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GPS Solutions
Journal Prestige (SJR): 1.674
Citation Impact (citeScore): 5
Number of Followers: 28  
 
  Hybrid Journal Hybrid journal (It can contain Open Access articles)
ISSN (Print) 1521-1886 - ISSN (Online) 1080-5370
Published by Springer-Verlag Homepage  [2469 journals]
  • Multi-GNSS real-time precise point positioning using BDS-3 global
           short-message communication to broadcast corrections

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      Abstract: Abstract The real-time precise point positioning (RTPPP) based on real-time service (RTS) products has attracted much interest with the increasing demand for real-time applications. It is difficult to achieve RTPPP for some areas where the available communication links for transmitting RTS products are limited, such as marine and desert areas. The global short-message communication (GSMC) function of the BeiDou global navigation satellite system (BDS-3) provides an option to transmit corrections for global RTPPP. However, the maximum size of each BDS-3 global short message is 560 bits, and the communication frequency is limited to 1 min, which brings challenges for broadcasting precise corrections using BDS-3 GSMC. In this contribution, based on dual-frequency GNSS data, we present a global RTPPP technique with BDS-3 GSMC. To overcome the limitations of communication bandwidth and frequency, at the server, the real-time precise orbits and clocks are predicted for 1 min, and then, the orbit and clock corrections of each satellite are converted into an equivalent range correction based on the user's approximate position obtained through BDS-3 GSMC. The range corrections for a maximum of 22 visible GPS, Galileo and BDS satellites are encoded into a BDS-3 global short message in accordance with the designed encoding strategy and are broadcast to users once per minute via BDS-3 GSMC. At the user, the range corrections of the observation moment are obtained by interpolating the corrections of the two adjacent epochs for RTPPP. Both simulated experiments using observations from IGS stations and field experiments using GNSS receivers with the BDS-3 GSMC function are conducted to evaluate the RTPPP performance. The results show that the proposed RTPPP scheme with GSMC can reach a positioning accuracy of better than 10 cm with GPS + BDS + Galileo observations.
      PubDate: 2022-06-30
       
  • Doppler frequency-code phase division multiple access technique for LEO
           navigation signals

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      Abstract: Abstract It is an important development direction to take advantage of low-earth-orbit (LEO) satellites by establishing a LEO satellite navigation system as a supplement to Global Navigation Satellite Systems in the future. On account of the fast motion of LEO satellites, there is a significant and fast change in the Doppler frequency of LEO navigation signals. Since a LEO navigation system usually consists of a large number of satellites, the search range of carrier frequencies and satellite numbers is correspondingly large in the signal acquisition process. Adopting the traditional code division multiple access (CDMA) technique will bring extremely high computational complexity to the acquisition process of LEO navigation signals, which leads to a much longer acquisition time. Considering the characteristics of LEO navigation signals, we proposed a Doppler Frequency-Code Phase Division Multiple Access (DFCP-DMA) technique in order to achieve a fast acquisition of LEO navigation signals. Because the motion of LEO satellites is fast, Doppler frequencies and code phases of LEO navigation signals arriving at the receiver differ significantly. Thus, receivers can distinguish LEO navigation signals by multiple combinations of different Doppler frequencies and code phases acquired. To decrease the acquisition complexity, all LEO satellites broadcast spread-spectrum navigation signals modulated by the same spreading code in DFCP-DMA, and receivers can acquire all navigation signals using only this spreading code. Theoretical analysis and simulation results show that, compared with CDMA, DFCP-DMA can significantly reduce the acquisition complexity without any loss in the acquisition sensitivity, which can shorten the acquisition time to 1/M, where M is the number of satellites. There is a high application prospect for DFCP-DMA in future LEO navigation systems.
      PubDate: 2022-06-28
       
  • Scalar and vector tracking loop simulation based on a uniform
           semi-analytic model and robustness analysis in multipath/NLOS situations

