PRIOR CALCULATION OF THE ACCURACY OF MONITORING OF CULTURAL HERITAGE OBJECTS USING UAVS AND LASER SCANNING

. In the last few years, intensive measures have been taken to monitor and inventory the cultural heritage of Ukraine. An important aspect is the preservation of such objects and their transmission to future generations. It is important to use such a methodology and technology when performing monitoring works, which in the future will make it possible to perform a number of other tasks, in relation to a certain specific object, based on previously obtained data. Therefore, this paper proposes a method of cultural heritage monitoring using UAV-filming. The work examines the methods of monitoring cultural heritage objects and presents an a priori assessment of the accuracy of monitoring of cultural heritage by means of UAV photography and laser scanning. The work focuses on the fact that the monitoring of cultural heritage sites should be carried out precisely with the help of modern filming methods, which have a number of advantages compared to traditional methods. The reliability of the proposed methods is presented and substantiated by calculating an a priori estimate of the accuracy of potential results.


Introduction
In the conditions of Russia's war against Ukraine, special attention should be paid to the objects of cultural heritage (OСH) in the interests of current and future generations.Military operations have already caused significant destruction to the OСH, and in the future the urgency of reconstruction and restoration will only increase.In order to ensure the performance of such works at a high-quality level, the task of preserving geospatial data on the OCS by methods that are optimal in terms of time, cost and quality arises.Today, photogrammetric, in particular laser scanning and UAVsurveying, are among the most common methods of executive surveys of the OCS, the result of which is a cloud of points as an initial stage for further processing and modeling (Chumak et al., 2022).
The use of UAV-removal and laser scanning technologies for the measurement of OСH will allow solving the following tasks: -creation of the OСH geo-information system; -creation of 1:20 scale drawings; complicated by the need to carry out additional research on camera calibration and integration of different types of data, but the result shows high efficiency.The work (Shults et al., 2017) describes an approach using smartphones, UAVs and PhotoScan software to solve the problem of inventorying a fortification structure of the Second World War near the city of Kyiv.The results of experimental tests conducted using the Dji Phantom 2 UAV equipped with a GoPro hero3 + Black Edition camera and the Photo-Scan software in comparison with high-precision simulations indicate the possibility of practical use of non-metric widely available cameras (Bolognesi et al., 2015).Supplementing ground laser scanning with additional classical photogrammetric surveying is described in the following studies (Roy, 2007;Hassani & Rafiee, 2013;Bohm, 2004).Digital surveying is also performed for further easier deciphering of contours and decorative elements of buildings.
Another vivid example of the application of the closerange photogrammetry method is the three-dimensional modeling of the tower of the Harrakan tomb in the work (Hassani & Rafiee, 2013), where the exact geometric dimensions of the building for actual drawings and documentation were established based on the results of shooting by amateur cameras and modeling in the PhotoModeler environment.
The purpose of the work is the analysis of errors that affect the result of executive surveys by photogrammetric methods, in particular laser scanning and UAV, and an a priori assessment of the accuracy of measurement results -point clouds as the basis for further modeling.
In order to calculate the accuracy of OСH monitoring, it is necessary to classify certain types of work.As you know, from traditional geodesy, the set of factors affecting the result of measurements is called a set of conditions.The set of conditions for the monitoring of the OСH includes: the object (the facade of the OСH, architectural structures, etc.) and the device (camera, total station, laser scanner).For each type of work, there are systematic errors that affect the measurement result (Table 1).The general equation for determining the a priori calculation of OСH monitoring will look like this: where: m S -RMS of the type of work; m i -RMS of the measuring device.
The sum of the root mean square errors included in the RMS of the camera measurement can be different and depends on the choice of the camera and its characteristics.The removal of OCH structures can also be performed by various methods, in particular, traditional removal methods, so in the work we do not stop at a detailed description of errors in such measurements.
For practical testing, an a priori assessment of the accuracy of the results of the removal of the cultural heritage object, the monument to Bohdan Khmelnytskyi in Kyiv, was calculated.The cloud of points is obtained by merging the results of a ground laser scanner and a UAV.The ultimate goal of the work is high-precision three-dimensional modeling of the object for the purpose of monitoring and preserving the cultural heritage.Photogrammetric work was performed using a DJI Mavic 2 Pro UAV with a 1"CMOS Hasselblad L1D-20c sensor and laser scanner of the Swiss firm Leica ScanStation C10.
The equation for a priori calculation of measurement accuracy for 3D model assembly will have the following form:   To calculate the camera error, we will use the classic approach, using the Hasselblad L1D-20c camera as an example of the calculation.Technical characteristics of the camera are given in Table 2.The equation for calculating the RMS measurement by the camera is as follows: where: m d -is RMS for camera lens distortion; m pzz -RMS position of the PZZ matrix relative to the focal plane; m Y -RMS determination of the ordinate.Errors due to distortion of shooting non-metric cameras have already been sufficiently studied and corrections are introduced pixel by pixel, which determines its minimum value (Glotov & Smoliy, 2008).The error due to m d distortion should not exceed 2 mm (Glotov & Chyzhevsky, 2005).The study of the slopes of the PZZ matrices with respect to the focal plane also confirmed the minimal error of these values, which can be neglected (Glotov & Smoliy, 2008).Deviation of the CCD matrix relative to the focal plane m pzz = 20′′, i.e. in linear form m pzz = 2 mm (Glotov & Pashchetnyk, 2008).According to (Lobanov, 1972) RMS coordinates m Y can be calculated using the equation: According to the technical characteristics of the Hasselblad L1D-20c camera: x = 11 mm, z = 7 mm.Average horizontal size of the object under investigation: X = 15 m.Measurement accuracy of the shooting base: m Xs = m Ys = 1 mm.The accuracy of measuring the coordinates of the points on the image in the software: m x = 5 μm.Accordingly, the internal orientation elements must be determined with the same accuracy, i.e.: m x0 = m f = 1 mm.The RMS of the angular elements of external orientation are equal to m α = 3.5′′, m ω = 3.6′′, m χ = 2.2′′ (Glotov & Smoliy, 2008).
Let's calculate m Y for the focal length f = 18 mm, as a result of the calculations we will get: m Y = 2.7 mm.According to expression (4), the RMS measurement by the camera is equal to: m c = 3.9 mm.Thus, the aggregated result of calculating the RMS of the cloud of points according to expression (2) is equal to m pc = 6 mm.
The basis for calculating the maximum accuracy is the construction tolerances and installation errors of volumetric planning and structural elements of the OCH.Marginal errors when measuring metal and reinforced concrete structures are accepted three times smaller than the corresponding construction tolerances of stone structures, therefore, based on this, when measuring stone buildings and structures up to 100 m in size, errors in the longitudinal and transverse directions of 2-5 cm are allowed, and in the vertical direction -1-2 cm.
Thus, during measurements performed for the purposes of reconstruction and restoration, it is necessary to ensure a root mean square measurement error of the order of 1-2 cm (Table 3), which is twice the a priori accuracy of the measurement results obtained by experimental calculations.

