Wyniki wyszukiwania - BazTech

1

Regional ionospheric model response of geomagnetic storm during March 2015 using data fusion mechanism: GPS, COSMIC RO and SWARM

Emmela Suneetha, Ratnam Devanaboyina Venkata

Acta Geophysica

|

2023

|

Vol. 71, no. 1

553--566

EN

The total electron content (TEC) maps are chosen as the elementary structures to provide ionospheric corrections for improving the positional accuracy for Global Navigational Satellite Systems (GNSS) users. Availability of total electron content data from a multi-constellation of satellite systems and various ground-based instruments possess an ability to monitor, nowcast and forecast the behavior of the ionosphere region. Conversely, combining ionospheric TEC data from different temporal and spatial scales is a difficult task to augment either ground or space-based ionospheric model's accuracy. And hence, a method like data fusion is essential to illustrate the ionospheric variability and to improve the accuracy of ionospheric models under equatorial ionization anomaly (EIA) conditions. This paper presented the weighted least square data fusion method with multi-instrument TEC data to analyze the EIA TEC structures in the low-latitude Indian region. Both ground-based (GPS TEC from 26 stations in the Indian region) and space-based (FORMOSAT-3/COSMIC RO and SWARM mini satellite constellation) observations are used for the analysis. The spherical harmonic function (SHF) model of order 2, which gives nine SHF coefficients, is implemented. The analysis illustrates that the SHF coefficients followed by TEC data fusion would be useful to investigate the entry, occupancy and exit TEC structures of EIA during geomagnetic storm conditions.

2

Ionospheric anomalies related to the Mw 6.5 Samar, Philippines earthquake

Eroglu Emre

Acta Geophysica

|

2023

|

Vol. 71, no. 2

601--611

EN

Models belonging to the ionosphere that is directly affected by factors such as solar activity, geomagnetic storm, earthquake, seasonal changes, and geographical location need to be considered altogether. In this sense, the cause of the ionospheric anomalies should be meticulously distinguished from each other. Ionospheric anomalies that occur before or (and) after an earthquake have a serious place in earthquake prediction studies. Total electron content (TEC) is one of the significant parameters to be able to discuss the anomalies of the ionosphere. This essay investigates ionospheric anomalies before and after the Mw 6.5 Samar, Philippines (12.025° N, 125.416° E and November 18, 2003, at 17:14 UT) earthquake. The paper analyzes anomalies with the aid of the TEC (TECU) map. In the paper, the time-domain TEC variables are transferred to the frequency-domain for observing some clues-peaks by short-term Fourier transformation spectral analysis. The discussion handles the effect of the solar activity with the F10.7 (sfu) index and the effect of geomagnetic storms with Bz (nT), v (km/s), P (nPa), E (mV/m), Kp (nT), and Dst (nT) parameters (index). The lower and upper boundaries of the TEC map obtained from the International Reference Ionosphere (IRI-2016) are calculated with the help of median and standard deviation. The boundary-setting process is named statistical analysis. TEC data exceeding the boundaries are marked as anomaly data. According to the paper, 11-day anomalies (9-day of which belong to pre-earthquake) are detected. Probably, the anomalies observed on November 6, 7, and 12 belong to the Samar earthquake.

3

Integrated observations on crustal strain‑ionosphere total electron content anomalies before the earthquake

Sharma Gopal, Singh Mutum Somorjit, Aggarwal Shiv Prasad, Romero-Andrade Rosendo

Acta Geophysica

|

2023

|

Vol. 71, no. 3

1173--1185

EN

Changes in strain (Linear and triangular) rate and Ionosphere Total Electron Content (TEC) before Mw 7.9 2018 Alaska Earthquake are investigated. Ten years of global positioning system (GPS) time series solutions were used for strain estimation in the region before the occurrence of the earthquake using the Haversine formula and triangulation method. Linear strain values suggest an anomaly in strain variation trend near the epicenter. Additionally, daily TEC variations for 30 days before the earthquake occurred were monitored and analysed. Analysis suggests TEC depletion on December 26 2017, and January 16 2018, respectively. TEC values from 60 GPS stations data were interpolated to study the spatial variations of TEC anomaly. Hourly TEC data derived from GPS stations on December 26 2017, and January 16 2018, suggest low TEC zone concentration near to the earthquake epicenter during 1 to 4 UTC. Spatial distribution of TEC values in 2-Dimension corresponding to anomaly time at 60 GPS stations in the vicinity of study area suggests lowest TEC values at stations that lie closer to the epicenter. The study suggests Lithosphere-Ionosphere coupling before Mw 7.9 2018 Alaska Earthquake and recommends developing a TEC-Strain Monitoring System for further validation of the work and for the better study of earthquake precursors based on TEC-Strain anomalies.

