Estimation and evaluation of hourly Meteorological Operational (MetOp) satellites' GPS receiver differential code biases (DCBs) with two different methods

Abstract

Abstract. Differential code bias (DCB) is one of the Global Positioning System (GPS) errors, which typically affects the calculation of total electron content (TEC) and ionospheric modeling. In the past, DCB was normally estimated as a constant in 1 d, while DCB of a low Earth orbit (LEO) satellite GPS receiver may have large variations within 1 d due to complex space environments and highly dynamic orbit conditions. In this study, daily and hourly DCBs of Meteorological Operational (MetOp) satellites' GPS receivers are calculated and evaluated using the spherical harmonic function (SHF) and the local spherical symmetry (LSS) assumption. The results demonstrated that both approaches could obtain accurate and consistent DCB values. The estimated daily DCB standard deviation (SD) is within 0.1 ns in accordance with the LSS assumption, and it is numerically less than the standard deviation of the reference value provided by the Constellation Observing System for Meteorology Ionosphere and Climate (COSMIC) Data Analysis and Archive Center (CDAAC). The average error's absolute value is within 0.2 ns with respect to the provided DCB reference value. As for the SHF method, the DCB's standard deviation is within 0.1 ns, which is also less than the standard deviation of the CDAAC reference value. The average error of the absolute value is within 0.2 ns. The estimated hourly DCB with LSS assumptions suggested that calculated results of MetOpA, MetOpB, and MetOpC are, respectively, 0.5 to 3.1 ns, −1.1 to 1.5 ns, and −1.3 to 0.7 ns. The root mean square error (RMSE) is less than 1.2 ns, and the SD is under 0.6 ns. According to the SHF method, the results of MetOpA, MetOpB, and MetOpC are 1 to 2.7 ns, −1 to 1 ns, and −1.3 to 0.6 ns, respectively. The RMSE is under 1.3 ns and the SD is less than 0.5 ns. The SD for solar active days is less than 0.43, 0.49, and 0.44 ns, respectively, with the LSS assumption, and the appropriate fluctuation ranges are 2.0, 2.2, and 2.2 ns. The variation ranges for the SHF method are 1.5, 1.2, and 1.2 ns, respectively, while the SD is under 0.28, 0.35, and 0.29 ns.