CN112629342B - Method for measuring attitude angle of projectile body - Google Patents
Method for measuring attitude angle of projectile body Download PDFInfo
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- F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
- F42—AMMUNITION; BLASTING
- F42B—EXPLOSIVE CHARGES, e.g. FOR BLASTING, FIREWORKS, AMMUNITION
- F42B35/00—Testing or checking of ammunition
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- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/002—Measuring arrangements characterised by the use of optical techniques for measuring two or more coordinates
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01B—MEASURING LENGTH, THICKNESS OR SIMILAR LINEAR DIMENSIONS; MEASURING ANGLES; MEASURING AREAS; MEASURING IRREGULARITIES OF SURFACES OR CONTOURS
- G01B11/00—Measuring arrangements characterised by the use of optical techniques
- G01B11/26—Measuring arrangements characterised by the use of optical techniques for measuring angles or tapers; for testing the alignment of axes
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
- G01C11/00—Photogrammetry or videogrammetry, e.g. stereogrammetry; Photographic surveying
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Abstract
The application discloses a method for measuring an attitude angle of an projectile body, which comprises the following steps: establishing an image coordinate system and an earth coordinate system of an projectile striking a target plate; calculating a mapping attitude angle of the projectile body; wherein the mapping attitude angle is an angle of an elastomer in an earth coordinate system, which is mapped to the image coordinate system; obtaining a mapping coordinate system according to the earth coordinate system, and calculating the angle of the mapping coordinate system in an image coordinate system; wherein the mapping coordinate system angle is an angle of the mapping coordinate system in the image coordinate system; calculating a mapping coefficient according to the mapping coordinate system angle; wherein the mapping coefficient represents a relationship between a mapping coordinate system angle and the earth coordinate system; and calculating the attitude angle of the projectile body in the earth coordinate system through the mapping coefficient and the mapping attitude angle. The application can efficiently and accurately measure the attitude angle of the projectile body in the high-speed flight process of the projectile body.
Description
Technical Field
The application relates to a measuring technology of an impact attitude of an projectile in a high-speed dynamic impact event, in particular to a measuring method of an attitude angle of the projectile.
Background
In the case of performing a high-speed impact test, it is not possible to accurately ensure that the projectile impacts the target plate in a posture that is completely consistent with the expectation, and therefore the attitude angle of the projectile must be determined. During the test, the attitude of the projectile body when striking the target cannot be determined by visual observation or conventional test means due to the high projectile body speed (100-1000 m/s).
On the one hand, the prior test technology has larger measurement error, the three-dimensional posture of the bullet cannot be determined, on the other hand, the measurement device is complex, the processing mode is complex, the measurement efficiency is low, the period is long, and the cost is high.
Disclosure of Invention
The application mainly aims to provide an elastomer attitude angle measuring method for solving the problems in the prior art, wherein:
the embodiment of the application provides a method for measuring an attitude angle of an projectile body, which comprises the following steps: establishing an image coordinate system and an earth coordinate system of an projectile striking a target plate; calculating a mapping attitude angle of the projectile body; wherein the mapping attitude angle is an angle of an elastomer in an earth coordinate system, which is mapped to the image coordinate system; obtaining a mapping coordinate system according to the earth coordinate system, and calculating the angle of the mapping coordinate system in an image coordinate system; wherein the mapping coordinate system angle is an angle of the mapping coordinate system in the image coordinate system; calculating a mapping coefficient according to the mapping coordinate system angle; wherein the mapping coefficient represents a relationship between a mapping coordinate system angle and the earth coordinate system; and calculating the attitude angle of the projectile body in the earth coordinate system through the mapping coefficient and the mapping attitude angle.
The step of establishing an image coordinate system and an earth coordinate system of the projectile striking the target plate comprises the following steps: acquiring an image of an impact of a projectile body on a target plate, and establishing an image coordinate system according to the image; establishing an earth coordinate system Oxyz by taking a boundary line of the target plate as a reference line as x and y axes and taking a straight line perpendicular to the target plate as a z axis; and acquiring two edge reference lines of the projectile body in the image coordinate system, and translating the two edge reference lines into the earth coordinate system to respectively obtain a first line segment and a second line segment.
