A manifold optimization based unmanned aerial vehicle positioning method and system

Abstract

The application discloses a kind of unmanned plane positioning method and system based on manifold optimization, and the positioning method is: based on the principle that the projection center of the camera carried by unmanned plane, the coordinate of the i control point and its corresponding image point coordinate are collinear, establish the pose solution model based on manifold optimization, the camera carried by unmanned plane takes picture, the industrial computer carried by unmanned plane automatically selects multiple control points in picture, and the coordinate information of control point is substituted into the solution model, the position and attitude of unmanned plane when taking picture are obtained by the solution of solution model, the solution model includes two contents: the confirmation method of rotation matrix and the confirmation method of spatial position, two parameters of rotation matrix and spatial position are confirmed using alternating minimization method until the set termination criterion is satisfied, the obtained rotation matrix and spatial position are respectively the attitude and position of unmanned plane.The application improves the positioning accuracy and robustness, and has strong engineering applicability.

Description

Technical Field

[0001] This invention belongs to the field of computer vision and unmanned system navigation and positioning technology, specifically a UAV positioning method and system based on manifold optimization. Background Technology

[0002] Drones typically carry cameras, and camera positioning is achieved by solving for the camera's exterior orientation elements. This exterior orientation element solution is a step in the single-image analysis process and is fundamental to photogrammetry. Its goal is to determine the camera's exterior orientation elements, i.e., its position and attitude, using ground control points in the shooting space. Spatial resection is based on the collinearity condition equations of images. It uses a camera with known intrinsic parameters to capture images of several global control points with known coordinates. Then, it establishes collinearity constraint equations by combining the image coordinates and control point coordinates, and iteratively solves these equations using the least squares principle to obtain the camera's exterior parameters in its current pose, thus achieving camera positioning. Spatial resection has low requirements for control point placement, low reception costs, and can quickly determine attitude information within a confined space. It has advantages such as simple structure, convenience, and flexibility, and has been widely used in photogrammetry. Currently, the solution for camera exterior orientation elements is mostly based on analytical processing using collinearity or coplanarity equations, and the rotation matrices involved are usually parameterized using Euler angles or quaternions. Traditional solution methods often linearize collinear equations by performing a first-order Taylor expansion before iterative optimization. However, linearization models are prone to introducing significant errors during approximation, limiting the accuracy and robustness of the solution. To overcome the inherent limitations of linearization methods, some researchers have proposed methods for solving exterior orientation elements based on nonlinear equation systems. However, these methods typically do not explicitly consider the orthogonality constraints of the rotation matrix during optimization, making it difficult to guarantee a high-precision feasible solution in the rotation matrix space. In other words, current UAV positioning solutions suffer from drawbacks such as complexity, low accuracy, and poor stability. Summary of the Invention

[0003] To address the aforementioned problems in existing technologies, the purpose of this invention is to provide a UAV positioning method and system based on manifold optimization. This solves the problem of larger model errors introduced by the first-order Taylor expansion of strongly nonlinear collinear equations in traditional methods. This invention does not use the three attitude angles and position as parameters to be solved, and eliminates the need for a first-order Taylor expansion of the collinear equations. Instead, it directly establishes a joint optimization model using the rotation matrix and position as unknown parameters. Without sacrificing model performance, the objective function is directly decomposed into two sub-problems for alternating optimization and solution. Considering the orthogonal constraint of the rotation matrix and combining it with the characteristics of the model on the manifold structure, manifold optimization theory is integrated with the pose solving problem, and a model and solution algorithm conforming to the geometric characteristics of the rotation matrix are designed. This method can effectively converge in various scenarios and has the advantages of accurate, stable, and reliable computational results.

