Generalized Minimum Norm And Constrained Total Least Squares With Applications To Array Signal Processing

Michael D. Zoltowski

doi:10.1117/12.948493

23 February 1988 Generalized Minimum Norm And Constrained Total Least Squares With Applications To Array Signal Processing

Michael D. Zoltowski

Author Affiliations +

Proceedings Volume 0975, Advanced Algorithms and Architectures for Signal Processing III; (1988) https://doi.org/10.1117/12.948493
Event: 32nd Annual International Technical Symposium on Optical and Optoelectronic Applied Science and Engineering, 1988, San Diego, CA, United States

Abstract

The minimum norm Total Least Squares (TLS) solution to the linear system of equations AX = B for the case where the rank of the composite matrix [A I B] under no-noise/error-free conditions is strictly less than the number of columns in A is derived. The resulting method of solution is applied to the covariance level ESPRIT problem encountered in the field of sensor array signal processing. The TLS concept is targeted in light of the fact that the linear system of equations derived from ESPRIT at the covariance level is of the form AX = B where A and B are both in error. In contrast, conventional Least Squares only accounts for errors in B. The derivation is based on a projection operator interpretation of TLS1 analogous to the situation with conventional Least Squares in which the solution to AX = B is obtained by first projecting the columns of B onto range CA). The projection operator approach is further utilized to derive the constrained TLS solution when certain columns of A are known to be exact, i. e., free of error. The applicability of the constrained TLS solution for this case to the problem of estimating the source covariance matrix in a uniformly-spaced linear array scenario is discussed.

Citation Download Citation

Michael D. Zoltowski "Generalized Minimum Norm And Constrained Total Least Squares With Applications To Array Signal Processing", Proc. SPIE 0975, Advanced Algorithms and Architectures for Signal Processing III, (23 February 1988); https://doi.org/10.1117/12.948493

ACCESS THE FULL ARTICLE

INSTITUTIONAL
Select your institution to access the SPIE Digital Library.

SELECT YOUR INSTITUTION

PERSONAL
Sign in with your SPIE account to access your personal subscriptions or to use specific features such as save to my library, sign up for alerts, save searches, etc.

PERSONAL SIGN IN

No SPIE Account? Create one

PURCHASE THIS CONTENT

SUBSCRIBE TO DIGITAL LIBRARY

50 downloads per 1-year subscription

Members: $195

Non-members: $335 ADD TO CART

25 downloads per 1 - year subscription

Members: $145

Non-members: $250 ADD TO CART

PURCHASE SINGLE ARTICLE

Includes PDF, HTML & Video, when available