Efficient Approximation for a Fully Populated Variance-Covariance Matrix in RTK Positioning

Abstract

Global navigation satellite system (GNSS) observations have been shown to be physically correlated. Disregarding the physical correlations in a variance-covariance matrix (VCM) will lead to adverse impacts on GNSS applications. Typically, physical correlations have three types in a fully populated VCM: spatial, cross, and temporal correlations. However, such a fully populated VCM cannot be easily estimated and inverted, especially in real-time kinematic (RTK) positioning. The authors propose an efficient approximation approach for processing these physical correlations. This method appropriately considers the significant covariance elements and efficiently transforms the time-dependent VCM to a time-independent block diagonal matrix. As an example, 1 data sets of BeiDou code and phase observations with different baseline lengths and receivers were collected. The results showed that this proposed method had fewer covariance elements to be estimated, thus decreasing the number of unknowns when using (co)variance component estimation (VCE). In addition, the proposed method had lower computation burden than the multiple-epoch method. For instance, the computation efficiency was increased by more than 5% in the case of the 6-epoch data window. It can also provide more realistic baseline solutions and precisions compared with the traditional single-epoch method.