# GPS Solutions

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### An analysis of the on-orbit performance of Galileo satellite antennas using reconstructed gain patterns

Fri, 06/05/2020 - 00:00
Abstract

The importance of having high levels of reliability in Global Navigation Satellite Systems (GNSS) signals has increased gradually in recent years. Among other factors, evaluating the available power and its spatial characteristics at the user location is a key task as part of signal quality verification processes. Due to a diversity of factors, the transmitting antennas of GNSS satellites may exhibit a non-nominal on-orbit performance. As a result, the effective isotropically radiated power of navigation signals may be affected, e.g., due to azimuthal asymmetries in the antenna gain pattern. If not analyzed and handled properly, such irregularities may lead to the use of weak signals from a given satellite, possibly resulting in non-admissible positioning errors. The present contribution aims at the analysis of the on-orbit performance of GNSS satellite antennas, using data from the Galileo system as a case study. Employing reconstructed gain patterns, a set of metrics is defined, which intend being used as performance evaluation values. In addition, the concept of antenna performance stability is explored by analyzing changes over time of reconstructed gain patterns. Results using data from the operational Galileo satellites (up to the beginning of 2019) have been obtained. From the computed example reconstructed patterns, gain variations below 0.5 dB and azimuthal asymmetries at the 0.6 dB level (95%) were found for most of the analyzed satellites. Likewise, the obtained results suggest the occurrence of an event that altered the nominal performance of the antenna of Galileo satellite 0102 during the first years of operation. The presented tools and results may be of particular interest for applications requiring navigation signal power monitoring tasks, such as GNSS reflectometry or safety–critical systems.

### GPS + Galileo + BeiDou precise point positioning with triple-frequency ambiguity resolution

Wed, 05/27/2020 - 00:00
Abstract

Along with the rapid development of GNSS, not only BeiDou, but also Galileo, and the newly launched GPS satellites can provide signals on three frequencies at present. To fully take advantage of the multi-frequency multi-system GNSS observations on precise point positioning (PPP) technology, this study aims to implement the triple-frequency ambiguity resolution (AR) for GPS, Galileo, and BeiDou-2 combined PPP using the raw observation model. The processing of inter-frequency clock bias (IFCB) estimation and correction in the context of triple-frequency PPP AR has been addressed, with which the triple-frequency uncalibrated phase delay (UPD) estimation is realized for real GPS observations for the first time. In addition, the GPS extra-wide-line UPD quality is significantly improved with the IFCB correction. Because of not being contaminated by the IFCB, the raw UPD estimation method is directly employed for Galileo which currently has 24 satellites in operation. An interesting phenomenon is found that all Galileo satellites except E24 have a zero extra-wide-lane UPD value. With the multi-GNSS observations provided by MGEX covering 15 days, the positioning solutions of GPS + Galileo + BeiDou triple-frequency PPP AR have been conducted and analyzed. The triple-frequency kinematic GNSS PPP AR can achieve an averaged 3D positioning error of 2.2 cm, and an averaged convergence time of 10.8 min. The average convergence time can be reduced by triple-frequency GNSS PPP AR by 15.6% compared with dual-frequency GNSS PPP AR, respectively. However, the additional third frequency has only a marginal contribution to positioning accuracy after convergence.

### Analysis and combination of multi-GNSS snow depth retrievals in multipath reflectometry

Sun, 05/24/2020 - 00:00
Abstract

The Global Navigation Satellite Systems (GNSS) continuously broadcast radio signals at two or more frequencies in the L-band, providing extensive data for GNSS multipath reflectometry. Multi-GNSS constellations provide more signals and more tracks than individual constellations, achieving greater azimuthal coverage and more frequent retrievals. The main aim of this study is to retrieve snow depth using multi-GNSS data, analyze the multi-GNSS retrievals, and then combine them. Data of four constellations from three GNSS sites are analyzed, including the BeiDou and Galileo signals, which are rarely used to retrieve snow depth. The snow depth retrievals are estimated for signal-to-noise ratio data of each signal at first. The retrievals of individual signals from four constellations, except that of the GPS P-code signal, have no detectable inter-signal bias, thus showing the same trend describing snow depth variation. Then a multi-GNSS combination method based on robust regression is used to combine the inter-constellation inter-signal retrievals, and the multi-GNSS combined retrievals show an improvement in precision, availability, and temporal sampling. Compared to that of individual signals, it achieves about 50% improvement in precision, a smaller uncertainty, and a constant sampling interval of 6 h.

