Performance Analysis of a Low-Rank Detector Under Training Data Contamination

We consider the problem of detecting a known M-dimensional target signature vector from an observation corrupted by an additive noise with unknown covariance matrix. In that case, standard statistical methods of detection usually assume that N - “target free” observations are available to perform estimation of the noise covariance matrix. However, in several applications, the target signal may contaminate the training data, resulting in a deviation of the expected performance of the detectors. In this paper, we consider the performance analysis of two low-rank detectors under the assumption that Nc elements of the training data are contaminated by the target signal. More precisely, we derive the asymptotic false alarm and detection probabilities in the high dimensional regime in which both the dimension M, the number of training data N and contaminated data Nc converge to infinity at the same rate. Numerical simulations illustrate the fact that, despite the asymptotic nature of the analysis, the results obtained are accurate for reasonable values of M, N and Nc.