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Biochemical transport modeling and Bayesian source estimation in realistic environments

IEEE TRANSACTIONS ON SIGNAL processing 2007年第6期55卷 2520-2532页

作者： Ortner, Mathias Nehorai, Arye Jeremic, Aleksandar Washington Univ St Louis MO 63130 USA McMaster Univ Dept Elect & Comp Engn Hamilton ON L8S 4K1 Canada

Early detection and estimation of the spread of a biochemical contaminant are major issues in many applications, such as homeland security and pollution monitoring. We present an integrated approach combining the measurements given by an array of biochemical sensors with a physical model of the dispersion and statistical analysis to solve these problems and provide system performance measures. We approximate the dispersion model of a contaminant in a realistic environment through numerical simulations of reflected stochastic diffusions describing the microscopic transport phenomena due to wind and chemical diffusion and use the Feynmann-Kac formula. We consider arbitrary complex geometries and account for wind turbulence. Numerical examples are presented for two real-world scenarios: an urban area and an indoor ventilation duct. Localizing the dispersive sources is useful for decontamination purposes and estimation of the cloud evolution. To solve the associated inverse problem, we propose a Bayesian framework based on a random field that is particularly powerful for localizing multiple sources with small amounts of measurements.

关键词： biochemical dispersion Feynman-Kac inverse problem random field sensor array processing source estimation

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Group decorrelation enhanced subspace method for identifying FIR MIMO channels driven by unknown uncorrelated colored sources

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IEEE TRANSACTIONS ON SIGNAL processing 2005年第12期53卷 4429-4441页

作者： An, SJ Hua, YB Manton, JH Fang, Z Australian Natl Univ Res Sch Informat Sci & Engn Dept Informat Engn Canberra ACT 0200 Australia Curtin Univ Technol Dept Comp Bentley WA 6102 Australia Univ Calif Riverside Dept Elect Engn Riverside CA 92521 USA

Identification of finite-impulse-response (FIR) and multiple-input multiple-output (MIMO) channels driven by unknown uncorrelated colored sources is a challenging problem. In this paper, a group decorrelation enhanced subspace (GDES) method is presented. The GDES method uses the idea of subspace decomposition and signal decorrelation more effectively than the joint diagonalization enhanced subspace (JDES) method previously reported in the literature. The GDES method has a much better performance than the JDES method. The correctness of the GDES method is proved assuming that 1) the channel matrix is irreducible and column reduced and 2) the source spectral matrix has distinct diagonal functions. However, the GDES method has an inherent ability to trade off between the required condition on the channel matrix and that on the source spectral matrix. Simulations show that the GDES method yields good results even when the channel matrix is not irreducible, which is not possible at all for the JDES method.

关键词： adaptive signal processing blind deconvolution blind identification machine learning MIMO channels sensor array processing source separation system identification

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

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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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Blind spatial signature estimation via time-varying user power loading and parallel factor analysis

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IEEE TRANSACTIONS ON SIGNAL processing 2005年第5期53卷 1697-1710页

作者： Rong, Y Vorobyov, SA Gershman, AB Sidiropoulos, ND Univ Duisburg Essen Dept Commun Syst D-47057 Duisburg Germany Tech Univ Crete Dept Elect & Comp Engn Khania 73100 Greece Univ Minnesota Dept Elect & Comp Engn Minneapolis MN 55455 USA

In this paper, the problem of blind spatial signature estimation using the parallel factor (PARAFAC) analysis model is addressed in application to wireless. communications. A time-varying user power loading in the uplink mode is proposed to make the model identifiable and to enable application of PARAFAC analysis. Then, identifiability issues are studied in detail and closed-form expressions for the corresponding modified Cramer-Rao bound (CRB) are obtained. Furthermore, two blind spatial signature estimation algorithms are developed. The first technique is based on the PARAFAC fitting trilinear alternating least squares (TALS) regression procedure, whereas the second one makes use of the joint approximate diagonalization algorithm. These techniques do not require any knowledge of the propagation channel and/or sensor array manifold and are applicable to a more general class of scenarios than earlier approaches to blind spatial signature estimation.

