| Title:
|
Linear conform transformation: Errors in both coordinate systems (English) |
| Author:
|
Kubáček, Lubomír |
| Author:
|
Kubáčková, Ludmila |
| Author:
|
Ševčík, Jan |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
47 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
361-380 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Linear conform transformation in the case of non-negligible errors in both coordinate systems is investigated. Estimation of transformation parameters and their statistical properties are described. Confidence ellipses of transformed nonidentical points and cross covariance matrices among them and identical points are determined. Some simulation for a verification of theoretical results are presented. (English) |
| Keyword:
|
linear conform transformation |
| Keyword:
|
regression model with constraints |
| MSC:
|
62H99 |
| MSC:
|
62J05 |
| MSC:
|
62J99 |
| idZBL:
|
Zbl 1091.62520 |
| idMR:
|
MR1914119 |
| DOI:
|
10.1023/A:1021705806841 |
| . |
| Date available:
|
2009-09-22T18:10:44Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134502 |
| . |
| Reference:
|
[1] L. Kubáček: Criterion of accuracy at linear conform tranformation.Geodetický a kartografický obzor 8 (1962), 181–187. (Czech) |
| Reference:
|
[2] L. Kubáček: Confidence regions in Helmert transformations.Studia Geoph. et Geod. 10 (1966), 124–136. 10.1007/BF02585752 |
| Reference:
|
[3] L. Kubáček: Some statistical aspects of the estimation of parameters of a linear conform transformation.Apl. Mat. 15 (1970), 190–206. MR 0261753 |
| Reference:
|
[4] L. Kubáček: About the generalization of an orthogonal regression.Apl. Mat. 20 (1975), 87–95. MR 0375650 |
| Reference:
|
[5] L. Kubáček, L. Bartalošová and J. Pecár: “Pandora-Box” matrix in the calculus of observation.Studia Geoph. et Geod. 21 (1977), 227–235. 10.1007/BF01613249 |
| Reference:
|
[6] L. Kubáček: Sequentional connecting of networks.Studia Geoph. et Geod. 22 (1978), 224–230. 10.1007/BF01627899 |
| Reference:
|
[7] L. Kubáček: Foundations of Estimation Theory.Elsevier, Amsterdam-Oxford-New York-Tokyo, 1988. MR 0995671 |
| Reference:
|
[8] L. Kubáček: Nonlinear error propagation law.Appl. Math. 41 (1996), 329–345. MR 1404545 |
| Reference:
|
[9] L. Kubáčková: Foundations of Experimental Data Analysis.CRC Press, Boca Ratton-Ann Arbor-London-Tokyo, 1992. MR 1244322 |
| Reference:
|
[10] C. R. Rao: Unified theory of linear estimation.Sankhya, Ser. A 33 (1971), 371–394. Zbl 0236.62048, MR 0319321 |
| Reference:
|
[11] J. Ševčík: Weak nonlinearity in model which arises from the Helmert transformation.Appl. Math, Submitted. |
| . |
