• Title/Summary/Keyword: Least Square Estimation

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Alternative robust estimation methods for parameters of Gumbel distribution: an application to wind speed data with outliers

  • Aydin, Demet
    • Wind and Structures
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    • v.26 no.6
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    • pp.383-395
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    • 2018
  • An accurate determination of wind speed distribution is the basis for an evaluation of the wind energy potential required to design a wind turbine, so it is important to estimate unknown parameters of wind speed distribution. In this paper, Gumbel distribution is used in modelling wind speed data, and alternative robust estimation methods to estimate its parameters are considered. The methodologies used to obtain the estimators of the parameters are least absolute deviation, weighted least absolute deviation, median/MAD and least median of squares. The performances of the estimators are compared with traditional estimation methods (i.e., maximum likelihood and least squares) according to bias, mean square deviation and total mean square deviation criteria using a Monte-Carlo simulation study for the data with and without outliers. The simulation results show that least median of squares and median/MAD estimators are more efficient than others for data with outliers in many cases. However, median/MAD estimator is not consistent for location parameter of Gumbel distribution in all cases. In real data application, it is firstly demonstrated that Gumbel distribution fits the daily mean wind speed data well and is also better one to model the data than Weibull distribution with respect to the root mean square error and coefficient of determination criteria. Next, the wind data modified by outliers is analysed to show the performance of the proposed estimators by using numerical and graphical methods.

Leakage Inductance Estimation of $Y-\triangle$ Transformer Using the Least Square Method (최소자승법을 이용한 $Y-\triangle$ 누설 인덕턴스 추정 방법)

  • Hwang, Tae-Keun;Lee, Byung-Eun;Jang, Sung-Il;Kim, Yong-Gyun;Kang, Yong-Cheol
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.56 no.4
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    • pp.645-650
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    • 2007
  • This paper proposes a parameter estimation technique of a power transformer. Based on the combined equation, it estimates separately the primary and secondary leakage inductances using the least square method from the instantaneous voltages and currents in the steady state. The performance of the proposed technique was investigated by varying the cut-off frequency of the filter and the number of samples per cycle. The estimated values are obtained based on the average value for 41 cycle.

Fuzzy Combined Polynomial Neural Networks (퍼지 결합 다항식 뉴럴 네트워크)

  • Roh, Seok-Beom;Oh, Sung-Kwun;Ahn, Tae-Chon
    • The Transactions of The Korean Institute of Electrical Engineers
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    • v.56 no.7
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    • pp.1315-1320
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    • 2007
  • In this paper, we introduce a new fuzzy model called fuzzy combined polynomial neural networks, which are based on the representative fuzzy model named polynomial fuzzy model. In the design procedure of the proposed fuzzy model, the coefficients on consequent parts are estimated by using not general least square estimation algorithm that is a sort of global learning algorithm but weighted least square estimation algorithm, a sort of local learning algorithm. We are able to adopt various type of structures as the consequent part of fuzzy model when using a local learning algorithm. Among various structures, we select Polynomial Neural Networks which have nonlinear characteristic and the final result of which is a complex mathematical polynomial. The approximation ability of the proposed model can be improved using Polynomial Neural Networks as the consequent part.

An Implementation of Discrete Mathematical Model for ECG waveform

  • Yimman, Surapun;Deeudom, Mongkon;Ittisariyanon, Jirawat;Junnapiya, Somyot;Dejhan, Kobchai
    • 제어로봇시스템학회:학술대회논문집
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    • 2005.06a
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    • pp.852-856
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    • 2005
  • This paper proposes a new design of the ECG simulator with high resolution by using small amount of memories based on discrete least square estimation equations instead of reading the stored data inside the look-up table. The experimental results have shown that the ECG simulator using discrete least square estimation equations can display the bipolar limb leads ECG signals with low PRD (percent root-mean-square difference) while taking the less amount of memories than the previous method which used the look-up table to store ECG data for ECG simulation.

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Preliminary test estimation method accounting for error variance structure in nonlinear regression models (비선형 회귀모형에서 오차의 분산에 따른 예비검정 추정방법)

  • Yu, Hyewon;Lim, Changwon
    • The Korean Journal of Applied Statistics
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    • v.29 no.4
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    • pp.595-611
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    • 2016
  • We use nonlinear regression models (such as the Hill Model) when we analyze data in toxicology and/or pharmacology. In nonlinear regression models an estimator of parameters and estimation of measurement about uncertainty of the estimator are influenced by the variance structure of the error. Thus, estimation methods should be different depending on whether the data are homoscedastic or heteroscedastic. However, we do not know the variance structure of the error until we actually analyze the data. Therefore, developing estimation methods robust to the variance structure of the error is an important problem. In this paper we propose a method to estimate parameters in nonlinear regression models based on a preliminary test. We define an estimator which uses either the ordinary least square estimation method or the iterative weighted least square estimation method according to the results of a simple preliminary test for the equality of the error variance. The performance of the proposed estimator is compared to those of existing estimators by simulation studies. We also compare estimation methods using real data obtained from the National Toxicology program of the United States.

