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The Autonomous Navigation (AutoNav) mode of a Global Navigation Satellite System (GNSS) utilizes Inter-Satellite Links (ISLs) to maintain satellite operations without the service from the ground control segment. The newly launched Beidou satellites are capable of conducting ISLs for orbit determination to improve their autonomy, integrity, reliability, and robustness. However, the satellite orbit errors can increase over time due to various force model errors, particularly that of Solar Radiation Pressure (SRP). Accelerometers aboard satellites can measure non-conservative forces directly and have been successfully used in satellite missions for gravity recovery and atmosphere study (i.e., GRACE, CHAMP, and GOCE). This study investigates the feasibility to use accelerometers aboard Beidou satellites to improve AutoNav accuracy and service span. The results show that in a simulated 180-day AutoNav period, the orbit accuracy with the aid of accelerometers is two times better than that of using ISL data only.

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 (

Attitude determination based on global navigation satellite systems (GNSS) is characterized by high-precision, low-cost, and no error accumulation. However, GNSS harsh-signal environments will degrade the accuracy and reliability of GNSS attitude. In this case, micro-electro-mechanical system (MEMS) inertial sensors are often integrated with dual-antenna GNSS for more reliable and continuous attitude determination. In this paper, we fused dual-antenna GNSS and MEMS to acquire heading, pitch, and roll with high accuracy in GNSS challenged environments. Instead of a Euler angle representation, the misalignment is used to build the state model in the integrated Kalman filter. Attitudes derived from dual-antenna GNSS and smoothed acceleration are adopted as measurements. It can be found that this filtering architecture is actually a subset of loosely coupled GNSS/MEMS integration. Therefore, the proposed module can be easily embedded into loosely coupled integration. In addition, due to the disadvantage that GNSS is sensitive to signal interference and obstacles, the fault detection and exclusion strategy was proposed to avoid the filtering divergence and to improve the reliability of attitude determination. Finally, two vehicular tests with a 1.12-m baseline conducted in GNSS friendly and challenged environments showed that the proposed attitude determination algorithm could detect and exclude all GNSS-attitude outliers, thus achieve the high accuracy of 0.2°, 0.39°, and 0.28° for heading, pitch, and roll angles in the challenged environment, respectively. With the MEMS-gyroscope aiding, the attitude gaps caused by GNSS outages are bridged. For a 300-s outage duration, the average accumulated attitudes errors are 2.37°, 0.88°, and 1.40°.

To ensure the compatibility and interoperability with modernized GPS, Galileo satellites are capable of broadcasting navigation signals on carrier phase frequencies that overlap with GPS, i.e., GPS/Galileo L1-E1/L5-E5a. Moreover, the GPS/Galileo L2-E5b signals have different frequencies with wavelength differences smaller than 4.2 mm. Such overlapping and narrowly spaced signals between GPS and Galileo bring the opportunity to use the tightly combined double-differenced (DD) model for precise real-time kinematic (RTK) positioning, resulting in improved performance of ambiguity resolution and positioning with respect to the classical standard or loosely combined DD model. In this paper, we focus on the model and performance assessment of tightly combined GPS/Galileo L1-E1/L2-E5b/L5-E5a RTK for short and long baselines. We first investigate the tightly combined GPS/Galileo DD observational model for both short and long baselines with simultaneously considering the GPS/Galileo overlapping and non-overlapping frequencies. Particularly, we introduce a reparameterization approach to solve the rank deficiency that caused by the correlation between the DISB parameters and the DD ionospheric parameters for both overlapping and non-overlapping frequencies. Then we present performance assessment for the tightly combined GPS/Galileo RTK model with real-time estimation of the differential inter-system bias (DISB) parameters for short and long baselines in terms of ratio value, ambiguity dilution of precision (ADOP), ambiguity conditional number, decorrelation number, search count, empirical success rate, time-to-first-fix (TTFF), and positioning accuracy. Results from both static and kinematic experiments demonstrated that compared to the loosely combined model, the tightly combined model can deliver improved performance of ambiguity resolution and precise positioning with different satellite visibility. For the car-driven short baseline experiment with 10° elevation cut-off angle, the tightly combined model can not only significantly increase the ratio value by approximately 27.5% (from 16.0 to 20.4), but also reduce the ambiguity ADOP, the conditional number, and the search count in LAMBDA by approximately 22.2% (from 0.027 to 0.021 cycles), 14.9% (from 199.2 to 169.6), and 25.4% (from 150.1 to 112.0), respectively. Comparable decorrelation number, empirical success rate, and positioning accuracy are also obtained. For the car-driven long baseline experiment, it is also observed that the ambiguity resolution performance in terms of the ratio value, the decorrelation number, the condition number, and the search count are significantly improved by approximately 18.5% (from 2.7 to 3.2), 22.0% (from 0.186 to 0.227), 55.9% (from 937.6 to 413.7), and 10.3% (from 43.8 to 39.3), respectively. Moreover, comparable ADOP, empirical success rate, and positioning accuracy are obtained as well. Additionally, the TTFF can be reduced (from 54.1 to 51.8 epochs with 10° elevation cut-off angle) as well from the results of static experiments.

