# GPS/BDS Medium/Long-Range RTK Constrained with Topospheric Delay Parameters from NWP Model
## 1 Introduction  
Real Time Kinematic (RTK) positioning with instantaneous ambiguity resolution (AR) and Precise Point Positioning (PPP) are currently popular techniques for real-time precise positioning based on carrier phase observation. These techniques have been widely used in surveying and navigation fields. A reliable real-time PPP service can provide precise positioning on a global scale [1]. However, PPP needs a comparatively long initialization time of about \(20\) min [2]. Generally, RTK provides centimeter-level positioning services with a relatively short initialization time over a baseline shorterthan about 80 km [3]. However, the GPS alone RTK shows limitations in the initialization time, convergence speed and positioning accuracy due to the insufficient visible satellite and limited spatial geometry, especially in urban areas where the signals are blocked or interrupted. In addition, RTK is limited to the local or regional area due to the significant ionospheric delay and tropospheric delay, especially over the medium/long-range baselines. Global Navigation Satellite Systems (GNSS) are evolving to a new era due to the modernization of the current GPS and the upcoming other systems. The US GPS system achieved its Full Operation Capacity (FOC) in 1995 and is currently improving through the GPS modernization programme [4]. China started constructing its own satellite navigation system in the 1980s, called BeiDou Navigation Satellite System (BDS). The first generation of BDS (BDS-1) started service from 2003 with two Geostationary Earth Orbit satellites (GEOs). The service area covered China and the surrounding region with functions of positioning, timing and short message communication. The positioning accuracy of BDS-1 is better than 20 m. At the end of 2012, BDS-2 started service with 14 satellites, including five GEOs, five Inclined Geosynchronous Satellite Orbit satellites (IGSOs) and four Medium Earth Orbit satellites (MEOs). BDS-3 with 30 satellites will be established in 2020, and China implemented the BDS-3 experimental project in order to demonstrate the new generation of BDS from 2015 to 2016. Compared to BDS-2, the User Equivalent Range Error (UERE) is reduced, the multipath effects have been weaken, and the estimation and prediction of satellite orbit, satellite clock offset have been greatly improved through support of the inter-satellite links [5]. Undoubtedly, the availability, reliability integrity, positioning accuracy and convergence speed of the GPS/BDS RTK, and even the multiple-constellation GNSS RTK, can be significantly improved in comparison with the GPS alone RTK [6; 7; 8]. As a result, improving the performance of GPS alone RTK and GPS/BDS RTK over the medium- and long-range baselines will be the main focus of this study. In GNSS positioning, the main errors can be grouped as three parts: satellite-related errors, propagation-related errors and receiver-related errors. Satellite-related errors, such as satellite clock error, orbit error, and wind-up effect, are very similar to receivers, and they can be removed or reduced by differential methods or using International GNSS Service (IGS) real-time product. Receiver related error sources include receiver clock errors, measurement noise and multipath. These errors are local environmental dependent, and cannot be removed by external augmentations. Fortunately, with the development of receiver technology, the accuracy of pseudorange is approaching 10 cm or less; carrier phase can achieve millimeter accuracy. Propagation-related effect is introduced by the troposphere and ionosphere when GPS signals traverse from the satellite to the receiver. As GNSS are providing triple-even multiple-frequency signals, ionospheric delays can be removed from the combinations of different frequencies [8; 9; 10]. As was reported in our paper [11], we developed a new ionosphere-free ambiguity resolution method for long-range baselines, which can eliminate the ionospheric delay in the ambiguity search stage.