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 one week period (GPS week 1810) of GPS/BDS observations for 18 distributed stations from the International GNSS Service (IGS) Multi-GNSS Experiment (MGEX) are processed. Primarily, the ISB is estimated by an extended Kalman filter (EKF) as a piece-wise parameter every 30 minutes. 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 analyzing the characteristics of the ISB_s, a short-term station-dependent ISB model based on a one 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 (LS). 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 team 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 increase of the time period. The one day period precision can achieve 0.57-1.21 ns, while the accuracy of the two day prediction decreases to 0.77-1.72 ns. Hence we recommend a predicting duration of one day. The proposed model will be beneficial for subsequent GPS/BDS PPP or Tianhe Xu ()

GNSS signals are blocked in forests, urban canyons, and indoors. Precise positioning can hardly be guaranteed in these challenging environments. A low earth orbit (LEO) constellation serving as a navigation system can provide stronger signal power to ground receivers due to its shorter transmission path than GNSS. The fast motion of LEO satellites contributes to the fast change of spatial geometry, allowing for rapid convergence of precise point positioning (PPP), and is effective in detecting carrier phase cycle slips. This study comprehensively analyzed the LEO-constellation-augmented multi-GNSS for real-time PPP in various challenging environments, including the blocking of satellite signals, cycle slips, the two issues occurring simultaneously, and significant multipath effects. An improved cycle slip detection and fixing algorithm taking advantage of LEO satellites is proposed. The GPS, BDS, and a 96-satellite polar-orbiting LEO constellation are designed, and observations at a mid-latitude station are simulated. The results show that the inclusion of LEO satellites shortens the convergence time and significantly improves the cycle slip fixing performance of multi-GNSS PPP. Three to four visible LEO satellites can shorten the GPS/BDS/LEO (GCL, C is the designation used in RINEX for BDS) PPP convergence time to 4 min compared to 20 min for the GPS/BDS (GC) solutions. Additionally, the correct cycle slip fixing time shortens from 3.3 min for the GC solution to 0.8 min for the GCL solution. When LEO satellites are free of cycle slips, the GNSS integer cycle ambiguities can be instantaneously fixed, and PPP instantaneous re-convergence is obtained. When significant multipath effects are considered, the time for GNSS/LEO first correct fixing is 3 min longer. The PPP solutions are noisier because the relatively shorter continuous observation time of LEO satellites is not beneficial for the smooth of multipath errors. In the case of GNSS and LEO satellites under both signal shielding and cycle slips, the GNSS/LEO PPP re-convergence and cycle slip fixing both degrade when the cut-off elevation increases from 20° to 40°, since LEO satellites are almost out of sight at a cut-off elevation of 40°. It is concluded that the inclusion of LEO satellites considerably improves the GNSS PPP in terms of the (re-)convergence and cycle slip fixing performance.

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