Search results for: error estimation

Authors: Josip Vasilj, Petar Sarajcev, Damir Jakus

Abstract:

One of the major difficulties introduced with wind power penetration is the inherent uncertainty in production originating from uncertain wind conditions. This uncertainty impacts many different aspects of power system operation, especially the balancing power requirements. For this reason, in power system development planing, it is necessary to evaluate the potential uncertainty in future wind power generation. For this purpose, simulation models are required, reproducing the performance of wind power forecasts. This paper presents a wind power forecast error simulation models which are based on the stochastic process simulation. Proposed models capture the most important statistical parameters recognized in wind power forecast error time series. Furthermore, two distinct models are presented based on data availability. First model uses wind speed measurements on potential or existing wind power plant locations, while the seconds model uses statistical distribution of wind speeds.

Keywords: Wind power, Uncertainty, Stochastic process, Monte Carlo simulation.

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Authors: Mohammad Ghavami, Reza S. Dilmaghani

Abstract:

This paper presents an adaptive framework for modelling financial markets using equity risk premiums, risk free rates and volatilities. The recorded economic factors are initially used to train four adaptive filters for a certain limited period of time in the past. Once the systems are trained, the adjusted coefficients are used for modelling and prediction of an important financial market index. Two different approaches based on least mean squares (LMS) and recursive least squares (RLS) algorithms are investigated. Performance analysis of each method in terms of the mean squared error (MSE) is presented and the results are discussed. Computer simulations carried out using recorded data show MSEs of 4% and 3.4% for the next month prediction using LMS and RLS adaptive algorithms, respectively. In terms of twelve months prediction, RLS method shows a better tendency estimation compared to the LMS algorithm.

Keywords: Prediction of financial markets, Adaptive methods, MSE, LSE.

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Authors: Soon-Hyun Park, Takami Matsuo

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This paper presents an adaptive differentiator of sequential data based on the adaptive control theory. The algorithm is applied to detect moving objects by estimating a temporal gradient of sequential data at a specified pixel. We adopt two nonlinear intensity functions to reduce the influence of noises. The derivatives of the nonlinear intensity functions are estimated by an adaptive observer with σ-modification update law.

Keywords: Adaptive estimation, parameter adjustmentlaw, motion detection, temporal gradient, differential filter.

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Authors: Mehdi Amoui, Mohammad Zarafshan, Caro Lucas

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In spite of all advancement in software testing, debugging remains a labor-intensive, manual, time consuming, and error prone process. A candidate solution to enhance debugging process is to fuse it with testing process. To achieve this integration, a possible solution may be categorizing common software tests and errors followed by the effort on fixing the errors through general solutions for each test/error pair. Our approach to address this issue is based on Christopher Alexander-s pattern and pattern language concepts. The patterns in this language are grouped into three major sections and connect the three concepts of test, error, and debug. These patterns and their hierarchical relationship shape a pattern language that introduces a solution to solve software errors in a known testing context. Finally, we will introduce our developed framework ADE as a sample implementation to support a pattern of proposed language, which aims to automate the whole process of evolving software design via evolutionary methods.

Keywords: Coding Errors, Software debugging, Testing, Patterns, Pattern Language

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Authors: Ilaria Lucrezia Amerise

Abstract:

The statistical modelling of precipitation data for a given portion of territory is fundamental for the monitoring of climatic conditions and for Hydrogeological Management Plans (HMP). This modelling is rendered particularly complex by the changes taking place in the frequency and intensity of precipitation, presumably to be attributed to the global climate change. This paper applies the Wakeby distribution (with 5 parameters) as a theoretical reference model. The number and the quality of the parameters indicate that this distribution may be the appropriate choice for the interpolations of the hydrological variables and, moreover, the Wakeby is particularly suitable for describing phenomena producing heavy tails. The proposed estimation methods for determining the value of the Wakeby parameters are the same as those used for density functions with heavy tails. The commonly used procedure is the classic method of moments weighed with probabilities (probability weighted moments, PWM) although this has often shown difficulty of convergence, or rather, convergence to a configuration of inappropriate parameters. In this paper, we analyze the problem of the likelihood estimation of a random variable expressed through its quantile function. The method of maximum likelihood, in this case, is more demanding than in the situations of more usual estimation. The reasons for this lie, in the sampling and asymptotic properties of the estimators of maximum likelihood which improve the estimates obtained with indications of their variability and, therefore, their accuracy and reliability. These features are highly appreciated in contexts where poor decisions, attributable to an inefficient or incomplete information base, can cause serious damages.

