A method for calibrating the optical axis of a head-up display of a tilt rotor aircraft

Abstract

The present application relates to a kind of head-up display optical axis calibration methods of exempting from flat plane aircraft, belong to the technical field of aircraft optics test.Calibration target terminal is solved and obtained the coordinate conversion relationship between the measurement coordinate system of range finder and angle finder, aircraft coordinate system and electronic target plate coordinate system;With aircraft design parameters, electronic target plate is automatically generated head-up display calibration pattern;Through the calibration camera of installation on flat display mounting bracket, real-time shooting calibration pattern on electronic target plate, calibration target terminal real-time display calibration attitude deviation.Through adjusting flat display mounting bracket, so that the image center of calibration camera shooting and the center of calibration cross in image coincide, the horizontal line and vertical line of calibration cross in image on electronic target plate are respectively parallel to image horizontal direction and vertical direction, realize head-up display optical axis calibration.The present application has the characteristics of high calibration precision, high test efficiency and good versatility compared with traditional calibration equipment.

Description

Technical Field

[0001] This invention relates to a method for calibrating the optical axis of a head-up display (HUD) on a top-down aircraft, belonging to the field of aircraft optical testing technology. Background Technology

[0002] Currently, there are few calibration devices used for aircraft head-up displays (HUDs), the calibration methods are limited, and the equipment structures used are mostly complex, inconvenient to operate, unreliable, and lack versatility. While a target plate device and calibration system have been disclosed to calibrate aircraft HUDs, several problems remain:

[0003] 1. It has low reliability, poor environmental adaptability, requires professional operation guidance and has relatively complex operation methods, resulting in poor human-machine efficiency;

[0004] 2. The calibration equipment is bulky, complex, and has poor versatility, making it unable to meet the needs of multiple models and types of equipment.

[0005] 3. The manual interpretation process involves many steps, introducing numerous human error factors and resulting in low calibration accuracy.

[0006] Therefore, designing a simple and effective head-up display calibration method is of great significance in improving work efficiency, reducing operational difficulty, and facilitating field maintenance. Summary of the Invention

[0007] The technical problem to be solved by this invention is:

[0008] To avoid the shortcomings of the prior art, the present invention provides a method for calibrating the optical axis of a head-up display for a top-down aircraft.

[0009] To solve the above-mentioned technical problems, the technical solution adopted by the present invention is as follows:

[0010] A method for calibrating the optical axis of a head-up display (HUD) on an aircraft without a top-mounted display. The technical solution includes a rangefinder and goniometer, a calibration camera, a calibration terminal, a transfer target ball, and an electronic target plate. The calibration camera is mounted on the HUD adjustment bracket. The calibration method comprises the following steps:

[0011] Step 1: Based on the head-up display (HUD) eye position, HUD optical axis parameters, and target calibration accuracy parameters, construct a virtual target board in the target calibration terminal under the aircraft coordinate system J, and establish a mathematical model of the target calibration pattern (target cross horizontal line, target cross vertical line, and target effective area).

[0012] Step 2: Set up target spheres around the aircraft, with the envelope space formed by the target spheres encompassing the aircraft's calibration reference point. On the right side of the aircraft, select a suitable position to construct a right-side measurement coordinate system R. Use a rangefinder and angle measuring instrument to measure the coordinates of the right-side calibration reference point and the target spheres. On the left side of the aircraft, select a suitable position to construct a left-side measurement coordinate system L. Use a rangefinder and angle measuring instrument to measure the coordinates of the left-side calibration reference point and the target spheres, thus determining the pose relationship between the left-side measurement coordinate system L and the aircraft coordinate system J.

[0013] Step 3: Place the electronic target board at the designated position between the virtual target board and the designed eye position. In the left-side standing position described in Step 2, use a rangefinder and angle measuring instrument to measure the target ball markings on the electronic target board to obtain the pose relationship between the left-side measurement coordinate system L and the target ball coordinate system D. Using the pose relationship between the target ball coordinate system D and the electronic target plate coordinate system B The target calibration terminal calculates the pose relationship between the aircraft coordinate system J and the electronic target plate coordinate system B.

[0014]

[0015] Step 4: The calibration terminal projects the calibration pattern, including the virtual target and the effective target area, onto the electronic target board, establishes a mathematical model of the projection transformation of the calibration pattern on the virtual target board onto the electronic target board, and displays the calibration pattern after projection transformation on the electronic target board.