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      Abstract: Abstract A semi-analytic model is proposed to efficiently analyze and compare the performance of both the scalar tracking loop (STL) and the vector tracking loop (VTL) in different operating situations. The quality of each satellite signal, including multipath and none-line-of-sight (NLOS) propagation problems, can be incorporated into the proposed model for different configurations of deteriorated situations. Theoretical analysis of multipath and NLOS induced bias to the VTL and STL is given, including the bias envelop, from which a conclusion is obtained that the VTL performance is not better than the STL in certain multipath situations. The results from the semi-analytic model verify the theoretical analysis. The effectiveness of the proposed model is verified by a comparison with the results from simulated NLOS data processed by a software-defined radio receiver.
      PubDate: 2022-06-27
       
  • A multipath mitigation method in long-range RTK for deformation monitoring

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      Abstract: Abstract The presence of non-negligible atmospheric delays and multipath errors makes it difficult for the long-range baselines to provide high-accuracy real-time kinematic (RTK) deformation monitoring services, as is the case for short baseline. Despite considerable efforts to model the effects of tropospheric errors, multipath errors remain a challenging issue in high-accuracy GNSS positioning applications. We describe a strategy for mitigating the multipath errors in long-range baselines, enabling precise RTK positioning results. First, the double-differenced ionospheric-free residuals are converted to un-differenced (UD) residuals for each satellite of the associated stations. The troposphere and multipath are the main error sources in these UD residuals. Taking advantage of the different features of UD tropospheric and multipath errors when displayed as a function of the scale factors provided by the wet mapping functions, the residual zenith tropospheric delays of each station are therefore constructed and used to resolve the practical tropospheric errors of each slant signal. The multipath errors are extracted by subtracting the computed tropospheric errors from the converted UD ionospheric-free residuals. After correcting the tropospheric and multipath errors, high-accuracy RTK positioning results can be obtained from long-range baselines. Compared with traditional methods, the proposed approach gives a 43.2% improvement in the average 3D root mean square error. Moreover, improvements of 22.2%, 52.4%, and 47.3% are achieved in the east, north, and up components for a 127 km baseline, giving a final epoch-wise positioning accuracy of 6.2 mm, 4.3 mm, and 11.8 mm, respectively. Experimental results show that the proposed strategy is an efficient and promising method in high-accuracy deformation monitoring applications for long-range baselines.
      PubDate: 2022-06-26
       
  • Statistical study on the CSES radio occultation data and its quality
           control in electron density inversion

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      Abstract: Abstract GNSS radio occultation (RO) plays an important role in ionospheric electron density inversion. As China's first seismo-electromagnetic satellite, China Seismo Electromagnetic Satellite (CSES) has collected the RO data with both GPS and BDS-2 satellites since March 2018. We analyzed the data quality of CSES GNSS occultation receiver (GOR) with almost one year of data in terms of signal-to-noise ratio, the cubic difference between epochs and the MP (multipath) combination. It was found that at the start of the signal acquisition, the GPS signal of GOR is affected to abnormal jumps on both P1 and P2 and large variations on P2, while the CSES BDS-2 GOR observation performed much better. To avoid potential contamination by these abnormal GPS observations in the CSES GOR ionospheric inversion, a quality control algorithm was promoted based on the MP2 combination. By removing the outliers using the quality control algorithm, the P2 observation integrity rate was 77.8% and 98.9% for GPS and BDS, respectively, and the abnormal values in the electron density profile can be detected and removed in the RO inversion efficiently. Then the comparison of F2 peak density and peak height was performed with respect to COSMIC for the whole experimental period with four different space–time matching criteria. The results of CSES GPS and BDS-2 suggested a significant correlation with that of COSMIC.
      PubDate: 2022-06-25
       
  • A GPS signal-in-space simulation model for equatorial and low latitudes in
           the Brazilian longitude sector

