Search results for: Oustaloup's Recursive Approximation

Authors: Miloje S. Radenkovic, Tamal Bose

Abstract:

This paper presents the convergence analysis of a prediction based blind equalizer for IIR channels. Predictor parameters are estimated by using the recursive least squares algorithm. It is shown that the prediction error converges almost surely (a.s.) toward a scalar multiple of the unknown input symbol sequence. It is also proved that the convergence rate of the parameter estimation error is of the same order as that in the iterated logarithm law.

Keywords: Adaptive blind equalizer, Recursive leastsquares, Adaptive Filtering, Convergence analysis.

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Authors: Nahid-Al-Masood, Jubaer Ahmed, Amina Hasan Abedin, S. R. Deeba, Faeza Hafiz, Mahmuda Begum

Abstract:

An electric utility-s main concern is to plan, design, operate and maintain its power supply to provide an acceptable level of reliability to its users. This clearly requires that standards of reliability be specified and used in all three sectors of the power system, i.e., generation, transmission and distribution. That is why reliability of a power system is always a major concern to power system planners. This paper presents the reliability analysis of Bangladesh Power System (BPS). Reliability index, loss of load probability (LOLP) of BPS is evaluated using recursive algorithm and considering no de-rated states of generators. BPS has sixty one generators and a total installed capacity of 5275 MW. The maximum demand of BPS is about 5000 MW. The relevant data of the generators and hourly load profiles are collected from the National Load Dispatch Center (NLDC) of Bangladesh and reliability index 'LOLP' is assessed for the period of last ten years.

Keywords: Recursive algorithm, LOLP, forced outage rate, cumulative probability.

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Authors: Mario Mastriani

Abstract:

We describe a new filtering approach in the wavelet domain for image denoising and compression, based on the projections of details subbands coefficients (resultants of the splitting procedure, typical in wavelet domain) onto the approximation subband coefficients (much less noisy). The new algorithm is called Projection Onto Approximation Coefficients (POAC). As a result of this approach, only the approximation subband coefficients and three scalars are stored and/or transmitted to the channel. Besides, with the elimination of the details subbands coefficients, we obtain a bigger compression rate. Experimental results demonstrate that our approach compares favorably to more typical methods of denoising and compression in wavelet domain.

Keywords: Compression, denoising, projections, wavelets.

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Authors: S. B. Mansuri

Abstract:

In this paper, at first we explain about negative hypergeometric distribution and its properties. Then we use the w-function and the Stein identity to give a result on the poisson approximation to the negative hypergeometric distribution in terms of the total variation distance between the negative hypergeometric and poisson distributions and its upper bound.

Keywords: Negative hypergeometric distribution, Poisson distribution, Poisson approximation, Stein-Chen identity, w-function.

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Authors: Yongxin Yuan, Hao Liu

Abstract:

In this paper, we first give the representation of the general solution of the following least-squares problem (LSP): Given matrices X ∈ Rn×p, B ∈ Rp×p and A0 ∈ Rr×r, find a matrix A ∈ Rn×n such that XT AX − B = min, s. t. A([1, r]) = A0, where A([1, r]) is the r×r leading principal submatrix of the matrix A. We then consider a best approximation problem: given an n × n matrix A˜ with A˜([1, r]) = A0, find Aˆ ∈ SE such that A˜ − Aˆ = minA∈SE A˜ − A, where SE is the solution set of LSP. We show that the best approximation solution Aˆ is unique and derive an explicit formula for it. Keyw

Keywords: Inverse problem, Least-squares solution, model updating, Singular value decomposition (SVD), Optimal approximation.

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Authors: A.S. Rebaï, M. Elloumi

Abstract:

The Shortest Approximate Common Superstring (SACS) problem is : Given a set of strings f={w1, w2, ... , wn}, where no wi is an approximate substring of wj, i ≠ j, find a shortest string Sa, such that, every string of f is an approximate substring of Sa. When the number of the strings n>2, the SACS problem becomes NP-complete. In this paper, we present a greedy approximation SACS algorithm. Our algorithm is a 1/2-approximation for the SACS problem. It is of complexity O(n2*(l2+log(n))) in computing time, where n is the number of the strings and l is the length of a string. Our SACS algorithm is based on computation of the Length of the Approximate Longest Overlap (LALO).

Keywords: Shortest approximate common superstring, approximation algorithms, strings overlaps, complexities.

