Geometric and statistical interpretation of correlation between fault tests in integrated GPS/INS systems

Abstract

Abstract Fault detection and identification (FDI) in either a stand-alone GPS or in integrated GPS/INS systems is essential for improving the quality of positioning, navigation, and many other applications. The assumption that the observations include a single fault has been considered intensively in literature. However, this assumption may not necessarily be valid due to the fact that multiple faults may exist simultaneously. In this study, separability of multiple faults in GPS/INS integration systems has been analysed geometrically and statistically. This has been achieved through testing how large correlation coefficient between any pair of fault tests statistics increases the probability of faults misidentification. In addition, a new calculation procedure of correlation coefficient when four faults appear in the observations has been developed. This procedure considers calculation the correlation between a single and a punch of measurements combined together. The results show that there is a strong relationship between the value of correlation coefficient and the probability of misidentification. Furthermore, a significant relationship between the correlation and the fault test values can be found when splitting the measurements combinations into groups based on the combination similarity. Nevertheless, this relationship can be defined without splitting the measurements into groups when using a new correlation procedure for four faults case. The geometric representation shows that large correlation coefficient reflects small angle between the correlation and the x-axis; whereas the angle between the fault-test vectors and the x-axis becomes wider when a tiny correlation exist.