Multi-frequency GNSS Research Articles

GNSS Reflectometry-Based Ocean Altimetry: State of the Art and Future Trends

For the past 20 years, Global Navigation Satellite System reflectometry (GNSS-R) technology has successfully shown its potential for remote sensing of the Earth’s surface, including ocean and land surfaces. It is a multistatic radar that uses the GNSS signals reflected from the Earth’s surface to extract land and ocean characteristics. Because of its numerous advantages such as low cost, multiple signal sources, and all-day/weather and high-spatiotemporal-resolution observations, this new technology has attracted the attention of many researchers. One of its most promising applications is GNSS-R ocean altimetry, which can complement existing techniques such as tide gauging and radar satellite altimetry. Since this technology for ocean altimetry was first proposed in 1993, increasing progress has been made including diverse methods for processing reflected signals (such as GNSS interferometric reflectometry, conventional GNSS-R, and interferometric GNSS-R), different instruments (such as an RHCP antenna with one geodetic receiver, a linearly polarized antenna, and a system of simultaneously used RHCP and LHCP antennas with a dedicated receiver), and different platform applications (such as ground-based, air-borne, or space-borne). The development of multi-mode and multi-frequency GNSS, especially for constructing the Chinese BeiDou Global Navigation Satellite System (BDS-3), has enabled more free signals to be used to further promote GNSS-R applications. The GNSS has evolved from its initial use of GPS L1 and L2 signals to include other GNSS bands and multi-GNSS signals. Using more advanced, multi-frequency, and multi-mode signals will bring new opportunities to develop GNSS-R technology. In this paper, studies of GNSS-R altimetry are reviewed from four perspectives: (1) classifications according to different data processing methods, (2) different platforms, (3) development of different receivers, and (4) our work. We overview the current status of GNSS-R altimetry and describe its fundamental principles, experiments, recent applications to ocean altimetry, and future directions.

THE APPLICABILITY OF LOW-COST MULTI-FREQUENCY MULTI-GNSS RECEIVERS FOR GEODETIC CONTROL SURVEYING

Abstract. In geodetic surveys, survey-grade receivers are conventionally used due to their accuracy. However, expensive survey-grade receivers deter users from performing geodetic surveys utilizing the technology. Considerably, multi-system and multi-frequency low-cost GNSS receivers are available today, which can already provide good positioning accuracy output. This paper evaluates the performance of low-cost GNSS receivers in single-point positioning, relative positioning, and network solutions compared to survey-grade GNSS receivers. The study used a survey-grade antenna to test the u-blox C099-F9P evaluation kit equipped with the ZED-F9P module, a low-cost GNSS receiver. Simultaneously, the survey-grade GNSS receiver utilizes the same antenna using a GPS splitter to ensure simultaneous observation. Based on the results, the low-cost GNSS receiver is comparable to the survey-grade GNSS receiver for single and relative positioning. For single-point positioning, the low-cost GNSS receiver achieved 1- and 1.5-meter accuracy in horizontal and vertical components at a 95% confidence level, respectively. In relative positioning, it achieved an accuracy of 1 millimeter on average at a 95% confidence level. The network solution utilizes four (4) Active Geodetic Stations of the National Mapping and Resource Information Authority within the National Capital Region, used as reference stations. The low-cost GNSS receiver achieved an average accuracy of 8 millimeters. In summary, the ublox C099-F9P low-cost GNSS receiver achieved better than 1:100,000 or first-order survey accuracy stipulated in DAO 2007-29 surveying standards. Results show that the u-blox C099-F9P is possible for geodetic and other land surveying applications, even for high-accuracy requirements surveys.

