Global Navigation Satellite System Model Research Articles

Real-time retrieval of high-precision ZTD maps using GNSS observation

Zenith Tropospheric Delay (ZTD) is an important factor that restricts the high-precision positioning of global navigation satellite system (GNSS), and it is of great significance in establishing a real-time and high-precision ZTD model. However, existing ZTD models only consider the impact of linear terms on ZTD estimation, whereas the nonlinear factors have rarely been investigated before and thus become the focus of this study. A real-time and high-precision ZTD model for large height difference area is proposed by considering the linear and nonlinear characteristics of ZTD spatiotemporal variations and is called the real-time linear and nonlinearity ZTD (RLNZ) model. This model uses the ZTD estimated from the Global Pressure and Temperature 3 (GPT3) model as the initial value. The linear impacts of periodic term and height on the estimation of ZTD difference between GNSS and GPT3 model is first considered. In addition, nonlinear factors such as geographical location and time are further used to fit the remaining nonlinear ZTD residuals using the general regression neural network method. Finally, the RLNZ-derived ZTD is obtained at an arbitrary location. The western United States, with height difference ranging from −500 to 4000 m, is selected, and the hourly ZTD of 484 GNSS stations provided by the Nevada Geodetic Laboratory (NGL) and the data of 9 radiosonde (RS) stations in the year 2021 are used. Experiment results show that a better performance of ZTD estimation can be retrieved from the proposed RLNZ model when compared with the GPT3 model. Statistical results show the averaged root mean square (RMS), Bias, and mean absolute error (MAE) of ZTD from GPT3 and RLNZ models are 33.7/0.8/25.7 mm and 22.6/0.1/17.4 mm, respectively. The average improvement rate of the RLNZ model is 33 % when compared to the GPT3 model. Finally, the application of the proposed RLNZ model in simulated real-time Precise Point Positioning (PPP) indicates that the accuracy of PPP in N, E and U components is improved by 8 %, 2 %, and 6 % when compared with that from the GPT3-based PPP. Meanwhile, the convergence time in N and U components is improved by 23 % and 7 %, respectively. Such results verify the superiority of the proposed RLNZ model in retrieving real-time ZTD maps for GNSS positioning and navigation applications.

Real-Time Adjustment and Spatial Data Integration Algorithms Combining Total Station and GNSS Surveys with an Earth Gravity Model

During the dynamic development of modern technologies based on advanced algorithmic and instrumental solutions, it is essential to integrate geospatial data efficiently. Such an approach is applied in all geo-information services, especially mobile ones, and is helpful in, for example, precise navigation or effective risk management. One leading application is deformation monitoring (structural monitoring) and displacement control surveying. In addition, spatial data integration methods are used in modern accessibility analysis, Smart City ideas, tracing utility networks, and building information modelling (BIM). The last aforementioned technology plays a crucial role in architectural design and construction. In this context, it is crucial to develop efficient and accurate algorithms supporting data fusion, which do not strain the computing resources and operate efficiently online. This paper proposes an algorithm for real-time adjustment of integrated satellite GNSS (global navigation satellite system), total station, and Earth Gravitational Model (EGM) vertical direction data in a geocentric coordinate system based on a statistical general linear mixed model. A numerical example shows that the proposed algorithm of the online adjustment works correctly. The results of the online adjustment are the same as those of the offline adjustment. It is also shown that the GNSS measurements are necessary only at the total station points in the spatial total station traverse. There is no need to add additional merging points of the total station positions because the differences between the results of the online adjustment, including and excluding the merging points, are very small (around 1–2 mm in standard deviation).

A Systematic Review of Machine Learning Techniques for GNSS Use Cases

In terms of the availability and accuracy of positioning, navigation, and timing (PNT), the traditional Global Navigation Satellite System (GNSS) algorithms and models perform well under good signal conditions. In order to improve their robustness and performance in less than optimal signal environments, many researchers have proposed machine learning (ML) based GNSS models (ML models) as early as the 1990s. However, no study has been done in a systematic way to analyze the extent of the research on the utilization of ML models in GNSS and their performance. In this study, we perform a systematic review of studies from 2000 to 2021 in the literature that utilizes machine learning techniques in GNSS use cases. We assess the performance of the machine learning techniques in the existing literature on their application to GNSS. Furthermore, the strengths and weaknesses of machine learning techniques are summarized. In this paper, we have identified 213 selected studies and ten categories of machine learning techniques. The results prove the acceptable performance of machine learning techniques in several GNSS use cases. In most cases, the models using the machine learning techniques in these GNSS use cases outperform the traditional GNSS models. ML models are promising in their utilization in GNSS. However, the application of ML models in the industry is still limited. More effort and incentives are needed to facilitate the utilization of ML models in the PNT context. Therefore, based on the findings of this review, we provide recommendations for researchers and guidelines for practitioners.

