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.
Highlights
The information approach leads to the conclusion that the criterion of proximity to the true value is a relative error
It is more reasonable to equalize the results of measurements under the condition of minimum sum of squares of relative rather than absolute corrections
It turned out an interesting fact: it turns out that the relative error of measurement makes sense of the probability characterizing the deviation of the measurement result from the true value
Summary
If you select absolute error as the criterion, the more accurate measurement is the first, and if relative error is the second. Which of these criteria can serve as a measure of proximity to the true value?. The author admits that the relative error is an important criterion in assessing the accuracy of the measurements, but often does not have much practical sense and value. The theory of equalization of geodetic measurements using the least squares method in all their sections and problems uses only absolute values of errors and corrections. We are convinced of it on examples of classical works of A. This article attempts to find an answer to the question about the criterion of proximity to the true value, using the information approach
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