A stochastic unknown input realization and filtering technique

This paper studies the state estimation problem of linear discrete-time systems with unknown inputs which can be treated as a wide-sense stationary process with rational power spectral density, while no other prior information needs to be known. We propose an autoregressive (AR) model based unknown input realization technique which allows us to recover the input statistics from the output data by solving an appropriate least squares problem, then fit an AR model to the recovered input statistics and construct an innovations model of the unknown inputs using the eigensystem realization algorithm. An augmented state system is constructed and the standard Kalman filter is applied for the state estimation. A reduced order model filter is also introduced to reduce the computational cost of the Kalman filter. A numerical example is given to illustrate the procedure.