Multi-GNSS global ionosphere modeling enhanced by virtual observation stations based on IRI-2016 model

The inhomogeneous distribution of Global Navigation Satellite System (GNSS) stations results in inaccurate vertical total electron contents (VTECs) in global ionosphere maps (GIMs) over areas with large GNSS data gaps. Incorporating VTECs from the International Reference Ionosphere (IRI) model is usually adopted as one approach to mitigate the inaccurate VTECs. However, large and complicated spatiotemporal varying VTEC biases between GNSS and IRI suggest a robust strategy to optimally combine GNSS and IRI VTECs for operational high-precision modeling. Here, we thoroughly analyze the characteristics of VTEC biases between GNSS and IRI-2016 model in different latitudes from 2009 to 2019, and develop an improved functional and stochastic model. An automated assimilation strategy of GNSS and IRI-2016 VTECs is proposed for Shanghai Astronomical Observatory final GIM (SHAG) routine estimation, and the reliability of GIMs in areas with lack of stations is enhanced by attaching Virtual Observation Stations (VOSs) based on IRI-2016 model and VOS bias parameters. Experimental results show that the root-mean-square errors (RMSEs) of SHAG with respect to VTECs retrieved from four independent GNSS assessment stations are reduced by 21.65–53.06% in the large data gaps with the assistance of VOSs. Furthermore, we validated the long-term reliability of SHAG spanned one solar cycle (2009–2019) with International GNSS Service (IGS) final GIMs and satellite altimetry VTECs. Validation results suggest that SHAG is in good agreement with IGS final GIMs, and reliability of SHAG in large GNSS data gap areas is significantly improved by attaching VOSs and biases. This methodology also represents an efficient tool for automated global ionospheric modeling integrating multi-source data.

Continuous and Precise Positioning in Urban Environments by Tightly Coupled Integration of GNSS, INS and Vision

Accurate, continuous and seamless state estimation is the fundamental module for intelligent navigation applications, such as self-driving cars and autonomous robots. However, it is often difficult for a standalone sensor to fulfill the demanding requirements of precise navigation in complex scenarios. To fill this gap, this letter proposes to exploit the complementariness of the global navigation satellite system (GNSS), inertial measurement unit (IMU) and vision via a tightly coupled integration method, aiming to achieve continuous and accurate navigation in urban environments. Specifically, the raw GNSS carrier phase and pseudorange measurements, IMU data, and visual features are directly fused at the observation level through a centralized Extended Kalman Filter (EKF) to make full use of the multi-sensor information and reject potential outlier measurements. Furthermore, the widely used high-precision GNSS models including precise point positioning (PPP) and real-time kinematic (RTK) are unified in the proposed integrated system to increase usability and flexibility. We validate the performance of the proposed method on several challenging datasets collected in urban canyons and compare against the loosely coupled and state-of-the-art methods.

Ionospheric scintillation impact on ambiguity resolution using ADOP in closed form

The Ambiguity Dilution of Precision (ADOP) is a well-known scalar measure that can be used to infer the strength of the Global Navigation Satellite System (GNSS) model of the carrier phase ambiguities involved in precise relative GNSS positioning. Odijk and Teunissen (2008a) derived closed-form expressions for single-baseline GNSS models that allow verifying the factors affecting the ambiguity resolution as well as the probability of its correct resolution as integer values. However, this weighted-ionosphere ADOP closed form assumes that the standard deviation of the ionosphere delay is dependent on a function associated with the baseline length. This means that a baseline of the same length at different locations around the world and in different moments in time would have the same standard deviation, which in practice is not true. This becomes even worse in regions like Brazil, where the ionospheric anomalies are more intense and frequent, especially in periods of high solar activity. In this work, a new method for calculating the ionospheric delay standard deviation that considers the ionospheric scintillation S4 index is proposed to improve the closed-form ADOP performance. Experiments with a baseline of 280 m located in Presidente Prudente, Brazil (magnetic latitude of around −13°), were carried out. The results showed that in periods of both weak and strong ionospheric scintillation, the introduction of S4 into the ionospheric delay standard deviation was beneficial for ADOP. The average improvement of the ADOP closed form was of around 72% in the analyzed period of weak scintillation and of 35% in the period of strong scintillation. In addition, the results showed that in periods of strong scintillation, relative positioning accuracy is around 100 times worse, up to 30 m, when compared to periods of weak ionospheric scintillation.