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.

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.

This paper first investigates the influencing factors of between-receiver Differential Inter-System Bias (DISB) between overlapping frequencies of the Global Positioning System (GPS), Galileo and the Quasi-Zenith Satellite System (QZSS). It was found that the receiver reboot and the type of observations may have an impact on DISBs. The impact of receiver firmware upgrades and the activation of anti-multipath filters are also investigated and some new results are presented. Then a performance evaluation is presented of tightly combined relative positioning for a short baseline with GPS/Galileo/QZSS L1-E1-L1/L5-E5a-L5 observations with the current constellations, in which the recently launched Galileo and QZSS satellites will also be included. It is demonstrated that when DISBs are a priori calibrated and corrected, the tightly combined model can deliver a much higher empirical ambiguity resolution success rate and positioning accuracy with respect to the classical loosely combined model, especially under environments where the observed satellites for each system are limited and only single-frequency observations are available. The ambiguity dilution of precision, bootstrapping success rate, and ratio values are analysed to illustrate the benefits of the tightly combined model as well.

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.

In precise relative positioning applications, an effective approach to improve the interoperability of GNSS systems is the tightly combining or inter-system double-differencing of observations from the common frequencies that are shared by different constellations. As the BeiDou satellites are currently transmitting a B2 signal at 1207.14 MHz that is identical to the Galileo E5b signal, the inter-system double-differenced observations can also be created between observations from both systems at that particular frequency. In this paper, we will focus on the instantaneous ambiguity resolution performance analysis of tightly combining BeiDou B2 and Galileo E5b observations. The size and stability of phase and code Differential Inter-System Biases (DISBs) between BeiDou B2 and Galileo E5b signals are first investigated, in which the new BeiDou and Galileo satellites launched recently will also be included. Then, first results of the Tightly Combined Model (TCM) with a priori corrected DISBs (TCM_C) are evaluated in comparison to the Loosely Combined Model (LCM) and tightly combined model with unknown DISBs (TCM_F) in an instantaneous approach. It is demonstrated that the instantaneous integer ambiguity resolution performance can be improved using the TCM_C with respect to LCM and TCM_F.

Medium-long baseline RTK positioning generally needs a long initial time to find an accurate position due to non-negligible atmospheric delay residual. In order to shorten the initial or re-convergence time, a rapid phase ambiguity resolution method is employed based on GPS/BDS multi-frequency observables in this paper. This method is realized by two steps. First, double-differenced un-combined observables (i.e., L1/L2 and B1/B2/B3 observables) are used to obtain a float solution with atmospheric delay estimated as random walk parameter by using Kalman filter. This model enables an easy and consistent implementation for different systems and different frequency observables and can readily be extended to use more satellite navigation systems (e.g., Galileo, QZSS). Additional prior constraints for atmospheric information can be quickly added as well, because atmospheric delay is parameterized. Second, in order to fix ambiguity rapidly and reliably, ambiguities are divided into three types (extra-wide-lane (EWL), wide-lane (WL) and narrow-lane (NL)) according to their wavelengths and are to be fixed sequentially by using the LAMBDA method. Several baselines ranging from 61 km to 232 km collected by Trimble and Panda receivers are used to validate the method. The results illustrate that it only takes approximately 1, 2 and 6 epochs (30 s intervals) to fix EWL, WL and NL ambiguities, respectively. More epochs’ observables are needed to fix WL and NL ambiguity around local time 14:00 than other time mainly due to more active ionosphere activity. As for the re-convergence time, the simulated results show that 90% of epochs can be fixed within 2 epochs by using prior atmospheric delay information obtained from previously 5 min. Finally, as for positioning accuracy, meter, decimeter and centimeter level positioning results are obtained according to different ambiguity resolution performances, i.e., EWL, WL and NL fixed solutions.

