Optimal Delay Estimation in a Multiple Sensor Array Having Spatially Correlated Noise.
Annual technical rept. 1 Nov 82-31 Oct 83,
WYOMING UNIV LARAMIE 5 DEPT OF ELECTRICAL ENGINEERING
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The maximal likelihood estimation of time-of-arrival differences for signals from a single source of target arriving at M or 2 sensors has been the subject of a large number of papers in recent years. These time differences or delays enable target location. Nearly all previous work has assumed noises which are independent among all sensors. Herein noises are taken to have complex correlation between sensors. A set of nonlinear equations is the unknown delays is derived and possible simplifications discussed. The unknowns are in one case the M-1 delays referred to the first sensor and in another case an M-1 dimensional subset of independent delays from the MM-12 pairwise delays. The Fisher information matrix FIM for the estimates is also derived. The Cramer Rao Matrix Bound CRMB, which is the inverse of FIM, will show optimal estimator covariances these are different than the covariances of correlator delay estimators derived by Hahn. Computer evaluations are given for CRMB elements with varied Signal to Noise Ratios and noise covariance values typical of turbulent boundary layer noise in towed arrays. Author
- Numerical Mathematics