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Authors: Properties, Approximation Distribution Reductions in Multigranulation Rough Set Model

Abstract:

Some properties of approximation sets are studied in multi-granulation optimist model in rough set theory using maximal compatible classes. The relationships between or among lower and upper approximations in single and multiple granulation are compared and discussed. Through designing Boolean functions and discernibility matrices in incomplete information systems, the lower and upper approximation sets and reduction in multi-granulation environments can be found. By using examples, the correctness of computation approach is consolidated. The related conclusions obtained are suitable for further investigating in multiple granulation RSM.

Keywords: Incomplete information system, maximal compatible class, multi-granulation rough set model, reduction.

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Authors: Jevgenijs Carkovs

Abstract:

The paper is devoted to stochastic analysis of finite dimensional difference equation with dependent on ergodic Markov chain increments, which are proportional to small parameter ". A point-form solution of this difference equation may be represented as vertexes of a time-dependent continuous broken line given on the segment [0,1] with "-dependent scaling of intervals between vertexes. Tending " to zero one may apply stochastic averaging and diffusion approximation procedures and construct continuous approximation of the initial stochastic iterations as an ordinary or stochastic Ito differential equation. The paper proves that for sufficiently small " these equations may be successfully applied not only to approximate finite number of iterations but also for asymptotic analysis of iterations, when number of iterations tends to infinity.

Keywords: Markov dynamical system, diffusion approximation, equilibrium stochastic stability.

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Authors: M.Asif, M.R.Arshad, P.A.Wilson

Abstract:

In this paper, a simple active contour based visual tracking algorithm is presented for outdoor AGV application which is currently under development at the USM robotic research group (URRG) lab. The presented algorithm is computationally low cost and able to track road boundaries in an image sequence and can easily be implemented on available low cost hardware. The proposed algorithm used an active shape modeling using the B-spline deformable template and recursive curve fitting method to track the current orientation of the road.

Keywords: Active contour, B-spline, recursive curve fitting.

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Authors: S. Heydarzadeh, A. Kadivarian, P. Torkzadeh

Abstract:

Implemented 5-bit 125-MS/s successive approximation register (SAR) analog to digital converter (ADC) on FPGA is presented in this paper.The design and modeling of a high performance SAR analog to digital converter are based on monotonic capacitor switching procedure algorithm .Spartan 3 FPGA is chosen for implementing SAR analog to digital converter algorithm. SAR VHDL program writes in Xilinx and modelsim uses for showing results.

Keywords: Analog to digital converter, Successive approximation, Capacitor switching algorithm, FPGA

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Authors: Noor Atinah Ahmad, Shazia Javed

Abstract:

We present a discussion of three adaptive filtering algorithms well known for their one-step termination property, in terms of their relationship with the minimal residual method. These algorithms are the normalized least mean square (NLMS), Affine Projection algorithm (APA) and the recursive least squares algorithm (RLS). The NLMS is shown to be a result of the orthogonality condition imposed on the instantaneous approximation of the Wiener equation, while APA and RLS algorithm result from orthogonality condition in multi-dimensional minimal residual formulation. Further analysis of the minimal residual formulation for the RLS leads to a triangular system which also possesses the one-step termination property (in exact arithmetic)

Keywords: Adaptive filtering, minimal residual method, projection method.

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Authors: S. Panda, S. K. Tomar, R. Prasad, C. Ardil

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Order reduction of linear-time invariant systems employing two methods; one using the advantages of Routh approximation and other by an evolutionary technique is presented in this paper. In Routh approximation method the denominator of the reduced order model is obtained using Routh approximation while the numerator of the reduced order model is determined using the indirect approach of retaining the time moments and/or Markov parameters of original system. By this method the reduced order model guarantees stability if the original high order model is stable. In the second method Particle Swarm Optimization (PSO) is employed to reduce the higher order model. PSO method is based on the minimization of the Integral Squared Error (ISE) between the transient responses of original higher order model and the reduced order model pertaining to a unit step input. Both the methods are illustrated through numerical examples.

Keywords: Model Order Reduction, Markov Parameters, Routh Approximation, Particle Swarm Optimization, Integral Squared Error, Steady State Stability.

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Authors: Yeonsoo Jang, Dongweon Yoon, Ki Ho Kwon, Jaeyoon Lee, Wooju Lee

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Phase error in communications systems degrades error performance. In this paper, we present a simple approximation for the average error probability of the binary phase shift keying (BPSK) in the presence of phase error having a uniform distribution on arbitrary intervals. For the simple approximation, we use symmetry and periodicity of a sinusoidal function. Approximate result for the average error probability is derived, and the performance is verified through comparison with simulation result.

