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With the help of constellations combined BDS-3 (BeiDou Navigation Satellite System) and LEO (Low Earth Orbit), we aim to improve the performances of PPP (Precise Point Positioning) and PPP Ambiguity Resolution (PPP-AR). First, LEO constellations with 66, 96, 156, 192, 270, and 288 satellites are designed to establish six LEO augmented constellations. Based on four challenge scenarios, PPP of six LEO augmented constellations are performed. Even in the strip-shaped obstruction area losing more than 60% of observations, the positioning accuracies of static PPP are improved by (1.0%, 5.7%, 0.2%) for BDS+66LEO, and (14.9%, 33.7%, 7.5%) for BDS+288LEO in the east, north, and up components. The positioning accuracy and convergence time improve quickly as the number of LEO satellites increased from 66 to 156, and slowdown from 192 to 288. Two constellations, BDS+156LEO and BDS+192LEO, are considered to strike the balance of acceptable PPP performance and constellation load. Then, the performance of PPP-AR is realized with the estimated UPD (Uncalibrated Phase Delay). The correlations among geodetic parameters and ambiguities deriving from the post-fit variance–covariance matrix are analyzed to illustrate the enhancement of LEO augmented constellations. Under the condition of 20°elevation angle occlusion with azimuth ranging from 0 to 360°, BDS+156LEO can achieve an ambiguity fix rate of up to 98.37% with a faster mean TTFF (Time To First Fix) of 12.76 min, and the positioning accuracies in the east, north, and up components are improved by 28.2%, 21.4%, and 15.1% respectively, compared with BDS-3. BDS+192LEO realized an 98.42% ambiguity fixing rate, and improved BDS-3 by 31.4%, 26.7% and 11.5% with its TTFF been 12.25 min. • Our work is to find cost-effective LEO augmented constellations to enhance BDS-3 PPP with acceptable positioning accuracy and convergence time, rather than realizing better performance by continuously increasing satellite number. • PPP-AR is realized with the help of our WL and NL UPD estimates of BDS-3 and LEO satellites. After analyzing the stochastic properties of UPD model theoretically, we illustrate how LEO to elevate the positioning performance through the changing of post-fit variance–covariance matrix. Then the enhancements of LEO augmented constellations are investigated. [ABSTRACT FROM AUTHOR]

In space magnetic exploration missions, the measurements obtained from the magnetic sensors mounted on a spacecraft are often influenced by the spacecraft's own magnetic interference. Therefore, to ensure precise magnetic exploration, it is imperative to conduct a thorough magnetic characterization of the spacecraft. Conducting the magnetic characterization of spacecraft within a magnetic shielded room (MSR) can mitigate the influence of environmental noise on the characterization process, thereby minimizing uncertainty and enhancing modeling accuracy. However, the utilization of high-permeability materials (such as permalloy) in the MSR introduces a disparity in magnetic characteristics between the spacecraft inside and outside the MSR. According to the method of images, the magnetic field generated by the spacecraft inside the MSR is the superposition of the magnetic fields produced by the spacecraft and that produced by several images of itself. Therefore, this may lead to an ambiguity problem, where spacecrafts with different magnetic characteristics and their corresponding images can generate identical magnetic field distribution in the MSR. To address the aforementioned issues, this paper proposes a novel method for magnetic characterization that integrates both the magnetic field vector data within the MSR and the magnetic field gradient data outside the MSR generated by the spacecraft, allowing for the elimination of the ambiguity problem without introducing environmental magnetic noise interference. As a result, it obtains a unique model for precisely representing the spacecraft's magnetic characteristics in terms of the spherical harmonic coefficients. [ABSTRACT FROM AUTHOR]

[Display omitted] • ZTD retrieval performance of GPS/BDS/Galileo frequency combinations are analyzed. • Optimal frequency combination of GPS/BDS/Galileo ZTD retrieval is L1/L2, B2/B6, and E1/E7. • GNSS-ZTD retrieval performance is related with similarity of the used frequency. • Effect analysis of ambiguity resolution and GNSS system combination on ZTD retrieval. • GNSS-ZTD retrieval performance is affected by La Niña event. The Global Navigation Satellite System (GNSS) is promising technology for zenith tropospheric delay (ZTD) retrieval. With the emergence of new multi-GNSS frequencies and maturity of precise point positioning ambiguity resolution (PPP-AR) technology, opportunities and challenges have arisen in high-precision GNSS-ZTD retrieval. However, certain strategies have usually been adopted, such as the traditional dual-frequency combination of American global positioning system (GPS) technology, for ZTD retrieval, but the influence of AR on ZTD retrieval has been ignored. To address this issue, in this study, the GNSS-ZTD retrieval performance of all existing dual-frequency combinations was first comprehensively evaluated by raw observations. Then, the influences of AR and system combinations were analysed with popular dual-frequency combinations. Finally, La Niña occurred during the GNSS data period considered in this article, and the effect on GNSS-ZTD retrieval was examined. The results of this study could not only provide a reference for GNSS-ZTD retrieval but also provide insight into the relationship between La Niña occurrence and GNSS-ZTD retrieval performance. [ABSTRACT FROM AUTHOR]

