Radar Target Detection with K-Nearest Neighbor Manifold Filter on Riemannian Manifold

In this paper, we propose a K-nearest neighbor manifold filter on the Riemannian manifold and apply it to signal detection within clutter. In particular, the correlation and power of sample data in each cell are modeled as an Hermitian positive definite (HPD) matrix. A K-nearest neighbor filter that performs the weight average of the set of K-nearest neighbor HPD matrices of each HPD matrix is proposed to reduce the clutter power. Then, the clutter covariance matrix is estimated as the Riemannian mean of a set of secondary HPD matrices. Signal detection is considered as distinguishing the matrices of clutter and target signal on the Riemannian manifold. Moreover, to speed up the convergence of matrix equation of Riemannian mean, we exploit a strategy to choose the initial input matrix and step size of this equation. Numerical results show that the proposed detector achieves a detection performance improvement over the conventional detector as well as its state-of-the-art counterpart in nonhomogeneous clutter.