4

Seismo-ionospheric anomalies before M7.2 Haiti earthquake of August 14, 2021, from GPS TEC

Thomas Jewel E., Ben Ubong C., Ekanem Aniekan M., George Nyakno J., Nathaniel Ekong U.

Acta Geophysica

|

2022

|

Vol. 70, no 6

2621--2627

EN

Satellite-based measurements of total electron content (TEC) have been employed extensively to detect seismo-ionospheric anomalies. In this research, analysis of Global Positioning System (GPS) and TEC data obtained from three stations within seismogenic zone of M7.2 Haiti earthquake (EQ) of August 14, 2021, has been considered. A statistical procedure was used on daily TEC for the detection of anomalous and differential TEC. The study showed both reduction and enhancement in diurnal TEC within the investigative period on days −14,−11,−9,−7,−6, −4, −3, −1, 2, 3, and 4. Based on results, the three stations on days −11, −9, and −6 were concurrently perturbed. The outcomes of the analysis, which were constrained by data of synchronously monitoring geomagnetic indices of Kernnifzer digit (kp), disturbance storm time (Dst), solar indices (sunspot number (SSN) and F10.7 cm), revealed 82% seismic-induced anomalies relating to the EQ. The differential TEC |∆TEC| data were mostly remarkable on −6 and −4 days to the EQ, and this called for spatial mapping of TEC indices for August 8 and 10, 2021, over the epicenter of the EQ in order to check for atypical UT hours. Unusual ionospheric clouds from 16:00 to 20:00 UT enveloped the epicenter. Thus, this study has uncovered strong seismo-ionospheric anomalies from GPS-TEC data related to M7.2 Haiti EQ of August 14, 2021. This work is promising as short-term precursor of EQ in order to alleviate loss of lives and properties associated with this particular seismic event among others.

5

Annual and semi-annual variations of TEC over Nepal during the period of 2007–2017 and possible drivers

Ghimire Basu Dev, Gautam Bibek, Chapagain Narayan P., Bhatta Karan

Acta Geophysica

|

2022

|

Vol. 70, no 2

929--942

EN

The total electron content (TEC) variation of the ionospheric layer is mostly controlled by Geomagnetic and solar activity. The TEC of the ionosphere can be estimated using the satellite signal delay recorded at GPS sites. In this study, the TEC data from three nearby GPS stations (CHLM, BMCL, and LMJG) from Nepal are extracted for about 11 years period (2007–2017). For the computation of the TEC data, wavelet transform, global wavelet power spectrum, cross wavelet trans form, and wavelet coherence techniques are used. Utilizing such long-term GPS TEC data, Annual Oscillation (AO) and Semi-annual Oscillation (SAO) are identified in the daytime and nighttime TEC over Nepal. The SAO is found to be dominating periodicity in the daytime TEC, whereas the AO is found to dominant at night. In addition, possible connections with the indicators of geomagnetic and solar activity were studied. The geomagnetic indices AE and AU are exhibit a change in phase and are most consistent with both daytime and nighttime AO, implying that these indices could be the likely drivers of TEC’s AO and SAO periodicities. The Dst index, on the other hand, is recognized as the most prominent driver of SAO in both daytime and nighttime TEC.

6

Modelowanie modułów termoelektrycznych w programie SPICE - przegląd

Posobkiewicz Krzysztof, Górecki Krzysztof

Przegląd Elektrotechniczny

|

2021

|

R. 97, nr 2

1--5

PL

W artykule przedstawiono wyniki badań dwóch literaturowych modeli modułów termoelektrycznych dedykowanych dla programu SPICE. Przedstawiono topologię oraz równania opisujące te modele. Pokazano także wyniki weryfikacji ich dokładności poprzez porównanie wyników pomiarów i obliczeń wykonanych w programie SPICE. Niezbędne wartości parametrów wyznaczono w oparciu o dane producenta.