[0016] Step 5: The calibration camera captures the calibration pattern on the electronic target plate. The calibration terminal calculates the deviation between the pixel coordinates of the midpoint of the crosshairs in the calibration pattern and the pixel coordinates of the image center based on the calibration pattern captured by the calibration camera, and displays the calibration posture deviation. Adjust the position adjustment knob on the mounting bracket so that the center of the image captured by the calibration camera coincides with the center of the crosshairs in the image, and the horizontal and vertical lines of the crosshairs on the electronic target plate in the image are parallel to the horizontal and vertical directions of the image, respectively, completing the calibration process.

[0017] In step one, a mathematical model is established for the target's horizontal crosshair, vertical crosshair, and effective target area in the target calibration pattern. The method for determining this mathematical model is as follows:

[0018] Assuming the eye position is designed as P(x) Jp ,y Jp ,z Jp The angle between the optical axis of the head-up display and the XOZ plane of the aircraft coordinate system. The angle between the projection of the optical axis of the head-up display onto the XOZ plane of the aircraft coordinate system and the x-axis is θ. The distance from the center M of the virtual target calibration pattern to the designed eye position P in the x-axis direction is L. The radius of the effective target area in the calibration pattern is r.

[0019] The mathematical model of the horizontal crosshair of the target on the virtual target plate in the aircraft coordinate system is as follows:

[0020]

[0021] Where π1=[100-x Jp +L],

[0022] The mathematical model of the vertical crosshair of the target on the virtual target plate in the aircraft coordinate system is as follows:

[0023]

[0024] Where π1=[100-x Jp +L],π3=[11 / tanθ0-x Jp -z Jp / tanθ.

[0025] The mathematical model of the target area on the virtual target plate in the aircraft coordinate system is as follows:

[0026]

[0027] Where π1=[100-x Jp +L],

[0028]

[0029] In step two, the pose relationship between the left-side measurement coordinate system L and the aircraft coordinate system J is determined using the following method:

[0030] Based on the coordinates of the target ball measured in the left measurement coordinate system L and the right measurement coordinate system R, the pose relationship between the left measurement coordinate system L and the right measurement coordinate system R can be obtained. use The coordinates of the right-side aircraft target calibration reference point measured in the right-side measurement coordinate system R can be transformed to the coordinates of the aircraft target calibration reference point in the left-side measurement coordinate system L. Using the coordinates of the aircraft target calibration reference point in the left-side measurement coordinate system L and the aircraft coordinate system J, the pose relationship between the left-side measurement coordinate system L and the aircraft coordinate system J can be obtained.

[0031] In step three, the electronic target plate is placed at a designated position between the virtual target plate and the designed eye position. The method for determining this designated position is as follows:

[0032] Assume the equation of the optical axis of the aircraft display is as follows:

[0033] P' = P + p l tt∈R(4)

[0034] Where P = (xp ,y p ,z p ) T To design eye position coordinates, p l =(x l ,y l ,z l ) T The direction vector of the axis

[0035] Assume the electron target is to be placed at the front x of the receiver. u If the target plane is perpendicular to the aircraft axis, then the plane of the electron target plate in the aircraft coordinate system can be represented as:

[0036] x = -x u (5)

[0037] The coordinates of the intersection of the display optical axis and the electron target surface in the aircraft coordinate system can be obtained using equations (4) and (5).

[0038]

[0039] Using the pose relationship between the left-side measurement coordinate system L and the aircraft coordinate system J The coordinates p of the intersection of the display's optical axis and the target plate in the left-side measurement coordinate system can be obtained. L0 =(x L0 ,y L0 ,z L0 ) T .

[0040]

[0041] The spherical coordinates (r, pitch, yaw) of the intersection point in the coordinate system of the distance measuring and goniometer can be obtained using equation (7).

[0042]

[0043] The rangefinder, pitch angle, and azimuth angle are set using the (r, pitch, yaw) parameters. A laser is then emitted to guide the placement of the electronic target plate, so that the laser spot falls on the center area of ​​the electronic target plate.

[0044] In step three, the pose relationship between the target ball coordinate system and the electronic target plate display coordinate system is utilized. The pose relationship between the target ball coordinate system and the electronic target plate display coordinate system is fixed but not variable, and can be obtained through pre-calibration.