Keywords: Average error probability, Phase shift keying, Phase error

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Authors: S. Seyedtabaii, E. Seyedtabaii

Abstract:

Rounding of coefficients is a common practice in hardware implementation of digital filters. Where some coefficients are very close to zero or one, as assumed in this paper, this rounding action also leads to some computation reduction. Furthermore, if the discarded coefficient is of high order, a reduced order filter is obtained, otherwise the order does not change but computation is reduced. In this paper, the Least Squares approximation to rounded (or discarded) coefficient FIR filter is investigated. The result also succinctly extended to general type of FIR filters.

Keywords: Digital filter, filter approximation, least squares, model order reduction.

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Authors: Diogo Silva, Fadul Rodor, Carlos Moraes

Abstract:

This work compares the results of multidimensional function approximation using two algorithms: the classical Particle Swarm Optimization (PSO) and the Quantum Particle Swarm Optimization (QPSO). These algorithms were both tested on three functions - The Rosenbrock, the Rastrigin, and the sphere functions - with different characteristics by increasing their number of dimensions. As a result, this study shows that the higher the function space, i.e. the larger the function dimension, the more evident the advantages of using the QPSO method compared to the PSO method in terms of performance and number of necessary iterations to reach the stop criterion.

Keywords: PSO, QPSO, function approximation, AI, optimization, multidimensional functions.

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Authors: Sirapat Lookrak, Anol Paisal

Abstract:

Space debris has numerous manifestations including ferro-metalize and non-ferrous. The electric field will induce negative charges to split from positive charges inside the space debris. In this research, we focus only on conducting materials. The assumption is that the electric charge density of a conducting surface is proportional to the electric field on that surface due to Gauss's law. We are trying to find the induced charge density from an external electric field perpendicular to a conducting spherical surface. An object is a sphere on which the external electric field is not uniform. The electric field is, therefore, considered locally. The localised spherical surface is a tangent plane so the Gaussian surface is a very small cylinder and every point on a spherical surface has its own cylinder. The electric field from a circular electrode has been calculated in near-field and far-field approximation and shown Explanation Touchless manoeuvring space debris orbit properties. The electric charge density calculation from a near-field and far-field approximation is done.

Keywords: Near-field approximation, far-field approximation, localized Gauss’s law, electric charge density.

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Authors: Edlira Donefski, Lorenc Ekonomi, Tina Donefski

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Edgeworth approximation is one of the most important statistical methods that has a considered contribution in the reduction of the sum of standard deviation of the independent variables’ coefficients in a Quantile Regression Model. This model estimates the conditional median or other quantiles. In this paper, we have applied approximating statistical methods in an economical problem. We have created and generated a quantile regression model to see how the profit gained is connected with the realized sales of the cosmetic products in a real data, taken from a local business. The Linear Regression of the generated profit and the realized sales was not free of autocorrelation and heteroscedasticity, so this is the reason that we have used this model instead of Linear Regression. Our aim is to analyze in more details the relation between the variables taken into study: the profit and the finalized sales and how to minimize the standard errors of the independent variable involved in this study, the level of realized sales. The statistical methods that we have applied in our work are Edgeworth Approximation for Independent and Identical distributed (IID) cases, Bootstrap version of the Model and the Edgeworth approximation for Bootstrap Quantile Regression Model. The graphics and the results that we have presented here identify the best approximating model of our study.

Keywords: Bootstrap, Edgeworth approximation, independent and Identical distributed, quantile.

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Authors: Hsun Su, Yuan-Kang Shih, Shin-Shin Kao

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Many well-known interconnection networks, such as kary n-cubes, recursive circulant graphs, generalized recursive circulant graphs, circulant graphs and so on, are shown to belong to the family of cycle composition networks. Recently, various studies about mutually independent hamiltonian cycles, abbreviated as MIHC-s, on interconnection networks are published. In this paper, using an improved construction method, we obtain MIHC-s on cycle composition networks with a much weaker condition than the known result. In fact, we established the existence of MIHC-s in the cycle composition networks and the result is optimal in the sense that the number of MIHC-s we constructed is maximal.

Keywords: Hamiltonian cycle, k-ary n-cube, cycle composition networks, mutually independent.

