Efficient operation of manufacturing and process industries relies on accurate sensor measurements and plant models. However, sensor measurements are often corrupted by both random and gross errors, compromising data quality and process reliability. This necessitates robust data reconciliation and gross error detection methods. While robust estimators coupled with nonlinear programming are commonly used for data reconciliation, deep learning networks, though employed, often disregard process constraints. Robust estimators are computationally intensive while deep learning networks require accurate labels for training purposes which are not always available. To address these challenges, we propose a novel approach: a robust estimator-guided neural network framework that can rectify the random errors, remain insensitive to gross errors, and capture the relations between process variables. It is possible to train the neural network without true values with the proposed framework. We have incorporated a quasi-weighted least squares estimator into the physics informed neural network framework and trained the model for steady state linear processes. Our framework’s performance is demonstrated for well-established benchmark like the steam metering system. It can be utilized for rectifying random and gross errors in data effectively and for enhancing the reliability of process industries.