Estimation of the directions of arrival of signals in unknown correlated noise. I. The MAP approach and its implementation

Wong, K.M.; Reilly, J.P.; Wu, Qiang; Qiao, Sanzheng

doi:10.1109/78.150002

Cited by 72 publications

(38 citation statements)

References 24 publications

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“…Despite its drawbacks, it is important to note that for applications where the eigenvalues are of minor importance, employing the Jeffreys prior on the unknown covariance may still be a suitable choice. The reason for this is that this prior, although in some sense unsound with respect to the eigenvalues, has the advantage of enabling analytical marginalization of the covariance matrix [18]. Due to this beneficial property, it is of interest to circumvent its weakness regarding the distribution of the eigenvalues while maintaining the possibility of analytical marginalization.…”

Section: Diagmentioning

confidence: 99%

“…For this parametrization and the complex data model, the prior is given by (14) (see [18]). Here, the differential volume element is given by Re Im .…”

Section: A Jeffreys Priormentioning

confidence: 99%

“…Deriving such priors is far from straightforward. In fact, formal ways of obtaining themarestillunderinvestigation [16].Amongthepriors that we investigate are common noninformative alternatives such as the Jeffreys prior [17], [18] and the Reference prior [9], [19]. Observations made in connection to this will also lead us to propose priors of our own.…”

mentioning

confidence: 99%

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On posterior distributions for signals in Gaussian noise with unknown covariance matrix

Svensson

Lundberg

2005

IEEE Trans. Signal Process.

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Abstract-A Bayesian approach to estimate parameters of signals embedded in complex Gaussian noise with unknown color is presented. The study specifically focuses on a Bayesian treatment of the unknown noise covariance matrix making up a nuisance parameter in such problems. By integrating out uncertainties regarding the noise color, an enhanced ability to estimate both the signal parameters as well as properties of the error is exploited. Several noninformative priors for the covariance matrix, such as the reference prior, the Jeffreys prior, and modifications to this, are considered. Some of the priors result in analytical solutions, whereas others demand numerical approximations. In the linear signal model, connections are made between the standard Adaptive Maximum Likelihood (AML) estimate and a Bayesian solution using the Jeffreys prior. With adjustments to the Jeffreys prior, correspondence to the regularized solution is also established. This in turn enables a formal treatment of the regularization parameter. Simulations indicate that significant improvements, compared to the AML estimator, can be obtained by considering both the derived regularized solutions as well as the one obtained using the reference prior. The simulations also indicate the possibility of enhancing the predictions of properties of the error as uncertainties in the noise color are acknowledged.

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Section: Diagmentioning

confidence: 99%

“…For this parametrization and the complex data model, the prior is given by (14) (see [18]). Here, the differential volume element is given by Re Im .…”

Section: A Jeffreys Priormentioning

confidence: 99%

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On posterior distributions for signals in Gaussian noise with unknown covariance matrix

Svensson

Lundberg

2005

IEEE Trans. Signal Process.

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“…A reasonable criterion used in array processing applications is to choose as an estimate the parameter vector that minimizes the Frobenius norm of the error matrix [24], [25]; that iŝ…”

Section: A Practical Estimation Algorithmmentioning

confidence: 99%

Estimation of the number of sources in unbalanced arrays via information theoretic criteria

Fishler

Poor

2005

IEEE Trans. Signal Process.

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Abstract-Estimating the number of sources impinging on an array of sensors is a well known and well investigated problem. A common approach for solving this problem is to use an information theoretic criterion, such as Minimum Description Length (MDL) or the Akaike Information Criterion (AIC). The MDL estimator is known to be a consistent estimator, robust against deviations from the Gaussian assumption, and non-robust against deviations from the point source and/or temporally or spatially white additive noise assumptions. Over the years several alternative estimation algorithms have been proposed and tested. Usually, these algorithms are shown, using computer simulations, to have improved performance over the MDL estimator, and to be robust against deviations from the assumed spatial model. Nevertheless, these robust algorithms have high computational complexity, requiring several multi-dimensional searches.In this paper, motivated by real life problems, a systematic approach toward the problem of robust estimation of the number of sources using information theoretic criteria is taken. An MDL type estimator that is robust against deviation from assumption of equal noise level across the array is studied. The consistency of this estimator, even when deviations from the equal noise level assumption occur, is proven. A novel low-complexity implementation method avoiding the need for multi-dimensional searches is presented as well, making this estimator a favorable choice for practical applications.

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“…Practically, DOA estimation using antenna array processing is a very efficient technique that has been used for a long time. Many methods have been proposed to estimate the DOA such as traditional maximum entropy and maximum likelihood methods or eigen-structure methods which utilize orthogonality between signal subspace and noise subspace [1][2][3][4][5]. From the various methods that have been proposed, eigen-structure methods have received wide attention because of their relatively high resolution [1].…”

Section: Introductionmentioning

confidence: 99%

Doa and Power Estimation by Controlling the Roots of the Antenna Array Polynomial

Mismar¹,

Ismail²

2016

PIER M

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Abstract-A new direction-of-arrival (DOA) and power estimation method of unknown number of source signals is proposed. The direction and power of coherent and/or noncoherent signals are estimated by controlling the roots of the array polynomial on the unit circle. The genetic algorithm is used to find the phases of the array polynomial roots that minimize the array output power. The pseudo-spectrum is obtained by phase rotation of the estimated roots, and the real power spectrum is derived from the pseudo-spectrum and the array factor. The results indicate that the direction of arrivals, power of the signals, and number of source signals are estimated from the real power spectrum.

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Estimation of the directions of arrival of signals in unknown correlated noise. I. The MAP approach and its implementation

Cited by 72 publications

References 24 publications

On posterior distributions for signals in Gaussian noise with unknown covariance matrix

On posterior distributions for signals in Gaussian noise with unknown covariance matrix

Estimation of the number of sources in unbalanced arrays via information theoretic criteria

Doa and Power Estimation by Controlling the Roots of the Antenna Array Polynomial

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