Formal analysis method and device for autonomous positioning of unmanned aerial vehicle

Abstract

The embodiment of the present disclosure discloses a method and device for formal analysis of autonomous positioning of a UAV. The method comprises: obtaining the same name image point coordinates, a preset homogeneous coordinate conversion matrix, a continuous homogeneous coordinate conversion matrix and a coordinate conversion formula, establishing a high-order logic expression of a ground target point in a geodetic coordinate system based on a high-order logic language; constructing a corresponding formal proposition based on the high-order logic expression, the formal proposition describing attribute constraint conditions in the high-order logic expression; verifying the formal proposition based on a theorem prover to determine whether the high-order logic expression meets the attribute constraint conditions. The high-order logic expression of the UAV for determining the non-homogeneous coordinates of the ground target point in the geodetic coordinate system is analyzed by the formal method, and the attribute constraint conditions that must be met by the high-order logic expression are verified, thereby ensuring the accuracy of the analysis result.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the technical field of unmanned aerial vehicle positioning, and particularly relates to a formal analysis method and device for autonomous positioning of unmanned aerial vehicles. BACKGROUND

[0002] An unmanned aerial vehicle is a complex cyber-physical system that autonomously flies and performs various tasks. Due to its flexibility, versatility and ease of deployment, unmanned aerial vehicles play an important role in military and civilian fields. Unmanned aerial vehicles equipped with cameras, sensors and global positioning systems can achieve autonomous positioning of ground target points and real-time image transmission when performing tasks.

[0003] In order to ensure the accuracy of the unmanned aerial vehicle in positioning the ground target point, the positioning method or positioning algorithm used by the unmanned aerial vehicle is usually analyzed and verified. At present, traditional paper and pen calculation and computer algebra system are usually used for analysis and verification. However, these traditional non-formal analysis and verification methods are prone to human errors, lack of necessary preconditions or assumption conditions, and cannot reliably handle boundary conditions and symbols, which cannot ensure the accuracy of the analysis results. Therefore, the traditional analysis method for autonomous positioning of unmanned aerial vehicles has the problem of inaccurate analysis results. SUMMARY

[0004] In order to solve the problems in the related art, the embodiments of the present disclosure provide a formal analysis method and device for autonomous positioning of unmanned aerial vehicles.

[0005] In a first aspect, the embodiments of the present disclosure provide a formal analysis method for autonomous positioning of unmanned aerial vehicles.

[0006] Specifically, the formal analysis method for autonomous positioning of unmanned aerial vehicles comprises:

[0007] obtaining a homonymous image point coordinate of a homonymous image point of a ground target point in a camera coordinate system, a preset homogeneous coordinate conversion matrix, a continuous homogeneous coordinate conversion matrix and a coordinate conversion formula;

[0008] establishing a high-order logic expression of the ground target point in a geodetic coordinate system based on a high-order logic language according to the homonymous image point coordinate, the homogeneous coordinate conversion matrix, the continuous homogeneous coordinate conversion matrix and the coordinate conversion formula, the high-order logic expression being used for the unmanned aerial vehicle to determine a non-homogeneous coordinate of the ground target point in the geodetic coordinate system;

[0009] constructing a corresponding formal proposition based on the high-order logic expression, the formal proposition describing an attribute constraint condition in the high-order logic expression;

[0010] verify the formalized proposition based on a theorem prover to determine whether the high-order logic expression satisfies the attribute constraint condition;

[0011] The homogeneous coordinate conversion matrix is used to realize coordinate conversion of the homonymous image point and the ground target point in the camera coordinate system, the continuous homogeneous coordinate conversion matrix is used to realize homogeneous coordinate conversion of the ground target point between the camera coordinate system, the carrier coordinate system, the geographic coordinate system and the geodetic rectangular coordinate system, and the coordinate conversion formula is used to realize non-homogeneous coordinate conversion of the ground target point between the geodetic rectangular coordinate system and the geodetic coordinate system.

[0012] In an implementation manner of the present disclosure, the high-order logic expression of the ground target point in the geodetic coordinate system is established based on a high-order logic language according to the homonymous image point coordinates, the homogeneous coordinate conversion matrix, the continuous homogeneous coordinate conversion matrix and the coordinate conversion formula, and the method comprises the following steps:

[0013] The high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system is established based on a high-order logic language according to the homonymous image point coordinates and the homogeneous coordinate conversion matrix;

[0014] The high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system is established based on a high-order logic language according to the continuous homogeneous coordinate conversion matrix and the high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system;

[0015] The high-order logic expression of the non-homogeneous coordinates of the ground target point in the geodetic coordinate system is established based on a high-order logic language according to the coordinate conversion formula and the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system.

[0016] In an implementation manner of the present disclosure, the high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system is established based on a high-order logic language according to the homonymous image point coordinates and the homogeneous coordinate conversion matrix, and the method comprises the following steps:

[0017] The high-order logic expression of the homogeneous coordinates of the homonymous image point in the camera coordinate system is established based on a high-order logic language according to the homonymous image point coordinates, the homonymous image point coordinates comprising initial coordinates of the homonymous image point on an X-axis and a Y-axis of the camera coordinate system and a camera focal length of a camera on the unmanned aerial vehicle;

[0018] The distance from the optical center of the camera to the ground target point is acquired;

[0019] According to the distance and the camera focal length, a high-order logic expression of the homogeneous coordinate conversion matrix is established based on a high-order logic language;

[0020] According to the high-order logic expression of the homogeneous coordinates of the same-named image point in the camera coordinate system and the high-order logic expression of the homogeneous coordinate conversion matrix, a high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system is established.

[0021] In an implementation form of the present disclosure, the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic coordinate system is established based on a high-order logic language according to the continuous homogeneous coordinate conversion matrix and the high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system, comprising:

[0022] An azimuth angle and an elevation angle of the UAV are acquired;

[0023] According to the azimuth angle and the elevation angle, a high-order logic expression of a first homogeneous coordinate conversion sub-matrix is established based on a high-order logic language, the first homogeneous coordinate conversion sub-matrix being contained in the continuous homogeneous coordinate conversion matrix and being used for realizing the homogeneous coordinate conversion between the camera coordinate system and the carrier coordinate system;

[0024] According to the high-order logic expression of the first homogeneous coordinate conversion sub-matrix and the high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system, a high-order logic expression of the homogeneous coordinates of the ground target point in the carrier coordinate system is established.

[0025] A roll angle, a pitch angle and a yaw angle of the UAV are acquired;

[0026] According to the roll angle, the pitch angle and the yaw angle, a high-order logic expression of a second homogeneous coordinate conversion sub-matrix is established based on a high-order logic language, the second homogeneous coordinate conversion sub-matrix being contained in the continuous homogeneous coordinate conversion matrix and being used for realizing the homogeneous coordinate conversion between the carrier coordinate system and the geographic coordinate system;

[0027] According to the high-order logic expression of the homogeneous coordinates of the ground target point in the carrier coordinate system and the high-order logic expression of the second homogeneous coordinate conversion sub-matrix, a high-order logic expression of the homogeneous coordinates of the ground target point in the geographic coordinate system is established.

[0028] A prime vertical curvature radius of the earth, a first eccentricity of the earth, rotation angles from the Y axis and the Z axis of the geographic coordinate system to the Y axis and the Z axis of the geodetic coordinate system respectively, and a translation amount from the X axis of the geographic coordinate system to the X axis of the geodetic coordinate system are acquired;

[0029] According to the meridian curvature radius of the earth, the first eccentricity of the earth, the rotation angle and the translation amount, a high-order logic expression of a third homogeneous coordinate conversion sub-matrix is established based on a high-order logic language, the third homogeneous coordinate conversion sub-matrix is contained in the continuous homogeneous coordinate conversion matrix, and is used to realize the homogeneous coordinate conversion between the geographic coordinate system and the geodetic rectangular coordinate system;

[0030] According to the high-order logic expression of the homogeneous coordinates of the ground target point in the geographic coordinate system and the high-order logic expression of the third homogeneous coordinate conversion sub-matrix, the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system is established.

[0031] In an implementation manner of the present disclosure, the high-order logic expression of the non-homogeneous coordinates of the ground target point in the geodetic coordinate system is established based on a high-order logic language according to the coordinate conversion formula and the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system, and includes:

[0032] The components of the homogeneous coordinates of the ground target point on the X axis, the Y axis and the Z axis of the geodetic rectangular coordinate system are determined according to the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system;

[0033] The coordinate conversion expression corresponding to the geodetic longitude of the ground target point is determined according to the coordinate conversion formula, the coordinate conversion formula describes the conversion relationship between the components of the homogeneous coordinates of the ground target point on the X axis, the Y axis and the Z axis of the geodetic rectangular coordinate system and the meridian curvature radius of the earth, the first eccentricity of the earth, the geodetic latitude of the ground target point, the geodetic longitude of the earth target point and the geodetic height of the earth target point;

[0034] The high-order logic expression of the geodetic longitude of the ground target point in the geodetic coordinate system is established based on a high-order logic language according to the component on the X axis and the component on the Y axis of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system;

[0035] The high-order logic expression of the geodetic height of the ground target point in the geodetic coordinate system is established based on a high-order logic language according to the component on the X axis, the component on the Z axis of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system, the meridian curvature radius of the earth, the first eccentricity of the earth and the coordinate conversion expression corresponding to the geodetic longitude of the ground target point;

[0036] According to the components of the homogeneous coordinates of the ground target point on the X-axis, the Y-axis and the Z-axis of the geodetic rectangular coordinate system, the meridian curvature radius of the earth, the first eccentricity of the earth and the coordinate conversion expression corresponding to the geodetic longitude of the ground target point, a high-order logic expression of the geodetic latitude of the ground target point in the geodetic coordinate system is established based on a high-order logic language.

[0037] In an implementation manner of the present disclosure, the constructing the corresponding formal proposition based on the high-order logic expression comprises:

[0038] A first formal proposition corresponding to the high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system is constructed, and an attribute constraint condition of the first formal proposition comprises that the focal length of the camera is not equal to zero.

[0039] A second formal proposition corresponding to the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system is constructed, and an attribute constraint condition of the second formal proposition comprises that the focal length of the camera is not equal to zero.

[0040] A third formal proposition corresponding to the high-order logic expression of the geodetic longitude of the ground target point in the geodetic coordinate system is constructed, and an attribute constraint condition of the third formal proposition comprises that a cosine value of the geodetic longitude of the ground target point in the geodetic coordinate system is greater than zero, a value range of the geodetic longitude is [-π / 2, π / 2], and a component of the ground target point on the X-axis of the geodetic rectangular coordinate system is greater than zero.

[0041] A fourth formal proposition corresponding to the high-order logic expression of the geodetic height of the ground target point in the geodetic coordinate system is constructed, and an attribute constraint condition of the fourth formal proposition comprises that the cosine value of the geodetic longitude of the ground target point in the geodetic coordinate system is not zero.

[0042] A fifth formal proposition corresponding to the high-order logic expression of the geodetic latitude of the ground target point in the geodetic coordinate system is constructed, and an attribute constraint condition of the fifth formal proposition comprises that the cosine value of the geodetic longitude of the ground target point in the geodetic coordinate system is greater than zero, a value range of the geodetic latitude is [-π / 2, π / 2], and the component of the ground target point on the X-axis of the geodetic rectangular coordinate system is greater than zero.

[0043] In an implementation manner of the present disclosure, the verifying the formal proposition based on the theorem prover to determine whether the high-order logic expression satisfies the attribute constraint condition comprises:

[0044] verify the first formal proposition based on the theorem prover to determine whether the high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system satisfies the corresponding attribute constraint condition;

[0045] verify the second formal proposition based on the theorem prover to determine whether the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system satisfies the corresponding attribute constraint condition;

[0046] verify the third formal proposition based on the theorem prover to determine whether the high-order logic expression of the geodetic longitude of the ground target point in the geodetic coordinate system satisfies the corresponding attribute constraint condition;

[0047] verify the fourth formal proposition based on the theorem prover to determine whether the high-order logic expression of the geodetic height of the ground target point in the geodetic coordinate system satisfies the corresponding attribute constraint condition;

[0048] verify the fifth formal proposition based on the theorem prover to determine whether the high-order logic expression of the geodetic latitude of the ground target point in the geodetic coordinate system satisfies the corresponding attribute constraint condition.

[0049] In a second aspect, the present disclosure provides a formal analysis device for autonomous positioning of a UAV.

