The principle of least squares assumes that a target function Q has to be minimized to find the nominal solution. The target function is formed with the sum of squares of the residuals , with . The residuals are normalized, as discussed in Section 3.3, thus Q is dimensionless. In our case, for Nobsastrometric observations of two angular coordinates. The residuals are functions of the estimated parameters . In the simplest problems of orbit determination N=6and X is some vector representing the orbital elements at some initial epoch t0: in this paper are the equinoctial elements as defined in Paper I, Sect. 4.1. Some of the coordinates of the vector X, e.g. in our case the mean longitude , are not real numbers, but are sometimes angles (defined ), and this introduces some complications which will be noted later.
Thus the target function also depends upon X, and the minimum of
Q(X) is obtained by solving the nonlinear equations:
Please note that to apply a single iteration of differential
correction, and even any fixed number of iterations, is not enough to
guarantee convergence; an iterative scheme with a tight convergence
control needs to be used. As an example, in our programs the
convergence is controlled by requiring that the correction norm