GNSS real-time instantaneous velocimetry based on moving-window polynomial modelling

The instantaneous kinematic velocity obtained by using a stand-alone global navigation satellite system (GNSS) receiver has attracted increasing attention, and has significant for numerous applications. Using the time difference carrier phase (TDCP) measurements, or the displacements they produced, we propose two real-time instantaneous velocity determination methods based on the moving-window polynomial model. The two methods are called the observation-domain and the coordinate-domain, correspondingly. In the calculation process, the Cholesky update method is utilized to improve numerical efficiency. The proposed methods are a finite impulse in nature, and hence are robust against modeling uncertainties, such as temporal outlying measurements, inaccurate information of noise statistics. Two vehicle-mounted experiments were performed to verify the performance of the coordinate-domain and observation-domain methods. The reference velocities used to evaluate the accuracy of velocity estimates are chosen as GNSS/INS smoothing solution and high-rate RTK solution in these two experiments, respectively. The results show that the coordinate-domain and observation-domain methods were comparable in performance, both better than that of the Nonlinear Tracking Differentiator (NTD) method. Specifically, the improvement in terms of root mean square of the proposed methods, compared with the NTD, can be 29.3-40.3% and 6.25-16.4% in the two experiments, respectively.