A Unified Theory of Adaptive Subspace Detection Part I: Detector Designs
Danilo Orlando, Giuseppe Ricci, Louis L. Scharf
Abstract
This paper addresses the problem of detecting multidimensional subspace signals in noise of unknown covariance. It is assumed that a primary channel of measurements, possibly consisting of signal plus noise, is augmented with a secondary channel of measurements containing only noise. The noises in these two channels share a common covariance matrix, up to a scale, which may be known or unknown. The signal model is a subspace model with variations: the subspace may be known or known only by its dimension; consecutive visits to the subspace may be unconstrained or they may be constrained by a prior distribution. The several original detectors derived in this paper, when organized with previously published detectors, comprise a unified theory of adaptive subspace detection from primary and secondary channels of measurements.