Equivalence of recursive three-step filter and infinity augmented Kalman filter for linear discrete-time stochastic systems with direct feedthrough

摘要

In this study, the recursive three-step filter method introduced by Gillijns and Moor (2007) is proved strictly to be equivalent to the augment Kalman filter (AKF) when the covariance of process noise about the input approaches infinity. This result indicates that if the information about the exogenous input is unknown, the AKF can also be used to simultaneously obtain the state and exogenous input estimation. Numerical examples illustrate the authors' main results.