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.
Published in | American Journal of Remote Sensing (Volume 7, Issue 1) |
DOI | 10.11648/j.ajrs.20190701.11 |
Page(s) | 1-4 |
Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
Copyright |
Copyright © The Author(s), 2019. Published by Science Publishing Group |
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
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APA Style
Ilya Feldman. (2019). On the Criterion of Proximity to the True Value: Information Approach. American Journal of Remote Sensing, 7(1), 1-4. https://doi.org/10.11648/j.ajrs.20190701.11
ACS Style
Ilya Feldman. On the Criterion of Proximity to the True Value: Information Approach. Am. J. Remote Sens. 2019, 7(1), 1-4. doi: 10.11648/j.ajrs.20190701.11
AMA Style
Ilya Feldman. On the Criterion of Proximity to the True Value: Information Approach. Am J Remote Sens. 2019;7(1):1-4. doi: 10.11648/j.ajrs.20190701.11
@article{10.11648/j.ajrs.20190701.11, author = {Ilya Feldman}, title = {On the Criterion of Proximity to the True Value: Information Approach}, journal = {American Journal of Remote Sensing}, volume = {7}, number = {1}, pages = {1-4}, doi = {10.11648/j.ajrs.20190701.11}, url = {https://doi.org/10.11648/j.ajrs.20190701.11}, eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajrs.20190701.11}, 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.}, year = {2019} }
TY - JOUR T1 - On the Criterion of Proximity to the True Value: Information Approach AU - Ilya Feldman Y1 - 2019/07/09 PY - 2019 N1 - https://doi.org/10.11648/j.ajrs.20190701.11 DO - 10.11648/j.ajrs.20190701.11 T2 - American Journal of Remote Sensing JF - American Journal of Remote Sensing JO - American Journal of Remote Sensing SP - 1 EP - 4 PB - Science Publishing Group SN - 2328-580X UR - https://doi.org/10.11648/j.ajrs.20190701.11 AB - 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. VL - 7 IS - 1 ER -