Dual-frequency GPS Research Articles

Topside Ionospheric Tomography Exclusively Based on LEO POD GPS Carrier Phases: Application to Autonomous LEO DCB Estimation

This paper presents a novel technique to estimate DCBs from GPS transmitters and receivers on-board Low Earth Orbit (LEO) satellites. The technique consists of obtaining the DCBs as residuals from the difference between the ionospheric combination of the code and the associated ionospheric delay. The ionospheric delay is computed with TOMION, a background-model-free ionospheric tomographic technique based on dual-frequency GPS carrier phase data only, and solved with a Kalman filter. Thus, DCBs are also estimated epoch-wise from the LEO Precise Orbit Determination (POD) GPS receiver as a secondary product. The results for GPS satellite DCBs, obtained exclusively from the three MetOp LEO POD GPS receivers over four consecutive weeks, are in full agreement (i.e., at the level of a few tenths of ns) with those reported independently with other techniques from hundreds of ground-based receivers exclusively, by JPL and CODE analysis centers.

Gulf of Mexico Loop-Current Signature Observed From GNSS-R Phase Altimetry Based on Spire Global CubeSat Data

Global Navigation Satellite System (GNSS) coherent ocean reflections collected at grazing-angles by Spire Global’s CubeSats are explored to retrieve Sea Level Anomalies (SLA) over the Gulf of Mexico. Dual-frequency GPS carrier phase estimations are derived from the 50-Hz I and Q samples generated onboard the low Earth orbit CubeSats. First order ionospheric phase advancement, troposphere delay, and precise orbit solutions for GPS satellites and CubeSats mitigate the range measurement errors. Comparisons between collocated specular reflection tracks from various Spire CubeSats and GPS satellites configurations demonstrate the self-consistency of the resulting SLA solutions. The Spire retrievals are then validated against conventional altimetry SLA products. There is a Root Mean Square (RMS) difference of ~ 20 cm between the Spire and the gridded model mesoscale SLAs, unless the reflected elevations are very low. To better evaluate the performance of the Spire retrievals they are examined over sharp ocean topography. About 40% of coherent reflections with elevations above 12° detected the signature of the energetic Loop-Current during the 2020-2021 period. The Spire retrievals were also compared with collocated Sentinel-3 tracks. One track with elevations above 12° demonstrated high correlation and agreement with the Sentinel-3 retrievals. The other two low-elevation tracks showed large magnitude discrepancies, but similar trends once appropriate scaling factors are applied. The study demonstrates the potential for GNSS reflectometry’s application to SLA mapping while also highlighting where significant improvements in error mitigations are needed. A particularly large error source is the troposphere error for signals with lower elevations.

A method of real-time long-baseline time transfer based on the PPP-RTK

Long-baseline time transfer can nowadays reach rather high frequency stability based on post-processed batch least-squares adjustment using the Precise Point Positioning (PPP) or Integer-PPP (IPPP) methods. For real-time PPP users, time transfer results are degraded due to the filter-based processing mode, and the degraded accuracy of the real-time satellite orbits and clocks compared to the final ones. The Real-Time Kinematic (RTK) time transfer can significantly reduce the satellite-related errors, but has limits on the baseline length similar to the RTK positioning. Also, the delivery of raw observations instead of State-Space Representation (SSR) products could result in pressure on data transfer and difficulties related to latency and prediction. In this study, the PPP-RTK technique, which combines the advantages of the PPP and the RTK methods, is tested for real-time long-baseline time transfer. As an alternative approach to the above two methods, it allows for the time transfer of long baselines, while not relying on external high-sampling and high-precision satellite clocks. By delivering the satellite clocks and satellite phase biases produced within the PPP-RTK regional network, time differences can be estimated between users and the reference network station, with which stable time transfer between users separated by long baselines can be realized. Using dual-frequency GPS and Galileo data, the PPP-RTK time transfer is tested using approximately a thousand-kilometer-scale network in Europe. The time transfer results between two hydrogen masers, i.e., those on the 884 km baseline BRUX-ONSA and the 920 km baseline WTZR-ONSA, are computed. At an averaging time of 105 s, Modified Allan Deviation (MDEV) at the level of sub-10-15 to 10-15 can be reached when processing the user coordinates in the station fixed, static, or kinematic modes. The median clock residuals can converge to 1 ns and 0.3 ns within 2 min and 15 min, respectively, in the kinematic mode, while in the static and fixed modes the convergence times are shorter. With the augmentation of 150 Low Earth Orbit (LEO) satellites having simulated observations, the clock residuals can converge to 1 ns and 0.3 ns within 30 s and 3.5 min, respectively, for all the three estimation modes.