• A novel integer ambiguity resolution method for GNSS deformation monitoring. • Utilized baseline prediction construct the mixed integer least-squares criterion. • A validation procedure using real-time dynamic baseline vector predictions. • Achieved substantial performance enhancements in challenging scenarios. Accurate integer ambiguity resolution (IAR) is pivotal for high-precision and high-reliability Global Navigation Satellite Systems (GNSS) positioning. However, traditional IAR methodologies, encompassing integer estimation and validation, often face significant challenges in harsh landslide environments. This paper proposes a new IAR method based on baseline vector predictions. Initially, the real-time baseline vectors predictions are used to substitute the true values of baseline vectors in the mixed integer least-squares (MILS) estimation equation, and the MILS estimation criterion is constructed which contains the quadratic form of baseline vectors. Subsequently, a novel baseline vector validation procedure, built on real-time dynamic predictions, is established. Experiments were carried out at two GNSS landslide monitoring area using GPS + BDS dual-frequency measurement data. These stations underwent both stable deformation stages within complex measurement environments and accelerated deformation stages in open environments. Results indicate that the proposed method overcomes the limitations associated with conventional ambiguity validation methods based on hypothesis testing, addressing the errors of "abandoning trueness" and "accepting mistake" simultaneously. Notably, the ambiguity fixed rate improved by 80.7 % for single-frequency experiments and 39.8 % for dual-frequency experiments at one monitoring station located in a complex environment. This work provides valuable IAR approach for GNSS deformation monitoring applications. [ABSTRACT FROM AUTHOR]

• A BDS-3/Galileo multi-frequency phase-only (MFPO) model suitable for long baseline is proposed. • Both theoretical precision and amplified carrier phase multipath effects are considered in the selection of the optimal combination of observations. • Best Integer Equivariant (BIE) estimation improves the incorrect fixing problem existing in the conventional fixed solution in the initialization stage. • The performance of the proposed multi-frequency phase-only model in the convergence stage is superior to that of the commonly used phase-code model. Currently, long baselines generally adopt phase-code models that include both phase and pseudorange observations, such as dual-frequency ionosphere-free (PC-DFIF) and multi-frequency uncombined (PC-MFUC) models. The more significant unmodeled errors in pseudorange are likely to reduce ambiguity resolution (AR) performance, and the phase-only model with only phase observations involved is expected to avoid this problem. In view of the fact that existing phase-only research is mainly focuses on GPS/BDS-2 triple-frequency signals, a BDS-3/Galileo multi-frequency phase-only (MFPO) model is proposed in this paper. Four linearly independent extra-wide-lane (EWL) phase ranges (i.e. IR1, IR2, EWL3 and EWL4) are determined stepwise with a sliding window, among which the first two belong to ionosphere-reduced (IR) combination. In the determination of EWL3/EWL4, in addition to theoretical precision, the amplified phase multipath is also considered. The aforementioned four EWL phase ranges are then equivalently transformed to wide-lane (WL) combinations with smaller coefficients, and further incorporated with narrow-lane (NL) equation to construct MFPO model. Meanwhile, the best integer equivariant (BIE) is introduced to improve AR performance. The MFPO model is evaluated with real-tracked long baseline data. The performance of EWL phase ranges can be significantly improved after phase multipath is considered. The float solution, fixed solution and BIE solution of MFPO model all achieve centimeter-level accuracy. However, during convergence stage, incorrect fixing might exist in fixed solution, while BIE solution can improve this situation. The MFPO model is further compared with commonly used PC-DFIF and PC-MFUC models. The accuracy of the three models after convergence is basically the same, while the MFPO model has higher accuracy during convergence stage. [ABSTRACT FROM AUTHOR]