Wherein the attitude angle includes a pitch angle and a yaw angle, and in the case where the attitude angle is the pitch angle, the method further includes: calculating a mapping pitch angle of the projectile body; wherein, the included angle between the first line segment and Oz is the mapping pitch angle; obtaining a first mapping coordinate system xOz according to the earth coordinate system, and calculating a first mapping coordinate system angle; wherein the first mapping coordinate system angle is the angle of the first mapping coordinate system xOz in the image coordinate system; calculating a first mapping coefficient according to the first mapping coordinate system angle, wherein the first mapping coefficient represents the relation between the first mapping coordinate system angle and the earth coordinate system; and calculating the pitch angle of the projectile body in the earth coordinate system through the first mapping coefficient and the mapping pitch angle.
Wherein the method further comprises: and calculating the slopes of the line segments OA, oz and Ox, and calculating the mapping pitch angle and the angle value of the first mapping coordinate system according to the slopes.
Wherein the first mapping coefficient f is calculated by the following formula α ：
Wherein the attitude angle includes a pitch angle and a yaw angle, and in the case where the attitude angle is the yaw angle, the method further includes: calculating a mapping deflection angle of the projectile body; wherein, the included angle between the second line segment and Oy is the mapping deflection angle; obtaining a second mapping coordinate system yOz according to the earth coordinate system Oxyz, and calculating a second mapping coordinate system angle; wherein the second mapping coordinate system angle is the angle of the second mapping coordinate system yOz in the image coordinate system; calculating a second mapping coefficient according to the second mapping coordinate system angle, wherein the second mapping coefficient represents the relationship between the second mapping coordinate system angle and the earth coordinate system; and calculating the deflection angle of the projectile body in the earth coordinate system through the second mapping coefficient and the mapping deflection angle.
Wherein the method further comprises: and calculating the slopes of the line segments OC, oz and Ox, and calculating the mapping deflection angle and the angle value of the second mapping coordinate system according to the slopes.
Wherein the second mapping coefficient f is calculated by the following formula β ：
Wherein in the earth coordinate systemAcquiring a reference line OY and a reference line O parallel to OY 1 Y 1 Will reference lines OY and O 1 Y 1 Translating to the image coordinate system to obtain O 'Y' and O 1 'Y 1 'A'; wherein, the included angle between PM and O 'Y' is the perspective angle, P is O 'Y' and O 1 'Y 1 ' intersecting perspective points, M being the midpoint of the projectile body front; calculating the perspective angle according to the slopes of the PM and O 'Y'; correcting errors of deflection angles in the earth coordinate system according to the perspective angle.
Based on the high-speed camera imaging principle, the precise attitude angle is calculated through the geometric relationship of the measured projectile body, the attitude angle of the projectile body can be efficiently and precisely measured in the high-speed flight process of the projectile body, and the method has the specific points with large measuring range and high precision.
Drawings
The accompanying drawings, which are included to provide a further understanding of the application and are incorporated in and constitute a part of this specification, illustrate embodiments of the application and together with the description serve to explain the application and do not constitute a limitation on the application. In the drawings:
FIG. 1A is a schematic illustration of relative motion relationship and coordinate system of a projectile and target plate according to an embodiment of the application;
FIG. 1B is a schematic view of a pitch angle α defining an attitude angle of an projectile in an earth coordinate system according to an embodiment of the application;
FIG. 1C is a schematic illustration of a yaw angle β defining an attitude angle of an projectile in an earth coordinate system according to an embodiment of the application;
FIG. 2 is a flow chart of a method of measuring an attitude angle of an projectile in accordance with an embodiment of the application;
FIGS. 3A-3C are schematic diagrams of the relative position of the attitude angle of an projectile body with respect to the earth coordinate system Oxyz in the coordinate system ηζ according to embodiments of the application;
fig. 4A and 4B are schematic diagrams of the earth coordinate system and the image perspective conversion relationship according to the embodiment of the present application.
