Determination of initial eigenorbits for asteroids

We consider initial determination of asteroid orbits in the case of small numbers of observations and short observational arcs. For asteroids having long arcs, we can assess the orbital uncertainties with the help of the covariance matrix that, in the phase space of the orbital elements, defines a set of probability ellipsoids. In initial orbit determination, because of the nonlinear characteristics and multiple solutions of the inversion problem, we cannot readily use the covariance matrix to estimate the orbital uncertainties. However, by computing the eigenvalues and eigenvectors of the formal correlation matrix (that is, by deriving the eigenorbits), we can discern the most indeterminate orbital elements. Here we solve the eigenproblem for 17 single-apparition asteroids.