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  • CPA Algorithm for S, R circle parameters in the determination of circular building objects using RTK/NRTK GNSS technology and linear measurements
  • https://doi.org/10.1080/00396265.2025.2489870Copy DOI Icon

CPA Algorithm for S, R circle parameters in the determination of circular building objects using RTK/NRTK GNSS technology and linear measurements

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Abstract

A building is a construction object that requires an accurate determination of its position in space by determining the coordinates of its break points (building corners). This is achieved by using classical geodetic surveying with the polar method or in RTK/NRTK GNSS mode. These are conventional surveying methods that can also be used to measure circular objects (these can also be buildings) directly accessible. In such cases, it is enough to measure the perimeter of such an object directly. Unfortunately, there are often cases in practice where we do not always have direct access to the object in question. In such cases, the position of circular objects must be determined in a slightly different way, i.e. by calculating the parameters: the coordinates of the centre of the object and its radius. It was these factors, i.e. the method of determining the parameters of a circular cross-section object and the potential difficulty of directly accessing it, that formed the genesis of the research carried out. The aim of the research carried out was to present surveying contractors with an alternative to using the suggested algorithm in RTK/NRTK GNSS measurements to determine the position of circular cross-section objects. The novelty of such a solution is the comprehensive application of the suggested calculation method together with the measurement of base points in the NRTK GNSS mode and linear measures. Test surveys were carried out on real field objects with circular cross-sections of 4, 60 and 150 m in diameter. The reference values of these objects were obtained by measuring their perimeter with a Leica TC 407 electronic total station with reference to the base points. The base points were determined in static mode with GNSS satellite technology using Leica GS16 receivers with reference to the ASG-EUPOS reference station network. The accuracy of the determination of the base points (mean position error) did not exceed 0.005 m. After application of the algorithm, linear deviations ΔL were obtained for the determined X, Y coordinates of the centre of a circular object and its radius at the level of single centimetres: from 0.01 to 0.05 m. The average errors m_P (0.01 to 0.03 m) for the position of the centre of the circular object and its radius are of a similar order and do not differ significantly from the reference values. This solution provides results that are reliable and at a high level of accuracy. Thus, it is of significant importance in a complex surveying environment, providing a guarantee of meeting any accuracy criteria used for a variety of needs, and as an alternative to conventional surveying techniques. The results of the study allow us to conclude the high suitability of the suggested algorithm for determining the position of a circular building object in real time.

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