Vision-based system and method for the relative positioning of an object with respect to a target surface and a navigation system for navigating said object

Abstract

The present invention relates to a vision-based system and method for relative positioning with respect to a target surface, characterised in that it comprises: at least three reference markers (1) located on the target surface on the vertices of an equilateral triangle (2) seen from an overhead view of said target surface; at least one image forming device located on the object; processing means configured to receive and process the captured images (4) and configured to either detect the reference markers (1) in the received image (4), or identify the centroid (5) of a triangle (7) formed by the reference markers (1) in the received image (4), or circumscribe the reference markers (1) by means of a circumscribed ellipse (6), or determine the relative position with respect to the target surface by means of the relationship between the circumscribed ellipse (6) and the position of the reference markers (1).

Description

System and method of relative positioning of an object with respect to a target surface based on vision and navigation system of said object Field of the Invention The invention relates to a system for a method of estimating the position of an object relative to a target surface. The method could be used as part of vehicle navigation systems, such as aircraft, to achieve accurate positioning and / or provide redundancy to traditional positioning systems in complex environments, for example with a negation Global Navigation Satellite System (GNSS). Background to the invention Vision-based navigation (VBN) refers to the use of optically acquired data, using cameras, for navigation purposes. The three main steps of vision-based navigation (VBN) are typically as follows: a) Capturing an image of a part of the environment surrounding an object. This image will contain the information that will allow you to generate a position measurement. b) Extracting and processing information from the captured image to generate the position measurement. In this step, computer vision techniques such as pattern recognition, object detection and identification or estimation of motion with visual odometry are usually used. c) Filtering the measurements to calculate an optimal position estimate. Landing on unpaved runways is known to make such an operation more demanding than usual. In these cases, instrument approaches with very high frequency omnidirectional range (VOR), distance measurement equipment (DME) and, much less, instrument landing systems (ILS) are not usually available. At airports, Ground-Based Augmentation Systems (ILS / GBAS) that allow assisted landings are today the main way to facilitate the piloting task during this phase. Thanks to these systems, the deviations of the aircraft from the ideal approach can be calculated and used in guidance laws. However, these systems are expensive and their availability is limited to airports that have deployed the necessary infrastructure. In addition, in the case of unpaved runways, relying solely on the Global Positioning System (GPS) poses some problems. Known vision-based systems typically have a limited range, and the airborne vehicle must be close to the target to achieve an accurate location. In addition, a vision-based system can be affected by lighting conditions such as glare and shadows, which make it difficult to see some features on unpaved runways. In certain environments, such as feature-free terrain, snow, and deserts, vision-based methods cannot be used because there are no distinctive visual features in the environment. Summary of the invention The object of the invention is to estimate the position of the object, e.g. an aircraft, relative to a target surface. To this end, the system object of the invention allows the relative position of said object to be estimated using spherical coordinates, providing two angles and a distance, which positions the object three-dimensionally. More specifically, the system and method, object of the invention enables providing the distance, the elevation and the azimuth of the object with respect to a template located on the target surface. In accordance with the foregoing, the object of the present invention is a system for estimating the relative position of an object with respect to a target surface based on vision, which comprises: - At least three reference markers configured to be located on the target surface such that they are located at the vertices of an equilateral triangle seen from a zenithal view of said target surface, where the three vertices have a centroid. The centroid of said triangle corresponds to the origin of the reference system to be used for relative positioning. Viewed from the air, the three reference markers could be circumscribed by a circumference called a circumcircle. - At least one imaging device, configured to be located on the object, the object being capable of performing a spatial location of the reference markers, and for capturing images of the target surface including the reference markers, wherein the imaging device has a focal length. - A means of processing configured to receive and process the images captured by the at least one imaging device and configured to: o detect the reference markers in the received image, o identify the centroid of a triangle formed by the reference markers in the received image, o circumscribe the reference markers in the received image by means of a circumscribed ellipse centred on the centroid of the triangle and passing through the vertices of the triangle, o determine the relative position of the object with respect to the target surface according to its spherical geometric coordinates distance, elevation and azimuth by means of the geometric relationship in the image received between the semi-axes and the angle of the semi-major axis of the circumscribed