Transfer function approach to the fixed-point continuous smoothing problem

Abstract

A transfer function approach to the steady-state fixed-point smoothing problem is introduced. The filtered estimate of the system state vector is first found by spectral factorizing the power spectral density matrix of the corrupted observation signal. The time-varying gain matrix that yields the time derivative of the optimal fixed-point smoothed estimate of the system output vector is then found from the partial fraction expansion of the transpose of the resulting optimal filter transfer function matrix. This approach is easily extended to cope with colored signals and the advantages of its computational method for systems having a small number of inputs and outputs is discussed.