[0050] Specifically, the formal analysis device for autonomous positioning of a UAV comprises:

[0051] an acquisition module configured to acquire a homonymous image point coordinate of a homonymous image point of a ground target point in a camera coordinate system, a preset homogeneous coordinate conversion matrix, a continuous homogeneous coordinate conversion matrix, and a coordinate conversion formula;

[0052] a building module configured to build a high-order logic expression of the ground target point in a geodetic coordinate system based on a high-order logic language according to the homonymous image point coordinate, the homogeneous coordinate conversion matrix, the continuous homogeneous coordinate conversion matrix, and the coordinate conversion formula, the high-order logic expression being used for a UAV to determine non-homogeneous coordinates of the ground target point in the geodetic coordinate system;

[0053] a constructing module configured to construct a corresponding formal proposition based on the high-order logic expression, the formal proposition describing an attribute constraint condition in the high-order logic expression;

[0054] a verifying module configured to verify the formal proposition based on a theorem prover to determine whether the high-order logic expression satisfies the attribute constraint condition;

[0055] The homogeneous coordinate conversion matrix is used to realize coordinate conversion of the homonymous image point and the ground target point in the camera coordinate system, the continuous homogeneous coordinate conversion matrix is used to realize homogeneous coordinate conversion of the ground target point between the camera coordinate system, the carrier coordinate system, the geographic coordinate system and the geodetic rectangular coordinate system, and the coordinate conversion formula is used to realize non-homogeneous coordinate conversion of the ground target point between the geodetic rectangular coordinate system and the geodetic coordinate system.

[0056] In a third aspect, an electronic device is provided, including a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the method of the first aspect and any possible implementation manner of the first aspect.

[0057] In a fourth aspect, a computer readable storage medium is provided, having computer instructions stored thereon, wherein the computer instructions are executed by a processor to implement the method of the first aspect and any possible implementation manner of the first aspect.

[0058] According to the technical scheme provided by the embodiments of the present disclosure, by obtaining the homonymous image point coordinates of the homonymous image point of the ground target point in the camera coordinate system, the preset homogeneous coordinate conversion matrix, the continuous homogeneous coordinate conversion matrix and the coordinate conversion formula, the high-order logic expression of the ground target point in the geodetic coordinate system is established based on the high-order logic language; the corresponding formal proposition is constructed based on the high-order logic expression, which describes the attribute constraint condition in the high-order logic expression; the formal proposition is verified based on the theorem prover to determine whether the high-order logic expression meets the attribute constraint condition. Since the formal proposition constructed by the technical scheme describes the attribute constraint condition necessary for the high-order logic expression of the unmanned aerial vehicle to determine the non-homogeneous coordinates of the ground target point in the geodetic coordinate system, and the established high-order logic expression is analyzed and the attribute constraint condition of the high-order logic expression is verified by using the formal method, the lack of premise conditions or assumption conditions and human-induced errors are avoided, and the accuracy of the analysis result is ensured.

[0059] It should be understood that the above general description and the following detailed description are only exemplary and explanatory, and cannot limit the present disclosure. BRIEF DESCRIPTION OF DRAWINGS

[0060] Other features, objects, and advantages of the present disclosure will become more apparent from the following detailed description of the non-limiting embodiments, taken in conjunction with the accompanying drawings. In the drawings:

[0061] Figure 1 A flowchart of a formal analysis method for autonomous positioning of an unmanned aerial vehicle according to an embodiment of the present disclosure is shown;

[0062] Figure 2A schematic diagram showing various coordinate systems according to an embodiment of the present disclosure is shown.

[0063] Figure 3 A schematic diagram showing the relationship between a ground target point and a homonymous image point according to an embodiment of the present disclosure is shown.

[0064] Figure 4 A schematic diagram showing the establishment of a high-order logical expression of a ground target point in a geodetic coordinate system according to an embodiment of the present disclosure is shown.

[0065] Figure 5 A schematic diagram showing the establishment of a high-order logical expression of a homogeneous coordinate of a ground target point in a camera coordinate system according to an embodiment of the present disclosure is shown.

[0066] Figure 6 A schematic diagram showing the establishment of a high-order logical expression of a homogeneous coordinate of a ground target point in a geodetic rectangular coordinate system according to an embodiment of the present disclosure is shown.

[0067] Figure 7 A schematic diagram showing the establishment of a high-order logical expression of a non-homogeneous coordinate of a ground target point in a geodetic coordinate system according to an embodiment of the present disclosure is shown.

[0068] Figure 8 A schematic diagram showing the construction of a corresponding formal proposition based on a high-order logical expression according to an embodiment of the present disclosure is shown.

[0069] Figure 9 A schematic diagram showing the verification of a formal proposition based on a theorem prover according to an embodiment of the present disclosure is shown.

[0070] Figure 10 A block diagram of a formal analysis device for autonomous positioning of a UAV according to an embodiment of the present disclosure is shown.

[0071] Figure 11 A schematic diagram of an electronic device suitable for implementing a formal analysis method for autonomous positioning of a UAV according to an embodiment of the present disclosure is shown. DETAILED DESCRIPTION

[0072] Hereinafter, exemplary embodiments of the present disclosure will be described in detail with reference to the accompanying drawings so as to be easily implemented by those skilled in the art. Also, portions irrelevant to the description of the exemplary embodiments are omitted in the accompanying drawings for the sake of clarity.

[0073] In the present disclosure, it is to be understood that terms such as "include" or "have" are intended to indicate that there are constituents, numbers, steps, actions, parts, or combinations thereof disclosed in the specification, and are not intended to exclude the possibility of additional one or more other constituents, numbers, steps, actions, parts, or combinations thereof.

[0074] In addition, it should be noted that the embodiments in the present disclosure and the features in the embodiments can be combined with each other without conflict. The present disclosure will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0075] It is mentioned above that currently, the analysis verification is usually performed by traditional paper and pen calculation, computer algebra system and the like. However, these traditional non-formalized analysis verification methods are prone to introduce errors by human, lack necessary preconditions or assumption conditions, and cannot reliably handle boundary conditions and symbols, so as to ensure the accuracy of the analysis result. Therefore, the current traditional analysis method for the autonomous positioning of the unmanned aerial vehicle has the problem of inaccurate analysis result.

[0076] In view of the above defects, the present disclosure provides a formalized analysis method for the autonomous positioning of the unmanned aerial vehicle. The method obtains the homonymous image point coordinates of the homonymous image point of the ground target point in the camera coordinate system, a preset homogeneous coordinate conversion matrix, a continuous homogeneous coordinate conversion matrix and a coordinate conversion formula, establishes a high-order logic expression of the ground target point in the geodetic coordinate system based on a high-order logic language, constructs a corresponding formalized proposition based on the high-order logic expression, the formalized proposition describes the attribute constraint condition in the high-order logic expression, and verifies the formalized proposition based on a theorem prover to determine whether the high-order logic expression meets the attribute constraint condition. Since the formalized proposition constructed describes the attribute constraint condition necessary for the high-order logic expression of the unmanned aerial vehicle to determine the non-homogeneous coordinates of the ground target point in the geodetic coordinate system, and the high-order logic expression is analyzed and the attribute constraint condition of the high-order logic expression is verified by using the formalized method, the lack of preconditions or assumption conditions and the errors introduced by human are avoided, and the accuracy of the analysis result is ensured.

[0077] Figure 1 A flowchart of the formalized analysis method for the autonomous positioning of the unmanned aerial vehicle according to an embodiment of the present disclosure is shown. As shown in Figure 1 The formalized analysis method for the autonomous positioning of the unmanned aerial vehicle includes the following steps S101-S104.

[0078] In step S101, the homonymous image point coordinates of the homonymous image point of the ground target point in the camera coordinate system, a preset homogeneous coordinate conversion matrix, a continuous homogeneous coordinate conversion matrix and a coordinate conversion formula are obtained.

[0079] In step S102, a high-order logic expression of the ground target point in the geodetic coordinate system is established based on a high-order logic language according to the homonymous image point coordinates, the homogeneous coordinate conversion matrix, the continuous homogeneous coordinate conversion matrix and the coordinate conversion formula.

[0080] The high-order logic expression is used for the unmanned aerial vehicle to determine the non-homogeneous coordinates of the ground target point in the geodetic coordinate system.

[0081] In step S103, a corresponding formal proposition is constructed based on the high-order logic expression, and the formal proposition describes the attribute constraint condition in the high-order logic expression.

[0082] In step S104, the formal proposition is verified based on a theorem prover to determine whether the high-order logic expression satisfies the attribute constraint condition.

[0083] Wherein, the homogeneous coordinate conversion matrix is used to realize the coordinate conversion of the homonymous image point and the ground target point in the camera coordinate system, the continuous homogeneous coordinate conversion matrix is used to realize the homogeneous coordinate conversion of the ground target point between the camera coordinate system, the carrier coordinate system, the geographic coordinate system and the geodetic rectangular coordinate system, and the coordinate conversion formula is used to realize the non-homogeneous coordinate conversion of the ground target point between the geodetic rectangular coordinate system and the geodetic coordinate system.

[0084] The formal analysis of the autonomous positioning of the unmanned aerial vehicle described above can be executed on a high-order logic theorem prover HOL Light, can be executed by a physical device capable of providing the function of the high-order logic theorem prover HOL Light, or can be executed by a component (such as a chip, etc.) configured in a physical device, or can be executed by a module capable of realizing part or all of the function of the high-order logic theorem prover HOL Light, etc., and the present disclosure does not limit this. For ease of understanding, the present disclosure will be described below by taking the high-order logic theorem prover HOL Light as an example.

[0085] In the present embodiment, five coordinate systems are involved in the autonomous positioning of the ground target point by the unmanned aerial vehicle, which are the camera coordinate system, the carrier coordinate system, the geographic coordinate system, the geodetic rectangular coordinate system and the WGS84 geodetic coordinate system.

[0086] Exemplarily, Figure 2 A schematic diagram of various coordinate systems according to an embodiment of the present disclosure is shown.

[0087] As Figure 2 shown, the camera coordinate system is a coordinate system established with the optical center of the camera deployed on the unmanned aerial vehicle, i.e., the center of the camera lens, as the coordinate origin, which can be represented by O t -X t Y t Z t . The carrier coordinate system and the geographic coordinate system are coordinate systems established with the center of mass of the unmanned aerial vehicle as the origin, and the carrier coordinate system can be represented by O a -X a Y a Z a , and the geographic coordinate system can be represented by O s -Xs Y s Z s It is shown that the geographic coordinate system can be obtained by rotating the three-axis around the carrier coordinate system. When the attitude angle of the unmanned aerial vehicle is zero, the geographic coordinate system and the carrier coordinate system coincide. In the embodiment, the coordinates of the ground target point in the camera coordinate system, the carrier coordinate system and the geographic coordinate system are expressed by Cartesian coordinates.

[0088] The geodetic rectangular coordinate system and the WGS84 geodetic coordinate system are both coordinate systems established with the earth center as the coordinate origin. The geodetic rectangular coordinate system can be expressed as O g -X g Y g Z g It is shown that the WGS84 geodetic coordinate system can be expressed as O w -X w Y w Z w It is shown that the WGS84 geodetic coordinate system can be expressed as O t -X t Y t Z t The difference between the two coordinate systems is that the ground target point is expressed by Cartesian coordinates in the geodetic rectangular coordinate system, while it is expressed by geodetic longitude L, geodetic latitude B and geodetic height H in the WGS84 geodetic coordinate system.

[0089] The ground target point is a target object selected on the ground and needed to be positioned by the unmanned aerial vehicle. The ground target point has a corresponding homonymous image point, which is also called a corresponding image point, which refers to the perspective point of any target point on different photos.

[0090] Exemplarily, Figure 3 A schematic diagram showing the relationship between the ground target point and the homonymous image point according to an embodiment of the present disclosure is shown. As Figure 3 shown, in the camera coordinate system O t -X t Y t Z t The distance from the ground target point P to the camera optical center O t is r, and the distance from the homonymous image point P' of the ground target point P to the camera optical center O t is the camera focal length f.

[0091] The coordinates of the homonymous image point of the ground target point in the camera coordinate system can be called the homonymous image point coordinates, which are composed of the initial coordinates of the homonymous image point on the X-axis and the Y-axis of the camera coordinate system and the camera focal length, that is, P'(x0, y0, f), f is the camera focal length, x0 is the initial coordinate of the homonymous image point on the X-axis of the camera coordinate system, and y0 is the initial coordinate of the homonymous image point on the Y-axis of the camera coordinate system.

[0092] The homonymous image point P' of the ground target point P in the camera coordinate system is obtained, and a preset homogeneous coordinate conversion matrix, a continuous homogeneous coordinate conversion matrix and a coordinate conversion formula are obtained.

[0093] The homonymous image point and the ground target point in the camera coordinate system can be converted by the homogeneous coordinate conversion matrix.

[0094] It can be understood that after the homonymous image point P' in the camera coordinate system is obtained, the homonymous image point coordinate (x0, y0, f) can be expressed in the form of homogeneous coordinates, for example, the homogeneous coordinates can be represented as (x0, y0, f, 1) T . Then, the homogeneous coordinates of the ground target point P in the camera coordinate system can be further obtained by combining the homogeneous coordinate conversion matrix, for example, the homogeneous coordinates can be represented as (x t , y t , z t , 1) T .