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Authors: Alina Mirza, Sumrin M. Kabir, Shahzad A. Sheikh

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The Orthogonal Frequency Division Multiplexing (OFDM) with high data rate, high spectral efficiency and its ability to mitigate the effects of multipath makes them most suitable in wireless application. Impulsive noise distorts the OFDM transmission and therefore methods must be investigated to suppress this noise. In this paper, a State Space Recursive Least Square (SSRLS) algorithm based adaptive impulsive noise suppressor for OFDM communication system is proposed. And a comparison with another adaptive algorithm is conducted. The state space model-dependent recursive parameters of proposed scheme enables to achieve steady state mean squared error (MSE), low bit error rate (BER), and faster convergence than that of some of existing algorithm.

Keywords: OFDM, Impulsive Noise, SSRLS, BER.

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Authors: Anosh Arshad Sundhu, Francesco Giordano, Giacomo Della Croce, Maurizio Arnone

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Digital Twin (DT) is a technology that generates a virtual representation of a physical system or process, enabling real-time monitoring, analysis, and simulation. DT of an Electrical Distribution System (EDS) can perform online analysis by integrating the static and real-time data in order to show the current grid status and predictions about the future status to the Distribution System Operator (DSO), producers and consumers. DT technology for EDS also offers the opportunity to DSO to test hypothetical scenarios. This paper discusses the development of a DT of an EDS by Smart Grid Controller (SGC) application, which is developed using open-source libraries and languages. The developed application can be integrated with Supervisory Control and Data Acquisition System (SCADA) of any EDS for creating the DT. The paper shows the performance of developed tools inside the application, tested on real EDS for grid observability, Smart Recursive Load Flow (SRLF) calculation and state estimation of loads in MV feeders.

Keywords: Digital Twin, Distribution System Operator, Electrical Distribution System, Smart Grid Controller, Supervisory Control and Data Acquisition System, Smart Recursive Load Flow.

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Authors: Hadi Sadoghi Yazdi, Mehri Sadoghi Yazdi, Mohammad Reza Mohammadi

Abstract:

This paper is concerned with studying the forgetting factor of the recursive least square (RLS). A new dynamic forgetting factor (DFF) for RLS algorithm is presented. The proposed DFF-RLS is compared to other methods. Better performance at convergence and tracking of noisy chirp sinusoid is achieved. The control of the forgetting factor at DFF-RLS is based on the gradient of inverse correlation matrix. Compared with the gradient of mean square error algorithm, the proposed approach provides faster tracking and smaller mean square error. In low signal-to-noise ratios, the performance of the proposed method is superior to other approaches.

Keywords: Forgetting factor, RLS, Inverse correlation matrix, human motion analysis.

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Authors: Erol Seke, Kemal Özkan

Abstract:

Linear approximation of point spread function (PSF) is a new method for determining subpixel translations between images. The problem with the actual algorithm is the inability of determining translations larger than 1 pixel. In this paper a multiresolution technique is proposed to deal with the problem. Its performance is evaluated by comparison with two other well known registration method. In the proposed technique the images are downsampled in order to have a wider view. Progressively decreasing the downsampling rate up to the initial resolution and using linear approximation technique at each step, the algorithm is able to determine translations of several pixels in subpixel levels.

Keywords: Point Spread Function, Subpixel translation, Superresolution, Multiresolution approach.

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Authors: Yasunori Sugita, Toshinori Yoshikawa

Abstract:

The design problem of Infinite Impulse Response (IIR) digital filters is usually expressed as the minimization problem of the complex magnitude error that includes both the magnitude and phase information. However, the group delay of the filter obtained by solving such design problem may be far from the desired group delay. In this paper, we propose a design method of stable IIR digital filters with prespecified maximum group delay errors. In the proposed method, the approximation problems of the magnitude-phase and group delay are separately defined, and these two approximation problems are alternately solved using successive projections. As a result, the proposed method can design the IIR filters that satisfy the prespecified allowable errors for not only the complex magnitude but also the group delay by alternately executing the coefficient update for the magnitude-phase and the group delay approximation. The usefulness of the proposed method is verified through some examples.

Keywords: Filter design, Group delay approximation, Stable IIRfilters, Successive projection method.

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Authors: E. Assareh, M.A. Behrang, M. Ghalambaz, A.R. Noghrehabadi, A. Ghanbarzadeh

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In this paper, a new approach is introduced to solve Blasius equation using parameter identification of a nonlinear function which is used as approximation function. Bees Algorithm (BA) is applied in order to find the adjustable parameters of approximation function regarding minimizing a fitness function including these parameters (i.e. adjustable parameters). These parameters are determined how the approximation function has to satisfy the boundary conditions. In order to demonstrate the presented method, the obtained results are compared with another numerical method. Present method can be easily extended to solve a wide range of problems.

