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The Helmert transformation: a proposal for the problem of post-transformation corrections

Gargula Tadeusz, Gawronek Pelagia

Advances in Geodesy and Geoinformation

2023

Vol. 72, no. 1

art. no. e34, 2023

The geodesy literature seems to offer comprehensive insight into the planar Helmert transformation with Hausbrandt corrections. Specialist literature is mainly devoted to the issues of 3D transformation. The determination of the sought values, coordinates in the target system, requires two stages of computations. The classical approach yields ‘new’ coordinates of reference points in the target system that should not be changed in principle. This requires the Hausbrandt corrections. The paper proposes to simplify the two-stage process of planar transformation by assigning adjustment corrections to reference point coordinates in the source system. This approach requires solving the Helmert transformation by adjusting conditioned observations with unknowns. This yielded transformation results consistent with the classical method. The proposed algorithm avoided the issue of correcting the official coordinates of the control network and using additional (post-transformation) corrections for the transformed points. The proposed algorithm for solving the plane Helmert transformation for [...] reference points simplifies the computing stages compared to the classical approach. The assignment of adjustment corrections to coordinates of reference points in the source system helps avoid correcting coordinates of the reference points in the target system and additional corrections for transformed points. The main goal of any data adjustment process with the use of the least squares method is (by definition) obtaining unambiguous quantities that would strictly meet the mathematical relationships between them. Therefore, this work aims to show such a transformation adjusting procedure, so that no additional computational activities related to the correction of already aligned results are necessary.

Transformation of magnetocardiograms between different multichannel devices

Burghoff M.

Biocybernetics and Biomedical Engineering

1999

Vol. 19, no. 3

5-13

In Europe several types of multichannel SQUID-devices are applied for magnetocardiography (MCG). The technical parameters of these devices, such as the SQUID specification, gradiometer design, sensor configuration and covered sensor area, are different. The dependency of temporaI recordings of the cardiac magnetic field from these parameters is demonstrated by an example of cardiac measurement. The absence of a standardized measurement setup hampers the comparison of biomagnetic results in multicentric clinical studies. This contribution presents a method for comparison of signals recorded with different sensor systems. The recorded signals are modeled by means of a multipole source model, which is used in the next step to simulate the signals of a second system. The efficiency of the algorithm is demonstrated by a measurement of the heart magnetic field using two different multichannel SQUID-devices.

Do pomiaru magnetokardiograrnów używane są w Europie różne wielokanałowe systemy pomiarowe o odmiennych parametrach konstrukcyjnych. Nie ma dotychczas standardu międzynarodowego dotyczącego tych systemów, co utrudnia porównywanie wyników uzyskiwanych w różnych ośrodkach badawczych. W pracy zaprezentowano metodę porównywania sygnałów mierzonych w różnych systemach przy wykorzystaniu modelowania multipolowego, która umożliwia symulowanie, sygnałów w dowolnie wybranym systemie pomiarowym. Skuteczność opracowanego algorytmu transformacji zilustrowano na przykładzie transformacji magnetokardiogramów dla dwóch różnych systemów wielokanałowych.