This work extends the optimum Neymann-Pearson methodology to detection of a subspace signal in the correlated additive Gaussian noise when the noise power may be different under the null (H0) and alternative (H1) hypotheses. Moreover, it is assumed that the noise covariance structure and power under the null hypothesis are known but under the alternative hypothesis the noise power can be unknown. This situation occurs when the presence of a small point (subpixel) target decreases the noise power. The conventional matched subspace detector (MSD) neglects this phenomenon and causes a consistent loss in the detection performance. We derive the generalized likelihood ratio test (GLRT) for such a detection problem comparing it against the conventional MSD. The designed detector is theoretically justified and numerically evaluated. Both the theoretical and computer simulation results have shown that the proposed detector outperforms the conventional MSD. As to the detection performance, it has been shown that the detectivity of the proposed detector depends on the additional adaptive corrective term in the threshold. This corrective term decreases the value of presumed threshold automatically and, therefore, increases the probability of detection. The influence of this corrective term on the detector performance has been evaluated for an example scenario.

This Letter presents the matched subspace detection in the presence of Gaussian background with known covariance structure but different variance for hypothesis H0 and H1. The performance degradation has been evaluated when there are the following mismatches between the actual and designed parameters: background variance in the case of hypothesis H1 and one-lag correlation coefficient of background. It has been shown that the detectability depends strongly on the fill factor of targets in the case of the mode signal matrix with high rank for a prescribed false alarm probability and a given signal-to-background ratio. These results have been also justified via Monte Carlo simulations for an example scenario.