[0004] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0005] A manifold optimization-based UAV localization method is proposed. Based on the principle that the projection center of the UAV's onboard camera, the coordinates of the i-th control point, and the corresponding image point coordinates are collinear, a manifold optimization-based pose calculation model is established. The UAV's onboard camera captures images, and the UAV's onboard industrial control computer automatically selects multiple control points in the images and substitutes the coordinate information of the control points into the calculation model. The position and attitude of the UAV at the time of image capture are obtained through the calculation model. The calculation model includes two components: a method for confirming the rotation matrix and a method for confirming the spatial position. Alternating minimization is used to confirm the two parameters, the rotation matrix and the spatial position, until a set termination criterion is met. The obtained rotation matrix and spatial position are the UAV's attitude and position, respectively.

[0006] As a further improvement to the above technical solution:

[0007] The objective function of the established pose calculation model includes two variables to be optimized: spatial position and rotation matrix. The spatial position represents the three-dimensional coordinates of the camera projection center in the ground coordinate system, and the rotation matrix represents the three-dimensional rotational relationship between the image space coordinate system and the auxiliary coordinate system. By alternately solving for the spatial position and rotation matrix, high-precision pose estimation is achieved. In other words, the rotation matrix represents the matrix of the rotational relationship between the image space coordinate system and the image space auxiliary coordinate system. Since the image space auxiliary coordinate system is parallel to the ground coordinate system, the rotation matrix can also be expressed as the matrix of the rotational relationship between the image space coordinate system and the ground coordinate system.

[0008] The method for alternately minimizing the spatial position and rotation matrix is ​​as follows: fix one variable, the spatial position, as the current value and use it as the first variable; optimize the objective function with respect to the other variable, the rotation matrix, to obtain the optimal value of the first variable and use it as the second variable; then fix the second variable as the current optimal value and optimize the first variable. Repeat the above steps until the preset termination criterion is met.

[0009] The method for confirming the rotation matrix employs the Riemann conjugate gradient algorithm based on manifold optimization to directly solve for the rotation matrix. This includes: mapping variables in Euclidean space to the manifold space containing the rotation matrix using the Cayley transform; calculating the gradient of the objective function on the manifold using gradient information in Euclidean space; determining the search direction on the manifold by combining the conjugate direction update strategy and the vector transfer operator; selecting an appropriate step size based on the line search criterion; and projecting the update result back to the manifold space using a shrinking mapping to obtain a new estimated value of the rotation matrix, thus completing one iterative update.

[0010] Determine if the gradient value on the manifold space is less than a set value. If so, solve the spatial location subproblem. In this case, the estimated value of the rotation matrix is... If not, continue iterating until the judgment condition is met.

[0011] The method for confirming a spatial location is as follows: Let the spatial location be... To avoid obtaining results too quickly The exact solution causes the algorithm to exit the loop prematurely. When calculating the spatial location, a neighboring term is added to the objective function because it contains... and Since it cannot be solved directly, it is converted into a classical least squares expression, and the final closed-form solution of the spatial location is obtained by using the least squares method. .

[0012] Determine whether the estimated updated values ​​of the rotation matrix and spatial position satisfy the termination condition of alternating minimization. If they do, terminate the iteration and obtain the final solution for the rotation matrix and spatial position. If they do not satisfy the condition, continue to iterate and solve for the rotation matrix and spatial position.

[0013] A manifold optimization-based UAV positioning system is provided to implement the aforementioned positioning method. From a hardware perspective, the positioning system includes a UAV, a camera, an industrial control computer (ICC), and a wireless communication module. The camera, ICC, and wireless communication module are all mounted on the UAV. The calculation model is embedded into the ICC in the form of a program. The UAV, camera, and wireless communication module are all electrically connected to the ICC. The camera transmits the captured images to the ICC. The ICC calculates the images based on its built-in program to obtain the position and attitude of the UAV when the images were captured. The wireless communication module can wirelessly transmit the information from the ICC to the ground control center.

