Peculiar properties of construction of initial regions of asteroids' possible motion from observational data in the form of probabilistic ellipsoids are investigated. For the objects which observed only in one appearance, this problem may be essentially nonlinear, and the usual method for their construction with the help of linear estimations of covariance matrices may became unacceptable. In order to make possible application of the linear estimation methods which has been developing in mathematical statistics the problem of decreasing nonlinearity is discussed. The solution of this problem with the help of appropriate system of initial parameters of asteroid orbits choice, as well as initial time and weighting matrices of observational errors is proposed. Efficiency of such technique had justified by numerical experiments with the usage of model and real observations.