Fractal analysis is one of the rapidly evolving branches of mathematics and finds its application in different analyses such as pore space description. It constitutes a new approach to the issue of their natural irregularity and roughness. To be properly applied, it should be encompassed by an error estimation. The article presents and verifies uncertainties along with imperfections connected with image analysis and expands on the possible ways of their correction. One of key aspects of such research is finding both appropriate place and the number of photos to take. A coarse- grained sandstone thin section was photographed and then pictures were combined into one, bigger image. Fractal parameters distributions show their change and suggest that the accurately gathered group of photos include both highly and less porous regions. Their amount should be representative and adequate to the sample. The resolution influence on the fractal dimension and lacunarity values was examined. For SEM limestone images obtained using backscattered electrons, magnification in the range of 120x to 2000x was used. Additionally, a single pore was examined. The acquired results point to the fact that the values of fractal dimension are similar to a wide range of magnifications, while lacunarity changes each time. This is connected with changing homogeneity of the image. The article also undertakes a problem of determining fractal parameters spatial distribution based on binarization. The available methods assume that it is carried out after or before the image division into rectangles to create fractal dimension and lacunarity values for interpolation. An individual binarization, although time consuming, provides better results that resemble reality to a closer degree. It is not possible to define a single, correct methodology of error elimination. A set of hints has been presented that can improve results of further image analysis of pore space.
The paper presents a summary of research activities concerning theoretical geodesy performed in Poland in the period of 2011–2014. It contains the results of research on new methods of the parameter estimation, a study on robustness properties of the M-estimation, control network and deformation analysis, and geodetic time series analysis. The main achievements in the geodetic parameter estimation involve a new model of the M-estimation with probabilistic models of geodetic observations, a new Shift-M split estimation, which allows to estimate a vector of parameter differences and the Shift- M split (+) that is a generalisation of Shift- M split estimation if the design matrix A of a functional model has not a full column rank. The new algorithms of the coordinates conversion between the Cartesian and geodetic coordinates, both on the rotational and triaxial ellipsoid can be mentioned as a highlights of the research of the last four years. New parameter estimation models developed have been adopted and successfully applied to the control network and deformation analysis. New algorithms based on the wavelet, Fourier and Hilbert transforms were applied to find time-frequency characteristics of geodetic and geophysical time series as well as time-frequency relations between them. Statistical properties of these time series are also presented using different statistical tests as well as 2 nd , 3 rd and 4 th moments about the mean. The new forecasts methods are presented which enable prediction of the considered time series in different frequency bands.
In this paper, two new sinusoidal signal frequency estimators calculated on the basis of four equally spaced signal samples are presented. These estimators are called four-point estimators. Simulation and experimental research consisting in signal frequency estimation using the invented estimators have been carried out. Simulation has also been performed for frequency tracking. The simulation research was carried out applying the MathCAD computer program that determined samples of a sinusoidal signal disturbed by Gaussian noise. In the experimental research, sinusoidal signal samples were obtained by means of a National Instruments PCI-6024E data acquisition card and an Agilent 33220A function generator. On the basis of the collected samples, the values of four-point estimators invented by the authors and, for comparison, the values of three- and four-point estimators proposed by Vizireanu were determined. Next, estimation errors of the signal frequency were determined. It has been shown that the invented estimators can estimate a signal frequency with greater accuracy.
In deformation analyses, it is important to find a stable reference frame and therefore the stability of the possible reference points must be controlled. There are several methods to test such stability. The paper’s objective is to examine one of such methods, namely the method based on application of R-estimation, for its sensitivity to gross errors. The method in question applies three robust estimators, however, it is not robust itself. The robustness of the method depends on the number of unstable points (the fewer unstable points there are, the more robust is the proposed method). Such property makes it important to know how the estimates applied and the strategy itself respond to a gross error. The empirical influence functions (EIF) can provide necessary information and help to understand the response of the strategy for a gross error. The paper presents examples of EIFs of the estimates, their application in the strategy and describes how important and useful is such knowledge in practice.
The sequential method of integrating navigational parameters obtained from non-simultaneous navigational measurements is presented. The proposed algorithm of position coordinates estimation is general and includes two modes of data processing – from simultaneous and non-simultaneous measurements. It can be used in hybrid receivers of radionavigation systems integrating non-homogeneous position lines or in integrated navigation systems, particularly in receivers combining the measurements of various satellite navigation systems.