[0014] From a functional perspective, the UAV positioning system includes an image acquisition module, a data storage module, an image processing module, a positioning calculation module, and a transmission module. The image acquisition module is used to acquire image information, the data storage module is used to store data, the image processing module processes the acquired images to obtain control points and their coordinate information, the positioning calculation module performs positioning calculation based on the calculation model and the input image information to obtain the position and attitude of the UAV, and the transmission module is used for data transmission.

[0015] The beneficial effects of this invention are as follows: By obtaining the optimal solution of the calculated rotation matrix and spatial position, a more accurate position and attitude of the UAV is obtained. This solves the problem of larger model errors introduced by the first-order Taylor expansion of strongly nonlinear collinear equations in traditional methods. This invention does not use the three attitude angles and position as parameters to be solved, and does not require the first-order Taylor expansion of the collinear equations. Instead, it directly establishes a joint optimization model with the rotation matrix and position as unknown parameters. Without sacrificing model performance, the objective function is directly decomposed into two sub-problems for alternating optimization and solution. Considering the orthogonal constraint of the rotation matrix and combining the characteristics of the model on the manifold structure, manifold optimization theory is combined with the pose solving problem to design a model and solution algorithm that conforms to the geometric characteristics of the rotation matrix. This method has a relatively simple calculation process, accurate calculation results, and the algorithm always converges. Attached Figure Description

[0016] Figure 1 This is the location map of exterior orientation elements for oblique photogrammetry according to the present invention;

[0017] Figure 2 This is a diagram showing the coordinate system transformation relationship used in this invention;

[0018] Figure 3 This is a flowchart of a pose calculation algorithm based on manifold alternation minimization;

[0019] Figure 4 This is a distribution map of control points in the photograph used in an embodiment of the present invention. Detailed Implementation

[0020] The specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0021] For ease of description, spatial relative terms such as "above," "on top of," "on the upper surface of," "above," etc., are used herein to describe the spatial positional relationship of a device or feature as shown in the figures to other devices or features. It should be understood that spatial relative terms are intended to encompass different orientations in use or operation beyond the orientation of the device as described in the figures. For example, if the device in the figures were inverted, a device described as "above" or "on top of" other devices or structures would subsequently be positioned as "below" or "under" other devices or structures. Thus, the exemplary term "above" can include both "above" and "below." The device may also be positioned in other different ways (rotated 60 degrees or in other orientations), and the spatial relative descriptions used herein will be interpreted accordingly.

[0022] A UAV positioning method and system based on manifold optimization, wherein the UAV positioning system is used to implement the positioning method.

[0023] From a hardware perspective, the positioning system includes a drone, a camera, an industrial control computer (ICC), and a wireless communication module. The camera, ICC, and wireless communication module are all mounted on the drone. The ICC is essentially a computer, and the computational model (described below) is programmed into it. The drone, camera, and wireless communication module are all electrically connected to the ICC. The camera transmits captured images to the ICC, which then processes the images based on its built-in program to obtain the drone's position and attitude when the images were captured. The wireless communication module wirelessly transmits information from the ICC to the ground control center.

[0024] From a functional perspective, the UAV positioning system includes an image acquisition module, a data storage module, an image processing module, a positioning calculation module, and a transmission module. The image acquisition module is used to acquire image information; this function is implemented by a camera and an industrial control computer program. The data storage module is used to store data. The image processing module analyzes and processes the acquired images. The positioning calculation module performs positioning calculations based on a calculation model and the input image information to obtain the UAV's position and attitude. The functions of the data storage module, image processing module, and positioning calculation module are all implemented by programs embedded in the industrial control computer. The transmission module is used for data transmission; this function is implemented by a wireless communication module and the industrial control computer program.

[0025] The drone positioning method is as follows:

[0026] Based on the principle that the camera projection center, the coordinates of the i-th control point, and the coordinates of its corresponding image point are collinear, a least-squares-based exterior orientation element solution model is established. The camera mounted on the UAV captures an image, and a program embedded in the industrial control computer automatically selects multiple control points from the image. The coordinate information of each control point is then substituted into the solution model, and the position and attitude of the UAV when capturing the image are obtained through the solution model's calculation.

