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



Published Oct 3, 2016
Rubén M. Clavería David Acuña René A. Méndez Jorge F. Silva Marcos E. Orchard


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 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.

How to Cite

Clavería, R. M., Acuña, D., Méndez, R. A., Silva, J. F., & Orchard, M. E. (2016). Application of Multiple-imputation-particle-filter for Parameter Estimation of Visual Binary Stars with Incomplete Observations. Annual Conference of the PHM Society, 8(1).
Abstract 184 | PDF Downloads 84



Model-based Prognostics, Parameter Estimation, Particle Filtering

Candy, J. (2009). Bayesian signal processing: Classical, modern and particle filtering methods. Wiley. Crisan, D., & Doucet, A. (2002). A survey of convergence results on particle filtering methods for practitioners. IEEE Transactions on Signal Processing, 50(3), 736-746.
Docobo, J. (1985). On the analytic calculation of visual double star orbits. Celestial mechanics, 36(2), 143–153.
Doucet, A., Godsill, S., & Andrieu, C. (2000). On sequential monte carlo sampling methods for bayesian filtering. Statistics and Computing, 10(2), 197-208.
Gordon, N. J., Salmond, D. J., & Smith, A. F. (2002). Novel approach to nonlinear/non-gaussian bayesian state estimation. In Iee proceedings f (radar and signal processing) (Vol. 140, pp. 107–113).
Graham, J., Olchowski, A., & Gilreath, T. (2007). How many imputations are really needed? some practical clarifications of multiple imputation theory. Prevention Science, 8, 206-213.
Housfater, A., Zhang, X., & Zhou, Y. (2006). Nonlinear fusion of multiple sensors with missing data. IEEE International Conference on Acoustics, Speech and Signal Processing, 4, 961-964.
Kitagawa, G., & Sato, S. (2001). Monte carlo smoothing and self-organising state-space model. In Sequential monte carlo methods in practice (pp. 177–195). Springer.
Liu, J., Kong, A.,&Wong,W. (1994). Sequential imputations and bayesian missing data problems. Journal of the American Statistical Association, 89(425), 278-288.
Liu, J., & West, M. (2001). Combined parameter and state estimation in simulation-based filtering. In Sequential monte carlo methods in practice (pp. 197–223). Springer.
Lucy, L. (2014). Mass estimates for visual binaries with incomplete orbits. Astronomy & Astrophysics, 563, A126.
Rubin, D. (1987). Multiple imputation for nonresponse in surveys. Wiley.
Torres, G., Claret, A., & Young, P. A. (2015). Capella ( -aurigae) revisited: Binary orbit, physical properties, and evolutionary state. The Astrophysical Journal, 807(26), 15pp.
Technical Research Papers