A Method for Determining the Optimum Flight Altitude of an Unmanned Aerial Vehicle for Aerial Photography Tasks

At present, worldwide practice tends to expand the use of UAVs in various realms, for example, to solve the problems of environmental monitoring, remote sensing of the Earth's surface, observing the objects of transport infrastructure, etc. In this case, UAV movement can occur in a variety of complex terrain conditions: in urban environment (among buildings), in mountainous terrain conditions, over deserted, forested parks, aquatic environments, etc. With the rapid development of UAV capable to move under complex terrain conditions, the task of planning and determining flight characteristics of UAVs is becoming increasingly relevant [1].


INTRODUCTION
At present, worldwide practice tends to expand the use of UAVs in various realms, for example, to solve the problems of environmental monitoring, remote sensing of the Earth's surface, observing the objects of transport infrastructure, etc. In this case, UAV movement can occur in a variety of complex terrain conditions: in urban environment (among buildings), in mountainous terrain conditions, over deserted, forested parks, aquatic environments, etc. With the rapid development of UAV capable to move under complex terrain conditions, the task of planning and determining flight characteristics of UAVs is becoming increasingly relevant [1].
Issues regarding the use of UAVs for aerial photography are discussed in reference [1]. References [2,3] are devoted to the process of planning the application of UAVs. In [4,5], the main indices that influence the quality of the obtained aerial photography results are analyzed, and reference [6] is aimed to determine the viewing area during the aerial photography. Still in these references the issue of the influence of the height on the quality of aerial photography using UAV has not been fully addressed.
In [7] the general concepts of the decisionmaking system are considered. References [8,9,10] are devoted to multicriteria problems and multicriteria optimization. These references consider in detail the conception of solving multicriteria problems, their advantages and disadvantages. The investigated approaches to minimizing vector performance indices are discussed in detail in [11].
Reference [12] is devoted to the methods of obtaining a generalized criterion. In this paper the multiplicative convolution has been analyzed in detail, as well as its advantages and disadvantages in comparison with other approaches.
All the same, the aforementioned papers did not pay enough attention to the aerial photography using UAVs. The issue of determining the UAV flight altitude considering the specifics of the tasks was not considered. Thus, it can be concluded that the issue of determining the UAV Section "Technics" 6002 flight altitude to perform aerial photography tasks is relevant.
Suppose it is given a particular type of UAV with a specific payload. A UAV has the defined parameters for aerial photography: resolution R , probability of object recognition in the image роз P , and frame area k S .
It is necessary to determine optimal flight altitude of UAVs opt H , which will satisfy the following conditions: The aim of the article is to invent a method to determine the optimal flight altitude of UAVs to ensure that the tasks are performed with a probability of not less than the specified ones.

RESULTS AND DISCUSSION
The UAVs application for aerial photography and terrain monitoring tasks creates an ambiguous practical task for choosing the height to perform the tasks. After all, the UAV flight altitude is one of the flight characteristics, which depends on the quality of the tasks performance and the flight route.
Therefore, at the same time when a UAV is flying at a certain altitude з H and with a known scan angle  , several target objects ( ) can be identified in the viewing area, as shown in Figure 1.
To find the solutions for the problems of aerial photography using UAVs, let us define the main indices that will affect the quality of the assigned tasks. These indices are supposed to define the resolution, the probability of recognizing the objects in the image, and the coverage area of the photography zone (the square of the obtained frame).
The introduced method of determining the optimal UAVs flight altitude when performing aerial photography tasks is based on finding a compromise solution that will take into account all the indices and will provide the necessary probability of successful completion of the assigned tasks. . cos   The image contrast is calculated as a relation of object background brightness о M and photography area background brightness by expression [4]: Step 2 assumes the calculation of probability of object recognition in the image роз P , which depends on resolution of the payload R , a required resolution 0 R and contrast K , and is determined by expression [4]: Then expressions (2-4) are used to calculate the photo height: After that we calculated the frame area, which depends on photography height з H , scan angle  , deflection angle of optical axis from the nadir  , and is determined by [5]: . cos Step 3 of the introduced method is to select an optimization scheme using a decision-making theory, which includes the following steps: 1. Selecting a compromise scheme. The selection of the principle of optimality transforms the vector problem of making a decision to the scalar one. Multicriteria optimization methods allow us to effectively solve problems of different type [7]. The analyzing of the known methods [8,10] and regarding the specificity of the tasks of aerial photography pointed to the superiority of a multiplicative convolution application under the given conditions as for there is a few partial criteria to be selected.  Further calculations were done on the selected multiplicative convolution which has the advan-Section "Technics" 6004 tage of defining the only optimal solution when we have a few partial criteria. Furthermore, when applying this type of convolution, there is no influence of different dimensions of the selected partial criteria. That is, there is no need to normalize the selected partial criteria, therefore there is no influence of the selected method of normalizing the criteria on the overall result [7,11].
For step 4 we are to calculate a generalized criterion by the selected multiplicative convolution to find the priority coefficients of the partial criteria (in the course of calculations, there was taken the same priority of the partial criteria): According to the developed mathematical model of the method, there was made a behavior modeling of a certain generalized criterion with increasing the height for two types of UAVs in the MathCAD software environment. Its results are shown in Figure 3. The final step is to calculate the optimal height that will correspond to the maximum value of the generalized criterion: were obtained, regarding required resolution 0 R , recognition probability роз P , and frame area k S . This enables the UAV operator to determine the optimum UAV flight altitude for a particular task, and (if several UAVs are available) to select one of them for the flight task, considering prior known information.

CONCLUSIONS
The article introduces a new approach to defining the UAVs optimal flight altitude when performing aerial photography tasks. In the course of the research the methods of combinatorial optimization and methods of solving multicriteria problems were used. In calculations, a multiplicative convolution of partial criteria was implemented. The flight altitude was determined by the required resolution to determine the assigned tasks, the probability of recognizing aerial photography objects and the frame area of imagery.
The prospect of further research is the program implementation of the method being introduced and further consideration of the specifics of the tasks. In addition, it is proposed to take into account meteorological and light conditions when performing the tasks.