Szczegóły publikacji
Opis bibliograficzny
Point-wise weighted solution for the similarity transformation parameters / Marcin LIGAS // Applied Geomatics [Dokument elektroniczny]. — Czasopismo elektroniczne ; ISSN 1866-928X. — 2020 — vol. 12 iss. 3, s. 371–377. — Wymagania systemowe: Adobe Reader. — Bibliogr. s. 377, Abstr. — Publikacja dostępna online od: 2020-05-26
Autor
Słowa kluczowe
Dane bibliometryczne
| ID BaDAP | 129744 |
|---|---|
| Data dodania do BaDAP | 2020-09-03 |
| Tekst źródłowy | URL |
| DOI | 10.1007/s12518-020-00306-7 |
| Rok publikacji | 2020 |
| Typ publikacji | artykuł w czasopiśmie |
| Otwarty dostęp |  |
| Creative Commons | |
| Czasopismo/seria | Applied Geomatics |
Abstract
In the paper, we consider solutions to the similarity transformation under different adjustment scenarios. We consider asymmetric cases, i.e., random errors included either in a target system (Gauss–Markov model, the most common case) or in a source system and a symmetric case when both systems are considered to be contaminated by random errors (Gauss–Helmert or errors-in-variables model). The presented solutions are based on Procrustes approach and all cases use point-wise weighting scheme. The asymmetric cases have closed-form solutions but the symmetric one, in the most general case considered herein, does not. In the latter case, weight matrices for a source and target systems are combined into one equivalent weight matrix which depends on a scale factor. This case is solved through a simple iterative process but there are some special instances which lead to closed-form solutions. The paper discusses the behavior of transformation parameters (rotations, translations, and a scale) under different adjustment scenarios.