ellipse and the position of the reference markers and the radius of its circumscribed circumference. According to the above, the means of processing has the input data provided by the three reference markers that constitute two-dimensional coordinates in pixels in the image taken by the imaging device. According to the claimed invention, the equilateral triangle formed by the three reference markers may be circumscribed by a circumference. When that triangle is viewed in perspective, that is, from an object, for example, an aircraft approaching a runway, the triangle ceases to be equilateral. The circumscribed circumference is then perceived as an ellipse, the parameters of which can be determined analytically on the image taken. This ellipse is called a circumscribed Steiner ellipse, which is the only ellipse that passes through the three vertices and has a centre at the centroid of the triangle. In accordance with the foregoing, the objective of the claimed invention is to obtain an estimate of the relative position of an object. The invention therefore solves the estimation of the relative 3D position of an object by the image capture device and the objects observed in the captured image. In addition, the installation of reference markers on the target surface, for example, on the target terrain, could allow the creation of a low-cost and easily transportable landing system. Various types of objects could benefit from the system of the invention: aircraft, helicopters, drones, first-stage reusable missiles, unmanned vehicles, etc. A specific application of the system and method object of the invention could be a landing aid on unpaved runways, thus reducing the pilot's workload. Other applications could be relative positioning during in-flight refuelling manoeuvres, landing on small or mobile helipads, the landing guide for the vertical retropropulsive landing of a reusable missile stage, as an aid to the landing of multicopters, etc. Another application in which vision-based landing (VBL) is of great help is when the landing surface is in motion, for example, on ship or aircraft carrier decks, as a few centimetres’ difference could endanger and compromise the mission. The invention is able to determine the relative position in 3D in these scenarios where landing aids are often not available. In addition, the ability to land accurately on unpaved terrain and in environments where there is no GPS would facilitate the logistics of humanitarian missions. The claimed system could reduce crew fatigue and crew training costs, thereby providing more efficient operations in, for example, in-flight refuelling. For the determination of the number of reference markers, the conjugation of the following two aspects is taken into account: o Using as few markers as possible. o Allowing the detection of the 3D position of the object. Placing three reference markers as if they were the vertices of an equilateral triangle is sufficient to solve the 3D positioning analytically, provided that the hypothesis that the object is within a azimuth sector of 120° is fulfilled since there are three possible solutions in azimuth and it is necessary to solve the ambiguity. This hypothesis is usually applicable to many of the scenarios described. The system, object of the invention, provides accurate results even with a basic camera such as an image capture device. The present invention includes the method for converting the 2D pixel coordinates of the three reference points in the captured image into a relative 3D position with respect to the centroid of the triangle formed by the reference points. Therefore, the method determines the relative 3D position with respect to the centroid of the equilateral triangle formed by the reference points, from the 2D pixel coordinates of said reference points. Thus, the reference markers facilitate the image processing task. Thus, the claimed system and method comprise a solution that provides results which are both accurate and quick to calculate. The claimed system has the following advantages: • It is able to use images from one or more imaging devices, e.g. cameras, installed on the object to estimate its 3D position, infrared sensors, etc. • It is a potentially certifiable system under aeronautical regulations. This is due to the deterministic nature of the method. • Initially, it is intended to be used as an external navigation aid system, in addition to certified sensor architectures, for example, ADIRUS (Air Data Inertial Reference Unit) and GPS on civil platforms. • It is compatible with the current protocols of the Flight Management System to be integrated into different avionics architectures. •    It is light. •  It is low energy consumption. •   It is inexpensive. • It allows real-time processing, i.e. the algorithm has a low processing time. •   It is reliable and complete. • Easy to install and maintain. • The markers are capable of being detected from a great distance. As mentioned above, this positioning system has been applied to develop a solution that allows an aircraft to land accurately without the need for complex infrastructures and at low cost. This innovative landing system allows specific applications such as landing on unpaved runways, as already indicated. Additionally, the claimed relative positioning system could also be used as part of the navigation systems of an object to achieve accurate positioning and / or make estimates redundant as well as traditional positioning sensors. The object of the invention is also a navigation system comprising a system for relative positioning of an object with respect to a target surface based on vision as explained above. The object of the present invention is also a method of estimating the position of an object with respect to a target surface, comprising the following steps: - providing at least three reference markers located on the target surface so that they are located at the vertices of an equilateral triangle