[0095] The ground target point can be converted from the camera coordinate system to the carrier coordinate system, to the geographic coordinate system, and then to the geodetic rectangular coordinate system by the continuous homogeneous coordinate conversion matrix.

[0096] It can be understood that after the homogeneous coordinates (x t , y t , z t , 1) T of the ground target point P in the camera coordinate system are obtained by the homogeneous coordinate conversion matrix, the homogeneous coordinates (x t , y t , z t , 1) T of the ground target point P in the camera coordinate system can be converted to the homogeneous coordinates (x a , y a , z a , 1) T in the carrier coordinate system by the continuous homogeneous coordinate conversion matrix, the homogeneous coordinates (x a , y a , z a , 1) T of the ground target point P in the carrier coordinate system can be converted to the homogeneous coordinates (x s , y s , z s , 1) T in the geographic coordinate system, and the homogeneous coordinates (x s , y s , zs , 1) T Converts to the homogeneous coordinates (x g , y g , z g , 1) T .

[0097] Wherein, the conversion between the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system and the non-homogeneous coordinates of the ground target point in the WGS84 geodetic coordinate system can be realized through the coordinate conversion formula.

[0098] It can be understood that after obtaining the homogeneous coordinates (x g , y g , z g , 1) T of the ground target point P in the geodetic rectangular coordinate system, the non-homogeneous coordinates of the ground target point P in the WGS84 geodetic coordinate system can be further obtained through the coordinate conversion formula, for example, the non-homogeneous coordinates can be represented as (B, L, H), so as to complete the positioning of the ground target point P. Wherein, B is the geodetic latitude, L is the geodetic longitude, and H is the geodetic height.

[0099] After obtaining the homonymous image point coordinates of the homonymous image point of the ground target point in the camera coordinate system, the preset homogeneous coordinate conversion matrix, the continuous homogeneous coordinate conversion matrix and the coordinate conversion formula, the HOL Light can establish a high-order logic expression of the ground target point in the WGS84 geodetic coordinate system based on the high-order logic language, and the high-order logic expression can be used for the unmanned aerial vehicle to determine the geodetic longitude, the geodetic height and the geodetic latitude of the ground target point. The high-order logic expression describes the conversion relationship between the homonymous image point coordinates of the homonymous image point of the ground target point in the camera coordinate system, the homogeneous coordinates of the ground target point in the camera coordinate system, the homogeneous coordinates of the ground target point in the carrier coordinate system, the homogeneous coordinates of the ground target point in the geographical coordinate system, the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system and the non-homogeneous coordinates of the ground target point in the WGS84 geodetic coordinate system.

[0100] Further, in order to verify whether the established high-order logic expression is correct, a corresponding formal proposition can be constructed based on the high-order logic expression, and in order to ensure the accuracy of the verification result, the constructed formal proposition describes the attribute constraint condition that must be met in the high-order logic expression. Then, the HOL Light can verify the constructed formal proposition. If the verification passes, it means that the established high-order logic expression meets the attribute constraint condition, and then in the subsequent autonomous positioning of the unmanned aerial vehicle, the geodetic latitude B, the geodetic longitude L and the geodetic height H of the ground target point in the WGS84 geodetic coordinate system can be directly determined through the established high-order logic expression, that is, the unmanned aerial vehicle can conveniently realize the autonomous positioning of the ground target point through the high-order logic expression. On the contrary, if the verification fails, it means that the established high-order logic expression does not meet the attribute constraint condition, and then the high-order logic expression can be re-established until the high-order logic expression meets the attribute constraint condition.

[0101] The embodiment of the present disclosure proposes a formal analysis method for autonomous positioning of an unmanned aerial vehicle. The method acquires a homonymous image point coordinate of a homonymous image point of a ground target point in a camera coordinate system, a preset homogeneous coordinate conversion matrix, a continuous homogeneous coordinate conversion matrix and a coordinate conversion formula, establishes a high-order logic expression of the ground target point in a geodetic coordinate system based on a high-order logic language, constructs a corresponding formal proposition based on the high-order logic expression, the formal proposition describes an attribute constraint condition in the high-order logic expression, and verifies the formal proposition based on a theorem prover to determine whether the high-order logic expression meets the attribute constraint condition. Since the constructed formal proposition describes the attribute constraint condition necessary for the high-order logic expression used by the unmanned aerial vehicle to determine the non-homogeneous coordinate of the ground target point in the geodetic coordinate system, and the formal method is used to analyze the established high-order logic expression and verify the attribute constraint condition of the high-order logic expression, the lack of premise conditions or assumption conditions and the human-induced errors are avoided, and the accuracy of the analysis result is ensured.

[0102] In an optional implementation of the embodiment, the step S102, that is, establishing the high-order logic expression of the ground target point in the geodetic coordinate system based on the high-order logic language according to the homonymous image point coordinate, the homogeneous coordinate conversion matrix, the continuous homogeneous coordinate conversion matrix and the coordinate conversion formula, can further include steps S401 to S403 as shown in the following table. Figure 4

[0103] In the step S401, the high-order logic expression of the homogeneous coordinate of the ground target point in the camera coordinate system is established based on the high-order logic language according to the homonymous image point coordinate and the homogeneous coordinate conversion matrix.

[0104] ​In step S402, a high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system is established based on the high-order logic language according to the high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system and the continuous homogeneous coordinate conversion matrix.

[0105] In step S403, a high-order logic expression of the non-homogeneous coordinates of the ground target point in the geodetic coordinate system is established based on the high-order logic language according to the coordinate conversion formula and the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system.

[0106] In this optional implementation, when the high-order logic expression of the ground target point in the WGS84 geodetic coordinate system is established, the high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system can be first established according to the homonymous image point coordinates (x0, y0, f) of the homonymous image point in the camera coordinate system and the homogeneous coordinate conversion matrix. Since the homogeneous coordinate conversion matrix can realize the coordinate conversion between the homonymous image point and the ground target point in the camera coordinate system, the high-order logic expression describes the conversion relationship between the homonymous image point coordinates of the homonymous image point and the homogeneous coordinates of the ground target point in the camera coordinate system.

[0107] Then, the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system can be further established according to the high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system and the continuous homogeneous coordinate conversion matrix. Since the continuous homogeneous coordinate conversion matrix can realize the homogeneous coordinate conversion between the ground target point in the camera coordinate system, the carrier coordinate system, the geographic coordinate system and the geodetic rectangular coordinate system, the high-order logic expression also correspondingly describes the conversion relationship between the homonymous image point coordinates of the homonymous image point in the camera coordinate system, the homogeneous coordinates of the ground target point in the camera coordinate system, the homogeneous coordinates of the ground target point in the carrier coordinate system, the homogeneous coordinates in the geographic coordinate system and the homogeneous coordinates in the geodetic rectangular coordinate system.

[0108] Finally, the high-order logic expression of the non-homogeneous coordinates of the ground target point in the WGS84 geodetic coordinate system can be established according to the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system and the coordinate conversion formula. Since the coordinate conversion formula can realize the conversion between the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system and the non-homogeneous coordinates in the WGS84 geodetic coordinate system, the high-order logic expression can overall describe the conversion relationship between the homonymous image point coordinates of the homonymous image point in the camera coordinate system, the homogeneous coordinates of the ground target point in the camera coordinate system, the homogeneous coordinates of the ground target point in the carrier coordinate system, the homogeneous coordinates in the geographic coordinate system, the homogeneous coordinates in the geodetic rectangular coordinate system and the geodetic latitude, the geodetic longitude and the geodetic height in the WGS84 geodetic coordinate system.

[0109] In an optional implementation of the embodiment, the step S401 of establishing the high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system based on the high-order logic language according to the homonymous image point coordinates and the homogeneous coordinate conversion matrix can further include steps S501 to S504 as shown. Figure 5

[0110] In step S501, the high-order logic expression of the homogeneous coordinates of the homonymous image point in the camera coordinate system is established based on the high-order logic language according to the homonymous image point coordinates.

[0111] The homonymous image point coordinates include initial coordinates of the homonymous image point on the X axis and the Y axis of the camera coordinate system and a camera focal length of the camera on the unmanned aerial vehicle.

[0112] In step S502, the distance from the optical center of the camera to the ground target point is obtained.

[0113] In step S503, the high-order logic expression of the homogeneous coordinate conversion matrix is established based on the high-order logic language according to the distance and the camera focal length.

[0114] In step S504, the high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system is established according to the high-order logic expression of the homogeneous coordinates of the homonymous image point in the camera coordinate system and the high-order logic expression of the homogeneous coordinate conversion matrix.

[0115] In this optional implementation, after obtaining the homonymous image point coordinates of the homonymous image point of the ground target point in the camera coordinate system through step S101, on one hand, the high-order logic expression of the homogeneous coordinates of the homonymous image point in the camera coordinate system can be established first, which describes the conversion from the homonymous image point coordinates of the homonymous image point in the camera coordinate system to the homogeneous coordinates.

[0116] In some embodiments, the high-order logic expression of the homogeneous coordinates of the homonymous image point in the camera coordinate system includes the following high-order logic expression D1:

[0117] D1. Homonymous image point coordinates in the camera coordinate system

[0118] imgpoint_cam_coor x0 y0 f = vector [x0; y0; f; &1]

[0119] wherein the input variable of the function imgpoint_cam_coor is the homonymous image point coordinates (x0, y0, f), x0 and y0 represent the homonymous image point coordinates on the X axis and the Y axis of the camera coordinate system respectively, and f represents the camera focal length of the camera on the unmanned aerial vehicle.​t Axis and Y t The initial coordinates on the axis, f represents the camera focal length, x0, y0 and f are all real numbers, and the return value is the homogeneous coordinates of the homonymous image point in the camera coordinate system, and the data type of the return value is a four-dimensional vector.

[0120] The function vector is a function defined in HOL Light, the input variable of the function vector is 4 variables, and the return value is a vector spliced with the four variables, and the type of the return value is a four-dimensional vector.

[0121] It can be understood that after obtaining the homonymous image point coordinates (x0, y0, f) of the homonymous image point in the camera coordinate system, the homogeneous coordinates (x0, y0, f, 1) of the homonymous image point in the camera coordinate system can be obtained through the high-order logic expression D1. T .

[0122] On the other hand, the high-order logic expression of the homogeneous coordinate conversion matrix obtained in step S101 is established based on the high-order logic language, and the homogeneous coordinate conversion matrix can be constructed by the distance from the optical center of the camera to the ground target point and the camera focal length. Therefore, after obtaining the distance from the optical center of the camera to the ground target point and the camera focal length, the high-order logic expression of the homogeneous coordinate conversion matrix can be established based on the high-order logic language.

[0123] In some embodiments, the high-order logic expression of the homogeneous coordinate conversion matrix includes the following high-order logic expression D2:

[0124] D2. Homogeneous coordinate conversion matrix between homonymous image point and ground target point

[0125] imgtar_trans_matrix r f = vector [vector [ -- r * inv f; & 0; & 0; & 0 ] ; vector [ & 0; -- r * inv f; & 0; & 0 ] ; vector [ & 0; & 0; -- r * inv f; & 0 ] ; vector [ & 0; & 0; & 0; & 1 ] ]

[0126] Wherein, the input variable of the function imgtar_trans_matrix is r and f, r is the distance from the optical center of the camera to the ground target point, f is the camera focal length, r and f are all real numbers, and the return value is the homogeneous coordinate conversion matrix between the homonymous image point and the ground target point, and the data type of the return value is a four-order real matrix. The input variable of the function vector is still vector, and the return type can be represented as a matrix.

[0127] In some embodiments, the homogeneous coordinate conversion matrix can be as follows:

[0128]

[0129] wherein, -r / f is the influence factor between the ground target point and the homonymous image point.

[0130] After the high-order logical expression D1 and D2 are established, the high-order logical expression of the homogeneous coordinates of the ground target point in the camera coordinate system can be correspondingly established.

[0131] In some embodiments, the high-order logical expression of the homogeneous coordinates of the ground target point in the camera coordinate system includes the following high-order logical expression D3:

[0132] D3. The homogeneous coordinates of the ground target point in the camera coordinate system

[0133] tarpoint_cam_coor x0 y0 r f=imgtar_trans_matrix r f**

[0134] imgpoint_cam_coor x0 y0 f

[0135] wherein, the input variables of the function tarpoint_cam_coor are x0, y0, r and f, and the return value is the homogeneous coordinates of the ground target point in the camera coordinate system, and the data type of the return value is a four-dimensional vector.

[0136] In some embodiments, the conversion relationship between the homogeneous coordinates of the ground target point and the homonymous image point in the camera coordinate system can be as follows:

[0137]

[0138] wherein, (x t , y t , z t , 1) T is the homogeneous coordinates of the ground target point in the camera coordinate system, and (x0, y0, f, 1) T is the homogeneous coordinates of the homonymous image point in the camera coordinate system.