A two-stage tropospheric correction model combining data from GNSS and numerical weather model

We have developed a new concept for providing tropospheric augmentation corrections. The two-stage correction model combines data from a Numerical Weather Model (NWM) and precise ZTDs estimated from Global Navigation Satellite System (GNSS) permanent stations in regional networks. The first-stage correction is generated using the background NWM forecast only. The second-stage correction results from an optimal combination of the background model data and GNSS (near) real-time tropospheric products. The optimum correction is achieved when using NWM for the hydrostatic delay modeling and for vertical scaling, while GNSS products are used for correcting the non-hydrostatic delay. The method is assessed in several variants including study of the combination of NWM and GNSS data, spatial densification of the original NWM grid, and GNSS ZTD densification using tropospheric linear horizontal gradients. The first-stage correction can be characterized by overall accuracy of about 10 mm for ZTD (1-sigma). The second-stage correction supported with GNSS tropospheric products improved the first-stage correction by a factor of 2–4 in terms of the ZTD accuracy and by a factor of 2.5 in terms of its spatio-temporal stability.

Instantaneous and controllable integer ambiguity resolution: review and an alternative approach

In the high-precision application of Global Navigation Satellite System (GNSS), integer ambiguity resolution is the key step to realize precise positioning and attitude determination. As the necessary part of quality control, integer aperture (IA) ambiguity resolution provides the theoretical and practical foundation for ambiguity validation. It is mainly realized by acceptance testing. Due to the constraint of correlation between ambiguities, it is impossible to realize the controlling of failure rate according to analytical formula. Hence, the fixed failure rate approach is implemented by Monte Carlo sampling. However, due to the characteristics of Monte Carlo sampling and look-up table, we have to face the problem of a large amount of time consumption if sufficient GNSS scenarios are included in the creation of look-up table. This restricts the fixed failure rate approach to be a post process approach if a look-up table is not available. Furthermore, if not enough GNSS scenarios are considered, the table may only be valid for a specific scenario or application. Besides this, the method of creating look-up table or look-up function still needs to be designed for each specific acceptance test. To overcome these problems in determination of critical values, this contribution will propose an instantaneous and CONtrollable (iCON) IA ambiguity resolution approach for the first time. The iCON approach has the following advantages: (a) critical value of acceptance test is independently determined based on the required failure rate and GNSS model without resorting to external information such as look-up table; (b) it can be realized instantaneously for most of IA estimators which have analytical probability formulas. The stronger GNSS model, the less time consumption; (c) it provides a new viewpoint to improve the research about IA estimation. To verify these conclusions, multi-frequency and multi-GNSS simulation experiments are implemented. Those results show that IA estimators based on iCON approach can realize controllable ambiguity resolution. Besides this, compared with ratio test IA based on look-up table, difference test IA and IA least square based on the iCON approach most of times have higher success rates and better controllability to failure rates.

Integer aperture estimation comparison between ratio test and difference test: from theory to application

Acceptance testing or ambiguity validation is a key step in global navigation satellite system (GNSS) ambiguity resolution, which combined with integer estimator is the so-called integer aperture (IA) estimator. The difference test and ratio test are the two most popular tests. In order to compare the performances of both IA estimators, their differences in different GNSS models are analyzed from algebraic and geometrical perspectives. Furthermore, both tests are connected by comparing with the optimal acceptance test, and then, they can be transformed each other based on certain numerical conditions. As to the instantaneous applications, both tests are first compared with their corresponding instantaneous approaches, including the fixed failure rate approach for ratio test IA (RTIA) and the instantaneous and controllable approach for difference test IA (DTIA). Advantages and drawbacks of both IA estimators in theory and application are analyzed based on these comparisons. In order to verify these conclusions, typical multi-frequency, multi-GNSS situations are constructed to evaluate the performances of DTIA and RTIA ambiguity resolution. Then, both IA estimators are compared based on their instantaneous approaches in the field test. All the simulation experiments and field test results indicate that DTIA has more advantages and is better than RTIA not only in theory, but also in the practical applications.

