m. a. sharifi

There are many instabilities in the earth's rotation due to celestial bodies, gravitational forces, and earth internal dynamics which make the calculation of Earth Orientation Parameters (EOP) and Polar Motion (PM) parameters a challenging task. In today's world due to the increasing requests for predicting EOP and PM parameters in a wide range of fields such as Astronomy, Geodesy, Oceanography, and Hydrography various methods are used. These days it is possible to calculate accurate values of EOP and PM parameters by means of global positioning system (GPS), very-long baseline interferometry (VLBI) and satellite laser ranging (SLR). The core reason for the short-term prediction of these parameters is the impossibility of calculating these parameters in real-time due to heavy preprocessing procedures. Hence, researchers are seeking to employ different methods for accurate short-term prediction of EOP and PM parameters. In recent years, non-parametric methods such as least square (LS) with autoregressive moving average (ARMA) and also singular spectrum analysis (SSA) have been used to estimate these parameters. Another method for the prediction of the aforementioned parameters was conventional artificial neural network (ANN). Currently, Deep Learning has become a popular field that attracts many researchers. Deep learning is a subset of artificial intelligence (AI) and machine learning that uses multiple layers and parameters in order to extract complex features from the inputs. It is widely used in computer vision and time series prediction applications. In this paper, we used three deep learning methods namely LSTM, CNN, and MLP in order to predict PM parameters (x and y parameters). Furthermore, we have used Least square harmonic estimation (LSHE) method in order to compare the final results with different networks. LSTM equipped with a short-term recursive memory. This recursive mechanism prepares LSTM for handling time series data. CNN extracts important features of input data by convolution multiplication and each convolution layer within CNN architecture produces feature maps as output. These Feature maps contain recognized patterns which will be used as input of next layer. CNN networks, which were primarily designed for the computer vision, are being used more and more in timeseries prediction applications. MLP networks are similar to conventional back propagation feedforward networks, however, new activation functions and optimizers could be used in MLP networks. For sufficient training of different architectures, we used 35 years of daily PM parameters from 1st January 1980 to 31 December 2015 and we predicted 40 days periods ahead for the future 5 years. For comparison of predicted values by different networks, we used mean absolute error (MAE) as a criterion and illustrate results in two tables. Also, we depicted different figures to show how networks are working. In addition, we used two LSTM, four CNN, and two MLP Networks with ADAM optimizer, ReLU activation function, and learning rate of 0.001- 0.0001 in order to select the best network with the lowest errors.  Moreover, the figures of predicted values vs actual values and plots of MAE for 40 days are shown on four figures for better comprehension of ultimate results. In the end, it turned out that LSTM networks outperformed CNN and MLP networks and in this network the final results are better than the others in most days. For the x parameter in the first, twentieth and fortieth days, the best MAE values are 0.41 mas, 5.58 mas, and 12.45 mas and the best values for RMSE are 0.49 mas, 6.69 mas, 15.05 mas, respectively. For the y parameter in the first, twentieth and fortieth days, the best values of MAE are 0.54 mas, 3.24 mas and 7.56 mas and the best values for RMSE are 0.68 mas, 4.72 mas, 9.22 mas, respectively. The final results show that the neural networks outperformed LSHE method and the accuracies of the deep learning networks are satisfying and LSTM and CNN networks are capable to predict values accurately.