Detailed Description
In order to make the objects, technical solutions and advantages of the present application more apparent, the technical solutions of the present application will be clearly and completely described below with reference to specific embodiments of the present application and corresponding drawings. It will be apparent that the described embodiments are only some, but not all, embodiments of the application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
The following describes in detail the technical solutions provided by the embodiments of the present application with reference to the accompanying drawings.
In the event of an impact, the projectile impacts the target plate as shown in fig. 1A, with the projectile velocity perpendicular to the target plate, and the projectile attitude in the ideal case with a rectangular edge being perpendicular to the target plate impact (the projectile leading edge face being parallel to the target plate face, i.e., α=β=0° in the case of a projectile fully perpendicular to the impact target plate). In the actual test process, ideal conditions cannot be achieved, so that the attitude angle of the projectile body in the test needs to be calculated. Before the gesture angle definition, a corresponding coordinate system needs to be established. Defining an earth coordinate system as: xyz (actual coordinate system in the experiment), the image coordinate system is: ηζ (two-dimensional coordinate system of picture acquired by camera). The projectile has the attitude as in fig. 1B and 1C when flying and striking the target plate, and the pitch angle of the attitude angle of the projectile under the earth coordinate system in the test is defined as alpha (in the xz plane coordinate system), the deflection angle is beta (in the yz plane coordinate system), namely the projectile has the impact attitude of the target plate which is not vertical (alpha not equal to 0 DEG and beta not equal to 0 DEG).
Before describing the present application in detail, some terms related to the present application are explained, and an earth coordinate system (Oxyz) refers to a real coordinate system in reality, and uses the earth as a reference system to determine the spatial position and posture of an object, which is a three-dimensional coordinate system and uses the length as a unit. The image coordinate system (ηζ) refers to a coordinate system established by the image plane for determining the pixel positions, which is a two-dimensional coordinate system, in which the image is established by image processing software with a single pixel size as a unit length. Projection scaling (mapping principle) refers to the formation of a two-dimensional geometry of a three-dimensional geometry in a two-dimensional plane by projection, which reduces or enlarges the angle of the three-dimensional object to some extent in proportion to the angle of the two-dimensional object. The imaging view angle (perspective principle) means that due to the camera imaging principle, perspective effect exists between a distant view and a close view, and perspective causes two parallel straight lines to have an intersection point at a distance (similar to shooting a train rail), and in reality (an earth coordinate system), the two straight lines are parallel, but an included angle is formed in a picture, and the included angle is called a perspective angle.
According to the method, the actual attitude angle of the projectile body is calculated through the camera image. In the image shot by the camera, the shape and the relative position relation of the image are greatly different from the reality due to the projection scaling (mapping principle) and the imaging view angle (perspective principle) of the object in the actual earth coordinate system caused by the imaging principle, namely, two problems of mapping and perspective exist in the transformation of the shot image and the real object. Therefore, the geometrical relation of the relative positions of the objects in the image needs to be restored to the real coordinates by eliminating mapping and perspective problems so as to obtain the real attitude angle of the projectile body.
According to an embodiment of the present application, a method for measuring an attitude angle of an projectile is provided, which may also be referred to as a calculation method or a determination method of an attitude angle of an projectile, as shown in fig. 2, and the method at least includes the following steps:
step S202, establishing an image coordinate system and an earth coordinate system of an elastomer impacting a target plate;
step S204, calculating a mapping attitude angle of the projectile body; wherein the mapped attitude angle is an angle at which an attitude angle of an elastomer in an earth coordinate system is mapped to the image coordinate system.
Step S206, obtaining a mapping coordinate system according to the earth coordinate system, and calculating the angle of the mapping coordinate system in an image coordinate system; wherein the mapping coordinate system angle is an angle of the mapping coordinate system in the image coordinate system;
step S208, calculating a mapping coefficient according to the mapping coordinate system angle; wherein the mapping coefficient represents a relationship between a mapping coordinate system angle and the earth coordinate system;
step S210, calculating the attitude angle of the projectile body in the earth coordinate system through the mapping coefficient and the mapping attitude angle.
In the embodiment of the present application, the attitude angle of the projectile includes a pitch angle and a yaw angle, and details of calculating the pitch angle of the projectile are described below first.