[0027] The method and principle for selecting control point coordinate information are as follows: The industrial control computer carries publicly available commercial map information, which contains the geographic coordinate information of each point on the map. The industrial control computer pre-sets the selection rules for control points on the image (for example, dividing the captured image into multiple grids and taking the center point of each grid as the control point). After the camera captures the image, the image processing module automatically selects multiple control points in the image according to the set rules. Then, the image processing module compares the control points on the image with the carried commercial map to find the location of each control point on the commercial map, thus obtaining the geographic coordinate information of each control point. To reduce the computational load during comparison, the current city, region, etc., are pre-set when launching the drone to narrow the comparison range and improve comparison efficiency and accuracy.

[0028] The solution model is described below:

[0029] Figure 1 This is a detailed diagram of the exterior orientation element calculation. The exterior orientation elements are solved based on the transformation relationship between the coordinates of the camera center, control points, and image points. The specific coordinate transformation process is as follows: Figure 2 As shown, assume the coordinates of the camera projection center S are denoted as... , No. The coordinates of the control points are: The corresponding image point coordinates are Generally, due to the oblique photography of drones, the image space coordinate system and the control point coordinate system are not parallel. An auxiliary image space coordinate system is used to reconcile the image point coordinates. a i And the coordinates of the camera center S, the coordinates of the control points On a straight line, the auxiliary coordinates in image space of the image point are: .

[0030] according to Figure 1 The spatial geometric relationship of the collinearity of ground control points, corresponding image points, and projection centers; the rotational relationship between the image space coordinate system and the image space auxiliary coordinate system; considering ground undulations, the scale corresponding to the coordinates of each image point and control point is not fixed; the scale coefficient corresponding to each control point is... , , Let be the focal length of the camera. Therefore, the least squares exterior orientation element solution model is expressed as:

[0031] (1)

[0032]

[0033] In formula (1) Indicates the first The coordinates of a visual base station in the object space coordinate system Indicates the coordinates of its image point. This indicates the coordinates of the camera's projection center in the ground coordinate system, i.e., its spatial position; Indicates the first The estimated coordinates of the projection center of the secondary camera in the ground coordinate system. Let represent the rotation matrix, T represent the transpose of the matrix, and the scale coefficient determines the mapping relationship between image point coordinates and actual ground coordinates, thereby achieving the accuracy conversion of image registration and measurement. In the above formula, st represents the constraint on minimizing the pose function to be solved. This represents a 3×3 identity matrix (diagonal elements are 1, and the rest are 0).

[0034] The solution model uses a pose estimation algorithm based on Stiefel-Manifold-based Alternating-minimization Pose-estimation (SMAP).

[0035] Considering the rotation matrix Having orthogonal constraints, which perfectly satisfy the geometric characteristics of manifold space, we can start from the manifold optimization thinking, transform the optimization problem in Euclidean space into an optimization problem in manifold space, and solve the difficulties brought about by the linearization of strongly nonlinear equations and orthogonal constraints from the manifold optimization framework, so as to ensure the reliability of the solution of the rotation matrix and the feasibility of its constraints. Without losing the performance of the model, the objective function (1) is directly decomposed into two subproblems and alternately minimized (AM) to solve the exterior orientation elements (position and orientation).

[0036] The principle of the alternating minimization algorithm is to first fix one variable as a constant value, such as fixing... The variable is Then, optimize another rotation matrix variable in the objective function. get Then keep The estimated value Unchanged, for Optimization results This process constitutes a loop in the alternating minimization process. The iteration continues until a certain termination criterion is met, causing the objective function to reach its optimal value, at which point the iteration stops. This is the optimal solution to the original problem. Therefore, by directly optimizing the original objective function using the alternating minimization algorithm, the original problem can be cleverly decomposed into two subproblems that are solved separately: Subproblem (rotation matrix subproblem) and Subproblem (spatial location subproblem). Among them, and They represent and The final value. Indicates the number of iterations. .