Two-epoch centimeter-level PPP-RTK without external atmospheric corrections using best integer-equivariant estimation

Ambiguity resolution enabled precise point positioning (PPP-AR or PPP-RTK) without atmospheric corrections requires the user to estimate tropospheric and ionospheric delay parameters. The presence of the unconstrained ionosphere parameters impedes fast and reliable ambiguity resolution, so a time-to-first-fix of around 30 min for GPS-only solutions is generally reported, which can, to some extent, be reduced when combining multiple GNSS. In this contribution, we investigate the capabilities of almost instantaneous PPP-RTK, using only a few observation epochs at a sampling interval of 30 s, with the ionosphere-float model. The considered key elements are (a) the MSE-optimal best integer-equivariant estimator, (b) a combination of dual-frequency GPS, Galileo, BDS, and QZSS, (c) an area with good visibility of BDS and QZSS, and (d) a proper weighting of the PPP-RTK corrections. We provide a formal and simulation-based analysis of kinematic and static PPP-RTK with perfect, i.e., deterministic, clock and bias corrections as well as corrections computed from only a single reference station. The results indicate that, on average, one can expect centimeter-level positioning results with just slightly more than two epochs already with single-station corrections. This is confirmed with real four-system GNSS data, for which the availability of two-epoch centimeter-level horizontal positioning results is 99.7% during an exemplary day.

Variations of ionospheric TEC due to coronal mass ejections and geomagnetic storm over New Zealand

The variations of ionospheric Total electron content (TEC) due to coronal mass ejections (CMEs) and geomagnetic storms over New Zealand were studied. TEC data were collected from dual-frequency GPS sites operated by the University NAVSTAR Consortium in New Zealand, at Ous2 (−45.86°N, 170.51°E), Dund (−45.89°N, 170.59°E), Mtjo (−43.99°N, 170.46°E), and Quar (−43.53°N, 169.81°E) stations. The findings of this study show that the variability of ionospheric TEC was more noticeable during the main phase of the storm on September 08, 2017 than the initial phase on September 07, 2017, recovery phase on September 09, 2017, and during the CME day on September 06, 2017. Also, the enhancements of change in TEC (ΔTEC) were pronounced more over the Mtjo station during the CME day and over the Quar station during the geomagnetic storm day than over other stations. On September 06, 2017, two X-class solar flares, specifically X2.2 and X9.3, were observed with quiet geomagnetic storm conditions throughout the CME day, resulting in an increase in TEC. On September 07, 2017, the M7.3, X1.3, and on September 08, 2017, the X8.1 solar flare classes with disturbed geomagnetic conditions led to a significant enhancement of TEC over the stations at 02:00 UT (13:00 LT). Finally, during the main phase of the storm, the solar wind electric field (IEF Ey) and prompt penetration electric field (PPEF) showed good correlations in which the fluctuation of PPEF, an increase in Ey, Dst minimum, and horizontal Earth’s magnetic field are well associated with strong changes in TEC.

Evaluation of BDS/GPS Multi-Frequency RTK Positioning Performance under Different Baseline Lengths

