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Abstract: Abstract Positioning an object with biased distance measurements is exactly solvable if exact knowledge of the reference locations and noise-free range measurements are assumed. By examining the positioning algebra, this paper obtains explicit necessary and sufficient conditions for the positioning problem to have a unique or twin solutions. The intersection of negative hyperconic halves is shown to be an exact geometric interpretation of the positioning solutions. The placement of non-coplanar references largely ensures but does not guarantee unique positioning. Given a set of references, object region for non-unique positioning is identifiable by using the conditions derived in this work. The placement of five references to form an asymmetric hexahedron is postulated to be sufficient for unique positioning in a three-dimensional environment. Illustrative examples explain these findings. PubDate: 2022-05-14
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Abstract: Abstract We propose a low-cost integrated navigation system to enhance navigation accuracy using multiple sensors such as the inertial measurement unit (IMU) and Global Positioning System (GPS). Due to the heterogeneity of the employed sensors, the suggested navigation system is equipped with a graph-based optimizer formulated as a maximum a posteriori estimator. As already known, graphic optimization methods are computationally more complex. To reduce this complexity, high-frequency IMU measurements are pre-integrated between lower-frequency GPS measurements. These pre-integrated measurements can be utilized in conjunction with the magnetometer and barometer sensor measurements to carry out navigation in case of GPS weak signal reception. The resulting optimization graph will be solved using the marginalization technique to attain a less computationally intensive optimization favorable in real-time applications. Incorporating internal sensors in navigation will come with problems like the initialization phase. This problem is tackled by integrating the inertial measurements between the required states in the body frame of the last state and then transforming them into the world frame. To evaluate the applicability of the proposed method in real-time situations, a dataset collected by a SkywalkerX8 Unmanned Aerial Vehicle is utilized. This dataset includes all the necessary maneuvers, including climb, descent, turn and cruise during the flight time. The results confirm that our proposed integrated system has superior statistical measures and temporal performance compared to the extended Kalman filter (EKF); it outperforms the conventional Factor Graph Optimization and EKF by approximately 45%. PubDate: 2022-05-13
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Abstract: In voxel-based tropospheric tomography, water vapor is computed for a set of voxels, each covering a specific part of the troposphere. The basic assumption is that water vapor is homogenous in any voxel. In this study, the Principal Component Analysis (PCA) has been applied to select the horizontal size of voxels. The application of PCA helps determine the horizontal size of voxels while keeping the atmospheric changes and the basic assumption intact. Application of the proposed method to a numerical atmospheric model in our case studies shows that the largest horizontal changes in wet refractivity ( \(N_{w}\) ) occurred in layers close to the earth. We also applied this method to tomography models with 30, 40, and 50 km horizontal resolutions. Results were compared using an initial model as a reference. The results indicated that in the lower layers of the atmosphere, the 40 km model has the strongest similarity with our reference in terms of scattering after the 30 km one. Due to limited changes in \(N_{w}\) at the upper layers, the size of voxels was increased to 50 km. \(N_{w}\) was reconstructed for tomographic models with horizontal resolutions of 40 and 50 km and a hybrid model with a combined horizontal resolution in which the model resolution is 40 km in the first seven layers and 50 km in the rest. Validity checks against the radiosonde profile show that the hybrid model reduces the bias and increases the redundancy of our model. PubDate: 2022-05-11
