  In this paper, a singular value decomposition (SVD) approach is developed for
implementing the cubature Kalman filter. The discussed estimator is one of the
most popular and widely used method for solving nonlinear Bayesian filtering
problem in practice. To improve its numerical stability (with respect to
roundoff errors) and practical reliability of computations, the SVD-based
methodology recently proposed for the classical Kalman filter is generalized on
the nonlinear filtering problem. More precisely, we suggest the SVD-based
solution for the continuous-discrete cubature Kalman filter and design two
estimators: (i) the filter based on the traditionally used Euler-Maruyama
discretization scheme; (ii) the estimator based on advanced It\^{o}-Taylor
expansion for discretizing the underlying stochastic differential equations.
Both estimators are formulated in terms of SVD factors of the filter error
covariance matrix and belong to the class of stable factored-form (square-root)
algorithms. The new methods are tested on a radar tracking problem.
