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Stochastic models play an important role in achieving high accuracy in positioning, the ideal estimator in the least-squares (LS) can be obtained only by using the suitable stochastic model. This study investigates the role of variance component estimation (VCE) in the LS method for Precise Point Positioning (PPP). This estimation is performed by considering the ionospheric-free (IF) functional model for code and the phase observation of Global Positioning System (GPS). The strategy for estimating the accuracy of these observations was evaluated to check the effect of the stochastic model in four modes: a) antenna type, b) receiver type, c) the tropospheric effect, and d) the ionosphere effect. The results show that using empirical variance for code and phase observations in some cases caused erroneous estimation of unknown components in the PPP model. This is because a constant empirical variance may not be suitable for various receivers and antennas under different conditions. Coordinates were compared in two cases using the stochastic model of nominal weight and weight estimated by LS-VCE. The position error difference for the east-west, north-south, and height components was 1.5 cm, 4 mm, and 1.8 cm, respectively. Therefore, weight estimation with LS-VCE can provide more appropriate results. Eventually, the convergence time based on four elevation-dependent models was evaluated using nominal weight and LS-VCE weight. According to the results, the LS-VCE has a higher convergence rate than the nominal weight. The weight estimation using LS-VCE improves the convergence time in four elevation-dependent models by 11, 13, 12, and 9 min, respectively.

Function approximation has gained significant attention in reinforcement learning research as it effectively addresses problems with large-scale, continuous state, and action space.Although the function approximation algorithm based on gradient descent method is one of the most widely used methods in reinforcement learning, it requires careful tuning of the step size parameter as an inappropriate value can lead to slow convergence, unstable convergence, or even divergence.To address these issues, an improvement was made around the temporal-difference (TD) algorithm based on function approximation.The weight update method was enhanced using both the least squares method and gradient descent, resulting in the proposed weights gradient descent (WGD) method.The least squares were used to calculate the weights, combining the ideas of TD and gradient descent to find the error between the weights.And this error was used to directly update the weights.By this method, the weights were updated in a new manner, effectively reducing the consumption of computing resources by the algorithm enhancing other gradient descent-based function approximation algorithms.The WGD method is widely applicable in various gradient descent-based reinforcement learning algorithms.The results show that WGD method can adjust parameters within a wider space, effectively reducing the possibility of algorithm divergence.Additionally, it achieves better performance while improving the convergence speed of the algorithm.

Function approximation has gained significant attention in reinforcement learning research as it effectively addresses problems with large-scale, continuous state, and action space.Although the function approximation algorithm based on gradient descent method is one of the most widely used methods in reinforcement learning, it requires careful tuning of the step size parameter as an inappropriate value can lead to slow convergence, unstable convergence, or even divergence.To address these issues, an improvement was made around the temporal-difference (TD) algorithm based on function approximation.The weight update method was enhanced using both the least squares method and gradient descent, resulting in the proposed weights gradient descent (WGD) method.The least squares were used to calculate the weights, combining the ideas of TD and gradient descent to find the error between the weights.And this error was used to directly update the weights.By this method, the weights were updated in a new manner, effectively reducing the consumption of computing resources by the algorithm enhancing other gradient descent-based function approximation algorithms.The WGD method is widely applicable in various gradient descent-based reinforcement learning algorithms.The results show that WGD method can adjust parameters within a wider space, effectively reducing the possibility of algorithm divergence.Additionally, it achieves better performance while improving the convergence speed of the algorithm.

