Global Navigation Satellite System Positioning Research Articles

Doppler‐aided Global Navigation Satellite System position estimation with B‐spline smoothing strategy

Smoothing process can effectively improve the accuracy of the Global Navigation Satellite System (GNSS) position estimation algorithm. In this study, a Doppler-aided GNSS position estimation algorithm with a B-spline smoothing strategy is proposed. B-spline signal processing is used to smoothen the code measurements with Doppler measurements, which were selected because they are more robust and immune to cycle slips than carrier phase measurements. Next, the mathematical expressions of the smoothing process and position estimation are derived. The smoothing process is based on the structure of a digital filter, which is especially suitable for real-time applications. The Cramer–Rao lower bound of the proposed algorithm is derived. Moreover, a complete implementation structure of the proposed algorithm is presented. The validity of the proposed algorithm is verified through scenario simulation in terms of static, kinematic, and adverse environments. The advantages of the proposed algorithm are demonstrated by comparison with existing algorithms.

Development and evaluation of the refined zenith tropospheric delay (ZTD) models

The tropospheric delay is a significant error source in Global Navigation Satellite System (GNSS) positioning and navigation. It is usually projected into zenith direction by using a mapping function. It is particularly important to establish a model that can provide stable and accurate Zenith Tropospheric Delay (ZTD). Because of the regional accuracy difference and poor stability of the traditional ZTD models, this paper proposed two methods to refine the Hopfield and Saastamoinen ZTD models. One is by adding annual and semi-annual periodic terms and the other is based on Back-Propagation Artificial Neutral Network (BP-ANN). Using 5-year data from 2011 to 2015 collected at 67 GNSS reference stations in China and its surrounding regions, the four refined models were constructed. The tropospheric products at these GNSS stations were derived from the site-wise Vienna Mapping Function 1 (VMP1). The spatial analysis, temporal analysis, and residual distribution analysis for all the six models were conducted using the data from 2016 to 2017. The results show that the refined models can effectively improve the accuracy compared with the traditional models. For the Hopfield model, the improvement for the Root Mean Square Error (RMSE) and bias reached 24.5/49.7 and 34.0/52.8 mm, respectively. These values became 8.8/26.7 and 14.7/28.8 mm when the Saastamoinen model was refined using the two methods. This exploration is conducive to GNSS navigation and positioning and GNSS meteorology by providing more accurate tropospheric prior information.

Kinematic ZTD Estimation from Train-Borne Single-Frequency GNSS: Validation and Assimilation

Water vapour is one of the most important parameters utilized for the description of state and evolution of the Earth’s atmosphere. It is the most effective greenhouse gas and shows high variability, both in space and time. Thus, detailed knowledge of its distribution is of immense importance for weather forecasting, and therefore high resolution observations are crucial for accurate precipitation forecasts, especially for the short-term prediction of severe weather. Although not intentionally built for this purpose, Global Navigation Satellite Systems (GNSS) have proven to meet those requirements. The derivation of water vapour content from GNSS observations is based on the fact that electromagnetic signals are delayed when travelling through the atmosphere. The most prominent parameterization of this delay is the Zenith Total Delay (ZTD), which has been studied extensively as a major error term in GNSS positioning. On the other hand, the ZTD has also been proven to provide substantial benefits for atmospheric research and especially Numerical Weather Prediction (NWP) model performance. Based on these facts, the scientific area of GNSS Meteorology has emerged. The present study goes beyond the current status of GNSS Meteorology, showing how reasonable estimates of ZTD can be derived from highly-kinematic, single-frequency (SF) GNSS data. This data was gathered from trains of the Austrian Federal Railways (ÖBB) and processed using the Precise Point Positioning (PPP) technique. The special nature of the observations yields a number of additional challenges, ranging from appropriate pre-processing and parameter settings in PPP to more sophisticated validation and assimilation methodologies . The treatment of the ionosphere for SF-GNSS data represents one of the major challenges of this study. Two test cases (train travels) were processed using different strategies and validated using ZTD calculated from ERA5 reanalysis data. The validation results indicate a good overall agreement between the GNSS-ZTD solutions and ERA5-derived ZTD, although substantial variability between solutions was still observed for specific sections of the test tracks. The bias and standard deviation values ranged between 1 mm and 8 cm, heavily depending on the utilized processing strategy and investigated train route. Finally, initial experiments for the assimilation of GNSS-ZTD estimates into a NWP model were conducted, and the results showed observation acceptance rates of 30–100% largely depending on the test case and processing strategy.

