2016
卷号：594
页码：1-16
DOI：10.1051/0004-6361/201628220
语种：English
出版社：EDP Sciences
摘要：Context. The best precision that can be achieved to estimate the location of a stellar-like object is a topic of permanent interest in the astrometric community. Aims. We analyze bounds for the best position estimation of a stellar-like object on a CCD detector array in a Bayesian setting where the position is unknown, but where we have access to a prior distribution. In contrast to a parametric setting where we estimate a parameter from observations, the Bayesian approach estimates a random object (i.e., the position is a random variable) from observations that are statistically dependent on the position. Methods. We characterize the Bayesian Cramér-Rao (CR) that bounds the minimum mean square error (MMSE) of the best estimator of the position of a point source on a linear CCD-like detector, as a function of the properties of detector, the source, and the background. Results. We quantify and analyze the increase in astrometric performance from the use of a prior distribution of the object position, which is not available in the classical parametric setting. This gain is shown to be significant for various observational regimes, in particular in the case of faint objects or when the observations are taken under poor conditions. Furthermore, we present numerical evidence that the MMSE estimator of this problem tightly achieves the Bayesian CR bound. This is a remarkable result, demonstrating that all the performance gains presented in our analysis can be achieved with the MMSE estimator. Conclusions. The Bayesian CR bound can be used as a benchmark indicator of the expected maximum positional precision of a set of astrometric measurements in which prior information can be incorporated. This bound can be achieved through the conditional mean estimator, in contrast to the parametric case where no unbiased estimator precisely reaches the CR bound.
关键词：astrometry;methods: statistical;methods: analytical;instrumentation: detectors;methods: data analysis