seen from the air, where the equilateral triangle has a centroid and a circumscribed circumference, - providing at least one imaging device located on the object to capture images of the target surface including the reference markers, wherein the imaging device has a focal length, - providing a means of processing that receives and processes the captured images received from the at least one imaging device that: o detects the reference markers in the received image, o identifies the centroid of the triangle formed by the reference markers in the received image, o circumscribes the reference markers in the received image by means of a circumscribed ellipse centred on the centroid of the triangle and passing through the vertices of the triangle, o determines the position of the object with respect to the target surface according to its spherical geometric coordinates: distance, elevation and azimuth, by means of the geometric relationship in the image received between the semi-axes and the angle of the semi-major axis of the circumscribed ellipse and the position of the reference markers and the radius of its circumscribed circumference. Description of the figures In order to complete the description and provide a better understanding of the invention, a set of figures is provided. These figures form an integral part of the description and illustrate the preferred embodiments of the invention. The drawings comprise the following figures. Figure 1 shows a schematic representation of three reference markers located at the vertices of an equilateral triangle having a centroid, the three vertices being circumscribed by a circumference. Figure 2 shows an image captured from an aircraft of a runway and its surroundings, in which there are three reference markers located on the runway as seen from a zenithal view. Figure 3 shows an image captured from an aircraft of the runway of figure 2 and its surroundings in which three reference markers located on the runway are seen from an aircraft approaching the runway. Figure 4 shows a schematic representation of three reference markers located at the vertices of an isosceles triangle; the three vertices are circumscribed by an ellipse. Figure 5 shows the three-dimensional polar coordinates that position an object: distance, elevation and azimuth. Figure 6 is a schematic representation of a camera, the image plane of the camera and the object observed in 3D space. Detailed description of the invention Figure 1 shows a schematic representation of three reference markers (1) located at the vertices of an equilateral triangle (2) having a centroid (5). The three vertices are circumscribed by a circumference (3). The three reference markers (1) are located on the target surface. The target surface may be a runway, as shown in Figures 2 and 3. Alternatively, ship or aircraft carrier decks may also be a target surface. Figure 2 shows an image of a runway (8) and its surroundings captured from an aircraft (10). The three reference markers (1) are located on the runway (8) and are seen from the air. The three reference markers (1) form an equilateral triangle (2) seen from the air. The captured images (4) of Figures 2 and 3 are taken from at least one image capture device located on an aircraft (10). It is clear from the images (4) captured in Figures 2 and 3 that, seen from above, that is, from its zenith, it is an equilateral triangle (2). There would be a circumscribed circumference (3) passing through the vertices of the equilateral triangle (2). However, seen in perspective, as in Figure 3, the equilateral triangle (2) would no longer be equilateral. In that case, the circumscribed circumference (3) would become a circumscribed ellipse (6) as seen in Figure 4. Accordingly, the means of processing are configured to receive and process the captured images (4) received from the at least one imaging device and configured to: o detect the reference markers (1) in the image (4) received, o identify the centroid (5) of the triangle (7) formed by the reference markers (1) in the received image (4), o circumscribe in the received image (4) the reference markers (1) by means of a circumscribed ellipse (6) with centre in the centroid (5) of the triangle (7) and that passes through the vertices of the triangle (7), o determine the relative position of the object with respect to the target surface according to its spherical geometric coordinates: distance, elevation and azimuth, by means of the geometric relationship in the received image (4) between the semi-axes and the angle of the semi-major axis of the circumscribed ellipse (6) and the position of the reference markers (1) and the radius of its circumscribed circumference (3). Said spherical geometric coordinates are represented in Figure 5 with respect to the aircraft object (10). Spherical geometric coordinates are distance, elevation, and azimuth. The parameters that define the circumscribed ellipse (6), Steiner's ellipse, have an analytical solution. It is the only ellipse that passes through the vertices of a triangle and has as its centre the centroid of the triangle (7). The circumscribed Steiner ellipse (6) is also the ellipse with the smallest area passing through the vertices. The parameters of the circumscribed ellipse (6) are known. With them, as explained above, an estimate of the relative position can be made analytically. Visual position estimation is the process of estimating the position of the object based on data provided, for example, by a camera (9). The semi-major axis of the circumscribed ellipse (6) measures the same for any azimuth taking into consideration a constant distance to the object. The semi-minor axis of the circumscribed ellipse (6) varies its dimensions according to the elevation of the object on the target for the same distance. The distance is the distance from the camera to the centre of the ellipse. By knowing the focal length of the camera and the actual measurements of the template