Cooperative fault detection and recovery in the GNSS positioning of mobile agent swarms based on relative distance measurements

Relative measurements are exploited to cooperatively detect and recover faults in the positioning of Mobile Agent (MA) Swarms (MASs). First, a network vertex fault detection method based on edge testing is proposed. For each edge, a property that has a functional relationship with the properties of its two vertices is measured and tested. Based on the edge testing results of the network, the maximum likelihood principle is used to identify the vertex fault sources. Second, an edge distance testing method based on the noncentral chi-square distribution is developed for detecting faults in the Global Navigation Satellite System (GNSS) positioning of MASs. Third, a recovery strategy for faults in the positioning of MASs based on distance measurement is provided. The effectiveness of the proposed methods is validated by a simulation case in which an MAS passes through a GNSS spoofing zone. The proposed methods are conducive to increasing the robustness of the positioning of MASs in complex environments. The main novelties include the following: (A) network vertex fault detection is based on concrete probability analysis rather than simple majority voting, and (B) the relation of detectability and recoverability of MAS positioning faults with the structure of the relative measurement network is first disclosed.

Position observation-based calibration method for an LDV/SINS integrated navigation system.

With the advantages of high velocity measurement accuracy and fast dynamic response, the laser Doppler velocimeter (LDV) is expected to replace the odometer to be combined with a strapdown inertial navigation system (SINS) to form a higher precision integrated navigation system. However, LDV scale factor error and misalignment angles between LDV and inertial measurement unit will affect the accuracy of navigation. Considering that not all global navigation satellite system (GNSS) receivers can directly provide velocity information and current mainstream calibration methods are sensitive to the measurement noise and outliers of velocity and position information, a robust calibration method aided by GNSS is proposed in this paper, which is based on position observation. Different from current popular calibration methods, the attitude information of the GNSS/SINS integrated navigation system obtained by an adaptive Kalman filter is used to construct the observation vector together with LDV velocity outputs and GNSS position outputs in this method. The LDV scale factor error and the misalignment angle are determined by the ratio of two observation vector modulus and the Davenport's q-method method, respectively. The accuracy and robustness of the calibration method are verified by one vehicle test with normal GNSS signals and one vehicle test with GNSS signals with outliers. And the horizontal position error of dead reckoning of the calibrated LDV/SINS integrated system are less than 0.0314% and 0.1033% of the mileage, respectively.

Implication between Geophysical Events and the Variation of Seasonal Signal Determined in GNSS Position Time Series

The seasonal signal determined by the Global Navigation Satellite System (GNSS), which is captured in the coordinate time series, exhibits annual and semi-annual periods. This signal is frequently modelled by two periodic signals with constant amplitude and phase-lag. The purpose of this study is to explore the implication of different types of geophysical events on the seasonal signal in three stages—in the time span that contains the geophysical events, before and after the geophysical event, but also the stationarity phenomena, which is analysed on approximately 200 reference stations from the EPN network since 1995. The novelty of the article is demonstrated by correlating three different types of geophysical events, such as earthquakes with a magnitude greater than 6° on the Richter scale, landslides, and volcanic activity, and analysing the variation in amplitude of the seasonal signal. The geophysical events situated within a radius of 30 km from the epicentre showed a higher seasonal value than when the timespan did not contain a geophysical event. The presence of flicker and random walk noise was computed using overlapping Hadamard variance (OHVAR) and the non-stationary behaviour of the time series of the CORS coordinates in the time frequency analysis was done using continuous wavelet transform (CWT).

