Mathematical processing of results of double equally accurate measurements

2015;
: pp. 74-81
https://doi.org/10.23939/istcgcap2015.01.074
Received: December 03, 2014
1
State Higher Educational Institution “National Mining University”
2
Department of Geodesy, Lviv PolytechnicNational University, State Higher Educational Institution “National Mining University”

Purpose. Run trial of criteria importance of systematic errors in the mathematical processing of results of measurements of double equally accurate and install the most efficient one. Thus, to determine how to calculate the probability of trust and develop a method of exclusion bias of the mean values of double equally accurate measurements. Methods of resolving the issues raised based on the comparative analysis formulas, experimental results of calculations, developing proposals and reports. Established that the literature significance tests are not the same bias. Results. Established theoretical value measurements based on the number of accepted of confidence as significance tests bias in double equally accurate dimensions match. The research quality and enable more accurate process results double equally accurate measurements. Scientific novelty. Improved selection criteria justify the importance of systematic error in the double equally accurate dimensions. The method of exclusion bias of the mean values of double equally accurate measurements and calculate the value of confidence. The practical significance of the work is to obtain more accurate results in mathematical processing of double equally accurate measurements, their evaluation of accuracy and more detailed investigation of these measurements through improved methods and formulas described in the literature. A selection criterion of significance bias in double equally accurate dimensions depending on the number of measurements and calculated confidence probability. In addition, the method is shown exclude systematic error of the mean values of double equally accurate measurements reduces the residual functional in those terms that are between the respective average values of these measurements.

1. Bol'shakov V. D. Teorija oshibok nabljudenij: ucheb. dlja vuzov. 2-e izd., pererab. i dop. [Theory of errors of observation Proc. for high schools. 2nd ed., Rev. and add]. Moscow: Nedra, 1983, 223 p.
2. Bol'shakov V. D., Ju. I. Markuze, V. V. Golubev. Uravnivanie geodezicheskih postroenij: spravochnoe posobie [Adjustment of geodetic constructions: handbook]. Moscow: Nedra, 1989, 413 p.
3. Viduev N. G. Verojatnostno-statisticheskij analiz pogreshnostej izmerenij [Probabilistic and statistical analysis of measurement errors]. NG Mind GS Kondra. Moscow: Nedra, 1969, 320 p.
4. Voitenko S. P. Matematychna obrobka heodezychnykh vymiriv. Teoriia pokhybok vymiriv: navchalnyi posibnyk [Mathematical processing of geodetic measurements. Theory of measurement errors: a tutorial]. Kyiv: KNUBA, 2003, 216 p.
5. Gajdaev P. A., Bol'shakov V. D. Teorija matematicheskoj obrabotki geodezicheskih izmerenij [The theory of mathematical processing of geodetic measurements ]. Moscow: Nedra, 1969, 400 p.
6. Zazuliak P. M., Havrysh V. I., Yevsieieva E. M., Yosypchuk M. D. Osnovy matematychnoho opratsiuvannia heodezychnykh vymiriuvan: navchalnyi posibnyk [Fundamentals of mathematical processing of geodetic measurements: a tutorial]. Lviv: Vyd-vo "Rastr-7", 2007. – 408 s.
7. Ivina D. S., Riabchii V. V. Porivniannia kryteriiv znachymosti systematychnoi pokhybky pry otsintsi tochnosti za riznytsiamy podviinykh rivnotochnykh vymiriv [Comparison of criteria importance of systematic error in assessing the accuracy of measuring differences double rivnotochnyh [text]. Tezy dopovidei ХIII Mizhnarodnoi naukovo-praktychnoi konferentsii molodykh uchenykh i studentiv "Polit. Suchasni problemy nauky" [Proceedings of XIII International scientific conference of young scientists and students "Flight. Challenges of Science"], Kyiv, 3–4 April 2013, P. 319.

8. Mazmishvili A. I. Teorija oshibok i metod naimen'shih kvadratov [The theory of errors and least squares method]. Moscow: Nedra, 1978, 311 p.
9. Papazov M. G., Mogil'nyj S. G., Teorija oshibok i sposob naimen'shih kvadratov [The theory of errors and the method of least squares]. Moscow: Nedra, 1968, 302 p.
10. Rjabchij V. A., Ivina D. S. Sravnenie kriteriev znachimosti sistematicheskoj oshibki pri ocenke tochnosti po raznostjam dvojnyh ravnotochnyh izmerenij [tekst] [Probability theory and mathematical statistics in the annex to geodesy]. Zbirnyk prats IV Vseukrainskoi naukovo-tekhnichnoi konferentsii studentiv, aspirantiv i molodykh vchenykh "Naukova vesna 2013" [Proceedings of the IV All-Ukrainian scientific-technical conference of students, graduate students and young scientists "Science Spring 2013"], Dnipropetrovsk, 28-29 March 2013, pp. 176–177
11. Riabchii V. A., Riabchii V. V. Ymovirno-matematychnyi analiz obmezhenoi kilkosti rezultativ nerivnotochnykh vymiriv odniiei velychyny [tekst] [Probably, a limited number of mathematical analysis results nerivnotochnyh a value measurements [text] ]. Suchasni dosiahnennia heodezychnoi nauky ta vyrobnytstva: zb. nauk. pr. Zakh. heodez. t-va UTHK. – L.: Vyd-vo Lvivskoi politekhniky [Modern achievements of geodetic science and industry: Coll. Science. pr. Zech. heodez. UTHK of the Society. – L .: Izd Lviv Polytechnic National University], 2013, Vol. II, pp. 25–30.
12. Riabchii V. A., Riabchii V. V. Teoriia pokhybok vymiriuvan: navchalnyi posibnyk [Theory of measurement errors: a tutorial ]. Dn-sk: Nats. hirn. un-t, 2006, 166 p.
13. Smirnov N. V., Belugin D. A. Teorija verojatnostej i matematicheskaja statistika v prilozhenii k geodezii [Probability theory and mathematical statistics in the annex to geodesy ]. Moscow: Nedra, 1969, 379 p.