Keywords: Generalized extreme values (GEV), likelihood estimation, precipitation data, Wakeby distribution.

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Authors: Mihai Brânzei, Ioan Plotog, Ion Pencea

Abstract:

The Pads have unique values of thermophysical properties (THP) having important contribution over heat transfer into the PCB structure. Materials with high thermal diffusivity (TD) rapidly adjust their temperature to that of their surroundings, because the HT is quick in compare to their volumetric heat capacity (VHC). In the paper is presenting the diffusivity tests (ASTM E1461 flash method) for PCBs with different core materials. In the experiments, the multilayer structure of PCBA was taken into consideration, an equivalent property referring to each of experimental structure be practically measured. Concerning to entire structure, the THP emphasize the major contribution of substrate in establishing of reflow soldering process (RSP) heat transfer necessities. This conclusion offer practical solution for heat transfer time constant calculation as function of thickness and substrate material diffusivity with an acceptable error estimation.

Keywords: heat transfer time constant, packaging, reflowsoldering process, thermal diffusivity.

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Authors: Somayeh Komeylian

Abstract:

Array signal processing techniques have been recently developing in a variety application of the performance enhancement of receivers by refraining the power of jamming and interference signals. In this scenario, biases induced to the antenna array receiver degrade significantly the accurate estimation of the carrier phase. Owing to the integration of frequency becomes the carrier phase, we have obtained the unbiased doppler frequency for the high precision estimation of carrier phase. The unbiased characteristic of Doppler frequency to the power jamming and the other interference signals allows achieving the highly accurate estimation of phase carrier. In this study, we have rigorously investigated the unbiased characteristic of Doppler frequency to the variation of the antenna array geometries. The simulation results have efficiently verified that the Doppler frequency remains also unbiased and accurate to the variation of antenna array geometries.

Keywords: Array signal processing, unbiased Doppler frequency, GNSS, carrier phase, slowly fluctuating point target.

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Authors: R. Oonsivilai, A. Oonsivilai

Abstract:

Realistic systems generally are systems with various inputs and outputs also known as Multiple Input Multiple Output (MIMO). Such systems usually prove to be complex and difficult to model and control purposes. Therefore, decomposition was used to separate individual inputs and outputs. A PID is assigned to each individual pair to regulate desired settling time. Suitable parameters of PIDs obtained from Genetic Algorithm (GA), using Mean of Squared Error (MSE) objective function.

Keywords: Gas Turbine, PID, Genetic Algorithm, Transfer function.Mean of Squared Error

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Authors: Peter Podbreznik, Božidar Potocnik

Abstract:

The camera parameters are changed due to temperature variations, which directly influence calibrated cameras accuracy. Robustness of calibration methods were measured and their accuracy was tested. An error ratio due to camera parameters change with respect to total error originated during calibration process was determined. It pointed out that influence of temperature variations decrease by increasing distance of observed objects from cameras.

Keywords: camera calibration, perspective projection matrix, epipolar geometry, temperature variation.

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Authors: H.Panahi, S.Asadi

Abstract:

In this article, we consider the estimation of P[Y < X], when strength, X and stress, Y are two independent variables of Burr Type XII distribution. The MLE of the R based on one simple iterative procedure is obtained. Assuming that the common parameter is known, the maximum likelihood estimator, uniformly minimum variance unbiased estimator and Bayes estimator of P[Y < X] are discussed. The exact confidence interval of the R is also obtained. Monte Carlo simulations are performed to compare the different proposed methods.

Keywords: Stress-Strength model, Maximum likelihood estimator, Bayes estimator, Burr type XII distribution.

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Authors: Ali Beydoun, Hamzé H. Alaeddine

Abstract:

MIMO-OFDM communication system presents a key solution for the next generation of mobile communication due to its high spectral efficiency, high data rate and robustness against multi-path fading channels. However, MIMO-OFDM system requires a perfect knowledge of the channel state information and a good synchronization between the transmitter and the receiver to achieve the expected performances. Recently, we have proposed two algorithms for channel estimation and timing synchronization with good performances and very low implementation complexity compared to those proposed in the literature. In order to validate and evaluate the efficiency of these algorithms in real environments, this paper presents in detail the implementation of 2 × 2 MIMO-OFDM system based on LabVIEW and USRP 2920. Implementation results show a good agreement with the simulation results under different configuration parameters.