Real-time GNSS attitude determination by a direct approach with efficiency and robustness

Estimating attitude directly from multi-antenna carrier phase measurements is known as the direct approach of global navigation satellite system attitude determination. Without the process of resolving baseline vectors in advance, this approach makes full use of raw observations. However, the known baseline constraints would be missing when the least squares method is used in the direct approach, of which the corresponding model contains no baseline parameter. The constraint information is important for real-time ambiguity resolution. Therefore, we propose using an adaptively robust Kalman filter for the direct approach, in which the predicted attitude plays the role of an attitude constraint. An observation model parameterized by the multiplicative quaternion error vector and the integer ambiguities is derived, accompanied with a state model consisting of the quaternion error vector, the ambiguities and the angular rate. Since the state vector contains three different types of parameters, the filter uses an adaptive matrix consisting of different adaptive factors instead of a single factor. The factor of the quaternion error vector is determined by a three-section function containing the ratio value from the ratio-test of ambiguity resolution. The factors of the ambiguities are calculated by the detected cycle slip. The equivalent weight matrix of the filtering can resist the influence of outliers in harsh environment. By the direct approach with the proposed adaptively robust filtering, the accuracy of the float solution and the variance-covariance matrix are significantly improved, and the ambiguity can be efficiently searched and fixed using the standard least-squares ambiguity decorrelation adjustment method. The proposed algorithm is suitable for real-time applications since no time-consuming and complex searching of ambiguity resolution is required. Finally, the efficiency and robustness of the algorithm is validated by a field test.

Weighted empirical mode decomposition for processing GNSS position time series with the consideration of formal errors

Empirical Mode Decomposition (EMD) is suitable to process the nonlinear and non-stationary time series for filtering noise out to extract the signals. The formal errors are provided along with Global Navigation Satellite System (GNSS) position time series, however, not being considered by the traditional EMD. In this contribution, we proposed a modified approach that called weighted Empirical Mode Decomposition (weighted EMD) to extract signals from GNSS position time series, by constructing the weight factors based on the formal errors. The position time series over the period from 2011 to 2018 of six permanent stations (SCBZ, SCJU, SCMN, HLFY, FJPT, SNXY) were analyzed by weighted EMD, as well as the traditional EMD. The results show that weighted EMD can extract more signals than traditional EMD from original GNSS position time series. Additionally, the fitting errors were reduced 14.52 %, 12.25 % and 8.06 % for North, East and Up components for weighted EMD relative to traditional EMD, respectively. Moreover, 100 simulations of four stations are further carried out to validate the performances of weighted EMD and traditional EMD. The mean Root Mean Squared Errors (RMSEs) are reduced from traditional EMD to weighted EMD with the reductions of 9.08 %, 9.63 % and 6.84 % for East, North and Up components, respectively, which highlights the necessity of considering the formal errors. Therefore, it reasonable to conclude that weighted EMD can extract the signals more than traditional EMD, which can be suggested to analyze GNSS position time series with formal errors.

A Comprehensive Evaluation of Key Tropospheric Parameters from ERA5 and MERRA-2 Reanalysis Products Using Radiosonde Data and GNSS Measurements

Tropospheric delay is a major error source in the Global Navigation Satellite System (GNSS), and the weighted mean temperature (Tm) is a key parameter in precipitable water vapor (PWV) retrieval. Although reanalysis products like the National Centers for Environmental Prediction (NCEP) and the European Center for Medium-Range Weather Forecasts (ECMWF) Re-Analysis-Interim (ERA-Interim) data have been used to calculate and model the tropospheric delay, Tm, and PWV, the limitations of the temporal and spatial resolutions of the reanalysis data have affected their performance. The release of the fifth-generation accurate global atmospheric reanalysis (ERA5) and the second Modern-Era Retrospective analysis for Research and Applications (MERRA-2) provide the opportunity to overcome these limitations. The performances of the zenith tropospheric delay (ZTD), zenith wet delay (ZWD), Tm, and zenith hydrostatic delay (ZHD) of ERA5 and MERRA-2 data from 2016 to 2017 were evaluated in this work using GNSS ZTD and radiosonde data over the globe. Taking GNSS ZTD as a reference, the ZTD calculated from MERRA-2 and ERA5 pressure-level data were evaluated in temporal and spatial scales, with an annual mean bias and root mean square (RMS) of 2.3 and 10.9 mm for ERA5 and 4.5 and 13.1 mm for MERRA-2, respectively. Compared to radiosonde data, the ZHD, ZWD, and Tm derived from ERA5 and MERRA-2 data were also evaluated on temporal and spatial scales, with annual mean bias values of 1.1, 1.7 mm, and 0.14 K for ERA5 and 0.5, 4.8 mm, and –0.08 K for MERRA-2, respectively. Meanwhile, the annual mean RMS was 4.5, 10.5 mm, and 1.03 K for ERA5 and 4.4, 13.6 mm, and 1.17 K for MERRA-2, respectively. Tropospheric parameters derived from MERRA-2 and ERA5, with improved temporal and spatial resolutions, can provide a reference for GNSS positioning and PWV retrieval.