In conventional ambiguity resolution method for single-epoch, narrow-lane (NL) observations are often inaccurately fixed due to improper treatment of error sources such as ionospheric and tropospheric delays. Therefore, based on the multi-frequency observation data of the BeiDou Global Navigation Satellite System (BDS-3), this paper adopts a single-epoch resolution method based on the ionosphere-reduced combinations. Firstly, select the appropriate combination observations of extra wide-lane (EWL) and wide-lane (WL) and get its fixed ambiguity. Then the ambiguity of the WL combination with high observation accuracy is obtained by linear combination, which goes to constrain the fixation of NL ambiguity. Secondly, different from the conventional method, the ionosphere-reduced combinations observations were selected as NL, thus significantly weakening the influence of first-order ionospheric delay error on the fixation of narrow-lane ambiguity. The experimental results show that compared with the conventional methods, the method adopted in this paper can significantly improve the fixing success rate of the wide-lane ambiguity. In the NL ambiguity resolution part, using the ionosphere-reduced combinations as NL for solving improved the average fixing success rate from 68.6%/44.4%/35.7%/27.6% to 97.4%/95.4%/95.6%/87.3% compared to the conventional method of using the base frequency as NL for solving. Furthermore, the N/E/U positioning accuracy improved by an average of 63.05%/64.37%/52.27%. To sum up, this method effectively improves the success rate of NL ambiguity fixing and positioning accuracy. [Display omitted] • The article Improved the BDS single-epoch ambiguity resolution method. • The ionosphere-reduced combination was used as narrow-lane observations for fixing. • The positioning performance has been improved by reducing ionospheric errors. • The method was verified by experiments with data ranging from 16 to 60 km. [ABSTRACT FROM AUTHOR]

Highlights • A new method for multiple soft fault diagnosis of linear analog circuits. • Reliability of the approach covering all objectives of analog circuit testing. • Considering practical aspects of fault diagnosis. Abstract The problem of testing and diagnosing multiple soft faults in analog linear electronic circuits is discussed in this paper. An efficient method which detects faulty elements and evaluates their parameters is developed. The algorithm employs two diagnostic tests, carried out in AC state, providing rms values of the measured voltages. One of them, called a principal test, is used by the diagnosis procedure whereas the other test serves the validation purpose. Each of the voltages is an algebraic function of the tested parameters. The proposed algorithm solves least squares problem by minimizing the sum of squares of the differences between the measured voltages and the parametrized functions using the Levenberg-Marquardt method. The algorithm is applied to all testable sets of the elements and every time the result is verified using the validating test. The method may provide more than one set of the parameters which satisfy both tests due to ambiguity groups existing in the circuit. To adapt the method to the conditions encountered in practice, perturbations of the fault–free parameters and measurement uncertainty are taken into account. For illustration of the method the diagnoses of three benchmark linear electronic circuits are discussed using laboratory performed tests. [ABSTRACT FROM AUTHOR]

• This study proposes a GNSS network RTK algorithm called virtual atmosphere constraint (VAC) for high-precision landslide monitoring. • The effectiveness of the proposed algorithm was validated compared to traditional virtual reference station (VRS) technology. • The VAC method exhibited better accuracy, stability, and ambiguity fixing rates than the VRS method, and noise reduction further reduced the error. • After noise reduction, the RMS values of the VAC method at the stable and the other corrupted monitoring point were both reduced to a mm-level accuracy. GNSS technology is an effective all-weather, continuous and real-time method of detecting three-dimensional landslide displacement. However, current positioning methods such as the network real-time kinematic (RTK) technique based on virtual reference station (VRS) technology have some limitations, particularly a sensitivity to atmospheric modeling error. In this study, taking advantage of existing GNSS continuously operating reference stations (CORS), we propose a network RTK algorithm (virtual atmosphere constraint (VAC)) for high-precision landslide monitoring. Network modeling atmosphere delays were used as virtual observations for the terminal position solution, by which their accuracy information can be considered. Additionally, a noise reduction method that combines complementary ensemble empirical mode decomposition and median filtering was proposed to reduce GNSS signal residual errors in the original RTK coordinate time series. To validate the effectiveness of the algorithm, we processed one week of data from two monitoring receivers on the Heifangtai landslide and four surrounding CORS using the VAC and VRS methods. Results show that the original displacement time series processed with VRS was prone to jitter, whereas the VAC method exhibited better accuracy, stability, and ambiguity fixing rates. Horizontal and vertical RMS errors at a stable monitoring point were 1.7 cm and 3.9 cm for VRS-RTK and 0.9 cm and 2.3 cm for VAC-RTK; thus, VAC reduced the error by 40.1% and 20.5%, respectively. After noise reduction, the RMS values of the VAC method at the stable and the other collapsed monitoring point were both reduced to an mm-level accuracy. [ABSTRACT FROM AUTHOR]

