Expectation Maximization Approach for Simultaneous Gross Error Detection and Data Reconciliation Using Gaussian Mixture Distribution

Process measurements play a significant role in process identification, control, and optimization. However, they are often corrupted by two types of errors, random and gross errors. The presence of gross errors in the measurements affects the reliability of optimization and control solutions. Therefore, in this work, we characterize the measurement noise model using a Gaussian mixture distribution, where each mixture component denotes the error distribution corresponding to random error and gross error, respectively. On the basis of this assumption, we propose a maximum likelihood framework for simultaneous steady-state data reconciliation and gross error detection. Since the proposed framework involves the noise mode as a hidden variable denoting the existence of gross errors in the data, it can be solved using the expectation maximization (EM) algorithm. This approach does not require the parameters of the error distribution model to be preset, rather they are determined as part of the solution. Several case studies are presented to demonstrate the effectiveness of the proposed approach.