The Asteroid Identification Problem

es. Tests on the values of these distances are used as preliminary filters, to allow more 1 extensive computations to be performed on a fraction of the total number of possible couples. The difficulties in the application of this algorithm arise from the fact that poorly observed orbits have badly conditioned covariance matrices: all the computations performed with these matrices are affected by large numerical errors. Moreover, it is clear that the larger the eigenvalues of the covariance matrix, the larger the nonlinear effects will be. For asteroids observed over a very short arc, and lost since a long time, the linear approximation fails. Nonlinear optimisation algorithms can be used but are computationally expensive [2]. Identifications based upon some of the orbital elements, e.g., excluding the mean longitude, can be effective in reducing the relevance of the nonlinear effects; the corresponding distances are defined by the marginal covariance matrices, using a formal