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سیگنال >> سایت تخصصی مهندسی برق - Introduction to Estimation Theory

## Introduction to Estimation Theory

تاریخ:یکشنبه 30 آبان 1389-15:32 In searching for methods of extracting information from noisy observations, this chapter describes estimation theory, which has the goal of extracting from noise-corrupted observations the values of disturbance parameters (noise variance, for example), signal parameters amplitude or propagation direction), or signal waveforms.  Estimation theory assumes that the observations contain an information-bearing quantity, thereby tacitly assuming that detection-based preprocessing has been performed (in other words, do I have something in the observations worth estimating?).  Conversely, detection theory often requires estimation of unknown parameters: Signal presence is assumed, parameter estimates are incorporated into the detection statistic, and consistency of observations and assumptions tested.  Consequently, detection and estimation theory form a symbiotic relationship, each requiring the other to yield high-quality signal processing algorithms.

In searching for methods of extracting information from noisy observations, this chapter describes estimation theory, which has the goal of extracting from noise-corrupted observations the values of disturbance parameters (noise variance, for example), signal parameters amplitude or propagation direction), or signal waveforms.  Estimation theory assumes that the observations contain an information-bearing quantity, thereby tacitly assuming that detection-based preprocessing has been performed (in other words, do I have something in the observations worth estimating?).  Conversely, detection theory often requires estimation of unknown parameters: Signal presence is assumed, parameter estimates are incorporated into the detection statistic, and consistency of observations and assumptions tested.  Consequently, detection and estimation theory form a symbiotic relationship, each requiring the other to yield high-quality signal processing algorithms.

Despite a wide variety of error criteria and problem frameworks, the optimal detector iis characterized by a single result: the likelihood ratio test.  Surprisingly, optimal detectors thus derived are usually easy to implement, not often requiring simplification to obtain a feasible realization in hardware or software.  In contrast to detection theory, no fundamental result in estimation theory exists to be summoned to attack the problem at hand. The choice of error criterion and its optimization heavily influences the form of the estimation procedure.  Because of the variety of criterion-dependent estimators, arguments frequently rage about which of several optimal estimators is "better."  its assumed error criterion; thus, the argument becomes which error criterion best describes some intuitive notion of quality. When more ad hoc, noncriterion-based procedures1 are used, we cannot assess the quality of the resulting estimator relative to the best achievable.  Bounds on the estimation error do exist, but their tightness and applicability to a given situation are always issues in assessing estimator quality.  At  best, estimation theory is less structured than detection theory.  Detection is science, estimation art.  Inventiveness coupled with an understanding of the problem (what types of errors are critically important, for example) are key elements to deciding which estimation procedure "fits" a given problem well.

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