Decoupled Maximum
Likelihood Angle
Estimation for Signals with Known Waveforms
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Jian Li
University of Florida
Department of Electrical Engineering
Gainesville, FL 32611
email: li@saturn.ee.ufl.edu |
Bijit Halder
Stanford University
Information Systems Laboratory
Stanford, CA 94305 |
Petre Stoica
Uppsala University
Systems and Control Group
Department of Technology
P.O. Box 27, S-751 03
Uppsala, Sweden |
Mats Viberg
Chalmers University of Technology
Department of Applied Electronics
S-412 96, Gothenburg, Sweden |
Abstract This presentation presents a large sample decoupled maximum likelihood (DEML)
angle estimator for uncorrelated narrowband plane waves with known waveforms and unknown
amplitudes arriving at a sensor array in the presence of unknown and arbitrary spatially
colored noise. The DEML estimator decouples the multidimensional problem of the exact
maximum likelihood (ML) estimator to a set of one-dimensional problems and hence is
computationally efficient. We derive the asymptotic statistical performance of the DEML
estimator and compare the performance with its Cramér-Rao bound, i.e., the best possible
performance. We show that the DEML estimator is asymptotically statistically efficient for
uncorrelated signals with known waveforms. We also show that for moderately correlated
signals with known waveforms, the DEML estimator is no longer a large sample ML estimator,
but the DEML estimator may still be used for angle estimation and the performance
degradation is small. To estimate the arrival angles of desired signals with known
waveforms in the presence or interfering of jamming signals we show that modeling the
interfering or jamming signals as random processes with an unknown spatial covariance
matrix may give lower CRD than modeling them as unknown deterministic incident signals.
Finally, several numerical examples showing the performance of the DEML estimator are
presented.
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