• BDS-3 quad-frequency phase OSB for all frequency ambiguity resolution is estimated. • The B1C/B2a/B3I combination achieved the highest positioning accuracy for the PPP-WAR. • The B1C/B2a combination of BDS-3 has a faster convergence speed than B1I/B3I. • Antenna phase center must be carefully handled as it threatens multi-frequency PPP-AR. In addition to the legacy of B1I and B3I signals, the BeiDou Global Navigation Satellite System (BDS-3) also broadcasts the new navigation signals B1C and B2a, which brings new challenges and opportunities for multi-frequency precise point positioning (PPP) ambiguity resolution. The observable-specific signal biases (OSBs) provide flexible frequency choice for multi-frequency ambiguity resolution. This work implemented an approach of BDS-3 quad-frequency OSBs estimation, making the generated OSBs suitable for ambiguity resolution using any frequency combinations. Besides, the benefits of B1C and B2a signals for wide-area decimeter-level and centimeter-level point positioning with ambiguity resolution are also investigated in depth. The BDS-3 B1C/B1I/B2a/B3I measurement data of 110 stations over one month were used to estimate the quad-frequency phase OSBs, and 20 different stations were selected for PPP verification. The results indicate that the BDS-3 quad-frequency phase OSBs are relatively stable, with a standard deviation of less than 0.06 cycle. The B1C/B2a/B3I combination achieved the highest positioning accuracy for instantaneous triple-frequency PPP wide-lane ambiguity resolution, with root-mean-square of 0.15 m, 0.17 m and 0.51 m in the east, north and up directions, respectively. Moreover, the use of B1C/B2a instead of the traditional frequency B1I/B3I as the WL combination improved the single-epoch PPP accuracy. Furthermore, after solving the narrow-lane ambiguity, the median convergence time of B1C/B2a for the kinematic and static mode was 26.5 min and 14.5 min, which was shortened by 29.3 % and 27.5 % compared to the results of the B1I/B3I combination, respectively. [ABSTRACT FROM AUTHOR]

• This paper proposes a rigorous modeling procedure of BDS2/BDS3 multipath hemispherical map with quality control. • This paper for the first time to form and compare different refined multipath hemispherical maps considering the systems, satellites, and frequencies systematically. • This paper is the first to comprehensively evaluate the positioning performance based on different types of multipath hemispherical maps considering the balance between accuracy and efficiency. Multipath is one of the critical constraints in millimeter-level BeiDou navigation satellite system (BDS) positioning. Since multipath hemispherical map (MHM) can be conducted in relatively real-time and kinematic scenarios, it has great potential in real BDS applications. However, limited studies focus on the mitigation performance and efficiency problem based on MHM with the second-generation regional system (BDS2) and third-generation global system (BDS3). In this paper, the MHM is systematically studied in BDS2/BDS3 relative precise positioning, including the issues of MHM about the modeling, refinement, and evaluation. Specifically, at first, a rigorous modeling procedure of MHM with quality control is given, where the high-precision and high-reliability multipath corrections can be obtained. Second, based on a consecutive eleven-day designed experiment, different MHM models considering the systems, satellites, and frequencies are formed and compared comprehensively. Third, the MHM models are systematically evaluated on the positioning performance, including ambiguity resolution, float solution, and fixed solution. The results show that in MHM models, the multipath corrections for low elevation angles are more significant, and the multipath effects are usually different in different directions due to the obstacles. The behaviors of MHM models are dependent on the system, satellite, and frequency types. Besides, the MHM models are relatively stable over seven consecutive days. After applying the MHM models, the success rate of ambiguity resolution can be improved in millimeter-level positioning. Approximately 7 cm improvements can be obtained for the float solution in the 3D direction. The MHM models can improve the positioning accuracy by approximately 13% for the fixed solution especially in locations where the multipath is more severe. Moreover, the unified MHM method of the previous day with quality control can replace the refined MHM method when considering the balance between accuracy and efficiency. [ABSTRACT FROM AUTHOR]

• The precise point positioning (PPP) cascading ambiguity resolution (AR) method (PPP-CAR) is extended to the GPS, Galileo, BDS-2, and BDS-3 all-frequency signals. • More wide-lane (WL) ambiguities are fixed instantaneously to accelerate the narrow-lane (NL) AR. • The performances of the multi-frequency PPP-CARs on a global scale were investigated in terms of the time to first fix (TTFF) of the NL ambiguities and convergence time (CT) • With increasing frequencies, the TTFF and CT decrease significantly, attributed to the contribution of additional frequency observations. To achieve global fast centimeter-level precise point positioning (PPP), ambiguity resolution (AR) is a prerequisite. We extended the PPP cascading AR method (PPP-CAR) to the GPS, Galileo, BDS-2, and BDS-3 all-frequency signals, in which more wide-lane (WL) ambiguities were fixed instantaneously to accelerate the narrow-lane (NL) AR. The performances of the multi-frequency PPP-CARs on a global scale were investigated in terms of the time to first fix (TTFF) of the NL ambiguities and convergence time (CT). The test results indicated that the TTFF and CT decreased significantly with increasing frequencies. The dual-frequency PPP-CAR achieved an average TTFF and CT of 9.4 and 7.8 min, respectively. The average TTFFs and CTs reached 7.6, 6.1, and 5.6 min, respectively, and 6.0, 4.4, and 4.3 min, respectively, for the triple-frequency, quad-frequency, and five-frequency PPP-CARs, with improvements of 19.1%, 35.1%, and 40.4%, respectively, and 23.1%, 43.6%, and 44.9%, respectively, compared to the dual-frequency PPP-CAR. [ABSTRACT FROM AUTHOR]

