A comparative study of anomaly detection methods for gross error detection problems.

•An extensive review of existing Anomaly Detection methods based on Machine Learning and Deep Learning was conducted.•The main challenges currently faced and potential research directions for the Gross Error Detection problem were mentioned.•A number of measurement datasets were generated, including training and testing data, associated with 16 systems introduced in the literature.•A learning system to detect Gross Errors by using Anomaly Detection methods was proposed.•Experiments were conducted on 19 ADMs on the training datasets associated with the 16 systems to generate detection models with a number of established performance metrics.