Keywords: MIMO-OFDM system, timing synchronization, channel estimation, STBC, USRP 2920.

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Authors: Takashi Shimizu, Tomoaki Hashimoto

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Controlling the flow of fluids is a challenging problem that arises in many fields. Burgers’ equation is a fundamental equation for several flow phenomena such as traffic, shock waves, and turbulence. The optimal feedback control method, so-called model predictive control, has been proposed for Burgers’ equation. However, the model predictive control method is inapplicable to systems whose all state variables are not exactly known. In practical point of view, it is unusual that all the state variables of systems are exactly known, because the state variables of systems are measured through output sensors and limited parts of them can be only available. In fact, it is usual that flow velocities of fluid systems cannot be measured for all spatial domains. Hence, any practical feedback controller for fluid systems must incorporate some type of state estimator. To apply the model predictive control to the fluid systems described by Burgers’ equation, it is needed to establish a state estimation method for Burgers’ equation with limited measurable state variables. To this purpose, we apply unscented Kalman filter for estimating the state variables of fluid systems described by Burgers’ equation. The objective of this study is to establish a state estimation method based on unscented Kalman filter for Burgers’ equation. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: State estimation, fluid systems, observer systems, unscented Kalman filter.

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Authors: G. Parmar, R. Prasad, S. Mukherjee

Abstract:

The authors present an algorithm for order reduction of linear dynamic systems using the combined advantages of stability equation method and the error minimization by Genetic algorithm. The denominator of the reduced order model is obtained by the stability equation method and the numerator terms of the lower order transfer function are determined by minimizing the integral square error between the transient responses of original and reduced order models using Genetic algorithm. The reduction procedure is simple and computer oriented. It is shown that the algorithm has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. The proposed algorithm has also been extended for the order reduction of linear multivariable systems. Two numerical examples are solved to illustrate the superiority of the algorithm over some existing ones including one example of multivariable system.

Keywords: Genetic algorithm, Integral square error, Orderreduction, Stability equation method.

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Authors: Md Shohidul Islam, Jongmyon Kim, Ui-pil Chong

Abstract:

Medical image is an integral part of e-health care and e-diagnosis system. Medical image watermarking is widely used to protect patients’ information from malicious alteration and manipulation. The watermarked medical images are transmitted over the internet among patients, primary and referred physicians. The images are highly prone to corruption in the wireless transmission medium due to various noises, deflection, and refractions. Distortion in the received images leads to faulty watermark detection and inappropriate disease diagnosis. To address the issue, this paper utilizes error correction code (ECC) with (8, 4) Hamming code in an existing watermarking system. In addition, we implement the high complex ECC on a graphics processing units (GPU) to accelerate and support real-time requirement. Experimental results show that GPU achieves considerable speedup over the sequential CPU implementation, while maintaining 100% ECC efficiency.

Keywords: Medical Image Watermarking (MIW), e-health system, error correction, Hamming code, GPU.

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Authors: K. K. Starkov, A. Y. Pogromsky, I. J. B. F. Adan, J. E. Rooda

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In this paper we present our results on the performance analysis of a multi-product manufacturing line. We study the influence of external perturbations, intermediate buffer content and the number of manufacturing stages on the production tracking error of each machine in the multi-product line operated under a surplusbased production control policy. Starting by the analysis of a single machine with multiple production stages (one for each product type), we provide bounds on the production error of each stage. Then, we extend our analysis to a line of multi-stage machines, where similarly, bounds on each production tracking error for each product type, as well as buffer content are obtained. Details on performance of the closed-loop flow line model are illustrated in numerical simulations.

Keywords: Flexible manufacturing systems, tracking systems, discrete time systems, production control, boundary conditions.

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Authors: Hongyan Dai

Abstract:

This work presents a matched field processing (MFP) algorithm based on Dopplerlet transform for estimating the motion parameters of a sound source moving along a straight line and with a constant speed by using a piecewise strategy, which can significantly reduce the computational burden. Monte Carlo simulation results and an experimental result are presented to verify the effectiveness of the algorithm advocated.