To enhance the positioning accuracy of standalone GNSS receivers in environments unable to provide precise ephemeris and clock offset, such as undeveloped forest areas that lack network communication and power supply, this study employed the Time Difference Carrier Phase (TDCP) technology to improve the positioning accuracy of Standard Point Positioning (SPP), where the Least-Squares (LS) and the extended Multi-Epoch Least Squares (MELS) method were applied in the position domain filtering for a single GNSS receiver and compare its performance with the existing observation domain filtering method. Firstly, the simulated data sets with various positioning accuracies were used to verify the effectiveness and convergence of the LS filtering methods. The results indicate that the LS filtering method produces a lower root mean square (RMS) error than the original strategy. Secondly, this study uses two kinematic GNSS data sets to evaluate the performance of the observation and position domain filtering, with an emphasis on the MELS method. The numerical experiment results show that the position domain LS filtering method outperforms the other two methods. The open environment experiments result shows that the positioning domain filtering method achieved positioning accuracies of 0.202 m, 0.843 m, and 2.036 m in the E, N, and U directions, respectively, with improvements of 68.0%, 21.6%, and 24.0%, compared to the original algorithm which achieved positioning accuracies of 0.631 m, 1.076 m, and 2.680 m. It also achieved improvements of 24.0%, 4.0%, and 18.3%, respectively, compared to the observation domain filtering method with positioning accuracies of 0.353 m, 0.886 m, and 2.526 m. The forest scenes experiments result shows that the positioning domain filtering method achieved positioning accuracies of 1.308 m, 1.375 m, and 2.133 m in the E, N, and U directions, respectively, with improvements of 42.4%, 36.2%, and 27.6%, compared to original algorithm which achieved positioning accuracies of 1.863 m, 1.873 m, and 2.722 m, and also achieved improvements of 27.0%, 19.4% and 10.6%, respectively, comparing to observation domain filtering method with positioning accuracies of 1.661 m, 1.642 m and 2.359 m. Moreover, the examination of the LS method results based on different epochs reveals that the filtering accuracy increases as more epochs are incorporated into the position domain integration and the enhancement value reaches a few millimeters.

We revisit the theory of distributed networks of cooperative agents under a broader perspective of diffusion adaptation, by exploiting proximity concepts. This leads to two main families of algorithms with enhanced convergence rate and mean-square-error performance. Part I of this work considers mainly single-task scenarios, which are based on formulating optimal learning and fusion steps via an adaptive network penalty function. The main recursions, which we refer to as Adapt-and-Fuse (AAF) diffusion, are reminiscent of a reweighted network regularized algorithm, usually seen in standalone formulations. This is in line with early approaches that promote proximity among agents in cooperative networks. The AAF strategy employs exact fusion in the least-squares sense, and outperforms the exact global least-squares solution that ignores the topology of the network. It also suggests simplified LMS-complexity algorithms, and motivates us to develop a normalized version of the relative variance diffusion algorithm, which also learns combination weights. It is verified that even when agents do not share estimates, but only their uncertainties, the simplified AAF improves accuracy over the NLMS-RV algorithm in the presence of intruders, and becomes more robust to noisy links. In order to cope with the computational burden associated with long parameter vectors and correlated inputs, an overlapped block multidelay adaptive frequency-domain (FD) version of each new algorithm is derived. It turns out that for correlated inputs, these FD-LMS versions outperform the exact fullband RLS solutions. In the accompanying Part II of this work, we pursue extensions to the multitask scenario. Extensive simulations illustrate the superiority of the new approaches.

In Part I of this presentation, we have formulated single and multitask quadratic optimization problems, where agents are subject to quadratic, smoothing constraints over a graph. We have focused particularly on single task designs, whereby node uncertainties and their strength relative to un-regularized cost are tackled altogether by means of an adaptive penalty function. In this sequel, we readdress the multitask problem and propose new distributed implementations for their corresponding exact leaky-RLS solutions. We motivate a network formulation from a standalone viewpoint by capitalizing on the fact that 1) for regressors having uncorrelated entries, the performance of an efficient ${\mathcal O}(M^2)$ conjugate-gradient (CG) realization of the leaky LS solution is identical to the one of an RLS filter; 2) a CG implementation does not require inversion of the underlying sample covariance matrix. Simple arguments yield an extended network-CG algorithm that relies on node-level recursions employing distinct step-sizes. Unlike the exponentially-weighted RLS algorithm, which tapers off regularization over time, a persistent penalty strength conforms with the very purpose of the equivalent network trust-region problem, while granting a well-conditioned solution. The approach further yields another family of single-task algorithms in terms of network linearly constrained solutions, which can be contrasted to the ones proposed in Part I. In particular, the exact linearly-constrained network LMS implementation proposed here outperforms the adaptive relative-variance NLMS, under much lower computational requirements.

