In this paper using generalized objective functions, within a probabilistic framework, a unified view on robust data reconciliation is provided. Conditions for robustness as well as efficiency are investigated for a set of objective functions and their associated influence functions. A partially adaptive estimator based on a generalized T distribution and a fully adaptive estimator based on density estimation are also proposed and discussed. Both give the efficiency interpretation in the maximum likelihood estimation. The performance of the proposed methods and their comparison with other existing approaches are illustrated through a chemical engineering example.