Algorithms exploiting hyperspectral imagery for target detection have continually evolved to provide improved detection results. Adaptive matched filters, which may be derived in many different fields, can be used to locate spectral targets by modeling the scene background as either structured (i.e., geometric, with endmembers or basis vectors) or unstructured (i.e., stochastic, with a mean and covariance matrix). In unstructured techniques, various methods of calculating the background covariance matrix have been developed, each involving either the removal of target signatures from the background model or the appropriate choice of a subset of the image to be used as training data based on spatial or spectral characteristics. The objective of these methods is to derive a background which matches the source of mixture interference for the detection of sub-pixel targets, or matches the source of false alarms in the scene for the detection of fully resolved targets. In addition, these techniques may increase the multivariate normality of the data from which the background is characterized, thus increasing adherence to the normality assumption inherent in the matched filter and ultimately improving target detection results. Such techniques for improved background characterization are widely practiced but not well understood or documented. This work describes in detail several methods for unstructured background characterization, both new methods and those taken from the literature. A comparison of methods across a common set of targets is presented. Training data are chosen either spatially, spectrally, or both prior to estimation of the background statistics. Evaluation of the methods indicates that consistent improvements over scene-wide statistics can be achieved through such spatial or spectral subsetting of the image data. However, results are not conclusive as to the overall "best" method for all targets in the test set.