On robust estimation of the Gauss-Markov model with a singular covariance matrix

Although the robust parameter estimation has been intensively investigated in statistics and measurement science, no one considers the robust estimation within the Gauss-Markov model (GMM) with a singular covariance matrix. In this contribution, a method of finding the robust solutions in the singular linear model has been suggested based on the generalization of the unified least-squares objective function. The equivalent cofactor matrix in the robust objective function is established by the bifactor strategy based on the IGG III function. The robustness of the proposed robust algorithms is demonstrated with the examples of geodetic coordinates transformation and the free network deformation analysis.