# Estimation of Inter-System Biases between BDS-3/GPS/Galileo and Its Application in RTK Positioning
## 1 Introduction  
The advent of modernized global positioning system (GPS), the Galileo satellite navigation system (Galileo), and BeiDou Navigation Satellite System (BDS) have provided vital improvements in the accuracy and robustness of satellite-based positioning, navigation, and timing (PNT) service applications [1]. Having provided PNT service in the Asia-Pacific region for six years, the China Satellite Navigation Office (CSNO) officially announced that the third generation of BDS (BDS-3) began to provide global service on 27 December 2018, which was a milestone as BDS enlarged the service region from Asia-Pacific to worldwide [2, 3, 4]. On 13 July 2020, the chairperson of China announced the official start of BDS-3, which provides a variety of services. Specifically, it provides the PNT, global short message communication, and international search and rescue services for global users; satellite-based augmentation, ground augmentation, precise point positioning (PPP), and regional short message communication services can be obtained throughout China [5]. As designed, the constellation of BDS-3 consists of 3 geostationary orbit (GEO) satellites, 3 inclined geo-synchronous orbit (IGSO) satellites, and 24 medium Earth orbit (MEO) satellites [6]. [PERSON] [7] comprehensively introduced BDS-3 in terms of its constellation, signal, service, etc. [PERSON] [6] assessed the system status and positioning performance of BDS-2/3 with large amounts of observation data distributed around the globe. The new signals ofBDS-3 were initially assessed by [PERSON] [8] from various aspects: its constellation, signal quality, and the accuracy of relative positioning with combined BDS-2/3. As for other GNSSs, the new generation of GPS III-A is gradually updating and a total of 31 operational satellites comprise the GPS constellation [9], whereas 26 satellites can be tracked in the Galileo constellation [10]. As a typical technology of relative positioning, real-time kinematic (RTK) positioning is widely applied in marine navigation, velocity measurements, automatic driving, etc. [11; 12; 13]. Centimeter-level precision can be achieved when the float ambiguities are correctly fixed to integers [14]. In the functional RTK model, various observational errors are eliminated by the double difference (DD). Specifically, the satellite-based and receiver-based observational errors are eliminated by between-receiver single difference (SD) and between-satellite SD, respectively [15]. In the DD observations, most of the atmosphere delay can be eliminated considering the short distance between the base station and the rover station [16]. In the past, extensive research on the single GPS RTK was conducted to evaluate its performance in different situations [17; 18; 19]. The application of single GPS RTK may be extremely limited due to the insufficient number of satellites and the poor configuration of the constellation in hostile environments. However, with the rapid development of GNSSs, the multi-system RTK has become accessible and the application scope of RTK was further broadened [20; 21; 22]. In multi-system RTK, not only the vital ambiguity resolution, but also the accuracy and reliability of positioning results are improved remarkably compared to the single-system RTK. [PERSON] [23] analyzed the performance of GPS + BDS RTK and found that the success rate (SR) and reliability of GPS + BDS RTK are better than those of GPS in instantaneous RTK. [PERSON] [22] reported that, with the combined system of GPS + BDS, much larger (40\({}^{\circ}\)) cutoff elevations than the customary value (10\({}^{\circ}\)) can be used in RTK positioning. [PERSON] [20] compared single-frequency dual-system (SF-DS) RTK with dual-frequency single-system (DF-SS) RTK in single-epoch mode, and the results showed that low-cost receivers for SF-DSs have the potential to achieve comparable ambiguity resolution performance to that of a DF-SS.