Boundary Control approach to the spectral estimation problem: the case of multiple poles.
- Resource Type
- Article
- Authors
- Avdonin, Sergei; Bulanova, Anna
- Source
- Mathematics of Control, Signals & Systems. Sep2010, Vol. 22 Issue 3, p245-265. 21p.
- Subject
- *ESTIMATION theory
*POLYNOMIALS
*DIFFERENTIAL dimension polynomials
*EXPONENTIAL sums
*LINEAR control systems
- Language
- ISSN
- 0932-4194
There exist many methods for solving the spectral estimation problem. This paper proposes a new approach to this problem based on the Boundary Control method. We show that the problem of decomposition of a signal modeled by a sum of exponentials with polynomial coefficients can be reduced to an identification problem for a discrete time linear dynamical system. It follows that values of exponentials can be found solving a generalized eigenvalue problem as in the Matrix Pencil method. We also give exact formulas for the polynomial amplitudes. [ABSTRACT FROM AUTHOR]