## 1 Introduction  
Real-time precise point position (PPP) is an innovative global positioning technique using a single receiver on the basis of real-time satellite orbit and clock products [1; 2; 3; 4]. With the assistance of the uncalibrated phase delay (UPD) products and some atmospheric products such as tropospheric and ionospheric delay corrections, the PPP real-time kinematic (RTK) method achieves position accuracy at the centimeter level with an initialization time of 1 min or better [5; 6; 7]. Compared to the traditional reference station-based RTK positioning approach, the real-time PPP technique overcomes the limitation of the distances between reference stations and could be performed in any place where satellite correction data are available [8; 9; 10; 11; 12]. In addition, the real-time PPP is experiencing rapid development towards multiple systems and multiple frequencies for further realizing high-precision and high-reliability positioning. Real-time global positioning system (GPS) PPP has been widely used in the real-time determination of integrated water vapor, precision agriculture applications, and natural hazards monitoring [13; 14; 15; 16; 17]. However, it takes much longer convergence time with only GPS in some cases, depending on satellite geometry and prevailing atmospheric conditions [18; 19]. With the newly emerging Galileo and Beidou navigation satellite system (BDS) as well as the ongoing modernization of GPS and global navigation satellite system (GLONASS), the prosperity of multiple global navigation satellite systems (multi-GNSS) brings great opportunities for PPP to accelerate initialization time and improve positioning performance [20]. Having more available satellites increases the number of redundant observations and improves satellite geometry remarkably [21]. Unfortunately, the quality control problem also arises inevitably as the number of observations increases. As a result, the parameter estimation of the multi-GNSS combined PPP will be influenced and it is difficult to take full advantage of the combined systems. Statistical testing procedures and robust estimation methods have been widely investigated in the adjustment of GNSS data in order to control the influences of outliers. Different strategies are proposed for quality control in different scenarios, such as the data snooping of a single outlier [22], the statistical testing procedure for multiple outliers [23; 24], and the quasi-accurate detection method and robust estimation scheme for correlated observations [25; 26]. The robust estimation method not only constructs the equivalent weights in the observation model, but also adjusts the updated parameters in the dynamic model to resist the influences of outlying kinematic model errors [27]. For statistical testing methods, the assumption of multiple alternative hypotheses is established using the test statistic to detect and identify outliers according to the critical region and the probability density function [28]. These methods are usually based on rigorous and perfect theory. However, the computation is complex and even practically impossible, although possible in theory. For these quality control methods, the outliers are first detected and identified according to the strict analysis of measurement residuals. They are then removed or downweighted until the normal distributions of a posteriori residuals are satisfied. The readjustment is carried out by adding model parameters or updating the weights of observations. To simplify the quality control procedure of the multi-GNSS combined PPP, an approach is proposed that uses the experienced thresholds of the maximum residual and the maximum unit weight standard deviation (STD) as the criteria to judge whether large abnormal measurements exist. The influences of outliers can be removed from the normal equation by the traditional method, which gives the outliers zero weights and then makes readjustments.