Dual-frequency GPS Research Articles

Impact of the October 28, 2021 Solar Flare and the November 4, 2021 Geomagnetic Storm on the Low, Middle, and High-Latitude Ionosphere

This study examines the ionospheric Total Electron Content (TEC) responses to a solar flare on October 28, 2021, and a geomagnetic storm on November 4, 2021, across low, middle, and high latitude regions. We utilized GPS-TEC data from the University NAVSTAR Consortium’s dual-frequency GPS devices at the IFR1, IISC, YIBL, YKRO, KERG, and SVTL stations. While the solar flare on October 28, 2021, triggered the geomagnetic storm on November 4, 2021, our analysis revealed notable TEC changes during the latter event. TEC fluctuations were observed across all stations during the geomagnetic storm, with significant disruptions and variable depletion rates. However, distinct TEC variations were noted at KERG and YIBL stations before the storm, likely due to the preceding solar flare. Continuous wavelet analysis (CWT) showed higher periodicity during the storm compared to the flare, proving CWT to be an effective tool for analyzing TEC variability by revealing periodicity fluctuations at all stations. In conclusion, we found that both solar flares and geomagnetic storms can cause significant positive TEC changes.

Ionospheric and meteorological response to total solar eclipses

Studies concerning solar eclipses have been rising significantly, yet, different circumstances during their occurrence provide uniqueness to every study. This paper studies the ionospheric and meteorological response to the total solar eclipses of August 21, 2017, March 20, 2015 and August 1, 2008. The ionospheric total electron content (TEC) was calculated from the signals beamed by the dual-frequency Global Positioning System (GPS) satellites and accessed from University NAVSTAR Consortium (UNAVCO) data archive. Similarly, the data of meteorological parameters were accessed from the historical climate archive of respective countries. The TEC drop of ∼2–7 TECU with a lag of ∼15–30 min is observed at varying latitudes which correspond with the findings of numerous past research. We analyzed the data of 15 stations under ∼100% obscuration to rule out the varying effects of different obscuration rates. Yet, given the turbulent nature of climate, we found varying changes at observed locations. A good relationship, however, was observed in 8 of the stations, where temperature drop ranged from 0.4 °C to 6.11 °C, and rise in relative humidity ranged from 0 to ∼77%. Wind speed has shown the most turbulent behavior. Their change was largely impacted by the eclipse on 5 of the stations, while the local factor was dominant on the others. In spite of this, the stations under observation showed distinct responses to the ionospheric change during the total solar eclipses, thus demonstrating the relation of meteorological parameters with eclipses.

Improving the Accuracy of Drone Measurements on Hydrotechnical Works

Abstract Topographic measurements made with the drone is an alternative way for creating 3D models, point clouds, etc., but they should be considered correct placement of ground control points to complete the required works precisely. To meet these needs to have a sub millimeter precision in this publication we will treat such as positioning, verification and comparison precisions achieved by attaching ground control points to the point cloud. These ground control points are measured with two different devices, namely the robotic total station and two dual-frequency GPS receivers used in base & rover mode. Errors made on ground control points can influence the whole cloud of points and we will demonstrate the extent to which this occurs.

A new model for plasmapause locations derived from IMAGE RPI and Van Allen probe data

The outer boundary of the plasmasphere, the plasmapause, is characterized by a sharp electron density gradient that changes under varying space weather conditions. We developed a new model, called Neustrelitz/ESOC PlasmaPause Model (NEPPM), for providing plasmapause location in terms of -shell utilizing electron density measurements from the Van Allen probes from 2012 to 2018 and the IMAGE satellite data from 2001 to 2005. Both datasets were preprocessed, and algorithms were developed for automatic detection of plasmapause location. The suggested model provides a simple ellipse-based approach determined by the semi-major axis, the eccentricity, and the orientation angle of the semi-major axis. The modelled varies as a function of the index and magnetic local time . The NEPPM results are compared with the Global Core Plasma Model (GCPM). The plasmapause bulge in the evening hours follows the level of geomagnetic activity. The NEPPM will complete the NPSM (Neustrelitz PlasmaSphere Model), which was derived from dual-frequency GPS measurements on-board the CHAMP satellite mission.

