Analysis of accuracy in evaluating gravimetric coefficients in the algorithm of spatial monitoring under conditions of excess

Authors

  • Yuri Kulyavets Kharkiv National University of Construction and Architecture 40 Sumskay str., Kharkiv,Ukraine, 61002, Ukraine
  • Oleg Bogatov Kharkiv National Automobile and Highway University 25 Petrovskogo str., Kharkiv, Ukraine, 61002, Ukraine
  • Elena Ermakova Kharkiv National Automobile and Highway University 25 Petrovskogo str., Kharkiv, Ukraine, 61002, Ukraine
  • Peter Karlash Kharkiv National University of Construction and Architecture 40 Sumskay str., Kharkiv,Ukraine, 61002, Ukraine
  • Vladimir Popov Kharkiv National Automobile and Highway University 25 Petrovskogo str., Kharkiv, Ukraine, 61002, Ukraine

DOI:

https://doi.org/10.15587/1729-4061.2016.66195

Keywords:

data integration, measuring of parameters, independent meters (measuring devices), filtering of estimates, weight coefficient matrix

Abstract

Information excess allows obtaining the resulting estimate by a variety of relatively simple measuring devices and using a minimally sufficient set of primary measurements. At the same time, the estimated parameters are typically associated with the initially measured estimates on the basis of nonlinear functional equations. Therefore, a direct use of the maximum likelihood method makes it necessary to solve a system of nonlinear equations. The use of the linearization method for nonlinear functional correlations allows obtaining explicitly optimal estimates (in this case, the most plausible ones) of the resulting parameter and the correlation matrix of assessment errors. The problem of an optimal use of assessments provided by the same state vector through different simultaneously applied methods can be solved by a consistent application of the estimates’ filtering algorithm. However, the weight coefficient matrix in the expression for determining the resulting estimate depends on the measured parameter values, and it is not always known a priori. One of the possible methods of obtaining the estimates of the weight coefficients matrix is to calculate direct estimates of error correlation matrices on the basis of independent discrete samples of estimates for the parameter state vector. Analytical expressions were obtained for mathematical expectation and variance of the assessment components of the error correlation matrix for determining the parameter state vector. The study has shown that the assessment accuracy depends both on the accuracy of the measuring devices and the length of the samples’ line taken to determine the error correlation matrix for the parameter evaluation.

Author Biographies

Yuri Kulyavets, Kharkiv National University of Construction and Architecture 40 Sumskay str., Kharkiv,Ukraine, 61002

PhD, Associate professor

Department of Life Safety & Environmental Engineering

 

Oleg Bogatov, Kharkiv National Automobile and Highway University 25 Petrovskogo str., Kharkiv, Ukraine, 61002

PhD, Associate professor

Department of Metrology and Life Safety

Elena Ermakova, Kharkiv National Automobile and Highway University 25 Petrovskogo str., Kharkiv, Ukraine, 61002

PhD, Associate professor

Department of Engineering and Computer Graphics

Peter Karlash, Kharkiv National University of Construction and Architecture 40 Sumskay str., Kharkiv,Ukraine, 61002

Senior teacher

Department of Life Safety & Environmental Engineering

Vladimir Popov, Kharkiv National Automobile and Highway University 25 Petrovskogo str., Kharkiv, Ukraine, 61002

PhD, Associate professor

Department of Metrology and Life Safety

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Published

2016-04-30

How to Cite

Kulyavets, Y., Bogatov, O., Ermakova, E., Karlash, P., & Popov, V. (2016). Analysis of accuracy in evaluating gravimetric coefficients in the algorithm of spatial monitoring under conditions of excess. Eastern-European Journal of Enterprise Technologies, 2(4(80), 4–10. https://doi.org/10.15587/1729-4061.2016.66195

Issue

Vol. 2 No. 4(80) (2016): Mathematics and Cybernetics - applied aspects

Section

Mathematics and Cybernetics - applied aspects

License

Copyright (c) 2016 Юрій Владленович Кулявець, Oleg Bogatov, Elena Ermakova, Peter Karlash, Vladimir Popov

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