Matched Subspace Detectors for Stochastic Signals

Our aim in this paper is to extend the matched subspace detectors (MSDs) of [1–3] to the detection of stochastic signals. In [1–3] the signal to be detected was assumed to be placed deterministically at an unknown location in a known signal subspace. The basis for the subspace was irrelevant. In this paper the signal is assumed to be placed randomly at an unknown location in a known subspace. If nothing is known a priori about the second-order moments of the placement, then the generalized likelihood ratio test (GLRT) for a stochastic signal turns out to be identical to the GLRT for a deterministic signal. Consequently, the MSDs are more general than originally thought, applying to the detection of a signal whose mean value or covariance matrix is modulated by a subspace signal. Moreover, the invariance sets for stochastic MSDs are identical to those of the corresponding deterministic MSD. The results of this paper extend the theory of MSDs to radar and sonar problems where random target effects may be modeled, and to data communication problems where symbols are coded by subspaces, rather than coordinates of subspaces. ∗This work supported by John Tague of ONR under contract N00014-00-C-0145. †This work supported by John Tague of ONR under contract N00014-01-1-1019-P0001.