The maximum likelihood (ML) and maximum a posteriori (MAP) estimation techniques are widely used to address the direction-of-arrival (DOA) estimation problems, an important topic in sensor array processing. Convention...
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ISBN:
(纸本)9781479999897
The maximum likelihood (ML) and maximum a posteriori (MAP) estimation techniques are widely used to address the direction-of-arrival (DOA) estimation problems, an important topic in sensor array processing. Conventionally the ML estimators in the DOA estimation context assume the sensor noise to follow a Gaussian distribution. In real-life application, however, this assumption is sometimes not valid, and it is often more accurate to model the noise as a non-Gaussian process. In this paper we derive an iterative ML as well as an iterative MAP estimation algorithm for the DOA estimation problem under the spherically invariant random process noise assumption, one of the most popular non-Gaussian models, especially in the radar context. Numerical simulation results are provided to assess our proposed algorithms and to show their advantage in terms of performance over the conventional ML algorithm.
Wideband conformal arrays are increasingly used in modern communication systems due to their flexibility in attaching to arbitrary surfaces. However, designing such arrays has been limited to pattern synthesis techniq...
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Wideband conformal arrays are increasingly used in modern communication systems due to their flexibility in attaching to arbitrary surfaces. However, designing such arrays has been limited to pattern synthesis techniques because of the complexity of their geometrical analysis and the different contribution of each sensor in the array response. These techniques are basically non-adaptive data independent methods and are not suitable for dynamic environments. In this letter, the conventional Frost space-time wideband beamforming method and its associated Linearly Constrained Minimum Variance (LCMV) algorithm are employed to develop an adaptive wideband beamforming method for an arbitrarily shaped conformal array. The constraint matrix used in the LCMV algorithm is modified to include the pattern of each individual sensor, thereby incorporating the element responses into the weight adjustment algorithm. A set of angle-frequency constraints are used in the proposed LCMV formulation to achieve the desired frequency-invariant beampattern. It is shown by a comprehensive example of a typical conical array that the desired beampattern can be obtained in an adaptive manner for a time-varying target.
An important problem in sensor array processing is the estimation of the number of transmitted signals. Most of the proposed solutions rely on the assumption of uniform additive white noise on the measured signals. In...
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ISBN:
(纸本)9781479928934
An important problem in sensor array processing is the estimation of the number of transmitted signals. Most of the proposed solutions rely on the assumption of uniform additive white noise on the measured signals. In this paper, an approach for estimating the number of sources in the presence of nonuniform white noise is proposed. The method is based on the computation of the maximal corank of the covariance matrix of the noisy data in the Frisch scheme context. The effectiveness of the method is tested by means of Monte Carlo simulations.
We consider the problem of dipole source signals estimation in electroencephalography (EEG) using IDeamforming techniques in ill-conditioned. settings. We take advantage of the link between the linearly constrained mi...
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ISBN:
(纸本)9781479903566
We consider the problem of dipole source signals estimation in electroencephalography (EEG) using IDeamforming techniques in ill-conditioned. settings. We take advantage of the link between the linearly constrained minimum-variance (LCMV) beamformer in sensor array processing and the best linear unbiased estimator (BLUE) in linear regression modeling. We show that the recently introduced reducedrank extension of BLUE, named minimum-variance pseudounbiased reduced-rank estimator (MV-PURE), achieves much lower estimation error not only than LCMV beamformer, but also than the previously derived reduced-rank principal components (PC) and cross-spectral metrics (CSM) beamformers in ill-conditioned settings. The practical scenarios where the considered estimation model becomes ill-conditioned are discussed, then we show the applicability of MV-PURE dipole source estimator under those conditions through realistic simulations.
Suppression of strong, spatially correlated background interference is a challenge associated with electroencephalography (EEG) source localization problems. The most common way of dealing with such interference is th...
