Identifiability of the Deconvolution Problem
8th IFAC/IFORS Symposium on
Identification and System Parameter Estimation, Beijing,
August 1988, pp 1387-1392.
A deconvolution filter estimates the input to a linear system.
In some situations, the system dynamics may be known,
while the properties of the input signal and the noise
have to be estimated from output data, before a filter can be
designed. The paper derives necessary and sufficient
conditions for this to be possible.
A deconvolution problem is stated and its identifiability properties
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.
An example shows that when these conditions are violated,
only generic results can be obtained.
A sufficient condition for generic parameter
identifiability is given. The results are global.
- Related publications:
Automatica 1990, on the above theme.
in IEEE Trans. ASSP 1989 on the design of linear scalar deconvolution
in IFAC ACASP 1989 on adaptive deconvolution.
in SPIE 1991 on adaptive deconvolution.