Method for calculating longitude and latitude of aircraft route passing point by using vector

Abstract

The invention provides a method for calculating longitude and latitude of an aircraft route passing point by using a vector, and belongs to the technical field of drawing of a large circle route of an aircraft, and the method specifically comprises the following steps: setting the earth as a regular sphere, establishing a spherical coordinate system by taking the center of the sphere as a coordinate origin, and calculating coordinates of a starting point A and a target point B in the spherical coordinate system; the method comprises the following steps: obtaining coordinates of a starting point A and a target point B in a space rectangular coordinate system, equally dividing a space vector of the starting point A pointing to the target point B according to the number m of required passing points to obtain a plurality of intermediate points, and calculating coordinates of each passing point in the space rectangular coordinate system; converting the coordinate of each passing point in the space rectangular coordinate system into the coordinate in a spherical coordinate system; the coordinates of the passing points in the spherical coordinate system are converted into radian values of the longitude and latitude, and the longitude and latitude of the passing points are obtained according to the radian values of the longitude and latitude of the passing points. According to the processing scheme, the complexity of latitude and longitude calculation of the passing points of the aircraft route is reduced.

Description

Technical Field

[0001] The present application relates to the field of great circle route drawing of an aircraft, and in particular to a method for calculating the longitude and latitude of waypoints of an aircraft route using vectors. Background Art

[0002] Considering the earth as a sphere, a plane is drawn through any two points on the ground and the center of the earth. The circumference obtained by the intersection of the plane and the earth's surface is a great circle. The great circle inferior arc between two points is the shortest distance between the two points on the ground. The route when sailing along this great circle arc is called a great circle route. The great circle route has the shortest distance, but navigation is more difficult. Therefore, in practice, it is usually adopted to approach the great circle route for long distances and take the equiangular route for short distances.

[0003] The existing great circle route calculation method is mainly based on the principles of spherical trigonometry. The process of calculating a waypoint in this method involves about 20 trigonometric function operations, and the calculation process is relatively complicated. Summary of the invention

[0004] In view of this, the present application provides a method for calculating the longitude and latitude of waypoints on an aircraft route using vectors, which solves the problems in the prior art and reduces the complexity of calculating the longitude and latitude of waypoints on an aircraft route.

[0005] The present application provides a method for calculating the longitude and latitude of a waypoint on an aircraft route using vectors, which adopts the following technical solution:

[0006] A method for calculating the longitude and latitude of a waypoint on an aircraft route using vectors comprises the following steps:

[0007] Determine the latitude and longitude information of the route starting point A and the destination point B;

[0008] Set the earth as a perfect sphere, establish a spherical coordinate system with the center of the sphere as the origin, and calculate the coordinates of the starting point A and the target point B in the spherical coordinate system;

[0009] Establish a spatial rectangular coordinate system with the center of the sphere as the origin, obtain the coordinates of the starting point A and the target point B in the spatial rectangular coordinate system, obtain the spatial vector from the origin to the starting point A, the spatial vector of the target point B, and the spatial vector from the starting point A to the target point B;

[0010] According to the number of required waypoints m, the space vector pointing from the starting point A to the target point B is equally divided to obtain several intermediate points, and then the coordinates of each waypoint in the spatial rectangular coordinate system are calculated using the intermediate points;

[0011] Convert the coordinates of each waypoint in the spatial rectangular coordinate system into the coordinates of the spherical coordinate system;

[0012] The coordinates of each waypoint in the spherical coordinate system are converted into radian values ​​of longitude and latitude, and then the longitude and latitude of the waypoint are obtained according to the radian values ​​of the longitude and latitude of the waypoint.

[0013] Optionally, the latitude and longitude information of the starting point A is The latitude and longitude information of target point B is Among them, λ A , B is the latitude, is the longitude;

[0014] The coordinates of the starting point A in the spherical coordinate system are:

[0015] The coordinates of the target point B in the spherical coordinate system are:

[0016] Where R is the radius of the Earth, λ Arad , Brad , is the latitude and longitude λ A , B , The value converted to radians.

[0017] Optional, the coordinates of the starting point A in the spatial rectangular coordinate system:

[0018]

[0019] The coordinates of target point B in the spatial rectangular coordinate system:

[0020]

[0021] Where R is the radius of the Earth, λ Arad , Brad , is the latitude and longitude λ A , B , The value converted to radians.

