Download e-book for iPad: Applied Optimal Estimation by The Analytic Sciences Corporation, Arthur Gelb

By The Analytic Sciences Corporation, Arthur Gelb

ISBN-10: 0262200279

ISBN-13: 9780262200271

Written through individuals of the technical employees, Analytic Sciences Corp.

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An unbiased estimate is one whose expected value is the same as that of the quantity being estimated. A miflimmrm vanonce (unbiased) estimate has the property that its error variance is less than or equal to that of any other unbiased estimate. A consisrenr estimate IS one which converges to the true value of x, as the number of measurements increases. Thus, we shall look for unbiased, minimum variance, consistent estimators. 0-4) where R-I is an P X P symmetric, positive definite weighting matrix, the weighted-leasr-squares estimate is obtained.

This is the continuous form ordinarily employed in modern estimation and control theory. 1-1 illustrates the equation. The state vector for a dynamic system is composed of any set of quantities sufficient to completely describe the unforced motion of that system. Given the state vector at a particular point in time and a description of the system forcing and control functions from that point in time forward, the state at any other time can be computed. ,(t)~"-' + . . 1-3) where D = dldt, we can defme a set of state variablesx,(t), .

Evaluation of Eq. 9- 19) for p successive shifts results in a set of p linear equations which can be written as To gain insight into how the characteristics of the time series model are affected by the coefficients of the difference equation, the general form of Eq. 9-1 2) is specialized to several particular cases. The characteristics of these forms are reflected in their autocorrelation functions. Therefore, by studying these specialized forms, it is easier to identify a model that matches the observed time series and also has a minimum number of parameters to be determined.

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Applied Optimal Estimation by The Analytic Sciences Corporation, Arthur Gelb


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