结合流形滤波的矩阵信息几何检测器

针对小样本、非均匀杂波下的信号检测问题,提出一种基于流形滤波的矩阵信息几何检测器,将信号检测问题转化为矩阵流形上的几何问题。将每一个样本的相关性数据建模为一个托普利兹正定矩阵,在此基础上,利用每一个样本数据的邻近矩阵进行加权平滑滤波,去除一部分杂波能量,提升目标与杂波间的区分性。计算了辅助样本数据对应矩阵的几何均值,通过比较待检测样本数据矩阵与几何均值矩阵之间的距离与检测门限的大小,以实现信号检测。实验结果表明,与自适应匹配滤波相比,本文方法在小样本、非均匀杂波下具有明显的性能优势。

Matrix information geometric detectors with manifold filter

Aiming at the problem of signal detection in small sample and nonhomogeneous clutter, a matrix information geometric detector based on manifold filter was proposed. The signal detection problem was transformed into a geometric problem on the matrix manifold. The correlation of each sample data was modeled as a Toeplitz positive definite matrix. On the basis, each matrix was replaced by a weighted smoothing filter of its surrounding matrices. The weighted smoothing filter removed part of the clutter energy and improved the discrimination between the target and the clutter. The geometric mean of a set of secondary sample data was calculated. By comparing the distance between the matrix under test and the geometric mean matrix with the detection threshold, the signal detection was realized. Simulation results demonstrate the superiority of the detection performance of the proposed method in small sample and nonhomogeneous clutter compared with adaptive matched filtering.