and those perceived in the image (4) it is possible to calculate the distance at which I am seeing that point. In the embodiment of figure 6, the frame of the imaging device x - y - z is a threedimensional frame with the origin as the projection centre and has its z axis pointing in the target direction. The frame of the image (4) u - v is a two-dimensional frame with the u and v axes parallel to the x and y axes of the frame of the imaging device, respectively. It is possible to relate the three-dimensional coordinates (x, y, z) to the image coordinates (u, v) as follows: X u z 7 either y v z 7 Where f is the focal length of the imaging device, u or v is the largest size of the semi-axes of the circumscribed ellipse (6) in the received image (4), x or y are the actual radii of the size of the circumscribed circumference (3) and z is the distance from the imaging device to the reference markers (1). f is a constant for a specific camera model and, for the above equations, their dimensions are in pixels. A parameter of the reference marker (1) will be selected to enter into the equation both its actual dimension (x) and its length measured on the image (4) (u). This parameter is the semi-major axis of the circumscribed ellipse (6). Therefore, in an exemplary embodiment for estimating the distance of the object from the reference markers (1), the processing means is configured to calculate the geometric relationship using the following equation: y v z 7 where f is the focal length of the imaging device, v is the size of the semi-major axis of the circumscribed ellipse (6) in the received image (4), y is the actual radius of the size of the circumscribed circumference (3) and z the distance of the object to the reference markers (1). In another exemplary embodiment for estimating the elevation of the object with respect to the reference markers (1), the means of processing is configured to calculate the geometric relationship by means of the arcsine of the relationship between the semi-minor axis and the semi-major axis of the circumscribed ellipse (6). In another embodiment to estimate the azimuth of the object with respect to the reference markers (1), the means of processing is configured to calculate the angle between the semi-major axis of the circumscribed ellipse (6) and one of the sides of the triangle (7) formed by the reference markers (1) in the received image (4) from a zenithal view to the target surface. The semi-major axis of the circumscribed ellipse provides information on the azimuth of the object. Said semi-major axis is perpendicular to the vector that joins the object with the origin projected in the plane, but only if we see it from a zenithal view. When the image is deformed due to being in another view, it is no longer fulfilled. In an exemplary embodiment, the means of processing is configured to undo said deformation and try to replicate the zenithal view. The calculation of said angle can be done in various ways. In an exemplary embodiment, the means of processing is configured to calculate the Steiner inellipse of the triangle (7) of the reference markers (1) and apply Marden's theorem to calculate the angle between the semi-major axis of said Steiner inellipse and one of the sides of the triangle (7), the base for example, which coincides with the angle of the semi-major axis of the circumscribed ellipse (6) and the base of the triangle (7). More specifically, starting from the basis of Marden's Theorem: Assume that the three complex zeros of a third-degree p(z) polynomial are z1, z2, and z3, and assume that these three points of the complex plane are not collinear. Then there is a single ellipse inscribed in the triangle of vertices z1, z2, z3 and tangential to the sides at their midpoints: the Steiner inellipse. The foci of said ellipse are precisely the zeros of the derived polynomial p' (z). The Steiner inellipse is an inellipse tangent to the sides of the triangle at its midpoints and has the maximum area of any inellipse. It is also the image of the Steiner circumellipse in homothetism with homothetic centre G and similarity ratio 1 / 2. The meaning of this is that the symmetry axis of the Steiner inellipse will have the same direction as the Steiner circumellipse. The foci of any ellipse are on the major axis and, taking advantage of Marden's theorem, obtaining their coordinates is facilitated. Finally, to obtain the angle between the major axis of the ellipse and the axis of one side of the triangle, for example, the base of the triangle, the foci of the Steiner inellipse are subtracted and the angle of the resulting complex number is calculated. This is the angle that defines the azimuth of the object. In an exemplary embodiment, the system comprises a fourth reference marker (1) located on one of the sides of the equilateral triangle (2) to univocally determine the azimuth. In this way, the ambiguity in the determination of azimuth is resolved, since, according to the calculation methods, it is possible to obtain three azimuth solutions if three reference points are used. One of the first aspects to solve is to determine what the reference markers should be: what type, what size, how many, etc. In an exemplary embodiment, the three reference markers (1) are passive cooperative targets. Passive cooperative targets, as opposed to active cooperative targets, are simpler, that is, mechanically less complicated. Active cooperative targets actively illuminate the scene, have blinking targets, or some other active mechanism. An example of such active reference markers (1) could be infrared lights. More specifically, the three reference markers (1) can be circles, as shown in figures 2 and 3. And more specifically, the circles can be white circles. The advantages of using white circles as passive cooperative targets are the following: o Cooperative targets are an optical aid to navigation. The target to be sought is known in advance. Therefore, algorithms can be adapted to