[0139] In an optional implementation of the present embodiment, the step S402, i.e., establishing the high-order logical expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system based on the high-order logical language according to the continuous homogeneous coordinate conversion matrix and the high-order logical expression of the homogeneous coordinates of the ground target point in the camera coordinate system, can further include steps S601 to S609 as shown in the following. Figure 6

[0140] In step S601, the azimuth and the elevation of the unmanned aerial vehicle are obtained.

[0141] ​In step S602, a high-order logic expression of a first homogeneous coordinate conversion sub-matrix is established based on a high-order logic language according to the azimuth angle and the elevation angle.

[0142] The first homogeneous coordinate conversion sub-matrix is included in the continuous homogeneous coordinate conversion matrix and is used to realize the homogeneous coordinate conversion between the camera coordinate system and the carrier coordinate system.

[0143] In step S603, a high-order logic expression of the homogeneous coordinates of the ground target point in the carrier coordinate system is established according to the high-order logic expression of the first homogeneous coordinate conversion sub-matrix and the high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system.

[0144] In step S604, a roll angle, a pitch angle and a yaw angle of the unmanned aerial vehicle are obtained.

[0145] In step S605, a high-order logic expression of a second homogeneous coordinate conversion sub-matrix is established based on a high-order logic language according to the roll angle, the pitch angle and the yaw angle.

[0146] The second homogeneous coordinate conversion sub-matrix is included in the continuous homogeneous coordinate conversion matrix and is used to realize the homogeneous coordinate conversion between the carrier coordinate system and the geographic coordinate system.

[0147] In step S606, a high-order logic expression of the homogeneous coordinates of the ground target point in the geographic coordinate system is established according to the high-order logic expression of the homogeneous coordinates of the ground target point in the carrier coordinate system and the high-order logic expression of the second homogeneous coordinate conversion sub-matrix.

[0148] In step S607, a prime vertical curvature radius of the earth, a first eccentricity of the earth, rotation angles of the Y axis and the Z axis of the geographic coordinate system around the Y axis and the Z axis of the geodetic rectangular coordinate system respectively, and a translation amount of the X axis of the geographic coordinate system to the X axis of the geodetic rectangular coordinate system are obtained.

[0149] In step S608, a high-order logic expression of a third homogeneous coordinate conversion sub-matrix is established based on a high-order logic language according to the prime vertical curvature radius of the earth, the first eccentricity of the earth, the rotation angles and the translation amount.

[0150] The third homogeneous coordinate conversion sub-matrix is included in the continuous homogeneous coordinate conversion matrix and is used to realize the homogeneous coordinate conversion between the geographic coordinate system and the geodetic rectangular coordinate system.

[0151] In step S609, a high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic coordinate system is established according to the high-order logic expression of the homogeneous coordinates of the ground target point in the geographic coordinate system and the high-order logic expression of the third homogeneous coordinate conversion sub-matrix.

[0152] In the optional implementation, the continuous second coordinate conversion matrix obtained in step S101 is composed of a first homogeneous coordinate conversion sub-matrix, a second homogeneous coordinate conversion sub-matrix and a third homogeneous coordinate conversion sub-matrix. The first homogeneous coordinate conversion sub-matrix is used to realize the conversion between the homogeneous coordinates of the ground target point in the camera coordinate system and the homogeneous coordinates of the ground target point in the carrier coordinate system, the second homogeneous coordinate conversion sub-matrix is used to realize the conversion between the homogeneous coordinates of the ground target point in the carrier coordinate system and the homogeneous coordinates of the ground target point in the geographic coordinate system, and the third homogeneous coordinate conversion sub-matrix is used to realize the conversion between the homogeneous coordinates of the ground target point in the geographic coordinate system and the homogeneous coordinates of the ground target point in the geodetic coordinate system.

[0153] In the embodiment, the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic coordinate system is established by the following method.

[0154] 1) The high-order logic expression of the first homogeneous coordinate conversion sub-matrix is established based on the high-order logic language, and the first homogeneous coordinate conversion sub-matrix is constructed by the azimuth angle of the UAV and the elevation angle of the UAV. Therefore, after the azimuth angle of the UAV and the elevation angle of the UAV are obtained, the high-order logic expression of the first homogeneous coordinate conversion sub-matrix is established based on the high-order logic language.

[0155] In some embodiments, the high-order logic expression of the first homogeneous coordinate conversion sub-matrix includes the following high-order logic expression D4:

[0156] D4. Homogeneous coordinate conversion matrix between camera coordinate system and carrier coordinate system

[0157] camcarr_trans_matrix alpha beta=zccw_rot_matrix alpha**

[0158] yccw_rot_matrix beta

[0159] The input variables of the function camcarr_trans_matrix are alpha and beta, alpha represents the azimuth angle of the unmanned aerial vehicle, beta represents the elevation angle of the unmanned aerial vehicle, alpha and beta are real numbers, and the return value of the function is the homogeneous coordinate conversion matrix between the camera coordinate system and the carrier coordinate system, that is, the first homogeneous coordinate conversion sub-matrix, and the type of the return value is a four-order real matrix.

[0160] In some embodiments, the first homogeneous coordinate conversion sub-matrix can be as follows:

[0161]

[0162] 2) After the high-order logic expression D3 and D4 are established, the high-order logic expression of the homogeneous coordinates of the ground target point in the carrier coordinate system can be established accordingly.

[0163] In some embodiments, the high-order logic expression of the homogeneous coordinates of the ground target point in the carrier coordinate system includes the following high-order logic expression D5:

[0164] D5. The homogeneous coordinates of the ground target point in the carrier coordinate system

[0165] tarpoint_carr_coor alpha beta x0 y0 r f=camcarr_trans_matrix alpha

[0166] beta**tarpoint_cam_coor x0 y0 r f

[0167] The input variables of the function tarpoint_carr_coor are alpha, beta, x0, y0, r and f, and they are all real numbers, the return value of the function is the homogeneous coordinates of the ground target point in the carrier coordinate system, and the data type of the return value is a vector.

[0168] In some embodiments, the conversion relationship between the homogeneous coordinates of the ground target point in the camera coordinate system and the homogeneous coordinates in the carrier coordinate system can be as follows:

[0169]

[0170] (x a , y a , z a , 1) T is the homogeneous coordinates of the ground target point in the carrier coordinate system, (x t , y t , z t , 1) TThe homogeneous coordinates of the ground target point in the camera coordinate system.

[0171] 3) The high-order logic expression of the second homogeneous coordinate conversion sub-matrix is established based on the high-order logic language, and the second homogeneous coordinate conversion sub-matrix can be constructed by the roll angle, the pitch angle and the yaw angle of the UAV. Therefore, after the roll angle, the pitch angle and the yaw angle of the UAV are obtained, the high-order logic expression of the second homogeneous coordinate conversion sub-matrix can be established based on the high-order logic language.

[0172] In some embodiments, the high-order logic expression of the second homogeneous coordinate conversion sub-matrix includes the following high-order logic expression D6:

[0173] D6. Homogeneous coordinate conversion matrix between the carrier coordinate system and the geographic coordinate system

[0174] carrgeou_trans_matrix psi theta phi=zccw_rot_matrix phi**yccw_rot_matrix theta**xccw_rot_matrix psi

[0175] Wherein, the input variables of the function camcarr_trans_matrix are psi, theta and phi, psi represents the roll angle φ of the UAV, theta represents the pitch angle θ of the UAV, and phi represents the yaw angle ψ of the UAV, psi, theta and phi are all real numbers, and the return value of the function is the homogeneous coordinate conversion matrix between the carrier coordinate system and the geographic coordinate system, that is, the second homogeneous coordinate conversion sub-matrix, and the type of the return value is a four-order real matrix.

[0176] In some embodiments, the second homogeneous coordinate conversion sub-matrix can be as follows:

[0177]

[0178] 4) After the high-order logic expressions D5 and D6 are established, the high-order logic expression of the homogeneous coordinates of the ground target point in the geographic coordinate system can be established accordingly.

[0179] In some embodiments, the high-order logic expression of the homogeneous coordinates of the ground target point in the geographic coordinate system includes the following high-order logic expression D7:

[0180] D7. Homogeneous coordinates of the ground target point in the geographic coordinate system

[0181] tarpoint_geou_coor alpha beta psi theta phi x0 y0 r f=

[0182] carrgeou_trans_matrix psi theta phi**tarpoint_carr_coor alpha beta x0y0 r f

[0183] wherein the input variables of the function tarpoint_carr_coor are alpha, beta, psi, theta, phi, x0, y0, r and f, and are all real numbers, and the return value of the function is the homogeneous coordinates of the ground target point in the geographic coordinate system, and the data type of the return value is vector.

[0184] In some embodiments, the conversion relationship between the homogeneous coordinates of the ground target point in the carrier coordinate system and the homogeneous coordinates in the geographic coordinate system can be as follows:

[0185]

[0186] wherein (x s , y s , z s , 1) T is the homogeneous coordinates of the ground target point in the geographic coordinate system, and (x a , y a , z a , 1) T is the homogeneous coordinates of the ground target point in the carrier coordinate system.

[0187] 5) Based on the high-order logic language, a high-order logic expression of a third homogeneous coordinate conversion sub-matrix is established, and the third homogeneous coordinate conversion sub-matrix can be constructed by the colatitude curvature radius of the earth, the first eccentricity of the earth, the rotation angle from the Y axis of the geographic coordinate system to the Y axis of the geodetic rectangular coordinate system, the rotation angle from the Z axis of the geographic coordinate system to the Z axis of the geodetic rectangular coordinate system, and the translation amount from the X axis of the geographic coordinate system to the X axis of the geodetic rectangular coordinate system. Therefore, after obtaining these related parameters, the high-order logic expression of the third homogeneous coordinate conversion sub-matrix can be established based on the high-order logic language.

[0188] In some embodiments, the high-order logic expression of the third homogeneous coordinate conversion sub-matrix includes the following high-order logic expression D8:

[0189] D8. Homogeneous coordinate conversion matrix between geographic coordinate system and geodetic rectangular coordinate system

[0190] geourec_trans_matrix bs ls hs N e=xpos_tra_matrix hs**

[0191] ycw_rot_matrix bs**zccw_rot_matrix ls**zpos_tra_matrix bs N e

[0192] wherein the input variables of the function camcarr_trans_matrix are bs, ls, hs, N and e, bs represents the rotation angle from the Z axis of the geographic coordinate system to the Z axis of the geodetic rectangular coordinate system, ls represents the rotation angle from the Y axis of the geographic coordinate system to the Y axis of the geodetic rectangular coordinate system, hs represents the translation amount from the X axis of the geographic coordinate system to the X axis of the geodetic rectangular coordinate system, N represents the radius of curvature of the prime vertical circle of the earth, and e represents the first eccentricity of the earth, and all are real numbers, and the return value of the function is the homogeneous coordinate conversion matrix between the geographic coordinate system and the geodetic rectangular coordinate system, i.e., the third homogeneous coordinate conversion sub-matrix, and the type of the return value is a four-order real matrix.

[0193] In some embodiments, the third homogeneous coordinate conversion sub-matrix can be as follows:

[0194]

[0195] 6) After the high-order logic expressions D7 and D8 are established, the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system can be established accordingly.

[0196] In some embodiments, the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system includes the following high-order logic expression D9:

[0197] D9. The homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system

[0198] tarpoint_georec_coor alpha beta psi theta phi x0 y0 r f bs ls hs N e=

[0199] geourec_trans_matrix bs ls hs N e**tarpoint_geou_coor alpha beta psi theta phi x0 y0 r f

[0200] wherein the input variables of the function tarpoint_carr_coor are alpha, beta, psi, theta, phi, x0, y0, r, f, bs, ls, hs, N and e, and all are real numbers, and the return value of the function is the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system, and the data type of the return value is a four-dimensional vector.

[0201] In some embodiments, the conversion relationship between the homogeneous coordinates of the ground target point in the geographic coordinate system and the homogeneous coordinates of the ground target point in the geodetic coordinate system can be as follows:

[0202]

[0203] wherein (x g , y g , z g , 1) T are the homogeneous coordinates of the ground target point in the geodetic coordinate system, and (x s , y s , z s , 1) T are the homogeneous coordinates of the ground target point in the geographic coordinate system.

[0204] In an optional implementation of the present embodiment, step S403, i.e., establishing, based on the high-order logic language, the high-order logic expression of the non-homogeneous coordinates of the ground target point in the geodetic coordinate system according to the coordinate conversion formula and the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic coordinate system, can further include steps S701 to S705 as shown in FIG. 7. Figure 7

[0205] In step S701, the components of the homogeneous coordinates of the ground target point on the X-axis, the Y-axis and the Z-axis of the geodetic rectangular coordinate system are determined according to the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system.

[0206] In step S702, the coordinate conversion expression corresponding to the geodetic longitude of the ground target point is determined according to the coordinate conversion formula.

