Some properties of physical measurements with application to system identification

✍ Scribed by J.L. Hammond Jr.

• Publisher: Elsevier Science
• Year: 1964
• Tongue: English
• Weight: 593 KB
• Volume: 278
• Category: Article
• ISSN: 0016-0032
• DOI: 10.1016/0016-0032(64)90307-2

✦ Synopsis

SUMMXRY:

The problem of characterizing a measurement instrument and examining its effect on the identi~eation of systems is considered in this paper. A model for a measurement instrument is given, and the e-information gain of the instrument is de£ned and expressed in terms of the parameters of the model. Vitushkin's e-entropy is shown to be a measure of the "cost" of identi~cation. One of his theorems is adapted to show that to measure a function from a given space to e-accuracy requires an e-information gain from the measurement instrument equal to or greater than the e-entropy of the input space.

An upper bound on the e-information gain for linear measurement instruments is obtained. For a ~xed space of input functions this upper bound on e-information gain speci~es a lower bound on e-accuracy.

The results obtained are applied to two classes of identilication problems. The ~rst is a problem posed by Zadeh which involves matching an unknown "black box" to some member of a class of "black boxes." In this case the c-information necessary to make the required identi~cation is computed. The upper bound on e-information is used to show that if a linear instrument is used, precise identi£cation is impossible in general, and identi~cation to some e-accuracy is suggested as an alternative requirement.

The second identi~cation problem involves measurement of a constant quantity and serves to indicate orders of magnitude for some of the variables.