The BeiDou Navigation Satellite System (BDS) is fully operational and provides positioning, navigation, and timing services to users worldwide. To comprehensively evaluate the BeiDou-3 Navigation Satellite System (BDS-3) global real-time kinematic (RTK) positioning performance, five sets of IGS/MEGX stations with different baseline lengths are selected in this research, and the visibility of current BDS-3, BDS-2+BDS-3, and Global Positioning System (GPS) system satellites are analyzed. The single frequency, dual-frequency, and triple-frequency positioning accuracy as well as ambiguity fixing rate under short baseline and long baseline are also analyzed. The experimental results show that the positioning accuracies of B1C, BII, L1, and B3I single-frequency bands were about the same, while for band B2a it was lower. For the short baseline dual-frequency RTK positioning mode, the accuracy of BDS-3 (B1C/B2a), BDS-3 (B1I/B3I), triple-frequency BDS-3 (B1C/B2a/B3I), and GPS (L1L2) is comparable and slightly better than that of BDS-3 (B1I/B3I). With the increase in baseline length, the advantages of dual-frequency BDS-3 (B1C/B2a) and triple frequency BDS (B1C/B2a/B3I) are more obvious, with triple-frequency BDS-3 (B1C/B2a/B3I) having the best positioning accuracy. In terms of ambiguity fixing performance, dual-frequency BDS-2+BDS-3 (B1I/B3I) and dual-frequency GPS (L1L2) have the highest ambiguity fixing rate. The ambiguity fixing rate of dual-frequency BDS-3 (B1C/B2a) and triple-frequency BDS-3 (B1C/B2a/B3I) can be higher than 90% within 100 km. In the case of positioning using only the BDS-3 system, the triple-frequency BDS-3 (B1C/B2a/B3I) is superior to both the dual-frequency BDS-3 (B1I/B3I) and dual-frequency BDS-3 (B1C/B2a) in terms of both positioning accuracy and ambiguity fixing rate. The BDS-2+BDS-3 (B1I/B3I) dual-frequency RTK, which has reached a level comparable to GPS, can provide global users with real-time centimeter-level differential positioning services.

Q-SAT for atmosphere and gravity field detection: Design, mission and preliminary results

Q-SAT, a small spherical satellite designed and developed by Tsinghua university, was successfully launched on Aug 6, 2020 at Jiuquan satellite launch center in China. The mission of Q-Sat is the joint measurement of long-wavelength Earth gravity field and upper atmosphere density, which is of great significance for improving spacecraft orbit prediction and promoting the development of satellite gravity measurement technology. The satellite is designed in spherical shape innovatively and deploys high dynamic dual-frequency GPS as the main payload. On-orbit data shows that the atmospheric density detection precision is in the order of 10−14kg/m3 and the gravity recovery precision achieves the level of 30 orders. All mission success criteria and objectives were achieved. This paper presents the design, space mission, key technologies, science capabilities and preliminary results of the satellite.

On the impact of meridional wind circulation changes in the electron density distribution over the Indian equatorial and low latitude ionospheric region during a severe geomagnetic storm

Using a suite of instruments, which included a chain of ground-based dual-frequency GPS receivers, and magnetometers, we have studied the importance of thermospheric meridional wind circulation in controlling the distribution of plasma over the Indian low latitude ionospheric regions during the period of a severe geomagnetic storm. The storm on 15 May 2005, which had its onset coinciding with the local noon time sector for the Indian ionospheric zone, was a severe geomagnetic storm with symH ∼ - 305 nT. A steep increase in the Total Electron Content (TEC) of the ionosphere over the entire Indian ionospheric region was observed on May 15. The enhancement in the TEC was well correlated with the increase in ΔH at the dip-equator due to the prompt penetration of the convection electric field associated with the storm. However, contrary to the previous studies on the storm impact over low latitude regions, a clear signature of disturbance dynamo was absent on the day after the storm. Enhancements in the TEC were observed on May 16, a day after the storm, as well, though the ΔH at the dip-equator was quite below the quite-time mean. The TEC remained well above its monthly mean over the entire Indian ionospheric region during the storm recovery period. We suggest that the TEC enhancement on May 16, even though it looked like due to a prompt penetration effect, was directly related to the compositional disturbances as given by the O/N2 ratio. We conclude that the meridional wind circulation plays an important role in the distribution of electron density over the equatorial and low latitudinal region during the period of a geomagnetic storm.

SBAS ionospheric grid delay estimation based on ionospheric tomography: a case study on September 7–9, 2017