An investigation into real-time GPS/GLONASS single-frequency precise point positioning and its atmospheric mitigation strategies

One of the challenges in the innovative application of global navigation satellite systems (GNSS) lies in real-time single-frequency precise point positioning (RT-SFPPP). The well-known problems associated with SFPPP are its slow convergence and lower positioning accuracy due to the effects of various errors inherited by the GNSS positioning, including the atmospheric error. In order to mitigate the two above-mentioned problems, several scenarios for the reduction of the atmospheric delays in RT-SFPPP, including the ionospheric constraint and tropospheric constraint, were investigated in this research. The performance of the RT-SFPPP utilizing the above-mentioned methods was evaluated using one-week observations from multi-GNSS experiment stations in a simulated kinematic mode. Results showed that the convergence time of the RT-SFPPP was significantly shortened when the slant ionospheric delays derived from the real-time ionospheric products provided by Centre National d’Études Spatiales were applied as the pseudo-observations. Results also showed that the convergence time of GPS + GLONASS RT-SFPPP can be reduced by modeling the frequency-dependent part of the GLONASS receiver uncalibrated code delay as a quadratic polynomial function of GLONASS frequency number. The a priori zenith wet delays (ZWDs) derived from forecast Vienna Mapping Functions 3 (VMF3_FC) were compared to the reference ZWDs from globally distributed radiosonde stations. The mean root mean square error of the a priori ZWDs resulting from VMF3_FC at 381 radiosonde stations in 2020 was 1.53 cm compared to the radiosonde-based ZWDs. When the ZWDs derived from VMF3_FC were used as pseudo-observations in the position estimation system, the convergence time for the vertical positioning reaching a 0.3 m accuracy was considerably shortened.

GPS-BDS-Galileo double-differenced stochastic model refinement based on least-squares variance component estimation

AbstractStochastic models are essential for precise navigation and positioning of the global navigation satellite system (GNSS). A stochastic model can influence the resolution of ambiguity, which is a key step in GNSS positioning. Most of the existing multi-GNSS stochastic models are based on the GPS empirical model, while differences in the precision of observations among different systems are not considered. In this paper, three refined stochastic models, namely the variance components between systems (RSM1), the variances of different types of observations (RSM2) and the variances of observations for each satellite (RSM3) are proposed based on the least-squares variance component estimation (LS-VCE). Zero-baseline and short-baseline GNSS experimental data were used to verify the proposed three refined stochastic models. The results show that, compared with the traditional elevation-dependent model (EDM), though the proposed models do not significantly improve the ambiguity resolution success rate, the positioning precision of the three proposed models has been improved. RSM3, which is more realistic for the data itself, performs the best, and the precision at elevation mask angles 20°, 30°, 40°, 50° can be improved by 4⋅6%, 7⋅6%, 13⋅2%, 73⋅0% for L1-B1-E1 and 1⋅1%, 4⋅8%, 16⋅3%, 64⋅5% for L2-B2-E5a, respectively.

A Regional Model for Predicting Tropospheric Delay and Weighted Mean Temperature in China Based on GRAPES_MESO Forecasting Products