Fig. 3A shows the relative positional relationship (α+.0° or β+.0°) of the projectile and the target plate in the case where the projectile is inclined (not vertical) to strike the target plate based on the position of the projectile in fig. 1. And selecting straight lines Ox and Oy which are parallel to an edge reference line (the edge reference line is perpendicular) in the target plate surface in the image coordinate system eta xi as x and y axes of the earth coordinate system, and selecting a straight line Oz which is perpendicular to the target plate surface (taking the edge reference line which is perpendicular to the target plate surface as a reference) as a z axis to obtain the earth coordinate system Oxyz. Edge reference lines of the projectile are selected in the image coordinate system, defined as A 'B' and C 'D'. And translating the A 'B' and the C 'D' into the Oxyz, so that the B 'point and the D' point coincide with the O point, and respectively obtaining AO and CO straight lines. It should be noted that the projectile and target plate of the present application have straight characteristic edges, such as having straight segments or being capable of projecting straight segments.
After the earth coordinate system is established, two mapping coordinate systems, namely a first mapping coordinate system xOz and a second mapping coordinate system yOz, are obtained according to the earth coordinate system Oxyz. Referring to fig. 3B, the angle (α') between AO and Oz is set as the mapped pitch angle of the projectile in the image coordinate system ηζ, and the angle (α) of the mapped coordinate system xOz (first mapped coordinate system) in the image coordinate system ηζ is set xOz ) Is the first mapping coordinate system angle. As shown in fig. 3A, the starting point O coordinates of the line segments OA, oz, and Ox in the image coordinate system are obtained in the image coordinate system ηζ as (η) O ，ξ O ) Wherein eta O And xi O Are three-dimensional column vectors (the values of each column vector are the same), and the end point coordinates are respectively ([ eta ] A ，η z ，η x ] T ，[ξ A ，ξ z ，ξ x ] T ). The slopes [ k ] of AO, oz and Ox can thus be obtained by the following slope formula (1) OA ，k Oz ，k Ox ] T ：
Δη in equation (1) α And delta xi α Substituting the coordinate values of the starting point and the end point into the formula (2) to obtain:
wherein E is an identity matrix, deltaeta α Is a 3 x 3 matrix, delta zeta α Is a 1 x 3 column vector.
After the slope is calculated by the formula (1), the mapping pitch angle alpha' and the mapping coordinate system angle alpha are calculated by the following included angle formula (3) xOz Value:
since the actual included angle of the selected coordinate system xOz in the earth coordinate system is 90 DEG, the angle alpha of the mapping coordinate system is defined xOz The mapping relation with the earth coordinate system is formed by a mapping coefficient f α And (3) determining:
calculating the pitch angle alpha of the projectile in the earth coordinate system through the mapping coefficient of the coordinate system xOz:
α＝f α α' (5)
the pixel coordinate values of each point are obtained through the coordinate system eta xi, and the pitch angle alpha of the projectile body under the earth coordinate system can be obtained through formulas (1) - (5).
Specific details of calculating the deflection angle β of the projectile are described below. Referring to fig. 3C, an included angle β 'between CO and Oy is set as a mapped deflection angle β' of the projectile in the image coordinate system ηζ, and an angle (β) of the mapped coordinate system yOz (second mapped coordinate system) in the image coordinate system ηζ is set yOz ) Is the second mapping coordinate system angle. Obtaining the starting point O coordinates of the line segments OC, oz and Oy under the image coordinate system as (eta) from the image coordinate system O ，ξ O ) Wherein eta O And xi O Are three-dimensional column vectors (the values of each column vector are the same), and the end point coordinates are respectively ([ eta ] C ，η z ，η y ] T ，[ξ C ，ξ z ，ξ y ] T ). The slopes [ k ] of OC, oz and Oy can thus be calculated by slope formula (6) OC ，k Oz ，k Oy ] T ：
Δη in equation (6) β And delta xi β Substituting the coordinate values of the starting point and the end point into a formula (7) to obtain:
wherein E is an identity matrix, deltaeta β Is a 3 x 3 matrix, delta zeta β Is a 1 x 3 column vector.
