A Unified Instrumental Variable Approach to Direction Finding in Colored Noise Fields | Stoica P. Viberg M. Wong M. Wu Q. A Unified Instrumental Variable Approach to Direction Finding in Colored Noise Fields Digital Signal Processing Handbook Ed. Vijay K. Madisetti and Douglas B. Williams Boca Raton CRC Press LLC 1999 1999 by CRC Press LLC 64 A Unified Instrumental Variable Approach to Direction Finding in Colored Noise Fields1 P. Stoica Uppsala University M. Viberg Chalmers University of Technology M. Wong McMaster University Q. Wu CELWAVE Introduction Problem Formulation The IV-SSF Approach The Optimal IV-SSF Method Algorithm Summary Numerical Examples Concluding Remarks References Appendix A Introduction to IV Methods The main goal herein is to describe and analyze in a unifying manner the spatial and temporal IV-SSF approaches recently proposed for array signal processing in colored noise fields. The acronym IV-SSF stands for Instrumental Variable - Signal Subspace Fitting . Despite the generality of the approach taken herein our analysis technique is simpler than those used in previous more specialized publications. We derive a general optimally-weighted optimal for short IV-SSF direction estimator and show that this estimator encompasses the UNCLE estimator of Wong and Wu which is a spatial IV-SSF method and the temporal IV-SSF estimator of Viberg Stoica and Ottersten. The latter two estimators have seemingly different forms among others the first of them makes use of four weights whereas the second one uses three weights only and hence their asymptotic equivalence shown in this paper comes as a surprising unifying result. We hope that the present paper along with the original works aforementioned will stimulate the interest in the IV-SSF approach to array signal processing which is sufficiently flexible to handle colored noise fields coherent signals and indeed also situations were only some of the sensors in the array are calibrated. 1 This work was supported in part by the Swedish Research Council for .