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      Abstract: Abstract The ionosphere affects the propagation of global positioning system signals. Due to their special features, the equatorial and low-latitude ionosphere may produce particularly severe effects on them. The ground-based augmentation system has been developed to meet the safety requirements of civil aviation. To evaluate the performance of such a system, a statistical simulation model of the global positioning system signal-in-space has been developed, considering several components. The present work will focus on: (1) the ionospheric delay, with basis on statistical distributions of vertical total electron content obtained by the combination of the International Reference Ionosphere with data from the Rede Brasileira de Monitoramento Contínuo, operated by Instituto Brasileiro de Geografia e Estatística; (2) cycle ambiguity, characterized through the processing of the same data set; (3) ionospheric amplitude scintillation, simulated with basis on proper indices and the α–μ probability distribution; and (4) ionospheric phase scintillation, generated according to its standard deviation. The statistical simulation model is based on a set of representative geophysical parameters and may be used to generate time series of pseudorange, carrier phase, and received signal power, to be applied as inputs to existing or future ground-based augmentation system testbeds. This provides an alternative to experimental data collection, which could be expensive and time-consuming. Additionally, such data may not be available for all regions and critical geophysical conditions of interest.
      PubDate: 2022-06-24
       
  • Positioning performance of the Neustrelitz total electron content model
           driven by Galileo Az coefficients

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      Abstract: Abstract To aid single-frequency GNSS users, the Neustrelitz Total Electron Content Model (NTCM) has been proposed as an adequate solution to mitigate propagation errors besides the GPS Klobuchar and Galileo NeQuick models. Using the three effective ionization coefficients broadcast in the Galileo navigation message as driver parameters, the version NTCM-GlAzpar, in general, performs equal to or better than NeQuickG when compared to the total electron content domain. In this work, we performed a global statistical validation of the NTCM-GlAzpar model in the position domain by comparing its results with the results of the Klobuchar and NeQuickG models for the first time. For this purpose, we used the GNSS analysis tool gLAB and its customization capabilities in the Standard Point Positioning mode. The data used for model validation correspond to a one-month period of perturbed solar and geomagnetic activity (December 2014) and another one-month period of quiet conditions (December 2019). The data have a worldwide coverage with up to 73 IGS stations. The statistical analysis of the hourly average 3D position error shows that the root mean squared (RMS) values of the Klobuchar model are 6.71 and 2.75 m for the perturbed and quiet conditions, respectively, whereas the NeQuickG model has RMS values of 4.61 and 2.35 m. In comparison, the corresponding RMS values of 4.36 and 2.32 m of the NTCM-GlAzpar model confirm its better positioning performance for both periods. However, we identify also that the performance of NTCM-GlAzpar slightly worsens toward higher latitudes and at night local time. Simple software adaptations and a low computational cost make NTCM-GlAzpar an alternative practicable algorithm to improve the accuracy of GNSS single-frequency applications.
      PubDate: 2022-06-23
       
  • A sequential ambiguity selection strategy for partial ambiguity resolution
           during RTK positioning in urban areas

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      Abstract: Abstract Usually, it is difficult to implement integer ambiguity resolution within a short amount of time for GNSS positioning in urban areas due to the contamination of non-line-of-sight signals and multipath. This study proposes a sequential ambiguity selection strategy for partial ambiguity resolution. First, the ambiguities are selected based on the filtered residuals of the phase and code measurements. In addition, the elevation angle and decorrelated variances are used as the metrics for selecting ambiguity subsets. Two kinematic experiments are carried out in urban areas to evaluate the performance of the strategy. Among the three independent strategies, the first one performs better than the others, as the dependency of observation quality on the elevation angle is low and the decorrelated variances are prone to be contaminated by biased ambiguities. When the proposed sequential ambiguity selection strategy is used, the percentage of correctly fixed epochs is increased by approximately 10–20%. The RMS of N/E/U is improved from the decimeter level (for full ambiguity resolution) to the centimeter level. The improvement is more obvious in the obstructed area and during the re-initialization phase.
      PubDate: 2022-06-21
       
  • Detection of synchronous spoofing on a GNSS receiver using weighed double
           ratio metrics

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      Abstract: Abstract Spoofing signal detection is an essential process in GNSS anti-spoofing. The detection probability of the existing metrics degrades significantly for many specific combinations of relative code phases and carrier phases of the spoofing signal relative to the authentic signal. To improve detection, we propose a four-complex-correlator metric, called weighted double ratio (WDR), which first constructs a metric named RatioQ exploiting the quadra-phase correlation outputs and then combines two pairs of complex correlators separated by a large correlator spacing and weighted according to their noise levels to form a WDR. Theoretical analysis and simulation results show that the detection coverage rate, the receiver operating characteristic, and the detection probability versus different carrier to noise ratios are significantly improved. The experiment using the Texas spoofing test battery data in all eight cases demonstrates that the proposed method outperforms the existing metrics, especially for high spoofing-signal-ratios and the unlocked-frequency mode.
      PubDate: 2022-06-20
       
