In this article, we investigate the problem of estimating the spectral characteristics of the intensity of moving objects under stochastic uncertainty based on the results of measuring the magnitudes of wave fields at separate points. We assume that the unknown spectral functions belong to known sets from the functional space, and certain restrictions are given for the unknown correlation matrices. For linear guaranteed estimates of the set of linear functionals from spectral functions, we prove that the guaranteed mean square estimates are expressed in terms of solutions of a certain system of linear algebraic equations.