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

##plugins.themes.bootstrap3.article.main##

##plugins.themes.bootstrap3.article.sidebar##

Rub´en M. Claver´ıa David Acu˜na Ren´e A. M´endez Jorge F. Silva Marcos E. Orchard

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 (; ) 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

Claver´ıa, R. M., Acu˜na, D., M´endez, 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). https://doi.org/10.36001/phmconf.2016.v8i1.2585
Abstract 17 | PDF Downloads 10

##plugins.themes.bootstrap3.article.details##

Keywords

Model-based Prognostics, Parameter Estimation, Particle Filtering

References
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.
Section
Technical Papers