Xuan Zou

The rapid development of unmanned aerial vehicles (UAVs) in recent years has promoted their application in various fields, such as precise agriculture, formation flight, etc. In these applications, the accurate and reliable real-time position and attitude determination between each moving device in the same platform system are the key issue for safe and effective cooperative works. In traditional ways, static reference stations should be set up near the platform to keep the stable position datum of the platform system. In this paper, we abandoned the static stations and expected to achieve stable position datums with the platform system itself. To achieve this goal, we proposed an improved method based on both the Global Positioning System (GPS)/Beidou Navigation Satellite System (BDS) data and the inertial navigation system (INS) data to obtain precise positions of the moving devices. The time-differenced carrier phase (TDCP) was used to get the position variations and update the positions over time, and then, the INS data was integrated to further improve the accuracy and reliability of the updated positions; thus, this method is denoted as the TDCP/INS method. To evaluate the performance of this method and compare it with the traditional single-point positioning (SPP) method and the Kalman filtered SPP (KFSPP) method, a field vehicle experiment was conducted, and the position results achieved from these three methods were compared with those from the tightly combined real-time kinematic positioning (RTK)/INS method, where centimeter-level accuracy was obtained and regarded as the reference. The quantitative analysis where the position variations were evaluated and the qualitative analysis where the vehicle trajectories in three typical urban driving scenarios were discussed were both made for the three methods. The numerical results showed that the accuracy of the position variations from the SPP, KSPP, and TDCP methods was at the meter level, while that from the TDCP/INS method improved to the centimeter level, and the accuracies were 1.9 cm, 2.9 cm, and 3.1 cm in the east, north, and upward directions. The trajectory results also demonstrated a perfect consistency of the driving positions between the TDCP/INS method and the reference. As a contrast, the trajectories from the SPP and KFSPP methods had frequent jumps or sways when the vehicle drove along a large, curved road, turned at a crossroad, and passed under an urban viaduct.

The multipath error is considered to be the most limiting factor for high precision positioning applications. The sidereal filtering (SF) method can be used to mitigate the multipath error in the observation domain, and it has been successfully applied in the multipath mitigation in global positioning systems (GPS) and regional BeiDou navigation satellite systems (BDS2). However, there are few reports on the SF method in other systems. The performance of the SF method relies on the explicit orbit repeat periods of satellites in diverse systems or even different types of constellations. It is therefore inconvenient to utilize the SF method for multi-GNSS multipath error mitigation. Alternatively, a space domain multipath error reduction method, which establishes the multi-point hemispherical grid model (MHGM) using the residuals of the double-differenced carrier phase observations in the ambiguity-fixed period, has been modified. It is an integrated model for multi-GNSS, without considering the diversity of different systems and constellations. To compare the performance of MHGM and SF from a multi-GNSS point of view, the determination method of orbit repeat periods via the broadcast ephemerides is summarized, and the SF method is extended to the global BeiDou navigation satellite system (BDS3) and Galileo navigation satellite system. Further test results show that the performance of MHGM and SF are comparable from the perspective of root mean squares (RMS) and the power spectrum analysis of double-differenced residuals, as well as the static positioning results. This implies that the space domain MHGM can obtain similar correction effects as the SF method in the observation domain, but the former is more flexible for modeling with various systems’ data. In addition, the established MHGM using the data of multi orbit periods demonstrates a better performance compared with that of only one orbit period, and an average improvement of 13.1% in the RMS of the double-differenced residuals can be achieved.

The multipath effect on carrier-phase observations is related to the observational environment of the station, and cannot be eliminated or attenuated by the differential method. In the actual dam environment of deformation monitoring, multipath is very complicated. It is the main error source of BDS-2 for high precision data processing. In this paper, a new method called the multi-point hemispherical grid model (MHGM) is studied and evaluated. This method uses the hemispheric grid model to attenuate the influence of multipath errors. The effectiveness and improvement of the new method with respect to the popular sidereal filter (SF) method were assessed and verified by the actual dam monitoring data with only the BDS-2. The MHGM and SF approach calculates the multipath corrections from multi-days historical data, and then corrects the multipath error from the observations on the day of interest. Compared with the SF method, the MHGM can also effectively provide a graphical display of multipath error interference around the stations, which matches the surrounding observation environment. The results show that the double-differenced (DD) residuals of the MHGM for GEO/IGSO and MEO satellites are slightly better than those of SF, but the RMS of MHGM for GEO/IGSO+MEO DD residuals is improved by about 17.0%. The performance of the MHGM method for different satellite constellations is consistent and not affected by the different orbital repeat times, which could solve the “zero mean” assumption problem of the SF method. Meanwhile, the RMS of static with a 2 h interval and kinematic positioning errors of the MHGM method in the horizontal and vertical direction can be up to 1.7, 3.6 and 2.4, 8.1 mm, respectively. The MHGM model could avoid the multipath reference problem caused by different orbital repetition periods, making it more suitable for the combined multipath modeling of BDS-2 and BDS-3.