[0022] Optionally, the coordinate origin points to the nth intermediate point T n The space vector in is the space vector from the origin to the starting point A, The nth middle point T of the straight line from the starting point A n The space vector of A is the spatial vector pointing from the starting point A to the target point B;

[0023] The direction is from the origin to the nth waypoint P n Vector Direction, The size and or is consistent with the radius of the earth, R, from which we get:

[0024] Waypoint P n The spatial rectangular coordinate system coordinates are (x n ,y n ,z n ).

[0025] Optional, P n The spherical coordinates of are:

[0026] Optional, waypoint P n The latitude in radians is:

[0027] Waypoint P n The longitude in radians is:

[0028] The waypoint P n The latitude and longitude radians are converted to the latitude and longitude of the waypoints

[0029]

[0030] In summary, this application includes the following beneficial technical effects:

[0031] This application applies spatial vectors to the longitude and latitude calculation process of great circle route waypoints, and uses coordinate system conversion to reduce trigonometric function operations and reduce calculation complexity. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0033] Figure 1 A flowchart of a method for calculating the longitude and latitude of waypoints on an aircraft route using vectors for this application;

[0034] Figure 2 This is a schematic diagram of the starting point, waypoints and target point of this application in the spherical coordinate system and the rectangular coordinate system. DETAILED DESCRIPTION

[0035] The embodiments of the present application are described in detail below with reference to the accompanying drawings.

[0036] The following describes the implementation methods of the present application through specific examples, and those skilled in the art can easily understand other advantages and effects of the present application from the contents disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. The present application can also be implemented or applied through other different specific implementation methods, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present application. It should be noted that, in the absence of conflict, the following embodiments and the features in the embodiments can be combined with each other. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without making creative work belong to the scope of protection of the present application.

[0037] It should be noted that various aspects of the embodiments within the scope of the appended claims are described below. It should be apparent that the aspects described herein can be embodied in a wide variety of forms, and any specific structure and / or function described herein is merely illustrative. Based on the present application, it should be understood by those skilled in the art that an aspect described herein can be implemented independently of any other aspect, and two or more of these aspects can be combined in various ways. For example, any number of aspects described herein can be used to implement the device and / or practice the method. In addition, other structures and / or functionalities other than one or more of the aspects described herein can be used to implement this device and / or practice this method.

[0038] It should also be noted that the illustrations provided in the following embodiments are only schematic illustrations of the basic concept of the present application. The illustrations only show the components related to the present application rather than being drawn according to the number, shape and size of the components in actual implementation. In actual implementation, the type, quantity and proportion of each component may be changed at will, and the component layout may also be more complicated.

[0039] Additionally, in the following description, specific details are provided to facilitate a thorough understanding of the examples. However, it will be understood by those skilled in the art that the aspects described may be practiced without these specific details.

[0040] The embodiment of the present application provides a method for calculating the longitude and latitude of waypoints on an aircraft route using vectors.

[0041] like Figure 1 As shown, a method for calculating the longitude and latitude of a waypoint on an aircraft route using vectors is characterized by comprising the following steps:

[0042] Determine the latitude and longitude information of the route starting point A and the target point B; set the earth as a perfect sphere, establish a spherical coordinate system with the center of the sphere as the coordinate origin, and calculate the coordinates of the starting point A and the target point B in the spherical coordinate system; the latitude and longitude information of the starting point A is The latitude and longitude information of target point B is Among them, λ A , B is the latitude, is the longitude; the coordinates of the starting point A in the spherical coordinate system are: The coordinates of the target point B in the spherical coordinate system are: Where R is the radius of the Earth, λ Arad , Brad , is the latitude and longitude λ A , B , The value converted to radians.

[0043] A spatial rectangular coordinate system is established with the center of the sphere as the origin, and the coordinates of the starting point A and the target point B in the spatial rectangular coordinate system are obtained. The conversion formula from the spherical coordinate system to the spatial rectangular coordinate system is as follows: z=r cosθ.

[0044] Coordinates of the starting point A in the spatial rectangular coordinate system:

[0045]

[0046] The coordinates of target point B in the spatial rectangular coordinate system:

[0047]

[0048] Where R is the radius of the Earth, λ Arad , Brad , is the latitude and longitude λ A , B , Converted to radians, we can get the space vector from the origin to the starting point A, the space vector from the target point B, and the space vector from the starting point A to the target point B.

