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Covariance matrix decomposition in deterministic sampling filters

Nonlinear filters have been developed for decades and a variety of methods have been utilized to improve the performance of these nonlinear filters. A class of nonlinear filters based on deterministic sampling method received widespread concern recently which can be used instead of EKFs. In the deterministic sampling filters, it needs matrix decomposition to get the square root of covariance matrix while choosing sample points, and usually uses Cholesky decomposition or singular value decomposition of covariance matrix directly. In this paper, the covariance matrix is decomposed into diagonal matrix of normal deviation and correlated coefficient matrix, which eliminates the dimension effect of the state. Then through an implementation of singular value decomposition to correlated coefficient matrix, a set of more accurate sampling points can be got which guarantee the new filter provides a superior performance. Finally, the effectiveness of the method is validated through a simulation.