Laplace-method algorithm for determining orbits from position observations

A method for evaluating the first and second derivatives of observed coordinates is presented. Two series of observations are approximated by a Chebyshev polynomial series; the number of polynomials used is determined by the behavior of the standard deviation of the regression curve. The obtained series are used to determine the required derivatives, which makes it possible to employ the Laplace method to determine the orbits of artificial earth satellites. Orbital elements obtained in this way are shown to agree with elements obtained by the PVD method.