Approximate maximum likelihood DOA estimation in multiplicative noise environments

We consider the problem of localizing a source by means of a uniform linear array of sensors when the received signal is corrupted by multiplicative noise. Since the exact maximum likelihood (ML) estimator is computationally intensive, two approximate solutions are proposed, originating from the analysis of the high and low signal to noise ratio (SNR) cases, respectively. First, starting with the no additive noise case, a very simple approximate ML (AML/sub 1/) estimator is derived. A theoretical expression for its asymptotic variance in the presence of additive noise is derived. It shows that the AML/sub 1/ estimator has a performance close to the Cramer-Rao bound (CRB) for moderate to high SNR. Next, the low SNR case is considered and the corresponding AML2 solution is derived. It is shown that the approximate ML criterion can be concentrated with respect to (w.r.t.) both the multiplicative and additive noise powers, leaving out a 2-D minimization problem instead of a 4-D problem required by the exact ML. Numerical results illustrate the performance of the estimators and confirm the validity of the theoretical analysis.

[1]  T. Kailath,et al.  Direction of arrival estimation by eigenstructure methods with imperfect spatial coherence of wave fronts , 1988 .

[2]  T. Söderström,et al.  On reparametrization of loss functions used in estimation and the invariance principle , 1989 .

[3]  V. I. Turchin,et al.  Simple maximum-likelihood estimator of structured covariance parameters , 1992 .

[4]  Shahrokh Valaee,et al.  Localization of distributed sources , 1993 .

[5]  Shahrokh Valaee,et al.  Parametric localization of distributed sources , 1995, IEEE Trans. Signal Process..

[6]  P. Stoica,et al.  On the concentrated stochastic likelihood function in array signal processing , 1995 .

[7]  Alex B. Gershman,et al.  Experimental results of localization of moving underwater signal by adaptive beamforming , 1995, IEEE Trans. Signal Process..

[8]  Björn E. Ottersten,et al.  Estimation of nominal direction of arrival and angular spread using an array of sensors , 1996, Signal Process..

[9]  Christoph F. Mecklenbräuker,et al.  Matrix fitting approach to direction of arrival estimation with imperfect spatial coherence of wavefronts , 1997, IEEE Trans. Signal Process..

[10]  A. Souloumiac,et al.  Matrix Fitting Approach to Direction of Arrival Estimation with Imperfect Spatial Coherence of Wavefronts , 1997 .

[11]  Raviv Raich,et al.  Bearing estimation for a distributed source via the conventional beamformer , 1998, Ninth IEEE Signal Processing Workshop on Statistical Signal and Array Processing (Cat. No.98TH8381).

[12]  Petre Stoica,et al.  Decoupled estimation of DOA and angular spread for spatially distributed sources , 1999, Conference Record of the Thirty-Third Asilomar Conference on Signals, Systems, and Computers (Cat. No.CH37020).

[13]  David Astély.  Spatial and spatio-temporal processing with antenna arrays in wireless systems , 1999 .

[14]  Petre Stoica,et al.  Approximate maximum likelihood estimators for array processing in multiplicative noise environments , 2000, IEEE Trans. Signal Process..