The Earth Orientation parameters (EOP) including the Length of Day (LOD) are vital to widely used applications of Satellite Geodesy. The precise satellite positioning and navigation and the Earth system monitoring satellites are a few applications with a near real time request for the EOP values. Data gathering from a globally distributed co-located geodetic sensors and processing the collected data for estimation of the parameters are time demanding tasks which makes delayed access to a real-time processed values unavoidable. Consequently, accurate prediction of the EOP parameters time-series has been defined as a highly demanding task in geodesy. Many different techniques have already been employed either for short- or long-term prediction of the time-series. However, the implemented methods for short-term prediction of the EOP temporal changes is in central focus of the research centers and institutes due to its applications in the Earth Centered inertial (ECI) and the Earth Centered Earth Fixed (ECEF) reference frames. Moreover, combined methods with the ability of simultaneous functional and stochastic behavior modeling of the time-series are more interested due to their functionality for one-step accurate prediction. For instance, the Least squares auto regressive (LS+AR) is the most recent published article for the LOD forecasting. In this paper, we will address an innovative approach for complicated and challenging time-series prediction. The proposed methodology consists of the Singular Spectrum Analysis (SSA) combined with the Auto Regressive Moving Average (ARMA) enabling to model the functional and stochastic constituents respectively. For more precise forecasting, the proposed method is equipped with two pre analysis statistical tests in order to detect and identify any possible outliers. Moreover, the Fast Fourier transform (FFT) is employed to give a first guess of the possible periodic pattern of the data with its later application in the SSA appropriate window length selection. The SSA setup consists of the lag-covariance matrix computation, Eigen value and Eigen vector decomposition of the lag-covariance matrix, the Eigen values clustering and the component reconstruction. Trend and offset removal before utilizing the SSA method and its restoration after performing perdition is also worth mentioning. Selection an optimal number of deterministic components plays a key role in effective implementation of the SSA approach which is fully explained in the methodology part of the paper. The stochastic behavior of LOD signal is characterized using the ARMA technique whose successful implementation is highly depend on the right selection of the Moving Average (MA) and Auto Regressive (AR) orders. The Akaike information criterion (AIC) as an estimator of prediction error as the well-known order selection criteria is used. Moreover, the Mean Absolute Error (MAE) is computed and different prediction scenarios are compared. The suggested approach has dominantly outperformed eight already published method. Publicly available LOD data from International Earth Reference System (IERS) is used for the method evaluation and numerical comparison. Daily LOD data for the years of 2005-2009 is used for model training while the year 2010 is taken for validation. A ten-day interval prediction during the whole year of 2011 is considered for evaluation. On average, accuracy improvement rate is about 1.6 and 1.84 for the 5th and 10th ahead day of prediction.

Increasing demand on the launch of the Earth orbiters with a variety of applications makes the problem of the initial orbit determination problem more interesting. The problem is to determine the Keplerian orbital elements of any orbiters using minimum number of observations.  Observing the orbiters in their initial phase of orbital launch using the ground optical tracking stations is one of the most reliable and frequently used methods for the problem solution. Slant distance, horizontal and vertical angles of satellite with respect to the local north and zenith are the observed quantities in the optical tracking systems. Short-arc of the observations in particular for the Low Earth Orbiters (LEO) and modeling the initial orbit determination as a two-body problem and ignoring perturbing forces are the main challenging issues in orbital mechanics. Neglecting the perturbation force contribution in the mathematical models of the initial orbit determination sets up of the observation equations with some errors or the so called Error In Variable (EIV) model. Moreover, fitting an ellipse to the observed three dimension position time series of the orbiter and determination of the Kepler elements is an ill-posed problem. It is due to fact of fitting an ellipse to a few closely distributed data points along the orbit in three dimensional space. Therefore, one has to implement the method of Total Least Squares (TLS) with an appropriate regularization technique for the orbital parameter estimation. Different regularization techniques have been already introduced for solution of ill-posed problems. Herein, Tikhonov regularization method with the aim of minimization of bias term along with the error in measurements is applied and the orbital elements are estimated. Implementation of regularization method significantly improves the results and in particular the LEO Kepler elements. Numerically, the proposed method is implemented on the estimation of the parameters with different orbital geometry type; including the LEO and Medium Earth Orbiter (MEO) satellite in the polar and non-polar orbits. In all cases, the orbital parameters and their variances are estimated and statistically tested. Moreover, relative errors of the estimated parameters and their meaningfulness are checked in different scenarios.     Theoretically, the problem of orbital parameter estimation is a nonlinear problem by its nature. We are implemented iterative gradient-based solution and therefore linearization of the nonlinear equations is required. For quarantined convergence of the linearized model, initial value of the unknowns with acceptable accuracy is needed. The classical methods, e.g., Gauss, Gibbs and Lambert method of the initial orbit determination problem provide an approximate solution with enough accuracy for initialization of the estimation problem. The Picard condition as an indicator of ill-posedness on the inverse problem is used to demonstrate in the orbital parameters estimation. The L-curve method is implemented to get the solution with minimum bias value. The method of Ordinary Least Squares (OLS) is simultaneously implemented on the problem to show how TLS can efficiently be used.

