IDENTIFIABILITY OF THE DECONVOLUTION PROBLEM

A deconvolution problem is stated and its identifiability properties are analysed. The information assumed available consists of the spectral density of the output measurements and a dynamical description of the system. The input to the system and the measurement noise are modelled as independent ARMA processes. In order to obtain an optimal estimate (in a mean square sense) of the input signal, the parameters of the input model and measurement noise are required either to be known a priori or correctly estimated. Since the normal situation requires estimation of the parameters, a successful estimate of the input signal depends crucially on the identifiability properties. Hence, necessary and sufficient conditions for parameter identifiability are derived, in terms of model orders, with the aid of spectral factorization. An example shows that when these conditions are violated, only generic results can be obtained. A sufficient condition for generic parameter identifiability is given. © 1990.