TY - JOUR

T1 - A Discussion of Various Approaches to the Linear System Identification Problem

AU - Sarkar, Tapan K.

AU - Dianat, Soheil A.

PY - 1984/6

Y1 - 1984/6

N2 - This paper deals with the pole zero identification of a linear system from a measured input-output record. One objective is to show that the pencil-of-function method minimizes a weighted version of the Kalman equation error. It follows that the pencil-of-function method is capable of yielding robust estimates for poles located in a given region of the complex s plane. The second objective of this paper is to illustrate that identical sets of equations arise in three supposedly different analytical techniques for obtaining the impulse response of a system. The techniques investigated are 1) the least squares technique based on the discrete Wiener-Hopf equation, 2) Pisarenko's eigenvalue method, and 3) Jain's pencil-of-function method. The proof of equivalence is valid only for the noise-free case when the system order is known. Instead of using the conventional differential equation formulation, equivalence is shown with the integral form utilized in the pencil-of-function method.

AB - This paper deals with the pole zero identification of a linear system from a measured input-output record. One objective is to show that the pencil-of-function method minimizes a weighted version of the Kalman equation error. It follows that the pencil-of-function method is capable of yielding robust estimates for poles located in a given region of the complex s plane. The second objective of this paper is to illustrate that identical sets of equations arise in three supposedly different analytical techniques for obtaining the impulse response of a system. The techniques investigated are 1) the least squares technique based on the discrete Wiener-Hopf equation, 2) Pisarenko's eigenvalue method, and 3) Jain's pencil-of-function method. The proof of equivalence is valid only for the noise-free case when the system order is known. Instead of using the conventional differential equation formulation, equivalence is shown with the integral form utilized in the pencil-of-function method.

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U2 - 10.1109/TASSP.1984.1164338

DO - 10.1109/TASSP.1984.1164338

M3 - Article

AN - SCOPUS:0021439919

VL - 32

SP - 654

EP - 656

JO - IEEE Transactions on Acoustics, Speech, and Signal Processing

JF - IEEE Transactions on Acoustics, Speech, and Signal Processing

SN - 1053-587X

IS - 3

ER -