An Improved Divergence-Free Hatch Filter Algorithm Toward Sub-Meter Train Positioning With GNSS Single- Frequency Observations Only

Train positioning is the core function in the application of Global Navigation Satellite Systems (GNSS) in Railway Transportation. However, the use of the differential GPS (DGPS) along the Qinghai-Tibet Railway is expensive and difficult to maintain. Thus, a novel single-frequency algorithm based on the divergence-free Hatch filter is proposed, and no real-time augmentation correction input is required. The classical Hatch filter is severely affected by the divergence problem due to the ionospheric variation. In our algorithm, a novel decomposition-ensemble model is proposed for denoising and modeling the ionospheric variation, where the Variational Mode Decomposition (VMD) method is applied. With the aid of a sliding ionospheric variation fitting window, the divergence-free Hatch filter is constructed. The entire method is a so-called self-modeling method, but more efficient than recent studies. Besides, the Kalman filter is used for keeping continuous positioning accuracy. Finally, a static experiment in Tibet and a kinematic field test on the Qinghai-Tibet Railway is performed. In the ionospheric variation calculation-experiment, the experimental results show that the sliding window of our method can be shortened to 5 minutes with the data of 1s sampling rate, which basically meets the requirements of train positioning. In terms of train positioning accuracy, only the horizontal accuracy is concerned. In the static experiment, our method satisfies the accuracy requirements of the sub-meter level with a Root Mean Square Error (RMSE) value of better than 0.5m. In the kinematic test, the accuracy of our method is basically at the sub-meter level, with an RMSE value of approximately 0.6m.