关键词： blind spatial signature estimation parallel factor analysis sensor array processing

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A sequential detector for biochemical release in realistic environments

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IEEE TRANSACTIONS ON SIGNAL processing 2007年第8期55卷 4173-4182页

作者： Ortner, Mathias Nehorai, Arye Univ Illinois Dept Elect & Comp Engn Chicago IL 60607 USA Washington Univ Dept Elect & Syst Engn St Louis MO 63130 USA

We develop a sequential detector for the release of a biochemical substance, with potential applications in environmental security. The proposed detector provides online detection of the appearance of a biochemical source in realistic complex environments. To obtain optimal performance, we use an integrated approach combining statistical analysis of measurements given by an array of biochemical sensors with a physical model of the dispersion, amenable to arbitrary geometries and wind turbulence. We first focus on formulating a detector that is applicable in the presence of unknown source parameters (e.g., release time, intensity, and location). We then derive a bound on the expected delay before a false detection in order to select the threshold of the test. For a fixed false-alarm rate, we obtain the detection probability of a release as a function of its location and initial concentration. Numerical examples illustrate the applicability of our methods to real-world scenarios of an urban area and indoor ventilation duct.

关键词： biochemical dispersion detection Feynman-Kac Monte Carlo realistic framework sensor array processing sequential detection

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Stochastic maximum-likelihood DOA estimation in the presence of unknown nonuniform noise

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IEEE TRANSACTIONS ON SIGNAL processing 2008年第7期56卷 3038-3044页

作者： Chen, Chiao En Lorenzelli, Flavio Hudson, Ralph. E. Yao, Kung Univ Calif Los Angeles Dept Elect Engn Los Angeles CA 90095 USA

This correspondence investigates the direction-of-arrival (DOA) estimation of multiple narrowband sources in the presence of nonuniform white noise with an arbitrary diagonal covariance matrix. While both the deterministic and stochastic Cramer-Rao bound (CRB) and the deterministic maximum-likelihood (ML) DOA estimator under this model have been derived by Pesavento and Gershman, the stochastic ML DOA estimator under the same setting is still not available in the literature. In this correspondence, a new stochastic ML DOA estimator is derived. Its implementation is based on an iterative procedure which concentrates the log-likelihood function with respect to the signal and noise nuisance parameters in a stepwise fashion. A modified inverse iteration algorithm is also presented for the estimation of the noise parameters. Simulation results have shown that the proposed algorithm is able to provide significant performance improvement over the conventional uniform ML estimator in nonuniform noise environments and require only a few iterations to converge to the nonuniform stochastic CRB.

关键词： direction-of-arrival (DOA) estimation nonuniform noise sensor array processing stochastic maximum likelihood (ML) algorithm

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Subspace Methods for Joint Sparse Recovery

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IEEE TRANSACTIONS ON INFORMATION THEORY 2012年第6期58卷 3613-3641页

作者： Lee, Kiryung Bresler, Yoram Junge, Marius Univ Illinois Coordinated Sci Lab Urbana IL 61801 USA Univ Illinois Dept Elect & Comp Engn Urbana IL 61801 USA Univ Illinois Dept Math Urbana IL 61801 USA

We propose robust and efficient algorithms for the joint sparse recovery problem in compressed sensing, which simultaneously recover the supports of jointly sparse signals from their multiple measurement vectors obtained through a common sensing matrix. In a favorable situation, the unknown matrix, which consists of the jointly sparse signals, has linearly independent nonzero rows. In this case, the MUltiple SIgnal Classification (MUSIC) algorithm, originally proposed by Schmidt for the direction of arrival estimation problem in sensor array processing and later proposed and analyzed for joint sparse recovery by Feng and Bresler, provides a guarantee with the minimum number of measurements. We focus instead on the unfavorable but practically significant case of rank defect or ill-conditioning. This situation arises with a limited number of measurement vectors, or with highly correlated signal components. In this case, MUSIC fails and, in practice, none of the existing methods can consistently approach the fundamental limit. We propose subspace-augmented MUSIC (SA-MUSIC), which improves on MUSIC such that the support is reliably recovered under such unfavorable conditions. Combined with a subspace-based greedy algorithm, known as Orthogonal Subspace Matching Pursuit, which is also proposed and analyzed in this paper, SA-MUSIC provides a computationally efficient algorithm with a performance guarantee. The performance guarantees are given in terms of a version of the restricted isometry property. In particular, we also present a non-asymptotic perturbation analysis of the signal subspace estimation step, which has been missing in the previous studies of MUSIC.