An investigation of PPP degradations over Asia-Pacific region during Tonga volcanic eruption on 15 January 2022

On 15 January 2022, a significant volcanic eruption occurred at Hunga Tonga-Hunga Ha’apai (HTHH), causing global ionospheric disturbances. To investigate ionospheric anomalies and the kinematic GNSS PPP responses to this volcanic eruption over the Asia-Pacific region, the rate of the total electron content index (ROTI) map derived from about 1100 GNSS stations data and ionospheric scintillation indices S4 and σφ are used. We first selected data from six stations for kinematic PPP experiments. Multi-constellation and multi-frequency Precision Positioning (GAMP) software and GNSS analysis software are employed in the process. We then found that the positioning errors of three directions (east, north, up) during disturbance time are larger than those on an ionospheric quiet day (3 January 2022). To explore the reasons for PPP degradation, we conduct a quality analysis of GNSS data on these two days, including carrier-to-noise power-density ratio (C/N0) and the number of cycle slips. The number of satellites affected by cycle slips increased obviously in the disturbance time. The statistics of cycle slip occurrence rate at low latitudes is 12.35 % while that on ionospheric quiet day is only 6.05 %. The strategy of expanding the cycle slip detection thresholds from 0.15 m to 1.5 m for phase geometry free (PGF) combination and 5 cycles to 12 cycles for Hatch–Melbourne-Wübbena (HMW) combination failed to significantly improve the PPP solutions based on data from 357 stations. It was found that only increasing the detection thresholds could not mitigate the PPP degradations. Our investigations contribute to the study of space weather and kinematic GNSS PPP responses to volcanic eruptions.

Analysis of Multifrequency GNSS Signals and an Improved Single-Epoch RTK Method for Medium-Long Baseline

In recent years, the quantity of visible satellites has increased significantly due to multiple satellite systems that leaped forward. The BeiDou Navigation Satellite System (BDS) and Galileo satellite navigation system (Galileo) broadcast triple-frequency signals and above to users, thus enhancing the reliability, continuity, and availability of the single-epoch real-time kinematic (RTK) positioning. In this study, an improved single-epoch multifrequency multisystem RTK method is successfully developed for the medium-long baseline. First, the Galileo and BDS extra-wide-lane (EWL) ambiguities are fixed at a high success rate, and the Galileo and BDS wide-lane (WL) ambiguity is achieved via the transformation process. Second, the fixed WL ambiguities of Galileo and BDS are exploited to elevate the fixed rate of GPS WL ambiguity. Third, the parametric strategies for ionospheric delay are carried out to upregulate the narrow-lane (NL) ambiguity-fixed rate of GPS. Further, the real-time data are adopted for verifying the feasibility of the method developed in this study. The experimental results demonstrate the optimal carrier-to-noise density ratio (C/N0) of full operational capability (FOC) E5a/E5b at all frequencies, followed by IIR-M L1, and IIR-A/B L2 exhibits the worst performance. Generally, the multipath combination (MPC) of Galileo signals shows root mean square (RMS) values within 0.4 m, ordered as follows: E 1 > E 5 b > E 5 a . For the BDS-2, the B3 signal exhibits optimal performance, while the B1 signal is the worst. The RMS of MPC errors of L1 signals is smaller than the L2 signals for the GPS. Furthermore, under the 50 km baseline, the GPS NL ambiguity-fixed rate using the ionosphere-free (IF) combination reaches only 47.74% at the ratio threshold of 2. Finally, compared to the ionosphere-free combination method, the GPS NL ambiguity-fixed rate is increased by 45.52% with the presented method. The proposed approach broadens the future application of deformation monitoring in medium-long baseline scenarios.

Design and Implementation of a Prototype Seismogeodetic System for Tectonic Monitoring.

This manuscript describes the design, development, and implementation of a prototype system based on seismogeodetic techniques, consisting of a low-cost MEMS seismometer/accelerometer, a biaxial inclinometer, a multi-frequency GNSS receiver, and a meteorological sensor, installed at the Doñana Biological Station (Huelva, Spain) that transmits multiparameter data in real and/or deferred time to the control center at the University of Cadiz. The main objective of this system is to know, detect, and monitor the tectonic activity in the Gulf of Cadiz region and adjacent areas in which important seismic events occur produced by the interaction of the Eurasian and African plates, in addition to the ability to integrate into a regional early warning system (EWS) to minimize the consequences of dangerous geological phenomena.

