Detection of Abnormal Data in GNSS Coordinate Series Based on an Improved Cumulative Sum

The global navigation satellite system (GNSS), as a high-time resolution and high-precision measurement technology, has been widely used in the field of deformation monitoring. Owing to the influence of uncontrollable factors, there are inevitably some abnormal data in the GNSS monitoring series. Thus, it is necessary to detect and identify abnormal data in the GNSS monitoring series to improve the accuracy and reliability of the deformation disaster law analysis and warning. Many methods can be used to detect abnormal data, among which the statistical process control theory, represented by the cumulative sum (CUSUM), is widely used. CUSUM usually constructs statistics and determines control limits based on the threshold criteria of the average run length (ARL) and then uses the control limits to identify abnormal data in CUSUM statistics. However, different degrees of the 'trailing' phenomenon exist in the interval of abnormal data identified by the algorithm, leading to a higher false alarm rate. Therefore, we propose an improved CUSUM method that uses breaks for additive season and trend (BFAST) instead of ARL-based control limits to identify abnormal data in CUSUM statistics to improve the accuracy of identification. The improved CUSUM method is used to detect abnormal data in the GNSS coordinate series. The results show that compared with CUSUM, the improved CUSUM method shows stronger robustness, more accurate detection of abnormal data, and a significantly lower false alarm rate.