Constrained subspace estimation via convex optimization. Santamaria, I., Via, J., Kirby, M., Marrinan, T., Peterson, C., & Scharf, L. In 2017 25th European Signal Processing Conference (EUSIPCO), pages 1200-1204, Aug, 2017.
Constrained subspace estimation via convex optimization [pdf]Paper  doi  abstract   bibtex   
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.

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