To fast estimate high-dimensional ambiguities, we propose a new lattice reduction algorithm based on QR decomposition, which achieves fast integer transformation through an iterative strategy of whole size reduction and the deep insertion of minimum basis vectors. It acquires better basis vectors for ambiguity resolution. The feasibility of the proposed algorithm is verified by comparing its performance with those of LAMBDA, LLL, the parallel Cholesky-based reduction algorithm with ascending sorting (ASCE), and a modified LLL algorithm with deep insertions (PotLLL) under three experimental scenarios. The Hermite defect and defined length ratio are used to measure the reduction quality. Both metrics verify that our proposed method acquires a good reduced basis for accelerating the ambiguity search. To evaluate the practical ambiguity resolution behaviour, we tracked the runtime of ambiguity resolution. The results show that the computational efficiency of the proposed algorithm is better than those of the ...

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.

Reliable and accurate carrier phase ambiguity resolution is the key to high-precision Global Navigation Satellite System (GNSS) positioning and application. With the fast development of modern GNSS, the increased number of satellites and ambiguities makes it hard to fix all ambiguities completely and correctly. The partial ambiguity fixing technique, which selects a suitable subset of high-dimensional ambiguities to fix, is beneficial for improving the fixed success rate and reliability of ambiguity resolution. In this contribution, the bootstrapping success rate, bounded fixed-failure ratio test, and the new defined baseline precision defect are used for the selection of the ambiguity subset. Then a model and data dual-driven partial ambiguity resolution method is proposed with the above three checks imposed on it, which is named the Triple Checked Partial Ambiguity Resolution (TC-PAR). The comprehensive performance of TC-PAR compared to the full-fixed LAMBDA method is also analyzed based on several criteria including the fixed rate, the fixed success rate and correct fixed rate of ambiguity as well as the precision defect and RMS of the baseline solution. The results show that TC-PAR could significantly improve the fixed success rate of ambiguity, and it has a comparable baseline precision to the LAMBDA method, both of which are at centimeter level after ambiguities are fixed.

In this contribution, we assess, for the first time, the tightly combined real-time kinematic (RTK) with GPS, Galileo, and BDS-3 operational satellites using observations from their overlapping L1-E1-B1C/L5-E5a-B2a frequencies. First, the characteristics of B1C/B2a signals from BDS-3 operational satellites is evaluated compared to GPS/Galileo L1-E1/L5-E5a signals in terms of observed carrier-to-noise density ratio, pseudorange multipath and noise, as well as double-differenced carrier phase and code residuals using data collected with scientific geodetic iGMAS and commercial M300Pro receivers. It’s demonstrated that the observational quality of B1C/B2a signals from BDS-3 operational satellites is comparable to that of GPS/Galileo L1-E1/L5-E5a signals. Then, we investigate the size and stability of phase and code differential inter-system bias (ISB) between BDS-3/GPS/Galileo B1C-L1-E1/B2a-L5-E5a signals using short baseline data collected with both identical and different receiver types. It is verified that the BDS-3/GPS/Galileo ISBs are indeed close to zero when identical type of receivers are used at both ends of a baseline. Moreover, they are generally present and stable in the time domain for baselines with different receiver types, which can be easily calibrated and corrected in advance. Finally, we present initial assessment of single-epoch tightly combined BDS-3/GPS/Galileo RTK with single-frequency and dual-frequency observations using a formal and empirical analysis, consisting of ambiguity dilution of precision (ADOP), ratio values, the empirical ambiguity resolution success rate, and the positioning accuracy. Experimental results demonstrate that the tightly combined model can deliver much lower ADOP and higher ratio values with respect to the classical loosely combined model whether for GPS/BDS-3 or GPS/Galileo/BDS-3 solutions. The positioning accuracy and the empirical ambiguity resolution success rate are remarkably improved as well, which could reach up to approximately 10%∼60% under poor observational conditions.

