Application of Multiple-imputation-particle-filter for Parameter Estimation of Visual Binary Stars with Incomplete Observations

Abstract

In visual binary stars, mass estimation can be accomplished through the study of their orbital parameters –Kepler’s Third Law establishes a strict mathematical relation between orbital period, orbit size (semi-major axis) and the system total mass. Although, in theory, few observations on the plane of the sky may be enough to obtain a decent estimate for binary star orbits, astronomers must frequently deal with the problem of partial measurements (i.e.; observations having one component missing, either in (X; Y ) or (rho, theta) representation), which are often discarded. This article presents a particlefilter-based method to perform the estimation and uncertainty characterization of these orbital parameters in the context ofpartial measurements. The proposed method uses a multiple imputation strategy to cope with the problem of missing data. The algorithm is tested on synthetic data of relative position of binary stars. The following cases are studied: i) fully available data (ground truth); ii) incomplete observations are discarded; iii) multiple imputation approach is used. In comparison to a situation where partial observations are ignored,a significant reduction in the empirical estimation variance is observed when using multiple imputation schemes; with no numerically significant decrease on estimate accuracy.