Archive
Special Issues Volume 7, Issue 1, June 2019, Page: 1-4
On the Criterion of Proximity to the True Value: Information Approach
Ilya Feldman, Moscow State University of Geodesy and Cartography, Moscow, Russia
Received: Mar. 25, 2019;       Accepted: May 28, 2019;       Published: Jul. 9, 2019
Abstract
What is the criterion of proximity to the true value of the measured value: absolute or relative error? The least squares method traditionally operates with absolute values of corrections to measured values, and the equalization is carried out under the condition of the minimum of the sum of squares of absolute corrections. However, as shown in the article, the informational approach leads to the conclusion that the measure of proximity to the true value is a relative measurement error. Therefore, it is advisable to carry out an equalization under the condition of a minimum of the sum of squares of not absolute, but relative corrections. This is equivalent to equalization, in which the weight of the correction depends on the size of the object being measured: the larger the object being measured, the smaller the weight of the corresponding amendment, and its value can be increased during equalization. In this case, the described approach leads to a kind of “method of least relative squares” (MLRS). Another interesting consequence of the information approach is that the relative measurement error modulus has the meaning of the probability of a measurement result deviating from the true value. The article presents the required information approach formulas for the weights of the amendments when using the MLRS. In particular, it is shown that the angular discrepancy distribution in a triangle depends on the lengths of the sides.
Keywords
The Criterion of Proximity, The True Value, Amount of Information, The Hartley-Shannon Formula, The Least Squares Method, The Weighting Factors to Amendments, The Distribution of Angular Discrepancy
Ilya Feldman, On the Criterion of Proximity to the True Value: Information Approach, American Journal of Remote Sensing. Vol. 7, No. 1, 2019, pp. 1-4. doi: 10.11648/j.ajrs.20190701.11
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