Bayesian Analysis of Lunar Laser Ranging Data

Abstract

In 1969, astronauts first placed a retrorefiector on the moon for laser ranging of the moon, and since then the McDonald Observatory of the University of Texas has been ranging to these and other later-placed retrorefiectors. By determining the round-trip time of a very short but powerful laser pulse, important and extremely precise information about lunar motion and earth rotation can be obtained. The problem is an interesting one from the point of view of signal-to-noise, for in unfavorable circumstances, nearly all of the detected photons are not laser returns but simply background photons. Other interesting features of this problem are the fact that the data are censored; and that it is necessary to take into account the Poisson nature of the data. Determining which photons are actual returns is critical to the initial data analysis. In this paper we describe how a Bayesian analysis of the return data can be used to improve the results.