The research of an initial matrix of the return scales of unknown at a recurrent way

Markuze, Yu.I.; Le, Anh Vinh; Tran, Cuong

doi:10.22389/0016-7126-2016-917-11-7-10

Cited by 3 publications

(2 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Note that the resulting inverse matrix will be the only one. 4) calculate the pseudo-inverse matrix by the known formula given by the authors of [12][13][14]:…”

Section: Resultsmentioning

confidence: 99%

“…The measurement results will be equated according to the least squares principle, i.e., the tar-get function is subject to minimization F(x) = V T PV = min, where V is a vector of corrections to measurement results, P and is a weight matrix of measurement results. Note that when performing the equalization, the mathematical procedure of matrix inversion is performed [12]. For example, in finding parameters for correct equalization the determination of the weight matrix P is essentially important, as it is inverse to the error covariance matrix of the observed quantities [7].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Equalization of free geodetic networks by search methods for geodetic monitoring of structures in arctic areas

2023

View full text Add to dashboard Cite

While carrying out work to ensure the technical safety of buildings and structures in the Arctic regions, one of the important stages is geodetic monitoring. Provided that the complexity of ensuring the stability of reference points in the Arctic zone when conducting geodetic monitoring of engineering facilities, geodetic networks should preferably be equated as free, i.e., to equate the reference points on a par with the defined ones. The present article provides variants how to to equalize geodetic networks to carry out a search method of non-linear programming, which is given a theoretical substantiation for the method and the order of estimating accuracy of the outcomes of the equalization of the generalized Makarov method. The procedure of pseudo transformation of a matrix of normal equations of unknowns with the application of an algorithm of a search method of nonlinear programming is given. The correctness of the application of the search method to the pseudo transformation of a matrix of normal equations of unknowns by the coincidence of outcomes of the pseudo transformation of the given matrix based on skeleton expansion done in M. Mashimov's work is proved. Equalization and estimation of accuracy of free leveling network with the application of search method and generalized Makarov's method are carried out. The conclusion about the correctness of the application of a search method of nonlinear programming for the processing of free geodetic networks at the performance of geodetic monitoring of buildings and constructions in the Arctic area is made.

show abstract

“…Note that the resulting inverse matrix will be the only one. 4) calculate the pseudo-inverse matrix by the known formula given by the authors of [12][13][14]:…”

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Equalization of free geodetic networks by search methods for geodetic monitoring of structures in arctic areas

2023

View full text Add to dashboard Cite

show abstract

Monitoring coarse measurement errors and initial data

Markuze

Cường

et al. 2018

G&C

View full text Add to dashboard Cite

Rough errors are a consequence of the observer’s miscalculations, device malfunctions, their displacements at the time of measurement, incorrect measurement techniques chosen, rapid and sharp deterioration of external conditions and other causes. That is why, one of the problems in the theory of mathematical processing geodetic measurements is culling measurements containing gross errors. In the last two decades received recursion equalization has been widespread. It enables evaluating the unknown while new measurements are added to the network and measurements with gross errors are deleted [3, 4]. In the article, a complementary recurrent equalization is developed. It is original, convenient and recommended for wide application in production.

show abstract

Inversion of matrix through the search method at equalizing geodetic networks

Shevshenko

Bryn

Naumova

2022

G&C

View full text Add to dashboard Cite

The theoretical substantiation of matrix inversion by the search method of nonlinear programming is given for equalizing and evaluating the accuracy of geodetic networks’ elements. A theorem on the uniqueness of the extremum point and its corollary (also a remark to the latter) are formulated and proved with minimizing the objective function by the search method at performing matrix inversion. A step-by-step algorithm for matrix conversion by the search method was compiled. The approbation of the developed algorithm was carried out when equalizing and evaluating the geodetic network elements’ accuracy, taking into account the errors of the source data. The correctness of the proposed solutions is confirmed by coinciding the covariance matrix of measurement errors results reversal and that of unknowns’ coefficients normal equations with the calculations performed by the MOBR function in Microsoft Excel, as well as the coincidence of the equalization results and evaluation of the geodetic network’s elements accuracy by the search method with similar calculations by parametric method in the NW program by Prof. V. A. Kougiya.

show abstract

The research of an initial matrix of the return scales of unknown at a recurrent way

Cited by 3 publications

References 0 publications

Equalization of free geodetic networks by search methods for geodetic monitoring of structures in arctic areas

Equalization of free geodetic networks by search methods for geodetic monitoring of structures in arctic areas

Monitoring coarse measurement errors and initial data

Inversion of matrix through the search method at equalizing geodetic networks

Contact Info

Product

Resources

About