About the Nonlinearity of the Problem of Estimating the Parameters of Asteroids with Small Perihelion Distances

The paper presents the results of the determining the nonlinearity extent of the problem of estimating the initial orbital parameters of asteroids with small perihelion distances. The values of the nonlinearity index χ were obtained for 53 asteroids known as of September 2021. It allowed to evaluate the nonlinearity as weak, moderate or strong one. The calculation of the parameter is based on the computation and comparison of the objective function values of the least square problem (LS) at the vertexes of the confidence ellipsoid. The study showed that for most asteroids (46 objects) the nonlinearity is weak, for six asteroids, it is moderate, and for one object, the nonlinearity is defined as strong. If the nonlinearity is moderate or strong, it is recommended to use nonlinear methods for constructing the initial confidence region to obtain the most adequate prediction of the asteroids motion. For asteroids with different nonlinearity extents, the initial confidence regions are constructed using the linear method and the method of perturbed observations. For four asteroids, the evolution of the linear and nonlinear initial regions was traced, and a comparative analysis of their behavior with time was carried out.