فهرست مطالب جمال عسگری

The effect of troposphere on the signals emitted from global navigation satellite system (GNSS) satellites, appears as an extra delay in the measurement of the signal traveling from the satellite to receiver. This delay depends on the temperature, pressure, humidity as well as the transmitter and receiver antennas location. In GNSS positioning, tropospheric delay effects on accuracy of different components of obtained coordinates. In RTK networks the amount of this parameter is determined by solving double difference observation equations between reference stations and then is interpolated for rover receiver. Tropospheric delay consists of a wet part and a dry part. The dry part that forms about 90 percent of total delay, is related to station height. So in the cases that the height of rover station is significantly different from the average height of reference stations, reduction in accuracy of interpolation is expectable. To investigating this issue, in this article we compared interpolation accuracy of double difference tropospheric delay in two networks with different structure. In both of networks, we have a central receiver that is surrounded with four other receivers. We considered the central receiver as rover station and the others as reference stations. The main difference between these networks is about stations height. In the first network that is named Sima, the difference between the height of rover station and average height of reference stations is 122 meters. The amount of this parameter is 1095 meters for the second network that is named Ebry. To comparing the accuracy of tropospheric delay interpolation in these networks, we determined zenith tropospheric delays (ZTD) for all stations by processing GNSS observations using CSRS-PPP (Canadian Spatial Reference System – Precise Point Positioning) online service. Then we selected the nearest reference station to rover as master reference station. In the following we identified the satellites that were visible in 100 epochs for all stations. Between these satellites, one of them with the most elevation angle was selected as reference satellite. ZTD’s were converted to slant tropospheric delay in satellite-receiver direction using global mapping function. Then double differenced tropospheric delays between the reference satellite and the others and between the master reference station and other reference stations, were determined. Finally this parameter was computed for the position of rover station using interpolation with a two parameter linear equation. After computing RMSE (Root Mean Square Error) of interpolated values, we found that the accuracy of interpolation decreased significantly in the second network. Therefore we can conclude that the difference between the height of rover station and the height of reference stations, has a direct effect on accuracy of tropospheric delay interpolation in RTK networks. So in the following of the article, we introduced a new method to eliminate height variations effects on interpolation accuracy of tropospheric delay. After using this method RMSE of interpolation decreases from 32 mm to 9 mm in the first network and in the second network decreases from 228 mm to 14 mm. in other words we have 69.2 and 93.7 percent of accuracy improvement in these networks. Due to these results, we expect a positive effect on positioning accuracy by applying this method in RTK networks.