[0207] wherein the coordinate conversion formula describes the conversion relationship between the components of the homogeneous coordinates of the ground target point on the X-axis, the Y-axis and the Z-axis of the geodetic rectangular coordinate system and the prime vertical curvature radius of the earth, the first eccentricity of the earth, the geodetic latitude of the ground target point, the geodetic longitude of the earth target point and the geodetic height of the earth target point.

[0208] In step S703, the high-order logic expression of the geodetic longitude of the ground target point in the geodetic coordinate system is established based on the high-order logic language according to the components of the homogeneous coordinates of the ground target point on the X-axis and the Y-axis of the geodetic rectangular coordinate system.

[0209] ​In step S704, according to the components of the homogeneous coordinates of the ground target point on the X-axis and the Z-axis of the geodetic rectangular coordinate system, the meridian curvature radius of the earth, the first eccentricity of the earth, and the coordinate conversion expression corresponding to the geodetic longitude of the ground target point, a high-order logic expression of the geodetic height of the ground target point in the geodetic coordinate system is established based on a high-order logic language.

[0210] In step S705, according to the components of the homogeneous coordinates of the ground target point on the X-axis, the Y-axis, and the Z-axis of the geodetic rectangular coordinate system, the meridian curvature radius of the earth, the first eccentricity of the earth, and the coordinate conversion expression corresponding to the geodetic longitude of the ground target point, a high-order logic expression of the geodetic latitude of the ground target point in the geodetic coordinate system is established based on a high-order logic language.

[0211] In this optional implementation, after the high-order logic expression D9 is established through step S402, a high-order logic expression of the non-homogeneous coordinates of the ground target point in the WGS84 geodetic coordinate system can be further established in combination with the coordinate conversion formula, that is, a high-order logic expression of the geodetic longitude of the ground target point in the WGS84 geodetic coordinate system, a high-order logic expression of the geodetic height of the ground target point in the WGS84 geodetic coordinate system, and a high-order logic expression of the geodetic latitude of the ground target point in the WGS84 geodetic coordinate system are established.

[0212] Before the high-order logic expression of the non-homogeneous coordinates of the ground target point in the WGS84 geodetic coordinate system is established, the components of the homogeneous coordinates of the ground target point on the axes of the geodetic rectangular coordinate system and the coordinate conversion expression corresponding to the geodetic longitude of the ground target point need to be determined.

[0213] When the components of the homogeneous coordinates of the ground target point on the axes of the geodetic rectangular coordinate system are determined, the homogeneous coordinates (x g , y g , z g , 1) T of the ground target point in the geodetic rectangular coordinate system can be obtained according to the high-order logic expression D9 established in step S402. g Then, the component of the ground target point on the X-axis of the geodetic rectangular coordinate system can be determined as x g , the component on the Y-axis as y g , and the component on the Z-axis as z .

[0214] When the coordinate conversion expression corresponding to the geodetic longitude of the ground target point is determined, it can be derived through the coordinate conversion formula obtained in step S101.

[0215] In some embodiments, the coordinate conversion formula between the geodetic rectangular coordinate system and the WGS84 geodetic coordinate system can be as follows:

[0216]

[0217] Where, x g Let y be the component of the ground target point on the X-axis of the geodetic rectangular coordinate system. g Let z be the component of the ground target point on the Y-axis of the geodetic rectangular coordinate system. g Let B be the component of the ground target point on the Z-axis of the geodetic rectangular coordinate system, L be the geodetic latitude of the ground target point, H be the geodetic height of the ground target point, N be the radius of curvature of the Earth's circumference and e be the first eccentricity of the Earth.

[0218] In some embodiments, a higher-order logical expression of the coordinate transformation formula can also be established based on a higher-order logic language. The higher-order logical expression of the coordinate transformation formula may include the following higher-order logical expression D10:

[0219] D10. Conversion between the geodetic rectangular coordinate system and the WGS84 geodetic coordinate system

[0220] georec_trans_coor N e BLH x g y g z g <=>x g = (N+H)*cos B*cos L / \

[0221] y g = (N+H)*cos B*sin L / \z g =(N*(&1-e pow 2)+H)*sin B

[0222] The input variable for the function georec_trans_coor is x. g y g z g N, e, B, L, and H are the three components x of the ground target point in the geodetic rectangular coordinate system. g y g z g This function determines the conversion between the geodetic latitude B, geodetic longitude L, and geodetic altitude H of a ground target point. The function returns either true or false, and the data type of the return value is Boolean.

[0223] It is understandable that the coordinate transformation formula describes x g y g z g The transformation relationships between N, e, B, L and H can be used to derive the expression for the geodetic longitude L of the ground target point through coordinate transformation formulas.

[0224] Further, the high-order logic expression of the geodetic latitude of the ground target point in the WGS84 geodetic coordinate system can be established based on the high-order logic language according to the component x g and the component y g of the homogeneous coordinates of the ground target point on the X-axis of the geodetic rectangular coordinate system. In some embodiments, the high-order logic expression of the geodetic latitude of the ground target point in the WGS84 geodetic coordinate system can include the following high-order logic expression D11:

[0225] D11. The geodetic latitude of the ground target point

[0226] geo_lng x g y g = atn(y g *inv x g )

[0227] wherein the input variables of the function geo_lng are x g and y g , both of which are real numbers, and the return value of the function is the geodetic latitude L of the ground target point in the WGS84 geodetic coordinate system, which is a real number.

[0228] Meanwhile, the high-order logic expression of the geodetic height of the ground target point in the WGS84 geodetic coordinate system can also be established based on the high-order logic language according to the component x g , the component z g of the homogeneous coordinates of the ground target point on the X-axis and the Z-axis of the geodetic rectangular coordinate system, the curvature radius N of the prime vertical circle of the Earth, the first eccentricity e of the Earth, and the coordinate conversion expression corresponding to the geodetic latitude of the ground target point.

[0229] In some embodiments, the high-order logic expression of the geodetic height of the ground target point in the WGS84 geodetic coordinate system can include the following high-order logic expression D12:

[0230] D12. The geodetic height of the ground target point

[0231] geo_heightNex g z g L= --(c_simpNe*inv(&4))-inv(&2)*sqrt(j_simpNex g z g L+s3_simpNex g z g L)-inv(&2)*sqrt(&2*j_simpNex g z g L-s3_simpNex g z gL - mg_simpNex g z g L * inv(&4 * sqrt(j_simpNex g z g L + s3_simpNex g z g L

[0232] wherein the input variables of the function geo_height are N, e, x g , y g , and L, all of which are real numbers, and the return value of the function is the geodetic height H of the ground target point in the WGS84 geodetic coordinate system, and the data type of the return value is real number.

[0233] Meanwhile, based on the classification of the homogeneous coordinates of the ground target point on the axes of the geodetic rectangular coordinate system, i.e., x g , y g , and z g , as well as the coordinate conversion expression corresponding to the prime vertical circle curvature radius N of the earth, the first eccentricity e of the earth, and the geodetic longitude of the ground target point, a high-order logic expression of the geodetic latitude of the ground target point in the WGS84 geodetic coordinate system is established based on a high-order logic language.

[0234] In some embodiments, the high-order logic expression of the geodetic latitude of the ground target point in the WGS84 geodetic coordinate system can include the following high-order logic expression D13:

[0235] D13. The geodetic latitude of the ground target point

[0236] geo_latNex g y g z g L = atn((z g * inv(sqrt(x g pow2 + y g pow2)) * (N + geo_heightNex g z g L) * inv(N * (&1 - epow2) + geo_heightNex g z g L

[0237] wherein the input variables of the function geo_lat are N, e, x g , y g , z g , and L, all of which are real numbers, and the return value of the function is the geodetic latitude B of the ground target point in the WGS84 geodetic coordinate system, and the data type of the return value is real number.

[0238] It should be noted that, in order to simplify the high-order logic expression D12 and D13, L in the high-order logic expression D12 and D13 should be understood as a coordinate conversion expression corresponding to the geodetic longitude of the ground target point.

[0239] In an optional implementation of the embodiment, the step S103, i.e., constructing the corresponding formal proposition based on the high-order logic expression, can further include the steps S801 to S805 as shown in the table. Figure 8

[0240] In the step S801, a first formal proposition is constructed based on the high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system.

[0241] The attribute constraint condition of the first formal proposition includes that the focal length of the camera is not equal to zero.

[0242] In the step S802, a second formal proposition is constructed based on the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system.

[0243] The attribute constraint condition of the second formal proposition includes that the focal length of the camera is not equal to zero.

[0244] In the step S803, a third formal proposition is constructed based on the high-order logic expression of the geodetic longitude of the ground target point in the geodetic coordinate system.

[0245] The attribute constraint condition of the third formal proposition includes that the cosine value of the geodetic longitude of the ground target point in the geodetic coordinate system is greater than zero, the value range of the geodetic longitude is [-π / 2, π / 2], and the component of the ground target point on the X-axis of the geodetic rectangular coordinate system is greater than zero.

[0246] In the step S804, a fourth formal proposition is constructed based on the high-order logic expression of the geodetic height of the ground target point in the geodetic coordinate system.

[0247] The attribute constraint condition of the fourth formal proposition includes that the cosine value of the geodetic longitude of the ground target point in the geodetic coordinate system is not zero.

[0248] In the step S805, a fifth formal proposition is constructed based on the high-order logic expression of the geodetic latitude of the ground target point in the geodetic coordinate system.

[0249] ​The attribute constraint condition of the fifth formalized proposition includes that a cosine value of the geodetic longitude of the ground target point in the geodetic coordinate system is greater than zero, a value range of the geodetic latitude is [-π / 2, π / 2], and a component of the ground target point on the X-axis of the geodetic rectangular coordinate system is greater than zero.

[0250] In the optional implementation, after the high-order logical expression of the homogeneous coordinates of the ground target point in the camera coordinate system, that is, the high-order logical expression D3 is established, a first formalized proposition corresponding to the high-order logical expression D3 can be correspondingly constructed.

[0251] In some embodiments, the first formalized proposition can include the following logical proposition Goal1:

[0252] Goal1. ~(f=&0)==>tarpoint_cam_coor x0y0 r f=vector

[0253] [--r*inv f*x0; --r*inv f*y0; --r; &1]

[0254] The inv is a high-order logical function defined in the HOL Light, an input variable of the function is a real number, and a return result is a reciprocal of the real number, and the reciprocal of 0 is still 0.

[0255] The necessary prerequisite condition, that is, the necessary attribute constraint condition for Goal1 to be established is that the focal length of the camera is not equal to 0.

[0256] It can be understood that Goal1 describes the relationship between the homogeneous coordinates of the ground target point in the camera coordinate system and the initial coordinates x0 and y0 of the homonymous image point on the camera coordinate system, the reciprocal of the focal length f of the camera, the distance r between the camera optical center and the ground target point in the case that the focal length of the camera is not 0.

[0257] And, after the high-order logical expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system, that is, the high-order logical expression D9 is established, a second formalized proposition corresponding to the high-order logical expression D9 can be correspondingly constructed.

[0258] In some embodiments, the second formalized proposition can include the following logical proposition Goal2:

[0259] Goal2. beta psi theta phi x0 y0 r f bs ls hs N e k1 k2 k3 k4 k5 k6 k7 m1 m2 m3.

[0260] ~ (f = & 0) /

[0261] k1 = r*cos alpha*sin beta - r*inv f*x0*cos alpha*cos beta - r*inv f*y0*sin alpha / \

[0262] k2 = r*inv f*x0*sin alpha*cos beta - r*inv f*y0*cos alpha - r*sin alpha*sin beta / \

[0263] k3 = cos psi*sin phi + sin psi*sin theta*cos phi / \

[0264] k4 = r*inv f*x0*sin beta + r*cos beta / \

[0265] k5 = sin psi*sin phi - cos psi*sin theta*cos phi / \

[0266] k6 = cos psi*cos phi - sin psi*sin theta*sin phi / \

[0267] k7 = sin psi*cos phi + cos psi*sin theta*sin phi / \

[0268] m1 = k1*cos theta*cos phi + k2*k3 - k4*k5 / \

[0269] m2 = k2*k6 - k4*k7 - k1*cos theta*sin phi / \

[0270] m3 = k1*sin theta - k2*sin psi*cos theta - k4*cos psi*cos theta

[0271] tarpoint_georec_coor1 alpha beta psi theta phi x0 y0 r f bs ls hs N e = m1*cos bs*cos ls + m2*cos bs*sin ls + m3*sin bs + hs - N*epow 2*sin bspow2

[0272] vector [m1*cos bs*cos ls + m2*cos bs*sin ls + m3*sin bs + hs - N*epow 2*sin bspow2;

[0273] m2*cos ls - m1*sin ls;

[0274] m3*cos bs - N*e pow 2*sin bs*cos bs - m1*sin bs*cos ls - m2*sin bs*sin ls;

[0275] &1]

[0276] wherein, sin is a high-order logic function defined in HOL Light, the input variable of the function is a real number representing a rotation angle, and the return value of the function is the sine value of the rotation angle. cos is a high-order logic function defined in HOL Light, the input variable of the function is a real number representing a rotation angle, and the return value of the function is the cosine value of the rotation angle. pow is a high-order logic function defined in HOL Light, the input variable of the function is a real number and a natural number k, and the return value of the function is the value of the k-th power of the real number, and the type of the return value is a real number.

