Infinity augmented state Kalman filter and its application in unknown input and state estimation

Abstract

This paper investigates the infinity augmented state Kalman filter (IASKF) to obtain the unknown input and state estimation for systems with the rank-deficient matrix. With the aid of input model, which is described as the random walk process with finite covariance, the augmented state Kalman filter (ASKF) is established. Then in light of matrix limiting, the IASKF is deduced from the ASKF as the covariance of the input signal tends to infinity. It is shown that the previous unbiased minimum-variance (UMV) algorithm and recursive three-step filter (RTSF) are the special cases of the proposed IASKF algorithm. Moreover, the condition of existence of the IASKF is given. The present work gives a new insight into unknown input and state estimation. It indicates that the ASKF can also be used to estimate the unknown input and state by only choosing a proper covariance matrix of the input signal. A simulation example is given to illustrate the effectiveness of the proposed results.