Modeling the relationship between vehicle speed and density on the road is a fundamental problem in traffic flow theory. Recent research found that using the least-squares (LS) method to calibrate single-regime speed-density models is biased because of the uneven distribution of samples. This paper explains the issue of the LS method from a statistical perspective: the biased calibration is caused by the correlations/dependencies in regression residuals. Based on this explanation, we propose a new calibration method for single-regime speed-density models by modeling the covariance of residuals via a zero-mean Gaussian Process (GP). Our approach can be viewed as a generalized least-squares (GLS) method with a specific covariance structure (i.e., kernel function) and is a generalization of the existing LS and the weighted least-squares (WLS) methods. Next, we use a sparse approximation to address the scalability issue of GPs and apply a Markov chain Monte Carlo (MCMC) sampling scheme to obtain the posterior distributions of the parameters for speed-density models and the hyperparameters (i.e., length scale and variance) of the GP kernel. Finally, we calibrate six well-known single-regime speed-density models with the proposed method. Results show that the proposed GP-based methods (1) significantly reduce the biases in the LS calibration, (2) achieve a similar effect as the WLS method, (3) can be used as a non-parametric speed-density model, and (4) provide a Bayesian solution to estimate posterior distributions of parameters and speed-density functions.

The COVID-19 pandemic was impacting the health and economy around the world. All countries have taken measures to control the spread of the epidemic. Because it is not known when the epidemic will end in several countries, then the prediction of the COVID-19 pandemic is a very important challenge. This study has predicted the temporal evolution of the COVID-19 pandemic in several countries using the logistic growth model. This model has analyzed several countries to describe the epidemic situation of these countries. The time interval of the actual data used as a comparison with the prediction results of this model was starting in the firstly confirmed COVID-19 cases to December 2020. This study examined an approach to the complexity spread of the COVID-19 pandemic using the logistic growth model formed from an ordinary differential equation. This model described the time-dependent population growth rate characterized by the three parameters of the analytical solution. The non-linear least-squares method was used to estimate the three parameters. These parameters described the rate growth constant of infected cases and the total number of confirmed cases in the final phase of the epidemic. This model is applied to the spread of the COVID-19 pandemic in several countries. The prediction results show the spread dynamics of COVID-19 infected cases which are characterized by time-dependent dynamics. In this study, the proposed model provides estimates for the model parameters that are good for predicting the COVID-19 pandemic because they correspond to actual data for all analyzed countries. It is based on the coefficient of determination, R2, and the R2 value of more than 95% which is obtained from the non-linear curves for all analyzed countries. It shows that this model has the potential to contribute to better public health policy-making in the prevention of the COVID-19 pandemic.

Abstract Everyone is talking about coronavirus from the last couple of months due to its exponential spread throughout the globe. Lives have become paralyzed, and as many as 180 countries have been so far affected with 928,287 (14 September 2020) deaths within a couple of months. Ironically, 29,185,779 are still active cases. Having seen such a drastic situation, a relatively simple epidemiological SIR model with Caputo derivative is suggested unlike more sophisticated models being proposed nowadays in the current literature. The major aim of the present research study is to look for possibilities and extents to which the SIR model fits the real data for the cases chosen from 1 April to 15 March 2020, Pakistan. To further analyze qualitative behavior of the Caputo SIR model, uniqueness conditions under the Banach contraction principle are discussed and stability analysis with basic reproduction number is investigated using Ulam–Hyers and its generalized version. The best parameters have been obtained via the nonlinear least-squares curve fitting technique. The infectious compartment of the Caputo SIR model fits the real data better than the classical version of the SIR model (Brauer et al. in Mathematical Models in Epidemiology 2019). Average absolute relative error under the Caputo operator is about 48% smaller than the one obtained in the classical case ( ν = 1 $\nu =1$ ). Time series and 3D contour plots offer social distancing to be the most effective measure to control the epidemic.

We present a robust recursive framework for the regulation of discrete-time linear systems subject to polytopic uncertainties. Based on regularized least-squares with a penalty parameter, we formulate a convex optimization problem and weight the polytope vertices altogether. In this sense, the main contribution of this paper consists of a robust recursive framework for the computation of stabilizing feedback gains. The solution does not require numerical optimization packages and relies ultimately on a single penalty parameter which is easily tuned. Moreover, the gains are obtained recursively through algebraic expressions, as opposed to related works which employ linear matrix inequalities. Under observability and controllability conditions, we demonstrate convergence and stability of the closed-loop system in terms of an algebraic Riccati equation. We provide numerical and real-world examples to validate the proposed approach and for comparison with a robust $H_{\infty }$ controller.