[0037] In this embodiment, firstly, the rotation matrix is ​​solved based on manifold optimization. .

[0038] For the attitude rotation matrix subproblem To solve this problem, a Riemann conjugate gradient algorithm based on manifold optimization is designed to directly solve for the rotation matrix. The rotation matrix represents the rotation relationship between the image space coordinate system and the auxiliary image space coordinate system. The rotation matrix is ​​obtained based on the properties of the Cayley transform, shrinkage mapping, and vector transfer mapping in manifold optimization. The estimated value is obtained by calculating the gradient of the manifold space (Riemann gradient) using the gradient of the Euclidean space. The search direction is determined by combining the conjugate parameter and the vector transfer operator. A suitable step size is found by using the line search criterion. The shrinkage operator is then used to map the result onto the manifold to obtain the new iteration point.

[0039] Determine the gradient on a manifold If the condition is met, proceed to the next step; otherwise, solve for the rotation matrix. Continue iterating until the gradient criterion is met. Generally... Pick .

[0040] Then, the estimated values ​​of the camera's three-dimensional coordinates are obtained.

[0041] Solving for the camera's three-dimensional coordinates is the spatial position subproblem – solving for the camera's pose and position, i.e., solving for the camera's three-dimensional coordinates. The The objective function estimated in the second step To avoid obtaining results too quickly The exact solution causes the algorithm to exit the loop prematurely, so in the calculation When dealing with subproblems, add a neighboring term to the objective function. ;

[0042] in, These are the neighboring term factors, which are set values; because the objective function contains... and It cannot be calculated directly; it must be transformed into an expression similar to classical least squares. Then, differentiate it and set the derivative to 0 to obtain a closed-form solution. That is, the final solution... The closed-form solution;

[0043] in, .

[0044] Finally, the judgment If the condition is met, the iteration terminates and the final solution is obtained. If the condition is not met, proceed to solving the rotation matrix. Continue iterating.

[0045] The following example illustrates the specific implementation process of this invention, specifically using the calculation of exterior orientation elements of images in scenarios with large and small flight altitudes and extremely large tilt angles.

[0046] The image shows the altitude of the aircraft carrier. Xiaohang Gaowei The camera's focal length is The interior orientation elements of the photography center are ;

[0047] Nine control points were selected. The coordinates of the control points, the corresponding image exterior orientation elements, and the image point coordinates are shown in Tables 1 to 4.

[0048] Table 1: Ground coordinates of 9 control points (unit: meters)

[0049]

[0050] Table 2: Image point coordinates corresponding to images in the high-altitude simulation scenario (unit: mm)

[0051]

[0052] Table 3: Image point coordinates corresponding to images in low-altitude simulation scenarios (unit: mm)

[0053]

[0054] Table 4: Exterior Orientation Elements of Images in Various Scenes

[0055]

[0056] In Table 4, The three attitude angles that make up the rotation matrix are pitch, roll, and yaw.

[0057] a1: Substitute the corresponding coordinates of the 9 points into the model, and initialize the initial value of the rotation matrix. It is the identity matrix. The search value is the average value of all control points, the search direction is the negative of the gradient, and the search step size is... , .

[0058] a2: The alternating minimization algorithm is used to decompose the model into two simple subproblems: Subproblem (rotation matrix subproblem) and Subproblem (spatial location subproblem).

[0059] a3: Solving the rotation matrix subproblem: Calculating the rotation matrix using the Riemann conjugate gradient algorithm based on manifold optimization. To obtain the optimal solution .

[0060] a4: Determine the gradient on a manifold If the condition is not met, continue iterating in a3; if it is met, jump to a5.

[0061] a5: Solving the spatial location subproblem: fixing the new problem found in a3. Calculate the three-dimensional coordinates of the new camera .

