Anomalous ambiguity detection between reference stations based on Box-Cox transformation of tropospheric residual estimation

With the increasing scale and complexity of network RTK, the reliability of ambiguity resolution becomes particularly crucial. Undetected incorrect fixings may trigger a chain reaction in subsequent atmospheric delay extraction and fitting stages, thereby affecting the reliability of user positioning services. Current methods for checking abnormal ambiguities suffer from issues such as inflexible threshold selection, excessive exclusion, and overlooking observational anomalies. Addressing these concerns, we propose a new method for ambiguity detection of reference stations, referred to as the “Box-Cox transformation & Secondary screening combining Chi-square Test” (BS-CT). Firstly, the tropospheric residuals after ambiguities fixing are extracted and they are unitized through their corresponding co-variance matrix. Secondly, the Box-Cox method is employed to transform the distribution of the unitized residuals, making them conform to a standard normal distribution. This enables the use of a chi-square test to eliminate satellites with observation anomalies. Finally, a secondary-screening method is applied to ensure the reliability of the fixed ambiguity quantity. In the experimental section, the BS-CT method was contrasted with the ordinary chi-square test, Partial Ambiguity Resolution method (PAR), and a method utilizing a decision function g for enhanced fixed fraction and variance strategy. The results indicate that, compared to the other three methods, lower fall-out ratio in anomaly ambiguity testing is observed with the BS-CT method. It is comparable to PAR in terms of omission ratio and performs lower than the other two methods.