Performance of IRI 2016 model in predicting total electron content (TEC) compared with GPS-TEC over East Africa during 2019–2021

This study evaluated the applicability of IRI-2016 model in predicting GPS TEC using the monthly means of the five (5) quiet days for equinoxes and solstices months. GPS-derived TEC data were obtained from the IGS network of ground based dual frequency GPS receivers from three stations [(KYN3 0.53° S, 38.53° E; Geom. Lat. 3.91.63° S), (MBAR 0.60° S, 30.74° E; Geom. Lat. 2.76° S) and HOID 1.45° S, 31.34° E; Geom. Lat. 3.71° S]. All the three options for topside Ne of IRI-2016 model and ABT-2009 for bottomside thickness have been used to compute the IRI TEC. The results were compared with the GPS TEC measurements. Correlation Coefficients between the two sets of data, the Root-Mean Square Errors of the IRI-TEC from the GPS-TEC, and the percentage RMSE of the IRI-TEC from the GPS-TEC have been computed. In general, the IRI-2016 model underestimated GPS-TEC during the nighttime, whereas the model overestimated GPS-TEC values during the daytime. At most of the stations and during all seasons where data were available, correlation coefficient was above 0.9, which is quite strong. The variation of O/N2 ratio may potentially be the cause of the IRI TEC deviation from the GPS TEC. This variation arises from lower thermosphere plasma drift that moves upward.

Determining of correlation relationship between angular elements of external orientation

The current state of development of science and technology definitely influenced the introduction of UAVs in various areas of economic development and military affairs. And this trend, since it brought positive results, will continue to grow. Therefore, the study of UAV capabilities, both design and operational, is a necessary component. The authors proposed a new algorithm for processing the results of digital shooting and determining the dependencies of the influence of the angular elements of the external orientation (EEO) of the images, which will make it possible to significantly improve the accuracy of the searched terrain coordinates. One of the main requirements for aircraft-type UAVs used in aerial surveying is absolutely horizontal flight. That is, maintaining the minimum angles of inclination of the external orientation of the images. And so, the idea arose to find the correlation coefficients between them when modeling the angles of inclination α and ω relative to the fixed angle ϰ (since this angle is actually compensated with the help of an aero device). So, if there is such a dependence, then based on the values of these values, it is possible to introduce a correction in the design of a micro-UAV and thereby increase stability during horizontal flight. Everything will depend on the value of the correlation coefficient: the larger it is, the more significant the possibility of improvement in the design of the UAV. Such modifications can be the displacement of the center of gravity of the structure, the profile and quantitative parameters of the plane, the shape of the fuselage, etc. The application of this direction will lead to the determination of the exact parameters of the EEO, since the installation of an accurate stabilization system and the determination of the angular EEO images (INS) on these devices is not possible, since there are often restrictions on the loading of UAVs. Regarding the determination of linear EEO, the issue can be solved by installing a dual-frequency GPS receiver on the UAV, which will allow obtaining the coordinates of the projection centers with an accuracy of 1–2 cm. The refinement of the EEO of digital images leads to an increase in the accuracy of the spatial coordinates of object points.

Impact of incorporating Spire CubeSat GPS observations in a global GPS network solution