Study of Water Vapor Variations Associated with Meso-γ Scale Convection: Comparison between GNSS and Non-Hydrostatic Model Data

Water vapor variations associated with a meso-γ scale convection were investigated using GNSS (Global Navigation Satellite System) derived PWV (precipitable water vapor) and high resolution numerical model data with a 250 m horizontal grid interval. A rapid increase of GNSS-derived PWV that occurred prior to the initiation of surface rainfall was well simulated by the numerical model.In the model, PWV values began to increase 16 min before the rainfall occurred at the surface. A local maximum of PWV was formed because of the generation of shallow free convection and surface water vapor flux convergence due to a lifting of an air parcel at approximately 1 km elevation by a preceding surface wind convergence. Due to the existence of a stable inversion layer between 2.2 and 3.5 km elevation, the shallow free convection took 11 min to rise above the inversion layer to form a deep convection. These results suggest that observation of local distributions of GNSS-derived PWV is useful for monitoring the generation of deep moist convection.

Success rate improvement of single epoch integer least-squares estimator for the GNSS attitude/short baseline applications with common clock scheme

The sub-centimeter level relative positioning can be accomplished anytime and anywhere on Earth, provided that the integer ambiguities of the very precise Global Navigation Satellite System (GNSS) carrier-phase observables are correctly resolved. The Integer Least-Squares (ILS) estimator is known to be efficient and optimal for Integer Ambiguity Resolution (IAR) of the unconstrained GNSS model, and the stronger the model strength, the higher the success rate. In this contribution, we investigate the model strength of the common clock scheme, in which the two receivers of the short baseline feed a common clock and the cables have the same delay and many GNSS-based attitude/short baseline applications benefit from this approach. For this scheme, the clock biases between two receivers will be zero and can be omitted, and thus it has a stronger model strength and a higher success rate, compared with the non-common clock scheme. In this contribution, the well-known Ambiguity Dilution of Precision (ADOP), which captures the main characteristics of the ambiguity precision, is utilized to assess the model strengthening when the perfectly synchronized receivers are employed. The mathematical expression of the single epoch ADOP is deduced by the given design parameters, and thus the ADOP-based approximate ILS success rate can be easily computed with the specified measurement set-up which includes the number of available satellites and frequencies and the precision of observation. We focus on the success rate assessment of the common clock scheme for stand-alone, unaided, single-frequency, single epoch observation with only five visible satellites, since it is the most challenging case of GNSS relative positioning and in this case the performance of the employed ambiguity resolution method can be investigated effectively. Thus, one can predict whether or not the required performance will be obtained for the worst case.

The ratio test for future GNSS ambiguity resolution

The performance of the popular ambiguity ratio test is analyzed. Based on experimental and simulated data, it is demonstrated that the current usage of the ratio test with fixed critical value is not sustainable in light of the enhanced variability that future global navigation satellite system (GNSS) ambiguity resolution will bring. As its replacement, the model-driven ratio test with fixed failure rate is proposed. The characteristics of this fixed-failure rate ratio test are described, and a performance analysis is given. The relation between its critical value and various GNSS model parameters is also studied. Finally, a procedure is presented for the creation of fixed failure rate look-up tables for the critical values of the ratio test.

