A subspace GLRT for vector-sensor array detection

Signal detection using the generalized likelihood ratio test is examined for data obtained from an arbitrary array of vector sensors. Vector sensors are sensing devices that simultaneously measure all six time-dependent, electromagnetic field quantities at a point in space. A signal model is developed for a point narrowband source with unknown amplitude. The maximum likelihood estimator for the signal amplitude is derived in the presence of colored multivariate Gaussian noise. The detection test statistic and its probabilities of false alarm and detection are obtained in closed form. A non-adaptive transformation is derived that compresses a high dimensional detection problem into a two-dimensional detection problem with no signal loss