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Abstract: Typically, navigation software processes global navigation satellite system (GNSS) phase observables along with the code observables to achieve high-precision positioning. However, the unmodeled code-related errors, typically multipath effects, may deteriorate the positioning performance. Such effects are well known for the second generation BeiDou navigation satellite system (BDS-2). To prevent this adverse effect on the state-of-the-art positioning technique, namely integer ambiguity resolution-enabled precise point positioning (PPP-RTK), we propose a multi-frequency phase-only PPP-RTK model. This model excludes the code observables and addresses the rank deficiency problem underlying the phase observation equations at the undifferenced and uncombined level. To verify the model, we collect five-day triple-frequency BDS 30-s data from a network of seven reference stations (about 112 km apart) to estimate the products on the network side. Based on these products, we conduct simulated dynamic positioning at a user station to test the phase-only PPP-RTK model and compare it with the customary code-plus-phase (CPP) model. The results show that the satellite phase biases, existing only at the third frequency, have a precision of better than two centimeters, while the precision of the satellite clock and ionospheric delay is better than eight centimeters. Due to the strong correlation between individual corrections, it is necessary to assess the quality of combined products, including the satellite clock, satellite phase bias and ionospheric delay, the precision of which is several millimeters to two centimeters, which is sufficiently precise for user positioning. Regarding BDS-2 positioning, the time-to-first-fix (TTFF) of the CPP PPP-RTK is 12 epochs, while it is only three epochs for the phase-only PPP-RTK. The reason why the CPP model underperforms the phase-only model is that the BDS-2 data collected are subject to notable code multipath. We show that the code multipath in the third-generation BDS (BDS-3) data is mild, so the CPP PPP-RTK achieves instantaneous centimeter-level positioning with a TTFF of one epoch. The BDS-3 phase-only PPP-RTK obtains virtually the same positioning results, but the TTFF is two epochs. When combining BDS-2 with BDS-3, the TTFF of both models remains unchanged compared to that of the BDS-3 solutions, implying that ambiguity resolution based on the stronger dual-system CPP model is robust to the BDS-2 code multipath. However, the ambiguity-float solution of the CPP PPP-RTK is adversely affected by the code multipath and requires 43 epochs to convergence, while its phase-only counterpart needs 36 epochs. PubDate: 2022-05-10
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Abstract: The equatorial plasma bubble evolution, its symmetric propagation away from the equator over north/south hemispheres, the vertical plasma drift asymmetry, and some implications between these phenomena are examples of the conjugate point experiment campaign results. However, the asymmetric transport of plasma may imply a distinct ionospheric background in each hemisphere. When the equatorial depletion reaches these regions, the ionospheric scintillation may present different patterns. In this work, data from scintillation monitors, ionosondes, and all-sky imagers deployed at geomagnetically antipodal stations around the equator during the campaign were evaluated along the months of October–December 2002. The results reveal asymmetries in the onset times and scintillation magnitudes. On the one hand, the scintillation onset occurred earlier in 80% of the cases over the southern hemisphere. On the other hand, 71% of the nights verified the larger scintillation values in the northern hemisphere. The distinct F region altitudes, thickness, bottomside electron density gradient scale lengths, and TEC over both stations seem to contribute to this asymmetric behavior. PubDate: 2022-05-09
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Abstract: Abstract Double-difference (DD) analysis and precise point positioning (PPP) are two widely used processing approaches to analyze ground-based GNSS measurements. We investigate the quality of the zenith tropospheric delay (ZTD) estimates produced from both processing approaches for a regional network over 1 year and show that DD solutions contain more numerous and larger ZTD outliers. The accuracy of both DD and PPP solutions strongly depends on the data processing procedure and models. We analyze the impact of mapping functions, satellite orbit and clock products and ambiguity resolution (fixed vs. float) on ZTD estimates. The results are assessed from station position repeatability and ZTD differences with respect to the ERA5 reanalysis. As expected, mapping functions have the strongest impact, with VMF1 being more accurate than GMF. Surprisingly, the impact of the ambiguity resolution and satellite products is rather weak in the PPP solution. We speculate that this results from the fact that final satellite products have reached a high level of accuracy and that other error sources now dominate static PPP solutions. A time and frequency analysis reveal unprecedented spurious sub-daily signals in the ZTD time series, which occur at the frequency of the GPS satellite repeat period and its harmonics. This suggests that sub-daily GPS ZTD estimates contain a significant part of the residual modeling errors due to satellite orbits, tidal models, mapping functions and multipath, which still need to be improved. PubDate: 2022-04-29