• The carrier phase measurements of NavIC are more precise that can provide better position accuracy. • Even after removing all the errors, the carrier phase measurements are biased by the receiver hardware. • Time differenced double difference technique is able compute the receiver noise in terms of differential phase bias. • The differential phase bias removed carrier phase measurements provide precise position. The pseudo-range (PR) and carrier phase (CP) observations of Global Navigation Satellite System (GNSS)/Navigation with Indian Constellation (NavIC) receivers are influenced due to various errors like ionosphere delay, troposphere delay, receiver and satellite clock error, multipath, integer ambiguity, receiver hardware noise etc. However, the real-time positioning and navigation applications are in quest of high-quality carrier phase measurements with zero bias. The GNSS/NavIC receiver hardware noise is one of the critical error sources that degrade the quality of carrier phase measurements. And it can be measured by computing the differential phase bias or carrier phase bias employing the double-difference method. This research article proposes a novel approach called Time Differenced Double Difference Carrier Phase (TDDDCP) for estimating differential phase bias or carrier phase bias of NavIC receiver. Moreover, the proposed TDDDCP technique has the advantage over the Double Difference Carrier Phase (DDCP) because it requires data from only one satellite with two zero base length receivers for which the differential phase bias is to be measured. The experimental results show that the differential phase bias value differs for different satellites, ranging from −0.3904 m to 0.3168 m. The bias-free carrier phase observations based on position coordinates (X, Y, Z) found improved precision of standard deviation of 0.4176 m, 0.645 m, and 0.328 m, respectively. [ABSTRACT FROM AUTHOR]

Precise point positioning (PPP) has been recognized as a powerful tool for various geophysical applications. However, the long convergence time required to resolve a reliable ambiguity impedes its further application in time-critical scenarios. Although PPP ambiguity resolution (AR) can shorten the convergence time, its performance is subject to the quality of float ambiguity estimates and the uncalibrated phase delay (UPD), which can be contaminated by multipath errors. Furthermore, the observation residuals derived from PPP are very likely to be affected by the common-mode error (CME), thereby deteriorating the multipath modeling accuracy. The principal component analysis (PCA) is employed to mitigate the CME effect, and the multipath is modeled using a multipath hemispherical map (MHM). Consequently, the narrow-lane (NL) UPDs with multipath correction have better temporal stability and residual distributions than those without correction. Compared with sidereal filtering (SF), the MHM 0.5 has comparable residual variance reduction percentages, indicating its capability of capturing high-frequency multipath. For static PPP AR, the averaged time to first fix (TTFF) can be reduced by 24.2% to about 26 min and the convergence time can be achieved within 16.2 min after multipath correction. The pseudorange multipath correction significantly contributes to shortening the TTFF and convergence time. Reducing the resolution of MHM increases the risk of extending the TTFF. For kinematic PPP AR with MHM 0.5 , the convergence time exhibits a remarkable improvement when compared with that of the uncorrected case (21.7 min versus 40.2 min), and 20% of the stations achieve convergence within 10 min. Meanwhile, a few stations only take one minute to achieve convergence. The contribution of the multipath correction to the fixing rate is comparatively small. After applying MHM 0.5 , the kinematic positioning accuracies are improved by 35.7%, 12.6%, and 24.4% to 1.26, 1.39, and 2.73 cm for the east, north, and up components, respectively. • Mitigating of common-mode error can ameliorate the multipath modeling accuracy. • NL UPD estimates with multipath correction have better temporal stability and residual distributions. • Correcting pseudorange multipath is beneficial for shortening the TTFF and convergence time. • Multipath correction can significantly improve the performance of real-time PPP AR. [ABSTRACT FROM AUTHOR]

