Generalization of Data Snooping and Data Refining

Based on the extended w-test, data snooping and data refining have been used to diagnose outliers caused by gross errors in geodetic applications. This study aims to generalize these methods by incorporating the likelihood ratio test (LRT), enabling the testing of various types of mismodeled errors, including both gross errors and systematic errors. First, the Gauss–Markov model is extended to encompass all potential mismodeled errors. Based on this model, multiple hypotheses are generated for each mismodeled error mode. Subsequently, using the LRT criterion, both the test statistics and the testing rules for these multiple hypotheses are developed, and (iterative) data snooping and data refining are generalized to address diverse types and numbers of mismodeled errors. These generalized methods are termed generalized data snooping (GDS) and generalized data refining (GDR), respectively. Finally, a global navigation satellite system (GNSS) positioning example shows that both GDS and GDR are effective in dealing with mismodeled errors with different types and numbers. The difference is that GDS is shown to be better suited for cases with satisfactory observation conditions demanding high estimation precision. Conversely, GDR demonstrates its superiority in cases with challenging observation environments that require high estimation robustness.