[0045] In step four, the calibration terminal projects the calibration pattern, including the virtual target and the effective target area, onto the electronic target plate, establishing a mathematical model of the projection transformation of the calibration pattern on the virtual target plate onto the electronic target plate. The method for determining this model is as follows:

[0046] Step one has yielded a mathematical model of the crosshairs on the virtual target plate and the effective area of ​​the target in the aircraft coordinate system.

[0047] The horizontal crosshair on the virtual target plate is represented in the aircraft coordinate system J as follows:

[0048]

[0049] The vertical crosshairs on the virtual target plate are represented in the aircraft coordinate system J as follows:

[0050]

[0051] The effective area of ​​the target is represented in the aircraft coordinate system J as follows:

[0052]

[0053] Step three has yielded the pose relationship between the aircraft coordinate system J and the electronic target plate coordinate system B. Then we have:

[0054]

[0055] The projection of the virtual target pattern (target crosshairs, effective target area) onto the electronic target plate is mathematically modeled as follows:

[0056] Substituting formula (11) into formula (8), we can obtain the representation of the horizontal crosshair of the calibration pattern on the electronic target plate in the electronic target plate coordinate system B:

[0057]

[0058] Substituting formula (11) into formula (9), we can obtain the representation of the vertical crosshairs of the calibration pattern on the electronic target plate in the electronic target plate coordinate system B:

[0059]

[0060] Substituting formula (11) into formula (10), we can obtain the effective area of ​​the target pattern on the electronic target plate in the electronic target plate coordinate system B:

[0061]

[0062] The beneficial effects of this invention are as follows:

[0063] This invention provides a method for calibrating the optical axis of a head-up display (HUD) on an aircraft without requiring a top-mounted display. The method involves measuring multiple marked points on a target sphere, the aircraft, and an electronic target board using a rangefinder and angle measuring instrument. The calibration terminal calculates the coordinate transformation relationship between the measurement coordinate system of the rangefinder and angle measuring instrument, the aircraft coordinate system, and the electronic target board coordinate system. Combined with aircraft design parameters, the electronic target board automatically generates calibration patterns such as the HUD calibration crosshairs and the effective target area. A calibration camera mounted on the HUD mounting bracket captures these calibration patterns on the electronic target board in real time, and the calibration terminal displays the calibration attitude deviation in real time. By adjusting the HUD mounting bracket, the center of the image captured by the calibration camera coincides with the center of the calibration crosshairs in the image. The horizontal and vertical lines of the calibration crosshairs on the electronic target board are parallel to the horizontal and vertical directions of the image, respectively, thus achieving HUD optical axis calibration. This invention eliminates the need for a top-mounted aircraft and has no strict limitations on the aircraft's landing state. Compared to traditional calibration equipment, this invention features high calibration accuracy, high testing efficiency, and good versatility. Attached Figure Description

[0064] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0065] Figure 1 This is a schematic diagram of the optical axis calibration process of the aircraft head-up display in Embodiment 1 of the present invention.

[0066] Figure 2 This is a schematic diagram of the calibration screen of the target calibration terminal during the calibration process in Embodiment 1 of the present invention. Detailed Implementation

[0067] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0068] A method for calibrating the optical axis of a head-up display (HUD) on an aircraft without a top-mounted display includes a rangefinder and angle measuring instrument 1, a calibration camera 2, a calibration terminal 3, a transfer station target ball 4, and an electronic target plate 5. The calibration camera 2 is mounted on the HUD adjustment bracket. The calibration method includes the following steps:

[0069] Step 1: Based on the head-up display (HUD) eye position, HUD optical axis parameters, and target calibration accuracy parameters, the target calibration terminal 3 constructs a virtual target board in the aircraft coordinate system J, and establishes a mathematical model of the target calibration pattern (target cross horizontal line, target cross vertical line, and target effective area).

[0070] Assuming the eye position is designed as P(x) Jp ,yJp ,z Jp The angle between the optical axis of the head-up display and the XOZ plane of the aircraft coordinate system. The angle between the projection of the optical axis of the head-up display onto the XOZ plane of the aircraft coordinate system and the x-axis is θ. The distance from the center M of the virtual target calibration pattern to the designed eye position P in the x-axis direction is L. The radius of the effective target area in the calibration pattern is r.

