Blind input, initial state, and system identification of SIMO Laguerre systems

Laguerre filters have infinite impulse responses (IIRs) but with finite tapped delay-line parameterizations. This paper investigates subspace-based blind identification of Laguerre filter tap coefficients, the internal filter state, and the input, given only noisy observations of the output. This paper deals only with single-input, multiple-output (SIMO) Laguerre models. A state space model for the SIMO Laguerre system is derived from which blind estimation algorithms are developed. As in the finite impulse response (FIR) case, the Laguerre filter taps coefficients can be estimated from the column space of a certain Hankel matrix constructed from noisy output observations, whereas the internal state and input can be estimated from the row space by exploiting state space structure. While not exactly uniquely identifiable, conditions are given for which the tap coefficients, the internal state, and the input can be determined to within a multiplicative scalar factor.