[0062] a6: Judgment If the condition is true, the iteration terminates and we obtain the result. If the condition is not met, jump to a3 and continue iterating.

[0063] Conclusion: The results of using the least squares method (Algorithm 1), the Leberveng-Marquardt method (Algorithm 2), and the method of this invention are compared in Tables 5 and 6.

[0064] Table 5: Comparison of solution results for scenarios with small flight altitude and large tilt angle

[0065]

[0066] Table 6: Comparison of solution results under the ultra-high tilt angle scenario of the high-altitude flight path

[0067]

[0068] Because traditional algorithms calculate directly from Euler angles, the rotation matrix calculated by the algorithm proposed in this paper... It also needs to be converted to Euler angles. This is done by using the conversion relationship between the rotation matrix and the three attitude angles to convert them to Euler angles.

[0069] As shown in Tables 5 and 6, under different flight altitudes, Algorithm 1 exhibits large iterative solution errors in scenarios with extremely large tilt angles, while Algorithm 2 and the method of this invention can effectively converge under such conditions. The method of this invention is superior to Algorithm 2 in terms of accuracy. This is mainly because Algorithms 1 and 2 use Euler angles to represent the rotation matrix and solve collinear equations containing sine and cosine, which can lead to errors during linearization expansion of the collinear equations. The method provided in this application, however, is based on the principle of collinear equations, directly using rotation matrices to represent the equations. It establishes a camera exterior orientation element solution model based on an alternating minimization algorithm, transforming the original problem into two simple subproblems: a rotation matrix subproblem and a spatial position subproblem. For the rotation matrix subproblem, the manifold optimization-based direct rotation matrix solution algorithm designed in this application can achieve... The method involves finding an accurate and efficient solution by alternating between solving one subproblem with a fixed solution from another subproblem until a certain termination criterion is met, causing the objective function to reach its optimal value. The iteration then stops, and the solution obtained at this point is... That is the optimal solution to the original problem, let This invention ensures that the solution to the problem to be solved always maintains convergence and constraint feasibility, and has the advantages of relatively simple calculation process, accurate calculation results, and algorithm that always maintains convergence.

[0070] Finally, it is necessary to clarify that the above examples are only used to further illustrate the technical solutions of the present invention in detail, and should not be construed as limiting the scope of protection of the present invention. Any non-essential improvements and adjustments made by those skilled in the art based on the above content of the present invention shall fall within the scope of protection of the present invention.