Polynomials are common algebraic structures, which are often used to approximate functions, such as probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of systems rather than to assume polynomials for only approximating known or empirically estimated distributions. Polynomial distributions offer great modeling flexibility and mathematical tractability. However, unlike canonical distributions, polynomial functions may have non-negative values in the intervals of support for some parameter values; their parameter numbers are usually much larger than for canonical distributions, and the interval of support must be finite. Hence, polynomial distributions are defined here assuming three forms of a polynomial function. Transformations and approximations of distributions and histograms by polynomial distributions are also considered. The key properties of the polynomial distributions are derived in closed form. A piecewise polynomial distribution construction is devised to ensure that it is non-negative over the support interval. A goodness-of-fit measure is proposed to determine the best order of the approximating polynomial. Numerical examples include the estimation of parameters of the polynomial distributions and generating polynomially distributed samples.

The integrity of data is an essential basis for analyzing power system operating status based on data. Improper handling of measurement sampling, information transmission, and data storage can lead to data loss, thus destroying the data integrity and hindering data mining. Traditional data imputation methods are suitable for low-latitude, low-missing-rate scenarios. In high-latitude, high-missing-rate scenarios, the applicability of traditional methods is in doubt. This paper proposes a reconstruction method for missing data in power system measurement based on LSGAN (Least Squares Generative Adversarial Networks). The method is designed to train in an unsupervized learning mode, enabling the neural network to automatically learn measurement data, power distribution patterns, and other complex correlations that are difficult to model explicitly. It then optimizes the generator parameters using the constraint relations implied by true sample data, enabling the trained Generator to generate highly accurate data to reconstruct the missing data. The proposed approach is entirely data-driven and does not involve mechanistic modeling. It can still reconstruct the missing data in the case of high latitude and high loss rate. We test the effectiveness of the proposed method by comparing three other GAN derivation methods in our experiments. The experimental results show that the proposed method is feasible and effective, and the accuracy of the reconstructed data is higher while taking into account the computational efficiency.

New iterative processes for numerical solution of big nonlinear systems of equations are considered. The processes do not require factorization and storing of Jacobi matrix and employ a special technique of convergence acceleration which is called least-squares error damping and requires solution of auxiliary linear least-squares problems of low dimension. In linear case the resulting method is similar to the general minimal residual method (GMRES) with preconditioning. In nonlinear case, in contrast to popular Newton – Krylov method, the computational scheme do not involve operation of difference approximation of derivative operator. Numerical experiments include three nonlinear problems originating from two-dimensional elliptic partial differential equations and exhibit advantage of the proposed method compared to Newton – Krylov method.

This paper considers the parameter estimation problems of Hammerstein finite impulse response moving average (FIR–MA) systems. Based on the matrix transformation and the hierarchical identification principle, the Hammerstein FIR–MA system is recast into two models, and a decomposition-based recursive least-squares algorithm is deduced for estimating the parameters of these two models. In order to further improve the accuracy of the parameter estimation, a multi-innovation hierarchical least-squares algorithm based on the data filtering theory proposed. Finally, a simulation example demonstrates the effectiveness of the proposed scheme.

Least-squares estimates are trustworthy with minimal variance if the correct stochastic model is used. Due to computational burden, diagonal models that neglect correlations are preferred to describe the elevation dependency of the variance of GPS observations. In this contribution, an improved stochastic model based on a parametric function to take correlations between GPS phase observations into account is presented. Built on an adapted and flexible Mátern function accounting for spatiotemporal variabilities, its parameters can be fixed thanks to Maximum Likelihood Estimation or chosen apriori to model turbulent tropospheric refractivity fluctuations. In this contribution, we will show in which cases and under which conditions corresponding fully populated variance covariance matrices (VCM) replace the estimation of a tropospheric parameter. For this equivalence “augmented functional versus augmented stochastic model” to hold, the VCM should be made sufficiently largewhich corresponds to computing small batches of observations. A case study with observations from a medium baseline of 80 km divided into batches of 600 s shows improvement of up to 100 mm for the 3Drms when fully populated VCM are used compared with an elevation dependent diagonal model. It confirms the strong potential of such matrices to improve the least-squares solution, particularly when ambiguities are let float.

