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The rapid development of mass-market sensors built in portable devices has inspired a variety of ubiquitous pedestrian navigation applications. However, seamless positioning of consumer applications is still a challenge, especially in GNSS-denied environments and complex pedestrian dynamics. We present an enhanced foot-mounted pedestrian dead-reckoning (PDR) method to achieve continuous indoor and outdoor positioning for walking pedestrians. In order to improve the availability and stability of PDR under real pedestrian conditions, an adaptive zero-velocity detection method is given, and then, more accurate magnetic heading changes and pressure-based altitude changes are extracted. During stable pedestrian motions, the heuristic drift reduction models are also applied to constrain the cumulative heading and altitude errors. The field test results demonstrate that the adaptive detector performs well under different walking speeds and stair climbing, and the cumulative distance error of enhanced PDR is only 0.23%. After integrating with smartphone GNSS position, the root mean square value of PDR horizontal position error is about 1.34 m, and the multi-source information-enhanced PDR has the capability to continuously positioning in open sky, building occlusion and indoor situations under complex pedestrian walking conditions.

The latest ECMWF global reanalysis, ERA5, is able to provide hourly surface pressure and water vapor-weighted mean temperature (Tm), which are two key factors in GPS precipitable water vapor (PWV) retrieval. Performance of surface pressure, surface air temperature, and Tm derived from ERA5 and its predecessor ERA-Interim (ERAI) are evaluated by comparing with more than 2000 meteorological stations and 89 radiosonde stations in the year of 2016 over China. Average pressure error RMS is 0.7 hPa for ERA5, compared to 1.0 hPa for ERAI, and ERA5 pressure diurnal variations agree much better than ERAI with in situ measurements. Temperature and Tm differences between ERA5 and ERAI are relatively smaller, with error RMS of 1.8 K and 1.6 K for ERA5-derived temperature and Tm, respectively. PWV error contributed by reanalysis-derived parameters is also estimated. The ERA5-induced PWV error is generally less than 1 mm, with smaller errors (

The BeiDou global navigation satellite system (BDS-3) constellation deployment has been completed on June 23, 2020, with a full constellation comprising 30 satellites. In this study, we present the performance assessment of single-epoch Real-Time Kinematic (RTK) positioning with tightly combined BeiDou regional navigation satellite system (BDS-2) and BDS-3. We first investigate whether code and phase Differential Inter-System Biases (DISBs) exist between the legacy B1I/B3I signals of BDS-3/BDS-2. It is discovered that the DISBs are in fact about zero for the baselines with the same or different receiver types at their endpoints. These results imply that BDS-3 and BDS-2 are fully interoperable and can be regarded as one constellation without additional DISBs when the legacy B1I/B3I signals are used for precise relative positioning. Then we preliminarily evaluate the single-epoch short baseline RTK performance of tightly combined BDS-2 and the newly completed BDS-3. The performance is evaluated through ambiguity resolution success rate, ambiguity dilution of precision, as well as positioning accuracy in kinematic and static modes using the datasets collected in Wuhan. Experimental results demonstrate that the current BDS-3 only solutions can deliver comparable ambiguity resolution performance and much better positioning accuracy with respect to BDS-2 only solutions. Moreover, the RTK performance is much improved with tightly combined BDS-3/BDS-2, particularly in challenging or harsh conditions. The single-frequency single-epoch tightly combined BDS-3/BDS-2 solution could deliver an ambiguity resolution success rate of 96.9% even with an elevation cut-off angle of 40°, indicating that the tightly combined BDS-3/BDS-2 could achieve superior RTK positioning performance in the Asia–Pacific region. Meanwhile, the three-dimensional (East/North/Up) positioning accuracy of BDS-3 only solution (0.52 cm/0.39 cm/2.14 cm) in the kinematic test is significantly better than that of the BDS-2 only solution (0.85 cm/1.02 cm/3.01 cm) due to the better geometry of the current BDS-3 constellation. The tightly combined BDS-3/BDS-2 solution can provide the positioning accuracy of 0.52 cm, 0.22 cm, and 1.80 cm, respectively.

Reliable and correct carrier phase ambiguity resolution is the key to global navigation satellite system (GNSS) high-precision navigation and positioning applications. For kinematic situations, such as moving-baseline-based positioning and attitude determination, the baseline length between two antennas is constant; such a priori information could contribute to integer ambiguity resolution, especially when only a few satellites are viewed. In this research, three different approaches using baseline information—the linearized joint adjustment method, validation method, and constrained LAMBDA (CLAMBDA) method—are comprehensively evaluated through theoretical and experimental analyses. The performance of each method is assessed in terms of the ambiguity success rate and baseline solution accuracy with static and kinematic GPS/BDS datasets. The additional baseline length constraint improves the precision of the float solution and the ambiguity fixed success rate (compared to the standard LAMBDA method), but there are differences in the performance of the three methods. Specifically, the performance of the linearized joint adjustment method primarily depends on baseline length and improves as the baseline length increases; however, caution should be exercised for short baselines. The validation method and CLAMBDA method both consider the quadratic form of ambiguity residuals and baseline length constraint for selecting the ambiguity solution. However, the validation method directly judges the ambiguity to obtain a locally optimal solution, whereas the CLAMBDA method constructs a rigorous mathematical formula to obtain a globally optimal solution. Moreover, because the linearized joint adjustment method and CLAMBDA method primarily contribute to the float and fixed solution, respectively, we fused the two methods to improve the ambiguity resolution success rate. The results confirm that the combined algorithm achieves better performance that exceeds that of either individual method for a baseline length of tens of meters.

