期刊
IEEE TRANSACTIONS ON SIGNAL PROCESSING
卷 62, 期 22, 页码 6059-6070出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TSP.2014.2360826
关键词
Geodesic convexity; complex elliptically symmetric distributions; M-estimator of scatter; regularization; robustness; normalized matched filter
资金
- National Science Foundation [DMS-1407751]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1407751] Funding Source: National Science Foundation
In this paper, a general class of regularized M-estimators of scattermatrix are proposed that are suitable also for low or insufficient sample support (small n and large p) problems. The considered class constitutes a natural generalization of M-estimators of scatter matrix (Maronna, 1976) and are defined as a solution to a penalized M-estimation cost function. Using the concept of geodesic convexity, we prove the existence and uniqueness of the regularized M-estimators of scatter and the existence and uniqueness of the solution to the corresponding M-estimating equations under general conditions. Unlike the non-regularized M-estimators of scatter, the regularized estimators are shown to exist for any data configuration. An iterative algorithm with proven convergence to the solution of the regularized M-estimating equation is also given. Since the conditions for uniqueness do not include the regularized versions of Tyler's M-estimator, necessary and sufficient conditions for their uniqueness are established separately. For the regularized Tyler's M-estimators, we also derive a simple, closed form, and data-dependent solution for choosing the regularization parameter based on shape matrix matching in the mean-squared sense. Finally, some simulations studies illustrate the improved accuracy of the proposed regularized M-estimators of scatter compared to their non-regularized counterparts in low sample support problems. An example of radar detection using normalized matched filter (NMF) illustrate that an adaptive NMF detector based on regularized M-estimators are able to maintain accurately the preset CFAR level.
作者
我是这篇论文的作者
点击您的名字以认领此论文并将其添加到您的个人资料中。
推荐
暂无数据