### Effects of a navigation spoofing signal on a receiver loop and a UAV spoofing approach

Sat, 05/09/2020 - 00:00
Abstract

A civil navigation signal is vulnerable to interference and tampering owing to its open interface and low signal power. We focus on navigation spoofing. First, using a piecewise function, we quantitatively analyze the effects of the navigation spoofing signal on the receiver tracking loop. For a phase-locked loop, the spoofing signal extends the pull-in range of the discriminator. The autocorrelation gain of the spoofing signal has a different effect on the slope of the discriminator, depending on whether the discriminator is related to the signal amplitude. For the delay-locked loop, taking the non-coherent early minus late power method as an example, the unlocking condition and interval are analyzed quantitatively using the spoofing amplitude gain and the initial phase cosine of the spoofing and authentic carriers. A carrier frequency difference between the spoofing signal and authentic signal causes a phase jump and attenuation of the amplitude gain. Second, in luring an unmanned aerial vehicle (UAV) to a designated location, we assume a UAV model and provide a spoofing strategy. Experimental results show that it is feasible to lure a civilian quadrotor UAV to a designated location about 50 m from where the UAV believes it is located.

### System-specific systematic errors in earth rotation parameters derived from GPS, GLONASS, and Galileo

Thu, 05/07/2020 - 00:00
Abstract

The earth rotation parameters (ERPs) are time-variable global geodetic parameters with a purely geophysical origin. Theoretically, the estimates of these parameters should be independent of the satellite constellation used in GNSS processing. Nonetheless, clear differences in the time series of ERPs are noticed when using different GNSS constellations. In this study, GPS, GLONASS, and Galileo estimates of ERP have been extensively evaluated in search of system-specific signals. Some of the processing details, such as modeling of the direct solar radiation pressure and length of the orbital arc, also have an impact on the ERP estimates. The GPS-based polar motion estimates are of better quality than those based on GLONASS and Galileo, which are susceptible to deficiencies in the orbit modeling. On the other hand, we observe a systematic bias of GPS-based length-of-day (LoD) with respect to the IERS-C04-14 values with a mean offset of − 22.4 µs/day. The Galileo-based solutions are almost entirely free of this issue. The extension of the orbital arc in the GNSS processing from 1 to 3 days is superior for the quality of the ERPs, especially for pole coordinate rates and LoD. The spurious signals inherently influence the Galileo-based and GLONASS-based ERPs at the frequencies which arise from the resonance between the satellite revolution period and earth rotation, e.g., 3.4 days for Galileo and 3.9 days for GLONASS. These and the draconitic signals overshadow the GNSS-based ERP estimates. Although all the system-specific solutions are affected by the artificial signals, the combination of different GNSS mitigates most of the uncertainties and improves the ERP results.

