Process measurements are susceptible to random and gross errors that may affect the reliability and decision making in process control and automation applications. In this work, we propose a Maximum a Posteriori (MAP) framework to deal with gross errors having equivalent sets, while simultaneously performing data reconciliation. Furthermore, in reality, the process may work under multiple operating regions. Hence, another contribution of this study is to solve a data rectification problem on a data set containing different steady-state operating regions. To address this case, a MAP formulation with two hidden variables is introduced - one for signifying the operating mode, and the other for characterizing the noise mode. Owing to the presence of hidden variables, an Expectation Maximization (EM) algorithm is presented to solve the resulting optimization problem. Several examples are presented to demonstrate the effectiveness of our proposed framework. (C) 2019 Elsevier Ltd. All rights reserved.