[0277] wherein, the necessary prerequisite condition for Goal2 to be true, i.e., the necessary attribute constraint condition, is that the focal length of the camera is not equal to 0.

[0278] It can be understood that Goal2 describes the relationship between the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system and the initial coordinates x0 and y0 of the homonymous image point on the camera coordinate system, the reciprocal of the focal length f of the camera, the distance r between the camera optical center and the ground target point, the sine and cosine values of the azimuth angle alpha of the camera, the sine and cosine values of the elevation angle beta of the camera, the sine and cosine values of the roll angle psi of the UAV, the sine and cosine values of the pitch angle theta of the UAV, the sine and cosine values of the yaw angle phi of the UAV, the rotation angle bs from the Z-axis of the geographic coordinate system to the Z-axis of the geodetic rectangular coordinate system, the rotation angle ls from the Y-axis of the geographic coordinate system to the Y-axis of the geodetic rectangular coordinate system, the translation amount hs from the X-axis of the geographic coordinate system to the X-axis of the geodetic rectangular coordinate system, the radius of curvature N of the prime vertical circle of the earth, and the first eccentricity e of the earth when the focal length of the camera is not 0.

[0279] Furthermore, after the high-order logic expression of the geodetic longitude of the ground target point in the WGS84 geodetic coordinate system, i.e., the high-order logic expression D11, is established, a third formalized proposition corresponding to the high-order logic expression D11 can be correspondingly constructed.

[0280] In some embodiments, the third formalized proposition can include the following logical proposition Goal3:

[0281] Goal3. N e B L H xg y g z g .

[0282] georec_trans_coor N e B L H x g y g z g / \&0<cos L / \&0<x g / \--(pi /

[0283] &2)<L / \L<pi / &2==>

[0284] L=atn(y g *inv x g )

[0285] wherein, pi represents a circular constant.

[0286] wherein, the necessary prerequisite condition for Goal3 to be established, i.e., the necessary attribute constraint condition is that: the function georec_trans_coor used to describe the conversion relationship between the ground target point in the geodetic rectangular coordinate system and the WGS geodetic coordinate system is established, the cosine value of the geodetic longitude L of the ground target point in the WGS geodetic coordinate system is greater than 0, the component x g of the ground target point on the X-axis of the geodetic rectangular coordinate system is greater than 0, and the value range of the geodetic longitude L is [-π / 2, π / 2].

[0287] It can be understood that Goal3 describes that the geodetic longitude L of the ground target point in the WGS84 geodetic coordinate system and the component x g of the ground target point on the X-axis of the geodetic rectangular coordinate system and the component y g of the ground target point on the Y-axis can be converted to each other.

[0288] And, after the high-order logical expression of the geodetic height of the ground target point in the WGS84 geodetic coordinate system, i.e., the high-order logical expression D12 is established, the fourth formal proposition corresponding to the high-order logical expression D12 can be correspondingly constructed.

[0289] In some embodiments, the fourth formal proposition can include the following logical proposition Goal4:

[0290] Goal4. N e B L H x g y g z g P Q c d m n S T M J t s1s2 s3.georec_trans_coor N e B L H x g y g zg / \

[0291] P=&1-e pow 2 / \Q=cos L / \~(Q=&0) / \~((N+H)*Q=&0) / \~(N*P+H=&0) / \

[0292] c=&2*N*P+&2*N / \

[0293] d=N pow 2+&4*N pow 2*P+N pow 2*P pow 2-z g pow 2-(x g *

[0294] inv Q)pow 2 / \

[0295] m=&2*N pow 3*P+&2*N pow 3*P pow 2-&2*N*z g pow 2-

[0296] &2*N*P*(x g *inv Q)pow 2 / \

[0297] n=N pow 4*P pow 2-N pow 2*z g pow 2-N pow 2*P pow 2*(x g *

[0298] inv Q)pow 2 / \

[0299] S=d pow 2-&3*c*m+&12*n / \

[0300] T=&2*d pow 3-&9*c*d*m+&27*m pow 2+&27*c pow 2*n-&72*d*n / \

[0301] M=(--c)pow 3+&4*c*d-&8*m / \

[0302] J=inv(&4)*c pow 2-&2*inv(&3)*d / \

[0303] Im(ccbrt(Cx((--T)+sqrt(&4*(--S)pow 3+(--T)))))=&0 / \

[0304] t = inv(&3) * d + Re(ccbrt(Cx(&2))) * (— S) * inv(&3 * Re(ccbrt(Cx((— T) + sqrt(&4 * (— S) pow 3 + (— T)))))) - Re(ccbrt(Cx((— T) + sqrt(&4 * (— S) pow 3 + (— T)))))*inv(&3 * Re(ccbrt(Cx(&2)))) / \

[0305] s1 = Re(ccbrt(Cx(&2))) / \

[0306] s2 = Re(ccbrt(Cx(T + sqrt(— (&4) * S pow 3 + T pow 2))) / \

[0307] s3 = (s1 * S) * inv(&3 * s2) + s2 * inv(&3 * s1) / \

[0308] H pow 4 + c * H pow 3 + d * H pow 2 + m * H + n = &0 = =

[0309] H = — (c * inv(&4)) - inv(&2) * sqrt(J + s3) - inv(&2) * sqrt((&2 * J) - s3 - (M * inv(&4 * sqrt(J + s3))))

[0310] Wherein, P, Q, c, d, m, n, S, T, M, J, s1, s2, s3 are parameters for simplifying the logical proposition Goal4 target, t is the real solution obtained when the fourth order equation about the geodetic height H is converted into a third order equation. It should be understood that only real solutions are kept when the fourth order equation about the geodetic height H is converted into a third order equation and further converted into two quadratic equations for solving.

[0311] Wherein, the necessary prerequisite for Goal4 to be true, i.e. the necessary attribute constraint condition is that the function georec_trans_coor for describing the conversion relationship between the geodetic rectangular coordinate system and the WGS84 geodetic coordinate system is true, the cosine value of the geodetic longitude L of the ground target point in the WGS84 geodetic coordinate system is not 0, and the coordinate conversion formula for non-homogeneous coordinate conversion is meaningful.

[0312] It can be understood that Goal4 describes that the geodetic height H of the ground target point in the WGS84 geodetic coordinate system and the component x g of the ground target point in the X axis of the geodetic rectangular coordinate system, the component y g of the ground target point in the Y axis of the geodetic rectangular coordinate system, and the component z g of the ground target point in the Z axis of the geodetic rectangular coordinate system can be converted to each other.

[0313] Furthermore, after establishing the higher-order logical expression of the geodetic latitude of the ground target point in the WGS84 geodetic coordinate system, namely the higher-order logical expression D13, the fifth formal proposition corresponding to the higher-order logical expression D13 can be constructed accordingly.

[0314] In some embodiments, the fifth formal proposition may include the following logical proposition Goal5:

[0315] Goal 5. N e BLH x g y g z g .georec_trans_coor N e BLH x g y g z g / \&0 <cosL / \&0<x g / \~(N+H=&0) / \~(N*(&1-e pow 2)+H=&0) / \--(pi / &2)

[0316] B = atn((zg*inv(sqrt(x)) g pow 2+y g pow 2)))*(N+H)*inv(N*(&1-e pow 2)+H))

[0317] The necessary prerequisites for Goal5 to be valid, namely the necessary attribute constraints, are: the function georec_trans_coor used to describe the transformation relationship between the geodetic rectangular coordinate system and the WGS84 geodetic coordinate system is valid; the cosine value of the geodetic longitude L of the ground target point in the WGS84 geodetic coordinate system is greater than 0; and the x-component of the ground target point on the X-axis in the geodetic rectangular coordinate system is valid. g The coordinate transformation formula is greater than 0 and is meaningful for non-homogeneous coordinate transformation, and the geodetic latitude B is in the range of [-π / 2, π / 2].

[0318] It is understandable that Goal5 describes the geodetic latitude B of the ground target point in the WGS84 geodetic coordinate system and the x-component of the ground target point on the X-axis in the geodetic rectangular coordinate system. g Y-axis component y g Z-axis component z g And the elevation H can be converted to each other.

[0319] In an optional implementation of this embodiment, step S104, namely verifying the formal proposition based on the theorem prover, may further include, for example: Figure 9 Steps S901 to S905 are shown.​

[0320] In step S901, the first formalized proposition is verified based on the theorem prover to determine whether the high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system satisfies the corresponding attribute constraint condition.

[0321] In step S902, the second formalized proposition is verified based on the theorem prover to determine whether the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system satisfies the corresponding attribute constraint condition.

[0322] In step S903, the third formalized proposition is verified based on the theorem prover to determine whether the high-order logic expression of the geodetic longitude of the ground target point in the geodetic coordinate system satisfies the corresponding attribute constraint condition.

[0323] In step S904, the fourth formalized proposition is verified based on the theorem prover to determine whether the high-order logic expression of the geodetic height of the ground target point in the geodetic coordinate system satisfies the corresponding attribute constraint condition.

[0324] In step S905, the fifth formalized proposition is verified based on the theorem prover to determine whether the high-order logic expression of the geodetic latitude of the ground target point in the geodetic coordinate system satisfies the corresponding attribute constraint condition.

[0325] In the optional implementation, after the Goal1 to Goal5 are established, the HOL Light can further verify each of the Goal1 to Goal5. For any one formalized proposition, if the verification is passed, it indicates that the corresponding high-order logic expression established satisfies the attribute constraint condition, if the verification is not passed, it indicates that the corresponding high-order logic expression established does not satisfy the attribute constraint condition, and then the corresponding high-order logic expression can be re-established until the high-order logic expression satisfies the corresponding attribute constraint condition.

[0326] In some embodiments, when the HOL Light verifies any one formalized proposition, if the verification is passed, the HOL Light returns a value of true; if the verification is not passed, the HOL Light returns a value of false.

[0327] The following is an apparatus embodiment of the present disclosure, which can be used to execute the method embodiments of the present disclosure.

[0328] Figure 10 A structural block diagram of a formalized analysis apparatus for autonomous positioning of a UAV according to an embodiment of the present disclosure is shown. The apparatus can be realized as part or all of an electronic device by software, hardware, or a combination of both. As shown in FIG. 1, the apparatus includes a processor 1001, a memory 1002, and a communication interface 1003. Figure 10As shown, the unmanned aerial vehicle autonomous positioning formal analysis device includes:

[0329] The acquisition module 1001 is configured to acquire a homonymous image point coordinate of a homonymous image point of a ground target point in a camera coordinate system, a preset homogeneous coordinate conversion matrix, a continuous homogeneous coordinate conversion matrix, and a coordinate conversion formula;

[0330] The establishment module 1002 is configured to establish, based on a high-order logic language, a high-order logic expression of the ground target point in a geodetic coordinate system according to the homonymous image point coordinate, the homogeneous coordinate conversion matrix, the continuous homogeneous coordinate conversion matrix, and the coordinate conversion formula, and the high-order logic expression is used for the unmanned aerial vehicle to determine non-homogeneous coordinates of the ground target point in the geodetic coordinate system;

[0331] The construction module 1003 is configured to construct a corresponding formal proposition based on the high-order logic expression, and the formal proposition describes attribute constraint conditions in the high-order logic expression;

[0332] The verification module 1004 is configured to verify the formal proposition based on a theorem prover to determine whether the high-order logic expression satisfies the attribute constraint conditions;

[0333] The homogeneous coordinate conversion matrix is used to realize coordinate conversion of the homonymous image point and the ground target point in the camera coordinate system, the continuous homogeneous coordinate conversion matrix is used to realize homogeneous coordinate conversion of the ground target point between the camera coordinate system, a carrier coordinate system, a geographic coordinate system, and a geodetic rectangular coordinate system, and the coordinate conversion formula is used to realize non-homogeneous coordinate conversion of the ground target point between the geodetic rectangular coordinate system and the geodetic coordinate system.

[0334] In an optional implementation of the embodiment, the establishment module 1002 includes:

[0335] The first establishment module is configured to establish, based on a high-order logic language, a high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system according to the homonymous image point coordinate and the homogeneous coordinate conversion matrix;

[0336] The second establishment module is configured to establish, based on a high-order logic language, a high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system according to the continuous homogeneous coordinate conversion matrix and the high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system;

[0337] The third establishing module is configured to establish, based on a high-order logic language, a high-order logic expression of the non-homogeneous coordinates of the ground target point in the geodetic coordinate system according to the coordinate conversion formula and a high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic coordinate system.