The troposphere is a layer of atmosphere that consists of dry gases and water vapor, which causes a time delay in the emission of electromagnetic waves resulting in an error in determining the precise position. In space geodesy, normally, the travelling time of the wave between an emission source in space (a satellite for GNSS or a quasar in VLBI) and a receiver located in a geodetic station on the surface of the Earth is measured. This time is then converted to distance by the speed of light in vacuum. There are two ways to manage the atmospheric delays in space geodetic data analysis; either, external measurements of the atmospheric delays are used to correct the measurements or, the atmospheric delays are estimated in a least square adjustment as the unknowns. To model this error using the first strategy, several methods have been proposed, among which, the most prominent ones are the three dimensional (3-D) ray tracing and the use of mapping functions. 3D ray tracing is considered to be a direct method for this estimation and the actual path of the wave which is curved, is estimated by using Eikonal equation and is compared with the theoretical straight path. It means we can find the amount of correction which should be considered. Contrary to this method, the use of mapping functions is considered as indirect method and by using proper functions, the amount of delay (hydrostatic and non-hydrostatic) in the vertical direction is plotted in the desired direction. The basic assumption in this method is to take the azimuth symmetry for the troposphere into considerations and therefore, the amount of delay will depend only on the elevation angle. In this paper, comparisons have been made between this method and the method of using mapping functions that are commonly used.
Based on this research, it is determined which method to be used in different conditions to achieve the desired accuracy for space geodesy techniques such as GNSS and VLBI, and which method is the priority. In this comparison, VMF (Vienna Mapping Function) and GMF (Global Mapping Function) which are used widely in space geodetic techniques were used. Coefficients in these mapping functions are obtained based on Numerical Weather Models (NWMs) and specially ECMWF. VMF is called Isobaric Mapping Function (IMF) based on the older mapping function, and GMF function has been created with changes in VMF, so that it can be used offline in some software including VieVs software. To this end, data from two observation campaigns managed by IVS (International VLBI Service) namedCONT08 and CONT11 have been used in the years 2008 and 2011 for VLBI stations. These two campaigns involve 15 days continuous observations. The results of this study show that the station with the highest humidity (KOKEE) requires ray tracing at all intervals of accuracy and mapping functions cannot be used to produce reasonable accuracy. Also, in order to achieve the accuracy of less than 10 mm in the station's elevation, it is necessary to use ray tracing at almost all angles of elevation, or in order to achieve the accuracy of less than 20 mm, it should be used at the angles of elevation of approximately 0 to 35 degrees, and mapping functions can be used for the rest of the angles of elevation.
Based on the diagrams and tables presented in this paper, the following results can also be extracted:-Use ray tracing method at the station with the highest humidity (KOKEE)
-Use ray tracing to achieve an accuracy of better than 10 mm for the stations’ elevation at all angles of elevation 
- Use ray tracing to achieve an accuracy of better than 20 mm for station’s elevation of approximately 0º to 35 º of the angles of elevation. Mapping functions can be used for the rest of the angles of elevation.
-Use ray tracing to achieve an accuracy of better than 30 mm for the station’s elevation of 0 to 26 degrees of the angles of elevation. Mapping functions can be used for the rest of elevation angles.
-At angles of elevation which do not require ray tracing, mapping functions are used. It can be said that in 2008, finally, GMF mapping function achieved a better accuracy than the VMF, while in 2011, the performance of VMF mapping function was better than that of GMF.

Global Satellite Navigation Systems are widely used for geodetic and geodynamics purposes. However the meteorological applications, such as Precipitable Water Vapor (PWV) estimation, are increased with GNSS permanent stations deployments all over the world. The continuity of GNSS observations and the spatial resolution of the permanent GNSS stations are some of the potentials of GNSS remote sensing using permanent arrays. In this study we are demonstrated one of the real-time meteorological applications of GNSS networks.
The spatial distribution of PWV was investigated during extreme rainfall. The PWV data from the SuomiNet network stations in the Texas state was implemented. Using linear interpolation, the PWV were determined for area within the stations.
It was observed that the estimated water vapor from the GNSS observations progresses gradually towards the precipitation site and then, with accumulation in the area of ​​precipitation, the rainfall begins, and then the PWV decreases. Therefore, using a network of uniformly distributed GNSS stations, GNSS observations can be used to measure the accumulation of atmospheric precipitation in a region and to investigate the probability of rainfall occurring. These predictions will be effective if the network is sufficiently dense and the perceptible water vapor is estimated with a short latency.
The estimation of zenith path delay from GNSS is possible using relative or absolute method. Furthermore the slant delay estimation is one of the possibility in the dense GNSS networks. Tropospheric tomography will aid the scientists in the future applications of GNSS. In this paper the precision of real time PWV estimation via GNSS data is investigated. French RGP GNSS networks data are used for PPP processing. The processing is performed by ultra-rapid IGS orbit and clock products and then it repeated using final IGS products. The precision of Zenith Total Delay (ZTD) of final ephemeris is about 3 mm. The Real time estimation of ZTD using ultra rapid data is compared by final solution and the RMSE for different stations are from 3 to 7 mm approximately that is sufficient for real time estimation of PWV and real time precipitations prediction. Investigation of raining occurrence and the PWV changes is performed in this paper.
In the investigation of PWV it may be possible to follow a pattern or patterns for a region prior to intense rainfall, spatial variations and spatial distribution of PWV, which can predict extreme rainfall. Therefore, it is suggested that by studying the PWV behavior accurately, the probability of such patterns is examined. Also, in order to determine the accuracy of the PWV obtained from GNSS observations by the PPP method with the ultra-rapid orbit and clock products, it is possible to compare the PWV obtained from the above-mentioned method with those obtained from the measurement of radiosondes as a reliable source. Also the results of the ultra-rapid products are compared with the final IGS products the consistency is about 3-7 millimeters for the estimated ZTD values.
It is also possible to predict the rainfall by the permanent GNSS stations in Iran. There are several permanent arrays which may provide the GNSS observation files instantaneously. The national geodynamic network, the Tehran's Instantaneous Network, The national cadastre RTK network and the Isfahan municipality RTK network, could be used for PWV estimation with high spatial and temporal resolution and instantaneous meteorological application of a unified network is possible.