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Abstract: Abstract Precise knowledge about the attitude of Global Navigation Satellite System (GNSS) satellites is essential for precise orbit determination (POD) and other high-precision GNSS applications. The first Quasi-Zenith Satellite System (QZSS) satellite QZS-1 applies two attitude modes, i.e., the yaw-steering (YS) and the orbit-normal (ON). QZS-1 has to perform the so-called attitude mode switch maneuvers to change its attitude mode between YS and ON. In this study, we present an empirical model for such attitude mode transitions. The QZSS operational history information released by the Cabinet Office is first analyzed. With a few exceptions, it is found that the threshold of the sun’s elevation angle above the orbital plane ( \(\beta\) ) was changed in the first half of 2017 from ± 20 degrees to ± 17 degrees for YS/ON switches and from ± 20 degrees to ± 18 degrees for ON/YS switches, respectively. In addition, the YS/ON switches start at the orbital angle of − 90 degrees, while the ON/YS switches end at − 90 degrees. Based on these features, the empirical model is established, which can describe the attitude mode switch maneuvers with an accuracy of better than 1 degree. With the proposed model, the root mean square values of phase residuals in POD processing can be reduced by 1.8–3.9 cm when compared with the “instant switch” approach at the \(\beta\) threshold of ± 20 degrees (abbreviated as “cutoff_20”). The proposed attitude model also has a better representation of the solar radiation pressure acceleration. As of the POD performances, the proposed attitude model can reduce the orbit overlapping discrepancies by 70–80% when compared with the "cutoff_20" approach. Furthermore, the standard deviation values of the residuals from satellite laser ranging validation are reduced by 3–5 times. PubDate: 2022-04-23
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Abstract: Abstract GPS Block IIR-M and Block IIF satellites have the capability of flex power, which can redistribute the transmitting power of different signal components. Flex power can effectively improve the anti-jamming performance of GPS signals and is part of the GPS modernization plans. Since 2020, two kinds of regional GPS flex power have been observed, one started on February 14, 2020, and ended on September 13, 2020, while the other one has been on-state since October 1, 2020. Both of these two kinds of flex power improved the power of L2 P(Y) signal. We establish a real-time detection system for flex power based on the random forest algorithm in machine learning, combined with polynomial fitting. Moreover, we establish a special voting detection system and use the constant false alarm detection technology (CFAR) to find the detection threshold of each satellite and determine whether the satellite has flex power. To verify the performance of system, three kinds of data are used for testing. Judging from the results of these three-mode data samples, the false alarm rate of the system is around \(10^{ - 5}\) , and the probability of missed alarm maintains around \(10^{ - 3}\) , which can effectively prove the detection performance of the GPS flex power. PubDate: 2022-04-23
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Abstract: Abstract In precise satellite clock estimation, the satellite clock offsets absorb the pseudorange and carrier phase time-variant hardware delays. The dissimilarity of the satellite clock estimated with observations at different frequencies is termed the inter-frequency clock bias (IFCB). The bias inconsistency suggests that the simple ionospheric-free satellite clock cannot directly be applied to the multi-frequency carrier phase observations in multi-frequency precise point positioning (PPP). We propose the carrier phase time-variant observable-specific signal bias (OSB) concept and the corresponding estimation approach to solve this. The definition, rationality, reliability and validity of the carrier phase time-variant OSB are clarified. The new concept advantage is that a set of the carrier phase time-variant OSB values can directly amend on the carrier phase observations, and thereafter, the IFCB effect can be eliminated, which provides the