State Sensitivity Evaluation Within UD Based Array Covariance Filters

TL;DR

This paper introduces a numerically stable method for computing system state sensitivities within UD-based Kalman filters, enhancing robustness and efficiency in sensitivity analysis and maximum likelihood estimation.

Contribution

It develops a novel, simple approach for sensitivity calculation in UD-based Kalman filters, solving an open problem from the 1990s and avoiding numerical instabilities of traditional methods.

Findings

Improved numerical stability in sensitivity computations.

Enhanced robustness against roundoff errors.

Applicable to sensitivity analysis and maximum likelihood estimation.

Abstract

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.