In Satellite-Based Augmentation Systems (SBASs), e.g., the US Wide-Area Augmentation System (WAAS), the planar method and the kriging method based on the thin-shell model have been used to estimate the ionospheric grid delay (IGD). Generally, the kriging method can achieve higher accuracy than the planar method. In comparison with the thin-shell model, ionospheric tomography overcomes the limitations of the 2D ionospheric delay modeling and can realize 3D or even 4D ionospheric electron density reconstructions, especially suitable over disturbed periods. For the first time by virtue of electron density inversions, a tomographic method and a kriging-combined tomographic method are proposed innovatively to apply for estimating IGDs over part of the WAAS region using 32 ground stations during ionospheric disturbances on September 7–9, 2017. Then, independent dual-frequency Global Positioning System (GPS) data at six stations are applied to validate estimated IGD results from these four methods. It is shown that the overall errors of the planar method, the kriging method, the tomographic method, and the kriging-combined tomographic method over 3 days are decreased one by one, while errors using the latter two methods are quite similar. When focusing on the strong disturbed times, the latter two tomographic methods can obtain more accurate IGD than the former two methods based on the thin shell model. Tomographic total electron content (TEC) maps over the study area are also reconstructed to help analyze the underlying mechanism at different stations. It is also noted that the kriging-combined tomography has little improvement in IGD estimates in comparison with the tomographic method alone during strong ionospheric disturbances.

Comparative Analysis of Smartphones and Survey-Grade GNSS Receivers for Parcel Boundary Determination

This paper advances the existing body of knowledge on the suitability of accuracy derivable from the use of smartphones for cadastral mapping. Zenvus App software was installed on two smartphones of a different make. A set of dual-frequency GPS Promark 3 receivers and two different smartphones of different make were used for data acquisition. Observations were carried out at the boundaries of ten parcels of land, comprising 46 boundary points. Coordinates of these points were obtained using Differential Global Positioning System (DGPS) observation in static mode and two android smartphones (Samsung A70 and Tecno Spark 3 Pro). Mean score, root means square error, and one-way analysis of variance was used to show significant differences in the equipment used. Overall, both the accuracy (mean) and precision (RMSE) were lower than those obtained by Differential GPS. A one-way analysis of variance (ANOVA) was calculated on the values of both X and Y. For X, the analysis was not significant, F (1, 45)= 0.88, p= 0.419 and for Y, the analysis was also not significant, F(1,45) =0.97, p=0.383. The total RMSE shows that coordinates of points as obtained by the Samsung smartphone (3.368) was more precise than Tecno (4.041). However, the two smartphones (Tecno and Samsung) were less accurate than differential GPS. This implies that there is a 95% chance that the errors in the estimates are less than 6.993m (for Tecno) and 5.848m (for Samsung) respectively. The variation in the observations obtainable with smartphones affects both linear and polygon estimates. The study concluded that the magnitude of these errors is significant in cadastral survey practices and hence not suitable for use. It is recommended that further studies be carried out on the use of the Zenvus app on centimeter grade smartphones probably this could yield a better result suitable for cadastral mapping.

Validating Precise Orbit Determination from Satellite-Borne GPS Data of Haiyang-2D

Haiyang-2D (HY-2D) is the fourth satellite in the marine dynamic satellite series established by China. It was successfully launched on 19 May 2021, marking the era of the 3-satellite network in the marine dynamic environment satellite series of China. The satellite’s precision orbit determination (POD) and validations are of great significance for ocean warning and marine altimetry missions. HY-2D is equipped with a laser reflector array (LRA), a satellite-borne Doppler Orbitography and Radiopositioning Integrated by Satellite (DORIS) receiver, and a satellite-borne dual-frequency GPS receiver named HY2 that was independently developed in China. In this paper, the quality of GPS data collected by the HY2 is analyzed based on indicators such as the multipath effect, cycle slips, and data completeness. The results suggest that the receiver can be used in POD missions involving low-Earth-orbit (LEO) satellites. The precise orbits of HY-2D are determined by the reduced-dynamics (RD) method. Apart from POD, validation of orbit accuracy is another important task for LEO POD. Therefore, two external validation methods are proposed, including carrier differential validation using one GPS satellite and inter-satellite differential validation using two GPS satellites. These are based on space-borne carrier-phase data, and the GPS satellites used for POD validation do not participate in orbit determination. The results of SLR range validation cannot illustrate the orbit accuracy in x, y, and z directions particularly, so to make validation results more intuitive, the SLR three-dimensional (3D) validation is proposed based on SLR range validation, and the RMSs in x, y, and z directions are 2.66, 3.32, and 2.69 cm, respectively. The results of SLR 3D validation are the same as those of SLR range validation, which proves that the new external validation method provided by SLR 3D is reliable. The RMSs of carrier differential validation and inter-satellite differential validation are 0.68 and 1.06 cm, respectively. The proposed validation methods are proved to be reliable.

