GPS/BDS short-term ISB modelling and prediction

The Chinese BeiDou Navigation Satellite System (BDS) has completed its first milestone by providing coverage of the Asia–Pacific area navigation service since December 27, 2012. With the combination of BDS, the GNSS precise point positioning (PPP) can improve its positioning accuracy, availability and reliability. However, in order to achieve the best positioning solutions, the inter-system bias (ISB) between GPS and BDS must be resolved as precisely as possible. In this study, a 1-week period (GPS week 1810) of GPS/BDS observations for 18 distributed stations from the International GNSS Service Multi-GNSS Experiment are processed. Primarily, the ISB is estimated by an extended Kalman filter as a piece-wise parameter every 30 min. Then we generate a smoothed ISB series (ISB_s) with a sliding window median filter to reject the outliers from the original estimated ISB series (ISB_o). After analysing the characteristics of the ISB_s, a short-term station-dependent ISB model based on a 1-week period is proposed in this study. This model consists of a quadratic polynomial in time and two or three periodic functions with diurnal and semi-diurnal periods. Frequency spectrum analysis is used to determine the periods of the periodic functions, and the coefficients of the quadratic function and the periodic functions are estimated by least squares. For model verification, we compare the ISB derived from the model (ISB_m) with ISB_s (assumed the true values). The comparisons indicate an almost normal distribution. It is found that the proposed model is consistent with the true values: the root-mean-square (RMS) values being about 0.7 ns, and some stations are even better. This means that the short-term ISB model proposed has a high fitting accuracy. Hence, it can be used for ISB prediction. Comparing the prediction ISB series (ISB_p) with ISB_s in the following week (GPS week 1811), we can draw the conclusion that the accuracy of the prediction declines with an increase in the time period. The 1-day period precision can achieve 0.57–1.21 ns, while the accuracy of the 2-day prediction decreases to 0.77–1.72 ns. Hence, we recommend a predicting duration of 1 day. The proposed model will be beneficial for subsequent GPS/BDS PPP or precise orbit determination (POD) since the ISB derived from this model can be considered as a priori constraint in the PPP/POD solutions. With this a priori constraint, the convergence time can be shortened by 19.6, 16.1 and 2.4 % in N, E and U components, respectively. The accuracy of result in the E component is remarkably improved by 11.9 %.