Global Positioning System (GPS) receivers in gravimetric satellites continuously measure valuable information about 3D satellite position. However، the velocity of satellites، which has important applications in the satellite geodesy such as gravity field recovery، cannot be directly measured. These data are used in the energy integral method or other methods based on the Earth gravity field motion equation to determine the velocity or acceleration of satellite. In this study، the velocity vector is computed using the numerical differentiation and the Kalman filtering for the Gravity Recovery And Climate Experiment (GRACE) twin satellites. The Numerical results show that the Kalman filtering yields more accurate results than numerical differentiation when they are compared with the intersatellite range-rate measurements. In the wake of the New Gravity Satellite era due to the launch of ChAllenging Minisatellite Payload (CHAMP)، GRACE and GOCE، processing methods of enormously large orbit data has become the focus of the geodetic interest. The input data are different from earlier times as they contain some millions of continuous position data per satellite per year. The huge number of data arises from continuous observation from these satellites to the GPS system. This can be done due to the much higher altitude of the GPS satellites (20،000 km) compared to that of the gravity satellites (between 250 and 500 km). The latter is often referred to as Low Earth Orbiter، i. e. LEO. The GPS-LEO constellation as described above in technical terms is called High-Low Satellite to Satellite Tracking (High-Low SST). Thus some million position-data of the LEOs are the basis of the global gravity field determination techniques. The concept behind the Solutions is that satellites are in free-fall in the gravity field of the Earth. After modeling and removing all further force sources (e. g. gravitation of the Sun and the Moon and other planets، direct and indirect tides، surface forces (atmospheric drag، solar radiation pressure)) the remaining orbit is a trajectory in space، which is governed purely by the gravity field of the Earth. Therefore، the task is only to determine the force behind the motion. Conservation laws can be applied for satellites successfully. The Newton’s equation of law states the conservation of forces in a closed system. Applying it for a satellite requires information of the acceleration along the orbit. In this article the velocity vector is derived as a part of the unknown vector in Kalman filter algorithm. Kalman filter is a well-known mathematical tool، which gives the answer to the most frequent engineering question: how can we get the best estimate of the system state from the noisy measurements? The Kalman filter is a data processing algorithm that estimates the state of a system from noisy measurements using least-squares. It gives the optimal system state estimate together with a measure of how precise is the state estimate compared to true state. The Kalman filter performs optimal solution for a linear process with uncorrelated، white، zero mean Gaussian process and measurement disturbances. The Kalman filter is a “one-step back recursive filter”، meaning that there is no need to store past measurements for the purpose of computing the present time. We assume that the discrete random kinematic process to be estimated can be modeled with two main Kalman filter equations: Process equation Measurement equation Where x is the system state vector، A is the state transition matrix and W is the process noise. From this discrete time linear formation of the Kalman filter، the discrete time nonlinear formation of the Extended Kalman Filter is based. For the state space model for the Extended Kalman Filter (EKF)، the above linear equations are replaced by one nonlinear function: In this study، the velocity vector is computed using numerical differentiation and the Kalman filtering for the GRACE twin satellites. The numerical analysis shows that the Extended Kalman filtering yields the optimal solution. The comparison is performed based on the intersatellite range-rate measurements.

Estimating accurate bathymetry has many applications in science and engineering. although ship borne sounding are precise method to create bathymetry chart but this method is time confusing and extensive، hence in many oceans region especially in the deeper region don’t exist sufficient data. For this reasons the use of methods that are cost-effective in terms of time and cost are taken into consideration. Satellite altimetry، for over three decades، measures sea level anomaly. For some time، scientists have used these data to measure the gravity field parameters such as gravity، geoid undulations and component of deflection of vertical. Subsurface structures in a region affect in the gravity anomaly. One of the main sources of gravity on sea is seafloor topography. Smith and Sandwell proved that in the wave domain gravity anomaly are most correlated with the seafloor topography in the wavelength range from 15 to 160 km. in this paper we will try to estimate seafloor topography in Oman sea first we filter gravity anomaly and then downward continue them to the mean depth and finally by using Weiner optimization method and ship track line gravity data estimate seafloor topography. It is shown that when we combine gravity data and ship borne track our result improve 7 m with comparisons to shipborne track only.