Keywords: matched field processing; Dopplerlet transform; motion parameter estimation; piecewise strategy

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Authors: R. N. Patel

Abstract:

This paper deals with the tuning of parameters for Automatic Generation Control (AGC). A two area interconnected hydrothermal system with PI controller is considered. Genetic Algorithm (GA) and Particle Swarm optimization (PSO) algorithms have been applied to optimize the controller parameters. Two objective functions namely Integral Square Error (ISE) and Integral of Time-multiplied Absolute value of the Error (ITAE) are considered for optimization. The effectiveness of an objective function is considered based on the variation in tie line power and change in frequency in both the areas. MATLAB/SIMULINK was used as a simulation tool. Simulation results reveal that ITAE is a better objective function than ISE. Performances of optimization algorithms are also compared and it was found that genetic algorithm gives better results than particle swarm optimization algorithm for the problems of AGC.

Keywords: Area control error, Artificial intelligence, Automatic generation control, Genetic Algorithms and modeling, ISE, ITAE, Particle swarm optimization.

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Authors: Babakina Alexandra, Yong Soo Kim

Abstract:

In this study, we analyzed the factors that affect research funds using linear regression analysis to increase the effectiveness of investments in national research projects. We collected 7,916 items of data on research projects that were in the process of being finished or were completed between 2010 and 2011. Data pre-processing and visualization were performed to derive statistically significant results. We identified factors that affected funding using analysis of fit distributions and estimated increasing or decreasing tendencies based on these factors.

Keywords: R&D funding, Cost estimation, Linear regression, Preliminary feasibility study.

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Authors: Stefan Schmidt

Abstract:

Lean production (or lean management respectively) gained popularity in several waves. The last three decades have been filled with numerous attempts to apply these concepts in companies. However, this has only been partially successful. The roots of lean production can be traced back to Toyota-s just-in-time production. This concept, which according to Womack-s, Jones- and Roos- research at MIT was employed by Japanese car manufacturers, became popular under its international names “lean production", “lean-manufacturing" and was termed “Schlanke Produktion" in Germany. This contribution shows a review about lean production in Germany over the last thirty years: development, trial & error and implementation as well.

Keywords: Application, JIT, lean production, review, trial and error.

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Authors: G. Parmar, S. Mukherjee, R. Prasad

Abstract:

The authors present an optimization algorithm for order reduction and its application for the determination of the relative mapping errors of linear time invariant dynamic systems by the simplified models. These relative mapping errors are expressed by means of the relative integral square error criterion, which are determined for both unit step and impulse inputs. The reduction algorithm is based on minimization of the integral square error by particle swarm optimization technique pertaining to a unit step input. The algorithm is simple and computer oriented. It is shown that the algorithm has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. Two numerical examples are solved to illustrate the superiority of the algorithm over some existing methods.

Keywords: Order reduction, Particle swarm optimization, Relative mapping error, Stability.

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Authors: Juan F. Gutierrez, Jesus M. Quintero, Diego Sandoval

Abstract:

An important feature of Lighting Emitting Diodes (LED) technology is the fast on-off commutation. This fact allows data transmission using modulation formats such as On-Off Keying (OOK) and Color Shift Keying (CSK). Since, CSK based on three color bands uses red, green, and blue monochromatic LED (RGB-LED) to define a pattern of chromaticities; this type of CSK provides poor color quality on the illuminated area. In this work, we present the design and implementation of a VLC system using RGB-based CSK with 16, 8, and 4 color points, mixing with a steady baseline of a phosphor white-LED, to improve the color quality of the LED-Fixture. The experimental system was assessed in terms of the Symbol Error Rate (SER) and the Color Rendering Index (CRI). Good color quality performance of the LED-Fixture was obtained with an acceptable SER. We describe the laboratory setup used to characterize and calibrate an LED-Fixture.

Keywords: Color rendering index, symbol error rate, color shift keying, visible light communications.

