A method for detecting targets comprises: a) receiving spectral data; b) using a normal compositional model for estimating background parameters from the spectral data and target components; c) estimating abundance values of classes of the normal compositional model from the background parameters and the spectral data; d) estimating target class covariance values from the spectral data, the background parameters, and the target components; e) estimating target-plus-background abundance values from the target class covariance values, the background parameters, the spectral data, and the target components; f) employing a normal compositional model for determining a likelihood ratio detection statistic from the target class covariance values, target-plus-background abundance values, spectral data, target components, background parameters, and background abundance values; and g) generating a determination output signal that represents whether an observation includes a target from the likelihood ratio detection statistic.