  The paper presents a new Kalman filter (KF) implementation useful in
applications where the accuracy of numerical solution of the associated Riccati
equation might be crucially reduced by influence of roundoff errors. Since the
appearance of the KF in 1960s, it has been recognized that the factored-form of
the KF is preferable for practical implementation. The most popular and
beneficial techniques are found in the class of square-root algorithms based on
the Cholesky decomposition of error covariance matrix. Another important matrix
factorization method is the singular value decomposition (SVD) and, hence,
further encouraging implementations might be found under this approach. The
analysis presented here exposes that the previously proposed SVD-based KF
variant is still sensitive to roundoff errors and poorly treats ill-conditioned
situations, although the SVD-based strategy is inherently more stable than the
conventional KF approach. In this paper we design a new SVD-based KF
implementation for enhancing the robustness against roundoff errors, provide
its detailed derivation, and discuss the numerical stability issues. A set of
numerical experiments are performed for comparative study. The obtained results
illustrate that the new SVD-based method is algebraically equivalent to the
conventional KF and to the previously proposed SVD-based method, but it
outperforms the mentioned techniques for estimation accuracy in ill-conditioned
situations.