  • Open-source optimization method for android smartphone single point
           positioning

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      Abstract: Abstract Nowadays, a chip-scale Global Navigation Satellite System (GNSS) receiver is ubiquitous in smartphones. In a smartphone GNSS receiver, the least square (LS) or Kalman Filter (KF) is implemented to estimate the position. With the aim to improve the smartphone GNSS position accuracy, we propose a position-smoothing method considering more historical information than the traditional methods, i.e., LS and KF. More past states are regarded as unknowns, and a cost function is constructed to optimize these states. An open-source smartphone dataset from Google was used for testing the proposed method. The experimental results indicate that the proposed method outperforms the other conventional methods in position errors. In addition, we open the source code. We expect that the optimization method implemented in the smartphone GNSS position smoothing application can be an illustrative example to clearly introduce such an optimization method and a reference for its implementation, which might inspire some other meaningful and exciting applications in GNSS.
      PubDate: 2022-06-18
       
  • Modeling and predicting inter-frequency clock bias of BDS-2 GEO, IGSO and
           MEO satellites for triple-frequency precise point positioning

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      Abstract: Abstract Due to inter-frequency clock bias (IFCB), the dual-frequency precise clock products cannot be directly applied to BDS-2 triple-frequency precise point positioning (PPP). In this study, the datasets collected at 195 ground tracking stations for a whole year are employed to investigate the modeling and prediction of BDS-2 IFCB. The modeling periods of IFCB are consistent with orbital repeat periods, namely a week for medium earth orbit (MEO) satellites and a day for geostationary orbit (GEO) and inclined geosynchronous orbit (IGSO) satellites. The harmonic analysis results show that the IFCB of MEO satellites has seven significant periods of (168, 84, 56, 42, 33.6, 28, 12.9) h, while there are six obvious periods of (24, 12, 8, 6, 4.8, 4) h for GEO and IGSO satellites. Two function models composed of a linear term and a harmonic term with seven orders for MEO satellites and six orders for GEO and IGSO satellites are established to describe the IFCB variations, and the model coefficients are fitted by least squares. The IFCB modeling accuracies are 4 mm for MEO satellites and 2 mm for GEO and IGSO satellites. The established model can predict the IFCBs with single-day prediction accuracies of 5.0 and 3.9 mm for GEO and IGSO satellites and single-week prediction accuracies of 5.0 mm for MEO satellites, respectively. After applying these predicted IFCBs to BDS-2 triple-frequency PPP, the positioning accuracies are improved by 14–29%.
      PubDate: 2022-06-14
       
  • Assessing partial ambiguity resolution and WZTD-constraint multi-frequency
           RTK in an urban environment using new BDS signals

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      Abstract: Abstract BeiDou Navigation Satellite System (BDS) began to provide global services of positioning, navigation, and timing on July 31, 2020. The Real-time Kinematic (RTK) is one of the essential services for BDS’ precise applications. In this contribution, a BDS-3 RTK model based on the constraint of the Wet component of Zenith Tropospheric Delay (WZTD) and the partial ambiguity resolution methods is provided, in which the impact of WZTD residuals caused by both horizontal distance and height is restrained. To evaluate the performance of such a BDS-3 RTK model, a set of triple-frequency multi-constellation Global Navigation Satellite Systems vehicle-borne data is collected and processed. Results demonstrate that (1) the positioning accuracy of BDS-3 is decimeter-level to centimeter-level in terms of root mean square value while using single, dual, and triple frequency observations, which is generally close to that of GPS; (2) the positioning accuracy of BDS-3 RTK based on the new signals (B1C, B1C + B2a, and B1C + B2a + B3I) are higher than that using B1I and B3I signals; (3) the ambiguity resolution fixed rate of BDS-3 RTK is improved after applying the partial ambiguity resolution methods and WZTD constraint.
      PubDate: 2022-06-13
       
