Cramér-Rao Bound for DOA Estimators Under the Partial Relaxation Framework: Derivation and Comparison

Trinh-Hoang, Minh; Viberg, Mats; Pesavento, Marius

doi:10.1109/tsp.2020.2992855

Cited by 9 publications

(9 citation statements)

References 42 publications

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“…As we will see, the processes in (3) and ( 4), although having the same spectra and covariance functions, display considerable differences when it comes to estimating the covariances (5). In particular, we will show that the convergence, as T → ∞, of the covariance estimates to their respective expectations depend on the structures of dµ x and dµ y , as well as on the choice of model ( 3) or (4). Specifically, we are interested in under what conditions the estimators in (5) are consistent estimators.…”

Section: Signal Modelmentioning

confidence: 74%

“…Modeling signals that impinge on sensor arrays appear in a large variety of signal processing applications, including radar, sonar, and audio signal processing [1]- [3]. Commonly in such applications, one seeks a spatial spectrum, describing the distribution of signal energy over the space of interest, e.g., azimuth and elevation in direction of arrival (DoA) estimation [4], allowing for localizing and tracking targets [5], [6] or for performing spatial filtering of the sensor signals [7]. In practice, the spatial spectrum is often inferred from the array covariance matrix as in, e.g., optimal filtering such as the Capon method [8], subspace methods as ESPRIT and MUSIC [9], [10], as well as more recent contributions exploiting sparse representations [11] as well as knowledge of underlying dynamics [6].…”

Section: Introductionmentioning

confidence: 99%

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Mixed-Spectrum Signals -- Discrete Approximations and Variance Expressions for Covariance Estimates

Elvander,

Karlsson

2021

Preprint

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The estimation of the covariance function of a stochastic process, or signal, is of integral importance for a multitude of signal processing applications. In this work, we derive closed-form expressions for the variance of covariance estimates for mixed-spectrum signals, i.e., spectra containing both absolutely continuous and singular parts. The results cover both finite-sample and asymptotic regimes, allowing for assessing the exact speed of convergence of estimates to their expectations, as well as their limiting behavior. As is shown, such covariance estimates may converge even for non-ergodic processes. Furthermore, we consider approximating signals with arbitrary spectral densities by sequences of singular spectrum, i.e., sinusoidal, processes, and derive the limiting behavior of covariance estimates as both the sample size and the number of sinusoidal components tend to infinity. We show that the asymptotic regime variance can be described by a time-frequency resolution product, with dramatically different behavior depending on how the sinusoidal approximation is constructed. In a few numerical examples we illustrate the theory and the corresponding implications for direction of arrival estimation.

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Section: Signal Modelmentioning

confidence: 74%

Section: Introductionmentioning

confidence: 99%

Mixed-Spectrum Signals -- Discrete Approximations and Variance Expressions for Covariance Estimates

Elvander,

Karlsson

2021

Preprint

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“…In (2), the speckles d(t) and e(t) are i.i.d. vectors drawn from d(t) ∼ CN (0, I) and e(t) ∼ CN 0, σ 2 I , respectively.…”

Section: Signal Modelmentioning

confidence: 99%

“…Recently, a class of Direction-of-Arrival (DOA) estimators have been proposed under the Partial Relaxation (PR) framework [1,2]. Similar to the MUSIC algorithm [3], PR estimators employ a one-dimensional spectral search to estimate the DOAs.…”

Section: Introductionmentioning

confidence: 99%

A Partially-Relaxed Robust DOA Estimator Under Non-Gaussian Low-Rank Interference and Noise

Trinh-Hoang

Korso

Pesavento

2021

ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)

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In practical applications, non-Gaussianity of the signal at the sensor array is detrimental to the performance of conventional Direction-of-Arrival (DOA) estimators developed under the Gaussian model. In this paper, we propose a novel robust DOA estimator from the data collected at the sensor array under the corruption of non-Gaussian interference and noise. Additionally, the Cramér-Rao bound for DOA parameters under the considered signal model is derived. Simulation results show that the proposed estimator exhibits near-optimal estimation performance under the assumed model while being robust to model mismatch and/or the presence of outliers.

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“…The popularity of the subspace-based methods over, for example, near optimal maximum likelihood (ML) estimators [19]- [21], comes from the fact that they achieve good estimation accuracy along with affordable computational complexity in contrast to the prohibitive computational cost of implementing ML estimators. In recent years, several works have proposed competitive algorithms to fill the performance gap between subspace-based methods and ML estimators including root-swap root-MUSIC [22], enhanced principal-singular-vector utilization for modal analysis (EPUMA) [23], standard ESPRIT using generalized least squares (SE GLS) and unitary ESPRIT using generalized least squares (UE GLS) [24], partial relaxation (PR)-based approaches [25], [26], root-clustering algorithm and root-certificate algorithm [27]. The aim of the aforementioned methods is to achieve an adequate performance in challenging scenarios like scarcity of available data samples, low signal-to-noise ratio (SNR), and/or presence of some correlated or even coherent sources.…”

Section: Introductionmentioning

confidence: 99%

DOA Estimation in Nonuniform Sensor Noise

Esfandiari¹,

Vorobyov²

2021

Preprint

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The problem of direction-of-arrival (DOA) estimation in the presence of nonuniform sensor noise is considered and a novel algorithm is developed. The algorithm consists of three phases. First, the diagonal nonuniform sensor noise covariance matrix is estimated using an iterative procedure that requires only few iterations to obtain an accurate estimate. The asymptotic variance of one iteration is derived for the proposed noise covariance estimator. Second, a forward-only rooting-based DOA estimator as well as its forward-backward averaging extension are developed for DOA estimation. The DOA estimators take advantage of using second-order statistics of signal subspace perturbation in constructing a weight matrix of a properly designed generalized least squares minimization problem. Despite the fact that these DOA estimators are iterative, only a few iterations are sufficient to reach accurate results. The asymptotic performance of these DOA estimators is also investigated. Third, a newly designed DOA selection strategy with reasonable computational cost is developed to select L actual sources out of 2L candidates generated at the second phase. Numerical simulations are conducted in order to establish the considerable superiority of the proposed algorithm compared to the the existing state-of-the-art methods in challenging scenarios in both cases of uniform and nonuniform sensor noise.

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Cramér-Rao Bound for DOA Estimators Under the Partial Relaxation Framework: Derivation and Comparison

Cited by 9 publications

References 42 publications

Mixed-Spectrum Signals -- Discrete Approximations and Variance Expressions for Covariance Estimates

Mixed-Spectrum Signals -- Discrete Approximations and Variance Expressions for Covariance Estimates

A Partially-Relaxed Robust DOA Estimator Under Non-Gaussian Low-Rank Interference and Noise

DOA Estimation in Nonuniform Sensor Noise

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