Performance Bounds and Statistical Analysis of DOA Estimation

Delmas, Jean

doi:10.1016/b978-0-12-411597-2.00016-3

Cited by 22 publications

(14 citation statements)

References 106 publications

(251 reference statements)

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“…There exist some relevant works that offer a comprehensive overview of typical performance bounds (including the CRB) and the asymptotic distributions of DOA estimates produced by many celebrated algorithms, see, e.g., [106], [107], but they did not elaborate in detail how a valuable analytical CRB expression can be reached. As emphasized in [23], a detailed and direct derivation of a closed-form CRB expression is important and requires painstaking efforts.…”

Section: F Motivation and Contributionmentioning

confidence: 99%

A Review of Closed-Form Cramér-Rao Bounds for DOA Estimation in the Presence of Gaussian Noise Under a Unified Framework

et al. 2020

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The Cramér-Rao Bound (CRB) for direction of arrival (DOA) estimation has been extensively studied over the past four decades, with a plethora of CRB expressions reported for various parametric models. In the literature, there are different methods to derive a closed-form CRB expression, but many derivations tend to involve intricate matrix manipulations which appear difficult to understand. Starting from the Slepian-Bangs formula and following the simplest derivation approach, this paper reviews a number of closed-form Gaussian CRB expressions for the DOA parameter under a unified framework, based on which all the specific CRB presentations can be derived concisely. The results cover three scenarios: narrowband complex circular signals, narrowband complex noncircular signals, and wideband signals. Three signal models are considered: the deterministic model, the stochastic Gaussian model, and the stochastic Gaussian model with the a priori knowledge that the sources are spatially uncorrelated. Moreover, three Gaussian noise models distinguished by the structure of the noise covariance matrix are concerned: spatially uncorrelated noise with unknown either identical or distinct variances at different sensors, and arbitrary unknown noise. In each scenario, a unified framework for the DOA-related block of the deterministic/stochastic CRB is developed, which encompasses one class of closed-form deterministic CRB expressions and two classes of stochastic ones under the three noise models. Comparisons among different CRBs across classes and scenarios are presented, yielding a series of equalities and inequalities which reflect the benchmark for the estimation efficiency under various situations. Furthermore, validity of all CRB expressions are examined, with some specific results for linear arrays provided, leading to several upper bounds on the number of resolvable Gaussian sources in the underdetermined case. INDEX TERMS Circular and noncircular, Cramér-Rao bound, direction of arrival estimation, narrowband and wideband, underdetermined and overdetermined.

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Section: F Motivation and Contributionmentioning

confidence: 99%

A Review of Closed-Form Cramér-Rao Bounds for DOA Estimation in the Presence of Gaussian Noise Under a Unified Framework

et al. 2020

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“…with the projector onto the noise subspace Π ⊥ A = I M − A(θ, φ)A † (θ, φ). In [44] it is shown that the CRB matrix for the coherent case (C-CRB) can be calculated as…”

Section: B Coherent Doa Estimationmentioning

confidence: 99%

On the Potential of Multi-Mode Antennas for Direction-of-Arrival Estimation

Pöhlmann

Almasri

Zhang

et al. 2019

IEEE Trans. Antennas Propagat.

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A multi-mode antenna (MMA) can be an interesting alternative to a conventional phased antenna array for directionof-arrival (DoA) estimation. By MMA we mean a single physical radiator with multiple ports, which excite different characteristic modes. In contrast to phased arrays, a closed-form mathematical model of the antenna response, like a steering vector, is not straightforward to define for MMAs. Instead one has to rely on calibration measurement or electromagnetic field (EMF) simulation data, which is discrete. To perform DoA estimation, an array interpolation technique (AIT) and wavefield modeling (WM) are suggested as methods with inherent interpolation capabilities, fully taking antenna nonidealities like mutual coupling into account. We present a non-coherent DoA estimator for low-cost receivers and show how coherent DoA estimation and joint DoA and polarization estimation can be performed with MMAs. Utilizing these methods, we assess the DoA estimation performance of an MMA prototype in simulations for both 2D and 3D cases. The results show that WM outperforms AIT for high SNR. The coherent estimation is superior to non-coherent, especially in 3D, because non-coherent suffers from estimation ambiguities. In conclusion, DoA estimation with a single MMA is feasible and accurate.

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“…As discussed in Sec. II, we have to constrain the density generator of the t-distribution to satisfy the constraint in (5).…”

Section: A T-distributed Datamentioning

confidence: 99%

“…Along with the statistical signal models and the related estimation methods, considerable efforts have been dedicated to the derivation of suitable performance bounds for DOA estimation (see e.g. the standard references [3], [4] and the overview provided in [5]). However, most of the works on array processing and, in particular, the ones on lower bounds, assume a Gaussian model for the collected data snapshots.…”

Section: Introductionmentioning

confidence: 99%

Semiparametric Stochastic CRB for DOA Estimation in Elliptical Data Model

Fortunati

Gini

Greco

2019

2019 27th European Signal Processing Conference (EUSIPCO)

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This paper aims at presenting a numerical investigation of the statistical efficiency of the MUSIC (with different covariance matrix estimates) and the IAA-APES Direction of Arrivals (DOAs) estimation algorithms under a general Complex Elliptically Symmetric (CES) distributed measurement model. Specifically, the density generator of the CES-distributed data snapshots is considered as an additional, infinite-dimensional, nuisance parameter. To assess the efficiency in the considered semiparametric setting, the Semiparametric Stochastic Cramér-Rao Bound (SSCRB) is adopted as lower bound for the Mean Square Error (MSE) of the DOA estimators.

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Performance Bounds and Statistical Analysis of DOA Estimation

Cited by 22 publications

References 106 publications

A Review of Closed-Form Cramér-Rao Bounds for DOA Estimation in the Presence of Gaussian Noise Under a Unified Framework

A Review of Closed-Form Cramér-Rao Bounds for DOA Estimation in the Presence of Gaussian Noise Under a Unified Framework

On the Potential of Multi-Mode Antennas for Direction-of-Arrival Estimation

Semiparametric Stochastic CRB for DOA Estimation in Elliptical Data Model

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