EN

In the paper results of research of two published in literature SPICE models of thermoelectric modules have been presented. Topology and equations describing these models, as well as results of experimental verification of their accuracy, based on comparison of results of SPICE calculation and measurements have been discussed. Required models parameters values have been calculated using manufacturer data.

7

TEC derived from local GPS network in Pakistan and comparison with IRI 2016 and IRI PLAS 2017

Mehmood Maria, Filjar Renato, Saleem Sajid, Shah Munawar, Ahmed Arslan

Acta Geophysica

|

2021

|

Vol. 69, no. 1

381--389

EN

The existing global network of continuously operating stand-alone GNSS reference stations provides an opportunity to estimate total electron content (TEC) from raw Global Positioning System (GPS) measurements. The TEC driven from a local GPS network in Pakistan was compared to two international models: IRI-2016 and IRI-PLAS 2017. The performance was analyzed statistically based on residual analysis, RMSE and correlation. It is observed that the TEC estimated by all three methods follows the same diurnal trend where it maximizes around noon (12 ∶ 00−14 ∶ 00LT) and reduces in the afternoon (15 ∶ 00−17 ∶ 00LT). Both empirical models provide a better estimation of nighttime TEC as compared to daytime TEC and exhibit maximum deviation in the month of April with the lowest deviation in December. The IRI-2016 underestimates TEC by 5 − 10TECU, whereas the IRI-PLAS 2017 overestimates TEC by 10 − 22TECU. However, the IRI-2016 conforms better to GPS-TEC (γ¯ = 0.9710) as compared to IRI-PLAS 2017 (γ¯ = 0.8337). The study shows that local GNSS stations in collaboration with TEC estimated from global models may be used in development of an efcient local TEC model over Pakistan which will not only assist in local ionosphere studies but also aid in improving the positioning accuracy.

8

Study of local ionospheric plasma perturbation induced by pre-seismic activities

Mahmoudian A., Saravani Ghayour A.

Acta Geophysica

|

2021

|

Vol. 69, no. 5

1585--1595

EN

The pre-seismic ionospheric anomalies coupled through well-proposed lithosphere–atmosphere–ionosphere processes are known to cause pre-seismic ionospheric disturbances (PIDs). The present paper investigates the regional variation of ionospheric densities in the Iran area with the purpose of anomalous ionospheric detection. The ionospheric reference model (IRI) is employed to examine the accuracy of such empirical models for typical TEC (total electron content) values in Iran to determine any deviation from the normal ionospheric state. Two strong consecutive earthquakes with a magnitude of larger than 6 in the northeast of Iran were selected along with the GPS data from 5 ground stations within 50 km of the epicenter. The local ionospheric plasma density mapping using the GPS signal for earthquake prediction is studied. The results show a very promising temporal variation of local ionospheric plasma between the stations from 4 weeks to almost a week leading to the event. The deviation of TEC from the mean value between the fve stations shows no enhancement or suppression of local plasma rather than a plasma motion. A very quiet PID signature could validate the lithosphere– atmosphere–ionosphere coupling (LAIC) process associated with pre-earthquake geochemical and dynamical mechanisms. To validate that the analyzed time period falls on the minimum of solar activity, the observed positive anomalies in the regional TEC correspond to fuctuations to pre-earthquake activity and not to geomagnetic activity, and the Kp and Dst indices are taken into consideration.

9

Deep learning for ionospheric TEC forecasting at mid latitude stations in Turkey

Ulukavak Mustafa

Acta Geophysica

|

2021

|

Vol. 69, no. 2

589--606

EN

Earth’s ionosphere is an important medium for navigation, communication, and radio wave transmission. The inadequate advances in technology do not allow enough realization of ionosphere monitoring systems globally, and most research is still limited to local research in certain parts of the world. However, new methods developed in the feld of forecasting and calculation contribute to the solution of such problems. One of the methods developed is artifcial neural networks-based deep learning method (DLM), which has become widespread in many areas recently and aimed to forecast ionospheric GPS-TEC variations with DLM. In this study, hourly resolution GPS-TEC values were obtained from fve permanent GNSS stations in Turkey. DLM model is created by using the TEC variations and 9 diferent SWC index values between the years 2016 and 2018. The forecasting process (daily, three-daily, weekly, monthly, quarterly, and semi-annual) was carried out for the prediction of the TEC variations that occurred in the frst half-year of 2019. The fndings show that the proposed deep learning-based long short-term memory architecture reveals changes in ionospheric TEC estimation under 1–5 TECU. The calculated correlation coefcient and R2 values between the forecasted GPS-TEC values and the test values are higher than 0.94.

