tailieunhanh - Bài 4: Estimation Theory

An important issue encountered in various branches of science is how to estimate the quantities of interest from a given finite set of uncertain (noisy) measurements. This is studied in estimation theory, which we shall discuss in this chapter. There exist many estimation techniques developed for various situations; the quantities to be estimated may be nonrandom or have some probability distributions themselves, and they may be constant or time-varying. | Independent Component Analysis. Aapo Hyvarinen Juha Karhunen Erkki Oja Copyright 2001 John Wiley Sons Inc. ISBNs 0-471-40540-X Hardback 0-471-22131-7 Electronic 4 Estimation Theory An important issue encountered in various branches of science is how to estimate the quantities of interest from a given finite set of uncertain noisy measurements. This is studied in estimation theory which we shall discuss in this chapter. There exist many estimation techniques developed for various situations the quantities to be estimated may be nonrandom or have some probability distributions themselves and they may be constant or time-varying. Certain estimation methods are computationally less demanding but they are statistically suboptimal in many situations while statistically optimal estimation methods can have a very high computational load or they cannot be realized in many practical situations. The choice of a suitable estimation method also depends on the assumed data model which may be either linear or nonlinear dynamic or static random or deterministic. In this chapter we concentrate mainly on linear data models studying the estimation of their parameters. The two cases of deterministic and random parameters are covered but the parameters are always assumed to be time-invariant. The methods that are widely used in context with independent component analysis ICA are emphasized in this chapter. More information on estimation theory can be found in books devoted entirely or partly to the topic for example 299 242 407 353 419 . Prior to applying any estimation method one must select a suitable model that well describes the data as well as measurements containing relevant information on the quantities of interest. These important but problem-specific issues will not be discussed in this chapter. Of course ICA is one of the models that can be used. Some topics related to the selection and preprocessing of measurements are treated later in Chapter 13. 77 78 ESTIMATION THEORY