LOW-COST MULTI-FREQUENCY GNSS RECEIVERS: PERFORMANCE EVALUATION FOR POSITIONING AND NAVIGATION

Abstract. In recent years, the possibility of using interoperable global constellations, the growing number of Continuously Operating Reference Stations (CORS) and the technological progress of instrumentation, computing algorithms and GNSS products are significantly marking the evolution of the various satellite survey techniques and the diffusion of mass-market technologies contributing to innovation transfers in different sectors including smart cities, smart mobility, connected automated driving, precision farming and others (Egea-Roca et al., 2022).Currently, the study of low-cost GNSS systems for navigation and precision positioning especially utilised in monitoring applications is the focus of numerous research activities (Joubert et al., 2020; Raza et al., 2022; Bellone et al., 2016; Hamza et al., 2020).The aim of this work is to test the performance of some of the latest generation multi-constellation and multi-frequency GNSS medium and low-cost sensors, evaluating their possible application in the mentioned fields. Differential and undifferential techniques were compared (Dardanelli et al., 2021; Ocalan et al.,2016); Precise Point Positioning (PPP) has become a valid alternative to differential methods allowing to obtain comparable accuracy offering greater flexibility (Lin, 2021). The multi-constellation permanent stations network GPS-Umbria was utilised for differential mode tests (Radicioni and Stoppini, 2019).The tests were carried out in different modes (static and kinematic) and operating conditions; various intermediate and low-cost sensors were employed, while the data of a high precision geodetic receiver were used as reference for the comparison of the different solutions.

Ionosphere Total Electron Content Modeling and Multi-Type Differential Code Bias Estimation Using Multi-Mode and Multi-Frequency Global Navigation Satellite System Observations

With the rapid development of multi-mode and multi-frequency GNSSs (including GPS, GLONASS, BDS, Galileo, and QZSS), more observations for research on ionosphere can be provided. The Global Ionospheric Map (GIM) products are generated based on the observation of multi-mode and multi-frequency GNSSs, and comparisons with other GIMs provided by the ionosphere analysis centers are provided in this paper. Taking the CODE (Center of Orbit Determination in Europe) GIM as a reference during 30 days in January 2019, for the GIMs from JPL (Jet Puls Laboratory), UPC (Technical University of Catalonia), ESA (European Space Agency), WHU (Wuhan University), CAS (Chinese Academy of Sciences), and MMG (The multi-mode and multi-frequency GNSS observations used in this paper), the mean bias with respect to CODE products is 1.87, 1.30, −0.10, 0.01, −0.02, and −0.71 TECu, and the RMS is 2.12, 2.00, 1.33, 0.88, 0.88, and 1.30 TECu, respectively. The estimated multi-type DCB is also in good agreement with the DCB products provided by the MGEX.

On estimating the phase scintillation index using TEC provided by ISM and IGS professional GNSS receivers and machine learning

