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.

Measuring the 3D displacement fields provide essential information regarding the Earth crust interaction and the mantle rheology. The interferometric synthetic aperture radar (InSAR) has an appropriate capability in revealing the displacements of the Earth’ s crust. Although, it measures the real 3D displacements in the line of sight (LOS) direction. The 3D displacement vectors can be retrieved through multiple InSAR measurements acquired from at LEAST three independent imaging geometries in a theoretical manner. However, this is a physically ill-posed inverse problem and consequently, the retrieving process of the COMPONENTs in 3D displacements become sensitive to observation errors, especially in the northern COMPONENT due to the near-polar orbiting of SAR missions. Combining different datasets regarding this issue requires proper treatment of the weight of observations, which otherwise will have a negative effect on both the precision and accuracy of the estimated 3D displacement field. In retrieving the 3D displacement fields through InSAR technique, we deal with two major issues, integration of inhomogeneous precision of observations and instability of the ESTIMATION problem. These facts constitute the motivations to address the Tikhonov regularization (TR) and LEAST SQUARES VARIANCE COMPONENT ESTIMATION (LS-VCE). In this article, to overcome these drawbacks, the regularized LEAST SQUARES VARIANCE COMPONENT ESTIMATION (RLS-VCE) is proposed for retrieving the 3D displacement vectors. Usually, the number of InSAR observations in relation to the three unknowns of 3D displacements for each pixel is not enough to apply VCE. Therefore, observations of some neighborhood cells are taken into account to increase the redundancy of stochastic model. In this context, a moving frame including a window of 3 × 3 pixels is considered to increase the number of observations and consequently, the degree of freedom of stochastic model. To assess the efficiency of the proposed method, the RADAR dataset of the Envisat and ALOS missions for the 17 June 2007 eruption of Kilauea volcano on Hawaiian island are applied. To validate the results of the proposed method, co-event displacement vectors of 19 GNSS stations around the Kilauea volcano are used. Furthermore, the 3D displacements of GNSS stations are applied for detrending the displacements of InSAR from systematic or random disturbing effects (e. g. orbit errors, curvature and topography of the Earth, atmosphere, etc. ) through fitting a two variates linear or quadratic polynomial. Comparing the co-event retrieved 3D displacement vectors through RLS-VCE method and GNSS measurements indicates that the COMPONENTial RMSE of northern displacements decreases drastically to 2. 2 cm from 11. 7 cm (for range displacements and primary weights). This is approximately equivalent to 80% improvement in the accuracy of estimating the northern COMPONENT of displacement. The overall RMSE of retrieving 3D displacement vectors decrease from 7. 8 cm to 2. 6 cm, which is equal to 66% improvement. Achieving to this overall accuracy and for northern COMPONENT is of major interest for all disciplines of geoscience dealing with 3D surface deformation analysis. Results indicate that retrieving the 3D displacement vectors through applying the RLS-VCE method has a meaningful improvement on the precision and accuracy of the results, the northern-southern COMPONENT in special.

In this paper, we propose a nonparametric rank-based alternative to the LEAST-SQUARES independent COMPONENT analysis algorithm developed. The basic idea is to estimate the squared-loss mutual information, which used as the objective function of the algorithm, based on its copula density version. Therefore, no marginal densities have to be estimated. We provide empirical evaluation of the proposed algorithm through simulation and real data analysis. Since the proposed algorithm uses rank values rather than the actual values of the observations, it is extremely robust to the outliers and suffers less from the presence of noise than the other algorithms.

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.

In this paper, various identification methods based on LEAST-SQUARES technique to estimate the unknown parameters of structural systems with hysteresis are investigated. The Bouc-Wen model is used to describe the behavior of hysteretic nonlinear systems. The adaptive versions are based on the fixed and variable forgetting factor and the optimized version is based on optimized adaptive coefficient matrix. Simulation results show the efficient performance of the proposed technique in identification and tracking of hysteretic structural system parameters compared with other LEAST square based algorithms.

Multiple-input multiple-output (MIMO) system has come forward as a generic technique that promises to be a strong contender for future generation wireless communication. In this paper, orthogonal matrix triangularization is utilized to carry out performance improvement and complexity reduction of MIMO channel ESTIMATION. The technique is applied on LEAST SQUARES (LS) channel ESTIMATION and the performance evaluations are validated through computer simulations using MATLABÒ in terms of bit error rate (BER). Simulation results indicate that the proposed method considerably improves the system performance and significantly reduces the complexity caused by matrix inversion. The performance and complexity of the proposed method clearly outperforms the conventional LS channel ESTIMATION method and proves itself a smart solution for MIMO channel ESTIMATION.

The development of communications and telecommunications infrastructure, followed by the extension of a new generation of smart distribution grids, has brought realtime control of distribution systems to electrical industry professionals’ attention. Also, the increasing use of distributed generation (DG) resources and the need for participation in the system voltage control, which is possible only with central control of the distribution system, has increased the importance of the real-time operation of distribution systems. In real-time operation of a power system, what is important is that since the grid information is limited, the overall grid status such as the voltage phasor in the buses, current in branches, the values of loads, etc. are specified to the grid operators. This can occur with an active distribution system state ESTIMATION (ADSSE) method. The conventional method in the state ESTIMATION of an active distribution system is the weighted LEAST SQUARES (WLS) method. This paper presents a new method to modify the error modeling in the WLS method and improve the accuracy SVs ESTIMATIONs by including load variations (LVs) during measurement intervals, transmission time of data to the information collection center, and calculation time of the state variables (SVs), as well as by adjusting the VARIANCE in the smart meters (SM). The proposed method is tested on an IEEE 34-bus standard distribution system, and the results are compared with the conventional method. The simulation results reveal that the proposed approach is robust and reduces the ESTIMATION error, thereby improving ADSSE accuracy compared with the conventional methods.