Autonomous orbit determination (AOD) is the ability of navigation satellites to estimate with accurate satellite orbit parameters using onboard using inter-satellite link (ISL) measurements. To overcome the unobservability of the constellation rotation error in AOD when using only the ISL measurements, the properties that the orbit inclination $$ i $$ and the longitude of the ascending node $$ \varOmega $$ of the medium earth orbit (MEO) navigation satellites, which can be predicted with high accuracy over a long time, are explored. This leads to an onboard extended Kalman filter (EKF) where $$ \left( {i,\varOmega } \right) $$ are subjected to constraints. Three experiments are carried out to assess the effectiveness of the proposed AOD EKF and analyze the causes of the constellation rotation error by processing 30-day ISL measurements of 18 MEO satellites of BDS-3 in a distributed mode. The results verify that the proposed EKF with $$ \left( {i,\varOmega } \right) $$ constraints can resolve the unobservable constellation rotation error issue effectively. When using precise EOP parameters, the 3D orbit errors of BDS-3 AOD in 30 days could be less than 2.30 m. The errors increase to 3.4 m when the predicted EOP parameters are used.

We derive orbit and clock errors for BeiDou satellites from March 1, 2013, to September 30, 2016 by comparing broadcast ephemerides with the precise ephemerides produced by Wuhan University. The broadcast ephemerides are pre-processed to filter out the “data-logging” errors, and a robust estimation is subsequently implemented for removing the time-varying common timescale bias between the broadcast and precise clocks. To obtain the nominal SISEs (Signal-In-Space Errors), the SIS (Signal-In-Space) outliers are excluded according to the standard of SIS integrity. The long-term satellite clock behavior reveals that for GEO, IGSO and MEO satellites, each category of satellites has its inter-category clock consistency, and the clocks of MEO as well as the clocks of IGSO satellites have better inter-category consistency than that of GEO satellites. Between different categories, GEO satellite clocks have been more divergent from IGSO satellite clocks since May 2014. The larger orbit errors, resulting in approximately 1–2 m orbit-only UREs (User Range Errors), periodically occur for all satellites every half year when the satellites are in eclipse period. For the GEO and IGSO satellites, several larger orbit errors may be caused by the effect of satellite maneuvering, resulting in 2–3 m orbit-only UREs. Most satellite clocks have a nonzero mean, and all MEO satellite clocks have a positive mean of approximately 1.0 m, whereas the IGSO satellite clocks have a negative mean at the same level. For the GEO satellites, the various means indicate that the clocks are divergent from one to another. The clock standard deviation of 1 m is achieved by all satellites except for C03. Near-zero means are obtained in along-track, cross-track and radial errors for the IGSO and MEO satellites but not for the GEO satellites. The average RMSs (Root Mean Square) of approximately 0.8, 1.7 and 2.0 m are obtained for the orbit-only UREs, global-average UREs and worst-UREs, respectively, for the constellation as a whole. The RMSs of clock errors for GEO, IGSO and MEO are 1.8, 1.4 and 1.3 m, respectively. Due to a nearly-static observation geometry, the GEO satellites always have the worst SISE performance, and as a result, they degrade the overall SISE statistical characterization. The analysis of URE and broadcast URA (User Range Accuracy) indicates that the broadcast URA of 2.0 m throughout is slightly optimistic. The unchanging URA of 2.0 m may not be able to describe adequately the accuracy of UREs. Instead, the upper-bound URA of 2.4 m is recommended to users. The cross-correlation analysis results show that there is a significant positive correlation between along-track errors and radial errors, whereas radial errors are not evidently correlated to clock errors as they are with GPS.

The Hatch---Melbourne---Wubbena (HMW) combination is a geometry-free and ionospheric-free (first-order) function that has been widely used for cycle slip detection and ambiguity resolution in GNSS dual-frequency data processing. We investigate the characteristics of HMW combinations for BeiDou navigation satellite system (BDS) observations for different types of satellites. We first study the characteristics of BDS undifferenced (UD) HMW combinations. Obvious systematic errors are found on BDS UD HMW combinations. The characteristics of single-differenced (SD) and double-differenced (DD) HMW combinations are then analyzed. The results indicate that the biases do not cancel in single-differencing between two satellites. On the contrary, they are amplified because of the superposition of the systematic biases of two satellite signals. In single-differencing between two receivers, different characteristics are found for different satellites types depending on baseline length. For inclined geostationary orbit (IGSO) and Medium Earth Orbit (MEO), the systematic biases cancel for single-differencing between receivers or double-differencing over short and medium baselines; however, they do not cancel in single-differencing between receivers or double-differencing over long baselines. Regarding geostationary earth orbit (GEO), the systematic biases do not cancel for single-differencing between receivers or double-differencing over both short and long baselines. In addition, we analyze the sources of the systematic biases of the BDS HMW combination. The systematic biases of IGSO and MEO HMW combinations mainly originate from multipath errors at the satellite; the systematic biases of GEO HMW combinations may also originate from multipath errors. Finally, we study the influence of the systematic errors on wide-lane ambiguity resolution by analyzing the consistency of the fractional part of the averaged SD HMW combinations and the fixing rate of DD wide-lane ambiguity resolution. The results are compared with those of GPS.