# GNSS RTK Positioning Augmented with Large LEO Constellation
## 1 Introduction  
With the fast development and widespread application of global navigation satellite system (GNSS), the demands of spatiotemporal information have already been changed from static to dynamic position, post to real-time process, and low to high precision. Currently, the real-time kinematic (RTK) positioning by using GNSS double-differenced (DD) observations can achieve centimeter-level positioning accuracy quickly after correctly performing the ambiguity resolution [1]. However, the RTK technique is limited to baseline length defined as the distance between the reference and rover stations, the main reason for which is that atmospheric activities above stations have an important influence on the DD ambiguity fixing [2]. For the short baselines with lengths usually shorter than 10 km, the remaining atmospheric delays, i.e., ionospheric and tropospheric delays can be significantly weakened or assumed negligible by forming DD observations, so that the carrier-phase ambiguitiescan be fixed correctly in short time, or even in one epoch [3]. On the other hand, the medium and long baselines with lengths up to tens or hundreds of kilometers, the remaining atmospheric errors, especially for ionospheric delays are hard to be eliminated by DD, which seriously affected the phase ambiguity fixing [4]. In order to solve this problem, there are many methods of addressing ionospheric residuals or improving ambiguity fixing within multiple frequencies or systems [5; 6; 7; 8; 9]. [PERSON] et al. analyzed the instantaneous long-baseline RTK performance using the ionosphere-float strategy, based on dual-frequency GPS and BDS data [10]. The results have been shown that GPS+BDS scheme can significantly shorten the time to first fix (TTFF) from 21 to 12 min in comparison to the GPS scheme and thus quickly achieve ambiguity-fixed baseline precisions at the mm-m level. Meanwhile, it is also demonstrated that the combined system can accelerate convergence to reach a dm-level precision under the circumstance of the ambiguity-float solution. In addition, the multi-baseline network based RTK system can significantly mitigate atmospheric delays at the rover station by using generated spatial information, [PERSON] et al. investigated the relationship between the ionospheric effect and the scale of two medium networks from the aspects of positioning result and ambiguity success rate [11]. While in some case, such as the forest and urban environments, RTK technique cannot be good enough to deliver practical application [12; 13]. Thanks to the appearance and development of low earth orbit (LEO) constellation with the orbit altitudes between 400 and 1500 km, which can provide much stronger signals against spoofing and jamming, as well as much faster movement speeds to improve satellites geometric distribution, compared with GNSS satellites [14; 15]. Possibly, it will be an alternative or a complement for existing solutions to enhance the RTK positioning and navigation performance by combining GNSS and LEO satellites. In recent years, some reliable data fusion algorithms utilizing LEO constellations to improve GNSS positioning performance have been under study. Back in the 1990s, [PERSON] et al. explored a method and an apparatus which using LEO satellite signals to augment GPS differential positioning in a [PERSON]'s patent [16]. [PERSON] et al. designed a receiver which is capable of tracking GPS and Globalstar LEO satellites [17]. It is found that the ambiguity resolution could be achieved within 4 min by introducing Globalstar LEO constellation alone to short-range (1-5 km) differential positioning, which attributes to the improvement of geometric condition at ground stations. Afterwards, some researches about integrating the iridium and current GNSS measurements have been carried out to investigate the contribution of LEO augmentation, such as fulfilling navigation integrity requirements, revisiting nominal measurement error models, and accelerating floating ambiguities estimation [18; 19]. [PERSON] et al.