• A Kalman filter-based full online method is proposed to reliably determine WL and NL FCBs in an epoch-by-epoch way as an embedded module for real-time ambiguity-fixing clock estimation. • A real-time recursive method to decrease the noise of float WL ambiguity, which only stores the average, precision, and weight, is developed for convenient online processing. • Quality control procedures are established throughout the whole FCB filter process to remove low-quality observations and mitigate the effects of incorrect integer ambiguities. Integer ambiguity resolution (IAR) is one of the most powerful methods to improve the precision and the convergence of estimating real-time satellite clocks, which is an indispensable prerequisite to support the real-time precise point position (PPP) service. In this study, a Kalman filter-based online fractional cycle bias (FCB) determination method is proposed to facilitate the real-time IAR for satellite clock estimation. A real-time recursive algorithm for smoothing the average float wide-lane (WL) ambiguity is developed to mitigate the impact of pseudorange noise. Quality control procedures are established throughout the entire FCB filter process to remove low-quality observations and mitigate the impact of incorrect integer ambiguities. This method is designed as an embedded module in the clock estimation procedure to fix both integer WL and narrow-lane (NL) ambiguities in an epoch-by-epoch way for recovering the integer property of the undifferenced ionosphere-free (IF) ambiguities in real-time. The performance of the FCB filter and the ambiguity-fixing clock estimation is validated with a GPS network from the international GNSS service (IGS). Experiments show that the WL and NL FCB estimation accuracy reaches 0.004 cycles and 0.080 cycles for GPS satellites. The WL and NL residuals fit the normal distribution well after several minutes and 1.5 h, respectively, making the ambiguity-fixing clocks converge rapidly in about two hours. The online FCB filter method improves real-time ambiguity-fixing clock estimation accuracy significantly. Compared to the ambiguity-float solution, the STD of the ambiguity-fixing real-time satellite clocks is averagely improved by 31.0 % to 0.040 ns with the ultra-rapid orbits. The ambiguity-fixing satellite clocks can be applied in the real-time kinematic PPP ambiguity resolution, and the positioning accuracy is improved by 24.1 % to 51.7 % compared to that of using the ambiguity-float clock products. [ABSTRACT FROM AUTHOR]

Broadcasting the multi-frequency signals is one of the outstanding advantages of BDS-3 (BeiDou Navigation Satellite System). In addition to the legacy signals B1I and B3I, we are interested in the performance of two new signals B1C and B2a. For the purpose of improving the orbit accuracy of BDS-3 backbone MEOs (Medium Earth Orbits), this study focuses on Precise Orbit Determination (POD) using B1C/B2a dual-frequency measurements. First, the performance of POD will be benefit from an increasing observation quantity and qualities. Observations from the public MGEX (Multi-GNSS Experiment) network are statistically collected, and the number of stations able to track B1C and B2a signals is analyzed. In recent years, the sustainable growth number of stations is up to more than one hundred, which brings the new chance to improve the POD accuracy based on B1C/B2a linear combination. Then, the multipath and post-fit residuals of observations are compared between B1C/B2a and B1I/B3I to investigate the observation qualities. Second, as a key strategy, the ambiguities are successfully fixed during POD processing of BDS-3 MEOs. The ambiguity fixing percentage is as high as 93.1% on average using B1C/B2a combination. Compared with float solutions, the improvements of ambiguity fixed orbits reach 36.2%, 19.9% and 36.6% on the radial, along-track and cross-track components, respectively. For the fixed solutions of B1I/B3I and B1C/B2a, it is noticed that the orbits achieve further benefits from B1C/B2a combination for 8.4%, 6.9% and 8.0% on the radial, along-track and cross-track components, respectively. Finally, the performance of B1C/B2a combination POD is validated by orbital overlapping, the orbit signal-in-space range error (SISRE) analysis, independent technology Satellite Laser Ranging (SLR) and Precise Point Positioning (PPP), respectively. SLR residuals show the radial orbital accuracy has an improvement of 8.0% for C20, C21, C29 and C30 on average when employing B1C/B2a measurements. Compared with B1I/B3I, both static and kinematic PPP based on B1C/B2a orbits indicate the improvement on the vertical component. And a faster and more stable convergence performance is also observed using B1C/B2a combination. • This paper focuses on precise orbit determination (POD) with B1C/B2a combination. • The ambiguities are successfully fixed for both Wide-Lane and Narrow-Lane in POD. • The performance of POD is validated using orbital overlapping, Satellite Laser Ranging and PPP. • PPP based on B1C/B2a combination achieves a faster and more stable convergence performance. [ABSTRACT FROM AUTHOR]

• A high-precision temporal relative localization method called Android-odometry is proposed. • Detect and repair temporal ambiguity variation with velocity constraint. • Provide temporal relative positions at centimeter-level with MI8 in a kinematic test. Following extant studies on temporal relative localization (TRL) methods, this study uses a doppler velocity constraint-based temporal ambiguity variation (TAV) detection method and a two-step TAV resolution method to obtain the high-precision temporal relative position variations over time based on raw GNSS observations of Android smartphones, commonly plagued by frequent half-cycle slips and lock-loss. Results show that the proportion of the detectable satellites over 0.65 reaches the 95.57% level and the fix rate of global TAV resolution reaches 82.93%. We then propose the Android-odometry method which is a real-time high-precision TRL method with time-differenced carrier-phase observations of Android smartphones. The experimental results show that the method achieves centimeter-level temporal relative position accuracy during the 13-min dynamic test with Xiaomi MI8, showing a dramatic improvement of over 90% compared to the traditional RTK method. [ABSTRACT FROM AUTHOR]