  • Three time spoofing algorithms for GNSS timing receivers and performance
           evaluation

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      Abstract: Abstract This study proposes three different time spoofing algorithms based on modified satellite position, modified pseudorange, and combined modified pseudorange and satellite position. Their effectiveness and performance are verified and evaluated via computational simulations and experiments using open-source data provided by the Curtin Group. The algorithm of modified pseudorange shows the best performance, with the average value of receiver clock bias offset from the offset expected by the spoofer being 5.72 × 10−8 m, and the average value of spatial change in the receiver position being 4.88 × 10−4 m, thus, fully achieving the purpose of time spoofing, i.e., spoofing causes the receiver clock bias to reach an offset as intended by spoofer. However, the target receiver could detect spoofing by assessing pseudorange time delay. The algorithm of modified satellite position shows the worst performance. The outcome of the combination algorithm is between that of the two other time spoofing algorithms; The latter two algorithms mentioned above have an average receiver clock bias offset from the spoofer’s intended offset being − 117.80 m and − 58.90 m, the average value of spatial change in the receiver position being 109.08 m and 54.55 m, thereby basically achieving the purpose of time spoofing, respectively. The algorithm of modified satellite position does not require pseudorange time delay addition, which could be done by modifying navigation message parameters, it was challenging for target receiver to detect any pseudorange time delay as spoofing. Hence, users who rely on time information should enhance the security and reliability of detecting time information.
      PubDate: 2022-06-11
       
  • SVR and ARIMA models as machine learning solutions for solving the latency
           problem in real-time clock corrections

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      Abstract: Abstract Real-time precise point positioning (PPP) has become a prevalent technique in global navigation satellite systems (GNSS). However, GNSS real-time users must receive space state representation (SSR) products to correct for satellite clock, orbit, and phase biases. The International GNSS Service (IGS) provides GNSS users with real-time services (RTSs) through different real-time correction SSR products. These products arrive at the GNSS users with some latency, which affects the quality of real-time PPP positioning. The autoregressive integrated moving average (ARIMA) and support vector regression (SVR) models are used in this research to predict those corrections to eliminate the latency effect. ARIMA model reduces the standard deviation by 28% and 13% for GPS and GLONASS constellations, respectively, compared to the real-time solution, which includes the latency effect, the research simulated the latency effect and named it a forced-latency solution, and the SVR model reduces the standard deviation by 28% and 23% for GPS and GLONASS constellations, respectively. The results for the permanent GNSS stations used in this study across different years 2013, 2014, 2015, 2019, and 2021 show a mean reduction in the 3D positioning standard deviation by 13% compared with the forced-latency solution for the ARIMA solution and 9% for the SVR solution. The potential of both models to overcome the latency effect is apparent based on the findings.
      PubDate: 2022-06-08
       
  • SBAS ionospheric grid delay estimation based on ionospheric tomography: a
           case study on September 7–9, 2017

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      Abstract: Abstract In Satellite-Based Augmentation Systems (SBASs), e.g., the US Wide-Area Augmentation System (WAAS), the planar method and the kriging method based on the thin-shell model have been used to estimate the ionospheric grid delay (IGD). Generally, the kriging method can achieve higher accuracy than the planar method. In comparison with the thin-shell model, ionospheric tomography overcomes the limitations of the 2D ionospheric delay modeling and can realize 3D or even 4D ionospheric electron density reconstructions, especially suitable over disturbed periods. For the first time by virtue of electron density inversions, a tomographic method and a kriging-combined tomographic method are proposed innovatively to apply for estimating IGDs over part of the WAAS region using 32 ground stations during ionospheric disturbances on September 7–9, 2017. Then, independent dual-frequency Global Positioning System (GPS) data at six stations are applied to validate estimated IGD results from these four methods. It is shown that the overall errors of the planar method, the kriging method, the tomographic method, and the kriging-combined tomographic method over 3 days are decreased one by one, while errors using the latter two methods are quite similar. When focusing on the strong disturbed times, the latter two tomographic methods can obtain more accurate IGD than the former two methods based on the thin shell model. Tomographic total electron content (TEC) maps over the study area are also reconstructed to help analyze the underlying mechanism at different stations. It is also noted that the kriging-combined tomography has little improvement in IGD estimates in comparison with the tomographic method alone during strong ionospheric disturbances.
      PubDate: 2022-06-08
       
