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 particle-filter-based method to perform the estimation and uncertainty characterization of these orbital parameters in the context of partial 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.