Practical Applications of bathymetry from ancient times until now، has attracted the attention of scientists to methods that compute it. Bathymetry with ship، despite high accuracy is very costly and time confusing and in the deep regions is impractical even. Hence، the use of indirect methods to predict bathymetry is taken into consideration. Satellite altimetry measure sea level anomaly over 30 years. With retracking methods and new satellite missions such as Cryo_sat، density and accuracy of satellite altimetry data has increased. In geodesy can convert this data to gravity field components such as geoid undulations، free air gravity anomaly، deflection of vertical and etc. on the other hand the internal sources of earth has an important effect on the gravity field components. One of the main this sources in sea is seafloor topography. An inverse can be made by parker relationship between seafloor topography and gravity anomaly data in the frequency domain. On the other hand، iterative least square collocation can be used as an effectively mathematical model to solve inverse problem. In this paper we use the gravity data derived from satellite altimetry and estimate bathymetry in Oman sea area using iterative least square collocation. And compare our result with ETOPO1 bathymetry model and some ship borne depth data in the area of study. Standard deviation between difference of ETOPO1 and ship borne depth data is 121. 4m while this for our computed model is 117. 87m. this is show that our model has better precision in this area compared with ETOPO1.

Modeling of gravity field has many application in geosciences such as geodesy، geophysics، and oceanography and tectonic. Marine Gravity observations due to factor such as oscillation and accelerations of ship، also mechanical errors that are greater in water have low precision. Satellite altimetry provide detailed information about geoid changes and its slope changes over the oceans. in geodesy we can convert geoid and its slope (deflection of vertical component)، to gravity anomaly using spectral analysis methods. There are two integral equation to estimate gravity anomaly from geoid and deflection of vertical، stokes integral and vening meinesz integral. In this paper method of marine gravity anomaly deriving from satellite altimetry are introduced and then using satellite altimetry data estimate marine gravity anomaly over Oman Sea that is a Deep region. Then for control precision of methods، use marine gravity anomaly points that have corrected and collected by national geophysical data center (NGDC). our result show that in gravity anomaly estimation from satellite altimetry using Deflections of vertical as observation and spectral kind of vening meinesz integral as method have a RMS of 4. 2 mgal in comparison with shipborne data، while the using geoid as observation and spectral kind of stokes integral as method، have 4. 38 mgal in comparison with shipborne data. This indicate spectral kind of vening meinesz integral have advantage in comparison with spectral kind of stokes integral.

Several landslides occur every year in the world, causing great damage to infrastructure and loss of life. Detection and monitoring of landslides is very important for implementing appropriate mitigation measure to reduce the loss of life and damage to property. Iran is prone to huge landslides due to its special continental conditions, topographic and tectonic situation and climate conditions. In this investigation, we use the technique of Interferometry Synthetic Aperture Radar (InSAR) to detect and monitor landslides in Taleghan region. The results are obtained from processing of 23 ASAR images acquired in the region by the Envisat satellite. We show evidence for several creeping landslides and obtain their deformation history between 2003 and 2009 via InSAR time-series analysis. We also report on our field investigation that we did to check the results of InSAR analysis.

Celestial positioning has been used for navigation purposes for many years. Stars as the extra-terrestrial benchmarks provide unique opportunity in absolute point positioning. However, astronomical field data acquisition and data processing of the collected data is very time-consuming. The advent of the Global Positioning System (GPS) nearly made the celestial positioning system obsolete. The new satellite-based positioning system has been very popular since it is very efficient and convenient for many daily life applications. Nevertheless, the celestial positioning method is never replaced by satellite-based positioning in absolute point positioning sense. The invention of electro-optical devices at the beginning of the 21st century was really a rebirth in geodetic astronomy. Today, the digital cameras with relatively high geometric and radiometric accuracy has opened a new insight in satellite attitude determination and the study of the Earth's surface geometry and physics of its interior, i.e., computation of astronomical coordinates and the vertical deflection components. This method or the so-called astrogeodetic vision-based method help us to determine astronomical coordinates with an accuracy better than 0.1 arc second. The theoretical background, an innovative transformation approach and the preliminary numerical results are addressed in this paper.