# GPS + BDS Network Real-Time Differential Positioning Using a Position Domain Estimation Method
## 1 Introduction  
Multi-constellation global navigation satellite system (GNSS) can provide more reliable and accurate position information than the standalone Global Positioning System (GPS). Since the BeiDou Navigation Satellite System (BDS) began to provide regional services in the Asia-Pacific region at the end of 2012 [1], many efforts have been made on its combination with GPS. GPS + BDS combination has been widely used in high precision positioning [2; 3; 4; 5] and the meter and sub-meter level's navigation [6; 7]. In this contribution we will look at the application and performance of GPS + BDS combination in the meter and sub-meter level's navigation. The real-time differential positioning technique, also referred to as the pseudorange differential positioning technique, is a good choice for the meter and sub-meter level's navigation due to itseasy implementation without ambiguity resolution and competent positioning accuracy. [PERSON] et al. (2018) and [PERSON] et al. (2018) have demonstrated the good performance of GPS + BDS real-time differential positioning for short baselines. However, the positioning accuracy and reliability deteriorates as the baseline length gets longer because of the reduced spatial correlation of several distance-dependent errors ([PERSON] et al., 2018). Thanks to the infrastructure of multiple reference stations, the network real-time differential positioning can provide a potential solution. Nowadays, numerous official and commercial ground-based and satellite-based augmentation systems, such as SAPOS (Satellitepositionierungsdienst), LAAS (Local Area Augmentation System), OmniStar VBS (Virtual Base Station) and EGNOS (European Geostationary Navigation Overlay Service), have provided the network real-time differential services ([PERSON] et al., 2018). The network real-time differential positioning technique has been widely used in marine transport ([PERSON] et al., 2018), vehicle navigation ([PERSON] et al., 2018) and Geographical Information Systems ([PERSON] et al., 2018). For the application of this technique, more attention has been paid to the GPS and GPS + GLONASS combination ([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018), and applications using GPS + BDS combination can hardly be found. In this contribution, we will focus on the GPS + BDS network real-time differential positioning. Considering the large noise of pseudorange observation, carrier-phase-smoothed pseudorange is usually used in the network real-time differential positioning to ensure the accuracy of both correction and position. The Hatch filter ([PERSON], 1988) is a popular method to smooth pseudorange measurements for single-frequency receiver, but it will be affected by the inappropriate smoothing window. Dual-frequency divergence free (DFree) Hatch filter ([PERSON], 1988) can avoid this problem, but it can only be used in a multi-frequency receiver. Many other efforts have been made to improve the performance of single-frequency carrier-phase-smoothing ([PERSON] et al., 2018; [PERSON] et al., 2018; [PERSON] et al., 2018), but the improvements are indistinctive. The carrier-phase-smoothing implements only in the range domain, which means the filtering procedure will be interrupted once the satellite signal is lost or a cycle slip occurs. Strictly speaking, \"smoothing\" here should be replaced by \"filtering\" since no future information is used. But, as commonly done, \"carrier-phase-smoothing\" is still used in this paper. Instead, by reducing the effect of observation noise in the position domain, the influence of the above situations can be greatly weakened. Based on the Kalman filter, the complementary filter ([PERSON], 1988) was proposed by using the Doppler measurements for the reference trajectory calculation and the pseudorange data for trajectory update. Similar methods can also be found in [PERSON] and [PERSON] (1988); [PERSON] (1988), [PERSON] et al. (2018) and [PERSON] et al. (2018).