Adaptive Gaussian Sum Filters for Space Surveillance
- 19 April 2011
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Automatic Control
- Vol. 56 (8), 1777-1790
- https://doi.org/10.1109/tac.2011.2142610
Abstract
The representation of the uncertainty of a stochastic state by a Gaussian mixture is well-suited for nonlinear tracking problems in high dimensional data-starved environments such as space surveillance. In this paper, the framework for a Gaussian sum filter is developed emphasizing how the uncertainty can be propagated accurately over extended time periods in the absence of measurement updates. To achieve this objective, a series of metrics constructed from tensors of higher-order cumulants are proposed which assess the consistency of the uncertainty and provide a tool for implementing an adaptive Gaussian sum filter. Emphasis is also placed on the algorithm's potential for parallelization which is complemented by the use of higher-order unscented filters based on efficient multidimensional Gauss-Hermite quadrature schemes. The effectiveness of the proposed Gaussian sum filter is illustrated in a case study in space surveillance involving the tracking of an object in a six-dimensional state space.Keywords
This publication has 14 references indexed in Scilit:
- Uncertainty Propagation for Nonlinear Dynamic Systems Using Gaussian Mixture ModelsJournal of Guidance, Control, and Dynamics, 2008
- On Unscented Kalman Filtering for State Estimation of Continuous-Time Nonlinear SystemsIEEE Transactions on Automatic Control, 2007
- Unscented Filtering and Nonlinear EstimationProceedings of the IEEE, 2004
- Estimation with Applications to Tracking and NavigationPublished by Wiley ,2002
- Gaussian filters for nonlinear filtering problemsIEEE Transactions on Automatic Control, 2000
- Satellite OrbitsPublished by Springer Science and Business Media LLC ,2000
- An adaptive Gaussian sum algorithm for radar trackingSignal Processing, 1999
- Some Techniques for Assessing Multivarate Normality Based on the Shapiro- Wilk WJournal of the Royal Statistical Society Series C: Applied Statistics, 1983
- Nonlinear Bayesian estimation using Gaussian sum approximationsIEEE Transactions on Automatic Control, 1972
- Measures of Multivariate Skewness and Kurtosis with ApplicationsBiometrika, 1970