Estimation of Aerodynamic Coefficients for a Skid-to-Turn Missile using Neural Network and Recursive Least Square (신경회로망과 순환최소자승법을 이용한 Skid-to-Turn 미사일의 공력 파라미터 추정)

  • Kim, Yun-Hwan;Park, Kyun-Bub;Song, Yong-Kyu;Hwang, Ick-Ho;Choi, Dong-Kyun
    • Journal of the Korean Society for Aviation and Aeronautics
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    • v.20 no.4
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    • pp.7-13
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    • 2012
  • This paper is to estimate aerodynamic coefficients needed to determine the missiles' controller design and stability from simulation data of Skid-to-Turn missile. Method of determining aerodynamic coefficients is to apply Neural Network and Recursive Least Square and results were compared and researched. Also analysing actual flight test data was considered and sensor noise was added. Estimate parameter of data with sensor noise added and estimated performance and reliability for both methods that did not need initial values. Both Neural Network and Recursive Least Square methods showed excellent estimate results without adding the noise and with noise added Neural Network method showed better estimate results.

THE CONSISTENCY OF NONLINEAR REGRESSION MINIMIZING $L_p$-NORM

  • Choi, Seung-Hoe;Park, Kyung-Ok
    • East Asian mathematical journal
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    • v.14 no.2
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    • pp.421-427
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    • 1998
  • In this paper we provide sufficient conditions which ensure the strong consistency of $L_p$-norm estimation in nonlinear regression model when the probability distribution of the errors term is symmetric about zero. The least absolute deviation and least square estimation are discussed as special cases of the proposed estimation.

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External Force Estimation by Modifying RLS using Joint Torque Sensor for Peg-in-Hole Assembly Operation (수정된 RLS 기반으로 관절 토크 센서를 이용한 로봇에 가해진 외부 힘 예측 및 펙인홀 작업 구현)

  • Jeong, Yoo-Seok;Lee, Cheol-Soo
    • The Journal of Korea Robotics Society
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    • v.13 no.1
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    • pp.55-62
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    • 2018
  • In this paper, a method for estimation of external force on an end-effector using joint torque sensor is proposed. The method is based on portion of measure torque caused by external force. Due to noise in the torque measurement data from the torque sensor, a recursive least-square estimation algorithm is used to ensure a smoother estimation of the external force data. However it is inevitable to create a delay for the sensor to detect the external force. In order to reduce the delay, modified recursive least-square is proposed. The performance of the proposed estimation method is evaluated in an experiment on a developed six-degree-of-freedom robot. By using NI DAQ device and Labview, the robot control, data acquisition and The experimental results output are processed in real time. By using proposed modified RLS, the delay to estimate the external force with the RLS is reduced by 54.9%. As an experimental result, the difference of the actual external force and the estimated external force is 4.11% with an included angle of $5.04^{\circ}$ while in dynamic state. This result shows that this method allows joint torque sensors to be used instead of commonly used external sensory system such as F/T sensors.

An Estimation of Parameters in Weibull Distribution Using Least Squares Method under Random Censoring Model (임의 중단모형에서 최소제곱법을 이용한 와이블분포의 모수 추정)

  • Lee, Woo-Dong
    • Journal of the Korean Data and Information Science Society
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    • v.7 no.2
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    • pp.263-272
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    • 1996
  • In this parer, under random censorship model, an estimation of scale and shape parameters in Weibull lifetime model is considered. Based on nonparametric estimator of survival function, the least square method is proposed. The proposed estimation method is simple and the performance of the proposed estimator is as efficient as maximum likelihood estimators. An example is presented, using field winding data. Simulation studies are performed to compare the performaces of the proposed estimator and maximum likelihood estimator.

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Comparison Study of Channel Estimation Algorithm for 4S Maritime Communications (4S 해상 통신을 위한 채널 추정 알고리즘 비교 연구)

  • Choi, Myeong Soo;Lee, Seong Ro
    • The Journal of Korean Institute of Communications and Information Sciences
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    • v.38C no.3
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    • pp.288-295
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    • 2013
  • In this paper, we compare the existing channel estimation technique for 4S (Ship to Ship, Ship to Shore) maritime communications under AWGN channel model, Rician fading channel model, and Rayleigh fading channel model respectively. In general, the received signal is corrupted by multipath and ISI (Inter Symbol Interference). The estimation of a time-varying multipath fading channel is a difficult task for the receiver. Its performance can be improved if an appropriate channel estimation filter is used. The simulation is performed in MATLAB. In this simulation, we use the popular estimation algorithms, LMS (Least Mean Square) and RLS (Recursive Least-Squares) are compared with respect to AWGN, Rician and Rayleigh channels.