10

Algorithm for modeling electromagnetic channel of seismo-ionospheric coupling (SIC) and the variations in the electron concentration

Rapoport Yuriy, Grimalsky Vladimir, Krankowski Andrzej, Pulinets Sergey, Fedorenko Alla, Petrishchevskii Sergei

Acta Geophysica

|

2020

|

Vol. 68, no. 1

253--278

EN

We present in detail the algorithm of the electrostatic–quasi-stationary–electromagnetic/MHD approximations and equivalent external sources (EQUEMES method) to develop the quasi-stationary–electromagnetic models of seismo-ionospheric coupling. The penetration of the electromagnetic feld created by near-Earth alternative currents of ULF range was simulated by solving equations for the horizontal electric feld components Ex, Ey of the second order with respect to the vertical coordinate z. This system of two second-order equations is derived from the system of Maxwell equations. The penetration of rather strong horizontal electric feld [of order of (1–10) mV/m] to the ionospheric E and F layers has been modeled. The corresponding variations in the electron concentration in the E and lower F layers of the ionosphere reach a value of order of (1–10)%. Farther increase in these variations can be connected with the related synergetic processes. A possibility of the efective initiation of electron concentration perturbations in the unstable near-equatorial plasma in the F layer of the ionosphere by the packet of atmospheric gravity waves radiated by the near-ground source is illustrated. A good correspondence of the results obtained on the basis of this model to the data of satellite observations is shown.

11

Total electron content and scintillations over Maseno, Kenya, during high solar activity year

Omondi G. E., Baki P., Ndinya B. O.

Acta Geophysica

|

2019

|

Vol. 67, no. 6

1661--1670

EN

Proper characterization of total electron content (TEC) and scintillation is very important to global positioning system (GPS) users in communication, navigation, ionospheric or atmospheric studies. Quiet time variation of TEC is useful in the estimation and removal of ionospheric delay for global navigation satellite systems single-frequency positioning. During geomagnetic storms, the variations of ionosphere deviate from their quiet day pattern and can cause significant effects on short-term prediction of various ionospheric parameters. The dynamics of the ionosphere change from region to region; therefore, in order to evaluate and improve the performance of global models of the ionosphere, numerous studies of variations using measured ionospheric parameters from stations globally are useful. This paper presents for the first time variations in the TEC and scintillation at Maseno University (geomagnetic coordinates, 9.64°S, 108.59°E), Kenya, investigated using a NovAtelGSV400B GPS receiver for the high solar activity year 2014. The GPS-measured TEC values were compared with the modeled TEC values by the latest International Reference Ionosphere model (IRI-2016), with a view to evaluate the performance of this version of the model. The largest TEC values were observed from 1300 to 1500 h local time throughout the year with the largest diurnal values occurring in March equinox and smallest during June solstice. The largest TEC values are attributed to extreme ultraviolet radiation coupled with upward →E ×→B plasma drift velocity. Nighttime enhancements in TEC attributed to the ‘fountain’ effect occurred during some months. Scintillation correlated with depletions in TEC occurred in the period between 1600 h local time to 1900 h local time (post-sunset) sector during some months, with the strongest value of − 0.91 being experienced in March equinox. Scintillation was absent during geomagnetic storms studied mainly as a result of the time of onset of the recovery phases of the storms. In addition, the geomagnetic storms were manifested in GPS-measured TEC as negative ionospheric storms. The IRI-2016 model gave a good prediction of measured values except for its overestimation of measured TEC in the months of May and June. Further, a new insight shown by the results is the ability of the IRI-2016 model to predict post-sunset TEC enhancements during some months contrary to previous versions reported by other researchers in East Africa. However, model is not quickly sensitive to transitions from one season to another. This result contributes to the improvement of the current IRI model by recommending the introduction of an input into the model that is sensitive to transitions in seasons in future versions of the model.

12

Sibsonian and non-Sibsonian natural neighbour interpolation of the total electron content value

Kotulak K., Froń A., Krankowski A., Pulido G. O., Henrandez-Pajares M.

