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Method of the Determination of Exterior Orientation of Sensors in Hilbert Type Space

Institute of Geoinformatics, Żołnierska 46, Maritime University of Szczecin, 71-250 Szczecin, Poland
This paper is an expanded version of “Method of the Determination of Exterior Orientation of Sensors in Hilbert Type Space” presented at the 5th International Symposium on Sensor Science (I3S 2017), Barcelona, Spain, 27–29 September 2017.
Sensors 2018, 18(3), 891; https://doi.org/10.3390/s18030891
Received: 3 January 2018 / Revised: 12 March 2018 / Accepted: 13 March 2018 / Published: 17 March 2018
(This article belongs to the Special Issue I3S 2017 Selected Papers)
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Abstract

The following article presents a new isometric transformation algorithm based on the transformation in the newly normed Hilbert type space. The presented method is based on so-called virtual translations, already known in advance, of two relative oblique orthogonal coordinate systems—interior and exterior orientation of sensors—to a common, known in both systems, point. Each of the systems is translated along its axis (the systems have common origins) and at the same time the angular relative orientation of both coordinate systems is constant. The translation of both coordinate systems is defined by the spatial norm determining the length of vectors in the new Hilbert type space. As such, the displacement of two relative oblique orthogonal systems is reduced to zero. This makes it possible to directly calculate the rotation matrix of the sensor. The next and final step is the return translation of the system along an already known track. The method can be used for big rotation angles. The method was verified in laboratory conditions for the test data set and measurement data (field data). The accuracy of the results in the laboratory test is on the level of 10−6 of the input data. This confirmed the correctness of the assumed calculation method. The method is a further development of the author’s 2017 Total Free Station (TFS) transformation to several centroids in Hilbert type space. This is the reason why the method is called Multi-Centroid Isometric Transformation—MCIT. MCIT is very fast and enables, by reducing to zero the translation of two relative oblique orthogonal coordinate systems, direct calculation of the exterior orientation of the sensors. View Full-Text
Keywords: isometric transformation; big rotation angles; similarity transformation; Total Free Station—TFS; oblique orthogonal coordinate system; exterior orientation of sensor; Multi-Centroid Isometric Transformation—MCIT; geodesy surveying; close range photogrammetry; Multi-Centroid Transformation—MCT isometric transformation; big rotation angles; similarity transformation; Total Free Station—TFS; oblique orthogonal coordinate system; exterior orientation of sensor; Multi-Centroid Isometric Transformation—MCIT; geodesy surveying; close range photogrammetry; Multi-Centroid Transformation—MCT
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Stępień, G. Method of the Determination of Exterior Orientation of Sensors in Hilbert Type Space. Sensors 2018, 18, 891.

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