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Tracking Radars
Published in Habibur Rahman, Fundamental Principles of Radar, 2019
Now if we assume that the measurement is unbiased, the variance of measurement error and the mean-squared error are the same. Thus if the variance of the error is denoted by σt^d2 in the measurement of t^d, the variance of error in the measurement of R^0, denoted by σR^02, is given by σR^02=(c2)2σt^d2.
Advanced Control Systems
Published in Arthur G.O. Mutambara, Design and Analysis of Control Systems, 2017
In almost all real data fusion problems, the state or environment of interest does not evolve linearly. Consequently, simple linear models will not be adequate to describe the system. Furthermore, the sensor observations may not depend linearly on the states that describe the environment. A popular approach to solve nonlinear estimation problems has been to use the extended Kalman filter (EKF) [3], [15]. This is a linear estimator for a nonlinear system obtained by linearization of the nonlinear state and observations equations. For any nonlinear system, the EKF is the best linear unbiased estimator with respect to minimum mean squared error criteria.
Estimation and Information Space
Published in Arthur G.O. Mutambara, Decentralized Estimation and Control for Multisensor Systems, 2019
In almost all real data fusion problems the state or environment of interest does not evolve linearly. Consequently simple linear models will not be adequate to describe the system. Furthermore, the sensor observations may not depend linearly on the states that describe the environment. A popular approach to solve nonlinear estimation problems has been to use the extended Kaiman filter (EKF) [12], [24]. This is a linear estimator for a nonlinear system obtained by linearization of the nonlinear state and observations equations. For any nonlinear system the EKF is the best linear, unbiased, estimator with respect to minimum mean squared error criteria.
An estimation method for an unknown covariance in cross-section adjustment based on unbiased and consistent estimator
Published in Journal of Nuclear Science and Technology, 2023
Shuhei Maruyama, Tomohiro Endo, Akio Yamamoto
For a more reliable prediction of core characteristics and their uncertainties, we proposed a new method for estimating the unknown covariance in the cross-section adjustment method for the development of an application library. The unknown covariance is defined by the difference between the true covariance and a prior covariance given by an analyst. We alternatively estimated the unknown covariance using the empirical covariance to be consistent with the observation data. To estimate this unknown covariance, we used an unbiased and consistent estimator for a variance that is used in regression analysis. It was clarified that this estimator derived from regression analysis corresponded to the chi-squared value divided by the degree of freedom. However, unlike the chi-squared value in the conventional adjustment method, the statistical properties of this estimator do not require the assumption of normal distribution. Since the observation data do not always follow a normal distribution, the general statistical properties with unrestricted probability distribution are important.
D- and A-Optimal Screening Designs
Published in Technometrics, 2023
Jonathan Stallrich, Katherine Allen-Moyer, Bradley Jones
When model (1) is believed to contain the true model and , we assume there exists at least one with a unique least-squares estimator . The estimator is unbiased and has variance . Then where and screening inferences for the elements of perform best under an whose has small diagonal elements. Designs may then be ranked based on a scalar function of that measures variance in some overall sense.
Statistical process control procedures for functional data with systematic local variations
Published in IISE Transactions, 2018
Young-Seon Jeong, Myong K. Jeong, Jye-Chyi Lu, Ming Yuan, Jionghua (Judy) Jin
In the case of Phase II process monitoring with an individual observation, can be used as an estimator for when the process mean does not change. The threshold estimate, , is not unbiased, but it is consistent in the operator norm, uniformly over the class of matrices as long as (log p)/N → 0 (Bickel and Levina, 2008). The estimator does not need to be unbiased, as the monitoring statistics based on a consistent estimator can capture the changes in when the process mean does not change. One way to improve the performance is to combine as much information contained in Ai as possible from data collected over time to utilize a EWMA chart (Macgregor and Harris, 1993).