A number of different types of estimators have been developed in the following, and several relationships between the estimators have been studied. We began our study of estimation with Bayes' cost method, which was used to derive the mean-square error, maximum a posteriori, maximum likelihood and absolute-cost estimators. Since these estimators require a rather complete probabilistic description of the estimation problem, the linear minimum variance and least-square estimators, that need only minimal statistical structure, are considered as a complement to the other methods. Furthermore, if we assume that the variable to be estimated, x, is a constant, the problems of this sort are referred to as parameter or point estimation. A brief introduction to state estimation of dynamical system is presented in the next chapters. There, the quantity to be estimated is the time-varying state of a dynamical system.

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Fundamentals of Estimation

  • Branko Kovačević,
  • Željko Đurović,
  • Zoran Banjac

摘要

A number of different types of estimators have been developed in the following, and several relationships between the estimators have been studied. We began our study of estimation with Bayes' cost method, which was used to derive the mean-square error, maximum a posteriori, maximum likelihood and absolute-cost estimators. Since these estimators require a rather complete probabilistic description of the estimation problem, the linear minimum variance and least-square estimators, that need only minimal statistical structure, are considered as a complement to the other methods. Furthermore, if we assume that the variable to be estimated, x, is a constant, the problems of this sort are referred to as parameter or point estimation. A brief introduction to state estimation of dynamical system is presented in the next chapters. There, the quantity to be estimated is the time-varying state of a dynamical system.