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.