A new unified mathematical framework for sensor array processing is proposed. The proposed framework combines Bayesian estimation with stochastic geometry to accommodate prior information, uncertainty in array paramet...
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ISBN:
(纸本)9781479949755
A new unified mathematical framework for sensor array processing is proposed. The proposed framework combines Bayesian estimation with stochastic geometry to accommodate prior information, uncertainty in array parameters, and unknown and stochastically time-varying number of nonstationary sources. A system model for a common signal setting is constructed to demonstrate the proposed framework.
In this work, we consider the self-calibration problem of joint calibration and direction-of-arrival (DOA) estimation using acoustic sensorarrays. Unlike many previous iterative approaches, we propose solvers that ca...
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In this work, we consider the self-calibration problem of joint calibration and direction-of-arrival (DOA) estimation using acoustic sensorarrays. Unlike many previous iterative approaches, we propose solvers that can be readily used for both linear and non-linear arrays for jointly estimating the sensor gain, phase errors, and the source DOAs. We derive these algorithms for both the conventional element-space and covariance data models. We focus on sparse and regular arrays formed using scalar sensors as well as vector sensors. The developed algorithms are obtained by transforming the underlying non-linear calibration model into a linear model, and subsequently by using convex relaxation techniques to estimate the unknown parameters. We also derive identifiability conditions for the existence of a unique solution to the self-calibration problem. To demonstrate the effectiveness of the developed techniques, numerical experiments, and comparisons to the state-of-the-art methods are provided. Finally, the results from an experiment that was performed in an anechoic chamber using an acoustic vector sensorarray are presented to demonstrate the usefulness of the proposed self-calibration techniques.
Existing sensorarray direction-finding algorithms in the open literature simplify the far-field source wavefront as exactly planar in order to facilitate the algorithmic development. In fact, since the wavefront of a...
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Existing sensorarray direction-finding algorithms in the open literature simplify the far-field source wavefront as exactly planar in order to facilitate the algorithmic development. In fact, since the wavefront of a point emitter is necessarily spherical, this planar wavefront assumption should actually be approximate, especially for large-scale arrays. Mismatch between the actual and approximate propagation models would introduce a non-random bias on the performance of the direction-finding algorithms. This non-random bias is inevitable due to the mismatch between the algorithm's presumptions and the data it actually processes. This work derives the mathematical expression of this non-random bias, along with several qualitative analyses. The analysis is carried out using the Taylor-series expansion. Also, the effect of the model mismatch on direction-finding algorithms is evaluated numerically.
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 u...
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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.
A coprime array receiver processes a collection of received-signal snapshots to estimate the autocorrelation matrix of a larger (virtual) uniform linear array, known as coarray. By the received-signal model, this matr...
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A coprime array receiver processes a collection of received-signal snapshots to estimate the autocorrelation matrix of a larger (virtual) uniform linear array, known as coarray. By the received-signal model, this matrix has to be (i) Positive Definite, (ii) Hermitian, (iii) Toeplitz, and (iv) its noise-subspace eigen-values have to be equal. Existing coarray autocorrelation matrix estimates satisfy a subset of the above conditions. In this work, we propose an optimization framework which offers a novel estimate satisfying all four conditions: we propose to iteratively solve a sequence of distinct structure-optimization problems and show that, upon convergence, we provably obtain a single estimate satisfying (i)-(iv). Numerical studies illustrate that the proposed estimate outperforms standard counterparts, both in autocorrelation matrix estimation error and Direction-of-Arrival estimation. (C) 2021 Published by Elsevier B.V.
The direction-of-arrival (DOA) estimation problem with a few noisy snapshots can be formulated as a problem of finding a joint sparse representation of multiple measurement vectors (MMV), and some algorithms based on ...
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The direction-of-arrival (DOA) estimation problem with a few noisy snapshots can be formulated as a problem of finding a joint sparse representation of multiple measurement vectors (MMV), and some algorithms based on compressive sensing (CS), such as the joint l(0) approximation DOA (JLZA-DOA) and Multiple Snapshot Matching Pursuit Direction of Arrival (MSMPDOA) algorithms, have recently been proposed for solving this problem. Compared with the conventional DOA methods, the CS-based methods can achieve super-resolution by using only small number of snapshots, without the necessity of an accurate initialization, with small sensitivity to the correlation of the source signals. However, these CS-based algorithms usually do not work well in low signal-noise ratio (SNR) environment. In addition, the increased number of sensors in massive multiple-input-multiple-output (MIMO) systems lead to a huge matrix, and the matrix inversion operation in each iteration of the CS-based algorithm results in a relatively high computational cost. The purpose of this paper is to propose a novel adaptive filtering algorithm, i.e., the l(2,0)-least mean square (l(2.0)-LMS) algorithm, which can be viewed as a generalization of the l(0)-LMS algorithm for single measurement vector (SMV) problem. Our proposed algorithm incorporates a mixed norm (l(2)(,0)-norm) to treat the joint sparsity and inherits the robustness against noise and the low complexity of the l(0)-LMS algorithm, and can thus work well for massive MIMO systems. Numerical experiments demonstrate that the proposed algorithm can achieve much better estimation performance with a lower computational cost than the existing ones. (C) 2019 Elsevier Inc. All rights reserved.