Keywords: Bees Algorithm (BA); Approximate Solutions; Blasius Differential Equation.

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Authors: Elena Kotevska

Abstract:

This paper presents a generalization kernel for gravitational potential determination by harmonic splines. It was shown in [10] that the gravitational potential can be approximated using a kernel represented as a Newton integral over the real Earth body. On the other side, the theory of geopotential approximation by harmonic splines uses spherically oriented kernels. The purpose of this paper is to show that in the spherical case both kernels have the same type of representation, which leads us to conclusion that it is possible to consider the kernel represented as a Newton integral over the real Earth body as a kind of generalization of spherically harmonic kernels to real geometries.

Keywords: Geopotential, Reproducing Kernel, Approximation, Regular Surface

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Authors: Jyh-Da Wei, Hsin-Chen Tsai

Abstract:

This work presents a novel means of extracting fixedlength parameters from voice signals, such that words can be recognized in linear time. The power and the zero crossing rate are first calculated segment by segment from a voice signal; by doing so, two feature sequences are generated. We then construct an FIR system across these two sequences. The parameters of this FIR system, used as the input of a multilayer proceptron recognizer, can be derived by recursive LSE (least-square estimation), implying that the complexity of overall process is linear to the signal size. In the second part of this work, we introduce a weighting factor λ to emphasize recent input; therefore, we can further recognize continuous speech signals. Experiments employ the voice signals of numbers, from zero to nine, spoken in Mandarin Chinese. The proposed method is verified to recognize voice signals efficiently and accurately.

Keywords: Speech Recognition, FIR system, Recursive LSE, Multilayer Perceptron

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Authors: Jiming Yang

Abstract:

An upwind difference approximation is used for a singularly perturbed problem in material science. Based on the discrete Green-s function theory, the error estimate in maximum norm is achieved, which is first-order uniformly convergent with respect to the perturbation parameter. The numerical experimental result is verified the valid of the theoretical analysis.

Keywords: Singularly perturbed, upwind difference, uniform convergence.

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Authors: Ali Abdrhman Ukasha

Abstract:

This paper presented two new efficient algorithms for contour approximation. The proposed algorithm is compared with Ramer (good quality), Triangle (faster) and Trapezoid (fastest) in this work; which are briefly described. Cartesian co-ordinates of an input contour are processed in such a manner that finally contours is presented by a set of selected vertices of the edge of the contour. In the paper the main idea of the analyzed procedures for contour compression is performed. For comparison, the mean square error and signal-to-noise ratio criterions are used. Computational time of analyzed methods is estimated depending on a number of numerical operations. Experimental results are obtained both in terms of image quality, compression ratios, and speed. The main advantages of the analyzed algorithm is small numbers of the arithmetic operations compared to the existing algorithms.

Keywords: Polygonal approximation, Ramer, Triangle and Trapezoid methods.

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Authors: Yeqing Guan, Fen Yang

Abstract:

To learn about China-s future energy demand, this paper first proposed GM(1,1) model group based on recursive solutions of parameters estimation, setting up a general solving-algorithm of the model group. This method avoided the problems occurred on the past researches that remodeling, loss of information and large amount of calculation. This paper established respectively all-data-GM(1,1), metabolic GM(1,1) and new information GM (1,1)model according to the historical data of energy consumption in China in the year 2005-2010 and the added data of 2011, then modeling, simulating and comparison of accuracies we got the optimal models and to predict. Results showed that the total energy demand of China will be 37.2221 billion tons of equivalent coal in 2012 and 39.7973 billion tons of equivalent coal in 2013, which are as the same as the overall planning of energy demand in The 12th Five-Year Plan.

Keywords: energy demands, GM(1, 1) model group, least square estimation, prediction

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Authors: Kyu Chul Lee, Sung Hyun Yoo, Choon Ki Ahn, Myo Taeg Lim

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Recent experimental evidences have shown that because of a fast convergence and a nice accuracy, neural networks training via extended kalman filter (EKF) method is widely applied. However, as to an uncertainty of the system dynamics or modeling error, the performance of the method is unreliable. In order to overcome this problem in this paper, a new finite impulse response (FIR) filter based learning algorithm is proposed to train radial basis function neural networks (RBFN) for nonlinear function approximation. Compared to the EKF training method, the proposed FIR filter training method is more robust to those environmental conditions. Furthermore , the number of centers will be considered since it affects the performance of approximation.

Keywords: Extended kalmin filter (EKF), classification problem, radial basis function networks (RBFN), finite impulse response (FIR)filter.

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