them, which translates into great efficiency and accuracy. o The circles are solidly detected and are, for the most part, insensitive to translations and rotations. o White circles are not a common geometric figure that can appear in aerial images. o It is desired that the reference marker (1) is viewed from as far away as possible. A smooth circle, without elements inside, meets this characteristic. In an exemplary embodiment, the centres of the circles form the vertices of the triangles (3, 7). In an exemplary embodiment, the template is a recursive pattern, for example, within the three circles there would be three other circles and so on. This is so, since, as the object approaches the target, the object may already have the three outer circles out of its field of view. In another exemplary embodiment, the passive cooperative targets are painted with a paint containing titanium dioxide. Thus, the white circles are painted with titanium dioxide. In another exemplary embodiment, the passive cooperative targets are part of a cover located on the target surface. Thus, the cover comprising, for example, the white circles, extends over the ground. The circles can be sewn to the cover, painted, glued, etc. Accordingly, in an exemplary embodiment, to determine the 3D position of an aircraft (10), the white circles of the reference marker (1) must be detected. In particular, the centres of the circles are the parameters sought. To obtain them, computer vision techniques are used. Then, it is expected that, if the threshold that discriminates whether a pixel is white or black is correctly chosen, white circles will appear in a binarized image. Once the centres have been achieved at this point, it is necessary to calculate the circumscribed ellipse (6) that passes through the vertices of the triangle (7). In an exemplary embodiment, the imaging device is located on an aircraft (10), preferably it is installed on a longitudinal axis of the aircraft (10). In an exemplary embodiment, the target surface is a runway (8) and the reference markers (1) are located at the beginning of the runway (8) on its longitudinal axis as shown in Figures 2 and 3. The imaging device may be a camera. There are several types of cameras (9) that use structured light technologies. However, for vision-based landing (VBL) the selection is preferably reduced to monocular and stereoscopic cameras (9). The selection of the camera (9) will influence the design of the reference markers (1). Preferably, the choice is to use a monocular camera (9). In an exemplary embodiment, the camera (9) is a greyscale camera. If the installed camera (9) captures colour images, an intermediate step in the computer vision process would be to convert the RGB image into a greyscale intensity image. Therefore, the best option is to install a greyscale camera (9) on the aircraft (10). This is because: o When loaded into memory, a greyscale image takes up one-third of the space needed for an RGB image. o As a greyscale image has a third of the data, it requires less computational power to process it and can reduce computational time. o A greyscale image is conceptually simpler than an RGB image, so developing an image processing algorithm may be simpler when working with greyscale. To meet the exact definition of estimating the position of the object, for example, an aircraft (10), the orientation of the aircraft (10) must also be obtained. The system object of the invention allows to obtain the orientation of the aircraft, for example, in the form of roll, pitch and yaw angles. - Roll: the angle could be obtained by trigonometry. - Pitch: the centre of the circumscribed ellipse (6) will appear higher in the captured image (4) as the pitch of the aircraft (10) increases. The angle is obtained by trigonometry. - Yaw: as the aircraft (10) yaws, the centre of the circumscribed ellipse (6) moves to the left 5 or right in the image (4) captured. By trigonometry, the angle is obtained. The object of the invention is also a navigation system comprising a system for relative positioning of an object with respect to a target surface based on vision as explained above. 10

Claims

1.- System of relative positioning of an object with respect to a target surface based on vision, characterised in that it comprises:- at least three reference markers (1) configured to be located on the target surface so that they are located at the vertices of an equilateral triangle (2) seen from an aerial view at the zenith of said target surface, wherein the equilateral triangle (2) has a centroid (5) and a circumscribed circumference (3),- at least one imaging device configured to be located on the object and to capture images (4) of the target surface including the reference markers (1), wherein the imaging device has a focal length,- means of processing configured to receive and process the images (4) captured by the at least one imaging device and configured to:o detect the reference markers (1) in the image (4) received,o identify the centroid (5) of a triangle (7) formed by the reference markers (1) in the image (4) received,o circumscribe in the received image (4) the reference markers (1) by means of a circumscribed ellipse (6) with centre in the centroid (5) of the triangle (7) and that passes through the vertices of the triangle (7),o determine the relative position of the object with respect to the target surface according to its spherical geometric coordinates: distance, elevation and azimuth, by means of the geometric relationship in the received image (4) between the semi-axes and the angle of the semi-major axis of the circumscribed ellipse (6) and the position of the reference markers (1) and the radius of its circumscribed circumference (3).2.