DETERMINING THE ELEMENTS OF EXTERIOR ORIENTATION IN AERIAL TRIANGULATION PROCESSING USING UAV TECHNOLOGY

Unmanned Aerial Vehicles (UAVs) are still an interesting and current research topic in photogrammetry. An important issue in this area is determining the elements of exterior orientation of image data acquired at low altitudes. The article presents selected mathematical methods (TGC, TIC, TAD) of estimating elements of exterior orientation for image data obtained at low altitudes. The measurement data for the experimental test were recorded by the Unmanned Aerial Vehicle platform Trimble UX-5. In the framework of the test photogrammetric flight, the authors obtained 506 images and navigation data specifying the position and orientation of the Unmanned Aerial Vehicle. As a result of the research, it is proven possible to show the usefulness of the mathematical models (TGC, TIC, TAD) in estimation of elements of exterior orientation.

recovers the YPR (Yaw, Pitch and Roll) values of rotation angles on the basis of the movement of the gyroscopes and specifying the acceleration value from the accelerometer sensors. The readings of the YPR angles indicate an UAV position in airspace, whereas the acceleration values make it possible to designate the aircraft relative position [8][9][10][11].
The navigation parameters from the GNSS receiver are usually referenced to the GPS system time and the INS measurement system may have a separate built-in time pattern to register the observed data. It must be stressed that the GNSS receiver determines the UAV position with the absolute positioning accuracy of up to 10 m, whereas the INS relative accuracy becomes considerably deteriorated during the measurements. Furthermore, the accuracy of recording the YPR rotation angles equals 5 0 for an UAV. In order to correct the designated navigation parameters for an UAV, it is necessary to use exterior mathematical models so as to smooth the obtained findings. One of the examples of the integration of GNSS/INS data is the implementation, in computing, the recursive Kalman filter, reducing and eliminating measurements that stand out from a set of recorded navigational data. In addition, Kalman filtering ensures increasing accuracy in determining the UAV accuracy during the experimental test [12][13][14].
For aerial photogrammetry, determining the coordinate values and rotation angles for an UAV is a key element in the process of determining the elements of exterior orientation. The designated position of an UAV using a GNSS sensor forms the basis for reconstructing the camera position at the moment of exposure. Besides, the YPR rotation angles are exploited in the process of transformation to determine the angle OPK (Omega, Phi, Kappa) elements

Introduction
Development of the UAV technology made it possible to acquire image data o at low altitudes, as well. Georeferencing of image data taken by the Unmanned Aerial Vehicle (UAV) is performed in the process of digital aerial triangulation [1][2]. Within the classical process of digital aerial triangulation, the elements of exterior orientation and also coordinates of the measured ground control points, are taken. In the case of elements of exterior orientation, the coordinates of the centre of projection are determined for each image, referenced to the ground layout and the deflection angles of the camera referenced to the photogrammetric camera system. The typical accuracy of determining the elements of exterior orientation in the process of digital aerial triangulation for linear elements is approximately at a level of 0.1 m, and for angle elements, is respectively higher than 0.1 0 . The approximate values of exterior orientation may be determined based on measurements of the GNSS/ INS sensors, mounted on an UAV platform [3][4]. The basic navigation equipment of an UAV should contain at least a GNSS single-frequency code receiver and additionally a measurement system of gyroscopes and accelerometers for the needs of the INS system operation. The GNSS satellite receiver primarily facilitates determining the position of an Unmanned Aerial Aircraft in the three dimensional Cartesian coordinate XYZ. It also allows determining the heading and airspeed of an Unmanned Aerial Vehicle [5][6][7]. The above-mentioned navigation parameters of the GNSS receiver are determined in near real-time by an UAV control system and stored in the device's memory at a specified time interval. The measurement system of the INS sensor W I E R Z B I C K I , K R A S U S K I In Equation (1) the determined parameters are the aircraft coordinates, , , X Y Z r r r h referenced to the phase centre of the antenna receiver mounted on the UAV platform and the receiver clock bias dtr. The unknown parameters from Equation (1) are determined using the Kalman filtering in accordance with interval recording of an observation. The UAV coordinates are used to determine the coordinates of the projection center for each image, see below [13][14]:

Mathematical models for designation of the exterior orientation angle elements
The INS sensor installed on a UAV platform ensures reconstruction of a UAV orientation in airspace by means of the YPR rotation angles. The values of YPR angles allow designating approximate angular elements of OPK exterior orientation based on the transformation between the INS sensor layout and the camera layout, as below [15]: where: CE B -orthogonal matrix, containing angular OPK elements, , cos cos cos sin sin sin cos sin sin cos sin cos cos sin cos cos sin sin sin sin cos cos sin cos sin sin cos cos cos Tb B -the determinant of the matrix is equal to 1, in the photogrammetric camera layout. The approximate values of exterior orientation are a valuable research and information material for conducting the process of digital aerial triangulation, using the coordinates of ground control points (GCPs). The aim of this paper is to present mathematical methods for establishing the approximate values of elements of exterior orientation and to verify the obtained results with regard to the final products of digital aerial triangulation. The measurement data for the experimental test come from a photogrammetric flight performed by the Trimble UX-5 rover in Tylicz.