RTK positioning based on the phase-only differential corrections

Multi-GNSS multi-frequency observations improve the accuracy, availability and reliability of the single-site RTK positioning but also simultaneously raise the communication bandwidth needed for the transmission of differential corrections. A RTK positioning algorithm is proposed that transmit the phase-only differential corrections to achieve the ambiguity-fixed RTK positioning, significantly reducing the communication bandwidth requirements. The essence of the presented method is that the code differential positioning solution implied in the conventional RTK positioning procedure can be replaced by the single point positioning solution of the rover receiver to realize RTK positioning. For typical application scenarios, the transmitted bits in a single epoch can be reduced by more than 25% when the corrections are sent with the RTCM protocol. The experiments by the GPS dual-frequency data over the 10 km and 180 km baselines shown that the performance of the presented RTK algorithm are comparable to that of the conventional RTK positioning, which verifies its feasibility and effectiveness.

Climatology of Medium-Scale Traveling Ionospheric Disturbances (MSTIDs) Observed with GPS Networks in the North African Region

We present for the first time the climatology of medium-scale traveling ionospheric disturbances (MSTIDs) by using Global Positioning System (GPS) receiver networks on geomagnetically quiet days (Kp ≤ 3) over the North African region during 2008–2016. The ionospheric Total Electron Content (TEC) were estimated from the dual-frequency GPS measurements, and the TEC perturbations (dTEC) data were derived from the estimated TEC data. We focused on the TEC perturbations (dTEC) associated MSTIDs and statistically analyzed its characteristics, occurrence rate, diurnal and seasonal behavior as well as the interannual dependence. The results show that MSTID is a local and seasonal dependence. The result reveals that occurrence of MSTIDs increases with solar activity. It also shows that MSTIDs predominantly propagates towards the South (equatorward). The MSTIDs event period is (12 ≤ period ≤ 53 min), while the dominant peak-to-peak amplitude is (0.08 ≤ amp ≤ ~ 1.5 dTECU). The study also shows that the amplitude of MSTIDs is higher at the northwest (Lat: ~ 32° N to ~ 38° N, Long: ~ 2° W to ~ 15° W) when compared with northeast (Lat: ~ 28° N to ~ 38° N, Long: ~ 23° E to ~ 40° E), and the disturbance occurrence time is more frequent within the hours of (1200–1600 LT), and (1000—1400 LT) in December solstice at daytime for stations located in the northwest and northeast part of the African region, respectively. While at the nighttime, the MSTIDs also exhibits variability in disturbance occurrence time around (northwest: 2100–0200 LT) and (northeast: 1900-0200 LT) in June solstice, but get extended to March equinox during solar maximum (2014). The mean phase velocity in daytime MSTIDs is higher than the nighttime in every season, except during June solstice.

Cost-Effective, Single-Frequency GPS Network as a Tool for Landslide Monitoring.

The constant monitoring of active landslides, particularly those located in the proximity of populated areas or touristic places, is crucial for early warning and risk-management purposes. The commonly used techniques deploy expensive instrumentation that can be hardly afforded, especially by small mountain communities in which landslide events often occur repeatedly. In recent years, the scientific community, as well as the private sector, have devoted growing effort to reducing the costs of monitoring systems. In this work, we present a monitoring network based on single-frequency Global Positioning System (GPS) sensors that have been activated to monitor an active landslide in the Carnic Alps, North-Eastern Italy. The system, which was composed of 12 single-frequency GPS stations, one seismometric station coupled with a single-frequency GPS instrument for real-time monitoring, and one permanent dual-frequency GPS station located in a stable area, provided daily reports of the landslide motion to the local authorities and administration. We show that this system is a valuable, flexible, and cost-effective tool for quick landslide characterization, and has high potential to be used as a landslide early warning system in case of emergency situations.