### Error analysis on ionospheric scintillation index S 4 measured by GNSS receiver

Thu, 05/07/2020 - 00:00
Abstract

Ionospheric scintillation is a challenging issue for the Global Navigation Satellite System (GNSS). Data collected by the globally distributed GNSS receivers provide abundant information about the ionosphere. S4 is one of the most important parameters of the scintillation, which can be measured by the GNSS receivers. We established a simplified probability model for S4 measured by the GNSS receiver. This model fully considers the correlation of the signal intensity and the ambient noise introduced by the receiver. A factor that reveals the correlation feature of scintillated intensity was proposed. Based on this model, the Cramer–Rao bound (CRB) and the minimum-variance unbiased estimator for S4 were deduced and analyzed. The CRB shows that the uncertainty of S4 increases as the scintillation becomes severe and the decorrelation time becomes longer. Then an approximate probability model was established to describe the statistics of the common estimator of S4. Simulation tests were carried out to validate the proposed model. Based on the approximate model, the statistics of the common estimator was analyzed. We found that, apart from ambient noise, the variation of signal intensity leads to a minus bias for S4 measurements, which seems to have been neglected in the past. A method to correct this bias was proposed. We also found that the increase in the carrier-to-noise ratio decreases the bias but helps little in reducing the variance of the measurements. Considering the accuracy of S4 measurements and the robustness of the tracking loop, we found that for weak scintillation, the value 0.02 s is an ideal coherent time. For moderate scintillation, a relatively ideal coherent time is 0.004 s and for severe scintillation, 0.001 s is an ideal coherent time. Based on this analysis, suggestions for GNSS receiver configurations were proposed.

### Global grid-based T m model with vertical adjustment for GNSS precipitable water retrieval

Thu, 05/07/2020 - 00:00
Abstract

Atmospheric weighted mean temperature, Tm, is a key parameter in ground-based GNSS precipitable water (PW) retrieval, especially for a real-time mode. Considering the seasonal variability of the Tm vertical gradient across the globe, a global grid-based Tm model with seasonal vertical adjustments was developed based on 6-hourly ERA-Interim pressure levels product from European Centre for Medium-Range Weather Forecasts (ECMWF) covering the period 2011–2017. The performance of the proposed global Tm model called GTm_R was evaluated by two kinds of data sources, including sounding profiles at 577 globally distributed radiosonde stations and ERA-Interim reanalysis product throughout the year 2018. Our results show the excellent performance of the developed model GTm_R against other models when compared with high-quality ERA-Interim product and radiosonde data, especially in the ocean area and regions with high-elevation terrain. GTm_R can generally achieve a global mean bias/RMSE of − 0.1/3.1 K in contrast to ERA-Interim-derived Tm and − 0.2/3.8 K in comparison with radiosonde-derived Tm, which is corresponding to a 5%-8% improvement against GPT2w and GTm_III across the globe. Moreover, GTm_R can achieve global mean $$\sigma_{{\text{PW}}}$$ and $$\sigma_{{\text{PW}}}$$/PW values of 0.26 mm and 1.36%, respectively. For the proportion of PW uncertainty in terms of RMSE below 0.4 mm, GTm_R increased by about 6%, 3%, and 2% over Bevis formula, GTm_III, and GPT2w, respectively. Thus, the developed global Tm model GTm_R that considers seasonal vertical adjustments is capable of deriving accurate and reliable Tm values for real-time or near real-time PW retrieval from GNSS measurements, which will be of great significance to real-time or nowcasting extreme weather forecasting.

### Initial results of distributed autonomous orbit determination for Beidou BDS-3 satellites based on inter-satellite link measurements

Thu, 05/07/2020 - 00:00
Abstract

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

### Empirical orthogonal function analysis and modeling of global ionospheric spherical harmonic coefficients

Wed, 04/29/2020 - 00:00
Abstract

We developed a global empirical model for computing spherical harmonic (SH) coefficients based on the empirical orthogonal function (EOF) method and periodic functions by utilizing global ionospheric SH coefficients data provided by Center for Orbit Determination in Europe (CODE) during the years 2005–2016. Results show that the first four-order base functions and corresponding associated coefficients can represent 97.15% of the basic characteristics of the original data. The first four-order associated coefficients have noticeable periodic variations, and the correlation between these coefficients and the solar activity intensity is high. By fitting the associated coefficients with the periodic function that takes into account the influence of solar activity, it is possible to establish an EOF model to characterize the variations of the ionospheric SH coefficients with few model parameters and further calculate the global vertical total electron content (VTEC). Relative to the existing global VTEC EOF models, this EOF method can achieve high-accuracy modeling of global VTEC with a smaller number of model coefficients. By comparing the SH coefficients and the global VTEC between the EOF model and CODE, results demonstrate that the EOF model can achieve high accuracy and reliability under different solar activities. The difference between the EOF model and CODE is basically at the same level as that between the individual ionospheric analysis centers and CODE. In the extreme event of magnetic storms, the EOF model can also present higher accuracy than the international reference ionosphere (IRI) model.