The European Global Navigation Satellite System Galileo is gradually deploying its constellation. In order to provide reliable navigation and position services, the effectiveness and reliability of ambiguity resolution between reference stations is necessary in network real-time kinematic (NRTK). The multifrequency signal of Galileo could much enhance the ambiguity resolution (AR) reliability and robustness. In this study, to exploit full advantage of this, the geometry-free (GF) TCAR and ionospheric-free (IF) triple-carrier ambiguity resolution (TCAR) methods were utilized in solving the ambiguity in the Hong Kong area, which is an ionosphere disturbance active area, and compared with each other. The IF TCAR method was then used to combine multi-systems to improve Galileo E1 AR performance, which is named as the combined IF (CIF) TCAR method. Three experiments were carried out in the Hong Kong area and the results showed that the Galileo-only system could fix ambiguities on all satellite pairs correctly and reliably by the IF TCAR method, while the GF TCAR method showed a weaker performance. The wide-lane (WL) convergence time of the IF TCAR method is improved by about 37.6%. The IF TCAR method with respect to the GF TCAR method could improve the WL accuracy by 21.6% and the E1 accuracy by 72.7%, respectively. Compared with GPS-only TCAR or Galileo-only TCAR, the ambiguity accuracy and the convergence time of the CIF TCAR method, which combines GPS and Galileo, could be improved by about 25.7% and 47.1%, respectively.

The multipath effect is a crucial error source caused by the environment around the station and cannot be eliminated or mitigated by differential algorithms. Theoretically, the maximum value for the carrier phase is a quarter the wavelength, i.e., about 4.8 cm for the GPS L1 signal. Considering the increasing demands of high-precision applications, the multipath error has become a major factor affecting the accuracy and reliability of GPS millimeter-level data processing. This paper proposes a multi-point hemispherical grid model (MHGM) to mitigate the multipath effect. In this method, the hemisphere centered on each station is divided into a grid, and the multipath error at the station is estimated based on the parameterization of the grid points. The double-differenced (DD) observed-minus-calculated (OMC) values on some previous days are treated as the observation values to model the present multipath error. Contrary to the present methods which rely much on the platform of data collection and processing, MHGM can be potentially applied to GPS data processing with the existing hardware and software. Experiments in high-multipath and low-multipath environments are designed by mounting a baffle or not. The experimental results show that MHGM is effective in mitigating the multipath effect. When using data from the previous day, an average improvement of about 63.3% in the RMS of DD OMC can be made compared with that without correction, and this is basically consistent with the sidereal filtering (SF) method which is 63.0%. Furthermore, the effectiveness of the above two methods is better than that of the empirical site model (ESM). The kinematic positioning results are also basically consistent with the statistical results of the RMS values of DD OMC. Historical data from more than one day can more explicitly and effectively model the MHGM. Furthermore, compared with the SF method, the MHGM can be used not only to mitigate the multipath error, but also to orientate the sources of the multipath error around the station, and give guidance in the physical elimination of these sources.

The loose combination (LC) and the tight combination (TC) are two different models in the combined processing of four global navigation satellite systems (GNSSs). The former is easy to implement but may be unusable with few satellites, while the latter should cope with the inter-system bias (ISB) and is applicable for few tracked satellites. Furthermore, in both models, the inter-frequency bias (IFB) in the GLObal NAvigation Satellite System (GLONASS) system should also be removed. In this study, we aimed to investigate the performance difference of ambiguity resolution and position estimation between these two models simultaneously using the single-frequency data of all four systems (GPS + GLONASS + Galileo + BeiDou Navigation Satellite System (BDS)) in three different environments, i.e., in an open area, with surrounding high buildings, and under a block of high buildings. For this purpose, we first provide the definition of ISB and IFB from the perspective of the hardware delays, and then propose practical algorithms to estimate the IFB rate and ISB. Thereafter, a comprehensive performance comparison was made between the TC and LC models. Experiments were conducted to simulate the above three observation environments: the typical situation and situations suffering from signal obstruction with high elevation angles and limited azimuths, respectively. The results show that in a typical situation, the TC and LC models achieve a similar performance. However, when the satellite signals are severely obstructed and few satellites are tracked, the float solution and ambiguity fixing rates in the LC model are dramatically decreased, while in the TC model, there are only minor declines and the difference in the ambiguity fixing rates can be as large as 30%. The correctly fixed ambiguity rates in the TC model also had an improvement of around 10%. Once the ambiguity was fixed, both models achieved a similar positioning accuracy.

The network real-time differential positioning technique is a good choice for meter and sub-meter level’s navigation. More attention has been paid to the Global Positioning System (GPS) and GPS + GLONASS (GLObal NAvigation Satellite System) network real-time differential positioning, but less on the GPS + BDS (BeiDou Navigation Satellite System) combination. This paper focuses on the GPS + BDS network real-time differential positioning. Since the noise of pseudorange observation is large, carrier-phase-smoothed pseudorange is usually used in the network real-time differential positioning to improve the positioning accuracy, while it will be interrupted once the satellite signal is lost or a cycle slip occurs. An improved algorithm in the position domain based on position variation information is proposed. The improved method is immune to the smoothing window and only depends on the number of available satellites. The performance of the network real-time differential positioning using the improved method is evaluated. The performance of GPS + BDS combination is compared with GPS-only solution as well. The results show that the positioning accuracy can be increased by around 10%–40% using the improved method compared with the traditional one. The improved method is less affected by the satellite constellation. The positioning accuracy of GPS + BDS solution is better than that of GPS-only solution, and can reach up to 0.217 m, 0.159 m and 0.330 m in the north, east and up components for the static user station, and 0.122 m, 0.133 m and 0.432 m for the dynamic user station. The positioning accuracy variation does not only depend on whether the user is inside or outside the network, but also on the position relation between the user and network.