Improving the performance of time varying spherical radial basis functions in regional VTEC modeling with sparse data

Least-squares parameterization of retrieved Vertical Total Electron Content (VTEC) from permanent dual-frequency GPS stations in terms of Time Varying Spherical Radial Basis Functions (TV-SRBFs) with optimal shape parameter leads to proper regional VTEC reconstruction at Ionospheric Pierce Points (IPPs). However, in the area where there is no observation, the modeling result is not satisfactory. This feature is especially tangible when the number of IPPs in the study area is low with poor geometric distribution, which leads to a rank deficient problem. Whereas, if the global ionospheric maps (GIMs) are used as a background in estimating the optimal shape parameter of TV-SRBFs and coefficients of the expansion, the stated obstacle to produce accurate regional ionospheric maps will be removed. For this purpose, an objective function is defined and optimized. The objective function consists of three terms. First, L-2 norm of the differences between the reproduced VTECs and values obtained from the receivers’ observations. Second, L-2 norm of the differences between the reproduced values on a regular grid with the values obtained from the spatial interpolation of GIM at a specific moment in the modeling interval. Third, the discrete smoothing norm of the coefficients of TV-SRBFs. Since the obtained VTECs from GPS receivers are more accurate than the resulted VTECs from interpolation of GIMs and also a regularization parameter is needed due to the ill-posedness, the three objectives cannot be considered with the same weights in the multi-objective optimization. Hence the weighted sum method with the preference-based solution is applied to obtain the optimal relative weight of GIMs, the regularization parameter and the coefficients. Moreover, utilizing the least-squares collocation (LSC) can also improve the modeling accuracy to some extent. The proposed method is applied for hourly regional VTEC modeling over Iran from 3 May to 9 May 2016, which had both low and very high geomagnetic activities. A portion of the retrieved VTECs which is excluded from the modeling dataset, is considered as test data. The Root Mean Square (RMS) of the differences between obtained VTECs from regional constructed model and test data is 0.94 TECU in the study period. RMS of the differences between obtained VTECs from the regional model and VTECs of two control stations which are not involved in the modeling are 1.12 TECU and 1.24 TECU. Also, the regional model performs well in ionospheric delay estimation and the accuracy of single-frequency positioning at control stations in the study period is better than 0.7 m.

Copernicus Sentinel–1 POD reprocessing campaign

Copernicus Sentinel–1 is a C-Band Synthetic Aperture Radar (SAR) satellite mission within the European Copernicus Programme. The two satellites Sentinel-1A and -1B were launched in April 2014 and 2016, respectively. The Copernicus POD (Precise Orbit Determination) Service is responsible for the determination of orbital and auxiliary products required by the Payload Data Ground Segment (PDGS). Precise orbits are determined based on the dual-frequency GPS (Global Positioning System) data delivered by dedicated geodetic-grade GPS receivers on-board the satellites. Several updates in the operational orbit determination were done during the years including an update of the GPS antenna reference point coordinates. The switch to GPS carrier phase ambiguity-fixing was a major improvement. A reprocessing of the entire mission span of both satellites became necessary to provide a consistent orbit time series for the mission based on state-of-the-art models and processing settings. Due to the lack of independent observation techniques, the Sentinel-1 orbit quality has been assessed by analysing processing metrics, orbit overlaps and orbit comparisons. For this purpose, members of the Copernicus POD Quality Working Group (QWG) provided reprocessed Sentinel-1 orbit time series based on their software packages and their orbit determination settings. A weighted average of all five delivered solutions - a combined orbit - serves as reference for the comparisons. The quality and reliability of this reference orbit depends among others on the number of available orbit solutions and whether a manoeuvre has been performed during the processed day or not. The mean orbit consistency between all orbit solutions is below 1 cm in 3D RMS for the entire mission time interval for both satellites. Only few days show inferior quality due to data gaps or orbit manoeuvres. Following this sophisticated validation process, the reprocessed Sentinel-1 orbits from the Copernicus POD Service have been made available to the user community.

GPS observations of ionospheric TEC variations over Nepal during 22 July 2009 solar eclipse

As the study of ionospheric behavior during various solar activities is an important task, various studies of ionospheric changes during eclipse events have been widely performed in the different regions of the globe. This paper investigates the ionospheric responses to the solar eclipse on 22 July 2009 over Nepal using the total electron content (TEC) measured by dual-frequency Global Positioning System (GPS) receivers. The time-averaged Vertical TEC (vTEC) of ten GPS stations from Nepal is analyzed and it is found that the value of ionospheric TEC decreases due to the reduction of ionizing radiation. In addition, the deviation in the TEC value on eclipse day from the mean vTEC value of the top five quietest days is found to lie in the range ~1–5 TECu at those regions which were associated with the partial eclipse shadow. On the other hand, the region with the total eclipse (BRN2 and RMTE) faced ~6–7 TECu on average reduction in the TEC value. Considering that the eclipse of 22 July 2009 occurred just at sunrise in the Nepalese zone, a maximum reduction of about 5 TECu is very significant. Higher deviation in TEC is therefore linked with the path of totality and the obscuration rate. This study reveals that the ionospheric TEC over Nepal was altered by wave-like energy and momentum transport, as well as obscuration of the solar disc due to the partial and total solar eclipse. Furthermore, the cross-correlation results presented similar type signatures of the eclipse-induced ionospheric modification over Nepal. This research work serves a crucial future reference for the comparative study of change of ionospheric TEC variability over the Nepal region during Eclipse events