Amplitude and phase scintillation indexes (S4 and σϕ) provided by Ionospheric Scintillation Monitoring (ISM) receivers are the most used GNSS-based indicators of the signal fluctuations induced by the presence of ionospheric irregularities. These indexes are available only from ISM receivers which are not as abundant as other types of professional GNSS receivers, resulting in limited geographic distribution. This makes the scintillation indexes measurements rare and sparse compared to other types of ionospheric measurements available from GNSS receivers. Total Electron Content (TEC), on the other hand, is an ionospheric parameter available from a wide range of multi-frequency GNSS receivers. Many efforts have worked on establishing scintillation indicators based on TEC, and geodetic receivers in general, introducing various metrics, including the Rate of TEC change (ROT) and ROT Index (ROTI). However, a possible relationship between TEC and its variation, and the corresponding scintillation index that an Ionospheric Scintillation Monitor (ISM) receiver would estimate is not trivial. In principle, TEC can be retrieved from carrier phase measurements of the GNSS receiver, as σϕ. We investigate how to estimate σϕ from time series of TEC and ROT measurements from an ISM in Ny-Ålesund (Svalbard) using Machine Learning (ML). To evaluate its usability to estimate σϕ from geodetic receivers, the model is tested using TEC data provided by a quasi-co-located geodetic receiver belonging to the International GNSS Service (IGS) network. It is shown that the model performance when TEC from the IGS receiver is used gives comparable results to the model performance when TEC from the ISM receiver is utilised. The model's ability to infer the exact value of the scintillation index is bound to Mean Square Error (MSE) = 0.1 radians2 when σϕ≤0.8 radians. For σϕ>0.8 the MSE reaches 0.18 and 0.45 radians2 in operative testing using ISM and IGS measurements, respectively. However, the model’s ability to detect phase scintillation from IGS TEC measurements is comparable to expert visual inspection. Such a model has potential in alerting against phase fluctuations resulting in enhanced σϕ, especially in locations where ISM receivers are not available, but other types of dual-frequency GNSS receivers are present.

ACCURACY ASSESSMENT OF PRECISE POINT POSITIONING WITH MULTI-CONSTELLATION GNSS DATA UNDER STRONG SOLAR BURST EFECTS

Solar variations modify a layer of the Earth’s upper atmosphere known as the ionosphere. This is of particular concern for the aviation sector because of the way its communications and navigation systems can be affected. At the same time, one of the most complex atmospheric effects is the response of ionospheric regions to geomagnetic storms. The ionospheric response during the same storm can vary in time in different locations, which can introduce significant errors/displacement (meters) in single-frequency relative GNSS positioning (DGNSS technology). The residual effect can be somewhat mitigated by using dual- or multi-frequency GNSS, but dual frequency is not a guarantee against degradation of relative observations results, especially during significant geomagnetic storms. In this regard, PPP absolute positioning technology can be effective. However, another atmospheric effect – ionospheric scintillation can have a significant impact on the accuracy of both GNSS positioning approaches. The main goal of this study was to analyze the effect of second-order ionospheric delay during geomagnetic storms and ionospheric scintillations on GNSS positioning using the PPP method. GNSS data corrected and uncorrected for higher-order ionospheric delay, respectively, were processed by the static PPP-AR method using the PRIDE-PPPAR ver.2.2.6 software for the selected periods of geomagnetic storms. From the analysis of the influence of second-order ionospheric errors, it follows that their values can reach almost 4 cm for first-frequency signals under different states of ionospheric disturbances for the GPS constellation and almost an order of magnitude less for the GNSS quadroconstellation. The appearance of stronger geomagnetic storms increases the second-order ionospheric errors by several millimeters.

Two modified multi-frequency GNSS approaches to estimate the pseudorange observable-specific signal bias for the CDMA and FDMA models

Two modified multi-frequency GNSS approaches to estimate the pseudorange observable-specific signal bias for the CDMA and FDMA models

Doprinos određivanju jonosferskog kašnjenja GNSS satelitskih signala na teritoriji Republike Srbije

Multi-frequency GNSS satellite signals and their availability enable research in undifferentiated and uncombined models in which a single signal at each frequency is a corresponding independent observation. Such possibilities are reflected by the significant interest in geodetic research as well as in many areas of application of GNSS observation. On the geometric path of the signal between the satellite and the receiver, a significant source of GNSS measurement errors comes from the medium of propagation of electromagnetic waves. Errors attributed to signal propagation are ionospheric and tropospheric signal delay. The mentioned error sources significantly affect the quality of certain pseudorange and, thus, the quality of the receiver's position in the form of three-dimensional coordinates. This paper presents the analysis and determination of the ionospheric delay of GNSS satellite signals based on the determination of Total Electron Content - TEC at five stations (Beograd, Leskovac, Sombor, Zaječar, and Kraljevo) in the territory of the Republic of Serbia. In order to determine TEC values, the software called "GPS-TEC analysis" developed within the Institute for Scientific Research, Boston College, USA was used, which enables the determination of the TEC value on the path between the satellite and the receiver. The data collection was carried out within the year 2022 so that the measurement sessions include characteristic dates when the most significant fluctuations are expected in the context of seasonal variations.

