To estimate the unknown parameters in a linear model in which the observations are linear functions of the unknowns, one of the conventional methods is the least-square estimation. The best linear unbiased estimation (BLUE) is achieved when the inverse of the variance covariance matrix of the observables is considered as the weight matrix in the estimation process. Therefore having a realistic assessment of the precision of the observations is an important issue. One of the methods to reach this goal is the use of the least-square variance component estimation (LS-VCE). However, in this method, it is not impossible to estimate negative variances. But, they are not acceptable from the statistical point of view. In this paper, numerical methods such as genetic algorithm and also iterative methods based on LS-VCE are presented for non-negative estimation of variance components. By using non-negative variance components estimation methods not only one guarantees the non-negative variance components but also one can investigate to incorporate different noise components into the stochastic model. Those components that are not likely present are automatically estimated zeros. In this paper, using the above-mentioned methods, we assess the noise characteristics of TIME SERIES of GPS permanent stations. The data used in this research are the coordinates of IGS stations located in Mehrabad-Tehran and also two other stations in Ahvaz and Mashhad (2005-2010). To deal with this amount of data, the iterative methods are superior over the numerical methods such as the genetic algorithm. The results indicate the noise of GPS POSITION TIME SERIES are a combination of white noise plus flicker noise, and in some cases combined with random walk noise.

GPS TIME SERIES consists of a linear trend, harmonic signals, probable offsets and also noise which is described as a stochastic part. Because of various applications of GPS TIME SERIES such as plate tectonics, crustal deformation and earthquake dynamics studies, these TIME SERIES should be modeled with high accuracy. For this purpose, systematic effects in functional model should be determined with high accuracy. In this paper the effect of earthquakes is also considered in the functional model in addition to mentioned behaviors. Because earthquakes cause crustal deformations, their effects can be observed in the shape of offsets (as coseismic effects) and (or) rate changes (as coseismic or postseismic effects) in the TIME SERIES. Neglecting these effects lead to biased estimation of noise amplitudes. To discover the effect of earthquakes, a manual solution is used for each station. Effects are detected graphically by comparison of behavior of TIME SERIES and epoch of occurred earthquakes in the region. The earthquakes which considering their effects, lead to the best fitting of functional model to TIME SERIES, are selected as effective ones. Because the Alborz range is the most seismically active region in the Northern Iran, 25 permanent GPS stations with the TIME span between 2005 and 2013 in this area are selected for this study. Analysis of TIME SERIES indicates similar behavior of TIME SERIES with the same offset TIMEs and common earthquake effects for most stations (also for those which are located in far distances from epicenters). This result means that systematic effects may propagate from one station to the others during the processing and the network adjustment. Furthermore, noise analysis of TIME SERIES using least squares (co) variance components estimation method, shows that neglecting seismic effects can result in the presence of random walk noise in 88%, 12% and 60% of north, east and up components, respectively. However, considering the seismic effects causes positive estimation of variances of random walk noise in 12%, 12% and 36% of north, east and up components, respectively. Finally, due to similar behavior of TIME SERIES, a reprocessing of them could be suggested.

The main purpose of this paper is using the probablity models, Auto Regressive Moving Average (ARMA) in order to modeling of daily POSITION TIME SERIES of permanent GPS station. The daily POSITION TIME SERIES of LLAS site in Southern California region from SCIGN array that were active during January 1,2000 to Dec 30, 2006 are evaluated for analysis and determinig of daily POSITION TIME SERIES. According of daily POSITION TIME SERIES, a site motion model is used to estimate simultaneously geodetic parameters such as: linear trend, annual harmonics, semi annual harmonics and offsets. In each daily POSITION TIME SERIES, model parameters are estimated using weighted least squares. In this study, Auto Correlation Function (ACF) and Partial Auto Correlation Function (PACF) are used as study tools for identification of behavior of daily POSITION TIME SERIES of permanent GPS station. These functions provide consideration of correlations between daily POSITIONs of daily TIME SERIES. Moreover, Akaike Information Criterion is used to identify model orders, because some kind of ARMA model may appropriate for a daily POSITION TIME SERIES of GPS station. In this study, some numerical results shows that a model order from (1, 1) is appropriate for direction N of permanent GPS station. Probabality model of ARMA (2, 1) is best model for direction E and a model order from (1, 1) is suitable for direction U. In the final step, a daily POSITION TIME SERIES of LLAS permanent station were predicted for seasonal component.