[0071] The mathematical model of the horizontal crosshair of the target on the virtual target plate in the aircraft coordinate system is as follows:

[0072]

[0073] Where π1=[100-x Jp +L],

[0074] The mathematical model of the vertical crosshair of the target on the virtual target plate in the aircraft coordinate system is as follows:

[0075]

[0076] Where π1=[100-x Jp +L],π3=[11 / tanθ0-x Jp -z Jp / tanθ.

[0077] The mathematical model of the target area on the virtual target plate in the aircraft coordinate system is as follows:

[0078]

[0079] Where π1=[100-x Jp +L],

[0080]

[0081] Step 2: Set up a transfer target sphere 4 around the aircraft. The envelope space formed by the transfer target sphere 4 covers the aircraft's calibration reference point. Select a suitable position on the right side of the aircraft to construct a right-side measurement coordinate system R. Use a rangefinder and angle measuring instrument 1 to measure the coordinates of the right-side calibration reference point and the transfer target sphere. Select a suitable position on the left side of the aircraft to construct a left-side measurement coordinate system L. Use the rangefinder and angle measuring instrument 1 to measure the coordinates of the left-side calibration reference point and the transfer target sphere. Based on the coordinates of the transfer target sphere measured in the left-side measurement coordinate system L and the right-side measurement coordinate system R, the calibration terminal 3 can obtain the pose relationship between the left-side measurement coordinate system L and the right-side measurement coordinate system R. use The coordinates of the right-side aircraft target calibration reference point measured in the right-side measurement coordinate system R can be transformed to the coordinates of the aircraft target calibration reference point in the left-side measurement coordinate system L. Using the coordinates of the aircraft target calibration reference point in the left-side measurement coordinate system L and the aircraft coordinate system J, the pose relationship between the left-side measurement coordinate system L and the aircraft coordinate system J can be obtained.

[0082] Step 3: Place the electronic target board at the designated position between the virtual target board and the designed eye position. In the left-side standing position described in Step 2, use the rangefinder 1 to measure the target ball marker on the electronic target board 5 to obtain the pose relationship between the left-side measurement coordinate system L and the target ball coordinate system D. Using the pose relationship between the target ball coordinate system D and the electronic target plate coordinate system B The target calibration terminal calculates the pose relationship between the aircraft coordinate system J and the electronic target plate coordinate system B.

[0083]

[0084] Assume the equation of the optical axis of the aircraft display is as follows:

[0085] P' = P + p l tt∈R(4)

[0086] Where P = (x p ,y p ,z p ) T To design eye position coordinates, p l =(x l ,y l ,z l ) T is the direction vector of the axis.

[0087] Assume the electron target is to be placed at the front x of the receiver. u If the target plane is perpendicular to the aircraft axis, then the plane of the electron target plate in the aircraft coordinate system can be represented as:

[0088] x = -x u (5)

[0089] The coordinates of the intersection of the display optical axis and the electron target surface in the aircraft coordinate system can be obtained using equations (4) and (5).

[0090]

[0091] Using the pose relationship between the left-side measurement coordinate system L and the aircraft coordinate system J The coordinates p of the intersection of the display's optical axis and the target plate in the left-side measurement coordinate system can be obtained. L0 =(x L0 ,y L0 ,zL0 ) T .

[0092]

[0093] The spherical coordinates (r, pitch, yaw) of the intersection point in the coordinate system of the distance measuring and goniometer can be obtained using equation (7).

[0094]

[0095] By using the (r, pitch, yaw) parameters to set the slant distance, pitch angle, and azimuth angle of the rangefinder and angle measuring instrument, a laser is emitted to guide the placement of the electronic target plate, so that the laser spot falls on the center area of ​​the electronic target plate, thus meeting the placement requirements of the electronic target plate.

[0096] Step 4: The target calibration terminal 3 projects the virtual target, the effective target area, and other calibration patterns onto the electronic target board, establishes a mathematical model of the projection transformation of the calibration patterns on the virtual target board onto the electronic target board, and the electronic target board 5 displays the calibration patterns after projection transformation.

[0097] Step one has yielded a mathematical model of the crosshairs on the virtual target plate and the effective area of ​​the target in the aircraft coordinate system.