• Observable-specific signal bias (OSBs) transformation for multi-frequency is deduced. • Inter-frequency clock bias and antenna phase center must be consistent with OSBs. • Quad-frequency is conductive to shorten the convergence time of BDS-3 kinematic PPP. • Quad-system multi-frequency PPP-AR achieve millimeter-level in horizontal direction. With the completion of the BeiDou Global Navigation Satellite System (BDS-3), more available frequencies have brought opportunities for precise point positioning ambiguity resolution (PPP-AR). This research theoretically deduced the multi-frequency PPP-AR model and the rule of observable-specific signal bias (OSBs) transformation. Then 34 International GNSS Service stations were selected to investigate the multi-frequency BDS-3 and multi-GNSS PPP-AR. The results suggested that the OSBs products provided by Centre National D'Etudes Spatiales (CNES) have absorbed the impact of inter-frequency clock bias and could be directly added to the original observations to restore the integer characteristics of the multi-frequency ambiguity. Meanwhile, the antenna phase center correction should keep consistent when using the CNES OSBs to restore the Melbourne-Wübbena ambiguity. The BDS-3 quad-frequency ambiguity-fixed convergence time was 39.0 and 25.1 min for kinematic and static PPP, which was shortened by nearly 15.0 and 3.4 min than the dual-frequency ambiguity-fixed solution. The quad-system multi-frequency PPP-AR showed the optimal state, which was 0.66, 0.76 and 2.66 cm for kinematic mode while 0.31, 0.31 and 1.02 cm for static mode in east, north, and up directions, respectively. [ABSTRACT FROM AUTHOR]

• Analyze the reference network size for PPP-RTK. • Evaluate spatial characteristics of the PPP-AR derived atmospheric delay. • A low-degree polynomial with regular grid residuals model. • Compare the accuracy of the atmospheric delay from GPS, Galileo and BDS. Combining advantages of precise point positioning (PPP) and real-time kinematic (RTK), PPP-RTK has become a promising technology in the mass-market positioning. When performing PPP-RTK, atmospheric corrections enable the user fast ambiguity resolution as well as centimeter accuracy. However, the legacy method of obtaining atmospheric corrections, i.e., interpolating the atmospheric delay based on nearby reference stations, is not regular in space and needs the reference station coordinate information, thereby limiting real-time professional applications. In this contribution, a low-degree polynomial with regular grid residuals is investigated. Forming between-satellite single-differenced slant ionospheric delay, we theoretically analyze the reference network size. Afterwards, the zenith tropospheric delay and slant ionospheric delay accuracy using zero-, first- and second-degree polynomials in calm atmospheric periods are about (5.6, 4.7 and 4.7) mm and (1.9, 1.3 and 1.3) cm. It is therefore recommended to adopt the first-degree polynomial model in terms of the accuracy and transmission load. [ABSTRACT FROM AUTHOR]

• There are two different error sources: one relates to the error propagation law and the other to the systematic bias of the interpolation model. • We verify the existence of systematic errors in the interpolation model. • We discuss the spatial changes in systemic errors of the interpolation model. • A algorithm for estimating the stochastic model of atmospheric corrections is proposed. Regional Augmented Precise Point Positioning (RA-PPP) is a method used to support PPP-Real Time Kinematic (PPP-RTK) based on state space representation. In case of RA-PPP, uncalibrated phase delays and undifferenced ionospheric and tropospheric corrections generated by the reference station network are interpolated at the rover in real time. This study proposes a set of algorithms for estimating the uncertainties of atmospheric corrections that are compatible for use with the RA-PPP model. There are two different error sources of interpolated atmospheric corrections: one relates to the error propagation law and the other to the systematic bias of the interpolation model. We discuss the spatial changes in systemic errors of the interpolation model and present a new interpolation method and its use in calculating the uncertainties of interpolated atmospheric corrections. In addition, we verify the existence of systematic errors in the interpolation model and discuss the correlation between zenith tropospheric delay and slant ionospheric corrections. The results of PPP ambiguity resolution experiments using GPS/Galileo observations are presented. For a reference station network with an interstation distance of more than 110 km, when the proposed method is used, the rate of successfully fixing ambiguities reaches 67.8% in 5 min, and the fixing rate is higher than 90%. It is considered that our method has enhanced applicability for use with large networks and in complex environments. [ABSTRACT FROM AUTHOR]