Acta Geophysica

|

2017

|

Vol. 65, no. 1

13--28

EN

In radioastronomy the interferometric measurement between radiotelescopes located relatively close to each other helps removing ionospheric effects. Unfortunately, in case of networks such as LOw Frequency ARray (LOFAR), due to long baselines (currently up to 1500 km), interferometric methods fail to provide sufficiently accurate ionosphere delay corrections. Practically it means that systems such as LOFAR need external ionosphere information, coming from Global or Regional Ionospheric Maps (GIMs or RIMs, respectively). Thanks to the technology based on Global Navigation Satellite Systems (GNSS), the scientific community is provided with ionosphere sounding virtually worldwide. In this paper we compare several interpolation methods for RIMs computation based on scattered Vertical Total Electron Content measurements located on one thin ionospheric layer (Ionospheric Pierce Points—IPPs). The results of this work show that methods that take into account the topology of the data distribution (e.g., natural neighbour interpolation) perform better than those based on geometric computation only (e.g., distance-weighted methods).

13

Comparative analysis of three ionospheric broadcast models for global navigation satellite systems

Li S., Li L., Wang S., Peng J., Xu Y., Zhao Y.

Acta Geophysica

|

2017

|

Vol. 65, no. 2

395--410

EN

An ionospheric model and corresponding coefficients broadcasted via GNSS navigation message are generally used to estimate the time delay for single-frequency GNSS users. In this article, the capabilities of three ionospheric models, namely, Klobuchar model, NeQuick Galileo version (NeQuick G), and Neustrelitz TEC broadcast model (NTCM-BC), were assessed. The models were examined in two aspects: total electron content (TEC) prediction and ionospheric delay correction effects in single-point positioning. Results show that both NeQuick G and NTCM-BC models outperformed Klobuchar model for predicting global TEC values during all the test days. Compared with Slant TEC (STEC) along the receiver-to-satellite ray path derived from IGS global ionosphere map (GIMs), STEC from NeQuick G and NTCM-BC models tend to have less bias than those from Klobuchar model in most situations. The point positioning results were improved by applying ionospheric broadcast models especially at the mid- and low-latitude stations.

14

Wykorzystanie ogniw Peltiera w układach chłodzących pojazdów autobusowych

Pniewski R., Kowalik R., Sadowski E.

Autobusy : technika, eksploatacja, systemy transportowe

|

2016

|

R. 17, nr 6

1083--1086

PL

W artykule omówiono zjawisko Peltiera z naciskiem na analizę modelu matematycznego opisującego zjawiska zachodzące na elemencie półprzewodnikowym odpowiedzialnym za regulacje temperatury. Zaprezentowany model matematyczny wykorzystany do opracowania programów symulacyjnych, z których uzyskane wyniki zaprezentowano w końcowej części referatu. Przedstawiono również opis możliwości wykorzystania ogniw Peltiera jako elementów wspomagających układ klimatyzacyjny w autobusach.

EN

Article shows the Peltier effect with emphasis on the analysis of the mathematical model describing the phenomena on semiconductor element responsible for regulating the temperature. Presented mathematical model used to develop simulation programs, of which the results were presented in the final part of the paper. Also contains a description of the possibilities of using a Peltier element supporting the air conditioning system in the buses.

15

Variability of Ionospheric TEC and the Performance of the IRI-2012 Model at the BJFS Station, China

Li S., Li L., Peng J.

Acta Geophysica

|

2016

|

Vol. 64, no. 5

1970--1987

EN

We studied variation characteristics of ionospheric total electron contents (TEC) and performance of the International Reference Ionosphere (IRI)-2012 model in predicting TEC at the BJFS (Beijing Fangshan station), China. Diurnal and seasonal variations were analyzed with TEC data derived from dual-frequency global positioning system (GPS) observations along with the solar activity dependence of TEC at the BJFS station. Data interpolated with information from IGS Global Ionosphere Maps (GIMs) were also used in the analysis. Results showed that the IRI-2012 model can reflect the climatic characteristics and solar activity dependence of ionospheric TEC. By using time series decomposition method, ionospheric daily averaged TEC values were divided into the periodic components, geomagnetic activity component, solar activity component and secular trend. Solar activity component and periodic components are supposed to be the main reasons which account for the difference between the GIMs TEC and the TEC from the IRI-2012 model.

16

Determination of parameters of the Peltier module without interference in its structure

Błażewicz A., Toborek K.