flexibilities for the GNSS carrier phase observation handing. Datasets collected from 144 Multi-GNSS Experiment (MGEX) stations are adopted for the carrier phase time-variant OSB estimation and an analysis of its effect on the GNSS multi-frequency PPP performance. The various multi-frequency PPP models are tested and evaluated considering the carrier phase time-variant OSB correction. The results indicate that the GPS, BDS-2 and BDS-3 carrier phase time-variant OSB time series have the obvious amplitudes and the amplitudes of the Galileo and QZSS carrier phase time-variant OSB are small. The GPS and BDS-2 multi-frequency PPP performance is significantly enhanced when correcting the carrier phase time-variant OSB. The GPS-only kinematic ionospheric-float PPP exhibits the positioning accuracy of 1.0 cm, 2.2 cm and 2.6 cm in the north, east and up components when correcting the carrier phase time-variant OSB, whereas the positioning accuracy of the case without the correction is 1.4 cm, 2.8 cm and 3.7 cm in three directions, respectively. The mean convergence time of two dual-frequency and three triple-frequency BDS-2-only kinematic PPP is reduced by 5.0%, 4.9%, 5.4%, 4.7% and 4.6%, respectively, with the carrier phase time-variant OSB correction. The carrier phase time-variant OSB improvement on BDS-3-only multi-frequency PPP is not obvious owing to the relatively few available and stable carrier phase time-variant OSB values. The reliability, suitability and effectiveness of the GNSS carrier phase time-variant OSB are demonstrated. PubDate: 2022-04-22
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Abstract: Abstract Weighted mean temperature (Tm) acts as a vital parameter in an extensive range of applications, such as atmospheric Precipitation Water Vapor (PWV) prediction based on the tropospheric delays from Global Navigation Satellite System (GNSS) measurements. However, few high-accuracy Tm models for the region of China were established in high temporal and high spatial resolution due to the complex topography in China. We utilize the latest version of the European Centre for Medium‐Range Weather Forecasts (ECMWF) Re-Analysis 5 (ERA5) data to establish a Tm model for the China region, named the CTm-FNN model. This new coalescent model is independent of meteorological parameters but based on combining the idea of the traditional grid model and the feedforward neural network (FNN) algorithm. Tm values can be obtained by inputting the 3-D coordinates of the station, day of year, and hour in UT to the CTm-FNN model. When validated by ERA5 and radiosonde data in 2019, the new model shows that the root mean square (RMS) error is 3.54 K and 4.72 K, respectively. Compared with the Chinese Tropospheric Model (CTrop) model, the RMS error of CTm-FNN is reduced by 29% and 8.5% with respect to ERA5 and radiosonde data, respectively. Compared with the global pressure and temperature 3 (GPT3) model, the reduction is 86% and 83%. The standard deviation (STD) of the CTm-FNN models is 3.54 K and 4.15 K, which are reduced by 26% and 20% compared with the CTrop model, and 82% and 79% compared with the GPT3 model when validated by the ERA5 and radiosonde data. This new model manifests its ability to capture high-accuracy Tm from the surface to almost the tropopause with high temporal and high spatial resolution, which can expand the application of GNSS-PWV inversion technique in China. PubDate: 2022-04-16
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Abstract: Abstract The widely used GNSS correction services for high precision positioning take advantage of accurate real-time TEC forecasting based on vertical total electron content (VTEC) maps. The methods for modeling and forecasting are mainly based on overly simplified assumptions, which in principle cannot reflect the real situations due to limitations of the mathematical formulations. Therefore, these methods cannot comprehensively capture the features of ionospheric TEC in spatial–temporal series. To overcome the problems caused by such assumptions, we combine ConvLSTM (convolutional long short-term memory) with spectrum analysis. The method allows the extraction of high-resolution spatial–temporal patterns of the ionospheric VTEC maps and accelerates the convergence time of neural networks. Extensive experiments have been carried out for short- and long-term forecasting and demonstrated that the performance of our method is better than other state-of-the-art models developed for various time series analysis methods. Based on the data from global ionospheric maps (GIMs) products, the results show that the root-mean-square error (RMSE) of global VTEC forecasting by our method substantially improves for two hours intervals over the years 2015, 2016, 2017 and 2019 compared to existing methods, specifically, 20–50% reduction on 1 or 2 h forecasting in terms of RMSE. In addition, the method is sufficient to support real-time forecasting since it takes less than one second to output global forecasting solutions. With these properties, we can facilitate real-time and highly accurate ionosphere correction services beneficial to numerous GNSS correct services and positioning terminals. PubDate: 2022-04-13
