On the optimality of the Kitanidis filter for state estimation rejecting unknown inputs

As a natural extension of the Kalman filter to systems subject to arbitrary unknown inputs, the Kitanidis filter has been designed by one-step minimization of the trace of the state estimation error covariance matrix. In this technical communique, it is shown that the Kitanidis filter is also optimal for the whole gain sequence in the sense of matrix positive definiteness, which notably implies that the Kitanidis filter minimizes not only the trace criterion, but also the matrix spectral norm criterion. (C) 2021 Published by Elsevier Ltd.

Automated summary

The Kitanidis filter is a natural extension of the Kalman filter and can be used for systems subject to arbitrary unknown inputs. It is designed by minimizing the trace of the state estimation error covariance matrix, and is shown to be optimal for the whole gain sequence in terms of matrix positive definiteness.