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Maximum-likelihood array processing in non-Gaussian noise with Gaussian mixtures

IEEE TRANSACTIONS ON SIGNAL processing 2000年第12期48卷 3520-3535页

作者： Kozick, RJ Sadler, BM Bucknell Univ Dept Elect Engn Lewisburg PA 17837 USA AMSRL CI CN Army Res Lab Adelphi MD 20783 USA

Many approaches have been studied for the array processing problem when the additive noise is modeled with a Gaussian distribution, but these schemes typically perform poorly when the noise is non-Gaussian and/or impulsive. This paper is concerned with maximum likelihood array processing in non-Gaussian noise. We present the Cramer-Rao bound on the variance of angle-of-arrival estimates for'arbitrary additive, independent, identically distributed (iid), symmetric, non-Gaussian noise. Then, we focus on non-Gaussian noise modeling with a finite Gaussian mixture distribution, which is capable of representing a broad class of non-Gaussian distributions that include heavy tailed, impulsive cases arising in wireless communications and other applications. Based on the Gaussian mixture model, we develop an expectation-maximization (EM) algorithm for estimating the source locations, the signal waveforms, and the noise distribution parameters. The important problems of detecting the number of sources and obtaining initial parameter estimates for the iterative EM algorithm are discussed in detail. The initialization procedure by itself is an effective algorithm for array processing in impulsive noise. Novel features of the EM algorithm and the associated maximum likelihood formulation include a nonlinear beamformer that separates multiple source signals in non-Gaussian noise and a robust covariance matrix estimate that suppresses impulsive noise while also performing a model-based interpolation to restore the low-rank signal subspace. The EM approach yields improvement over initial robust estimates and is valid for a nide SNR range. The results are also robust to pdf model mismatch and work well with infinite variance cases such as the symmetric stable distributions. Simulations confirm the optimality of the EM estimation procedure in a variety of cases, including a multiuser communications scenario. We also compare with existing array processing algorithms for non-Gaussian no

关键词： EM algorithm impulsive noise maximum-likelihood estimation non-Gaussian noise robust covariance matrix sensor array processing

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Estimating evoked dipole responses in unknown spatially correlated noise with EEG/MEG arrays

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IEEE TRANSACTIONS ON SIGNAL processing 2000年第1期48卷 13-25页

作者： Dogandzic, A Nehorai, A Univ Illinois Dept Elect Engn & Comp Sci Chicago IL 60607 USA

We present maximum likelihood (ML) methods for estimating evoked dipole responses using electroencephalography (EEG) and magnetoencephalography (MEG) arrays, which allow for spatially correlated noise between sensors with unknown covariance. The electric source is modeled as a collection of current dipoles at fixed locations and the head as a spherical conductor. We permit the dipoles' moments to vary with time by modeling them as linear combinations of parametric or nonparametric etc. basis functions. We estimate the dipoles' locations and moments and derive the Cramer-Rao bound for the unknown parameters. We also propose an ML-based method for scanning the brain response data, which can be used to initialize the multidimensional search required to obtain the true dipole location estimates. Numerical simulations demonstrate the performance of the proposed methods.

关键词： Cramer-Rao bound dipole source EEG evoked responses maximum likelihood parameter estimation MEG sensor array processing unknown noise covariance

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Performance analysis of the approximate dynamic programming algorithm for parameter estimation of superimposed signals

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IEEE TRANSACTIONS ON SIGNAL processing 2000年第5期48卷 1274-1286页

作者： Yau, SF Bresler, Y Integrated Display Technol Ltd Hong Kong Hong Kong Peoples R China Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA