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Abstract: Abstract Benefiting from global navigation satellite systems (GNSS), the spatial distribution of satellites and the positioning accuracy of receivers have improved. However, the processing load for tracking all visible satellites has increased significantly. In this study, the temporal correlation in satellite selection results is analyzed, and a fast satellite selection algorithm based on a modified beetle antennae search (MBAS) is proposed to fulfill the requirements of continuous real-time positioning. This approach encodes the satellite, regards the satellite selection set as the position of the beetle, and generates beetle antennae signals through single- and multi-direction searches to randomly optimize the selected satellites. In addition, the geometric dilution of precision is used as an adaptive function to evaluate the intensity of the antennae signal, and the position of the beetle is updated to gradually approach the optimal solution. Experimental results show that the application of MBAS provides better positioning accuracy, has stronger time correlation, and derives in lower computational complexity than other meta-heuristic algorithms, such as the Genetic Algorithm and Particle Swarm Optimization. The proposed algorithm can be applied to continuous and real-time multi-GNSS positioning with different number of satellites. PubDate: 2022-04-13
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Abstract: Abstract A new GNSS/IMU tightly coupled positioning system is introduced to train positioning. To fulfil a train control system’s aim of reducing the need to install trackside equipment, the GNSS precise point positioning (PPP) method is applied in place of the conventional differential GNSS method. As the railway environment has the character of long operational mileage and complex GNSS measurement conditions, the GPS and BDS constellations are combined with measurement processing to improve the system’s continuity and stability. Ultra-rapid GNSS orbit and clock product is used for real-time PPP. The GNSS-PPP and IMU are tightly coupled using an Extended Kalman filter with single-differenced ionospheric-free GPS + BDS carrier phase and pseudorange observations. The carrier phase ambiguities are estimated as “float” values every epoch to reduce the impact of GNSS signal loss-of-lock and cycle slips. A train experiment was conducted on the Qinghai-Tibet Railway to evaluate system performance. The results show that the proposed system has a better performance than the conventional methods, including GPS + BDS PPP, LC GPS + BDS PPP/IMU and TC GPS PPP/IMU, with 52.1%, 49.4% and 52.1%, respectively. The tightly-coupled GPS + BDS PPP/IMU system under conditions of partly blocked GNSS coverage was evaluated to evaluate the system's continuity. It was confirmed that the proposed system had more stable positioning results and higher positioning accuracy. PubDate: 2022-04-08
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Abstract: Abstract The Galileo High Accuracy Service (HAS), aiming at providing a Precise Point Positioning (PPP) service worldwide, will soon transmit precise orbits, clocks and biases, for both Galileo and GPS, in the signal-in-space and through a ground channel. This will be complemented in the future with precise ionosphere corrections and HAS data authentication. This work provides an overview of Galileo initial HAS, focusing on its overall message structure, architecture, and early performance. The initial HAS is strictly based on the existing Galileo monitoring and uplink capabilities already available for the other Galileo services. This contribution assesses the service coverage, the accuracy of the broadcast corrections, and the user PPP performance of Galileo HAS for the first time. The results show that Galileo HAS can provide broad coverage with few-centimeter broadcast correction accuracy and fulfill the targeted two-decimeter user horizontal accuracy in the evaluated conditions even in its initial phase. PubDate: 2022-04-07