[0098] The horizontal crosshair on the virtual target plate is represented in the aircraft coordinate system J as follows:

[0099]

[0100] The vertical crosshairs on the virtual target plate are represented in the aircraft coordinate system J as follows:

[0101]

[0102] The effective area of ​​the target is represented in the aircraft coordinate system J as follows:

[0103]

[0104] Step three has yielded the pose relationship between the aircraft coordinate system J and the electronic target plate coordinate system B. Then we have:

[0105]

[0106] The projection of the virtual target pattern (target crosshairs, effective target area) onto the electronic target plate is mathematically modeled as follows:

[0107] Substituting formula (11) into formula (8), we can obtain the representation of the horizontal crosshair of the calibration pattern on the electronic target plate in the electronic target plate coordinate system B:

[0108]

[0109] Substituting formula (11) into formula (9), we can obtain the representation of the vertical crosshairs of the calibration pattern on the electronic target plate in the electronic target plate coordinate system B:

[0110]

[0111] Substituting formula (11) into formula (10), we can obtain the effective area of ​​the target pattern on the electronic target plate in the electronic target plate coordinate system B:

[0112]

[0113] Step 5: The calibration camera 2 captures the calibration pattern on the electronic target plate 5. The calibration terminal 3 calculates the deviation between the pixel coordinates of the midpoint of the crosshairs in the calibration pattern and the pixel coordinates of the image center based on the calibration pattern captured by the calibration camera 2, and displays the calibration posture deviation. Adjust the position adjustment knob on the mounting bracket so that the center of the image captured by the calibration camera coincides with the center of the calibration crosshairs in the image, and the horizontal and vertical lines of the calibration crosshairs on the electronic target plate 5 in the image are parallel to the horizontal and vertical directions of the image, respectively, completing the calibration process.

[0114] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any person skilled in the art can easily conceive of various equivalent modifications or substitutions within the scope of the technology disclosed in the present invention, and such modifications or substitutions should all be covered within the scope of protection of the present invention.

Claims

1. A method for calibrating the optical axis of a head-up display (HUD) in a top-down aircraft, characterized in that, include: Step 1: Based on the head-up display (HUD) eye position, HUD optical axis parameters, and target calibration accuracy parameters, the target calibration terminal constructs a virtual target board and establishes a mathematical model of the target calibration pattern in the aircraft coordinate system; the target calibration pattern includes the target crosshair horizontal line, the target crosshair vertical line, and the effective target area; Step 2: Set up target spheres around the aircraft, with the envelope space formed by the target spheres covering the aircraft's calibration reference points; construct a right-side measurement coordinate system on the right side of the aircraft. The rangefinder and angle measuring instrument measures the coordinates of the target reference point on the right side of the aircraft and the target ball at the transfer station; a left-side measurement coordinate system is constructed on the left side of the aircraft. The rangefinder and angle measuring instrument measures the coordinates of the target reference point on the left side of the aircraft and the target ball at the transfer station to determine the left-side measurement coordinate system. and aircraft coordinate system pose relationship between ; Step 3: Place the electronic target board at the designated position between the virtual target board and the designed eye position. From the left-side standing position described in Step 2, use a rangefinder and angle measuring instrument to measure the target ball marker on the electronic target board to obtain the left-side measurement coordinate system. With the target ball coordinate system pose relationship between Using the target sphere coordinate system Coordinate system with electron target plate pose relationship between The target calibration terminal calculates the aircraft coordinate system. Coordinate system with electron target plate pose relationship between ; Step 4: The target calibration terminal projects the target calibration pattern onto the electronic target board, establishes a mathematical model of the projection transformation of the target calibration pattern on the virtual target board onto the electronic target board, and the electronic target board displays the target calibration pattern after projection transformation. Step 5: The calibration camera captures the calibration pattern on the electronic target plate. The calibration terminal calculates the deviation between the pixel coordinates of the midpoint of the crosshairs in the calibration pattern and the pixel coordinates of the image center based on the calibration pattern captured by the calibration camera, and displays the calibration posture deviation. Adjust the position adjustment knob on the mounting bracket so that the center of the image captured by the calibration camera coincides with the center of the crosshairs in the image. The horizontal and vertical lines of the crosshairs on the electronic target plate in the image are parallel to the horizontal and vertical directions of the image, respectively, completing the calibration process.

