Two collective estimation strategies, the Unbiased Estimation Technique (Rollins and Davis, 1992) and the recursive Generalized Likelihood Ratio (Keller er al., 1994), have been shown to be very efficient in detecting and estimating multiple gross errors in linear process systems. However, these strategies run into singularities and uncertainties that prevent them from being used in automatic schemes. This paper uses a recently presented theory on gross error equivalency to explain when and how these singularities and uncertainties take place. The procedures presented by these two methods are modified to prevent the singularities from appearing and allowing their automatic implementation.