State Sensitivity Evaluation Within UD Based Array Covariance Filters
For researchers and engineers using Kalman filtering in sensitivity analysis and maximum likelihood estimation, this provides a numerically stable solution to a long-standing problem.
This paper extends UD factorization-based Kalman filtering to compute state sensitivities to unknown parameters, solving a problem open since the 1990s. The method avoids numerical instabilities of conventional approaches, improving robustness against roundoff errors.
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.