Commonly, Global Positioning System (GPS)-based precise orbit determination (POD) of a low Earth orbiting (LEO) satellite is conducted by introducing fixed GPS orbits and clock corrections that were derived in a previous independent network solution using ground-based GPS receivers only. There have been a number of studies showing that the integration of LEO GPS observations can be advantageous in global network solutions, particularly when it comes to estimating geodetic parameters, such as the Earth’s center-of-mass. There has been an increase in GPS data available from LEO CubeSats over the past few years, such as from the Spire satellites, which are equipped with dual-frequency GPS receivers. The goal of the present study is to determine how GPS observations collected by specific Spire satellites affect global network solutions when combined with GPS observations from ground stations of the International GNSS Service. To obtain a combined GPS-LEO solution, GPS observations collected from receivers of selected Spire satellites and additional scientific LEOs are used to obtain combined GPS-LEO solutions by performing one joint least-squares adjustment process. Using this method, LEO satellite orbit parameters are determined along with GPS orbit parameters and geodetic parameters, namely GNSS station coordinates, Earth rotation parameters (ERPs), and the Earth’s center-of-mass. The influence of the Spire LEOs is assessed by analyzing different solutions that use GPS observations from different Spire and LEO satellites. Besides comparing the different global network solutions with one another, a comparison to a solution using only terrestrial GPS data is performed as well. As part of the quality assessment of the GPS-LEO solution, quality characteristics are analyzed, which are the geodetic parameters, orbit overlaps at arc boundaries, and formal errors determined for the estimated parameters. The results show that the estimation of the Earth’s center-of-mass coordinates benefits from including GPS-LEO observations. The solution is more improved by integrating GPS-LEO observations from scientific LEOs than from GPS-Spire-included solutions. The analysis reveals that GPS orbits are improved using the LEO-integrated approach, while orbit misclosures of LEO and Spire trajectories currently indicate a decrease in LEO orbit precision due to LEO orbit modeling deficiencies.

Evaluation of The Effect of Spoofing on Dual-Frequency Global Navigation Satellite System (GNSS)

This paper aims to assess the impact of Global Navigation Satellite System (GNSS) spoofing on the performance of a Garmin GPSMAP 66sr dual-frequency GNSS receiver. The evaluation is conducted through field assessments under three conditions: 1) single-frequency GPS L1 coarse acquisition (C/A) only, 2) single-frequency GPS L1 C/A and Galileo E1 open service (OS), and 3) dual-frequency GPS L1 C/A and L5, as well as Galileo E1 OS and E5a. The results emphasise the critical role of multifrequency GNSS in mitigating spoofing. In the dual-frequency multi-GNSS mode, spoofing does not occur as the GPS L5 and Galileo E5a signals remain unaffected by spoofing signals in the L1 / E1 band. In the single-frequency multi-GNSS mode, the higher number of observed GNSS satellites contributes to higher minimum spoofing power levels and longer durations between position fix loss and spoofing as compared to the GPS only mode.

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 the 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 makes were used for data acquisition. Observations were carried out at the boundaries of ten parcels of land, comprising 46 boundary points. The coordinates of these points were obtained using Differential Global Positioning System (DGPS) observation in static mode and two Android smartphones (the Samsung A70 and the Tecno Spark 3 Pro). Mean score, root mean square error, and one-way analysis of variance were 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 the coordinates of points as obtained by the Samsung smartphone (3.368) were more precise than those obtained by 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.

The implementation of dual frequency positioning for ionospheric effects correction

Brazil is located in a tropical region near the equator line, where the solar incidence is more intense. For this reason, the effect of ionospheric refraction on satellite signals is more expressive. In order to mitigate this effect, the use of dual frequency positioning technique is effective in the position solution, reducing distortions caused by ionospheric refraction. In this article, dual frequency GPS data was analyzed, in order to prove its effectiveness in correcting the ionospheric error in comparison with single frequency GPS data.

Instrumental Receiver Bias Estimation for Ionospheric Total Electron Content by Neural Network Model

Total Electron Content (TEC) is one of the most important parameters in the study of the ionosphere, especially for determining ionospheric disturbances. The TEC levels are typically estimated from dual-frequency GPS observation data. Since the measured TEC contains discrepancies such as satellite and receiver biases, they need to be removed to obtain more accurate TEC values. In this work, we estimate the receiver bias using a neural network technique. Based on the exhaustive evaluation, we design a neural network (NN) model with two-hidden layers, and it is trained with datasets from three GNSS observation stations in Thailand. The prediction from the proposed neural network deviates from the baseline reference using the minimum standard deviation method with significantly faster computational time. The trained NN model is also tested for estimating the receiver bias values at other untrained stations in Thailand.