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Authors: Abdul Hafiizh, Shigeki Obote, Kenichi Kagoshima

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This report aims to utilize existing and future Multiple-Input Multiple-Output Orthogonal Frequency Division Multiplexing Wireless Local Area Network (MIMO-OFDM WLAN) systems characteristics–such as multiple subcarriers, multiple antennas, and channel estimation characteristics–for indoor location estimation systems based on the Direction of Arrival (DOA) and Radio Signal Strength Indication (RSSI) methods. Hybrid of DOA-RSSI methods also evaluated. In the experimental data result, we show that location estimation accuracy performances can be increased by minimizing the multipath fading effect. This is done using multiple subcarrier frequencies over wideband frequencies to estimate one location. The proposed methods are analyzed in both a wide indoor environment and a typical room-sized office. In the experiments, WLAN terminal locations are estimated by measuring multiple subcarriers from arrays of three dipole antennas of access points (AP). This research demonstrates highly accurate, robust and hardware-free add-on software for indoor location estimations based on a MIMO-OFDM WLAN system.

Keywords: Direction of Arrival (DOA), Indoor location estimation method, Multipath Fading, MIMO-OFDM, Received Signal Strength Indication (RSSI), WLAN, Hybrid DOA-RSSI

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Authors: Mahmud Hesain ALdwaik, Omar Hsiain Eldwaik

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This paper deals with tracking and estimating time delay between two signals. The simulation of this algorithm accomplished by using Mathcad package is carried out. The algorithm we will present adaptively controls and tracking the delay, so as to minimize the mean square of this error. Thus the algorithm in this case has task not only of seeking the minimum point of error but also of tracking the change of position, leading to a significant improving of performance. The flowchart of the algorithm is presented as well as several tests of different cases are carried out.

Keywords: Tracking time delay, Algorithm simulation, Mathcad, MSE

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Authors: G. Parmar, S. Mukherjee, R. Prasad

Abstract:

The authors present an algorithm for order reduction of linear time invariant dynamic systems using the combined advantages of the eigen spectrum analysis and the error minimization by particle swarm optimization technique. Pole centroid and system stiffness of both original and reduced order systems remain same in this method to determine the poles, whereas zeros are synthesized by minimizing the integral square error in between the transient responses of original and reduced order models using particle swarm optimization technique, pertaining to a unit step input. It is shown that the algorithm has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. The algorithm is illustrated with the help of two numerical examples and the results are compared with the other existing techniques.

Keywords: Eigen spectrum, Integral square error, Orderreduction, Particle swarm optimization, Stability.

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Authors: T. P. Athira, Gibin Chacko George

Abstract:

This paper proposes a dual tree complex wavelet transform (DT-CWT) based directional interpolation scheme for noisy images. The problems of denoising and interpolation are modelled as to estimate the noiseless and missing samples under the same framework of optimal estimation. Initially, DT-CWT is used to decompose an input low-resolution noisy image into low and high frequency subbands. The high-frequency subband images are interpolated by linear minimum mean square estimation (LMMSE) based interpolation, which preserves the edges of the interpolated images. For each noisy LR image sample, we compute multiple estimates of it along different directions and then fuse those directional estimates for a more accurate denoised LR image. The estimation parameters calculated in the denoising processing can be readily used to interpolate the missing samples. The inverse DT-CWT is applied on the denoised input and interpolated high frequency subband images to obtain the high resolution image. Compared with the conventional schemes that perform denoising and interpolation in tandem, the proposed DT-CWT based noisy image interpolation method can reduce many noise-caused interpolation artifacts and preserve well the image edge structures. The visual and quantitative results show that the proposed technique outperforms many of the existing denoising and interpolation methods.

Keywords: Dual-tree complex wavelet transform (DT-CWT), denoising, interpolation, optimal estimation, super resolution.

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Authors: Swadhin Ku. Mishra, Sidhartha Panda, Simanchala Padhy, C. Ardil

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In this paper, real-coded genetic algorithm (RCGA) optimization technique has been applied for large-scale linear dynamic multi-input-multi-output (MIMO) system. The method is based on error minimization technique where the integral square error between the transient responses of original and reduced order models has been minimized by RCGA. The reduction procedure is simple computer oriented and the approach is comparable in quality with the other well-known reduction techniques. Also, the proposed method guarantees stability of the reduced model if the original high-order MIMO system is stable. The proposed approach of MIMO system order reduction is illustrated with the help of an example and the results are compared with the recently published other well-known reduction techniques to show its superiority.

