## 1 Introduction
[19] used the uncombined dual-frequency PPP mathematical model with the prediction technique for data gaps and carrier-to-noise power density ratio (C/N\({}_{0}\)) stochastic model, and the kinematic horizontal root mean square (RMS) was approximately 7 m with the Mi 8 placed on the dashboard of the car in a realistic environment, compared with the SwiftNav Piksi real-time kinematic (RTK) solution. However, with the development of intelligent transportation system (ITS) [20] and location-based service (LBS) [21; 22], based on the requirements of applications such as augmented reality [23] and seamless positioning [20; 24], it is necessary to use some technologies such as the IMU-aided smartphones PPP scheme to achieve continuous position output with approximate positioning accuracy when GNSS signals are blocked. Therefore, some researchers have suggested work on multi-sensor fusion such as GNSS/MEMS to enable more accurate and continuous positioning in the GNSS-signal-denied environment [25; 26]. The characteristics of IMU data of some smartphones have been studied in depth. [PERSON] et al. [27] analyzed the quality of available IMU and GNSS measurements provided by Mi 8 both in static and kinematic mode, respectively. The experimental results showed that the high-precision IMU clearly outperforms Mi 8 in terms of sensor noise, and the accelerometer data errors of the \(z\)-axis are higher than the \(x\)-axis and \(y\)-axis, while the gyroscope measurements of the \(z\)-axis perform best followed by the \(y\)-axis and finally the \(x\)-axis. [PERSON] et al. [28] investigated the effects of initial attitude estimation errors on loosely coupled GPS/IMU of the Samsung Galaxy A5 with the parameter estimation model based on extended Kalman filter (EKF), and the experimental results showed that the estimated roll, pitch, and yaw angles tend to deviate rapidly with the initial estimation errors increase. [PERSON] et al. [29] processed the IMU data of Mi 8 and Honor Play using a 15-state Kalman filter for a GNSS/INS coupled navigation model. Althoughthe yaw estimation accuracy is only a few degrees and is significantly worse than that of the other attitude parameters, the authors still believe that the IMUs of Mi 8 and Honor Play have a good performance for three-dimensional (3D) positioning and the determination of the velocity and attitude angles. Then, [PERSON] et al. [30] proposed a modified Kalman filter which was used in the GNSS/IMU coupled navigation to integrate the different rate data of gyroscope and accelerometer in smartphones; the experimental results showed that the attitude solution was improved obviously in the simulated GNSS-denied situation. [PERSON] et al. [31] integrated the smartphone sensor data, including IMU, GNSS, and cameras using the parameter estimation model based on EKF to enhance the navigation performance. Although the location information of the smartphone GNSS/INS coupled model can be obtained directly from the serial port or estimated by standard single point positioning (SPP), the absolute positioning performance of the smartphone is also limited due to the lack of GNSS carrier phase observations and the larger pseudorange measurement noise. Meanwhile, in view of characteristics of smartphone GNSS and IMU sensors data, the PPP/INS coupled model suitable for conventional geodetic receiver cannot directly be used for GNSS and IMU sensors data from a smartphone. Therefore, the GNSS PPP/IMU coupled mathematical model of smartphones with multiple parameters and variable signal quality in GNSS-degraded environments still needs to be further studied and improved. In this paper, we analyze in detail the characteristics of GNSS and IMU data from smartphones in dynamic mode under GNSS-degraded environments. Accordingly, we propose a comprehensive positioning model by fusing uncombined PPP and MEMS-IMU mathematical models for smartphones.