After the slope is calculated by the formula (6), the mapping deflection angle beta' and the mapping coordinate system angle beta are calculated by the following included angle formula (8) yOz Value:
since the actual included angle of the selected coordinate system yOz in the earth coordinate system is 90 DEG, and beta' is beta yOz Within the complementary angle of (2), thus define beta yOz The mapping coefficient with the earth coordinate system is f β ：
Similarly, the deflection angle beta of the projectile body in the earth coordinate system is calculated through the mapping coefficient of the mapping coordinate system yOz:
β＝f β β' (10)
the pixel coordinate values of each point are obtained through the coordinate system eta xi, and the deflection angle beta of the projectile body under the earth coordinate system can be obtained through formulas (6) - (10).
In the shooting process of the camera, the angle and the position of the camera can be adjusted, the Oz straight line is adjusted to be a horizontal straight line in the coordinate system eta zeta, and the processing method is convenient for simplifying the calculation process. Therefore, according to the imaging principle of the image capturing view angle, there is no perspective error in the included angle of the horizontal direction (Oz direction), that is, two parallel straight lines parallel to the horizontal direction are still parallel in the earth coordinate system. So that the pitch angle alpha calculated by the above method has no perspective error. Whereas the deflection angle is obtained with reference to the vertical line Oy, so that there may be a perspective error.
Referring to fig. 4A and 4B, in the earth coordinate system, O is set for a deflection angle β between CD and OY 1 Y 1 Is a reference line segment parallel to OY. CD. OY and O 1 Y 1 In the image coordinate system C 'D', O 'Y' and O 1 'Y 1 '. The perspective view point of the shooting visual angle is set as a point P (two parallel straight lines are converged at the point P after shooting and imaging), M is set as the middle point of the front end of the projectile body, and an included angle between the characteristic reference line PM and O 'Y' is defined as a perspective angle gamma. Beta' is the deflection angle of the projectile in the coordinate system eta < xi > after the perspective is eliminated.
Obtaining O 'Y' and O from an image coordinate system 1 'Y 1 ' origin coordinates:and endpoint coordinates: />
O 'Y' and O are calculated by the formula (11) 1 'Y 1 ' slope of
O 'Y' and O are calculated by the formula (12) 1 'Y 1 Intercept of'
Position coordinates (η) of perspective point P P ,ξ P ) Can be calculated by formulas (11) and (12):
up to this point P (eta) P ,ξ P ) And M (eta) M ,ξ M ) The slope k of the straight lines PM and O 'Y' is calculated from the slope formula with known point coordinate values PM And k O'Y' . Thereby obtaining a perspective angle γ:
the geometry according to fig. 4A and 4B yields the deflection angle β″ of the projectile after elimination of perspective errors:
taking perspective errors into consideration, the beta 'of the formula (10) must be calculated by using the deflection angle beta' after the perspective errors are eliminated, namely, the beta 'of the formula (10) is replaced by the beta' to obtain the actual deflection angle beta of the projectile body:
β＝f β (β'-γ) (16)
so far, through the coordinate values of the projectile body and the reference line of the target plate in the image, the pitch angle and the deflection angle of the attitude angle of the projectile body under the earth coordinate system are calculated. Wherein the pitch angle alpha can be calculated by the formula (5), and the yaw angle beta can be calculated by the formula (10) or (16).
Through the technical scheme provided by the application, the method has at least the following effects:
1. the application provides a method for calculating the attitude angle of a platy projectile body in an impact test efficiently and accurately, which can accurately calculate the pitch angle and the deflection angle of the projectile body.
2. The application does not need any reference object size to participate in calculation in the process of calculating the angle, thereby reducing the introduction of size measurement and errors.
3. According to the application, all the calculation is performed based on a single frame image, and all the reference objects are shot at the same moment, so that the camera shake does not have any influence on the result.
4. The boundary lines of the projectile body and the target plate are used as reference lines of a space coordinate system, so that unnecessary steps and factors such as adding references in the test process are reduced.
5. Meanwhile, perspective and mapping errors caused by shooting imaging are considered, and the calculated result is closer to the real result.