We consider the classical problem of fitting a model composed of multiple superimposed signals to noisy data using the criteria of maximum likelihood (ML) or subspace fitting, jointly termed generalized subspace fitting (GSF), We analyze a recently proposed: approximate dynamic programming algorithm (ADP), which provides a computationally efficient solution to the associated multidimensional multimodal optimization problem. We quantify the error introduced by the approximations in ADP and deviations from the key local interaction signal model (LISMO) modeling assumption in two ways. First, we upper bound the difference between the exact minimum of the GSF criterion and its value at the ADP estimate and compare the ADP with GSF estimates obtained by exhaustive multidimensional search on a fine,lattice. Second, motivated by the similar accuracy bounds, we use perturbation analysis to derive approximate expressions for the MSE of the ADP estimates. These various results provide, for the first time, an effective tool to predict the performance of the ADP algorithm for various signal models at nonasymptotic conditions of interest in practical applications. In particular, they :demonstrate that for the classical problems of sinusoid retrieval and array processing, ADP performs comparably to enact (but expensive) maximum likelihood (ML) over a wide range df signal-to-noise ratios (SNR's) and is therefore an attractive algorithm.

关键词： dynamic programming model fitting nonlinear regression optimization parameter estimation radar sensor array processing sinusoid retrieval sonar

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Direction estimation in partially unknown noise fields

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IEEE TRANSACTIONS ON SIGNAL processing 1999年第9期47卷 2375-2385页

作者： Göransson, B Ottersten, B Royal Inst Technol Dept Signals Sensors & Syst Signal Proc Grp S-10044 Stockholm Sweden

The problem of direction of arrival estimation in the presence of colored noise with unknown covariance is considered, The unknown noise covariance is assumed to obey a linear parametric model. Using this model, the maximum likelihood directions parameter estimate is derived, and a large sample approximation is formed. It is shown that a priori information on the source signal correlation structure is easily incorporated into this approximate ML (AML) estimator. Furthermore, a closed-form expression of the Cramer-Rao bound on the direction parameter is provided. A perturbation analysis with respect to a small error in the assumed noise model is carried out, and an expression of the asymptotic bias due to the model mismatch is given. Computer simulations and an application of the proposed technique to a full-scale passive sonar experiment is provided to illustrate the results.

关键词： colored noise maximum likelihood sensor array processing source localization

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A source tracking sensor array testbed

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MICROPROCESSORS AND MICROSYSTEMS 1999年第4期23卷 207-216页

作者： Scott, ED Pierre, JW Hamann, JC Univ Wyoming Dept Elect Engn Laramie WY 82071 USA

The University of Wyoming Source Tracking array Testbed (UW STAT) was developed as a platform to experimentally investigate recent advances in sensor array source tracking algorithms. UW STAT is a six sensor array with one or more sources which may be moving. This system is unique in its compactness and its emphasis on the source tracking problem with the ability to precisely know the true source location for comparison with array tracking algorithm results. Experimental tracking results are presented to demonstrate the performance of the system. Experimental data, along with information about UW STAT, is available on the World Wide Web (http://***/electrical/***) for other researchers to test their tracking algorithms. (C) 1999 Elsevier Science B.V. All rights reserved.

关键词： sensor array processing source tracking signal processing

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Design of chemical sensor arrays for monitoring disposal sites on the ocean floor

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IEEE JOURNAL OF OCEANIC ENGINEERING 1998年第4期23卷 334-343页

作者： Jeremic, A Nehorai, A Univ Illinois Dept Elect Engn & Comp Sci Chicago IL 60607 USA

We develop methods for automatic environmental monitoring of disposal sites on the deep ocean door using chemical sensor arrays and statistical hypothesis testing. Such sites have been proposed to relocate dredge materials from harbors and shipping channels. The transport of pollutants is modeled as a diffusion process, and the measurement and statistical models are derived by exploiting the spatial and temporal evolution of the associated concentration distribution. We derive two detectors, the generalized likelihood ratio (GLR) test and the mean detector, and determine their performance in terms of the probabilities of false alarm and detection. The results are applied to the design of chemical sensor arrays satisfying criteria specified in terms of these probabilities, and to optimally select a number of sensors and time samples. Numerical examples are used to demonstrate the applicability of our results.