[0049] like Figure 2 As shown in the figure, according to the number of required waypoints m, the space vector pointing from the starting point A to the target point B is equally divided to obtain several intermediate points, and then the coordinates of each waypoint in the spatial rectangular coordinate system are calculated using the intermediate points; the origin of the coordinate points to the nth intermediate point T n The space vector in is the space vector from the origin to the starting point A, The nth middle point T of the straight line from the starting point A n The space vector of A is the spatial vector pointing from the starting point A to the target point B.

[0050] The direction is from the origin to the nth waypoint P n Vector Direction, The size and or is consistent with the radius of the earth, R, from which we get: Waypoint P n The spatial rectangular coordinate system coordinates are (x n ,y n ,z n ).

[0051] Convert the coordinates of each waypoint in the spatial rectangular coordinate system into the coordinates of the spherical coordinate system; n The spherical coordinates of are:

[0052] Convert the coordinates of each waypoint in the spherical coordinate system into the radian value of longitude and latitude; the waypoint P n The latitude in radians is: Waypoint P n The longitude in radians is:

[0053] Then, the longitude and latitude of the waypoint are obtained according to the arc value of the longitude and latitude of the waypoint.

[0054]

[0055] This application applies spatial vectors to the longitude and latitude calculation process of great circle route waypoints, uses coordinate system conversion to reduce trigonometric function operations, and only involves trigonometric function operations during coordinate system conversion, thereby reducing calculation complexity.

[0056] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application shall be based on the protection scope of the claims.

Claims

1. A method for calculating the longitude and latitude of a waypoint on an aircraft route using vectors, characterized in that: The steps include: Determine the latitude and longitude information of the route starting point A and the destination point B; Set the earth as a perfect sphere, establish a spherical coordinate system with the center of the sphere as the origin, and calculate the coordinates of the starting point A and the target point B in the spherical coordinate system; Establish a spatial rectangular coordinate system with the center of the sphere as the origin, obtain the coordinates of the starting point A and the target point B in the spatial rectangular coordinate system, obtain the spatial vector from the origin to the starting point A, the spatial vector of the target point B, and the spatial vector from the starting point A to the target point B; According to the number of required waypoints m, the space vector pointing from the starting point A to the target point B is equally divided to obtain several intermediate points, and then the coordinates of each waypoint in the spatial rectangular coordinate system are calculated using the intermediate points; Convert the coordinates of each waypoint in the spatial rectangular coordinate system into the coordinates of the spherical coordinate system; The coordinates of each waypoint in the spherical coordinate system are converted into radian values ​​of longitude and latitude, and then the longitude and latitude of the waypoint are obtained according to the radian values ​​of the longitude and latitude of the waypoint.

2. The method for calculating the longitude and latitude of a waypoint on an aircraft route using vectors according to claim 1, characterized in that: The latitude and longitude information of the starting point A is The latitude and longitude information of target point B is Among them, λ A , B is the latitude, is the longitude; The coordinates of the starting point A in the spherical coordinate system are: The coordinates of the target point B in the spherical coordinate system are: Where R is the radius of the Earth, λ Arad , Brad , is the latitude and longitude λ A , B , The value converted to radians.

3. The method for calculating the longitude and latitude of a waypoint on an aircraft route using vectors according to claim 2, characterized in that: Coordinates of the starting point A in the spatial rectangular coordinate system: The coordinates of target point B in the spatial rectangular coordinate system: Where R is the radius of the Earth, λ Arad , Brad , is the latitude and longitude λ A , B , The value converted to radians.

4. The method for calculating the longitude and latitude of a waypoint on an aircraft route using vectors according to claim 3, characterized in that: The coordinate origin points to the nth intermediate point T n The space vector in is the space vector from the origin to the starting point A, The nth middle point T of the straight line from the starting point A n The space vector of A is the spatial vector pointing from the starting point A to the target point B; The direction is from the origin to the nth waypoint P n Vector Direction, The size and or is consistent with the radius of the earth, R, from which we get: Waypoint P n The spatial rectangular coordinate system coordinates are (x n ,y n ,z n ).

5. The method for calculating the longitude and latitude of a waypoint on an aircraft route using vectors according to claim 4, characterized in that: P n The spherical coordinates of are:

6. The method for calculating the longitude and latitude of a waypoint on an airplane route using vectors according to claim 4, characterized in that: Waypoint P n The latitude in radians is: Waypoint P n The longitude in radians is: The waypoint P n The latitude and longitude radians are converted to the latitude and longitude of the waypoints

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