### SIMuRG: System for Ionosphere Monitoring and Research from GNSS

Fri, 04/24/2020 - 00:00
Abstract

Currently, more than 6000 operating GNSS receivers deliver observations to multiple servers. Ionospheric data are derived from these measurements providing outstanding space coverage and time resolution. There are about 200 million independent measurements daily. Researchers need sophisticated software tools to deal with such a large amount of data. We present recent advances and products from the System for Ionosphere Monitoring and Research from GNSS (SIMuRG). Currently, SIMuRG provides the total electron content (TEC) variations filtered within 2–10 min, 10–20 min, and 20–60 min, the Rate of the TEC Index, the Along Arc TEC Rate index, and the vertical TEC. SIMuRG is an online service at http://simurg.iszf.irk.ru. The system can be used free of charge and allows calculating both maps and series for arbitrary time intervals and geographic regions. All the data products are available in the form of data or figures. We discuss the system and its geophysics applications.

### FH-BOC: generalized low-ambiguity anti-interference spread spectrum modulation based on frequency-hopping binary offset carrier

Fri, 04/24/2020 - 00:00
Abstract Objective

The paper aims to present a generalized modulation scheme that can improve the anti-interference performance of global navigation satellite systems (GNSS) and mitigate the ambiguity problem in BOC modulation.

Summary background data

With the exponential growth of location-based services, there is a need to improve the positioning accuracy and the capability to resist against external interference in challenging environments, such as urban canyons, forested terrains, and indoor areas, in which signal attenuation, interference, and multipath fading can seriously degrade the positioning accuracy of global navigation satellite systems (GNSS) and GNSS-like systems. The binary offset carrier (BOC) modulation has been adopted in GNSSs because of its good spectral isolation from heritage signals, high accuracy, multipath interference resistance, and flexibility in signal implementation compared with BPSK-R modulation. However, for high-order BOC modulation, the main drawback is the ambiguity in tracking due to the multiple side peaks of the autocorrelation function (ACF). The receiver may incorrectly lock onto one of these side peaks, causing intolerable measurement bias, and this undesirable behavior limits the application of this modulation scheme in navigation systems.

Methods

We present a generalized low-ambiguity anti-interference spread spectrum modulation based on frequency-hopping BOC (FH-BOC). First, we formulate the mathematical model of FH-BOC modulation and derive the analytical expressions for the normalized ACF and PSD, and we analyze the time and frequency properties of several representative FH-BOC signals. Next, we present recommended parameter selections, a generation and detection scheme for FH-BOC modulation. Finally, we analyze the characteristics of the ACF and PSD, the tracking performance, the spectral separation, and the anti-narrowband interference and multipath interference performance for several specific BOC and FH-BOC signals.

Results

The results show that FH-BOC with the largest frequency-hopping band has lower ACF ambiguity, better anti-interception performance, and better anti-intrasystem interference, narrowband interference, and multipath interference performance than BOC modulation with the same main lobe bandwidth (MLB). The tracking and anti-interference performance of FH-BOC is similar to that of BOC modulation with the same ACF main peak width.

Conclusions

FH-BOC is a generalized type of modulation that includes BOC modulation. The proposed FH-BOC signal improves the anti-interference performance and mitigates the ACF ambiguity problem of BOC modulation. The acquisition time and complexity of the receiving process for the proposed FH-BOC signal are the same for the BOC signal with the same MLB. The new modulation scheme which we proposed can serve as a new paradigm for the next-generation GNSS signal design, especially military signal design. It can also be used in the signal design for GNSS-like systems, such as systems for indoor positioning, GNSS enhancement, and pseudolite-based positioning.