关键词： chemical sensing environmental monitoring pollutant detection sensor array processing

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Preliminary results in B-spline enhanced source-tracking

Preliminary results in B-spline enhanced source-tracking

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9th IEEE Signal processing Workshop on Statistical Signal and array processing (SSAP98)

作者： Green, RA Pierre, JW Univ Wyoming Dept Elect Engn Laramie WY 82071 USA

ISBN: (纸本)0780350103

Source-tracking algorithms typically require estimation of an array's unknown correlation matrix. Time-averaging forms the basis of estimating the correlation matrix in most applications. This paper provides a preliminary investigation in the use of B-splines rather than time-averages to estimate the correlation matrix. The smooth, continuous character of splines can accurately match the behaviour of an array's true correlation matrix. Preliminary results indicate tracking estimates based on the spline-fit correlation:matrix have improved smoothness over time-averaging methods and can have comparable or better accuracy. Furthermore, B-splines are computationally efficient and are easily adapted to near real-time processing.

关键词： sensor array processing source-tracking nonstationary signals and time-varying systems B-splines

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Estimation of nominal direction of arrival and angular spread using an array of sensors

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SIGNAL processing 1996年第1-2期50卷 57-69页

作者： Trump, T Ottersten, B ROYAL INST TECHNOL S-10044 STOCKHOLMSWEDEN

The problem of estimating the nominal direction of arrival and angular spread of a source surrounded by a large number of local scatterers using an array of sensors is addressed. This type of propagation occurs frequently in, for example, mobile communications. The maximum likelihood estimator is considered and two computationally less complex estimators are also proposed. They are based on least-squares fits of the sample covariance to the theoretical covariance matrix derived from the measurement model. The performance of the least-squares-based algorithm is analyzed and based on this, an optimally weighted least-squares criterion is proposed. The weighted least-squares algorithm is shown to be asymptotically efficient. Results of numerical experiments are presented to indicate small sample behavior of the estimators. The nominal direction-of-arrival (DOA) estimates are compared with those provided by a standard subspace algorithm. Finally, the methods are applied to experimental array data to determine spread angles for non line of sight scenarios.

关键词： sensor array processing parameter estimation mobile communications

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Detection-estimation in sensor arrays without eigendecompositions

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IEICE TRANSACTIONS ON COMMUNICATIONS 1996年第8期E79B卷 1147-1155页

作者： KloucheDjedid, A Miura, R ATR OPT & RADIO COMMUN RES LABS KYOTO 61902 JAPAN

High resolution algorithms in sensor arrays lead to accurate results but with expensive eigendecompositions making its use in real-time applications such as mobile communications relatively difficult. In this paper, a trade-off between accuracy and computational load is accomplished through a simplified algorithm which instead of eigendecompositions, uses the robust QR decomposition for which many efficient parallel (systolic, wavefront array) implementations exist. First, a simple detection scheme is presented and, through simulations, is shown to work very well for sufficient SNR, even when signals are coherent. Outputs of the detection process include simultaneously estimates of signals Direction Of Arrivals (DOA's) and a simple beamformer vector resulting in an estimate of the desired signal. Extensive simulations are performed assuming different scenarios of variations in SNR, DOA's leading to discussions on the possibilities and limitations of the proposed solution.

关键词： antennas and propagation sensor array processing

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NONWAVE FIELD processing USING sensor array APPROACH

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SIGNAL processing 1995年第2期44卷 197-210页

作者： GERSHMAN, AB TURCHIN, VI Ruhr-Universität Bochum Lehrstuhl für Signaltheorie D-44780 Germany Institute of Applied Physics of Russian Academy of Science 46 Uljanov Street 603600 Nizhny Novgorod Russian Federation

The application of sensor array processing methods for estimation and localization of wavefield sources is well known and has been intensively studied in literature. In this paper we extend sensor array processing approach to estimating the parameters of the fields of nonwave nature (the so-called nonwave fields). Considering the static and the diffusion field as typical examples of nonwave fields, and assuming that measurements are carried out by an antenna array, we derive the Cramer-Rao bounds of source parameter estimation errors. These theoretical results are completed by the experimental results of localization of the diffusion sources in distilled water by chemical sensor array, showing high performance of sensor array processing approach to the problem considered. A modified version of the well-known CLEAN deconvolution algorithm has been used for experimental data processing.

关键词： sensor array processing NONWAVE FIELD CRAMER-RAO BOUNDS CLEAN ALGORITHM DECONVOLUTION

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