Direction finding of multiple emitters by spatial sparsity and linear programming

Picard, Joseph S.; Weiss, A.J.

doi:10.1109/iscit.2009.5341085

Cited by 15 publications

(14 citation statements)

References 20 publications

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“…6 Subarray processing [1], [127] utilizes a similar principle wherein a large array is separated into smaller subarrays for processing to reduce complexity. Exploiting input structure is a fairly common strategy in the computation of covariance matrices in array processing, e.g., [71], [100], [128], [134], [137], [160], [180].…”

Section: The Challenges Of Exploiting Input Structurementioning

confidence: 99%

Graphical model driven methods in adaptive system identification

Yellepeddi¹

2016

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Identifying and tracking an unknown linear system from observations of its inputs and outputs is a problem at the heart of many different applications. Due to the complexity and rapid variability of modern systems, there is extensive interest in solving the problem with as little data and computation as possible.This thesis introduces the novel approach of reducing problem dimension by exploiting statistical structure on the input. By modeling the input to the system of interest as a graph-structured random process, it is shown that a large parameter identification problem can be reduced into several smaller pieces, making the overall problem considerably simpler.Algorithms that can leverage this property in order to either improve the performance or reduce the computational complexity of the estimation problem are developed. The first of these, termed the graphical expectation-maximization least squares (GEM-LS) algorithm, can utilize the reduced dimensional problems induced by the structure to improve the accuracy of the system identification problem in the low sample regime over conventional methods for linear learning with limited data, including regularized least squares methods.Next, a relaxation of the GEM-LS algorithm termed the relaxed approximate graph structured least squares (RAGS-LS) algorithm is obtained that exploits structure to perform highly efficient estimation. The RAGS-LS algorithm is then recast into a recursive framework termed the relaxed approximate graph structured recursive least squares (RAGS-RLS) algorithm, which can be used to track time-varying linear systems with low complexity while achieving tracking performance comparable to much more computationally intensive methods.The performance of the algorithms developed in the thesis in applications such as channel identification, echo cancellation and adaptive equalization demonstrate that the gains admitted by the graph framework are realizable in practice. The methods have wide applicability, and in particular show promise as the estimation and adaptation algorithms for a new breed of fast, accurate underwater acoustic modems.The contributions of the thesis illustrate the power of graphical model structure in simplifying difficult learning problems, even when the target system is not directly structured.Thesis Supervisor: James C. Preisig Title: Scientist Emeritus, Woods Hole Oceanographic Institution AcknowledgmentsPiglet noticed that even though he had a Very Small Heart, it could hold a rather large amount of Gratitude. Winnie the PoohA.A.MilneMy years at MIT have been about so much more than a degree. In the past six years you have introduced to more worlds than I ever knew existed. As this long and wonderful journey ends, I find that my heart can, too, hold so much gratitude, for everything that you have given.Of course, I haven't said who "you" is, so here goes.It is impossible to write any list of acknowledgements without having at the very top my thesis advisor Dr. James Preisig, who has truly been a wide-angle lens f...

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Section: The Challenges Of Exploiting Input Structurementioning

confidence: 99%

Graphical model driven methods in adaptive system identification

Yellepeddi¹

2016

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“…When the number of snapshots increases, the computational load becomes too high for practical real-time source location. Recently, new techniques based on a covariance matrix fitting approach have been considered to summarize multiple snapshots, e.g., [26][27][28]. Basically, these methods try to fit the covariance matrix to a certain model.…”

Section: Sparse Representation In Source Locationmentioning

confidence: 99%

“…The technique proposed by Yardibi et al [26] leads to an optimization problem that can be solved efficiently using Quadratic Programming (QP). In the case of the approach exposed by Picard and Weiss [27], the solution is obtained by means of linear programming (LP). The main drawback of this last method is that it depends on a user defined parameter that is difficult to adjust.…”

Section: Sparse Representation In Source Locationmentioning

confidence: 99%

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Sparse covariance fitting for direction of arrival estimation

Blanco

Nájar

2012

EURASIP J. Adv. Signal Process.

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This article proposes a new algorithm for finding the angles of arrival of multiple uncorrelated sources impinging on a uniform linear array of sensors. The method is based on sparse signal representation and does not require either the knowledge of the number of the sources or a previous initialization. The proposed technique considers a covariance matrix model based on overcomplete basis representation and tries to fit the unknown signal powers to the sample covariance matrix. Sparsity is enforced by means of a l 1 -norm penalty. The final problem is reduced to an objective function with a non-negative constraint that can be solved efficiently using the LARS/homotopy algorithm. The method described herein is able to provide high resolution with a low computational burden. It proceeds in an iterative fashion solving at each iteration a small linear system of equations until a stopping condition is fulfilled. The proposed stopping criterion is based on the residual spectrum and arises in a natural way when the LARS/homotopy is applied to the considered objective function.

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“…For example, [11] proposes the idea that the eigenvectors of the array covariance matrix have a sparse representation over a dictionary constructed from the steering vectors. In [12,14], it is shown that when the received signals are uncorrelated, the array covariance matrix has a sparse representation over a dictionary constructed using the atoms, i.e. the correlation vectors.…”

Section: Introductionmentioning

confidence: 99%

A subspace method for array covariance matrix estimation

Rahmani

Atia

2016

2016 IEEE Sensor Array and Multichannel Signal Processing Workshop (SAM)

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This paper introduces a subspace method for the estimation of an array covariance matrix. It is shown that when the received signals are uncorrelated, the true array covariance matrices lie in a specific subspace whose dimension is typically much smaller than the dimension of the full space. Based on this idea, a subspace based covariance matrix estimator is proposed. The estimator is obtained as a solution to a semi-definite convex optimization problem. While the optimization problem has no closed-form solution, a nearly optimal closed-form solution is proposed making it easy to implement. In comparison to the conventional approaches, the proposed method yields higher estimation accuracy because it eliminates the estimation error which does not lie in the subspace of the true covariance matrices.The numerical examples indicate that the proposed covariance matrix estimator can significantly improve the estimation quality of the covariance matrix.

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Direction finding of multiple emitters by spatial sparsity and linear programming

Cited by 15 publications

References 20 publications

Graphical model driven methods in adaptive system identification

Graphical model driven methods in adaptive system identification

Sparse covariance fitting for direction of arrival estimation

A subspace method for array covariance matrix estimation

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