### An improved constrained simultaneous iterative reconstruction technique for ionospheric tomography

Sat, 04/18/2020 - 00:00
Abstract

Global Navigation Satellite System (GNSS) is now widely used for continuous ionospheric observations. Three-dimensional computerized ionospheric tomography (3DCIT) is an important tool for the reconstruction of electron density distributions in the ionosphere through effective use of the GNSS data. More specifically, the 3DCIT technique is able to resolve the three-dimensional electron density distributions over the reconstructed area based on the GNSS slant total electron content (STEC) observations. We present an Improved Constrained Simultaneous Iterative Reconstruction Technique (ICSIRT) algorithm that differs from the traditional ionospheric tomography methods in 3 ways. First, the ICSIRT computes the electron density corrections based on the product of the intercept and electron density within voxels so that the assignment of corrections at different heights becomes more reasonable. Second, an Inverse Distance Weighted (IDW) interpolation is used to restrict the electron density values in the voxels not traversed by GNSS rays, thereby ensuring the smoothness of the reconstructed region. Also, to improve the reconstruction accuracy around the HmF2 (the peak height of the F2 layer) altitude, a multiresolution grid is adopted in the vertical direction, with a 10-km resolution from 200 to 420 km and a 50-km resolution at other altitudes. The new algorithm has been applied to the GNSS data over the European and North American regions in different case studies that involve different seasonal conditions as well as a major storm. In the European region experiment, reconstruction results show that the new ICSIRT algorithm can effectively improve the reconstruction of the GNSS data. The electron density profiles retrieved from ICSIRT are much closer to the ionosonde observations than those from its predecessor, namely, the Constrained Simultaneous Iteration Reconstruction Technique (CSIRT). The reconstruction accuracy is significantly improved. In the North American region experiment, the electron density profiles in ICSIRT results show better agreement with incoherent scatter radar observations than CSIRT, even for the topside profiles.

### An analysis of PPP-GPS-based decentralized train multi-sensor navigation system

Sat, 04/18/2020 - 00:00
Abstract

GPS precise point positioning (PPP) is increasingly being used in many precise positioning applications to achieve sub-meter level accuracy using a stand-alone user receiver. To achieve the full-scale navigation parameters of position, velocity and attitude, GPS is often combined with the inertial navigation system (INS) to deliver navigation solutions in high update rate. However, GPS signals cannot always be tracked in difficult areas, which leads to an integration performance degradation because of INS sensor errors. Therefore, the authors propose a PPP-GPS/INS/odometer/map-matching integrated navigation system. The positioning performance based on the different International GNSS Service (IGS) products for train kinematic positioning applications is investigated. A field test was conducted on a specific low-density line to evaluate the proposed system. The test results confirm that the proposed multi-sensor navigation system can provide seamless navigation in both GPS available and unavailable situations with the accuracy of decimeter. Different IGS satellite orbits and clock offset products were used to generate the PPP results, and it was concluded that the IGS final products provide the best performance, with a distance root mean square (DRMS) of 0.138 m, and the IGS ultra-rapid product can also generate acceptable positioning solutions with a DRMS of 0.222 m.

### MG-APP: an open-source software for multi-GNSS precise point positioning and application analysis

Sat, 04/11/2020 - 00:00
Abstract

To meet the demands of research and precise point positioning (PPP) in a multi-GNSS environment, we developed a GNSS data processing software named multi-GNSS automatic precise positioning software (MG-APP). MG-APP is an open-source software that can be run on Windows/Linux/UNIX and other operating systems. It can simultaneously process GPS/GLONASS/BDS/Galileo observations using a Kalman filter or a square root information filter (SRIF). Compared to the Kalman filter, the SRIF has better numerical stability and maintains stable convergence even with a significant round-off error. MG-APP has a comprehensive and friendly graphical user interface that conveniently allows the user to select models and set parameters. It also contains several types of tropospheric and estimation models that make it easy to analyze the impact of different models and parameters on PPP data processing. After the data processing finishes, zenith tropospheric delays, receiver clock offsets, satellite ambiguity parameters, observation residuals, and other results will be saved into files. Users can further analyze the solution results and construct graphs easily.

