Within the context of a problem of monitoring of the Earth's underlying surface and cloudiness, new estimating Bayes decision rules for pattern recognition and automated classification were synthesized to extract complete information from a set of satellite video images as well as cartographic information and results of contact measurements under conditions of a priori indeterminacy. The rules take into account high dimensionality of miscellaneous observations, meager tutorial sequences, and degeneracy of support functions of approximating distributions.