Claims

1. A method for unmanned aerial vehicle positioning based on manifold optimization, characterized in that, Based on the camera projection center mounted on the drone, the first Based on the principle that the coordinates of control points and their corresponding image points are collinear, a pose calculation model based on manifold optimization is established. The camera on the UAV takes pictures, and the industrial control computer on the UAV automatically selects multiple control points in the pictures and substitutes the coordinate information of the control points into the calculation model. The position and attitude of the UAV when taking pictures are obtained through the calculation model. The calculation model includes two parts: the method for confirming the rotation matrix and the method for confirming the spatial position. The two parameters of rotation matrix and spatial position are confirmed by alternating minimization until the set termination criterion is met. The obtained rotation matrix and spatial position are the attitude and position of the UAV, respectively. Due to the tilt photography of the unmanned aerial vehicle, the image space coordinate system and the control point coordinate system are not parallel, and the image point coordinate, the photography center coordinate and the control point coordinate are on a straight line by means of the image space auxiliary coordinate system; According to the spatial geometric relationship that the ground control point, the corresponding image point and the photography center are collinear, the rotation relationship between the image space coordinate system and the image space auxiliary coordinate system, and the ground fluctuation, a least square-based exterior orientation element solving model is established, the objective function of the solving model includes two to-be-optimized variables: the spatial position and the rotation matrix, the spatial position represents the three-dimensional coordinates of the photography center in the ground coordinate system, and the rotation matrix represents the three-dimensional rotation relationship between the image space coordinate system and the auxiliary coordinate system, the high-precision estimation of the position and the pose is realized by alternately solving the spatial position and the rotation matrix, and the solving model is: ； ； in, Represents the rotation matrix. Let T represent the three-dimensional coordinates of the camera's projection center in the ground coordinate system, and let T denote the transpose of the matrix. Indicates the first The coordinates of a visual base station in the object space coordinate system Indicates the coordinates of its image point. , For the camera's focal length, Indicates the first The estimated coordinates of the projection center of the secondary camera in the ground coordinate system, where st represents the constraint on minimizing the pose function to be solved. Represents a 3×3 identity matrix; The rotation matrix confirmation method is: a Riemann conjugate gradient algorithm based on manifold optimization is designed for direct solving of the rotation matrix, the rotation matrix represents the rotation relationship between the image space coordinate system and the image space auxiliary coordinate system, the estimated value of the rotation matrix is obtained according to the properties of the contraction mapping and the vector transmission mapping in the Kailai transformation and the manifold optimization, the Riemann gradient of the manifold space is calculated through the gradient of the Euclidean space, the search direction is determined by combining the conjugate parameters and the vector migration operator, a suitable step size is found through the line search criterion, the new iteration point is obtained by mapping to the manifold through the contraction operator, and it is judged whether the gradient on the manifold is less than the set threshold value, if yes, the next step is performed, otherwise, the rotation matrix is iteratively solved, until the gradient judgment condition is met.

2. The positioning method of claim 1, wherein: The method for alternately minimizing the rotation matrix and the spatial position in the model is: fixing one variable, the spatial position, as the current value as the first variable, optimizing and solving the other variable, the rotation matrix, to obtain the optimal value of the variable as the second variable; fixing the second variable as the current optimal value, optimizing the first variable, and the above steps are iterated until a preset termination criterion is met.

3. The positioning method of claim 2, wherein: The method for confirming the spatial position is: setting the spatial position as In order to avoid obtaining the accurate solution of too fast and causing the algorithm to jump out of the loop in advance, a proximate term is added to the target function when the spatial position is calculated. Since the proximate term contains and , it cannot be directly solved, so it is converted into a classical least square expression form, and the least square solving method is used to obtain the final closed solution of the spatial position .

4. The positioning method of claim 3, wherein: It is judged whether the estimated update value of the rotation matrix and the spatial position meets the termination condition of the alternately minimizing, if yes, the iteration is terminated, and the final solution of the rotation matrix and the spatial position is obtained, otherwise, the rotation matrix and the spatial position are iteratively solved.

5. A manifold optimization based unmanned aerial vehicle positioning system for implementing the positioning method of any one of claims 1-4, characterized in that, From the hardware point of view, the positioning system comprises an unmanned aerial vehicle, a camera, an industrial computer and a wireless communication module, the camera, the industrial computer and the wireless communication module are all mounted on the unmanned aerial vehicle, the solving model is implanted in the industrial computer in the form of a program, the unmanned aerial vehicle, the camera and the wireless communication module are electrically connected with the industrial computer, the camera transmits the photographed pictures to the industrial computer, the industrial computer solves the pictures based on the built-in program, and the position and the pose of the unmanned aerial vehicle when the pictures are photographed are obtained, and the wireless communication module can wirelessly transmit the information of the industrial computer to the ground control center.

6. The positioning system of claim 5, wherein: From the functional point of view, the unmanned aerial vehicle positioning system comprises an image acquisition module, a data storage module, an image processing module, a positioning calculation module and a transmission module, the image acquisition module is used for acquiring picture information, the data storage module is used for storing data, the image processing module processes the acquired picture to obtain the control point and the coordinate information thereof, the positioning calculation module performs positioning calculation based on a calculation model and the input picture information to obtain the position and the attitude of the unmanned aerial vehicle, and the transmission module is used for data transmission.

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