Single-Epoch Ambiguity Resolution of a Large-Scale CORS Network with Multi-Frequency and Multi-Constellation GNSS

Ambiguity resolution at Continuously Operating Reference Station (CORS) network sites is the key step in the whole processing chain of Network Real Time Kinematic (NRTK). An appropriate ambiguity-resolution speed is important, and single-epoch ambiguity resolution has not been realized yet, especially for large-scale CORS. We attempt to realize single-epoch ambiguity resolution for a large-scale CORS network by neglecting tropospheric delay through forming difference between satellites with close mapping functions whether they belong to the same or different GNSSs. As only two frequency bands are shared among GPS, Galileo and BeiDou, the biggest challenge is how to get this single-epoch ambiguity solution for wide-lane combinations of L1 and L5 when the difference is formed between satellites of different GNSSs. The proposed method includes five steps for ambiguity resolution for different combinations: extra wide-lane, wide-lane, inter-GNSS wide-lane, subset narrow-lane and narrow-lane. The single-epoch ambiguity-resolution performance is assessed based on GNSS observations from two long-distance baselines formed with IGS stations, BRUX-REDU and BAUT-LEIJ, separated by distances of approximately 104 km and 151 km, respectively. The numerical results show that the fixing rate of the single-epoch ambiguity resolution can reach more than 90%, so for a large-scale CORS network, single-epoch ambiguity resolution is feasible and can be realized in the future.

OPTIMAL LINEAR COMBINATIONS SELECTION BASED ON FUZZY CLUSTERING ANALYSIS FOR MULTI-FREQUENCY GNSS

Abstract. Currently, satellite navigation and positioning systems, such as BDS, GPS, and Galileo, can broadcast 3 or more navigation signals. In theory, multi-frequency signals can form more high-quality carrier-phase linear combinations, which is conducive to improving the performance of multi-frequency carrier ambiguity resolution (MCAR). In this paper, focusing on the selection of the optimal combinations in the multi-frequency GNSS carrier phase ambiguity resolution, according to the long wavelength of the combinations, the influence of weak ionospheric delay, and low noise, the fuzzy clustering analysis method is used to realize objective selection of multi-frequency optimal linear combinations (e.g., GPS, BDS-2, BDS-3, Galileo) and introduced the total noise level (TNL) for the analysis of the combinations characteristics under different baseline length scenarios. In order to verify the ambiguity resolution performance of the extra-wide lane combinations selected by the fuzzy clustering analysis method, the GF_MCAR model was used to solve the BDS-2, BDS-3 triple-frequency combination ambiguities and the BDS-3 five-frequency combination ambiguities of the baseline JNFG and WUH2. The results manifest that the number of high-quality linear combinations of multi-frequency GNSS increases sharply with the increase of the frequencies number, which is conducive to the formation of combinations with a lower total noise level, and the experiments show that the difference between adjacent epochs of the combination ambiguities of the extra-wide lane obtained by GF_MCAR is basically less than ±0.5 cycles, and the single epoch rounding can be used to directly fix the ambiguity of the extra-wide lane.