This paper presents an algorithm for restoring telescope images corrupted by turbulence effects and readout noise of a telescope system in order to determine centroid positions of stars, especially the position of a reference star. A computation method employing an accurate centroid estimation algorithm reconstructing a point spread function (PSF) from the recorded astronomical images has been used. Minimisation of turbulence effects and telescope control system noise in long exposure images acquired and recorded by the ground telescope is proposed. As a solution of the distortion error a minimisation signal is dedicated to GoTo calibration procedures built in control mechanisms of the electromechanical telescope system. The proposed method has been verified in the Matlab environment for real deep sky images recorded by the ground telescope system.
The paper presents a new method for simultaneous tracking of varying grid impedance and its uncertainty bounds. Impedance tracking consists of two stages. In the first stage, the actual noise estimate is obtained from least squares (LS) residua. In the second stage, the noise covariance matrix is approximated with the use of residual information. Then weighted least squares (WLS) method is applied in order to estimate impedance and background voltage. Finally uncertainty bounds for impedance estimation are computed. The robustness of the method has been verified using simulated signals. The proposed method has been compared to sliding LS. The results have shown, that the method performs much better than the LS for all considered cases, even in the presence of significant background voltage variations.
Velocity is one of the main navigation parameters of moving objects. However some systems of position estimation using radio wave measurements cannot provide velocity data due to limitation of their performance. In this paper a velocity measurement method for the DS-CDMA radio navigation system is proposed, which does not require full synchronization of reference stations carrier frequencies. The article presents basics of FDOA (frequency difference of arrival) velocity measurements together with application of this method to an experimental radio navigation system called AEGIR and with some suggestions about the possibility to implement such FDOA measurements in other kinds of asynchronous DS-CDMA radio networks. The main part of this paper present results of performance evaluation of the proposed method, based on laboratory measurements
In this paper, we propose a new method of measuring the target velocity by estimating the scaling parameter of a chaos-generating system. First, we derive the relation between the target velocity and the scaling parameter of the chaos-generating system. Then a new method for scaling parameter estimation of the chaotic system is proposed by exploiting the chaotic synchronization property. Finally, numerical simulations show the effectiveness of the proposed method in target velocity measurement.
In this paper, a discrete wavelet transform (DWT) based approach is proposed for power system frequency estimation. Unlike the existing frequency estimators mainly used for power system monitoring and control, the proposed approach is developed for fundamental frequency estimation in the field of energy metering of nonlinear loads. The characteristics of a nonlinear load is that the power signal is heavily distorted, composed of harmonics, inter-harmonics and corrupted by noise. The main idea is to predetermine a series of frequency points, and the mean value of two frequency points nearest to the power system frequency is accepted as the approximate solution. Firstly the input signal is modulated with a series of modulating signals, whose frequencies are those frequency points. Then the modulated signals are decomposed into individual frequency bands using DWT, and differences between the maximum and minimum wavelet coefficients in the lowest frequency band are calculated. Similarities among power system frequency and those frequency points are judged by the differences. Simulation results have proven high immunity to noise, harmonic and inter-harmonic interferences. The proposed method is applicable for real-time power system frequency estimation for electric energy measurement of nonlinear loads.
The pathological states of biological tissue are often resulted in attenuation changes. Thus, information about attenuating properties of tissue is valuable for the physician and could be useful in ultrasonic diagnosis. We are currently developing a technique for parametric imaging of attenuation and we intend to apply it for in vivo characterization of tissue. The attenuation estimation method based on the echoes mean frequency changes due to tissue attenuation dispersion, is presented. The Doppler IQ technique was adopted to estimate the mean frequency directly from the raw RF data. The Singular Spectrum Analysis technique was used for the extraction of mean frequency trends. These trends were converted into attenuation distribution and finally the parametric images were computed. In order to reduce variation of attenuation estimates the spatial compounding method was applied. Operation and accuracy of attenuation extracting procedure was verified by calculating the attenuation coefficient distribution using the data from the tissue phantom (DFS, Denmark) with uniform echogenicity while attenuation coefficient underwent variation.