A TIME-dependent periodic coefficients (TDPC) model was proposed to analyze the Global POSITIONing System (GPS) TIME SERIES. Due to the variations of the amplitude and phase-lag of the GPS signals over TIME, we propose a TDPC to analyze the daily TIME SERIES. A new solution approach, where the serial correlations of the disturbances are eliminated by sequentially differencing the measurements, was used to estimate the model parameters using weighted least squares. As a numerical performance of the proposed method, the TIME SERIES of 19 permanent stations in the United States via the Website of Scripps Orbit and Permanent Array Center (SOPAC) between the 2000 and 2010 year was selected. The results show a decrease in the RMS values of the residuals, especially for the height components. Moreover, using the 90 simulated GPS data analysis, in which their noises were different combinations of white noise and flicker noise, we demonstrate that the proposed model can extract amplitude varying periodic variabilities from GPS coordinate TIME SERIES.

in this paper, Hilbert Huang transform (HHT) for TIME SERIES analysis of the status of permanent GPS stations can be provided. Hilbert Huang transform and its, related spectrun is a new method for the analysis of nonlinear processes. This method represents not only a precision analysis in the TIME-frequency space, but also it declares the physics of the dynamic processes. This method has two speps. At the first step, the data is disintegrated into IMF elements by EMD method. At the second step Hilbert transform is applied for IMF elements and distribution of the TIME-frequency-Hilbert energy spectrum is then determined. In this spectrum, Location, frequency and energy defined by TIME events for the Hillbert transform will be reserved. So instantaneous frequency will have a major role in this method.

Earth deformation is a three-dimensional phenomenon; therefore crust analysis also must be done in three dimension. Analysis of deformation using two epochs can be replaced by analysis of TIME SERIES, which is more effective for modeling of geodynamics phenomena. GPS permanent stations provide such observations. At the first part of this study, TIME SERIES of 19 GPS permanent stations in Washington region have been used. With simultaneous analysis of common observations, displacements in three directions were obtained. According to the obtained results, estimation accuracy of horizontal displacements is nearly 3.5 TIMEs better than estimation accuracy of vertical displacements. In the next section, Lagrangian method has been used to analyze the deformation. Generally, by generalization of the mathematical model of this method, from two-dimensional to three-dimensional, there is a possibility of problem’s instability. The results of this study show that generalized three-dimensional model necessarily does not lead to instability of the problem. It seems that POSITION of points relative to each other and topography of the region are more important elements which can make coefficients matrix ill-conditioned. As an important point, we can mention that deformation pattern obtained using two dimensional and three-dimensional analysis are consistence. This consistency can be obviously found in most stations. But in terms of values, we can find serious differences between horizontal main values of strain tensors and compression values even up to two decimals. These differences may come from ignoring vertical component in analysis of two-dimensional deformation.

Today, one of the main objectives of the geodesy is to identify the changes over TIME at the surface of the earth. It is critical to the design of the infrastructures to know these changes and to be able to predict their trends with TIME, as any ignorance could lead to in compensable losses to the society. One way to investigate and measure the changes is to establish permanent GPS stations and to process the TIME SERIES data from the stations. The amplitude and mode of the periodic movements and the parameters of the linear movements can be investigated by the application of the maximum likelihood of the type and amplitude of the noises in the TIME SERIES.The noise analysis in TIME SERIES allows the real changes recorded in any stations in the geodynamic network to be accurately measured. With the application of the measured parameters in the deformation equations, the changes in the crust of the earth can be appropriately interpreted. This research shows that the white and flicker noises in vertical components are more than those in the horizontal components. Without the application of noise analysis on TIME SERIES, the estimated errors for the rate of changes in the geodynamic stations would be underestimated by 8 TIMEs.

There are many studies discussing the correlation between air pollution and human health hazards. Yet, in Tehran there is not a survey using TIME SERIES methodology. Thus, we conducted a study based on TIME SERIES data on the topic in Tehran, Iran. Mean levels of NO, NO2, NOX, CO, 03, SO2 and PM10 (particulate matters smaller than 10micrometer in diameter) were measured in one station of Tehran's Air Quality Control Corporation and were used as main independent variables. Mean temperature, mean humidity, day of the week, month and season were considered as potential confounders and deaths in people older than 64 years in Tehran was the dependent variable. All the variables were measured during Mar. 1998 to Dec. 1999. Concentrations of air pollutants were different between seasons and so were the means of daily deaths. Out of main independent variables, SO2, CO and PM10 showed statistically significant relations with the dependent variable (P<0.05). After controling for confounders, there was 3.4%, 2.6% and 3.36% increase in death rates, respectively, for each interquartile ascending (increase from 25th centile to 75th centile) in association to the mentioned pollutant centile concentration. No autocorrelation between residuals was observed (r= -0.059). The study showed that meteorological variables can confound the relation between air pollution and rate of deaths per day.  

Precise guidance and navigation is one of the necessities of every moving vehicle in the transportation industry. Different methods of navigation has been used to determine exact location of the vehicle in each moment. Inertial navigation is a newton-based method that provides POSITION of the vehicle regardless of any external communication equipment. Inertial navigation is always subject to different disturbing errors that consistently reduce the performance of the system, therefore, for long-term navigation purposes, there should be at least one navigation assisting system to maintain POSITIONing accuracy. Consequently, a GPS/INS data fusion using a Robust Extended Kalman Filter (REKF) is investigated in this paper. When vehicles enter an area with a signal jammer, GPS POSITION would be unavailable, and, filter observations will not be updated. Thus, a trained nonlinear neural network is used to predict POSITION in this scenario. In order to test the algorithm in real-world circumstances, a custom designed board with military standards is employed. The results show about 70% of POSITION improvement towards each axis. The proposed algorithm has improved the POSITION accuracy in GPS/INS integrated system in defined scenario.