  This technical note addresses the UD factorization based Kalman filtering
(KF) algorithms. Using this important class of numerically stable KF schemes,
we extend its functionality and develop an elegant and simple method for
computation of sensitivities of the system state to unknown parameters required
in a variety of applications. For instance, it can be used for efficient
calculations in sensitivity analysis and in gradient-search optimization
algorithms for the maximum likelihood estimation. The new theory presented in
this technical note is a solution to the problem formulated by Bierman in ,
which has been open since 1990s. As in the cited paper, our method avoids the
standard approach based on the conventional KF (and its derivatives with
respect to unknown system parameters) with its inherent numerical instabilities
and, hence, improves the robustness of computations against roundoff errors.