[0338] In an optional implementation of the embodiment, the first establishing module comprises:

[0339] The first establishing submodule is configured to establish, based on a high-order logic language, a high-order logic expression of the homogeneous coordinates of the homonymous image point in the camera coordinate system according to the homonymous image point coordinates, the homonymous image point coordinates comprising initial coordinates of the homonymous image point on an X-axis and a Y-axis of the camera coordinate system and a camera focal length of the camera on the unmanned aerial vehicle.

[0340] The first obtaining submodule is configured to obtain a distance from an optical center of the camera to the ground target point.

[0341] The second establishing submodule is configured to establish, based on a high-order logic language, a high-order logic expression of the homogeneous coordinate conversion matrix according to the distance and the camera focal length.

[0342] The third establishing submodule is configured to establish, based on the high-order logic expression of the homogeneous coordinates of the homonymous image point in the camera coordinate system and the high-order logic expression of the homogeneous coordinate conversion matrix, a high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system.

[0343] In an optional implementation of the embodiment, the second establishing module comprises:

[0344] The second obtaining submodule is configured to obtain an azimuth angle and an elevation angle of the unmanned aerial vehicle.

[0345] The first establishing submodule is configured to establish, based on a high-order logic language, a high-order logic expression of a first homogeneous coordinate conversion submatrix according to the azimuth angle and the elevation angle, the first homogeneous coordinate conversion submatrix being included in the continuous homogeneous coordinate conversion matrix and being used for realizing homogeneous coordinate conversion between the camera coordinate system and the carrier coordinate system.

[0346] The fifth establishing submodule is configured to establish, based on the high-order logic expression of the first homogeneous coordinate conversion submatrix and the high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system, a high-order logic expression of the homogeneous coordinates of the ground target point in the carrier coordinate system.

[0347] The third obtaining submodule is configured to obtain a roll angle, a pitch angle and a yaw angle of the unmanned aerial vehicle.

[0348] The sixth establishing submodule is configured to establish a high-order logic expression of a second homogeneous coordinate conversion submatrix based on a high-order logic language according to the roll angle, the pitch angle and the yaw angle, the second homogeneous coordinate conversion submatrix being contained in the continuous homogeneous coordinate conversion matrix and being used to realize the homogeneous coordinate conversion between the carrier coordinate system and the geographic coordinate system;

[0349] The seventh establishing submodule is configured to establish a high-order logic expression of the homogeneous coordinates of the ground target point in the geographic coordinate system according to a high-order logic expression of the homogeneous coordinates of the ground target point in the carrier coordinate system and a high-order logic expression of the second homogeneous coordinate conversion submatrix.

[0350] The fourth obtaining submodule is configured to obtain a meridian curvature radius of the earth, a first eccentricity of the earth, rotation angles of Y and Z axes of the geographic coordinate system around Y and Z axes of the geodetic rectangular coordinate system respectively, and a translation amount of an X axis of the geographic coordinate system to an X axis of the geodetic rectangular coordinate system.

[0351] The eighth establishing submodule is configured to establish a high-order logic expression of a third homogeneous coordinate conversion submatrix based on a high-order logic language according to the meridian curvature radius of the earth, the first eccentricity of the earth, the rotation angles and the translation amount, the third homogeneous coordinate conversion submatrix being contained in the continuous homogeneous coordinate conversion matrix and being used to realize the homogeneous coordinate conversion between the geographic coordinate system and the geodetic rectangular coordinate system.

[0352] The ninth establishing submodule is configured to establish a high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system according to a high-order logic expression of the homogeneous coordinates of the ground target point in the geographic coordinate system and a high-order logic expression of the third homogeneous coordinate conversion submatrix.

[0353] In an optional implementation of the embodiment, the third establishing module comprises:

[0354] The first determining submodule is configured to determine components of the homogeneous coordinates of the ground target point on X, Y and Z axes of the geodetic rectangular coordinate system according to the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system.

[0355] a second determining sub-module, configured to determine a coordinate conversion expression corresponding to the geodetic longitude of the ground target point according to the coordinate conversion formula, the coordinate conversion formula describing a conversion relationship between components of the homogeneous coordinates of the ground target point on the X-axis, the Y-axis and the Z-axis of the geodetic rectangular coordinate system and the meridional circle curvature radius of the earth, the first eccentricity of the earth, the geodetic latitude of the ground target point, the geodetic longitude of the ground target point and the geodetic height of the ground target point;

[0356] a tenth establishing sub-module, configured to establish a high-order logic expression of the geodetic longitude of the ground target point in the geodetic coordinate system based on a high-order logic language according to the components of the homogeneous coordinates of the ground target point on the X-axis and the Y-axis of the geodetic rectangular coordinate system;

[0357] an eleventh establishing sub-module, configured to establish a high-order logic expression of the geodetic height of the ground target point in the geodetic coordinate system based on a high-order logic language according to the components of the homogeneous coordinates of the ground target point on the X-axis, the Z-axis of the geodetic rectangular coordinate system, the meridional circle curvature radius of the earth, the first eccentricity of the earth and the coordinate conversion expression corresponding to the geodetic longitude of the ground target point;

[0358] a twelfth establishing sub-module, configured to establish a high-order logic expression of the geodetic latitude of the ground target point in the geodetic coordinate system based on a high-order logic language according to the components of the homogeneous coordinates of the ground target point on the X-axis, the Y-axis and the Z-axis of the geodetic rectangular coordinate system, the meridional circle curvature radius of the earth, the first eccentricity of the earth and the coordinate conversion expression corresponding to the geodetic longitude of the ground target point.

[0359] In an optional implementation of the embodiment, the construction module 1003 comprises:

[0360] a first construction sub-module, configured to construct a corresponding first formalized proposition based on the high-order logic expression of the homogeneous coordinates of the ground target point in the camera coordinate system, the attribute constraint condition of the first formalized proposition comprising that the focal length of the camera is not equal to zero;

[0361] a second construction sub-module, configured to construct a corresponding second formalized proposition based on the high-order logic expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system, the attribute constraint condition of the second formalized proposition comprising that the focal length of the camera is not equal to zero;

[0362] a third constructing submodule configured to construct a third formalized proposition corresponding to a high-order logical expression of the geodetic longitude of the ground target point in the geodetic coordinate system, the attribute constraint condition of the third formalized proposition comprising: a cosine value of the geodetic longitude of the ground target point in the geodetic coordinate system being greater than zero, a value range of the geodetic longitude being [-π / 2, π / 2], and a component of the ground target point on an X-axis of the geodetic rectangular coordinate system being greater than zero;

[0363] a fourth constructing submodule configured to construct a fourth formalized proposition corresponding to a high-order logical expression of the geodetic height of the ground target point in the geodetic coordinate system, the attribute constraint condition of the fourth formalized proposition comprising: the cosine value of the geodetic longitude of the ground target point in the geodetic coordinate system being not zero;

[0364] a fifth constructing submodule configured to construct a fifth formalized proposition corresponding to a high-order logical expression of the geodetic latitude of the ground target point in the geodetic coordinate system, the attribute constraint condition of the fifth formalized proposition comprising: the cosine value of the geodetic longitude of the ground target point in the geodetic coordinate system being greater than zero, a value range of the geodetic latitude being [-π / 2, π / 2], and the component of the ground target point on the X-axis of the geodetic rectangular coordinate system being greater than zero.

[0365] In an optional implementation of the embodiment, the verification module 1004 comprises:

[0366] a first verification submodule configured to verify the first formalized proposition based on the theorem prover to determine whether the high-order logical expression of the homogeneous coordinates of the ground target point in the camera coordinate system satisfies the corresponding attribute constraint condition;

[0367] a second verification submodule configured to verify the second formalized proposition based on the theorem prover to determine whether the high-order logical expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system satisfies the corresponding attribute constraint condition;

[0368] a third verification submodule configured to verify the third formalized proposition based on the theorem prover to determine whether the high-order logical expression of the geodetic longitude of the ground target point in the geodetic coordinate system satisfies the corresponding attribute constraint condition;

[0369] a fourth verification submodule configured to verify the fourth formalized proposition based on the theorem prover to determine whether the high-order logical expression of the geodetic height of the ground target point in the geodetic coordinate system satisfies the corresponding attribute constraint condition;

[0370] The fifth verification submodule is configured to verify the fifth formal proposition based on the theorem prover, in order to determine whether the higher-order logical expression of the geodetic latitude of the ground target point in the geodetic coordinate system satisfies the corresponding attribute constraints.

[0371] The formal analysis device for UAV autonomous localization in this embodiment corresponds to the formal analysis method for UAV autonomous localization described above. For details, please refer to the description of the formal analysis method for UAV autonomous localization above, which will not be repeated here.

[0372] Figure 11 This is a schematic diagram of the structure of an electronic device suitable for implementing a formal analysis method for autonomous localization of a drone according to an embodiment of the present disclosure.

[0373] like Figure 11 As shown, the electronic device 1100 includes a processing unit 1101, which can be implemented as a CPU, GPU, FPGA, NPU, or other processing unit. The processing unit 1101 can execute various processes according to any of the methods described above in this disclosure, based on a program stored in the read-only memory (ROM) 1102 or a program loaded from the storage portion 1108 into the random access memory (RAM) 1103. The RAM 1103 also stores various programs and data required for the operation of the electronic device 1100. The processing unit 1101, ROM 1102, and RAM 1103 are interconnected via a bus 1104. An input / output (I / O) interface 1105 is also connected to the bus 1104.

[0374] The following components are connected to I / O interface 1105: an input section 1106 including a keyboard, mouse, etc.; an output section 1107 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and speakers, etc.; a storage section 1108 including a hard disk, etc.; and a communication section 1109 including a network interface card such as a LAN card, modem, etc. The communication section 1109 performs communication processing via a network such as the Internet. A drive 1110 is also connected to I / O interface 1105 as needed. Removable media 1111, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., are installed on drive 1110 as needed so that computer programs read from them can be installed into storage section 1108 as needed.

[0375] In particular, according to embodiments of the present disclosure, the above-mentioned methods with reference to any of the embodiments of the present disclosure can be implemented as a computer software program. For example, embodiments of the present disclosure include a computer program product comprising a computer program tangibly embodied on a machine-readable medium, the computer program containing program code for executing any of the methods described in embodiments of the present disclosure. In such embodiments, the computer program can be downloaded and installed from a network via the communication section 1109, and / or installed from the removable medium 1111.

[0376] The flow and block diagrams in the drawings show the architectural, functional and operational views of possible implementations of systems, methods and computer program products according to various embodiments of the present disclosure. In this regard, each block in the flow and block diagrams can represent a module, a segment, or a portion of code which comprises one or more executable instructions for implementing the specified logical function. It should also be noted that in some alternative implementations, the functions noted in the blocks can occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may

[0377] The units or modules described in the embodiments of the present disclosure can be implemented by means of software, or by means of hardware. The described units or modules can also be provided in a processor, and the names of these units or modules do not constitute a limitation on the units or modules themselves in some cases.

[0378] As another aspect, the present disclosure also provides a computer-readable storage medium, which can be the computer-readable storage medium included in the apparatus described in the above embodiments, or can exist separately from the apparatus and not be assembled into the apparatus. The computer-readable storage medium stores one or more programs, which are used by one or more processors to execute the methods described in the present disclosure.

[0379] The above description is merely that of the preferred embodiments of the present disclosure and a description of the technical principles of the present disclosure. It should be understood by those skilled in the art that the inventive scope involved in the present disclosure is not limited to the technical solutions formed by the specific combinations of the above technical features, and should also cover other technical solutions formed by the combinations of the above technical features or equivalent features without departing from the inventive concept. For example, the technical solutions formed by the mutual replacement of the above features and the technical features with similar functions disclosed in the present disclosure (but not limited to) without departing from the inventive concept.