Multi-GNSS Fast Precise Point Positioning with Multi-Frequency Uncombined Model and Cascading Ambiguity Resolution

Conventional ambiguity resolution (AR) strategy of directly fixing all raw frequency ambiguities for uncombined precise point positioning (PPP) generally requires a long initial time to ensure fixing reliability. The rich signals from multi-frequency GNSS can provide new opportunities for rapid PPP AR. In this paper, based on a unified multi-frequency uncombined PPP model, the raw frequency ambiguities are linearly transformed to the between-satellite-single-differenced extra-wide-lane (EWL), wide-lane (WL), and narrow-lane (NL) ambiguities, and a cascading ambiguity resolution (CAR) method of fixing EWL/WL/NL ambiguities sequentially is proposed. Meanwhile, a partial ambiguity fixing (PAF) strategy with ambiguity subset adaptively selected based on the successively increased elevations is also adopted in each step to improve the fixing rate. Further, experiments with globally distributed stations are carried out to verify the algorithm. With the constraints of EWL/WL AR, the precision of NL ambiguity and its variance-covariance matrix can be effectively optimized, so the time to first fix (TTFF) is significantly shortened, and the ratio value is also improved to varying degrees. As for BDS-only solution, the average TTFF is shortened from 23.7 min to 10.9 min, with an improvement over 50%; for GPS/BDS, GPS/Galileo, and GPS/Galileo/BDS combined solutions, the TTFF is shortened from 14.3 min, 9.4 min, and 6.7 min to 8.1 min, 2.6 min, and 1.8 min, which are, respectively, shortened by 43.4%, 72.3%, and 73.1%. In general, the proposed CAR strategy can shorten the TTFF of multi-GNSS multi-frequency PPP to about 2 min. The performance of EWL/WL/NL ambiguity-fixed solutions is also analyzed. The NL solution is generally at centimeter-level accuracy over the entire period; however, limited by the atmosphere errors during the convergence stage, the EWL/WL solutions can only obtain decimeter-level accuracy, and the difference between them and NL solution gradually decreases with the continuous improvement of atmosphere accuracy.

CASPA-ADM: a mission concept for observing thermospheric mass density

Cold Atom technology has undergone rapid development in recent years and has been demonstrated in space in the form of cold atom scientific experiments and technology demonstrators, but has so far not been used as the fundamental sensor technology in a science mission. The European Space Agency therefore funded a 7-month project to define the CASPA-ADM mission concept, which serves to demonstrate cold-atom interferometer (CAI) accelerometer technology in space. To make the mission concept useful beyond the technology demonstration, it aims at providing observations of thermosphere mass density in the altitude region of 300–400 km, which is presently not well covered with observations by other missions. The goal for the accuracy of the thermosphere density observations is 1% of the signal, which will enable the study of gas–surface interactions as well as the observation of atmospheric waves. To reach this accuracy, the CAI accelerometer is complemented with a neutral mass spectrometer, ram wind sensor, and a star sensor. The neutral mass spectrometer data is considered valuable on its own since the last measurements of atmospheric composition and temperature in the targeted altitude range date back to 1980s. A multi-frequency GNSS receiver provides not only precise positions, but also thermosphere density observations with a lower resolution along the orbit, which can be used to validate the CAI accelerometer measurements. In this paper, we provide an overview of the mission concept and its objectives, the orbit selection, and derive first requirements for the scientific payload.

Mapping of S4 Over the Arabian Peninsula During Solar Minimum

In this letter, we study the temporal and spatial variability of ionospheric irregularities by generating high-resolution maps of the observed amplitude scintillation index (S4) using data from a multi-constellation and multi-frequency GNSS receiver. The study is located in the Arabian Peninsula region, which falls under the northern crest of the equatorial ionization anomaly (EIA). Even though the study was conducted during a solar minimum period, considerable pre-sunset scintillation occurrences have been observed between 15-17 local time, particularly during the winter solstices. While most scintillation occurrences have been observed at low elevation (20 to 25 degrees), a considerable number of scintillation causing ionospheric irregularities have been observed towards the north, east, and southeast of the receiver location, for elevation ranging from 40 to 60 degrees. Out of all the GNSS constellations with medium-earth-orbit (MEO) satellites, GPS was the most impacted by amplitude scintillation, while BeiDou and Galileo satellites were the least affected. It is anticipated that the patches of ionospheric irregularities reported in this work will be further enhanced as solar activity increases in the coming years. Therefore, this work can serve as a reference for future studies during periods of increased geomagnetic activity.

