Dilution of precision for LEO satellite precise orbit and clock determination

Abstract

Precise orbital and clock products for Low Earth Orbit (LEO) satellites are prerequisites for augmenting traditional Global Navigation Satellite Systems (GNSS) in the positioning, navigation and timing services. To effectively utilize LEO signals for real-time, high-precision positioning and timing on the ground, servers may need to broadcast LEO satellite orbital and clock products while simultaneously assessing their formal precision. The concept of Dilution of Precision (DOP) has been widely used to assess GNSS satellite geometry for ground-based receiver positioning and timing based on the Standard Point Positioning (SPP) technology. This concept can also be extended to LEO satellite Precision Orbit Determination (POD) and clock estimation. In this contribution, an extended concept of DOP is proposed for LEO POD using dual-frequency Ionosphere-Free (IF) observations. Similar to concepts of Position DOP (PDOP) and Time DOP (TDOP), a series of LEO orbit and clock DOP concepts are first defined, followed by a detailed analysis based on Reduced-Dynamic (RD) and kinematic batch least squares POD methods. Additionally, the correlations between the radial, along-track and cross-track LEO orbits and the LEO satellite clocks are assessed for the RD and kinematic POD modes. Based on real GPS+Galileo observations collected onboard the Sentinel-6A satellite, the DOP of LEO orbits and clocks among four strategies are calculated to evaluate the formal precision, i.e., the GPS-only RD (RD-G), GPS-only kinematic (KN-G), GPS+Galileo RD (RD-GE) and GPS+Galileo kinematic (KN-GE) modes. The RD-GE mode can achieve the highest formal precision for both orbit and clock, with a 7-day average orbit DOP of 0.87, 1.16, and 0.91 along the radial, along-track, and cross-track directions, respectively, and a clock DOP of 5.81. It was found that increasing the number of GNSS observations, and accordingly the geometry of their transmitting satellites, can significantly reduce the DOPs for the kinematic LEO satellite orbits and clocks. With the average number of GNSS satellites increasing from 7 to 14, the 7-day average percentage improvements in the DOPs in the radial orbits (RDOP), along-track orbits (SDOP), cross-track orbits (WDOP) and clocks (TDOP) are 32.6%, 37.3%, 40%, and 19.8%, respectively. However, increasing the number of GNSS observations has limited improvements on the RD POD, with improvements in the radial orbits and clocks amounting to 17.1% and 12.0%, respectively. It was also verified that the correlations between the radial orbits and the clocks are significantly reduced in the RD modes compared to the KN modes, i.e., from -0.31 to 0.05 in the GPS+Galileo case on average and from -0.34 to 0.1 in the GPS-only case.