This overview paper presents and compares different methods traditionally used for estimating damped sinusoid parameters. Firstly, direct nonlinear least squares fitting the signal model in the time and frequency domains are described. Next, possible applications of the Hilbert transform for signal demodulation are presented. Then, a wide range of autoregressive modelling methods, valid for damped sinusoids, are discussed, in which frequency and damping are estimated from calculated signal linear self-prediction coefficients. These methods aim at solving, directly or using least squares, a matrix linear equation in which signal or its autocorrelation function samples are used. The Prony, Steiglitz-McBride, Kumaresan-Tufts, Total Least Squares, Matrix Pencil, Yule-Walker and Pisarenko methods are taken into account. Finally, the interpolated discrete Fourier transform is presented with examples of Bertocco, Yoshida, and Agrež algorithms. The Matlab codes of all the discussed methods are given. The second part of the paper presents simulation results, compared with the Cramér-Rao lower bound and commented. All tested methods are compared with respect to their accuracy (systematic errors), noise robustness, required signal length, and computational complexity.
Conventionally, the filtering technique for attitude estimation is performed using gyros or attitude dynamics models. In order to extend the application range of an attitude filter, this paper proposes a quaternionbased filtering framework for gyroless attitude estimation without an attitude dynamics model. The attitude estimation system is established based on a quaternion kinematic equation and vector observation models. The angular velocity in the system is determined through observation vectors from attitude sensors and the statistical properties of the angular velocity error are analysed. A Kalman filter is applied to estimate the attitude error such that the effect from the angular velocity error is compensated with its statistical properties at each sampling moment. A numerical simulation example is presented to illustrate the performance of the proposed algorithm.
MP estimation is a method which concerns estimating of the location parameters when the probabilistic models of observations differ from the normal distributions in the kurtosis or asymmetry. The system of Pearson’s distributions is the probabilistic basis for the method. So far, such a method was applied and analyzed mostly for leptokurtic or mesokurtic distributions (Pearson’s distributions of types IV or VII), which predominate practical cases. The analyses of geodetic or astronomical observations show that we may also deal with sets which have moderate asymmetry or small negative excess kurtosis. Asymmetry might result from the influence of many small systematic errors, which were not eliminated during preprocessing of data. The excess kurtosis can be related with bigger or smaller (in relations to the Hagen hypothesis) frequency of occurrence of the elementary errors which are close to zero. Considering that fact, this paper focuses on the estimation with application of the Pearson platykurtic distributions of types I or II. The paper presents the solution of the corresponding optimization problem and its basic properties. Although platykurtic distributions are rare in practice, it was an interesting issue to find out what results can be provided by MP estimation in the case of such observation distributions. The numerical tests which are presented in the paper are rather limited; however, they allow us to draw some general conclusions.
The work presents the results of studies on dependence of effectiveness of chosen robust estimation methods from the internal reliability level of a geodetic network. The studies use computer-simulated observation systems, so it was possible to analyse many variants differing from each other in a planned way. Four methods of robust estimation have been chosen for the studies, differing substantially in the approach to weight modifications. For comparative reasons, the effectiveness studies have also been conducted for the very popular method in surveying practice, of gross error detection basing on LS estimation results, the so called iterative data snooping. The studies show that there is a relation between the level of network internal reliability and the effectiveness of robust estimation methods. In most cases, in which the observation contaminated by a gross error was characterized by a low index of internal reliability, the robust estimation led to results being essentially far from expectations.
Generally, gross errors exist in observations, and they affect the accuracy of results. We review methods to detect the gross errors by Robust estimation method based on L1-estimation theory and their validity in adjustment of geodetic networks with different condition. In order to detect the gross errors, we transform the weight of accidental model into equivalent one using not standardized residual but residual of observation, and apply this method to adjustment computation of triangulation network, traverse network, satellite geodetic network and so on. In triangulation network, we use a method of transforming into equivalent weight by residual and detect gross error in parameter adjustment without and with condition. The result from proposed method is compared with the one from using standardized residual as equivalent weight. In traverse network, we decide the weight by Helmert variance component estimation, and then detect gross errors and compare by the same way with triangulation network In satellite geodetic network in which observations are correlated, we detect gross errors transforming into equivalent correlation matrix by residual and variance inflation factor and the result is also compared with the result from using standardized residual. The results of detection are shown that it is more convenient and effective to detect gross errors by residual in geodetic network adjustment of various forms than detection by standardized residual.