Dual-frequency GPS Cycle Slip Detection and Repair Based on Dynamic Test

How to solve the multi-values and accurately detect the cycle slip of each frequency was particularly critical of dual-frequency GPS. This paper used the geometry-free phase combinations, proposed a dynamic test method to detect cycle slip outliers, which determined the cycle slip by constraining the value range of the cycle slip sequences of the dual-frequency GPS through the constantly updated its standard deviation. The dynamic test of cycle slip detection and repair method has been tested by using GPS data with sampling interval of 1s, 5s, 10 s and 15s. The method can not only solve the problem of multi-values, but also accurately detect the cycle slip values at various frequencies, whether the fixed cycle slip is added to the random position or the random cycle slip is added to the random position. Experiments with four different sampling intervals, the results showed that the proposed method of cycle slip detection and repair calculation success rate reaches 98.75%.

Precise orbit determination of Spire nano satellites

Spire Global, Inc. operates a growing fleet of currently more than 100 CubeSats in different low Earth orbits for commercial Earth observation. These satellites are equipped with dual-frequency GPS receivers and an attitude determination and control system, allowing for precise orbit determination. For three different satellites and a time span of six months we analyze the performance and quality of the on-board collected GPS and attitude data and employ it for precise orbit determination using the Bernese GNSS Software and Napeos, two independent state-of-the-art GNSS processing software packages. We describe technical details crucial for POD and present and compare the in-flight calibrated phase center variation maps. Reduced-dynamic and kinematic orbits are then inter-compared between the two software packages as well as to the orbit solutions produced by Spire Global. We report pseudo-range and carrier phase residuals at the level of 3–4 m and 8–9 mm RMS and a good agreement between the reduced-dynamic and kinematic orbits of around 5 cm 3D RMS. The reduced-dynamic orbit positions and velocities produced with the two employed software packages agree in average on the level of 6–7 cm and 0.05–0.07 mm/s 3D RMS, while the comparison to the orbits produced by Spire Global is markedly worse with 27–30 cm and 0.32–0.36 mm/s 3D RMS. The presented results are an encouraging first step towards using GPS data from the Spire constellation for geodetic, geophysical and ionospheric applications.

Analysis of differential code biases for GPS receivers over the Indian region

Abstract The GPS Aided Geo Augmented Navigation (GAGAN) system provides the navigational services for single-frequency GNSS user via broadcasting the differential corrections with GEO stationary satellites. The significant differential correction contribution comes from ionospheric time delays and is necessary to be determined precisely. Dual-frequency GPS receivers measure the ionospheric time delays using GPS code and carrier phase measurements. The determination of absolute ionospheric Total Electron Content (TEC) requires the calibration of GPS satellites and receiver hardware biases due to different frequency-dependent signals (L1 and L2) due to environmental changes (Temperature and Humidity). In this paper, A receiver-based Differential Code Biases (DCB) algorithm is implemented to derive a joint estimation of TEC and RDCB parameters using the weighted Least Square (WLS) method. The daily averaged DCBs data for 26 GPS receivers are obtained for 3 years (2014–2016) from 26 GPS reeivers over Indian region. The receiver DCB algorithmis validated with the Fitted Receiver Biases (FRB) method. The correlation (R) between VTEC and RDCB is conducted to investigate the RDCB stability. The results would be useful for the accurate determination of ionospheric differential corrections to GAGAN users.

GALILEO HAS – FIRST PERFORMANCE TESTS DURING ITS INITIAL PHASE OF OPERATION

Galileo High Accuracy Service (HAS) became available in January 2023. As declared, in its final operational capability, it should be able to provide to users the Precise Point Positioning (PPP) at horizontal accuracy level better than 20 cm in real-time with 95% confidence globally. At the moment Galileo HAS works in its initial phase of operation with some limitations regarding its availability, convergence time and accuracy but gives the chance to observe the performance of positioning tool at the accuracy level which was available before by using differential measurement only. Galileo HAS PPP, free of charge and based only on satellite signals delivered by nominal Galileo constellation is unique in its kind between various GNSS positioning modes. This article presents the results of first, preliminary tests on Galileo HAS performance conducted in July 2023 in Gdynia, Poland. The field tests were conducted with Galileo HAS capable receiver in static conditions and focused on the verification the declared service performance in the real positioning scenarios. Additionally, the Galileo HAS PPP performance was compared with the simultaneous performance of other GNSS positioning methods such as EGNOS, DGPS, dual frequency GPS+Galileo or dual frequency GPS and dual frequency Galileo. This first experiences with Galileo HAS positioning should show all potential users what performance level can be achieved with this new, unique in its kind GNSS positioning method at the present state of its implementation.