2. The method for calibrating the optical axis of a head-up display in a top-down aircraft according to claim 1, characterized in that, In step one, a mathematical model is established for the target's horizontal crosshair, vertical crosshair, and effective target area in the target calibration pattern. The method for determining this mathematical model is as follows: Assuming eye position design The optical axis of the head-up display relative to the aircraft coordinate system Plane angle The optical axis of the head-up display in the aircraft coordinate system Plane projection and Axis angle Virtual target board calibration pattern center exist Axial distance design eye position for The effective radius of the target area in the calibration pattern is ; The mathematical model of the horizontal crosshair of the target on the virtual target plate in the aircraft coordinate system is as follows: (1) in, , ; The mathematical model of the vertical crosshair of the target on the virtual target plate in the aircraft coordinate system is as follows: (2) in, , ; The mathematical model of the target area on the virtual target plate in the aircraft coordinate system is as follows: (3) in, , 。 3. The method for calibrating the optical axis of a head-up display in a top-down aircraft according to claim 1, characterized in that, In step two, the left-side measurement coordinate system is determined. and aircraft coordinate system The pose relationship between them is determined by the following method: According to the measurement coordinate system on the left and the right-side measurement coordinate system The coordinates of the target ball at the lower station can be used to obtain the left-side measurement coordinate system. and the right-side measurement coordinate system Pose relationship between ,use The right-side measurement coordinate system can be The coordinates of the right-side aircraft target calibration reference point measured below are transformed to the left-side measurement coordinate system. The coordinates of the aircraft target calibration reference point are used; the coordinate system is measured on the left side using the aircraft target calibration reference point. Lower coordinates and in the aircraft coordinate system The coordinates below can be used to obtain the measurement coordinate system on the left. With the aircraft coordinate system pose relationship between .

4. The method for calibrating the optical axis of a head-up display in a top-down aircraft according to claim 1, characterized in that, In step three, the electronic target plate is placed at a designated position between the virtual target plate and the designed eye position. The method for determining this designated position is as follows: Assume the equation of the optical axis of the aircraft display is as follows: (4) in To design eye position coordinates, The direction vector of the axis Assuming the electron target is to be placed in front of the receiver head. If the target plane is perpendicular to the aircraft axis, then the plane of the electron target plate in the aircraft coordinate system can be represented as: (5) The coordinates of the intersection of the display optical axis and the electron target surface in the aircraft coordinate system can be obtained using equations (4) and (5). ; Using the left-side coordinate system With the aircraft coordinate system pose relationship between This allows us to obtain the coordinates of the intersection point of the display's optical axis and the target plate in the left-side measurement coordinate system. ; (6) The spherical coordinates of the intersection point in the coordinate system of the distance measuring and goniometer can be obtained using equation (7). ; (7) use The parameters of the rangefinder and angle measuring instrument are set to slope distance, elevation angle, and azimuth angle. A laser is emitted to guide the placement of the electronic target plate so that the laser spot falls on the center area of ​​the electronic target plate.

5. The method for calibrating the optical axis of a head-up display (HUD) in a top-down aircraft according to claim 1, characterized in that, In step three, the pose relationship between the target ball coordinate system and the electronic target plate display coordinate system is utilized. The pose relationship between the target ball coordinate system and the electronic target plate display coordinate system is fixed but not variable, and can be obtained through pre-calibration.

6. The method for calibrating the optical axis of a head-up display in a top-down aircraft according to claim 2, characterized in that, In step four, the calibration terminal projects the calibration pattern, including the virtual target and the effective target area, onto the electronic target plate, establishing a mathematical model for the projection transformation of the calibration pattern on the virtual target plate onto the electronic target plate; the method for determining this model is as follows: Step one has obtained a mathematical model of the crosshairs on the virtual target board and the effective area of ​​the target in the aircraft coordinate system; The horizontal crosshair on the virtual target plate in the aircraft coordinate system The following is represented as: (8) The vertical crosshairs on the virtual target plate in the aircraft coordinate system The following is represented as (9) The effective area of ​​the target in the aircraft coordinate system The following is represented as: (10) The aircraft coordinate system has been obtained in step three. Coordinate system with electron target plate pose relationship between Then we have: (11) The mathematical model for the projection transformation of the virtual target pattern onto the electronic target is as follows: Substituting formula (11) into formula (8), we can obtain the horizontal crosshair of the calibration pattern on the electronic target plate in the electronic target plate coordinate system. The following indicates: (12) Substituting formula (11) into formula (9), we can obtain the vertical crosshairs of the calibration pattern on the electronic target plate in the electronic target plate coordinate system. The following indicates: (13) Substituting formula (11) into formula (10), we can obtain the effective area of ​​the target pattern on the electronic target plate in the electronic target plate coordinate system. The following indicates: 。

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