关键词： Compressed sensing joint sparsity multiple measurement vectors (MMV) restricted isometry property (RIP) sensor array processing spectrum-blind sampling subspace estimation

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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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Detecting and estimating biochemical dispersion of a moving source in a semi-infinite medium

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IEEE TRANSACTIONS ON SIGNAL processing 2006年第6期54卷 2213-2225页

作者： Zhao, Tong Nehorai, Arye Univ Illinois Dept Elect & Comp Engn Chicago IL 60607 USA

Statistical methods for detecting and estimating biochemical dispersion by a moving source using model-based integrated sensor array processing are developed. Two possible cases are considered: a homogeneous semi-infinite medium (corresponding to the environment such as air above the ground for an airborne source) or a two-layer semi-infinite medium (e.g., shallow water). The proposed methods can be extended to more complex scenarios. The goals are to detect and localize the biochemical source, determine the space-time concentration distribution of the dispersion, and predict its cloud evolution. Potential applications include security, environmental monitoring, pollution control, simulating hazardous accidents, and explosives detection. Diffusion models of the biochemical substance concentration distribution are derived under various boundary and environmental conditions. A maximum-likelihood algorithm is used to estimate the biochemical concentration distribution in space and time, and the Cramer-Rao bound is computed to analyze its performance. Two detectors (generalized-likelihood ratio test (GLRT) and a mean-difference detector) are derived and then their performances are determined in terms of the probabilities of detection and false alarm. The results can be used to design the sensor array for optimal performance. Numerical examples illustrate the results of the concentration distribution and the performances of the proposed methods.

关键词： biochemical dispersion estimation moving sources sensor array processing signal detection

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Asymptotically Optimal Blind Calibration of Uniform Linear sensor arrays for Narrowband Gaussian Signals

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IEEE TRANSACTIONS ON SIGNAL processing 2020年 68卷 5322-5333页

作者： Weiss, Amir Yeredor, Arie Weizmann Inst Sci Fac Math & Comp Sci Dept Comp Sci & Appl Math IL-7610001 Rehovot Israel Tel Aviv Univ Fac Engn Sch Elect Engn IL-69978 Tel Aviv Israel

An asymptotically optimal blind calibration scheme of uniform linear arrays for narrowband Gaussian signals is proposed. Rather than taking the direct Maximum Likelihood (ML) approach for joint estimation of all the unknown model parameters, which leads to a multi-dimensional optimization problem with no closed-form solution, we revisit Paulraj and Kailath's (P-K's) classical approach in exploiting the special (Toeplitz) structure of the observations' covariance. However, we offer a substantial improvement over P-K's ordinary Least Squares (LS) estimates by using asymptotic approximations in order to obtain simple, non-iterative, (quasi-)linear Optimally-Weighted LS (OWLS) estimates of the sensors gains and phases offsets with asymptotically optimal weighting, based only on the empirical covariance matrix of the measurements. Moreover, we prove that our resulting estimates are also asymptotically optimal w.r.t. the raw data, and can therefore be deemed equivalent to the ML Estimates (MLE), which are otherwise obtained by joint ML estimation of all the unknown model parameters. After deriving computationally convenient expressions of the respective Cramer-Rao lower bounds, we also show that our estimates offer improved performance when applied to non-Gaussian signals (and/or noise) as quasi-MLE in a similar setting. The optimal performance of our estimates is demonstrated in simulation experiments, with a considerable improvement (reaching an order of magnitude and more) in the resulting mean squared errors w.r.t. P-K's ordinary LS estimates. We also demonstrate the improved accuracy in a multiple-sources directions-of-arrivals estimation task.

关键词： sensor array processing direction-of-arrival gain estimation phase estimation self calibration weighted least squares maximum likelihood Cramer-Rao lower bound

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