With the advent of the digital computer, time series analysis has gained wide attention and is being applied to many fields of science. This paper reviews many traditional and recent techniques for time series analysis and change detection, including spectral and wavelet analyses with their advantages and weaknesses. First, Fourier and least-squares-based spectral analysis methods and spectral leakage attenuation methods are reviewed. Second, several time-frequency decomposition methods are described in detail. Third, several change or breakpoints detection methods are briefly reviewed. Finally, some of the applications of the methods in various fields, such as geodesy, geophysics, remote sensing, astronomy, hydrology, finance, and medicine, are listed in a table. The main focus of this paper is reviewing the most recent methods for analyzing non-stationary time series that may not be sampled at equally spaced time intervals without the need for any interpolation prior to the analysis. Understanding the methods presented herein is worthwhile to further develop and apply them for unraveling our universe.

In this paper, we develop a method to solve for periodic orbits, i.e., Lyapunov and Halo orbits, using a functional interpolation scheme called the Theory of Functional Connections (TFC). Using this technique, a periodic constraint is analytically embedded into the TFC constrained expression. By doing this, the system of differential equations governing the three-body problem is transformed into an unconstrained optimization problem where simple numerical schemes can be used to find a solution, e.g., nonlinear least-squares is used. This allows for a simpler numerical implementation with comparable accuracy and speed to the traditional differential corrector method.

This work presents an initial analysis of using bijective mappings to extend the Theory of Functional Connections to non-rectangular two-dimensional domains. Specifically, this manuscript proposes three different mappings techniques: (a) complex mapping, (b) the projection mapping, and (c) polynomial mapping. In that respect, an accurate least-squares approximated inverse mapping is also developed for those mappings with no closed-form inverse. Advantages and disadvantages of using these mappings are highlighted and a few examples are provided. Additionally, the paper shows how to replace boundary constraints expressed in terms of a piece-wise sequence of functions with a single function, which is compatible and required by the Theory of Functional Connections already developed for rectangular domains.

This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits the underlying functional structure presented in the seminal paper on the Theory of Functional Connections to ease the derivation of these interpolating functionals—called constrained expressions—and provides rigorous terminology that lends itself to straightforward derivations of mathematical proofs regarding the properties of these constrained expressions. Furthermore, the extension of the technique to and proofs in n-dimensions is immediate through a recursive application of the univariate formulation. In all, the results of this reformulation are compared to prior work to highlight the novelty and mathematical convenience of using this approach. Finally, the methodology presented in this paper is applied to two partial differential equations with different boundary conditions, and, when data is available, the results are compared to state-of-the-art methods.

In this paper we analyze the bias in a general linear least-squares parameter estimation problem, when it is caused by deterministic variables that have not been included in the model. We propose a method to substantially reduce this bias, under the hypothesis that some a-priori information on the magnitude of the modelled and unmodelled components of the model is known. We call this method Unbiased Least-Squares (ULS) parameter estimation and present here its essential properties and some numerical results on an applied example.

El artículo presenta una descripción detallada de las técnicas más utilizadas para hacer ajuste racional de funciones del dominio de la frecuencia. Las técnicas son: Aproximación Asintótica de Bode, Mínimos Cuadrados Ordinarios, Mínimos Cuadrados Iterativamente Reponderados, Ajuste Vectorial y Levenberg-Marquardt. Estas técnicas se comparan aproximando una función analítica. Después, se aplican al ajuste racional de parámetros dependientes de la frecuencia de una línea de transmisión monofásica. El efecto del ajuste se evalúa considerando los casos de línea abierta, corto circuito y perfectamente acoplada. La transformada numérica de Laplace (NLT) se utiliza como referencia para la evaluación. Se concluye que la adecuada implementación de cada técnica depende de varios factores; del tipo de función a ajustar, del rango de ajuste, y otros. Además, no es posible garantizar que una de las técnicas siempre converja al mejor resultado. El artículo propone algunas guías para seleccionar la técnica más adecuada para una aplicación particular. This paper provides a detailed description of the rational fitting techniques that are most used to approximate frequency domain functions. The techniques are: Bode asymptotic approximations, Ordinary Least-Squares, Iteratively Reweighted Least-Squares, Vector Fitting and Levenberg-Marquardt. These techniques are compared by approximating of an analytic function. Then, the techniques are applied to the rational-fitting of the frequency-dependent parameters corresponding to a single-phase transmission line. The effect of the rational representations is evaluated considering transients on cases of open-ended, short-circuited and perfectly matched lines. The numerical Laplace transform technique (NLT) is used as reference for the evaluations. It follows that the proper implementation of each fitting technique depends on various factors; the type of function being adjusted, the desired frequency range, an others. Moreover, one cannot guarantee that there is one of these techniques that will always yield the best fitting. The paper provides guidelines for selecting the most convenient one for a particular application.