### Estimation of tropospheric wet refractivity using tomography method and artificial neural networks in Iranian case study

Fri, 04/10/2020 - 00:00
Abstract

Using the observations from local and regional GPS networks, the estimation of slant wet delays (SWDs) is possible for each line of sight between satellite and receiver. The observations of SWD are used to model horizontal and vertical variations of the wet refractivity in the atmosphere above the study area. This work is done using the tomography method. In tomography, the horizontal variations of tropospheric wet refractivity are modeled with the polynomial in degree and rank of 2 with latitude and longitude as variables. Also, altitude variations are modeled in the form of discrete layers with constant heights. The main innovation is to estimate the tropospheric parameters for each line of sight by the artificial neural networks (ANNs). The SWD obtained from GPS observations for the different signals at each station is compared with the SWD generated by the ANNs (SWDGPS–SWDANNs). The square of the difference between these two values is introduced as the cost function in the ANNs. To evaluate, we used observations from October 27 to 31, 2011. The availability of GPS and radiosonde data is the main reason for choosing this timeframe. The correlation coefficient, root mean square error (RMSE), and relative error allow for evaluation of the proposed model. The results were also compared with the results of the voxel-based troposphere tomography method. For a more detailed evaluation, four test stations are selected and ANN zenith wet delays (ZWDANN) are compared with the ZWDGPS. Observations of test stations are not used in the modeling step. The correlation coefficient in the testing step for TomoANN and Tomovoxel is 0.9006 and 0.8863, respectively. The mean RMSE at 5 days for TomoANN and Tomovoxel is calculated as 0.63 and 0.71 mm/km, respectively. Also, the average relative error at the four test stations for TomoANN is 15.37% and for Tomovoxel it is 19.69%. The results demonstrate the better capability of the proposed method in the modeling of the tropospheric wet refractivity in the region of Iran.

### GNSS code and carrier phase observations of a Huawei P30 smartphone: quality assessment and centimeter-accurate positioning

Thu, 04/02/2020 - 00:00
Abstract

In 2016, an application programming interface was added to the Android operating systems, which enables the access of GNSS raw observations. Since then, an in-depth evaluation of the performance of smartphone GNSS chips is very much simplified. We analyzed the quality of the GNSS observations, especially the carrier phase observations, of the dual-frequency GNSS chip Kirin 980 built into Huawei P30 and other smartphones. More than 80 h of static observations were collected at several locations. The code and carrier phase observations were processed in baseline mode with reference to observations of geodetic-grade equipment. We were able to fix carrier phase ambiguities for GPS L1 observations. Furthermore, we performed an antenna calibration for this frequency, which revealed that the horizontal phase center offsets from the central vertical axis of the smartphone and also the phase center variations do not exceed 1–2 cm. After successful ambiguity fixing, the 3D position errors (standard deviations) are smaller 4 cm after 5 min of static observation session and 2 cm for long observation session.

### Framework for GREIS-formatted GNSS data manipulation

Sat, 03/21/2020 - 00:00
Abstract

We introduce an application framework that enables easy implementation of applications that process GNSS Receiver External Interface Specification (GREIS)-formatted GNSS measurement data. The framework utilizes anti-aging techniques such as automatic code generation, documentation renewal, building, and component testing, which makes this framework effectively an always-up-to-date (“evergreen”) software. We also include an example case of the framework: a simple data inspection software for measurement data produced by Javad receivers, and compatible receivers, and data acquisition software with real-time telemetry. The framework is written in C++ and is available online.

