Covariance-informed detection in compound-Gaussian clutter without secondary data

We consider the problem of detecting a signal of interest in the presence of compound-Gaussian clutter, without resorting to secondary data in order to infer the clutter covariance matrix. Towards this end, we assume that both the texture τ and the speckle covariance matrix R are random variables with some a priori distributions. Marginalizing with respect to these variables, the probability density function of the observed primary data is derived, leading to a closed-form expression for the generalized likelihood ratio test (GLRT) of the problem at hand. Accordingly, the GLRT assuming that τ is deterministic is also derived. The two detectors are assessed through numerical simulations.