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Abstract: Abstract Due to the three-step implementation of the BeiDou Navigation Satellite System (BDS), users face the coexistence of BDS-2 and BDS-3 for a period of time. In particular, the real-time BDS-2/BDS-3 clock is the prerequisite for real-time precise point positioning (PPP) and precise orbit determination of low earth orbit satellites. Although the undifferenced clock estimation model can obtain all useful information in the parameter domain, many phase ambiguities make the clock estimation time-consuming. We develop a high-rate clock estimation algorithm without external complex matrix library, which can be easily implemented in cross-platforms. First, the recursive Kalman filter based on a single observation is used to avoid the complex matrix inversion. In addition, parallel computing is also employed to reduce the complexity of the update of the covariance matrix and the data preprocessing of multiple stations. Considering the continuous update of receiver firmware and that 60 globally distributed stations cover two different periods, the algorithm is validated in terms of computational efficiency, clock precision and accuracy of kinematic PPP. The results illustrated that the calculation time per epoch is approaching 0.5 s when the filter's matrix dimension reaches 1300. With the benefit of upgraded receivers, the average precision of BDS-3 C19–C37 is improved by 13.8%, while the precision of BDS-3 C38–C46 is 0.124 ns. The accuracy of kinematic PPP using all estimated BDS-2/BDS-3 satellites was 2.78 cm, 4.44 cm and 7.48 cm in north, east and up directions, respectively. PubDate: 2022-04-07
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Abstract: Abstract Traditional intersatellite communications for shared timing information rely on microwave transceivers such as those in Milstar, AEHF, and Iridium constellations. With extensive space heritage and well-established engineering and performance specifications, these methods have typified the field of high-performance satellite synchronization for decades, recently introduced into active GNSS satellite constellations such as BeiDou. Optical crosslinks, currently investigated as an augmentation or alternative to traditional microwave-based methods, can provide enhanced precision to intersatellite ranging and time transfer, performing beyond one-way or uplink/downlink microwave-based communications. The challenges of time transfer through optical links and crosslinks can significantly impact the systems architecture, optical terminal complexity, and agreements on international standards. Orders-of-magnitude precision enhancement can enable novel timing and ranging technologies allowing for advanced navigation capabilities. Additionally, basic scientific studies with a fleet of synchronized satellites could inform fundamental physics studies on a truly global scale. We evaluate the benefits, drawbacks, and potential applications of satellite synchronization through microwave and optical crosslinks for shared timing and ephemeris data in support of enhanced constellation state estimation and reduced range error. The risks and value associated with these technologies are also discussed with an emphasis on challenges for aerospace. PubDate: 2022-04-05
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Abstract: Abstract Currently, four GLONASS-M+ satellites and two GLONASS-K1 satellites transmit CDMA signals on the G3 frequency. It is important to understand the inconsistency between the new G3 and traditional FDMA G1 and G2 signals, wherein inter-frequency clock bias (IFCB) is one of the important indexes to find the difference of triple-frequency carrier phase hardware delays. Using the geometry-free and ionospheric-free (GFIF) phase combinations and an epoch-differenced method, we use 152 globally distributed MGEX stations spanning 30 days to estimate GLONASS IFCB. GLONASS-K1 satellite R09 and GLONASS-M+ satellite R21 are selected for analysis in the experiment owing to enough G3 observations. Results indicate that the magnitudes of the multipath error and SNR on G3 frequency are noticeably smaller than those of the other two frequencies. A satellite-induced multipath error seems to exist on the G3 frequency of R21, whereas R09 has none, which needs to be quantized and modeled further. The intra-day peak-peak amplitudes of R09 and R21 IFCBs are about 0.01 and 0.2 m, while inter-day amplitudes are about 0.03 and 0.3 m, respectively; R21 is even larger than that of GPS Block-IIF satellites (about 0.2 m). The RMS and STD of the IFCB series of R09 and R21 are 0.90, 0.89 cm, and 10.56, 10.53 cm, respectively. Therefore, the IFCB errors must be carefully corrected in GLONASS G3-frequency applications. Fortunately, the IFCBs of R21 present both intra-day and inter-day sine-wave periodic variations, which may be modeled, and even well predicted in the future. PubDate: 2022-04-02