Tidal observations have been widely used for a variety of applications. Realistic functional and stochastic models of tidal observation are then required. The functional model is complete if one knows the tide characteristics such as tidal frequencies (M2 and S2 for instance). The stochastic model is complete if we know noise characteristics of tidal observations. There is always a prediction error between the predicted values and the observed tide heights. This can be investigated when taking the noise characteristics of tidal time series observations. Functional model identification is however the subject of discussion in the present contribution. Tide data are frequently used for different applications such as safe navigation. Real tide gauge data can be expressed by their tidal constituents (frequencies) and a noise structure. Using tidal frequencies and tidal observations one can employ the functional model to predict tide. Therefore identifying tidal frequencies is an important issue for tidal analysis. So far, most of the available methods to determine tidal frequencies have been based on the theory, and sea level height observations have not seriously been used to extract tidal frequencies. The theory-based methods usually apply the ephemeris of Moon, Sun and other planets to extract tidal frequencies without the use of tidal observations. Following-up the study by Amiri-Simkooei et al. (2014), we further focus on extracting tidal frequencies using tidal observations. For this purpose, we apply the least squares harmonic estimation (LS-HE) to the multivariate tidal time series. As a generalization of the Fourier spectral analysis, LS-HE is neither limited to evenly spaced data nor to integer frequencies. We may also note that the main tidal constituents may change from one area to another area. In this contribution, we use the data sets of eight coastal tide gauge stations in Persian Gulf and Oman Sea between 1999 and 2010 with a sampling rate of 30 min using a multivariate analysis. In multivariate analysis, the frequencies contributed in tide structure are more obvious than in the univariate analysis. Such signals can thus simply be detected in the multivariate analysis. Using the above-mentioned data, 414 main tidal constituents have been extracted. Our extracted lists of frequencies (of the Persian Gulf and Oman Sea) are compared with the two lists of frequencies consisting of 50 and 121 frequencies by the study of Amiri-Simkooei et al. (2014), which was applied to UK tide gauge stations. In the present contribution, new frequencies that belong to the tide gauge stations of the Persian Gulf and Oman Sea have been identified. Finally, a six-month prediction is performed for all stations using the two lists of main frequencies obtained in the two studies. The prediction results of the two studies are then compared using the estimated root mean squared error (RMSE). The RMSE difference of our predicted data show a reduction ranging from 2 cm to 7 cm compared to that predicted using the frequency lists of Amiri-Simkooei et al. (2014). The estimated RMSE of tide prediction using the frequencies obtained in this study ranges from 9 to 16 cm.