An improved Kloubuchar ionospheric correction model for single frequency GNSS receivers

Abstract The enhancement of positional accuracy of single frequency ionospheric correction models is an urgent need for low-cost and smartphone GNSS users. The available single frequency ionospheric correction models such as Klobuchar, NeQuick-G, NTCM, and Klob-BDS are providing ionospheric corrections for multi GNSS systems such as GPS, Galileo, BDS, and NAVIC systems. Otherwise, Global Ionospheric Map (GIM) Total Electron Content (TEC) corrections are also available to the GNSS users. In this letter, an improved Klobuchar ionospheric model is implemented. The slant TEC of dual Frequency GPS TEC observations is considered a reference. The Klobuchar model slant TEC observations are improved by taking the grid-based residual TEC corrections with the Adjusted Spherical Harmonic Function model. The Single frequency users can improve the ionospheric delay estimation using Klobuchar model and grid-based TEC residual corrections. The improved ionospheric correction model is tested under the biggest geomagnetic storm conditions during 24th Solar cycle that occurred in March 2015 over India. The proposed hybrid slant ionospheric TEC algorithms are evaluated with individual single frequency ionospheric models (Klobuchar, and GPS TEC) under adverse space weather conditions.

Occurrence pattern of large-scale ionospheric irregularities over Ilorin, Nigeria - During solar cycle 24

Ionospheric plasma density irregularities are regular features of the nighttime equatorial ionosphere especially around solar maximum. These irregularities exist in different scales ranging from small sizes of meters to very large scales of hundreds of kilometers and are responsible for the scintillation of Global Navigation Satellite Systems (GNSS) signals. Occurrence of these irregularities poses serious danger to GNSS signals and their applications. It is therefore necessary to continuously study their occurrence pattern and the severity of their effects on radio signals when new data are available. GNSS data for the whole of solar cycle 24 for Ilorin, Nigeria (Lat. = 8.48 °N, Long. = 4.67 °E, Dip = 4.1 °S) acquired using dual frequency GPS receiver (GPStation-2) and Novatel GISTM receiver (GPStation-6) were used to study the trend of large-scale irregularities. The indices used are the rate of change of TEC Index (ROTI) and ROTI average (ROTIAVE) obtained from 30 s RINEX data. The results showed two peaks in the level and frequency of occurrence of large-scale irregularities at Ilorin - one in March and the other in September. The level and frequency of occurrence of irregularities widened around these 2 months as the level of solar activity increases. It was observed that the frequency of occurrence is higher in March equinox than in September for all the years. Similarly, the spread of irregularities in terms of the monthly average number of satellites affected with irregularities was found to be higher in March equinox than in September during the increasing phase of the solar cycle; while during the decreasing phase, the spread for September was found to be higher than that of March. In terms of the local time of occurrence, irregularities are more pronounced between 1900 LT and 2400 LT. The level of irregularities was found to be correlated with solar indices (i.e. EUV and F10.7). A correlation study between solar indices (i.e. EUV and F10.7) with irregularities showed consistency pattern during the scintillation season i.e. during equinox. A slightly higher correlation values were however obtained between the level/spread of irregularities and EUV compared to that with F10.7.

Regional ionospheric electron density modeling by assimilation of GPS-derived TEC into IRI-provided grids on May 8, 2016