  • A unified model of GNSS phase/code bias calibration for PPP ambiguity
           resolution with GPS, BDS, Galileo and GLONASS multi-frequency observations
           

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      Abstract: Abstract The performance of high-precision Global Navigation Satellite System (GNSS) positioning in multi-frequency and multi-constellation environments strongly depends on the understanding and handling the biases that inevitably exist between the different systems and signals. The usage of observable-specific signal bias (OSB), allowing to map biases to each individual observation type involved, provides full flexibility for the multi-GNSS bias processing. In this contribution, the OSB estimation model is extended from the traditional dual-frequency model to multi-frequency and multi-GNSS one to provide GPS/GLONASS triple-frequency, Galileo five-frequency, BDS six-frequency phase/code bias products for precise point positioning (PPP) ambiguity resolution (AR). Results indicate that the code bias products exhibit high stability with average standard deviations (STDs) of 0.06–0.10 ns for GPS and 0.16–0.33 ns for BDS/Galileo/GLONASS. Likewise, the daily phase bias is extremely stable, with average STDs of 0.01–0.02 ns for GPS and Galileo, 0.03–0.05 ns for BDS and 0.05–0.07 ns for GLONASS. Particularly, for the modernized binary offset carrier signals of Galileo E5 and BDS-3 B2, their phase/code biases present relatively high consistency between the different tracking modes and different frequencies. In addition, obvious differences in the range of 10.92–28.58 ns can be noted between the receiver-specific code bias of BDS-2 and BDS-3 for their common frequency signals. Based on the observable-specific phase and code biases, a multi-frequency PPP cascade integer resolution model is developed to make full use of all available observations from different GNSSs. After applying these bias products, PPP AR with GPS, BDS, Galileo and GLONASS multi-frequency observations is achieved with an average convergence time of 4.44 min, showing remarkable improvements of 56.8% and 16.8% compared to dual-frequency PPP float and fixed solutions, respectively.
      PubDate: 2022-06-01
       
  • A new parallel algorithm for improving the computational efficiency of
           multi-GNSS precise orbit determination

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      Abstract: Abstract The computational efficiency is critical with the increasing number of GNSS satellites and ground stations since many unknown parameters must be estimated. Although only active parameters are kept in the normal equation in sequential least square estimation, the computational cost for parameter elimination is still a heavy burden. Therefore, it is necessary to optimize the procedure of parameter elimination to enhance the computational efficiency of GNSS network solutions. An efficient parallel algorithm is developed for accelerating parameter estimation based on modern multi-core processors. In the parallel algorithm, a multi-thread guided scheduling scheme, and cache memory traffic optimizations are implemented in parallelized sub-blocks for normal-equation-level operations. Compared with the traditional serial scheme, the computational time of parameter estimations can be reduced by a factor of three due to the new parallel algorithm using a six-core processor. Our results also confirm that the architecture of computers entirely limits the performance of the parallel algorithm. All the parallel optimizations are also investigated in detail according to the characteristics of CPU architecture. This gives a good reference to architecture-oriented parallel programming in the future development of GNSS software. The performance of the multi-thread parallel algorithm is expected to improve further with the upgrade of new multi-core coprocessors.s
      PubDate: 2022-05-27
       
  • Non-consecutive GNSS signal tracking-based ultra-tight integration system
           of GNSS/INS for smart devices

