We consider the problem of parameters estimation in the situation where a subset of parameters of the underlying model has already been estimated. Potential errors in the pre-estimated parameters limit the accuracy in the computation of the still unknown parameters in a way that crucially depends on the symmetries of the data set. In this article, we develop an optimization approach that minimizes the sensitivity to errors in the determination of parameters by determining optimal weights that depend on both the model and the input data in the situation where the data are incomplete. We apply the method to the problem of calibrating the sensor positions in an array of magnetometers whose scale factors and biases have been estimated beforehand.