The downlink communication channel from high-altitude platform (HAP) to high-speed train (HST) in the Ka-band is a slowly time-varying Rician distributed flat fading channel with 10-25 dB Rician K factor. In this respect, the received signal is mainly affected by the Doppler shift of the line-of-sight (LOS) link. In order to increase receiver performance, we propose to firstly compensate the Doppler shift of the received signal before least-squares (LS) adaptive filtering is pursued. Implementing the proposed method requires a priori knowledge of the time-varying phase of the LOS component. This is justified since signalling between the train and the controller exists such that the train velocity and location are predictable. Implementing the proposed method to the recursive LS (RLS) received beamforming algorithm shows reduction of mean square error (MSE) and bit error rate (BER).

Metal oxide (MOX) sensors are widely used for chemical sensing due to their low cost, miniaturization, low power consumption and durability. Yet, getting instantaneous measurements of fluctuating gas concentration in turbulent plumes is not possible due to their slow response time. In this paper, we show that the slow response of MOX sensors can be compensated by deconvolution, provided that an invertible, parametrized, sensor model is available. We consider a nonlinear, first-order dynamic model that is mathematically tractable for MOX identification and deconvolution. By transforming the sensor signal in the log-domain, the system becomes linear in the parameters and these can be estimated by the least-squares techniques. Moreover, we use the MOX diversity in a sensor array to avoid training with a supervised signal. The information provided by two (or more) sensors, exposed to the same flow but responding with different dynamics, is exploited to recover the ground truth signal (gas input). This approach is known as blind deconvolution. We demonstrate its efficiency on MOX sensors recorded in turbulent plumes. The reconstructed signal is similar to the one obtained with a fast photo-ionization detector (PID). The technique is thus relevant to track a fast-changing gas concentration with MOX sensors, resulting in a compensated response time comparable to that of a PID.

This paper is concerned with the identification problem for multivariable equation-error systems whose disturbance is an autoregressive moving average process. By means of the hierarchical identification principle and the iterative search, a hierarchical least-squares-based iterative (HLSI) identification algorithm is derived and a least-squares-based iterative (LSI) identification algorithm is given for comparison. Furthermore, a hierarchical multi-innovation least-squares-based iterative (HMILSI) identification algorithm is proposed using the multi-innovation theory. Compared with the LSI algorithm, the HLSI algorithm has smaller computational burden and can give more accurate parameter estimates and the HMILSI algorithm can track time-varying parameters. Finally, a simulation example is provided to verify the effectiveness of the proposed algorithms.

Displacement and deformation are fundamental measures of Earth surface mass movements such as glacier flow, rockglacier creep and rockslides. Ground-based methods of monitoring such mass movements can be costly, time consuming and limited in spatial and temporal coverage. Remote sensing techniques, here matching of repeat optical images, are increasingly used to obtain displacement and deformation fields. Strain rates are usually computed in a post-processing step based on the gradients of the measured velocity field. This study explores the potential of automatically and directly computing velocity, rotation and strain rates on Earth surface mass movements simultaneously from the matching positions and the parameters of the geometric transformation models using the least squares matching (LSM) approach. The procedures are exemplified using bi-temporal high resolution satellite and aerial images of glacier flow, rockglacier creep and land sliding. The results show that LSM matches the images and computes longitudinal strain rates, transverse strain rates and shear strain rates reliably with mean absolute deviations in the order of 10−4 (one level of significance below the measured values) as evaluated on stable grounds. The LSM also improves the accuracy of displacement estimation of the pixel-precision normalized cross-correlation by over 90% under ideal (simulated) circumstances and by about 25% for real multi-temporal images of mass movements.

When two datasets are fused using least-squares adjustment, usually all the results will be affected by some change, even the reference data that are meant to provide information of such high quality that they should remain stable. In order to avoid this effect, the sequential adjustment is to be replaced by a strictly hierarchical method in which the esti-mation procedure is designed to reproduce everything that belongs to a "higher category" and to perform an adjustment in the least-squares sense for everything else. After presenting such a suboptimal estimator, but with the "reproducing property," this technique is applied to the integration of photogrammetric networks of substantially different scales.

