• Title/Summary/Keyword: least squares estimation

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Estimation of infection distribution and prevalence number of Tsutsugamushi fever in Korea (국내 쯔쯔가무시증의 감염자 분포와 유병자수 추정)

  • Lee, Jung-Hee;Murshed, Sharwar;Park, Jeong-Soo
    • Journal of the Korean Data and Information Science Society
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    • v.20 no.1
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    • pp.149-158
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    • 2009
  • Tsutsugamushi fever occupies more than 80% of total fall epidemic diseases and has an incubation period of 1 or 2 weeks as well. We have assumed that the incubation period distribution is gamma and therefore, reach an agreement that the infected distribution is normal with ${\hat{\mu}}=309.92$, ${\hat{\sigma}}=14.154$ by back calculation method. The infection cases are found severely large around the month of October. The infection case distribution demonstrates the incidence number increasing rapidly and progresses fast during the month of November. In this study, we have calculated the future prevalence number of maximum 1,200 people by inferred infection probability and incubation period distribution with some sort of limitation that the trend of increasing incidence number is not taking into an account. We considered the SIRS model which is also known as epidemic model, familiar to interaction between epidemiological classes. Our estimated parameters converged well with the initial parameter values.

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Approaching Target above Ground Tracking Technique Based on Noise Covariance Estimation Method-Kalman Filter (잡음 공분산 추정 방식을 적용한 칼만필터 기반 지면밀착 접근표적 추적기법)

  • Park, Young-Sik
    • The Journal of Korean Institute of Electromagnetic Engineering and Science
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    • v.28 no.10
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    • pp.810-818
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    • 2017
  • This paper presents the approaching target above ground tracking based on Kalman filter applied to the proximity sensor for the active defense system. The proximity sensor located on the front of the countermeasure is not easy to detect when the anti-tank threat enters a fragment dispersion range due to limited antenna beamwidth. In addition, it is difficult for the proximity sensor to detect the anti-tank threat accurately at a terrestrial environment including various clutters. To solve these problems, this study presents the approaching target above ground tracking based on Kalman filter and applies the novel estimation method for a noise covariance matrix to improve a tracking performance. Then, a high tracking performance of Kalman filter applied the proposed noise covariance matrix is presented through field firing test results and the validity of the proposed study is examined.

Particle Filter SLAM for Indoor Navigation of a Mobile Robot Using Ultrasonic Beacons (초음파 비이컨을 사용한 이동로봇 실내 주행용 파티클 필터 SLAM)

  • Kim, Tae-Gyun;Ko, Nak-Yong;Noh, Sung-Woo
    • The Journal of the Korea institute of electronic communication sciences
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    • v.7 no.2
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    • pp.391-399
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    • 2012
  • This paper proposes a particle filter approach for SLAM(Simultaneous Localization and Mapping) of a mobile robot. The SLAM denotes estimation of both the robot location and map while the robot navigates in an unknown environment without map. The proposed method estimates robot location simultaneously with the locations of the ultrasonic beacons which constitute landmarks for navigation. The particle filter method represents the locations of the robot and landmarks in probabilistic manner by the distribution of particles. The method takes care of the uncertainty of the landmarks' location as well as that of the robot motion. Therefore, the locations of the landmarks are updated including uncertainty at every sampling time. Performance of the proposed method is verified through simulation and experiments. The method yields practically useful mapping information even if the range data from the landmarks include random noise. Also, it provides more accurate and robust estimation of the robot location than the usual least squares methods or dead-reckoning method.

Domestic Automotive Exterior Lamp-LEDs Demand and Forecasting using BASS Diffusion Model (BASS 확산 모형을 이용한 국내 자동차 외장 램프 LED 수요예측 분석)