The successful launch of five new-generation experimental satellites of the China’s BeiDou Navigation Satellite System, namely BeiDou I1-S, I2-S, M1-S, M2-S, and M3-S, marks a significant step in expanding BeiDou into a navigation system with global coverage. In addition to B1I (1561.098 MHz) and B3I (1269.520 MHz) signals, the new-generation BeiDou-3 experimental satellites are also capable of transmitting several new navigation signals in space, namely B1C at 1575.42 MHz, B2a at 1176.45 MHz, and B2b at 1207.14 MHz. For the first time, we present an initial characterization and performance assessment for these new-generation BeiDou-3 satellites and their signals. The L1/L2/L5 signals from GPS Block IIF satellites, E1/E5a/E5b signals from Galileo satellites, and B1I/B2I/B3I signals from BeiDou-2 satellites are also evaluated for comparison. The characteristics of the B1C, B1I, B2a, B2b, and B3I signals are evaluated in terms of observed carrier-to-noise density ratio, pseudorange multipath and noise, triple-frequency carrier-phase ionosphere-free and geometry-free combination, and double-differenced carrier-phase and code residuals. The results demonstrate that the observational quality of the new-generation BeiDou-3 signals is comparable to that of GPS L1/L2/L5 and Galileo E1/E5a/E5b signals. However, the analysis of code multipath shows that the elevation-dependent code biases, which have been previously identified to exist in the code observations of the BeiDou-2 satellites, seem to be not obvious for all the available signals of the new-generation BeiDou-3 satellites. This will significantly benefit precise applications that resolve wide-lane ambiguity based on Hatch–Melbourne–Wubbena linear combinations and other applications such as single-frequency precise point positioning (PPP) based on the ionosphere-free code–carrier combinations. Furthermore, with regard to the triple-frequency carrier-phase ionosphere-free and geometry-free combination, it is found that different from the BeiDou-2 and GPS Block IIF satellites, no apparent bias variations could be observed in all the new-generation BeiDou-3 experimental satellites, which shows a good consistency of the new-generation BeiDou-3 signals. The absence of such triple-frequency biases simplifies the potential processing of multi-frequency PPP using observations from the new-generation BeiDou-3 satellites. Finally, the precise relative positioning results indicate that the additional observations from the new-generation BeiDou-3 satellites can improve ambiguity resolution performance with respect to BeiDou-2 only positioning, which indicates that observations from the new-generation BeiDou-3 satellites can contribute to precise relative positioning.

The continual miniaturization of mass-market sensors built in mobile intelligent terminals has inspired the development of accurate and continuous navigation solution for portable devices. With the release of Global Navigation Satellite System (GNSS) observations from the Android Nougat system, smartphones can provide pseudorange, Doppler, and carrier phase observations of GNSS. However, it is still a challenge to achieve the seamless positioning of consumer applications, especially in environments where GNSS signals suffer from a low signal-to-noise ratio and severe multipath. This paper introduces a dedicated android smartphone application called Walker that integrates the GNSS navigation solution and MEMS (micro-electromechanical systems) sensors to enable continuous and precise pedestrian navigation. Firstly, we introduce the generation of GNSS and MEMS observations, in addition to the architecture of Walker application. Then the core algorithm in Walker is given, including the time-differenced carrier phase improved GNSS single-point positioning and the integration of GNSS and Pedestrian Dead Reckoning (PDR). Finally, the Walker application is tested and the observations of GNSS and MEMS are assessed. The static experiment shows that, with GNSS observations, the RMS (root mean square) values of east, north, and up positioning error are 0.49 m, 0.37 m, and 1.01 m, respectively. Furthermore, the kinematic experiment verifies that the proposed method is capable of obtaining accuracy within 1–3 m for smooth and continuous navigation.

