Fast Kalman-like filtering for large-dimensional linear and Gaussian state-space models
Type
ArticleKAUST Department
Applied Mathematics and Computational Science ProgramEarth Fluid Modeling and Prediction Group
Earth Science and Engineering Program
Physical Science and Engineering (PSE) Division
Date
2015-08-14Online Publication Date
2015-08-14Print Publication Date
2015-11Permanent link to this record
http://hdl.handle.net/10754/575243
Metadata
Show full item recordAbstract
This paper considers the filtering problem for linear and Gaussian state-space models with large dimensions, a setup in which the optimal Kalman Filter (KF) might not be applicable owing to the excessive cost of manipulating huge covariance matrices. Among the most popular alternatives that enable cheaper and reasonable computation is the Ensemble KF (EnKF), a Monte Carlo-based approximation. In this paper, we consider a class of a posteriori distributions with diagonal covariance matrices and propose fast approximate deterministic-based algorithms based on the Variational Bayesian (VB) approach. More specifically, we derive two iterative KF-like algorithms that differ in the way they operate between two successive filtering estimates; one involves a smoothing estimate and the other involves a prediction estimate. Despite its iterative nature, the prediction-based algorithm provides a computational cost that is, on the one hand, independent of the number of iterations in the limit of very large state dimensions, and on the other hand, always much smaller than the cost of the EnKF. The cost of the smoothing-based algorithm depends on the number of iterations that may, in some situations, make this algorithm slower than the EnKF. The performances of the proposed filters are studied and compared to those of the KF and EnKF through a numerical example.Citation
Fast Kalman-like filtering for large-dimensional linear and Gaussian state-space models 2015:1 IEEE Transactions on Signal Processingae974a485f413a2113503eed53cd6c53
10.1109/TSP.2015.2468674