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By Andrew P. Sage and James L. Melsa (Eds.)

ISBN-10: 0126144508

ISBN-13: 9780126144505

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2-22) It is now clear that maximizing Eq. 2-23) * This is true if ' I is not a function of x and is a useful result in general. 2. 2-24) to subject to the differential equality constraint of Eq. 2-5). This relation, Eq. 2-24), is a least squares curve fit cost function and, if the prior variances are chosen correctly and appropriate Gaussian assumptions on x(k,), v(k) and w(k) hold, is equivalent to the maximum a posteriori cost function. 2-23) is of the form that suggests application of the discrete maximum principle or the discrete Euler-Lagrange (Sage, 1968) equations.

Even when noise can be neglected, there will generally be some error in the measurement of yR . This is partly due to the fact that y is rarely bandwidth limited in the strictest sense. Consequently, some overlapping of the “tails” of the subspectra occurs. This produces an anomalous component in the output of the filter. Another source of distortion results from the nonideal filter characteristics which must be accepted if on-line identification is to be performed. Both of these effects may be made negligible through proper design, if the system is varying slowly enough.

T h a t is, it is the error in the measurement of A that is of paramount concern. Even when noise can be neglected, there will generally be some error in the measurement of yR . This is partly due to the fact that y is rarely bandwidth limited in the strictest sense. Consequently, some overlapping of the “tails” of the subspectra occurs. This produces an anomalous component in the output of the filter. Another source of distortion results from the nonideal filter characteristics which must be accepted if on-line identification is to be performed.

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System Identification by Andrew P. Sage and James L. Melsa (Eds.)


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