The integrated Singular Value Decomposition (SVD) and Unscented Kalman Filter (UKF) method can recursively estimate the attitude and attitude rates of a nanosatellite. At first, Wahba’s loss function is minimized using the SVD and the optimal attitude angles are determined on the basis of the magnetometer and Sun sensor measurements. Then, the UKF makes use of the SVD’s attitude estimates as measurement results and provides more accurate attitude information as well as the attitude rate estimates. The elements of “Rotation angle error covariance matrix” calculated for the SVD estimations are used in the UKF as the measurement noise covariance values. The algorithm is compared with the SVD and UKF only methods for estimating the attitude from vector measurements. Possible algorithm switching ideas are discussed especially for the eclipse period, when the Sun sensor measurements are not available.
Precise measurement of rail vehicle velocities is an essential prerequisite for the implementation of modern train control systems and the improvement of transportation capacity and logistics. Novel eddy current sensor systems make it possible to estimate velocity by using cross-correlation techniques, which show a decline in precision in areas of high accelerations. This is due to signal distortions within the correlation interval. We propose to overcome these problems by employing algorithms from the field of dynamic programming. In this paper we evaluate the application of correlation optimized warping, an enhanced version of dynamic time warping algorithms, and compare it with the classical algorithm for estimating rail vehicle velocities in areas of high accelerations and decelerations.
The determination of the form of a probability density function (PDF3) of diameters for nodular particles by using a probability density function (PDF2), which form is empirically estimated from cross-sections of these nodules in a metallographic specimen, can be regarded as a special case of Wicksell's corpuscle problem (WCP). The estimation of the PDF3 for the nodular particles provides information about the kinetics of these particles nucleation, and so about the kinetics of their growth. This information is essential for building more accurate mathematical models of the alloy crystallization. In the paper there are presented two derivations of the methods used for the estimation of the PDF3 form. The first method bases on diameters received from a planar cross-section. The second one uses also data from the planar cross-section but not the diameters only chords. Both methods provide practical rules for the analysis of the empirical diameters’ and chord’s size distribution and allow to estimate the mean value of the external surface area of the particles.
This paper proposes a modification of the classical process for evaluating the statistical significance of displacements in the case of heterogeneous (e.g. linear-angular) control networks established to deformation measurements and analysis. The basis for the proposed solution is the idea of local variance factors. The theoretical discussion was complemented with an example of its application on a simulated horizontal control network. The obtained results showed that the evaluation of the statistical significance of displacements in the case of heterogeneous control networks should be carried out using estimators of local variance factors.
Osier (salix viminalis) is a promising energy crop for the growing bioenergy purposes in Ukraine. It is unpretentious to the conditions of growth, marked with simplicity of cultivation technology, well-withdrawn for fertilization. Sewage sludge, due to its chemical composition and high content of organic matter, can be successfully used to fertilize the willow. The calculations of bioenergetic and economic efficiency showed that application of sewage sludge and compost with sawdust and straw in a ratio of 3: 1 at osier is marked with a high effect. In the studies performed in conditions of Ukraine’s Precarpathians on sod-podzolic soils we found that the highest biomass output and, therefore, gross energy per unit of area in agrocenoses of osier provided the application of fresh sewage sludge at a rate of 80 t / ha. In this option the dry biomass output made 39.4 t / ha, gross energy with the yield - 1,580 GJ / ha, the costs of energy generation - 6.2 UAH / GJ, the costs of gross output - 17.8 thousand UAH / ha, the rate of energy efficiency - 1.69. However, the highest rates of economic and bioenergetic efficiency after the fourth year of the willow vegetation we observed when the sewage sludge compost with straw of grain crops at a doze 40 and 60 t / ha was applied. In these variants the lowest cost of the biomass production was obtained (at the level 109 - 111 UAH / ton), the cost of the received energy from the biomass (5.6 - 5.7 UAH / GJ), the highest profitability value (97 - 101%) and the best performing of energy efficiency coefficient - 1.85 - 1.89.