Coordinate systems transformation has an important role in mapping activities, geodesy and spatial science. New and efficient methods are needed in order to increase the accuracy in the transformation between these systems. The main purpose of this article in the first part, is a local coordinates transformation in Isfahan City to UTM coordinates
and vice versa. This method is based on the combined scale factor. So, the coordinates of 500 GPS stations in Isfahan City was used,and with reduction of distanceson the surface of the earth to the map, coordinates of the GPS points in the local system was calculated.Study on changing of combined scale factor for the GPS points of Isfahan City shows that if a unit scale factor is used for whole the city, in long lengths occurs a few decimeter differences and it is not suitable for accurate mapping. LIDAR is a mature remote sensing technology which can provide accurate elevation data for both topographic surfaces and above-ground objects. So in the second part of the article, we presented an algorithm to provide height interpolation for the points in the passage network of Isfahan City by using LIDAR data,because the inverse transformation from local system to UTM using new methods such as Rational Functions, needs vertical component in addition to horizontal position of points. A height bias of 30 centimeter has been detected in the LIDAR data using GPS control points. After removal of this systematic component, the final RMSE of LIDAR heights are 43 centimeters.

In traditional hydrographic surveys, chart datum is usually determined using spectral analysis of coastal tide gauge observations based on the lowest water level. Due to the variation of tidal amplitude and phase components in different locations, such chart datum is only valid in coastal areas around the tide gauge stations; it is then hardly accurate when a few tens of kilometers away from the tide gauge stations in the off-shore areas. This study models the separations between the elliptical reference WGS84 and the chart datum using the data collected by the satellites Topex/Poseidon and Jason-1 for the periods of 1992-2002 and 2002-2008 in Persian Gulf and the coastal tide gauge data of the Oman Sea. The major advantages of the technique used in this study are highlighted as follows. The satellite altimetry observations on the shores and also in the shallow water is not of good accuracy and precision. An appropriate solution to this problem is to use coastal tide gauge observations near the time series generated from the satellite observations. On the other hand, chart datum determination based on the coastal tide gauge observations is suitable only for the areas close to the coastal tide gauge stations. However, due to the amplitude and phase variations of the tidal components in different parts of the sea, the accuracy of such a chart datum is not appropriate for the areas that are far away from the tide gauge stations. In this study, the satellite altimetry observations are combined with the data obtained from the coastal tide gauge stations. Due to the existence of point-wise time series in the study area and also creation of the “quasi tide gauge” points using the satellite altimetry observations, both of the problems mentioned above (i.e. weakness of the satellite altimetry observations and the chart datum determination based on the use of the coastal tide gauge observations only) can be solved. This will then lead to higher accuracy of the chart datum determination in the entire area. To achieve higher accuracy, observations of the tide gauge stations are also used. It is because the distances between the tide gauge stations and the time series obtained from the satellite observations are considerably large (sometimes more than 20 km). Therefore, this combination will lead to the establishment of a regular and continuous network of tide gauge observations in the entire area having acceptable accuracy. To determine this model, sea level variations due to the tide, polar motion variations, plates tectonic movements and all the factors affecting the potential tide with significant components (M2, S2, K1, O1) and even less important components such as signals with the period of 14 days, monthly, semi-annual, annual, 8.5 year and 18.6 year are considered in the case study area. It is also highlighted that because the satellite altimetry observations are only available on periods of 9.915 days, the high-frequency tidal signals cannot be detected using these data. Therefore, these frequencies are also included into the functional part of the model. Based on the above strategy, the separation between the elliptical reference and the chart datum has been computed by comparing the tide gauge data and the satellite altimetry data for the period of 2002-2005.

Due to wide spread usage of the satellite positioning techniques especially GPS, we need to precisely determine geoid model in order to use GPS measurements for height determination, as an alternative of traditional leveling techniques in geodetic applications. Precise local geoid modelling using GPS/Leveling data, apart from the existing models such as geopotential models and gravimetric geoid models could be an interesting investigation topic. An important question is, ‘What accuracy level can be achieved using this approach?’ However precession of this modelling could be influenced by some issues such as data quality or modelling techniques. In this paper, we attempt to assess the implementation of modern learning-based computing techniques including artificial neural networks and adaptive network-based fuzzy inference systems compared with multivariate polynomial regression equations in GPS/Leveling Geoid modeling. This assessment carried out in a small and dense network of GPS/Leveling benchmarks in contrast with previous studies, located in shahin-shahr, Isfahan. And these high quality data make it possible to achieve an accuracy of better than 1 cm. The results show a few millimeter superiority of ANN and ANFIS derived geoid models in terms of root mean square error, as well as in terms of coefficient of determination. And RMSE=8cm, R2=0.9949 and RMSE=7cm, R2=0.9964 achieved for this models respectively. Therefore ANFIS derived geoid model provide the most accurate geoid heights in the study area.