Claims

1. A formal analysis method for autonomous localization of unmanned aerial vehicles (UAVs), characterized in that, include: Obtain the coordinates of the corresponding image points of the ground target points in the camera coordinate system, the preset homogeneous coordinate transformation matrix, the continuous homogeneous coordinate transformation matrix, and the coordinate transformation formula; Based on the coordinates of the corresponding image points, the homogeneous coordinate transformation matrix, the continuous homogeneous coordinate transformation matrix, and the coordinate transformation formula, a high-order logical expression of the ground target point in the geodetic coordinate system is established using a high-order logic language. This high-order logical expression is used by the UAV to determine the non-homogeneous coordinates of the ground target point in the geodetic coordinate system. Based on the higher-order logic expression, a corresponding formal proposition is constructed, which describes the attribute constraints in the higher-order logic expression. The formal proposition is verified based on the theorem prover to determine whether the higher-order logic expression satisfies the attribute constraints. The homogeneous coordinate transformation matrix is ​​used to realize the coordinate transformation of the corresponding image point and the ground target point in the camera coordinate system. The continuous homogeneous coordinate transformation matrix is ​​used to realize the homogeneous coordinate transformation of the ground target point between the camera coordinate system, the carrier coordinate system, the geographic coordinate system and the geodetic rectangular coordinate system. The coordinate transformation formula is used to realize the non-homogeneous coordinate transformation of the ground target point between the geodetic rectangular coordinate system and the geodetic coordinate system. The formal propositions constructed based on the higher-order logic expression include: A first formal proposition is constructed based on the higher-order logical expression of the homogeneous coordinates of the ground target point in the camera coordinate system. The attribute constraint of the first formal proposition includes that the camera focal length is not equal to zero. A second formal proposition is constructed based on the higher-order logical expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system. The attribute constraint of the second formal proposition includes that the camera focal length is not equal to zero. A third formal proposition is constructed based on the higher-order logical expression of the geodetic longitude of the ground target point in the geodetic coordinate system. The attribute constraint of the third formal proposition includes that the cosine value of the geodetic longitude of the ground target point in the geodetic coordinate system is greater than zero, and that the value of the geodetic longitude is within the range of [-π / 2, π / 2]. Furthermore, the component of the ground target point on the X-axis of the geodetic rectangular coordinate system is greater than zero; based on the higher-order logical expression of the geodetic height of the ground target point in the geodetic coordinate system, a corresponding fourth formal proposition is constructed, the attribute constraints of which include the cosine value of the geodetic longitude of the ground target point in the geodetic coordinate system being non-zero; based on the higher-order logical expression of the geodetic latitude of the ground target point in the geodetic coordinate system, a corresponding fifth formal proposition is constructed, the attribute constraints of which include the cosine value of the geodetic longitude of the ground target point in the geodetic coordinate system being greater than zero, the range of the geodetic latitude being [-π / 2, π / 2], and the component of the ground target point on the X-axis of the geodetic rectangular coordinate system being greater than zero.

2. The method according to claim 1, characterized in that, The step of establishing a high-order logical expression of the ground target point in the geodetic coordinate system based on the coordinates of the corresponding image points, the homogeneous coordinate transformation matrix, the continuous homogeneous coordinate transformation matrix, and the coordinate transformation formula, using a high-order logic language, includes: Based on the coordinates of the corresponding image points and the homogeneous coordinate transformation matrix, a high-order logical expression of the homogeneous coordinates of the ground target points in the camera coordinate system is established using a high-order logic language. Based on the continuous homogeneous coordinate transformation matrix and the higher-order logical expression of the homogeneous coordinates of the ground target point in the camera coordinate system, the higher-order logical expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system is established based on the higher-order logic language. Based on the coordinate transformation formula and the higher-order logical expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system, a higher-order logical expression of the non-homogeneous coordinates of the ground target point in the geodetic coordinate system is established based on a higher-order logic language.

3. The method according to claim 2, characterized in that, The step of establishing a high-order logical expression for the homogeneous coordinates of the ground target points in the camera coordinate system based on the coordinates of the corresponding image points and the homogeneous coordinate transformation matrix, using a high-order logic language, includes: Based on the coordinates of the corresponding image points, a high-order logic expression of the homogeneous coordinates of the corresponding image points in the camera coordinate system is established based on a high-order logic language. The coordinates of the corresponding image points include the initial coordinates of the corresponding image points on the X-axis and Y-axis of the camera coordinate system and the camera focal length of the camera on the UAV. Obtain the distance from the optical center of the camera to the ground target point; Based on the distance and the camera focal length, establish a high-order logical expression for the homogeneous coordinate transformation matrix using a high-order logic language. Based on the higher-order logical expression of the homogeneous coordinates of the corresponding image points in the camera coordinate system and the higher-order logical expression of the homogeneous coordinate transformation matrix, the higher-order logical expression of the homogeneous coordinates of the ground target points in the camera coordinate system is established.

4. The method according to claim 3, characterized in that, The step of establishing a higher-order logical expression for the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system based on the continuous homogeneous coordinate transformation matrix and the higher-order logical expression of the homogeneous coordinates of the ground target point in the camera coordinate system, using a higher-order logic language, includes: Obtain the azimuth and elevation angles of the drone; Based on the azimuth angle and the elevation angle, a high-order logic expression of the first homogeneous coordinate transformation submatrix is ​​established using a high-order logic language. The first homogeneous coordinate transformation submatrix is ​​included in the continuous homogeneous coordinate transformation matrix and is used to realize the homogeneous coordinate transformation between the camera coordinate system and the carrier coordinate system. Based on the higher-order logical expression of the first homogeneous coordinate transformation sub-matrix and the higher-order logical expression of the homogeneous coordinates of the ground target point in the camera coordinate system, the higher-order logical expression of the homogeneous coordinates of the ground target point in the carrier coordinate system is established. Obtain the roll angle, pitch angle, and yaw angle of the UAV; Based on the roll angle, pitch angle and yaw angle, a high-order logic expression for the second homogeneous coordinate transformation submatrix is ​​established using a high-order logic language. The second homogeneous coordinate transformation submatrix is ​​included in the continuous homogeneous coordinate transformation matrix and is used to realize the homogeneous coordinate transformation between the aircraft coordinate system and the geographic coordinate system. Based on the higher-order logical expression of the homogeneous coordinates of the ground target point in the aircraft coordinate system and the higher-order logical expression of the second homogeneous coordinate transformation sub-matrix, the higher-order logical expression of the homogeneous coordinates of the ground target point in the geographic coordinate system is established. Obtain the Earth's radius of curvature in the geocentric region, the Earth's first eccentricity, the rotation angles from the Y-axis and Z-axis of the geographic coordinate system to the Y-axis and Z-axis of the geodetic rectangular coordinate system, respectively, and the translation amount from the X-axis of the geographic coordinate system to the X-axis of the geodetic rectangular coordinate system; Based on the Earth's circumpolar curvature radius, the Earth's first eccentricity, the rotation angle, and the translation amount, a high-order logic expression for the third homogeneous coordinate transformation submatrix is ​​established using a high-order logic language. The third homogeneous coordinate transformation submatrix is ​​included in the continuous homogeneous coordinate transformation matrix and is used to realize the homogeneous coordinate transformation between the geographic coordinate system and the geodetic rectangular coordinate system. Based on the higher-order logical expression of the homogeneous coordinates of the ground target point in the geographic coordinate system and the higher-order logical expression of the third homogeneous coordinate transformation submatrix, the higher-order logical expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system is established.

5. The method according to claim 4, characterized in that, The step of establishing a higher-order logical expression for the non-homogeneous coordinates of the ground target point in the geodetic coordinate system based on the coordinate transformation formula and the homogeneous coordinates of the ground target point in the geodetic coordinate system, using a higher-order logic language, includes: The components of the homogeneous coordinates of the ground target point on the X-axis, Y-axis and Z-axis of the geodetic rectangular coordinate system are determined based on the higher-order logical expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system. The coordinate transformation formula is used to determine the coordinate transformation expression corresponding to the geodetic longitude of the ground target point. The coordinate transformation formula describes the transformation relationship between the components of the homogeneous coordinates of the ground target point on the X-axis, Y-axis and Z-axis of the geodetic rectangular coordinate system and the radius of curvature of the Earth's circumference, the Earth's first eccentricity, the geodetic latitude of the ground target point, the geodetic longitude of the Earth target point and the geodetic height of the Earth target point. Based on the components of the homogeneous coordinates of the ground target point on the X-axis and Y-axis of the geodetic rectangular coordinate system, a high-order logical expression of the geodetic longitude of the ground target point in the geodetic coordinate system is established using a high-order logic language. Based on the coordinate transformation expressions corresponding to the homogeneous coordinates of the ground target point on the X-axis and Z-axis of the geodetic rectangular coordinate system, the radius of curvature of the Earth's zonal and tropomorphic orbits, the first eccentricity of the Earth, and the geodetic longitude of the ground target point, a high-order logical expression of the geodetic height of the ground target point in the geodetic coordinate system is established based on a high-order logic language. Based on the components of the homogeneous coordinates of the ground target point on the X, Y, and Z axes of the geodetic rectangular coordinate system, the radius of curvature of the Earth's circumpolar region, the first eccentricity of the Earth, and the coordinate transformation expression corresponding to the geodetic longitude of the ground target point, a high-order logical expression of the geodetic latitude of the ground target point in the geodetic coordinate system is established using a high-order logic language.

6. The method according to claim 5, characterized in that, The theorem prover-based verification of the formal proposition to determine whether the higher-order logic expression satisfies the attribute constraints includes: Based on the theorem prover, the first formal proposition is verified to determine whether the higher-order logical expression of the homogeneous coordinates of the ground target point in the camera coordinate system satisfies the corresponding attribute constraint conditions. Based on the theorem prover, the second formal proposition is verified to determine whether the higher-order logical expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system satisfies the corresponding attribute constraint conditions. Based on the theorem prover, the third formal proposition is verified to determine whether the higher-order logical expression of the geodetic longitude of the ground target point in the geodetic coordinate system satisfies the corresponding attribute constraint conditions. Based on the theorem prover, the fourth formal proposition is verified to determine whether the higher-order logical expression of the geodetic height of the ground target point in the geodetic coordinate system satisfies the corresponding attribute constraint conditions. The theorem prover verifies the fifth formal proposition to determine whether the higher-order logical expression of the geodetic latitude of the ground target point in the geodetic coordinate system satisfies the corresponding attribute constraints.

7. A formal analysis device for autonomous localization of unmanned aerial vehicles (UAVs), characterized in that, include: The acquisition module is configured to acquire the coordinates of the corresponding image points of the ground target point in the camera coordinate system, the preset homogeneous coordinate transformation matrix, the continuous homogeneous coordinate transformation matrix, and the coordinate transformation formula. The module is configured to establish a high-order logical expression of the ground target point in the geodetic coordinate system based on the coordinates of the corresponding image points, the homogeneous coordinate transformation matrix, the continuous homogeneous coordinate transformation matrix and the coordinate transformation formula, and the high-order logical expression is used by the UAV to determine the non-homogeneous coordinates of the ground target point in the geodetic coordinate system. The construction module is configured to construct a corresponding formal proposition based on the higher-order logic expression, wherein the formal proposition describes the attribute constraints in the higher-order logic expression; The verification module is configured to verify the formal proposition based on the theorem prover in order to determine whether the higher-order logic expression satisfies the attribute constraints. The homogeneous coordinate transformation matrix is ​​used to realize the coordinate transformation of the corresponding image point and the ground target point in the camera coordinate system. The continuous homogeneous coordinate transformation matrix is ​​used to realize the homogeneous coordinate transformation of the ground target point between the camera coordinate system, the carrier coordinate system, the geographic coordinate system and the geodetic rectangular coordinate system. The coordinate transformation formula is used to realize the non-homogeneous coordinate transformation of the ground target point between the geodetic rectangular coordinate system and the geodetic coordinate system. The formal propositions constructed based on the higher-order logic expression include: A first formal proposition is constructed based on the higher-order logical expression of the homogeneous coordinates of the ground target point in the camera coordinate system. The attribute constraint of the first formal proposition includes that the camera focal length is not equal to zero. A second formal proposition is constructed based on the higher-order logical expression of the homogeneous coordinates of the ground target point in the geodetic rectangular coordinate system. The attribute constraint of the second formal proposition includes that the camera focal length is not equal to zero. A third formal proposition is constructed based on the higher-order logical expression of the geodetic longitude of the ground target point in the geodetic coordinate system. The attribute constraint of the third formal proposition includes that the cosine value of the geodetic longitude of the ground target point in the geodetic coordinate system is greater than zero, and that the value of the geodetic longitude is within the range of [-π / 2, π / 2]. Furthermore, the component of the ground target point on the X-axis of the geodetic rectangular coordinate system is greater than zero; based on the higher-order logical expression of the geodetic height of the ground target point in the geodetic coordinate system, a corresponding fourth formal proposition is constructed, the attribute constraints of which include the cosine value of the geodetic longitude of the ground target point in the geodetic coordinate system being non-zero; based on the higher-order logical expression of the geodetic latitude of the ground target point in the geodetic coordinate system, a corresponding fifth formal proposition is constructed, the attribute constraints of which include the cosine value of the geodetic longitude of the ground target point in the geodetic coordinate system being greater than zero, the range of the geodetic latitude being [-π / 2, π / 2], and the component of the ground target point on the X-axis of the geodetic rectangular coordinate system being greater than zero.

8. An electronic device, wherein, It includes a memory, a processor, and a computer program stored on the memory, wherein the processor executes the computer program to implement the method of any one of claims 1-6.

9. A computer-readable storage medium having computer instructions stored thereon, wherein, When executed by a processor, the computer instructions implement the method of any one of claims 1-6.

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