Positioning bias of different frequency observations in double-differenced relative positioning

Abstract

In this study, the double-differenced positioning bias of different frequency observations (PBDFO) in a code division multiple access (CDMA) signal system is analyzed based on real-time kinematic (RTK) positioning using raw observations at different frequencies. To test and verify the existence of the DD PBDFO, a set of ultra-short baseline (25 m) GNSS observation data were collected. The stations NT03 and NT04 were located in Xi’an City, Shaanxi Province. The observation time ranged from UTC 11:00 to 17:00 for 10 consecutive days from DOY 012 to DOY 021 in 2017. The results showed that there are mm–cm differences in the RTK solution results for the raw observations at different frequencies, the mean bias and the standard deviation (STD) of the positioning results of GPS L1 and L2 in the East, North, and Up components are (−0.595 mm, 1.35 mm, −0.133 mm) and (3.11 mm, 3.32 mm, 6.44 mm), respectively, but for BDS B1 and B2, the corresponding values are (2.16 mm, −4.24 mm, 9.48 mm) and (3.35 mm, 4.85 mm, 7.41 mm), respectively. The PBDFO between GPS L1 and L2 frequencies is lower in magnitude and more stable than the PBDFO between BDS B1 and B2 frequencies, the mean and the STD of the PBDFO between GPS L1 and L2 obtained from the parameter estimation method in the East, North, and Up components are (−0.606 mm, 1.03 mm, −0.217 mm) and (0.162 mm, 0.169 mm, 0.276 mm), respectively; but for BDS B1 and B2, the corresponding values are (3.00 mm, −3.83 mm, 8.59 mm) and (0.375 mm, 1.14 mm, 2.47 mm), respectively. Both PBDFO correction model and parameter estimation approach can achieve consistency in terms of the RTK positioning results at different frequencies. The double-differenced (DD) PBDFO obtained from the direct difference method and parameter estimation approach are consistent and relatively stable for the same period of continuous days.