On the generator polynomial for system identification with application to the harmonic retrieval problem

Consideration is given to the use of more detailed information for identifying the poles of a rational system driven by white noise. The observation process correlation Hankel matrix is utilized. In particular, the eigenfilters corresponding to the kernel of this operator are used to identify the system characteristic polynomial. This polynomial is the generator of the polynomial ideal corresponding to increasing kernel dimensions. Numerical results for the harmonic retrieval problem indicate the potential of this approach and point to areas for further research