Accurate tropospheric delay (TD) and weighted mean temperature (Tm) are important for Global Navigation Satellite System (GNSS) positioning and GNSS meteorology. For this purpose, plenty of empirical models have been built to provide estimates of TD and Tm. However, these models cannot resolve TD and Tm variations at synoptic timescales since they only model the average annual, semi-annual, and/or daily variations. As a result, the existed empirical models cannot perform well under extreme weather conditions. To address this limitation, we propose to estimate Zenith Hydrostatic Delay (ZHD), Zenith Wet Delay (ZWD), and Tm directly from the stratified numerical weather forecasting products of the mesoscale version of the Global/Regional Assimilation and PrEdiction System (GRAPES_MESO) of China. The GRAPES_MESO forecasting data has a temporal resolution of 3 h, which provides the opportunity to resolve the synoptic variation. However, it is found that the estimated ZWD and Tm exhibit apparent systematic deviation from in situ observation-based estimates, which is due to the inherent biases in the GRAPES_MESO data. To solve this problem, we propose to correct these biases using a linear model and a spherical cap harmonic model. The estimates after correction are termed as the “CTropGrid” products. When validated by the radiosonde data, the CTropGrid product has biases of 1.5 mm, −0.7 mm, and −0.1 K, and Root Mean Square (RMS) error of 8.9 mm, 20.2 mm, and 1.5 K for ZHD, ZWD, and Tm. Compared to the widely used GPT2w model, the CTropGrid products have improved the accuracies of ZHD, ZWD, and Tm by 11.9%, 55.6%, and 60.5% in terms of RMS. When validating the Zenith Tropospheric Delay (ZTD) products (the sum of ZHD and ZWD) using the IGS ZTD data, the CTropGrid ZTD has a bias of −0.7 mm and an RMS of 35.8 mm, which is 22.7% better than the GPT2w model in terms of RMS. Besides the accuracy improvements, the CTropGrid products well model the synoptic-scale variations of ZHD, ZWD, and Tm. Compared to the existing empirical models that only capture the tidal (seasonal and/or diurnal) variations, the CTropGrid products capture well the non-tidal variations of ZHD, ZWD, and Tm, which enhances the tropospheric delay corrections and GNSS water vapor monitoring at synoptic timescales. Therefore, the CTropGrid product is an important progress in GNSS positioning and GNSS meteorology.

Analysis of the Impact of Multipath on Galileo System Measurements

Multipath is one of the major source of errors in precise Global Navigation Satellite System positioning. With the emergence of new navigation systems, such as Galileo, upgraded signals are progressively being used and are expected to provide greater resistance to the effects of multipath compared to legacy Global Positioning System (GPS) signals. The high quality of Galileo observations along with recent development of the Galileo space segment can therefore offer significant advantages to Galileo users in terms of the accuracy and reliability of positioning. The aim of this paper is to verify this hypothesis. The multipath impact was determined both for code and phase measurements as well as for positioning results. The code multipath error was determined using the Code-Minus-Carrier combination. The influence of multipath on phase observations and positioning error was determined using measurements on a very short baseline. In addition, the multipath was classified into two different types: specular and diffuse, using wavelet transform. The results confirm that the Galileo code observations are more resistant to the multipath effect than GPS observations. Among all of the observations examined, the lowest values of code multipath errors were recorded for the Galileo E5 signal. However, no advantage of Galileo over GPS was observed for phase observations and for the analysis of positioning results.

Inverting COSMIC-2 Phase Data to Bending Angle and Refractivity Profiles Using the Full Spectrum Inversion Method

The radio occultation technique provides stable atmospheric measurements that can work as a benchmark for calibrating and validating satellite-sounding data. Launched on 25 June 2019, the Constellation Observing System for Meteorology, Ionosphere, and Climate 2 and Formosa Satellite Mission 7 (COSMIC-2/FORMOSAT-7) are expected to produce about 5000 high-quality RO observations daily over the tropics and subtropics. COSMIC-2 constellation consists of 6 Low Earth Orbit (LEO) satellites in 24° inclination orbits at 720 km altitude and distributed mainly between 45°N to 45°S. The COSMIC-2 observations have uniform temporal coverage between 30°N to 30°S. This paper presents an independent inversion algorithm to invert COSMIC-2 geometry and phase data to bending angle and refractivity. We also investigate the quality of Global Navigation Satellite System (GNSS) and LEO position vectors derived from the UCAR COSMIC Data Analysis and Archive Center (CDAAC). The GNSS and LEO position vectors are stable with LEO position variations < 1.4 mm/s. The signal-to-noise ratio (SNR) on the L1 band ranges from 300–2600 v/v with a mean of 1600 v/v. The inversion algorithm developed at NOAA Center for Satellite Applications and Research (STAR) uses the Full Spectrum Inversion (FSI) method to invert COSMIC-2 geometry and phase data to bending angle and refractivity profiles. The STAR COSMIC-2 bending angle and refractivity profiles are compared with in situ radiosonde, the current COSMIC-2 products derived from CDAAC, and the collocated European Center for Medium-Range Weather Forecasts (ECMWF) climate reanalysis data ERA5. The mean bias at 8–40 km altitude among the UCAR, ERA5, and STAR is <0.1% for both bending and refractivity, with a standard deviation in the range of 1.4–2.3 and 0.9–1.1% for bending angles refractivity, respectively. In the lowest 2 km, the RO bias relative to ERA-5 shows a strong latitudinal and SNR dependence.