Keywords: Multi-input-multi-output (MIMO) system.Modelorder reduction. Integral squared error (ISE). Real-coded geneticalgorithm

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Authors: Jin-Hyeok Kim, Won-Chul Choi, Seung-Ri Jin, Dong-Jo Park

Abstract:

In this paper, an analysis of a target location estimation system using the best linear unbiased estimator (BLUE) for high performance radar systems is presented. In synthetic environments, we are here concerned with three key elements of radar system modeling, which makes radar systems operates accurately in strategic situation in virtual ground. Radar Cross Section (RCS) modeling is used to determine the actual amount of electromagnetic waves that are reflected from a tactical object. Pattern Propagation Factor (PPF) is an attenuation coefficient of the radar equation that contains the reflection from the surface of the earth, the diffraction, the refraction and scattering by the atmospheric environment. Clutter is the unwanted echoes of electronic systems. For the data fusion of output results from radar detection in synthetic environment, BLUE is used and compared with the mean values of each simulation results. Simulation results demonstrate the performance of the radar system.

Keywords: Best linear unbiased estimator (BLUE) , data fusion, radar system modeling, target location estimation

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Authors: Mingren Shi, Michael Renton

Abstract:

There is a world-wide need for the development of sustainable management strategies to control pest infestation and the development of phosphine (PH3) resistance in lesser grain borer (Rhyzopertha dominica). Computer simulation models can provide a relatively fast, safe and inexpensive way to weigh the merits of various management options. However, the usefulness of simulation models relies on the accurate estimation of important model parameters, such as mortality. Concentration and time of exposure are both important in determining mortality in response to a toxic agent. Recent research indicated the existence of two resistance phenotypes in R. dominica in Australia, weak and strong, and revealed that the presence of resistance alleles at two loci confers strong resistance, thus motivating the construction of a two-locus model of resistance. Experimental data sets on purified pest strains, each corresponding to a single genotype of our two-locus model, were also available. Hence it became possible to explicitly include mortalities of the different genotypes in the model. In this paper we described how we used two generalized linear models (GLM), probit and logistic models, to fit the available experimental data sets. We used a direct algebraic approach generalized inverse matrix technique, rather than the traditional maximum likelihood estimation, to estimate the model parameters. The results show that both probit and logistic models fit the data sets well but the former is much better in terms of small least squares (numerical) errors. Meanwhile, the generalized inverse matrix technique achieved similar accuracy results to those from the maximum likelihood estimation, but is less time consuming and computationally demanding.

Keywords: mortality estimation, probit models, logistic model, generalized inverse matrix approach, pest control simulation

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Authors: Masoud Nasri, Sadat Feiznia, Mohammad Jafari, Hasan Ahmadi

Abstract:

Today, incorrect use of lands and land use changes, excessive grazing, no suitable using of agricultural farms, plowing on steep slopes, road construct, building construct, mine excavation etc have been caused increasing of soil erosion and sediment yield. For erosion and sediment estimation one can use statistical and empirical methods. This needs to identify land unit map and the map of effective factors. However, these empirical methods are usually time consuming and do not give accurate estimation of erosion. In this study, we applied GIS techniques to estimate erosion and sediment of Menderjan watershed at upstream Zayandehrud river in center of Iran. Erosion faces at each land unit were defined on the basis of land use, geology and land unit map using GIS. The UTM coordinates of each erosion type that showed more erosion amounts such as rills and gullies were inserted in GIS using GPS data. The frequency of erosion indicators at each land unit, land use and their sediment yield of these indices were calculated. Also using tendency analysis of sediment yield changes in watershed outlet (Menderjan hydrometric gauge station), was calculated related parameters and estimation errors. The results of this study according to implemented watershed management projects can be used for more rapid and more accurate estimation of erosion than traditional methods. These results can also be used for regional erosion assessment and can be used for remote sensing image processing.

Keywords: Erosion and sedimentation, Gully, Rill, GIS, GPS, Menderjan Watershed

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Authors: M. I. Youssef, A. E. Emam, M. Abd Elghany

Abstract:

In this paper, a residue number arithmetic is used in direct sequence spread spectrum system, this system is evaluated and the bit error probability of this system is compared to that of non residue number system. The effect of channel bandwidth, PN sequences, multipath effect and modulation scheme are studied. A Matlab program is developed to measure the signal-to-noise ratio (SNR), and the bit error probability for the various schemes.

Keywords: Spread Spectrum, Direct sequence, Bit errorprobability and Residue number system.

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