A methodology relying on relating terms of a two-port error network to the scattering (S-) parameters of a two-port network or device is applied to extract its full S-parameters. The new methodology has only one sign ambiguity problem (two solutions) in evaluation of S 11 (and thus S 22) while the similar methodology in the literature has two sign ambiguity problems (4 solutions). This ambiguity problem of our method is shown to be eliminated by applying an approach based on continuity of the argument of S 11 in the frequency domain. On the other hand, our methodology, as compared with the thru-reflect-line calibration technique, does not necessitate usage of any reflection standard in determining full S-parameters of a two-port network or device. Finally, it gives information about error networks. For its validation, S-parameters of a microwave phase shifter and a polyethylene sample flushed with the left/bottom terminal of the coaxial cell were extracted. • Error networks are related to scattering parameters of a two-port device. • The new methodology has only one sign ambiguity problem in evaluation of S 11. • A continuity-based approach in frequency-domain is applied to eliminate this problem • It does not necessitate usage of any reflection standard in determining full S-parameters. • The proposed methodology gives information about error networks. [ABSTRACT FROM AUTHOR]

• Eliminating the biases caused by code inter-system biases (ISBs) between the BDS-2 and BDS-3 at overlapping frequencies on BDS double-difference (DD) ambiguity resolution. • Improving the success rate of BDS hybrid ambiguity resolution. • Improving the accuracy of BDS precise orbit determination. The BeiDou Regional Navigation Satellite System (BDS-2) and BeiDou Global Navigation Satellite System (BDS-3) satellites will be utilized in conjunction to provide positioning, navigation and timing (PNT) services. Precise orbit products are essential preconditions and guarantees for providing PNT services. To improve the quality of the BeiDou Navigation Satellite System (BDS) orbits determination, a method for eliminating the biases caused by code inter-system biases (ISBs) between the BDS-2 and BDS-3 at overlapping frequencies on BDS double-difference (DD) ambiguity resolution (AR) is proposed. To validate the contribution of the proposed method, the dataset spanning from day of year (DOY) 170, 2019, to DOY 170, 2020 is analyzed in the BDS precise orbit determination (POD) with different processing strategies. The results show that the fractional cycle biases (FCBs) in wide-lane and narrow-lane ambiguities are related to the receiver types, which are stable and can be estimated as constants in a POD arc length. After applying the proposed calibration method, the success fixing rate for the BDS-2/3 inter-system wide-lane ambiguities is improved by more than 25%, and that of the narrow-lane ambiguities by approximately 6%. Compared with that for BDS-2/2 and BDS-3/3 intra-system AR independently, the overlapping accuracy is improved by 13.7%, 4.8% in the along-track, cross-track directions, respectively, after adding BDS-2/3 inter-system AR. [ABSTRACT FROM AUTHOR]

• A survey-grade GNSS antenna is connected to smartphone Mi 8. • Centimeter level positioning can be achieved with Mi'8 dual-frequency GNSS data. • Applications in mass market may benefit from the smartphone's dual-frequency GNSS. A vast of applications that need low-cost and high-precision positions may arise with the advent of the world's first dual-frequency GNSS smartphone Xiaomi Mi 8. In this paper we succeeded in replacing the Mi 8's embedded GNSS antenna with an external survey-grade one and performing precise point positioning ambiguity resolution (PPP-AR) on this enhanced device. As for fixed static hourly solutions, all three components achieved centimeter-level accuracy, and the position errors were 1.6 cm, 1.0 cm and 2.4 cm in the east, north and up components. Compared with float solutions the improvements were up to 61%, 41% and 48% respectively. The kinematic solutions also showed remarkable improvements. In addition, we also studied ambiguity features and found that the ambiguity residuals were quite larger than those of survey-grade receivers due to frequent cycle slips and noisier raw measurements. Overall, we believe that it is possible to fix undifferenced ambiguities with Android dual-frequency GNSS data. [ABSTRACT FROM AUTHOR]

• We propose a mixed fields algorithm for MEMS vector hydrophone array. • We analyze the characteristics of steering vector matrix. • The direction vector array is decomposed into different matrices. • The DOA and range are separated efficiently. • Simulation test have proven the advantage of MEMS vector hydrophone array. A mixed near and far field sources localization algorithm is proposed which applied to the uniform linear MEMS vector hydrophone array. The algorithm includes three steps: firstly, the steering vector contains common azimuthal information in both near and far field, direction-of-arrival (DOA) can be obtained by using the MUSIC algorithm. Secondly, the direction vector array is decomposed into different matrices and DOA and range are separated efficiently. All DOAs can be obtained through searching for a feature matrix. Thirdly, one-dimensional spectrum search in Fresnel zone is carried out to realize the accurate estimation of range in near-field. Finally, the performance of the algorithm was simulated. The results verify that the proposed algorithm can achieve DOA estimation within the range of [0:2*π] and solve the problem of port and starboard ambiguity. The vector matrix algorithm does not require construction the high-order cumulants and multi-dimensional search, and can avoid parameter matching procedure. [ABSTRACT FROM AUTHOR]