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Suppression of strong, spatially correlated background interference is a challenge associated with electroencephalography (EEG) source localization problems. The most common way of dealing with such interference is through the use of a prewhitening transformation based on an estimate of the covariance of the interference plus noise. This approach is based on strong assumptions regarding temporal stationarity of the data, which do not commonly hold in EEG applications. In addition, prewhitening cannot typically be implemented directly due to ill conditioning of the covariance matrix, and ad hoc regularization is often necessary. Using both simulation examples and experiments involving real EEG data with auditory evoked responses, we demonstrate that a straightforward interference projection method is significantly more robust than prewhitening for EEG source localization.
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 obtai...
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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.
Source signals that have strong temporal correlation can pose a challenge for high-resolution EEG source localization algorithms. In this paper, we present two methods that are able to accurately locate highly correla...
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Source signals that have strong temporal correlation can pose a challenge for high-resolution EEG source localization algorithms. In this paper, we present two methods that are able to accurately locate highly correlated sources in situations where other high-resolution methods such as multiple signal classification and linearly constrained minimum variance beamforming fail. These methods are based on approximations to the optimal maximum likelihood (ML) approach, but offer significant computational advantages over ML when estimates of the equivalent EEG dipole orientation and moment are required in addition to the source location. The first method uses a two-stage approach in which localization is performed assuming an unstructured dipole moment model, and then the dipole orientation is obtained by using these estimates in a second step. The second method is based on the use of the noise subspace fitting concept, and has been shown to provide performance that is asymptotically equivalent to the direct ML method. Both techniques lead to a considerably simpler optimization than ML since the estimation of the source locations and dipole moments is decoupled. Examples using data from simulations and auditory experiments are presented to illustrate the performance of the algorithms.
The problem of estimating the regularization parameter for source localization in sparse-regularization framework is considered in this paper. We employ the distribution about every entry of the square of the Frobeniu...
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ISBN:
(纸本)9781424484447
The problem of estimating the regularization parameter for source localization in sparse-regularization framework is considered in this paper. We employ the distribution about every entry of the square of the Frobenius norm of noise to obtain a larger and more appropriate regularization parameter. The paper analyzes the reason that we can not simply set it equal to the square of the Frobenius norm of noise and presents the estimation in two practical cases: one works without taking singular value decomposition (SVD) of sensor outputs;the other works after that pretreatment for large data quantity. The simulation results demonstrate that the proposed method has many advantages, including enhancing resolution, effectively suppressing spurious peaks, improving robustness to noise, as well as increasing the number of resolvable sources.
A set of vectors is called jointly sparse when its elements share a common sparsity pattern. We demonstrate how the direction-of-arrival (DOA) estimation problem can be cast as the problem of recovering a joint-sparse...
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A set of vectors is called jointly sparse when its elements share a common sparsity pattern. We demonstrate how the direction-of-arrival (DOA) estimation problem can be cast as the problem of recovering a joint-sparse representation. We consider both narrowband and broadband scenarios. We propose to minimize a mixed l(2,0) norm approximation to deal with the joint-sparse recovery problem. Our algorithm can resolve closely spaced and highly correlated sources using a small number of noisy snapshots. Furthermore, the number of sources need not be known a priori. In addition, our algorithm can handle more sources than other state-of-the-art algorithms. For the broadband DOA estimation problem, our algorithm allows relaxing the half-wavelength spacing restriction, which leads to a significant improvement in the resolution limit.
By simultaneously transmitting and receiving mul- tiple coded waveforms with multiple-input multiple-output (MIMO) configuration,the MIMO radar appears more at- tractive than the traditional phased-array radar in perf...
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ISBN:
(纸本)9781457713675
By simultaneously transmitting and receiving mul- tiple coded waveforms with multiple-input multiple-output (MIMO) configuration,the MIMO radar appears more at- tractive than the traditional phased-array radar in perfor- ***,when applied in the MIMO radar system,the classical subspace-based methods for high-resolution DOA estimation are computationally prohibited as the observed covariance matrix is the Krvnecker product of the transmit and rcccivc covariancc matriccs,considcrably incrcasing the sizc of the covariance *** cure this problem,a computationally efficient subspace-based method for DOA estimation is ad- dressed in this *** proposed method only needs vector- vector operations,and does not involve the covariance matrix calculation and its EVD or inversion ***,the proposed method is computationally attractive for practical *** results are included to illustrate the performance of the proposed method.
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