Abstract in Bahasa Indonesia : Meshless Numerical Analysis Method adalah suatu metode analisa numerik yang berkembang dengan pesat sebagai alternatif metode elemen hingga (Finite Element Method) yang sudah cukup terkenal. Makalah ini merupakan seri pertama dari dua untuk mengenalkan salah satu shape function yang banyak digunakan untuk Meshless Numerical Analysis Method. Makalah seri kedua akan memperkenalkan salah satu Meshless Numerical Analysis Method yang dikenal sebagai Meshless Local Petrov-Galerkin Method.

In the present study buffalo herds of Murrah breed at various centres are studied to evaluate the sires on the basis of as many daughters as possible. The data pertaining to first lactation monthly test-day milk yield (FLMTDMY) and first lactation 305-days or less milk yield (FL305DMY) of 1,105 Murrah buffalo during 1993 to 2010 at National Dairy Research Institute, Karnal (NDRI); Central Institute for Research on Buffalo, Hisar (CIRB); Guru Angad Dev Veterinary and Animal Sciences University, Ludhiana (GADVASU) and Choudhary Charan Singh Haryana Agricultural University, Hisar (CCSHAU) were collected and adjusted against significant environmental influences. In the present study FLMTDMY and FL305DMY were significantly affected by farm. First lactation records of 832 Murrah buffalo were used for evaluating 95 sires used in 7 sets. First lactation monthly test-day 6 milk yield (FLMTD6MY) had the highest genetic (0.99 ± 0.04) and phenotypic (0.78 ± 0.02) correlation with FL305DMY in Murrah buffaloes. An attempt was being made in the present investigation to estimate and compare the estimated breeding values (EBVs) of Murrah bulls through different sire evaluation methods, viz. contemporary comparison (CC), least-squares (LS), simple regressed least-squares (SRLS) and best linear unbiased prediction (BLUP) for FLMTDMY. The rank correlations among all the 4 methods of sire evaluation were highly statistically significant. BLUP method was found to be more efficient, accurate and stable with lowest genetic variation.

The article presents a study on the least-squares construction of the yield curves for Italian government securities from 1957 to 1967. The author provides a general introduction to the Italian financial system and the initial results, before considering the technical aspects. In the first section of the paper a brief outline of the Italian bond market is provided, so as to give the reader a brief knowledge of the institutional system in Italy. The main features of the estimated yield curves are then detailed and some implications of the data are considered with regard to recent attempts of the monetary authorities to prevent the increase in interest rates. Some general considerations are made before the free-hand interpolation of Durand’s “basic yields” and the U.S. treasury securities curves is considered. The linear interpolation of Grant’s British government securities yield curves is then assessed. Finally, the method for least-squares interpolation is explained before the regression model used for Italian B.T.P. and the resulting estimated yield curves are presented. JEL: G12, H63, E43

This is the first part of a study on the least-squares construction of the yield curves for Italian government securities from 1957 to 1967, in which the author provides a general introduction to the Italian financial system and the initial results. In the first section of the paper the author provides a brief outline of the Italian bond market, so as to give the reader a brief knowledge of the institutional system in Italy. The author also provides an explanation of the reasons which led to the selection of a certain group of Treasury securities - The B.T.P. - for the construction of the yield curves and the quantitative analysis of the term structure in relation to the Italian experience. In section two the main features of the estimated yield curves are detailed and some implications of the data are considered with regard to recent attempts of the monetary authorities to prevent the increase in interest rates. JEL: G12, H63, E43

This is the second part of a study on the least-squares construction of the yield curves for Italian government securities from 1957 to 1967, in which the author considers the technical aspects. Some general considerations are made before the free-hand interpolation of Durand’s “basic yields” and the U.S. treasury securities curves is considered. The linear interpolation of Grant’s British government securities yield curves is then assessed. Finally, the method for least-squares interpolation is explained before the regression model used for Italian B.T.P. and the resulting estimated yield curves are presented. JEL: G12, H63, E43

When two datasets are fused using least-squares adjustment, usually all the results will be affected by some change, even the reference data that are meant to provide information of such high quality that they should remain stable. In order to avoid this effect, the sequential adjustment is to be replaced by a strictly hierarchical method in which the esti-mation procedure is designed to reproduce everything that belongs to a "higher category" and to perform an adjustment in the least-squares sense for everything else. After presenting such a suboptimal estimator, but with the "reproducing property," this technique is applied to the integration of photogrammetric networks of substantially different scales.