Objectives  The rapid development of unmanned aerial vehicles (UAV), autonomous driving and other fields have put forward higher accuracy requirements for global navigation satellite system real-time kinematic positioning. However, the traditional filtering model with constant velocities based on the Doppler measurements, or the filtering model with position variations based on the time-differenced carrier phase measurements, is difficult to describe the accurate state of the moving targets, and thus cannot acquire their real-time, accurate, and stable location information, especially when the receiver can only observe a single system. To solve this issue, we propose a novel filtering model for real-time kinematic positioning, and its performance is compared with the above two filtering models.

  Methods  The time-variable parameters, including the coordinates and the receiver clock error, are eliminated according to the equivalent elimination principle.The integer ambiguities are removed and the atmospheric delays are reduced using the time-differenced observations. The quasi-static Kalman filtering model is constructed by considering the impact of the model residuals, and the described state in the filtering model becomes much more consistent with the reality. The estimated model residuals are used to correct the position information of moving targets. In this way, the accumulation of the model residuals when directly using the time-differenced phase observables to obtain the position variations are greatly alleviated. The kinematic positioning experiments were carried out using the single-frequency GPS and BeiDou satellite navigation system(BDS) data collected by the UAV and the vehicle platforms, respectively, and the obtained results from three different filtering models are compared with the referenced results from real-time kinematic positioning.

  Results  Experimental results show that: (1) The filtering model based on the equivalent elimination principle can achieve positioning convergence better than 30 s. Compared with the filtering model based on time-differenced phase observables, the convergence time of the proposed method is improved by about 50%. (2) The standard deviations of the three-dimensional relative positioning errors with respect to the position at the initial epoch are generally within 10 cm, and the horizontal accuracy can reach 3 cm. In addition, the positioning accuracy of UAV in open environment is better than that of vehicle. (3) The number of observed BDS satellites is obviously more than that of the GPS satellites, whether on the UAV platform or on the vehicle platform. This makes a great contribution to a faster convergence speed and better stability of kinematic positioning for the BDS than those for the GPS.

  Conclusions  The filtering model based on the equivalent elimination principle can achieve shorter convergence time and more accurate positioning results relative to the position at the initial epoch. But it is still susceptible to cycle slips, and cannot obtain accurate absolute positions. In the future work, the approach to accurate absolute position determination at the initial epoch will be investigated, and the real trajectory of the moving target will be achieved thereby.