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      Abstract: Abstract Consecutively tracking the global navigation satellite system (GNSS) signal can cause power and computation difficulties to a smart GNSS device with small battery capacity and weak computation capability. We propose a novel computationally efficient ultra-tight integration of GNSS and inertial navigation system (INS). Rather than be consecutively tracked in the traditional receiver as well as its integration with INS, the GNSS signal is non-consecutively tracked in the proposed ultra-tight integration. Compared to traditional GNSS duty cycling (DC) techniques, the proposed ultra-tight integration does not have a tracking loop inside the receiver baseband and only GNSS code signals are tracked with the assistance of INS. The non-consecutive tracking control methods for the GNSS code signals with different wavelengths are investigated, and a moving window-based method is also designed to monitor the non-consecutive code tracking. To validate the proposed ultra-tight integration, a vehicle-based experiment is performed in which global positioning system (GPS), Galileo and BDS (BeiDou Navigation Satellite System) signals are non-consecutively tracked by a developed multi-constellation and multi-frequency software-defined receiver and ultra-tightly coupled with micro-electro-mechanical system (MEMS) inertial measurement unit (IMU)-based INS. The experiment results show that the proposed ultra-tight integration can significantly reduce system computation burden and power consumption and can get a better navigation solution than traditional GNSS receiver and DC techniques.
      PubDate: 2022-05-23
       
  • Implementation and performance analysis of the PDR/GNSS integration on a
           smartphone

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      Abstract: Abstract Pedestrian dead reckoning (PDR) is an effective technology for pedestrian navigation. In PDR, the steps are detected with the measurements of self-contained sensors, such as accelerometers, and the position is updated with additional heading angles. A smartphone is usually equipped with a low-cost microelectromechanical system accelerometer, which can be utilized to implement PDR for pedestrian navigation. Since the PDR position errors diverge with the walking distance, the global navigation satellite system (GNSS) is usually integrated with PDR for more reliable position results. This paper implemented a smartphone PDR/GNSS via a Kalman filter and factor graph optimization (FGO). In the FGO, the PDR factor is modeled, and the states are correlated with a dead reckoning algorithm. The GNSS position is modeled as the “GNSS” factor to constrain the states at each step. With a graphic model representing the states and measurements, the state estimation is converted to a nonlinear least square problem, and we utilize the Georgia Tech Smoothing and Mapping graph optimization library to implement the optimization. We tested the proposed method on a Huawei Mate 40 Pro handset with a standard playground field test, and the field test results showed that the FGO effectively improved the smartphone position accuracy. We have released the source codes and hope that they will inspire other works on pedestrian navigation, i.e., constructing an adaptive multi-sensor integration system using FGO on a smartphone.
      PubDate: 2022-05-20
       
  • Performance evaluation of BDS-2/BDS-3 combined precise time transfer with
           B1I/B2I/B3I/B1C/B2a five-frequency observations

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      Abstract: Abstract The third-generation BeiDou Navigation Satellite System (BDS-3) has provided worldwide positioning, navigation and timing since July 2020. BDS-3 is compatible with the previous B1I and B3I signals of BDS-2 and transmits the new signals of B1C, B2a and B2b. In this study, BDS-2/BDS-3 combined precise point positioning (PPP) models with B1I, B2I, B3I, B1C and B2a five-frequency observations are established, including dual-frequency (DF), triple-frequency (TF) and quad-frequency (QF) ionospheric-free (IF) combination PPP models. The proposed BDS-2/BDS-3 combined PPP models time transfer performance using four links (1331.6 km to 9501.9 km) formed from five external high-precision hydrogen clock stations. The experimental results demonstrated that compared with traditional DF1 (B1I/B3I) IF PPP solutions, the positioning accuracies of TF and QF PPP solutions are improved by 7% and 25% on average, respectively. However, the time transfer performances of TF and QF PPP solutions are not improved compared with traditional DF1 PPP solutions. Influenced by the day boundary jumps of the BDS satellite precision clock offsets, the short-term stabilities of BDS-2/BDS-3 combined PPP solutions are worse than that of GPS PPP solutions, but the long-term stabilities of BDS-2/BDS-3 combined PPP solutions are close to or even better than GPS PPP solutions. Compared with GPS PPP solutions, the frequency stabilities of BDS-2/BDS-3 combined DF1, TF1, TF3, TF4, QF1, QF2, QF4 and QF6 PPP solutions at 120,000 s are improved by 15%, 1.1%, 8.6%, 7.0%, 9.9%, 1.0%, 11% and 15% on average, respectively. With the advances in multi-frequency signal modeling, precise time transfer may substantially motivate time and frequency technology.
      PubDate: 2022-05-18
       
 
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