Modeling and Performance Assessment of Precise Point Positioning with Multi-Frequency Gnss Signals

Modeling and Performance Assessment of Precise Point Positioning with Multi-Frequency Gnss Signals

Improving the Accuracy of Aerial Photography Using Ground Control Points

The authors showed that it is possible to quickly collect up-to-date information on the agricultural land condition using an unmanned aerial vehicle. It was noted that the use of ground control points increases the accuracy of project measurements, helps to compare the project post-processing results with the real measurements. (Research purpose) To compare the results of standard and high-precision post-processing of aerial survey data using ground control points. (Materials and methods) Aerial photography was carried out on a 1.1- hectare breeding field. The authors used DJI Matrice 200 v2 unmanned aerial vehicle with a GNSS L1/L2 receiver and a modified DJI X4S camera, five control points sized 50 × 50 centimeters and an EMLID Reach RS2 multi-frequency GNSS receiver. The results of scientific research into the use of ground control points during aerial photography were studied. (Results and discussion) It was found out that the error of georeferencing images obtained by an unmanned aerial vehicle without control points is significantly higher during the standard data processing compared to the high-precision one. The project error when using five control points is 3.9 times higher during the standard data processing. (Conclusions) It was shown that using ground control points it is possible to improve the project measurement accuracy, as well as compare the project post-processing results with the measurements on the ground. It was detected that the high-precision monitoring enables the use of fewer ground control points. It was found out that in order to obtain data with the accuracy of 2-4 centimeters in plan and height, at least 3 ground control points need to be used during the high-precision post-processing.

Prediction of Total Electron Content (TEC) using Neural Network over Anomaly Crest Region Bhopal

In the present work neural network has been developed for the prediction of Vertical Total Electron Content (VTEC) over Bhopal (23.2°N, 77.4°E & MLAT 14.2°N), an equatorial anomaly crest region. The study is based on the VTEC data recorded by a multi-frequency multi-constellation GNSS receiver installed at Bhopal during May 2016 to August 2017. Neural Network (NN) consists of artificial neurons that are used to learn data patterns adjusting weights between input, hidden and output layers by computational modelling. In order to obtain the optimal number of neurons in the hidden layer, the performance of four systems of neural network have been tested. Out of which, the fourth neural network has been used to predict VTEC with 7 input neurons in the present study. The number of hidden layer neurons is a factor that affects the performance of the trained networks. The input layer of the network includes the year, day of the year, hour of the day, geographic latitude, geographic longitude, SSN and IRI NmF2. We have compared the TEC obtained from the neural network prediction (NN TEC), GPS derived TEC (GPS TEC) and TEC from IRI-2016 model (IRI TEC) and analysis has been made. We observed that the Root Mean Square Error (RMSE) decreases with increase in the number of hidden layer neurons. The RMSE comes out to be lowest (1.96 TECU), when the number of hidden layer neurons are 41.The TEC predicted from the NN model and estimated from GPS receiver have same trend at 01:00 and 07:00 UT. The modelled NN TEC values are in good agreement with GPS TEC values for all seasons and 0.99 correlation coefficient was calculated for summer months, but IRI TEC always underestimates GPS TEC in all seasons. The NN model excellently predicted the TEC values of August 2017 by putting the credentials of August 2016 and only 0.55–32.16% relative errors were estimated between them whereas it reaches up to 93.86% with IRI TEC. Thus, the result shows that the proposed NN model can predict the diurnal and seasonal GPS TEC more accurate than IRI over anomaly crest region Bhopal. However, the inclusion of IRI-NmF2 as input layer neuron increases the network performance.

Characteristics of the short-term temporal variations of multi-constellation and multi-frequency GNSS receiver differential phase biases

Characteristics of the short-term temporal variations of multi-constellation and multi-frequency GNSS receiver differential phase biases