Prace Instytutu Elektrotechniki

|

2011

|

Z. 251

57-65

EN

This work describes new method to determine parameters of Peltier module. Classical method requires module to be disassembled, rendering it useless after the experiment. Described new method does not require interference in structure of the module allowing it to be used after experiment. This is helpful in designing of new modules, where there is few samples to test.

PL

Praca opisuje nową metodę wyznaczania parametrów modułów Peltiera. Metody klasyczne wymagają rozmontowania modułu, co powoduje jego zniszczenie. Prezentowana metoda zapewnia precyzyjny pomiar parametrów modułu Peltiera bez konieczności ingerencji w jego fizyczną strukturę. Jest ona szczególnie pomocna przy wytwarzaniu i testowaniu modułów prototypowych.

17

Ionospheric trough in GPS signal

Świątek A.

Acta Geophysica

|

2008

|

Vol. 56, no. 4

1162-1178

EN

The article presents research conducted by means of the GPS technique through TEC (Total Electron Content) computation for individual satellites. The proposed method makes it possible to investigate small ionospheric structures. For strong ionospheric disturbances, at high and middle latitudes, one can observe a ionospheric trough shift towards the lower latitudes. The results presented in this paper were obtained for strong disturbances observed in October 2003. The paper shows a comparison for chosen quiet and strongly disturbed days. To avoid differences caused by changing position of the Sun (seasonal zenith angle changes), all the analysed information was related to the same period of time.

18

GPS observations at quasi-conjugate points under disturbed conditions

Momani M.A., Mohd Ali M.A., Yatim B., Abdullah M., Misran N.

Acta Geophysica

|

2008

|

Vol. 56, no. 4

1179-1201

EN

The conjugacy effects of the GPS scintillation activities during the geomagnetic storms of October 2003, November 2003 and July 2004 have been investigated at the approximately geomagnetically conjugate stations: Scott Base, Antarctica (SBA) and Resolute Cornwallis Island (RESO) in the high Arctic region. The measurements aim at investigation of the similarities and differences of the scintillation activities occurring at the conjugate points in the polar regions under storm conditions and examine the relationship between the Storm Enhanced Density (SED) and scintillation activity. The measurements of the scintillation activities obtained from total scintillation index during these storm periods at both hemispheres showed asymmetry in the ionospheric scintillation occurrence at the conjugate points. Pronounced scintillation activity was observed at the nightside hemisphere with the total scintillation index higher than at the dayside hemisphere. The results also show that the durations of severe scintillation activity were longer at the nightside hemisphere. The measurements showed that the intense scintillation periods were corresponding to the presence of the SED events where more pronounced SED events were observed over the nightside hemisphere.

19

MOF/MUF behavior over one European path

Maltseva O.A., Barabashov B.G., Rodionova V.T., Shlyupkin A.S.

Acta Geophysica

|

2007

|

Vol. 55, no. 3

424-440

EN

Many applications of HF propagation via the ionosphere (e.g. bearing-fingers, single station location, emergency systems and so on) demand an accurate description of ionospheric conditions. The International Reference Ionosphere (IRI) model is very often used for such a description. A lot of publications were devoted to the verification and improvement of this model. But most of them were based on data from vertical sounding (VS). Not so many comparisons with oblique sounding results have been reported. Specifically, this concerns parameters of the maximum usable frequency (MUF) and a ground range, D. In this paper errors of MUF and D determination by means of the IRI model are estimated on the example of the MOF data on Inskip–Rome path for December 2003. Adaptation of the model to current conditions by means of VS and total electron content TEC-GPS data is used to reduce these errors.

20

Effects of ionospheric horizontal gradients on differential GPS

Abdullah M., Strangeways H.J., Walsh D.M.A.

Acta Geophysica

|

2007

|

Vol. 55, no. 4

509-523

EN

This paper outlines the effect of horizontal ionospheric gradients on transionospheric path propagation such as for the case of GPS signals. The total electron content (TEC) is a function of time of day, and is much influenced by solar activity and also the receiving station location. To make the model applicable for long baselines, for which the ionosphere is not generally well correlated between receiving stations, the ionospheric gradients should be taken into account. In this work the signal path is determined using a modified ray-tracing technique together with a homing-in method. Results show that horizontal gradients can have a significant effect on GPS positioning for both single station positioning and differential GPS. For differential GPS, the ionospheric delay can, however, be either increased or decreased compared with the case of no gradient, depending on the gradient direction.