### Hybrid constellation design using a genetic algorithm for a LEO-based navigation augmentation system

Thu, 03/19/2020 - 00:00
Abstract

A low earth orbit (LEO) constellation can support broadband Internet access and can also be a platform for navigation augmentation for global navigation satellite systems. LEO satellites have the potential to transmit very strong navigation signals; they also show rapid changes in spatial geometry as they come closer to earth and travel faster over stations than satellites in medium or high orbits do. Before the establishment of a LEO-based navigation augmentation system, constellation design is a critical task. Previous LEO constellations have usually employed single polar or near-polar orbits for global coverage, resulting in fewer visible satellites at low latitudes. We propose and optimize several hybrid LEO-augmented constellations using a genetic algorithm to realize globally even coverage. When there are 100 LEO satellites, the average numbers of visible satellites during a regression period are 5.49, 5.44 and 5.47, with standard deviations of 0.44, 0.18 and 0.28, for the optimized hybrid polar-orbit/Walker, orthogonal circular-orbit/Walker and Walker/Walker constellations, respectively. For the hybrid orthogonal circular-orbit/Walker constellation type, the necessary numbers of LEO satellites to realize globally even coverage with six visible satellites are 109, 172 and 221 for elevation mask angles of 7°, 15° and 20°, respectively. For coverages with four and five visible satellites with an elevation mask angle of 7°, the required numbers of satellites are 90 and 93, respectively. All proposed hybrid constellations can provide 100% global coverage availability with one to three visible satellites for broadband Internet access.

### A second generation of the neural network model for predicting weighted mean temperature

Tue, 03/17/2020 - 00:00
Abstract

In global navigation satellite system (GNSS) meteorology, the weighted mean temperature (Tm) is a variable parameter in the conversion between zenith wet delay errors of GNSS and precipitable water vapor. The combined models of Tm, which are modeled with a combination of Tm seasonal variations and relationships between Tm and site meteorological measurements (mainly site measured temperature), have been proven to be of relatively higher accuracy. In this study, an improved combined model for Tm called the NN-II model was developed and is the second generation of the NN model. Similar to the NN model, NN-II is a combined model and is modeled by using the neural network model. The NN model was only designed for Tm estimates near the surface, while NN-II was designed for Tm estimates from the surface to almost the top of the troposphere. Compared with the NN model, the NN-II model shows some advanced features in terms of model design: modeled Tm data cover from the surface to almost the top of the troposphere, a more accurate seasonal Tm from the GTrop-Tm model is used, and the input variables are refined. Due to these refinements, the bias and RMSE of NN-II for global Tm from the surface to almost the top of the troposphere are 0.08 K and 3.34 K, respectively, and this new model shows 29.1% and 40.6% improved accuracies compared to those of the GTrop-Tm model and the NN model, respectively. The accuracy advantage is maintained over different heights of the troposphere on a global scale.

### Sky visibility estimation based on GNSS satellite visibility: an approach of GNSS-based context awareness

Mon, 03/16/2020 - 00:00
Abstract

Global navigation satellite system (GNSS) positioning in urban areas does not currently provide accurate and stable performance because surrounding buildings can block and reflect satellite signals. However, if we can determine the environment in which the receiver is located, appropriate positioning can be applied. For example, GNSS real-time kinematic and 3D-mapping-aided GNSS (3DMA GNSS) are used for positioning in open sky and urban areas, respectively. Thus, the context awareness of the GNSS receiver is important. In fact, an urban canyon can be further categorized into different levels based on sky visibility. We propose an innovative algorithm based on this categorization, which can provide information on surrounding buildings and give an estimation of sky visibility from raw GNSS measurements. This idea was inspired by the use of low-orbit satellite data for remote sensing applications. The recent development of multi-GNSS has led to a notable increase in the number of navigation satellites. Crucially, the visibility of satellites and the blockage of line-of-sight satellite signals are representative of the surrounding environment. The visibility of satellites can be classified by machine learning techniques, and an accurate classification can afford an estimation that is close to the real-sky visibility, as derived from a 3D building model and ground truth location. To assess the sensitivity of our proposed sky visibility estimation algorithm, we simulate different classification accuracies to investigate their effect on the performance of the algorithm.

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