Conclusions
The general method of a priori assessment of the accuracy of the results of executive works in the monitoring of OCS is a reliable justification for one or another shooting method.It is the choice of optimal equipment and methodical approach that will ensure effective preservation of high-quality data on unique objects in extreme conditions of war.The calculated total root mean square errors of the object and the device cannot exceed the limit values specified by regulatory documents or practical requirements.
According to the results of the practical implementation of the method, namely the calculation of total errors when performing UAV photography with a Hasselblad L1D-20c camera and a Leica ScanStation C10 laser scanner, it can be stated that the a priori estimate of the accuracy of the resulting cloud is 6 mm, which is significantly less than the normative indicator of the ultimate accuracy of this type works (1-2 cm).
Measurements of architectural ensembles and individual historical buildings can be carried out by various methods, but the use of UAVs and ground-based laser scanning has a number of advantages, including high accuracy and speed of work.
m -RMS point cloud; c m -RMS measurement by camera; ls m -RMS of laser scanning.The measurement error of laser scanning ls m is calculated taking into account the technical characteristics of the device used.
where: m r -RMS rangefinder; m a.m -RMS of angular measurements; m comp -RMS compensator.According to the technical characteristics of the Leica ScanStation C10 device: m r = 4 mm m a.m = 12'' i.e. in linear form 1.2 µm, m comp = 2 mm, then by substituting the value in Equation (3) we get: m ls = 4.6 mm.

Table 1 .
Classification of works during monitoring of OСH where: m ∑c -RMS measurement by camera; m d -RMS for camera lens distortion; m pzz -RMS position of the PZZ-matrix relative to the focal plane; Y m -RMS definition of the ordinate where: m ∑3D-m -RMS measurements for 3D modeling; m ∑c -RMS measurement by camera; m ∑ls -RMS of laser scanning; m ∑t -RMS measurement with a tacheometer

Table 3 .
Characteristics of accuracy of measuring works