Retrieved vertical total electron content (VTEC) via dual-frequency GPS measurements is a valuable observation for regional VTEC modeling of the ionosphere (3D), and also ionospheric electron density (IED) modeling (4D). In the case of 4D modeling, spatial and temporal changes in IED are imaged. 4D reconstruction of IED in different ionosphere layers is not possible only by retrieved VTECs. In all IED modeling methods, in addition to VTEC observations, a priori knowledge of how electron density is distributed in different layers is required, which is often taken from global empirical models. One of these methods is data assimilation, in which the information of a global model is considered as background and both observations and background are used optimally for IED modeling. Data assimilation has more prominent importance in regions where the observations are sparse. In this study, a grid-based data assimilation method is proposed for IED modeling. The optimum interpolation method (OI) is presented with a modification to find the optimal variance factor related to the background covariance matrix. The covariance matrix of the background during the data assimilation interval is estimated by an optimization process. The method is utilized for regional assimilative IED modeling over Iran with sparse VTEC data from a low number of permanent GPS stations on May 8, 2016 which is the most active ionospheric day in that year. International reference ionosphere (IRI) is considered as background, and although it has a significant bias in the study region, the proposed method resulted in an accurate regional IED model. The model is evaluated in two ways. First, by measuring RMS of the differences between parts of VTECs that are excluded from observations as test data and the obtained VTECs from the model. Second, by examining the accuracy of ionospheric delay estimation via single-frequency positioning at a control station in Tehran. Despite the use of sparse data on an active ionospheric day and poor background accuracy in the study region, the constructed regional assimilative model is accurate both in RMS with test data and ionospheric delay estimation.

Design of a Multi-modal Sensor Fusion Unmanned Vehicle System based on Computer Vision

With the development of artificial intelligence and Internet of Things technology, more and more intelligent products are appearing around us, such as sweeping robots, library service robots and drug delivery robots, etc. In the practical application of these intelligent robots, the core technology of spatial positioning is inseparable, and considering the cost, signal interference and positioning accuracy, it is necessary to study the positioning technology with low cost, small size and strong anti-interference factors. To solve the problem of poor performance of positioning accuracy when using low-cost sensors in the physical environment, we use a four-wheel drive vehicle model as a carrier to build an unmanned vehicle system based on multi-modal sensor fusion, binocular vision localization and other technologies. The core of the system is the MM32F3277G9P chip from MindMotion and the Raspberry Pi embedded development board. The proposed vision information is based on the Intel Realsense T265 camera, which is fused with the data from the nine-axis inertial measurement unit (IMU) and the dual-frequency global positioning system (GPS), so that the positioning algorithm can continuously provide robust and accurate state estimation results in the physical environment through the complementary advantages.

GNSS standard point positioning method based on spherical harmonic expansion of signal propagation path relating errors

The errors affecting standard point positioning mainly include the ionospheric delay error, tropospheric delay error, clock bias, and multipath effect. The errors are divided into two categories depending on the relation to the signal propagation path: errors related to the propagation path and errors unrelated to the propagation path. The ionospheric delay error, tropospheric delay error, and multipath effect are related to the satellite signal propagation path. Based on this characteristic, a new GPS standard point positioning algorithm based on spherical harmonic expansion (SPP-SH) is proposed, which uses spherical harmonic expansion to represent the errors related to the propagation path. We hope to continuously promote the further development of standard point positioning (SPP) by proposing this new algorithm and to further reduce the redundancy of SPP algorithms and improve the efficiency and reliability of the algorithms. The most important purpose of this manuscript is to validate the proposed SPP-SH algorithm based on GPS data provided by IGS stations. Pseudorange data of multiple continuous epochs are used to achieve a sequential sliding point positioning solution, and the truncated singular value decomposition and iteration method correcting characteristic values are used to solve the ill-conditioned equations in the SPP-SH algorithm. The SPP-SH algorithm is implemented and verified using IGS station data. The positioning accuracy of the SPP-SH algorithm for both dual-frequency data and single-frequency data is better than that of a traditional SPP algorithm. By analyzing the positioning results of the stations at different latitudes, when the spherical harmonic expansion is expanded to the same degree, the positioning accuracy in low latitude areas is poor because the station is seriously affected by factors such as the ionosphere and water vapor, while the positioning accuracy at high latitude stations is the best. The proposed SPP-SH algorithm is also realized in the kinematic scene based on the dual-frequency data collected dynamically. The kinematic data is collected by an Android phone which supports receiving dual-frequency GPS observations. To validate the reliability of the SPP-SH algorithm, two strategies are designed to validate the results, which proves that the newly proposed method can be used for positioning with low accuracy in kinematic conditions.