Cycle slip detection and repair is a prerequisite for high-precision global navigation satellite system (GNSS)-based positioning. With the modernization and development of GNSS systems, more satellites are available to transmit triple-frequency signals, which allows the introduction of additional linear combinations and provides new opportunities for cycle slip detection and repair. In this paper, we present a new real-time cycle slip detection and repair method under high ionospheric activity for undifferenced Global Positioning System (GPS)/BeiDou Navigation Satellite System (BDS) triple-frequency observations collected with a single receiver. First, three optimal linearly independent geometry-free pseudorange minus phase combinations are selected to correctly and uniquely determine the cycle slips on the original triple-frequency carrier phase observations. Then, a second-order time-difference algorithm is employed for the pseudorange minus phase combinations to mitigate the impact of between-epoch ionospheric residuals on cycle slip detection, which is especially beneficial under high ionospheric activity. The performance of the approach is verified with static GPS/BDS triple-frequency observations that are collected with a 30 s sampling interval under active ionospheric conditions, and observations are manually inserted with simulated cycle slips. The results show that the method can correctly detect and repair cycle slips at a resolution as small as 1 cycle. Moreover, kinematic data collected from car-driven and airborne experiments are also processed to verify the performance of the method. The experimental results also demonstrate that the method is effective in processing kinematic data.

Inertial navigation system needs to be initialized through the alignment process, before the transition into the navigation stage can be made. In this article, a robust cascaded strategy of alignment which aims to provide an automatic operating alignment strategy for different application scenarios is proposed. The robust cascaded strategy of alignment utilizes the advantages of several alignment methods to form a cascaded alignment strategy. As a result, the robust cascaded strategy of alignment can be utilized in applications with different grade inertial measurement units under complex dynamic condition. In addition, several control measures are added into the robust cascaded strategy of alignment process to increase its robustness and to ensure that acceptable performance may be attained. A filed test using two inertial measurement units (tactical-grade FSAS and micro-electro-mechanical-system-grade SBG) shows that the proposed robust cascaded strategy of alignment can achieve alignment under various dynamic conditions, such as low speed motion, turns, stationary positions, and straight motion. The mean heading error and level angle error are 0.10° and −0.08° for the FSAS, respectively, and −0.44° and −0.02° for the SBG, respectively. The root mean square of the heading error and level angle error for the FSAS are 2.08° and 0.50°, respectively, while those for the SBG are 2.95° and 1.44°, respectively.

The BeiDou satellite-induced code biases have been confirmed to be orbit type-, frequency-, and elevation-dependent. Such code-phase divergences (code bias variations) severely affect absolute precise applications which use code measurements. To reduce their adverse effects, an improved correction model is proposed in this paper. Different from the model proposed by Wanninger and Beer (2015), more datasets (a time span of almost two years) were used to produce the correction values. More importantly, the stochastic information, i.e., the precision indexes, were given together with correction values in the improved model. However, only correction values were given while the precision indexes were completely missing in the traditional model. With the improved correction model, users may have a better understanding of their corrections, especially the uncertainty of corrections. Thus, it is helpful for refining the stochastic model of code observations. Validation tests in precise point positioning (PPP) reveal that a proper stochastic model is critical. The actual precision of the corrected code observations can be reflected in a more objective manner if the stochastic model of the corrections is taken into account. As a consequence, PPP solutions with the improved model outperforms the traditional one in terms of positioning accuracy, as well as convergence speed. In addition, the Melbourne-Wübbena (MW) combination which serves for ambiguity fixing were verified as well. The uncorrected MW values show strong systematic variations with an amplitude of half a wide-lane cycle, which prevents precise ambiguity determination and successful ambiguity resolution. After application of the code bias correction models, the systematic variations can be greatly removed, and the resulting wide lane ambiguities are more likely to be fixed. Moreover, the code residuals show more reasonable distributions after code bias corrections with either the traditional or the improved model.