Mathematical models for designation of the exterior orientation elements
The chapter describes the mathematical models for the determination of elements of exterior orientation with the on-board GNSS/INS data registered by an UAV and on the basis of the method of digital aerial triangulation.

Mathematical models for designation of the projection centre coordinates
A single-frequency GNSS receiver, mounted on a UAV platform, can be used to determine approximate coordinate values of the centre of projection. Coordinates of the centre of projection are determined in a two-step process, i.e. in the first stage a UAV position is determined and in the second stage the coordinates of the projection center of each image are designated, taking into account the correction of eccentricity between the position of the GNSS receiver antenna and the camera. The basic observation equation to determine a UAV position for the GNSS sensor can be expressed in the following manner [4]: , l c dtr dts Trop rel ion bias Ml where: l -measurement code C/A at L1 frequency, r -geometric distance between the satellites GNSS and the receiver,

Experimental test
In the framework of the experimental test, the exterior orientation elements were determined based on equations [2,[5][6]18]. The navigation data to determine the elements of the exterior orientation from Equations (2) and (3) were recorded during the flight by the Trimble UX-5 unmanned aircraft system. The coordinate values of the platform Trimble UX-5 and YPR orientation angles are recorded by measurement instruments mounted on the platform and stored in the universal text format "log". The typical accuracy of the obtained coordinates of the Trimble UX-5 platform ranges from 5 m to 10 m and for the YPR orientation angles it is between 1 0 and 5 0 , respectively [19]. The photogrammetric flight took place in Tylicz, in the south of Poland, in 2016. During the flight, 506 aerial images were taken, using a Sony NEX5R camera. All the aerial images were arranged in 22 rows (see Figure 1). The photogrammetric flight was executed at an altitude of 150 m, with an assumption that the average height of the terrain is approximately equal to 650 m.
Over the tested area, 10 ground control points and 5 independent check points were also measured for the needs of conducting digital aerial triangulation. The mutual orientation was performed based on an automatic measurement of tie points [16]. All of the measured points were signalled and their coordinates were designated by means of the GNSS RTK technique, with an accuracy no worse than 0.05 m. The process of digital aerial triangulation was carried out in the commercial UASMaster software. After conducting the process of digital aerial triangulation, the value of the mean error of typical observations equalled 5.4 μm (1.1 pixel). Moreover, the determined standard deviations for angle elements of the exterior orientation were over 0.043 0 , whereas for the linear elements of exterior orientation they were higher than 0.1 m, accordingly. In addition, the RMS error at the control points equalled 0.21 m for the X coordinate, 0.04 m for the Y coordinate, and 0.11 m for the Z coordinate.

Results and discussion
For the sake of the executed experimental test, the elements of exterior orientation were determined based on the following research methods, which were defined by the authors as follows: Tn E -the determinant of the matrix is equal to 1.

Mathematical models for designation of the exterior orientation elements using the digital aerial triangulation method
The method of digital aerial triangulation allows determining exterior orientation of elements with high accuracy: for linear elements of exterior orientation above 0.1 m and for elements of the angular exterior orientation above 0.1 0 , respectively. The basic equation of digital aerial triangulation in the classic approach assumes the following form [16][17]:     Figure 8 shows a difference in coordinate values of the centre of projection along the XYZ axis on the basis of the research methods TGC and DAT. The difference in coordinates of the centre of projection along the X, Y and Z axes were determined based on dependency [11]: where: , , The average value of parameter dω is equal to -0.07 0 with the scatter of results ranging from -15.40 0 to 14.05 0 . Moreover, the standard value for parameter dω is 4.41 0 and the median is equal to -0.20 0 . The average value of parameter dφ is equal to -0.33 0 with the scatter of results 12.58 m. The standard deviation for parameter dZ equals 4.20 m, with the median being equal to -1.23 m. Among the calculated parameters dX, dY and dZ, the smallest dispersion (scatter) of results is noticeable for parameter dX. In addition, the dY parameter has the smallest standard values of deviation and of the median. Then, the largest scatter of results and standard deviation are visible for the value of the dZ parameter. Figure 9 shows a difference in the exterior rotation angle elements on the example of the research methods TIC and DAT. The difference in the values of angle elements of exterior orientation was determined based on dependency [15]:

Conclusions
The article describes and presents the results of exploiting three test methods for determining the elements of exterior orientation in photogrammetry for the needs of photogrammetry for aerospace applications. The paper used: • the TGC method, which allows determining the linear elements of exterior orientation based on navigation data from the GNSS receiver, mounted on an unmanned aircraft system, • the TIC method, which allows determining the angular elements of exterior orientation based on YPR parameters recorded by the INS sensor, • the TAD method, which allows designating the linear and angular elements of exterior orientation in the model of digital aerial triangulation. The research experiment was carried out for navigational data derived from the Trimble UX-5 rover.