- System of relative positioning of an object with respect to a target surface based on vision, according to claim 1, characterized in that to estimate the distance of the object withrespect to the reference markers (1) the processing means is configured to calculate the geometric relationship using the equation:y v 2  1where f is the focal length of the imaging device, v is the size of the semi-major axis of the circumscribed ellipse (6) in the received image (4), y is the radius of the size of the circumscribed circumference (3) on the target surface and z the distance of the object to the reference markers (1).3.- System of relative positioning of an object with respect to a target surface based on vision, according to any one of the preceding claims, characterised in that for the calculation of the elevation of the object with respect to the target surface the means of processing is configured to calculate the arcsine of the relationship between the semi-minor axis and the semi-major axis of the circumscribed ellipse (6).4.- System of relative positioning of an object with respect to a target surface based on vision, according to any one of the preceding claims, characterised in that for the calculation of the azimuth of the object with respect to the target surface the processing means is configured to calculate the angle between the semi-major axis of the circumscribed ellipse (6) and one of the sides of the triangle (7) formed by the reference markers (1) in the image (4) received in a zenithal view to the target surface.5.- System of relative positioning of an object with respect to a target surface based on vision, according to claim 4, characterized in that to calculate the angle between the semimajor axis of the circumscribed ellipse (6) and the side of the triangle (7) formed by the reference markers (1) the means of processing is configured to calculate the Steiner inellipse of the triangle (7) of the reference markers (1) and apply Marden's theorem for the calculation of the angle between the semi-major axis of the Steiner inellipse and the side of the triangle (7) that coincides with the angle of the semi-major axis of the circumscribed ellipse (6) and the side of the triangle (7).6.- System of relative positioning of an object with respect to a target surface based on vision, according to any one of the preceding claims, characterised in that it comprises a fourth reference marker (1) located on one of the sides of the equilateral triangle (2) for the univocal determination of the azimuth.7.- System of relative positioning of an object with respect to a target surface based on vision, according to any one of the preceding claims, characterised in that the three reference markers (1) are passive cooperative targets.8.- System of relative positioning of an object with respect to a target surface based on vision, according to claim 7, characterized in that the three reference markers (1) are circles.9.- System of relative positioning of an object with respect to a target surface based on vision, according to claim 8, characterized in that the centres of the circles form the vertices of the triangles (3, 7).10.- System of relative positioning of an object with respect to a target surface based on vision, according to claim 8 or 9, characterized in that the circles are white circles.11.- System of relative positioning of an object with respect to a target surface based on vision, according to any one of the preceding claims 7 to 10, characterized in that the passive cooperative targets are painted with a paint comprising titanium dioxide.12.- System of relative positioning of an object with respect to a target surface based on vision, according to any one of the preceding claims 7 to 11, characterized in that the passive cooperative targets form part of a cover configured to be located on the target surface.13.- System of relative positioning of an object with respect to a target surface based on vision, according to any one of the preceding claims, characterised in that the object is an aircraft (10) and the imaging device is configured to be installed on a longitudinal axis of the aircraft (10).14.- System of relative positioning of an object with respect to a target surface based on vision, according to claim 13, characterized in that the target surface is a runway (8) and the reference markers (1) are configured to be located at the beginning of the runway (8) on its longitudinal axis.15.- Navigation system, characterized in that it comprises a relative positioning system of an object with respect to a target surface based on vision according to any one of the preceding claims.16.- Method of relative positioning of an object with respect to a target surface based on vision, characterized in that it comprises the following steps:- providing at least three reference markers (1) located on the target surface so that they are located at the vertices of an equilateral triangle (2) seen from a zenithal view, where the equilateral triangle (2) has a centroid (5) and a circumscribed circumference (3),- providing at least one imaging device located on the object for capturing images (4) of the target surface including the reference markers (1), wherein the imaging device has a focal length,- providing a means of processing that receives and processes the captured images (4) received from at least one imaging device that:o detects the reference markers (1) in the image (4) received,o identifies the centroid (5) of the triangle (7) formed by the reference markers (1) in the image (4) received,o circumscribes in the received image (4) the reference markers (1) by means of a circumscribed ellipse (6) with centre at the centroid (5) of the triangle (7) and which passes through the vertices of the triangle (7),o determines the position of the object with respect to the target surface according to its spherical geometric coordinates: distance, elevation and azimuth, by means of the geometric relationship in the image (4) receivedbetween the semi-axes and the angle of the semi-major axis of the circumscribed ellipse (6) and the position of the reference markers (1) and the radius of its circumscribed circumference (3).

Images