  • Lee, Jae-Heun
    • Journal of Korean Society for Quality Management
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    • v.50 no.3
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    • pp.349-371
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    • 2022
  • Purpose: Compared to the rapid growth rate of the domestic automotive LED industry so far, the predictive analysis method for demand forecasting or market outlook was insufficient. Accordingly, product characteristics are analyzed through the life trend of LEDs for automotive exterior lamps and the relative strengths of p and q using the Bass model. Also, future demands are predicted. Methods: We used sales data of a leading company in domestic market of automotive LEDs. Considering the autocorrelation error term of this data, parameters m, p, and q were estimated through the modified estimation method of OLS and the NLS(Nonlinear Least Squares) method, and the optimal method was selected by comparing prediction error performance such as RMSE. Future annual demands and cumulative demands were predicted through the growth curve obtained from Bass-NLS model. In addition, various nonlinear growth curve models were applied to the data to compare the Bass-NLS model with potential market demand, and an optimal model was derived. Results: From the analysis, the parameter estimation results by Bass-NLS obtained m=1338.13, p=0.0026, q=0.3003. If the current trend continues, domestic automotive LED market is predicted to reach its maximum peak in 2021 and the maximum demand is $102.23M. Potential market demand was $1338.13M. In the nonlinear growth curve model analysis, the Gompertz model was selected as the optimal model, and the potential market size was $2864.018M. Conclusion: It is expected that the Bass-NLS method will be applied to LED sales data for automotive to find out the characteristics of the relative strength of q/p of products and to be used to predict current demand and future cumulative demand.

Threshold heterogeneous autoregressive modeling for realized volatility (임계 HAR 모형을 이용한 실현 변동성 분석)

  • Sein Moon;Minsu Park;Changryong Baek
    • The Korean Journal of Applied Statistics
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    • v.36 no.4
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    • pp.295-307
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    • 2023
  • The heterogeneous autoregressive (HAR) model is a simple linear model that is commonly used to explain long memory in the realized volatility. However, as realized volatility has more complicated features such as conditional heteroscedasticity, leverage effect, and volatility clustering, it is necessary to extend the simple HAR model. Therefore, to better incorporate the stylized facts, we propose a threshold HAR model with GARCH errors, namely the THAR-GARCH model. That is, the THAR-GARCH model is a nonlinear model whose coefficients vary according to a threshold value, and the conditional heteroscedasticity is explained through the GARCH errors. Model parameters are estimated using an iterative weighted least squares estimation method. Our simulation study supports the consistency of the iterative estimation method. In addition, we show that the proposed THAR-GARCH model has better forecasting power by applying to the realized volatility of major 21 stock indices around the world.

Improvement of Rating Curve Fitting Considering Variance Function with Pseudo-likelihood Estimation (의사우도추정법에 의한 분산함수를 고려한 수위-유량 관계 곡선 산정법 개선)

  • Lee, Woo-Seok;Kim, Sang-Ug;Chung, Eun-Sung;Lee, Kil-Seong
    • Journal of Korea Water Resources Association
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    • v.41 no.8
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    • pp.807-823
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    • 2008
  • This paper presents a technique for estimating discharge rating curve parameters. In typical practical applications, the original non-linear rating curve is transformed into a simple linear regression model by log-transforming the measurement without examining the effect of log transformation. The model of pseudo-likelihood estimation is developed in this study to deal with heteroscedasticity of residuals in the original non-linear model. The parameters of rating curves and variance functions of errors are simultaneously estimated by the pseudo-likelihood estimation(P-LE) method. Simulated annealing, a global optimization technique, is adapted to minimize the log likelihood of the weighted residuals. The P-LE model was then applied to a hypothetical site where stage-discharge data were generated by incorporating various errors. Results of the P-LE model show reduced error values and narrower confidence intervals than those of the common log-transform linear least squares(LT-LR) model. Also, the limit of water levels for segmentation of discharge rating curve is estimated in the process of P-LE using the Heaviside function. Finally, model performance of the conventional log-transformed linear regression and the developed model, P-LE are computed and compared. After statistical simulation, the developed method is then applied to the real data sets from 5 gauge stations in the Geum River basin. It can be suggested that this developed strategy is applied to real sites to successfully determine weights taking into account error distributions from the observed discharge data.

Estimation of kerosene demand function using time series data (시계열 자료를 이용한 등유수요함수 추정)

  • Jeong, Dong-Won;Hwang, Byoung-Soh;Yoo, Seung-Hoon
    • Journal of Energy Engineering
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    • v.22 no.3
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    • pp.245-249
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    • 2013
  • This paper attempts to estimate the kerosene demand function in Korea over the period 1981-2012. As the kerosene demand function provides us information on the pattern of consumer's kerosene consumption, it can be usefully utilized in predicting the impact of policy variables such as kerosene price and forecasting the demand for kerosene. We apply least absolute deviations and least median squares estimation methods as a robust approach to estimating the parameters of the kerosene demand function. The results show that short-run price and income elasticities of the kerosene demand are estimated to be -0.468 and 0.409, respectively. They are statisitically significant at the 1% level. The short-run price and income elasticities portray that demand for kerosene is price- and income-inelastic. This implies that the kerosene is indispensable goods to human-being's life, thus the kerosene demand would not be promptly adjusted to responding to price and/or income change. However, long-run price and income elasticities reveal that the demand for kerosene is price- and income-elastic in the long-run.