Developing an Error Map for Cognitive Navigation System

Global Navigation Satellite System (GNSS) positioning is a widely used and a key intelligent transportation system (ITS) technology. An automotive navigation system is necessary when driving to an unfamiliar location. One difficulty regarding GNSS positioning occurs when an error is caused by various factors, which reduces the positioning accuracy and impacts the performance of applications such as navigation systems. However, there is no way for users to be aware of the magnitude of the error. In this paper, we propose a cognitive navigation system that uses an error map to provide users with information about the magnitude of errors to better understand the positioning accuracy. This technology can allow us to develop a new navigation system that offers a more user-friendly interface. We propose that the method will develop an error map by using two low-cost GNSS receivers to provide information about the magnitude of errors. We also recommend some applications that will work with the error map.

A global grid model for the correction of the vertical zenith total delay based on a sliding window algorithm

Reanalysis products have been applied to calculate the tropospheric delay for Global Navigation Satellite System (GNSS) positioning purposes widely. It is necessary to obtain high-precision tropospheric delay information from GNSS users with a high-precision tropospheric vertical stratification model because the height of the grids of the atmospheric reanalysis data is inconsistent with that of GNSS users, especially in regions with high terrains. In addition, the variation of the tropospheric delay in the vertical direction is much higher than that in the horizontal direction. The zenith total delay (ZTD) vertical stratification model is also key to the development of real-time and high-precision ZTD models. A new approach, the sliding window algorithm, is proposed to develop a ZTD vertical stratification model. In this work, a ZTD vertical stratification model considering spatiotemporal factors is developed based on the second Modern-Era Retrospective analysis for Research and Applications (MERRA-2) data, which is named the GZTD-H model. Radiosonde and International GNSS Service (IGS) data are treated as reference values to evaluate the performance of the GZTD-H model, which is compared to the model GPT2w. The results show that the GZTD-H model realizes the highest performance in ZTD layered vertical interpolation against ZTD layered profiles obtained at radiosonde sites, which achieves an improvement of 10% over the model GPT2w. Compared to model GPT2w, the GZTD-H model attains a spatial interpolation improvement of 8% for the Global Geodetic Observing System (GGOS) Atmosphere gridded ZTD over the surface ZTD calculated from radiosonde profiles. Furthermore, compared to model GPT2w, the model GZTD-H also attains improvements of 11% over the precise ZTD products acquired at IGS sites. In terms of model parameters, the GZTD-H model is greatly reduced and optimized over model GPT2w. Hence, the applicability of this model is enhanced in terms of GNSS atmospheric sounding and precise GNSS positioning.

Optical clock technologies for global navigation satellite systems

Future generations of global navigation satellite systems (GNSSs) can benefit from optical technologies. Especially optical clocks could back-up or replace the currently used microwave clocks, having the potential to improve GNSS position determination enabled by their lower frequency instabilities. Furthermore, optical clock technologies—in combination with optical inter-satellite links—enable new GNSS architectures, e.g., by synchronization of distant optical frequency references within the constellation using time and frequency transfer techniques. Optical frequency references based on Doppler-free spectroscopy of molecular iodine are seen as a promising candidate for a future GNSS optical clock. Compact and ruggedized setups have been developed, showing frequency instabilities at the 10–15 level for averaging times between 1 s and 10,000 s. We introduce optical clock technologies for applications in future GNSS and present the current status of our developments of iodine-based optical frequency references.