Development, Verification, and Analysis of a Small Satellite Thrust Determination Filter

A current challenge for the Advanced Propulsion Experiment (APEX) CubeSat, under development by Missouri University of Science and Technology, is the accurate determination of thrust for its experimental multimodal propulsion system main payload. A consider batch least-squares filter is proposed that processes downlinked dual-frequency GPS pseudorange data to estimate the average thrust magnitude of a maneuver in conjunction with the initial dynamic states, static coefficients of drag and solar radiation pressure, and GPS receiver clock biases from each measurement epoch. Two Monte Carlo analyses were performed to test the statistical consistency of the filter and the robustness under the influence of unmodeled dynamics. The filter was found to perform nominally with matching truth and filter dynamics models and acceptably when the truth model used to synthesize measurements was a higher fidelity than the filter model. Filter performance was assessed using flight data from NASA’s Gravity Recovery and Climate Experiment Follow-On mission. A trade study was conducted to identify acceptable orbital regimes for the APEX mission. Thrust estimates using this method were shown to meet APEX mission requirements for a range of acceptable orbits.

The Advantages and Limitations of Low-Cost Single Frequency GPS/MEMS-Based INS Integration

Global Positioning System (GPS) provides a method for directly obtaining instantaneous position and velocity estimates using satellites-based passive range measurements. GPS is a whole day, all-weather, passive, satellite positioning system. Inertial Navigation System (INS) is a navigation aid system that uses a computer and Inertial Measurement Unite (IMU). IMU includes motion sensors and rotation sensors to continuously calculate relative position, orientation, and velocity. The integration of GPS/INS can help to overcome the limitations of the two systems providing integrated system better than either on a stand-alone basis. The integration of low-cost INS with dual frequency GPS has been widely studied and the same for the integration of tactical grid INS with low-cost GPS. However, during the last a few years, a number of low-cost GPS\low-cost INS integrated systems have been introduced and become popular in various engineering applications. However, reliable investigations into the advantages, limitations and quality of such integration level are still needed and more efforts are required, which will be the focus of this paper. The methodology followed in this paper for evaluating the integration of low-cost GPS/INS sensors depends on evaluating the two sensors individually and comparing the results with the integrated system. The results show that low-cost single frequency GPS receivers are able to provide a comparable accuracy level in both static and kinematic carrier phase differential GPS (DGPS). As for low-cost Micro-Electro-Mechanical System (MEMS)-based IMU, the accelerometers have provided instability comparing to gyros. The performance of gyros can be improved based on modelling the nearly-linear behaviour of the gyro drift. Tests show that the integration of low-cost GPS sensors with MEMS-based INS degrades the quality of gyro measurements and may not add any improvements to the quality of the individual GPS positioning.

Enhanced Kalman Filter Navigation Algorithm Based on Correntropy and Fixed-Point Update

The accuracy of position estimation plays a key role in many of the precise positioning applications such as category I (CAT-I) aircraft landings, survey work, etc. To improve the accuracy of position estimation, a novel kinematic positioning algorithm designated as correntropy Kalman filter (CKF) is proposed in this study. Instead of minimum mean square error (MMSE), correntropy criterion (CC) is used as the optimality criterion of CKF. The prior estimates of the state and covariance matrix are computed in CKF and a novel fixed-point algorithm is then used to update the posterior estimates. The data of a dual-frequency global positioning system (GPS) receiver located at Indian Institute of Science (IISc), Bangalore (13.021°N/77.5°E) is collected from Scripps Orbit and Permanent Array Centre (SOPAC) to implement the proposed algorithm. The results of the proposed CKF algorithm are promising and exhibit significant improvement in position estimation compared to the conventional methods.