Finite-Interval Innovation Representations for LPV Stochastic Systems

This paper studies linear parameter-varying (LPV) stochastic systems to explore noise models for system identification. It is known that, in the conventional LPV stochastic systems, where system matrices and noise covariances statically depend on the present parameter, the Kalman gain and innovation covariance in the finite-interval innovation representation dynamically depend on parameters. Using the output covariance, this paper demonstrates that, in the finite-interval innovations representation of the LPV stochastic system whose input and direct transmission matrices are functions of parameters from the infinite past, the Kalman gain and innovation covariance also dynamically depend on parameters from the infinite past.