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Abstract: Abstract Efficiency evaluations of statistical decision probabilities with multiple alternative hypotheses are a prerequisite for data quality control in positioning, navigation, and many other applications. Commonly, one uses a time-consuming simulation technique to obtain the statistical decision probabilities or builds lower and/or upper bounds to control the probability, which may be unconvincing when the bounds are loose. We aim to provide a computationally efficient way to calculate the multivariate statistical decision probabilities when performing data snooping in quality control. However, accurate evaluation of those probabilities is complicated considering the complexity of the critical region where the integration intervals contain a variable corresponding to the one with the largest absolute value. Hence, to improve the calculation of statistical decision probabilities, a simplified algorithm for computing the probabilities under the critical region is proposed based on a series of transformation strategies. We implement the proposed algorithm in a simulated numerical experiment and a GPS single-point positioning experiment. The results show that the probabilities computed with the proposed algorithm approximate the results of the simulation technique, but the proposed algorithm is computationally more efficient. PubDate: 2022-04-02
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Abstract: Abstract The lower bound of the GDOP is an important parameter to benchmark satellite selection algorithms. Existing GDOP lower bound formulations do not consider the satellite azimuth and elevation angle constraints with respect to the user for Geostationary Earth Orbit (GEO) and Inclined Geosynchronous Orbit (IGSO)-based regional navigation constellations. A GDOP lower bound formulation considering the azimuth and elevation angle constraints is formulated for GEO- and IGSO-based navigation constellations. Using numerical simulation, it is demonstrated that the GDOP lower bound for using the Navigation Indian Constellation (NavIC) is significantly higher than the Global Positioning System (GPS), whereas the existing GDOP lower bound formulation provides comparable GDOP lower bound for the GPS and NavIC. It also indicates that one or more navigation constellations should be used with the NavIC to achieve better position accuracy. In this context, an unsupervised learning-based satellite selection (ULiSeS) algorithm is also proposed and the effectiveness of the algorithm is demonstrated through numerical simulation for the GPS and the NavIC constellations. A meta-cognitive component is also introduced to enable the ULiSeS algorithm to decide when to learn and when to use the available model. The ULiSeS algorithm selects a better set of satellites than the Quasi-optimal selection algorithm and requires 89.12% less processing time than the fast satellite selection algorithm. PubDate: 2022-03-31
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Abstract: Abstract We focus on the impacts of the polar cap ionospheric sporadic-E (Es) layer that occurred at Resolute Bay, Canada, on September 5, 2012, on the quality of the Global Positioning System (GPS) observable and the positioning performance. Mainly, we are concerned about the relationship between the thin Es layer and the ionosphere scintillation and the reason behind the degraded positioning performance during the event of the polar cap Es. The results show that the polar cap Es can trigger weak-to-moderate amplitude scintillation and the maximum positioning errors in the up component for the Ionospheric-Free Precise Point Positioning (IF-PPP) model can reach up to 0.51 m while that for the Uncombined PPP (UC-PPP) model can reach 1.20 m. The maximum positioning errors occur simultaneously with the time of the maximum amplitude scintillation induced by the polar cap Es. The degraded positioning performance can be attributed mostly to falsely detected cycle slips (CSs), which are influenced by the polar cap Es layer-induced scintillation. To mitigate this, we propose the 3-sigma rule to determine the threshold of the CS detection observables. The preliminary results show that compared with the commonly adopted threshold values, the positioning accuracy improvement in the up component is 14.1% for the IF-PPP model while the corresponding improvement is 40.8% for the UC-PPP model, suggesting that the high accuracy positioning performance can be achieved in the high latitude region by statistic characterization of the CS thresholds. PubDate: 2022-03-28
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