Doubly-robust Q-estimation in observational studies with high-dimensional covariates (고차원 관측자료에서의 Q-학습 모형에 대한 이중강건성 연구)

  • Lee, Hyobeen;Kim, Yeji;Cho, Hyungjun;Choi, Sangbum
    • The Korean Journal of Applied Statistics
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    • v.34 no.3
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    • pp.309-327
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    • 2021
  • Dynamic treatment regimes (DTRs) are decision-making rules designed to provide personalized treatment to individuals in multi-stage randomized trials. Unlike classical methods, in which all individuals are prescribed the same type of treatment, DTRs prescribe patient-tailored treatments which take into account individual characteristics that may change over time. The Q-learning method, one of regression-based algorithms to figure out optimal treatment rules, becomes more popular as it can be easily implemented. However, the performance of the Q-learning algorithm heavily relies on the correct specification of the Q-function for response, especially in observational studies. In this article, we examine a number of double-robust weighted least-squares estimating methods for Q-learning in high-dimensional settings, where treatment models for propensity score and penalization for sparse estimation are also investigated. We further consider flexible ensemble machine learning methods for the treatment model to achieve double-robustness, so that optimal decision rule can be correctly estimated as long as at least one of the outcome model or treatment model is correct. Extensive simulation studies show that the proposed methods work well with practical sample sizes. The practical utility of the proposed methods is proven with real data example.

Robust 3-D Motion Estimation Based on Stereo Vision and Kalman Filtering (스테레오 시각과 Kalman 필터링을 이용한 강인한 3차원 운동추정)

  • 계영철
    • Journal of Broadcast Engineering
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    • v.1 no.2
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    • pp.176-187
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    • 1996
  • This paper deals with the accurate estimation of 3- D pose (position and orientation) of a moving object with reference to the world frame (or robot base frame), based on a sequence of stereo images taken by cameras mounted on the end - effector of a robot manipulator. This work is an extension of the previous work[1]. Emphasis is given to the 3-D pose estimation relative to the world (or robot base) frame under the presence of not only the measurement noise in 2 - D images[ 1] but also the camera position errors due to the random noise involved in joint angles of a robot manipulator. To this end, a new set of discrete linear Kalman filter equations is derived, based on the following: 1) the orientation error of the object frame due to measurement noise in 2 - D images is modeled with reference to the camera frame by analyzing the noise propagation through 3- D reconstruction; 2) an extended Jacobian matrix is formulated by combining the result of 1) and the orientation error of the end-effector frame due to joint angle errors through robot differential kinematics; and 3) the rotational motion of an object, which is nonlinear in nature, is linearized based on quaternions. Motion parameters are computed from the estimated quaternions based on the iterated least-squares method. Simulation results show the significant reduction of estimation errors and also demonstrate an accurate convergence of the actual motion parameters to the true values.

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GPS Baseline Estimation of the $2^{nd}$ Order Geodetic Control Network (2등 측지기준점 GPS 관측데이터의 기선벡터 추정)

  • Lee, Young-Jin;Lee, Hung-Kyu;Kwon, Chan-Oh;Cha, Sang-Heon
    • Journal of the Korean Society of Surveying, Geodesy, Photogrammetry and Cartography
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    • v.26 no.2
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    • pp.157-164
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    • 2008
  • GPS baseline analysis is a mathematical procedure which estimates a baseline vector from carrier-phase double-differenced observations. Least squares technique is generally applied for the processing and integer ambiguities in the observations should be resolved to obtain maximum accuracy of the solution. In GPS control surveying, after assembling the baseline solutions into a network, adjustment is performed to derive final coordinate sets of unknown points. This paper deals with details of GPS baseline analysis for the $2^{nd}$ order national geodetic network adjustment. After reviewing GPS campaigns carried out by National Geographic Information Institute (NGII) and their observations. technical issues and considerations for the GPS baseline analysis are presented with emphasis of selecting the processing strategies and software. Finally, the analyzed results will be evaluated by examining the close of figures formed by joining the processed baseline vectors.