This paper presents a novel sequential estimator for the direction-of-arrival and polynomial coefficients of wideband polynomial-phase signals impinging on a sensorarray. Addressing the computational challenges of ma...
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This paper presents a novel sequential estimator for the direction-of-arrival and polynomial coefficients of wideband polynomial-phase signals impinging on a sensorarray. Addressing the computational challenges of maximum-likelihood estimation for this problem, we propose a method leveraging random sampling consensus (RANSAC) applied to the time-frequency spatial signatures of sources. Our approach supports multiple sources and higher-order polynomials by employing coherent arrayprocessing and sequential approximations of the maximum-likelihood cost function. We also propose a low-complexity variant that estimates source directions via angular domain random sampling. Numerical evaluations demonstrate that the proposed methods achieve Cramér-Rao bounds in challenging multi-source scenarios, including closely spaced time-frequency spatial signatures, highlighting their suitability for advanced radar signal processing applications.
Blind gain and phase calibration (BGPC) is a bilinear inverse problem involving the determination of unknown gains and phases of the sensing system, and the unknown signal, jointly. BGPC arises in numerous application...
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Blind gain and phase calibration (BGPC) is a bilinear inverse problem involving the determination of unknown gains and phases of the sensing system, and the unknown signal, jointly. BGPC arises in numerous applications, e.g., blind albedo estimation in inverse rendering, synthetic aperture radar autofocus, and sensorarray auto-calibration. In some cases, sparse structure in the unknown signal alleviates the illposedness of BGPC. Recently, there has been renewed interest in solutions to BGPC with careful analysis of error bounds. In this paper, we formulate BGPC as an eigenvalue/eigenvector problem and propose to solve it via power iteration, or in the sparsity or joint sparsity case, via truncated power iteration. Under certain assumptions, the unknown gains, phases, and the unknown signal can be recovered simultaneously. Numerical experiments show that power iteration algorithms work not only in the regime predicted by our main results, but also in regimes where theoretical analysis is limited. We also show that our power iteration algorithms for BGPC compare favorably with competing algorithms in adversarial conditions, e.g., with noisy measurement or with a bad initial estimate.
We revisit the problem of blind calibration of uniform linear sensors arrays for narrowband signals and set the premises for the derivation of the optimal blind calibration scheme. In particular, instead of taking the...
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ISBN:
(纸本)9789082797039
We revisit the problem of blind calibration of uniform linear sensors arrays for narrowband signals and set the premises for the derivation of the optimal blind calibration scheme. In particular, instead of taking the direct (rather involved) Maximum Likelihood (ML) approach for joint estimation of all the unknown model parameters, we follow Paulraj and Kailath's classical approach in exploiting the special (Toeplitz) structure of the observed covariance. However, we offer a substantial improvement over Paulraj and Kailath's Least Squares (LS) estimate by using asymptotic approximations in order to obtain simple, (quasi-)linear Weighted LS (WLS) estimates of the sensors' gains and phases offsets with asymptotically optimal weighting. As we show in simulation experiments, our WLS estimates exhibit near-optimal performance, with a considerable improvement (reaching an order of magnitude and more) in the resulting mean squared errors, w.r.t. the corresponding ordinary LS estimates. We also briefly explain how the methodology derived in this work may be utilized in order to obtain (by certain modifications) the asymptotically optimal ML estimates w.r.t. the raw data via a (quasi)-linear WLS estimate.
Disturbed by strong jamming, the compressive sensing (CS) based direction-of-arrival (DOA) estimation methods in colocated multiple-input-multiple-output (MIMO) radars are distorted easily. In this paper, a CS based a...
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ISBN:
(纸本)9781538668122;9781538668115
Disturbed by strong jamming, the compressive sensing (CS) based direction-of-arrival (DOA) estimation methods in colocated multiple-input-multiple-output (MIMO) radars are distorted easily. In this paper, a CS based anti-jamming DOA estimation method employing a blocking matrix is proposed. In the new DOA estimation method, the QR decomposition algorithm is used to construct a blocking matrix which is orthogonal to the steering vector of jamming. After the preprocessing with the blocking matrix, the jamming component is removed from the received snapshots. Then, the DOA estimation problem with the blocking matrix is formulated as a CS sparse recovery problem, and CS algorithms are used to solve it. Computer simulations show that the proposed method performs than the traditional methods.
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