## 1 Introduction  
Accuracy, precision and availability requirements are very stringent in urban navigation, advanced driver assistance system (ADAS) and autonomous driving. In order to meet these requirements at a few cm to dm level, Global Navigation Satellite System (GNSS) carrier phase observations must be used in a relative positioning mode [1]; the observations and their uncertainty must be modelled adequately in the positioning filter. Unfortunately, a sound quality description of GNSS observations in kinematic applications with different receivers is still missing, which is important for a stringent quality control of the observations and subsequent improved integrity of the positioning application. For static applications, double difference (DD) residuals of geodetic-grade receivers were tested in zero and short baseline setups, indicating optimum and more realistic performance including multipath, respectively. Also, the need for improvement in the Global Positioning System (GPS) stochastic models was stressed based on the obtained results, particularly elevation dependency of carrier phase observations per satellite and correlation between L1 and L2 phase observations [2, 3]. Based on this type of study, adequate observation weighting models have been derived, for example, based on carrier-to-noise density ratios [4; 5; 6] or taking atmospheric correlations into account [7; 8]. Specifically, in [4], the Sigma-\(\epsilon\) model is proposed and its use in resolving the poor satellite geometry problem by considering data from low elevating satellites is described with a real data-set. The Sigma-\(\epsilon\) model extended by the Danish method can be used to remove outliers due to multipath and diffraction from the phase data and consequently improve the positioning precision [5]. An improved observation weighting model based on signal-to-noise ratio measurements is proposed in [6]; it shows that about 10% more ambiguities could be resolved with low elevation data when compared to the standard elevation-dependent weighting model. A variance-covariance model (VCM) based on the turbulence theory is developed to explain the stochastic characteristics of carrier phase observations due to atmospheric fluctuations [7]. A study considering correlation among observations with a diagonal covariance matrix shows a significant improvement in the positioning solution of the simulated and real data-set compared with positions estimated using a standard diagonal dependent elevation model [8]. The performance of low-cost and geodetic-grade receiver combinations is studied by a static zero-baseline experiment [9]; results show that the DD carrier phase noise is about 2.2 mm with a low-cost receiver combination and convey the feasibility of integrating low-cost equipment in a multi-sensor system. For characterisation of GNSS receivers in kinematic applications, position deviations or carrier phase residuals are analysed with respect to a reference trajectory often obtained from a GNSS/inertial measurement unit (IMU) tightly coupled solution [10; 11]. Moreover, high sensitivity GNSS receivers can track very weak signals in comparison to geodetic-grade receivers [12]. It is also shown that high sensitivity GNSS receivers when fed with a miniaturised atomic clock would lead to an improvement in the precision of vertical position and velocity estimates. For real-time kinematic (RTK) processing over short baselines in an urban environment, multipath errors are significant and degrade the positioning results. In order to apply proper weighting to the observations, an elevation dependent exponential function weighting is proposed for GPS code range and phase range measurements [13]. It is shown that by using C/N\({}_{0}\) weighting with appropriate models for phase observations, diffracted observations at high elevation could be identified [4; 10]. A weighting model combining both elevation and C/N\({}_{0}\) for both code and phase observations in open-sky and suburban scenarios for horizontal RTK positioning is explained in [14].