Discussions on the loss functions of attitude determination

This paper extends the optimal linear attitude estimator optimality loss function based on the weighted-least-squares theory and gives an analysis of the relationship between the extended loss function and the others. Covariance analysis shows that, for the appropriate weighting matrix and zero-mean Gaussian noise, minimization of the extended loss function is equivalent to both the maximum likelihood estimation and the minimum covariance estimation. The extended loss function is equivalent to Wahba´s loss function if the suggested weighting matrices are used.