Constrained subspace estimation via convex optimization
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AuthorSantamaría Caballero, Luis Ignacio; Vía Rodríguez, Javier; Kirby, Michael; Marrinan, Tim; Peterson, Chris; Scharf, Louis L.
© EURASIP. First published in the Proceedings of the 25th European Signal Processing Conference (EUSIPCO-2017) in 2017, published by EURASIP. IEEE is granted the nonexclusive, irrevocable, royalty-free worldwide rights to publish, sell and distribute the copyrighted work in any format or media without restriction.
25th European Signal Processing Conference (EUSIPCO), Kos island, Greece, 2017, 1200-1204
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Given a collection of M experimentally measured subspaces, and a model-based subspace, this paper addresses the problem of finding a subspace that approximates the collection, under the constraint that it intersects the model-based subspace in a predetermined number of dimensions. This constrained subspace estimation (CSE) problem arises in applications such as beamforming, where the model-based subspace encodes prior information about the direction-of-arrival of some sources impinging on the array. In this paper, we formulate the constrained subspace estimation (CSE) problem, and present an approximation based on a semidefinite relaxation (SDR) of this non-convex problem. The performance of the proposed CSE algorithm is demonstrated via numerical simulation, and its application to beamforming is also discussed.