Real-Time Precise Point Positioning (RT-PPP) has been one of the research hotspots in GNSS (Global Navigation Satellite System) community for decades. Real-time precise products of satellite orbits and clocks are the prerequisite for RT-PPP. Thus, it is of great importance to investigate the current multi-GNSS real-time precise products in State Space Representation (SSR) from different analysis centers. In this article, SSR products from 10 analysis centers are comprehensively evaluated by comparing them with the final products and performing the kinematic PPP. The results show that analysis centers CNES (Centre National D'Etudes Spatiales) and WHU (GNSS Research Center of Wuhan University) provide the most complete products with the best quality. Concerning the accuracy of real-time products for the GNSSs, the accuracies of orbit and clock products are better than 5 cm and 0.15 ns, respectively, for Global Positioning System (GPS), followed by Galileo navigation satellite system (Galileo), BeiDou-3 Navigation Satellite System (BDS-3), GLObal NAvigation Satellite System (GLONASS), and BeiDou-2 Navigation Satellite System (BDS-2). Meanwhile, the results of the RT-PPP with quad-system show that the positioning accuracies are 1.76, 1.12 and 2.68 cm in east, north, and up directions, respectively, and the convergence time to 0.1, 0.1, 0.2 m for corresponding directions is 15.35 min.

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The Global Navigation Satellite System (GNSS) is a widely used positioning technique. Computational efficiency is crucial to applications such as real-time GNSS positioning and GNSS network data processing. Many researchers have made great efforts to address this problem by means such as parameter elimination or satellite selection. However, parameter estimation is rarely discussed when analyzing GNSS algorithm efficiency. In addition, most studies on Kalman filter (KF) efficiency commonly have defects, such as neglecting application-specified optimization and limiting specific hardware platforms in the conclusion. The former reduces the practicality of the solution, because applications that need such analyses on filters are often optimized, and the latter reduces its generality because of differences between platforms. In this paper, the computational cost enhancement of replacing the conventional KF with the information filter (IF) is tested considering GNSS application-oriented optimization conditions and hardware platform differences. First, optimization conditions are abstracted from GNSS data-processing scenarios. Then, a thorough analysis is carried out on the computational cost of the filters, considering hardware–platform differences. Finally, a case of GNSS dynamic differencing positioning is studied. The simulation shows that the IF is slightly faster for precise point positioning and much faster for the code-based single-difference GNSS (SDGNSS) with the constant velocity (CV) model than the conventional KF, but is not a good substitute for the conventional KF in the other algorithms mentioned. The real test shows that the IF is about 50% faster than the conventional KF handling code-based SDGNSS with the CV model. Also, the information filter is theoretically equivalent to and can produce results that are consistent with the Kalman filter. Our conclusions can be used as a reference for GNSS applications that need high process speed or real-time capability.

With the combination of multi-GNSS data, the precise-point positioning (PPP) technique can improve its accuracy, availability and reliability: Inter-system bias (ISB) is the non-negligible parameter in multi-GNSS PPP. To further enhance the performance of multi-GNSS PPP, it is crucial to analyze the characterization of inter system biases (ISBs) and model them properly. In this contribution, we comprehensively investigate the characterization of ISBs between global positioning system (GPS) and BeiDou navigation satellite system (BDS) in different situations. (1) We estimate ISB by using different precise products from the Center for Orbit Determination (CODE), Deutsches GeoForschungsZentrum (GFZ) and Wuhan University (WHU). The results indicate that the one-day estimates of ISB are stable when using CODE and WHU products, whereas the estimates based on GFZ products vary remarkably. As for the three-day time series of ISB, a sudden jump exists between two adjacent days, which is due to the change of satellite clock datum; (2) We investigate the ISB characterization affected by the ambient environments of the receivers. The result shows that the ISBs estimated from receivers (and antennas) with same type are still inconsistent, which indicates that the ambient environment, probably the temperature, influences the ISB characterization as well, since the receivers are in different areas; (3) We analyze the ISB characterization affected by receiver and antenna type with the same ambient environment. To ensure the same ambient environment, the ultra-short baselines were applied to investigate the ISB characterization affected by the receiver and antenna type. With the insights into ISB characterizations, we carry out combined GPS and BDS PPP with modeling the ISB as time constant, random walk process and white noise. The results suggest that the random walk process outperforms in most cases, since it strengthens the model to some extend and, at the same time, considers the variation of ISBs.

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