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A Bayes approach to parameter estimation, based on the minimum mean square error criterion, applied to the problem of identifying such radar target characteristics as dimensions, shape, rate of rotation, and axis of rotation, as well as the more usually considered range, range rate, and range acceleration. Emphasis is on estimation of linear or quadratic functionals of the scatterer amplitudes, such as the average scattering cross section attributable to specific regions of the target. Theoretically, results can be obtained for nonstationary cases, such as those involving specular flashes, for any signal- to-noise ratio, and for any degree of prior knowledge of target characteristics. However, most cases require solution of certain integral equations for which the computer programs are as yet unwritten. Initial steps toward computer implementation are discussed. Applications include satellite identification, radar astronomy, and radar ground mapping.