Rate estimation by corrective tracking method and determination of physical quantities based on this principle.
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AbstractThis paper wile a measuring system operating on the principle of the captioned method of rate estimation, whereby estimated values of the quantities of data being continuously collected on a chronological basis are caused to track, in real time, the average values of measurement obtained on the same data. The discussions will also cover examples of actual measurements made by using this measuring system. The principle of tracking used for closing the deference between estimated and averaged measured values consists in a process in which, as a first step, an estimated value is compared with the measured value corresponding to it. If there is variance between them which is greater then a prescribed magnitude, the two values are regarded as equal to each other; thus, estimated value=measured value. In the following step, the next measured value is deducted by the estimated value obtained in the first step; and the difference that results is multiplied by a correction factor assigned with a value considered appropriate for approximation purposes. This product of multiplication is then added to prior estimated value to correct it for the variance. In the third and, further, in each of the steps that follows, the same process of calculation is made to obtain a series of such corrections while the estimated value will close on the average measured value corresponding to it, each successive step producing an effect of correction achieved by tracking. As soon as a state of constancy is attained, an estimated value can be regarded and used as a measured value corresponding to it. This method has a feature in that the precision of measurement can be enhanced to the extent to which the correction factor used is made smaller. When targeted quantity of measurement is shifting over time, the tracking can become infeasible if the correction factor used is too small in value to be able to negotiate the rate of change encountered. In such a case, the rate of change in the quantity of measurement need first be estimated by making estimated rates of change track the averaged difference between two values obtained from two consecutive measurement and, then, by adding the estimated rate of change this obtained to the estimated value in question, prior to it. Provided this procedure of correction is observed, an estimated value can reasonably track a shifting quantity of measurement even in the case where a shifting quantity of measurement even in the case where a small- in-value correction factor is used. In the case of data that associate with pronounced pulsated noises occurring infrequently, a tracking system not susceptible to such changes in noise level can be structured if and when estimated values are corrected by using a factor standardized to a unit constant, with the difference between measured and estimated value noted only for the sign that results. This procedure was tried in various simulations, using old data of measurement from the Loran-C, Acoustic Log, Terrestrial magnetism and lnfrared Emission Temperature Gage. The finding. in each case, was that the accuracy of measurement was higher by a factor of 10 to 100.
JournalReport of Hydrographic and Oceanographic Researches