A Unified Theory of Adaptive Subspace Detection. Part I: Detector Designs

TL;DR

This paper develops a comprehensive framework for detecting multidimensional subspace signals in noise, introducing generalized likelihood ratio detectors that adapt to various known or unknown parameters, unifying existing methods.

Contribution

It presents a unified theory of adaptive subspace detection using GLR detectors for different scenarios of known or unknown subspace and noise scale.

Findings

Derived GLR detectors for four classes of subspace detection scenarios.

Unified framework combining previous detectors into a comprehensive theory.

Applicable to signals with known or unknown subspace and noise scale.

Abstract

This paper addresses the problem of detecting multidimensional subspace signals, which model range-spread targets, 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. As a consequence, there are four general classes of detectors and, within each class, there is a detector for the case where the scale between the primary and secondary channels is known, and for the case where this scale is unknown. The generalized likelihood ratio (GLR) based detectors derived in this paper, when organized with previously published GLR detectors, comprise a unified theory of adaptive subspace detection from primary and secondary channels of measurements.