Enhanced fault detection and exclusion based on Kalman filter with colored measurement noise and application to RTK

With the development of high-precision safety–critical applications using global navigation satellite systems (GNSS), fault detection and exclusion (FDE) is indispensable to guaranteeing the integrity of a GNSS positioning and navigation system. Many FDE algorithms have been developed based on the standard Kalman filter (KF), assuming that GNSS measurements come with Gaussian uncorrelated white noise. The existence of colored noise in GNSS measurements, which is typical for positioning with low-cost receivers and in challenging environments will, however, degrade the performance of KF-based FDE algorithms. We proposed an FDE scheme based on improved KF considering colored noise (CKF) as a first-order autoregressive model to improve the FDE performance. The performance of the proposed CKF-based FDE algorithm was evaluated with an application to real-time kinematic positioning using a low-cost receiver. A CKF-based fault detection test, a fault identification test, a minimum detectable bias (MDB), error distribution, and positioning results were examined. The results showed that the CKF-based FDE can obtain realistic statistical information to improve integrity monitoring reliability. The fault detection test achieved a 17.83% improvement in FDE performance and a reduction in the false alarm rate, from 23.33 to 5.50%, compared with KF-based FDE. The tests also indicated that the CKF-based FDE can detect multiple faults with zero-miss detection. The fault identification test had an average improvement of 32.14%, and a more realistic MDB was obtained. The results of this study contribute to making objective decisions for the integrity monitoring of practical, precise GNSS positioning.

Smartphone-based GNSS Method for Covid-19 Information on Android (Case Study: Surabaya City)

Coronavirus disease 2019 (Covid-19) is the respiration diasease that can be transmitted from individual to another. There have been 3906 ODP (individual on monitoring) cases, 3303 PDP (patient under surveillance) cases, 2918 confirmed cases, 766 recovered patients, and 282 deaths in Surabaya, as recorded on June 6th, 2020. GIS (Geographical information system) is a science based on computer software, to provide digital form information and the earth’s geographic surface analysis. GNSS (global navigation satellite system) is the positioning system method using satellite, which can be used by a lot of people at the same time and designed to obtain three-dimension position. The combination of Smartphone’s GNSS positioning and the spatial data of Covid-19 distribution in Surabaya is expected to be able to give useful information about health condition toward citizen, especially about Covid-19 pandemic via application based. The outcome is a color-level based distribution of Covid-19 cases which can be accessed android smartphone. Sub district with the highest rate of Covid-19 cases does not necessarily have proper health protocol facilities, and so does other sub districts with high rates of Covid-19 cases. In fact, none of Covid-19 referral hospital located in the sub district with high rate of Covid-19 cases. Based on the results of the questionnaire, the applications namely “Cegah Covid-19 Surabaya” has received good responses. This application is currently able to run on Android smartphones with the versions of Android 10, Pie, Oreo, Nougat, Marshmallow, and Lollipop.

Artificial neural network for predicting global sub-daily tropospheric wet delay

Zenith Wet Delay (ZWD) represents an important parameter in the Global Navigation Satellite Systems (GNSS) positioning, meteorology, and weather forecasting as it assembled to the Integrated Water Vapour (IWV) that is important for weather prediction. It is difficult to be predicted due to its temporal and spatial resolution. With the increasing development in machine learning, Artificial Neural Network (ANN) started to be used for predicting different nonlinear problems. In this paper, ANN is used for predicting ZWD from previous epoch of temperature, pressure, and Water Vapour Pressure (WVP) using twelve years (2008–2019) of data from 505 globally distributed stations. Four scenarios were followed in this study, using previous epochs from 6, 12, 18 and 24 h lags, as input for ANN. The results showed that ZWD can be predicted using ANN for all the stations using the 6-h lag scenario at the published required level of accuracy, 3.0 cm Root Mean Square Error (RMSE) and 60.2% of them have RMSE lower than 1.5 cm with 97.6% of them have the correlation coefficient (R) values ≥ 0.9. Although the accuracy of the remaining three scenarios was found to be, as expected, lower than the first scenario, their predicted ZWD showed promising R-values ≥ 0.9 to be 78.6%, 64.1% and 58.2% of the stations, for the three remaining scenarios respectively. While 68.5%, 68.9% and 65.7% of the stations were below 3.0 cm RMSE. The conclusion is that, the ANN with the suggested strategy can produce a reliable ZWD. The finding of this paper could help to improve the predicted ZWD for GNSS positioning and meteorology as well as weather forecasting.