Integer least-squares theory for the GNSS compass

Global navigation satellite system (GNSS) carrier phase integer ambiguity resolution is the key to highprecision positioning and attitude determination. In this contribution, we develop new integer least-squares (ILS) theory for the GNSS compass model, together with efficient integer search strategies. It extends current unconstrained ILS theory to the nonlinearly constrained case, an extension that is particularly suited for precise attitude determination. As opposed to current practice, our method does proper justice to the a priori given information. The nonlinear baseline constraint is fully integrated into the ambiguity objective function, thereby receiving a proper weighting in its minimization and providing guidance for the integer search. Different search strategies are developed to compute exact and approximate solutions of the nonlinear constrained ILS problem. Their applicability depends on the strength of the GNSS model and on the length of the baseline. Two of the presented search strategies, a global and a local one, are based on the use of an ellipsoidal search space. This has the advantage that standard methods can be applied. The global ellipsoidal search strategy is applicable to GNSS models of sufficient strength, while the local ellipsoidal search strategy is applicable tomodels for which the baseline lengths are not too small. We also develop search strategies for the most challenging case, namely when the curvature of the non-ellipsoidal ambiguity search space needs to be taken into account. Two such strategies are presented, an approximate one and a rigorous, somewhat more complex, one. The approximate one is applicable when the fixed baseline variance matrix is close to diagonal. Both methods make use of a search and shrink strategy. The rigorous solution is efficiently obtained by means of a search and shrink strategy that uses nonquadratic, but easy-to-evaluate, bounding functions of the ambiguity objective function. The theory presented is generally valid and it is not restricted to any particular GNSS or combination of GNSSs. Its general applicability also applies to the measurement scenarios (e.g. single-epoch vs. multiepoch, or single-frequency vs. multi-frequency). In particular it is applicable to the most challenging case of unaided, single frequency, single epoch GNSS attitude determination. The success rate performance of the different methods is also illustrated.

Testing of a new single-frequency GNSS carrier phase attitude determination method: land, ship and aircraft experiments

Global navigation satellite system (GNSS) ambiguity resolution is the process of resolving the unknown cycle ambiguities of the carrier phase data as integers. The sole purpose of ambiguity resolution is to use the integer ambiguity constraints as a means of improving significantly on the precision of the remaining GNSS model parameters. In this contribution, we consider the problem of ambiguity resolution for GNSS attitude determination. We analyse the performance of a new ambiguity resolution method for GNSS attitude determination. As it will be shown, this method provides a numerically efficient, highly reliable and robust solution of the nonlinearly constrained integer least-squares GNSS compass estimators. The analyses have been done by means of a unique set of extensive experimental tests, using simulated as well as actual GNSS data and using receivers of different manufacturers and type as well as different platforms. The executed field tests cover two static land experiments, one in the Netherlands and one in Australia, and two dynamic experiments, a low-dynamics vessel experiment and high-dynamics aircraft experiment. In our analyses, we focus on stand-alone, unaided, single-frequency, single-epoch attitude determination, as this is the most challenging case of GNSS compass processing.

On the Availability of Fault Detection and Exclusion in GNSS Receiver Autonomous Integrity Monitoring

Global Navigation Satellite System (GNSS) Receiver Autonomous Integrity Monitoring (RAIM) is essential for safety-of-life and liability critical applications. This paper discusses two fundamentally different ways to assess the integrity risk of an operation with RAIM, based on a different amount of information available: the expected (or average) performance that is computed using the GNSS models only and the real-time (or actual) performance, which also uses information on the internal status of a GNSS receiver. It is shown both theoretically and by simulation that the real-time integrity risk significantly exceeds the expected risk after the detection and exclusion of a failing satellite. Therefore, while most published RAIM algorithms base their performance assessment on the expected performance only, this is only correct when the requirements allow the risk evaluation to be averaged over multiple operations. However, when the GNSS integrity requirement is to be applied on a ‘per operation’ basis, real-time integrity measures are more appropriate.

Penalized GNSS Ambiguity Resolution

Global Navigation Satellite System (GNSS) carrier phase ambiguity resolution is the process of resolving the carrier phase ambiguities as integers. It is the key to fast and high precision GNSS positioning and it applies to a great variety of GNSS models which are currently in use in navigation, surveying, geodesy and geophysics. A new principle of carrier phase ambiguity resolution is introduced. The idea is to give the user the possibility to assign penalties to the possible outcomes of the ambiguity resolution process: a high penalty for an incorrect integer outcome, a low penalty for a correct integer outcome and a medium penalty for the real valued float solution. As a result of the penalty assignment, each ambiguity resolution process has its own overall penalty. Using this penalty as the objective function which needs to be minimized, it is shown which ambiguity mapping has the smallest possible penalty. The theory presented is formulated using the class of integer aperture estimators as a framework. This class of estimators was introduced elsewhere as a larger class than the class of integer estimators. Integer aperture estimators, being of a hybrid nature, can have integer outcomes as well as non-integer outcomes. The minimal penalty ambiguity estimator is an example of an integer aperture estimator. The computational steps involved for determining the outcome of the minimal penalty estimator are given. The additional complexity in comparison with current practice is minor, since the optimal integer estimator still plays a major role in the solution of the minimal penalty ambiguity estimator.