It will be appreciated by those skilled in the art that embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The above description is only an example of the present application and is not intended to limit the present application, but various modifications and variations can be made to the present application by those skilled in the art. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the scope of the claims of the present application.
Claims (4)
1. An elastomer attitude angle measurement method, characterized by comprising the following steps:
establishing an image coordinate system and an earth coordinate system of an projectile striking a target plate;
calculating a mapping attitude angle of the projectile body; wherein the mapping attitude angle is an angle of an elastomer in an earth coordinate system, which is mapped to the image coordinate system;
obtaining a mapping coordinate system according to the earth coordinate system, and calculating the angle of the mapping coordinate system in an image coordinate system; wherein the mapping coordinate system angle is an angle of the mapping coordinate system in the image coordinate system;
calculating a mapping coefficient according to the mapping coordinate system angle; wherein the mapping coefficient represents a relationship between a mapping coordinate system angle and the earth coordinate system;
calculating the attitude angle of the projectile body in the earth coordinate system through the mapping coefficient and the mapping attitude angle;
the step of establishing an image coordinate system and an earth coordinate system of the projectile striking the target plate comprises the following steps: acquiring an image of an impact of a projectile body on a target plate, and establishing an image coordinate system according to the image; establishing an earth coordinate system Oxyz by taking a boundary line of the target plate as a reference line as x and y axes and a straight line perpendicular to the target plate as a z axis; acquiring two edge reference lines of an elastomer in the image coordinate system, and translating the two edge reference lines into the earth coordinate system to respectively obtain a first line segment and a second line segment;
the attitude angle includes a pitch angle and a yaw angle, and in the case where the attitude angle is the pitch angle, the method further includes: calculating a mapping pitch angle of the projectile body; wherein, the included angle between the first line segment and Oz is the mapping pitch angle; obtaining a first mapping coordinate system xOz according to the earth coordinate system, and calculating a first mapping coordinate system angle; wherein the first mapping coordinate system angle is the angle of the first mapping coordinate system xOz in the image coordinate system; calculating a first mapping coefficient according to the first mapping coordinate system angle, wherein the first mapping coefficient represents the relation between the first mapping coordinate system angle and the earth coordinate system; calculating the pitch angle of the projectile body in the earth coordinate system through the first mapping coefficient and the mapping pitch angle; further comprises: calculating the slopes of a first line segment, oz and Ox, and calculating the mapping pitch angle and the first mapping coordinate system angle according to the slopes of the first line segment, oz and Ox;
the attitude angle includes a pitch angle and a yaw angle, and in the case where the attitude angle is the yaw angle, the method further includes: calculating a mapping deflection angle of the projectile body; wherein, the included angle between the second line segment and Oy is the mapping deflection angle; obtaining a second mapping coordinate system yOz according to the earth coordinate system Oxyz, and calculating a second mapping coordinate system angle; wherein the second mapping coordinate system angle is the angle of the second mapping coordinate system yOz in the image coordinate system; calculating a second mapping coefficient according to the second mapping coordinate system angle, wherein the second mapping coefficient represents the relation between the second mapping coordinate system angle and the earth coordinate system; calculating the deflection angle of the projectile body in the earth coordinate system through the second mapping coefficient and the mapping deflection angle; further comprises: and calculating the slopes of the second line segment, oz and Oy, and calculating the mapping deflection angle and the angle value of the second mapping coordinate system according to the slopes of the second line segment, oz and Oy.
2. The method according to claim 1, wherein the first mapping coefficient f is calculated by the following formula α ：
3. The method according to claim 1, characterized in that the second mapping coefficient f is calculated by the following formula β ：
4. A method according to claim 3, further comprising:
acquiring a reference line OY and a reference line O parallel to OY in the earth coordinate system 1 Y 1 Will reference lines OY and O 1 Y 1 Translating to the image coordinate system to obtain O 'Y' and O 1 'Y 1 'A'; wherein, the included angle between PM and O 'Y' is the perspective angle, P is O 'Y' and O 1 'Y 1 ' intersecting perspective points, M being the midpoint of the projectile body front;
calculating the perspective angle according to the slopes of the PM and O 'Y';
correcting errors of deflection angles in the earth coordinate system according to the perspective angle.
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