One important source of errors on GNSS signals is the ionospheric effect. This layer of the atmosphere is filled with charged particles. Ionospheric effects on the waves are dependent on the amount of TEC. This paper uses the least square harmonic estimation (LS-HE) that is one of the analytical methods in the frequency domain. We used the vertical TEC values obtained from GIM models with global cover provided by the JPL analysis center. We use 15 years of bihourly data gathered from the 152th day in 1998 to the first day of 2014. We first determine the important periodic signals by applying the univariate and multivariate harmonic estimate on the TEC time series. The multivariate analysis revealed the presence of daily periodic signal with its higher harmonics and annual period with its higher harmonics. We then calculate the spectral power of a number of identified signals in all available data range. The result indicate that the higher harmonics of the daily signal (tri and quad diurnal) show their maximum spectral values in the dip equator. This indicates that the earth's magnetic field is one of the cause, to these provide patterns.

During last two decades Precise Point Positioning has been considered as one of the most important methods in satellite geodesy. Despite the efforts to improve the PPP precision, this method has not yet achieved the precision of Relative positioning methods. Most of the efforts on PPP improvement focus on the processing models and phase ambiguity. Modeling the tropospheric delay is very crucial to achieve high precision in Precise Point Positioning. There are different methods to estimate this delay such as ray-tracing or using appropriate mapping functions e.g. GMF, VMF,, …, which relate the zenith path delay to slant path delay.In this paper, the ray-tracing slant path delay has been used as a reference value. Then three other delays are calculated using zenith path delay obtained from PPP and Global mapping function in different ways. The difference between the delay computed by ray-tracing method and those three other delays is applied to the RINEX observation files. The new RINEX files are implemented for PPP reprocessing. Comparing the achieved results, with the ITRF coordinates of points, shows that applying the difference of slant path delay from ray-tracing and slant path delay which is computed by zenith path delay of PPP (using 88% of hydrostatic global mapping function and 12% of non-hydrostatic global mapping function) to the RINEX files, improve positioning accuracy.

Geodetic data processing usually is performed using the least-squares method. To achieve the best linear unbiased estimation، it is necessary to use the proper and realistic stochastic model of the observables. The estimation of the unknown (co) variance components of the observables is referred to as variance component estimation (VCE). In geodetic applications، VCE is also known as the observables weights estimation. In this paper، least-squares variance component estimation is applied in a straightforward manner to GPS observables for determination of the realistic stochastic model. For this purpose، the functional model used in the analysis is the GPS geometry-based observation model (GFOM). The numerical results for two receivers، namely Trimble 4000 SSi and Trimble R7، are presented. The results indicate that the correlation between observation types is significant. A positive correlation of 0. 55 is observed between the code observations on CA and P2 for Trimble 4000 SSi. Also، a significant positive correlation of 0. 64 is observed between the phase observations on L1 and L2 for Trimble R7.

Tropospheric delay is one of the main error sources on GNSS measurements. Neutral atmosphere refraction causes Tropospheric bias. One may uses GNSS observations to estimate the zenith tropospheric delay on static mode but kinematic tropospheric delay estimation is not a standard method. The kinematic estimation is in particular importance for hydrographic community whereas they have GNSS receiver onboard. The distance of these receivers to mainland stations are rather long for kinematic tropospheric estimation. The Precise Point Positioning (PPP) method is an alternative to traditional relative positioning methods. In this paper this approach is developed using Bernese 5 software and the NRCAN online PPP service (CRS-PPP). A static observation is used as a reference data for kinematic results. The results are rather promising for atmospheric applications of GNSS over oceans and open seas.

