## 1 Introduction  
The use of survey-grade Global Navigation Satellite System (GNSS) receivers and antennas has traditionally been the only solution to achieve fast and high precision positioning. With the emerging GNSSs, such as the BeiDou Navigation Satellite System (BDS), Galileo and the Quasi-Zenith Satellite System (QZSS), low-cost receivers have been proven to be capable to bring a near competitive ambiguity resolution and mm-cm level positioning performance to that of more expensive survey-grade GNSS receivers and antennas [1, 2, 3, 4]. Before 2005, there were fewer than ten smartphone models equipped with GPS [5]. Currently, it is hard to find any smartphone that is without GPS (or GNSS) positioning functionality. There has also been a recent rapid development in small-size and low-cost GNSS smartphone chipsets that adopt dual-frequency, multi-GNSS, code and phase measurements for enhanced positioning precisions [6, 7]. Several studies [8, 9, 10, 11, 12] have highlighted that smartphone antennas are highly sensitive to multipath effects. [PERSON] et al. [8] showed by using an auxiliary external antenna connected to a smartphone that it was possible to overcome the multipath sensitivity of the smartphone antennas and subsequently achieved cm level positioning precision. A few other recent studies [12; 13] have further suggested that cm level positioning precision can be achieved in a short-baseline model while using the smartphone internal antennas and a Kalman filter to link parameters in time (multi-epoch model). [PERSON] and [PERSON] [14] and [PERSON] et al. [15] recently confirmed that there is a presence of carrier phase drifts in some smartphone observation data with an arbitrary phase offset, whereas similar phase offsets and drifts appeared in other earlier and later smartphone positioning studies as well (e.g., [8; 9; 12; 16; 17; 18]). In this contribution, we will assess such anomalies in the phase data and the instantaneous (single-epoch) real-time kinematic (RTK) performance of two Samsung Galaxy S20 and two Google Pixel 4 smartphones, all forming their individual RTK baselines. In our model and different from other studies above is that _all_ parameters will be unlinked in time, and the benefit of using the instantaneous RTK model is that it then becomes insensitive to cycle slips. For all analysed baselines we will make use of several hours of data with a one second measurement interval, so that our conclusions will be statistically significant. As a part of our analysis, we will explicitly investigate two setup configurations, namely having the smartphones in an (_i_) upright and (_ii_) lying down position, while tracking GNSS signals from both external and internal antennas. This is motivated by the fact that we want the internal smartphone antennas to be as uninfluenced from the surrounding environment as possible to minimize possibility of signal interference or other effects coming from the poor antenna gain of the smartphones [13]. This contribution is organised as follows. In Section 2, the multi-GNSS RTK functional model is described and in Section 3 the smartphone GNSS data and stochastic model settings are presented. The combined dual-frequency GPS L1 + L5, Galileo E1 + E5a, QZSS L1 + L5 and BDS B1 code and carrier phase observations, are then evaluated in Section 4 by empirical integer least square (ILS) ambiguity success rates (SR) and the obtainable positioning precisions for a zero-baseline experiment. The tracked BDS constellation consists of BDS-2 [19] and BDS-3 satellites [20]. The zero-baseline is formed by placing the smartphones inside a Radio Frequency (RF) shielding box with a re-radiating antenna, which is further connected through an amplifier to an external low-cost antenna. The instantaneous smartphone RTK positioning performance is then assessed, and the characteristics of the double-differenced (DD) carrier-phase and code residuals are analysed while having the smartphones in an upright and lying down position.