A new approach of multi-dimensional correlation as a separability measure of multiple outliers in GNSS applications

Abstract Detecting and identifying outliers/failures in GNSS measurements has garnered significant attention among researchers aiming to enhance the quality of GNSS positioning and navigation. This study delves into the analysis of the separability of multiple outliers when single, double, and triple outliers occur in single-point positioning (SPP) measurements. To achieve this, a novel method includes introducing a multi-dimensional correlation coefficient among test statistics. This coefficient functions as a measure of outliers separability and, in turn, assesses the possible impact of outliers on other measurements. This multi-dimensional correlation approach is based on a nested correlation ( ρ nested θ , φ ${\rho }_{\text{nested}}^{\theta ,\varphi }$ ) that explains the variations in test statistic values with and without common measurements in two pairs/combinations. The performance of the ρ nested θ , φ ${\rho }_{\text{nested}}^{\theta ,\varphi }$ is then compared with other two existing methods of multi-dimensional correlation namely the maximum ( ρ max θ , φ ${\rho }_{\mathrm{max}}^{\theta ,\varphi }$ ) and global ( ρ Global θ , φ ${\rho }_{\text{Global}}^{\theta ,\varphi }$ ) correlation. The results show that under the presence of two outliers and with and without common measurements in two pairs, the ρ nested θ ${\rho }_{\text{nested}}^{\theta }$ outperforms the, ρ max θ ${\rho }_{\mathrm{max}}^{\theta }$ and ρ Global θ ${\rho }_{\text{Global}}^{\theta }$ exhibiting a determination coefficient ( R 2 ) value of approximately 0.95 and 0.62 respectively. The results furthermore reveal that for three outliers and with one, two, and noncommon measurements intersecting between two combinations, the values of R 2 are 0.62, 0.96, and 0.34. respectively. This means that the ρ nested θ , φ ${\rho }_{\text{nested}}^{\theta ,\varphi }$ can explain the variations in outlier test statistic values particularly in the case that common measurements appear in two pairs/combinations.