Ray-tracing is a solution for tropospheric delay estimation, which recently has found an important role in space geodesy techniques. There are different data sets, which can be considered as input of this method, for example numerical weather models, rdiosonde observations and direct measurements. We have developed a constrained ray-tracing method for estimation of tropospheric total delay based on surface meteorological parameters, radiosonde observations and numerical weather models. We show results of two different methods (regional and zonal) and compare with ray-tracing using only numerical weather models. We can find that discrepancies between these methods come mainly from nonhydrostatic component, which means uncertainty in wet observations. In addition, as validation of methods, we compare our results with results of a comparison campaign, which was carried in first half of 2010 under umbrella of the IAG working group 4.3.3. The comparison shows an agreement between results, particularly in terms of slant factors.

GNSS kinematic techniques provide precise coordinates from short observations time span, or even while the receiver is moving. The accuracy of stop and go kinematic methods is lower than static method, while the required time for processing is shorter. Augmenting the GNSS kinematic equations by constraints increases the degrees of freedom and the accuracy of the estimated unknowns. These constraints could be derived from geometric relations between receiver positions during the observations. In this contribution the constraint which is added to the system is a circle. Application of this known constraint increases the accuracy of the estimated unknowns. Meanwhile the designed and the estimated radiuses will identical by the hundredths of a millimeter level (for simulated RINEX observations). In this paper stop and go kinematic positioning with virtual observation by known constraint (the center and radius of the circle assumed to be known) and unknown constraint (the center and radius of the circle assumed to be unknown) was carried out. The results of these two constraints were similar, in other words if the center and radius of the circle are unknown, prior to constraint implementation, one can compute these parameters with estimated GNSS positions. Kinematic positioning with true observations was carried out applying constraint. The results state that the constraint increases the accuracy of processing, especially in horizontal component. Again the computed radius from processed coordinates was equivalent to the designed one.

Different application of GPS position time series in geodetic and geophysical studies such as plate tectonics, glacial isostatic rebound, crustal deformation and earthquake dynamics requires proper assessment of the time series. A functional model for GPS time series consists of a linear trend, periodic signals with annual and semiannual periods and probabilistic offset. The undeterministic effects can best be described as a noise. The correct detection of offset requires a proper estimation of noise and the covariance matrix of the data. Towards this end, the least-squares variance component estimation is used. It is shown that how a correct analysis of the noise components can affect the offset detection method. Ignoring colored noise of GPS time series degrade the offset detection power. We first use the univariat time series analysis. To increase the offset detection power, the multivariate analysis is then recommended. In univariat analysis, only one of the coordinate components is used, while in the multivariate analysis all three components, which is assumed to have the same structure of noise and offsets, are simultaneously used. In this paper, some simulated daily time series of positions during 8 years are used. Finally, offsets having different size and positions are located through them and detected successfully, using the multivariate analysis.

Concepts of multiple reference stations—Virtual Reference Station (VRS) for instance—have been developed during the last two decades to overcome the traditional RTK deficiencies. The basic idea behind the VRS method is the application of spatiotemporal dependence of errors to reduce the effects of biases on virtually generated observations. This amelioration improves the final coordinates and reduces the number of permanent stations settlement over a regional network. The virtual station must be as close as possible to the rover station. For this purpose, the rovers have to transmit their approximate coordinates to a data process center (the master reference station), which can be obtained using the navigation solution. The approximate coordinates of the rover are then selected as the position of the virtual station. Therefore the virtual observations can be generated at the VRS position and corrections due to the dispersive and nondispersive biases are implemented to the observations. This generation of virtual observations improves the final coordinates and reduces the number of permanent stations settlement over a regional network. In this article the VRS generation algorithm is developed and applied to six GPS stations of NGS (National Geodetic Survey) permanent network. Various error interpolation methods are tested for the VRS algorithm efficiency. The results prove that the VRS algorithm works correctly, which can be used for regional and national networks. The results were shown not much to be dependent on the choice of the interpolation method. However, the error mitigation algorithm plays the most important role.

