Characteristics of receiver-related biases between BDS-3 and BDS-2 for five frequencies including inter-system biases, differential code biases, and differential phase biases

It is foreseeable that the BeiDou navigation satellite system with global coverage (BDS-3) and the BeiDou navigation satellite (regional) system (BDS-2) will coexist in the next decade. Care should be taken to minimize the adverse impact of the receiver-related biases, including inter-system biases (ISBs), differential code biases (DCB), and differential phase biases (DPB) on the positioning, navigation, and timing (PNT) provided by global navigation satellite systems (GNSS). Therefore, it is important to ascertain the intrinsic characteristics of receiver-related biases, especially in the context of the combination of BDS-3 and BDS-2, which have some differences in their signal level. We present a method that enables time-wise retrieval of between-receiver ISBs, DCB, and DPB from multi-frequency multi-GNSS observations. With this method, the time-wise estimates of the receiver-related biases between BDS-3 and BDS-2 are determined using all five frequencies available in different receiver pairs. Three major findings are suggested based on our test results. First, code ISBs are significant on the two overlapping frequencies B1II and B2b/B2I between BDS-3 and BDS-2 for a baseline with non-identical receiver pairs, which disrupts the compatibility of the two constellations. Second, epoch-wise DCB estimates of the same type in BDS-3 and BDS-2 can show noticeable differences. Thus, it is unreasonable to treat them as one constellation in PNT applications. Third, the DPB of BDS-3 and BDS-2 may have significant short-term variations, which can be attributed to, on the one hand, receivers composing baselines, and on the other hand, frequencies.

A new method to estimate GPS satellite and receiver differential code biases using a network of LEO satellites

The differential code biases (DCBs) of the global positioning system (GPS) receiver onboard low-Earth orbit (LEO) satellites are commonly estimated by a local spherical symmetry assumption together with the known GPS satellite DCBs from ground-based observations. Nowadays, more and more LEO satellites are equipped with GPS receivers for precise orbit determination, which provides a unique chance to estimate both satellite and receiver DCBs without any ground data. A new method to estimate the GPS satellite and receiver DCBs using a network of LEO receivers is proposed. A multi-layer mapping function (MF) is used to combine multi-LEO satellite data at varying orbit heights. First, model simulations are conducted to compare the vertical total electron content (VTEC) derived from the multi-layer MF and the reference VTEC obtained from the empirical ionosphere model International Reference Ionosphere and Global Core Plasmasphere Model. Second, GPS data are collected from five LEO missions, including ten receivers used to estimate both the satellite and receiver DCBs simultaneously with the multi-layer MF. The results show that the GPS satellite DCB solutions obtained from space-based data are consistent with ground-based solutions provided by the Centre for Orbit Determination in Europe. The proposed normalization procedure combining topside observations from different LEO missions has the potential to improve the accuracies of satellite DCBs of Global Navigation Satellite Systems as well as the receiver DCBs onboard LEO satellites, although the number of LEO missions and spatial–temporal coverage of topside observations are limited.

Estimation and Analysis of GNSS Differential Code Biases (DCBs) Using a Multi-Spacing Software Receiver

In the use of global navigation satellite systems (GNSS) to monitor ionosphere variations by estimating total electron content (TEC), differential code biases (DCBs) in GNSS measurements are a primary source of errors. Satellite DCBs are currently estimated and broadcast to users by International GNSS Service (IGS) using a network of GNSS hardware receivers which are inside structure fixed. We propose an approach for satellite DCB estimation using a multi-spacing GNSS software receiver to analyze the influence of the correlator spacing on satellite DCB estimates and estimate satellite DCBs based on different correlator spacing observations from the software receiver. This software receiver-based approach is called multi-spacing DCB (MSDCB) estimation. In the software receiver approach, GNSS observations with different correlator spacings from intermediate frequency datasets can be generated. Since each correlator spacing allows the software receiver to output observations like a local GNSS receiver station, GNSS observations from different correlator spacings constitute a network of GNSS receivers, which makes it possible to use a single software receiver to estimate satellite DCBs. By comparing the MSDCBs to the IGS DCB products, the results show that the proposed correlator spacing flexible software receiver is able to predict satellite DCBs with increased flexibility and cost-effectiveness than the current hardware receiver-based DCB estimation approach.

GNSS-Based Non-Negative Absolute Ionosphere Total Electron Content, its Spatial Gradients, Time Derivatives and Differential Code Biases: Bounded-Variable Least-Squares and Taylor Series

Global navigation satellite systems (GNSS) allow estimating total electron content (TEC). However, it is still a problem to calculate absolute ionosphere parameters from GNSS data: negative TEC values could appear, and most of existing algorithms does not enable to estimate TEC spatial gradients and TEC time derivatives. We developed an algorithm to recover the absolute non-negative vertical and slant TEC, its derivatives and its gradients, as well as the GNSS equipment differential code biases (DCBs) by using the Taylor series expansion and bounded-variable least-squares. We termed this algorithm TuRBOTEC. Bounded-variable least-squares fitting ensures non-negative values of both slant TEC and vertical TEC. The second order Taylor series expansion could provide a relevant TEC spatial gradients and TEC time derivatives. The technique validation was performed by using independent experimental data over 2014 and the IRI-2012 and IRI-plas models. As a TEC source we used Madrigal maps, CODE (the Center for Orbit Determination in Europe) global ionosphere maps (GIM), the IONOLAB software, and the SEEMALA-TEC software developed by Dr. Seemala. For the Asian mid-latitudes TuRBOTEC results agree with the GIM and IONOLAB data (root-mean-square was < 3 TECU), but they disagree with the SEEMALA-TEC and Madrigal data (root-mean-square was >10 TECU). About 9% of vertical TECs from the TuRBOTEC estimates exceed (by more than 1 TECU) those from the same algorithm but without constraints. The analysis of TEC spatial gradients showed that as far as 10–15° on latitude, TEC estimation error exceeds 10 TECU. Longitudinal gradients produce smaller error for the same distance. Experimental GLObal Navigation Satellite System (GLONASS) DCB from TuRBOTEC and CODE peaked 15 TECU difference, while GPS DCB agrees. Slant TEC series indicate that the TuRBOTEC data for GLONASS are physically more plausible.