Inertial Navigation System (INS) and Global Positioning System (GPS), are used in various navigation and positioning applications. Because each of the INS and GPS technologies has some limitations and advantages, during last two decades, the systems integration has been widely used for accurate and reliable navigation and positioning. In an integrated system, accurate GPS observations are used to estimate the high rate INS errors and state vector (including INS error vector, position, velocity and other optional parameters). A field test results are presented in this paper. The goal of this test is to compare the coordinates of a relatively low cost INS, GPS RTK coordinates, and the integrated GPS/INS results. The decentralized approach has been used for this integration.

Deformation survey using geodetic techniques for large buildings and landslides monitoring can be performed using multiple epoch’s method. The first step is the design of a reliable monitoring network. To compute the displacement, a coordinate system (datum) is to be established. Such a system is defined over a few points that are assumed to be stable during the campaign. We therefore require an efficient method for stable points’ detection. The simultaneous adjustment method is presented in the present contribution. L1 norm minimization method and global congruency test are the other two methods for this purpose. We aim to study the performance and sensitivity of simultaneous adjustment to identify the stable and unstable points using simulated data at four epochs. This method is then compared with the L1 norm method and the global congruency test for simulated and real data at two epochs. The results illustrates that increasing the observation epochs augments the ability of deformation analysis and stable points detection for simultaneous adjustment. In addition, simultaneous adjustment provides superior results over small displacements compared to the other two methods.

In order to Ionospher behavior monitoring and obtain periodic Ionospher global range, spectral analysis on data models that contain Ionospher TEC values are carried. These ionospheric models are obtained from processing of dual GNSS receivers data. These maps cover the whole earth, and consist of 73 × 71 points. According to data of over 12 years, 152 days of 1998 to the last day of 2010, the suitable time series for processing on a regular network is producedSpectral analysis was performed on the time series and main periodic ranges are calculated. The main periodic ranges: the period of the third day, half daily, daily, 27- daily, quarterly, half-yearly, annual and 3/11 years old. The relation between these periodic ranges with phenomena such as periodic and translational motions of Earth and its magnetic fields, and the solar activity is clear. On the other hand, some periodic ranges are calculated that there are no good physical reasons for them. However, this component could be due to clutter spectrum of data in Spectral leakage. In order to understand the behavior and the changes in periodic ranges, the profiles of their normalized spectra are studied in points with same latitude or longitude.

The least squares harmonic estimation is applied to the hourly time-series of Total Electron Contents (TEC) derived from ionospheric models using seven years of GPS observations processed by Bernese software. The frequencies of dominant spectral components in the spectrum are estimated. We observe significant periodic patterns with periods of 24 h and its fractions 24h/n, n=2,…,11, which are the well-known Fourier series decomposition of the diurnal periodic pattern of the ionospheric variations. The principal component with daily signal is due to the day-night variation of TEC values. The semidiurnal and tri-diurnal components can be explained by the substorm signatures in both auroral electrojet (in layer E) and ring current variations (related to magnetosphere at low latitudes) and tidal effects. Also, the spectrum shows the well-known 27-day period of solar cycle variations. We observe annual, semi-annual and tri-annual signals in the series. The detected signals are then applied to perform an ionospheric prediction. The results indicate that a substantial part (in the absolute sense) of the TEC values can be predicted using this base function, and an undetectable part remains as disturbed noise which can exceed 20 TEC units for the disturbed ionosphere. In comparison with the standard Klobuchar model, the model presented in this contribution will significantly improve the single frequency GPS positioning accuracy.