Method and device for obtaining aircraft collision probability based on non-central chi-square distribution

Abstract

The present application provides a method and device for obtaining the probability of aircraft collision based on non-central chi-square distribution, and relates to the field of aircraft collision technology. The method obtains the protection box radius of a spherical collision protection box with the center of mass of any aircraft as the sphere center based on the area radius of the collision area of ​​the two aircraft; for any aircraft, in a three-dimensional Cartesian coordinate system, the relative position vector of the center of mass position of the aircraft relative to the center of mass position of the other aircraft is determined, and the nominal track data and actual flight track data in the cruise phase are obtained; based on the error values ​​between the nominal track data and the actual flight track data corresponding to each aircraft, the relative position error matrix and the corresponding eigenvalues ​​are determined; the relative position vector, the relative position error matrix and the corresponding eigenvalues ​​are processed using a preset three-degree-of-freedom non-central chi-square distribution algorithm to obtain the collision probability between the two aircraft. The method improves the efficiency and accuracy of collision probability estimation.

Description

Technical Field

[0001] The present application relates to the technical field of aircraft collision, and in particular to a method and device for obtaining aircraft collision probability based on non-central chi-square distribution. Background Art

[0002] With the rapid development of urban low-altitude traffic, the use of drones and electric vertical take-off and landing aircraft is becoming more and more popular, and the flow of aircraft in low-altitude airspace has shown a significant growth trend. However, unlike traditional civil aviation traffic, aircraft in urban low-altitude traffic may collide at any angle, so traditional collision probability calculation methods are difficult to meet the accuracy and efficiency requirements.

[0003] Existing methods usually simplify the calculation by establishing a spherical collision box, but it requires complex triple integral operations, has limited calculation accuracy and low efficiency. Summary of the invention

[0004] The purpose of the embodiments of the present application is to provide a method and device for obtaining aircraft collision probability based on non-central chi-square distribution. By using non-central chi-square distribution, the complex integration process is avoided, the calculation time is significantly shortened, and the accuracy of collision probability estimation is improved.

[0005] In a first aspect, a method for obtaining an aircraft collision probability based on a non-central chi-square distribution is provided, and the method may include:

[0006] Based on the area radius of the collision area of ​​the two aircraft, the protection box radius of a spherical collision protection box with the center of mass of any aircraft as the sphere center is obtained; wherein the collision area is the smallest spherical area that wraps the aircraft; the spherical collision protection box represents the collision protection range of the corresponding aircraft; the protection box radius is the sum of the area radii corresponding to the two aircraft;

[0007] For any aircraft, determine the relative position vector of the center of mass position of the aircraft relative to the center of mass position of another aircraft in a three-dimensional Cartesian coordinate system, and obtain the nominal track data and actual flight track data of the aircraft in the cruise phase;

[0008] Determine the relative position error matrix of the two aircraft and the eigenvalue of the corresponding relative position error matrix based on the error value between the nominal track data and the actual flight track data corresponding to each aircraft;

[0009] The relative position vector, the relative position error matrix and the eigenvalues ​​of the corresponding relative position error matrix are processed using a preset three-degree-of-freedom non-central chi-square distribution algorithm to obtain the collision probability between the two aircraft.

[0010] In one possible implementation, the nominal track data includes the nominal speed, the longitude and latitude of the nominal track points at different timestamps, and the altitude above the ground, and the actual flight track data includes the actual speed, the longitude and latitude of the actual flight track points at different timestamps, and the altitude above the ground.

[0011] In a possible implementation, determining the relative position error matrix of two aircraft and the eigenvalue of the corresponding relative position error matrix based on the error value between the nominal track data and the actual flight track data corresponding to each aircraft respectively includes:

[0012] For any aircraft, when the actual speed is the nominal speed, obtain the error value and corresponding error covariance between the position of the actual flight track point and the position of the nominal track point in different coordinate axis directions and at different time stamps in the three-dimensional Cartesian coordinate system;

[0013] Based on the error covariance of the two aircrafts obtained, a relative position error matrix is ​​constructed;

[0014] Get the eigenvalues ​​of the relative position error matrix.

[0015] In a possible implementation, the error value includes an error value between the position of the actual flight trajectory point in the x-axis direction and the position of the nominal track point, an error value between the position of the actual flight trajectory point in the y-axis direction and the position of the nominal track point, and an error value between the position of the actual flight trajectory point in the z-axis direction and the position of the nominal track point;

[0016] The error covariance includes a first variance of the error value between the position of the actual flight trajectory point in the x-axis direction and the position of the nominal track point, a second variance of the error value between the position of the actual flight trajectory point in the y-axis direction and the position of the nominal track point, and a third variance of the error value between the position of the actual flight trajectory point in the z-axis direction and the position of the nominal track point; and a first covariance of the error value between the position of the actual flight trajectory point in the x-axis direction and the position of the nominal track point and the position of the actual flight trajectory point in the y-axis direction, a second covariance of the error value between the position of the actual flight trajectory point in the x-axis direction and the position of the nominal track point and the position of the actual flight trajectory point in the z-axis direction, and a third covariance of the error value between the position of the actual flight trajectory point in the y-axis direction and the position of the nominal track point.

[0017] In a possible implementation, the relative position error matrix is ​​a 3X3 covariance matrix; wherein a first relative variance determined based on a first variance of the two aircraft, a second relative variance determined based on a second variance of the two aircraft, and a third relative variance determined based on a third variance of the two aircraft are main diagonal elements of the covariance matrix; a first relative covariance determined based on the first covariance of the two aircraft, a second relative covariance determined based on the second covariance of the two aircraft, and a third relative covariance determined based on the third covariance of the two aircraft are non-main diagonal elements of the covariance matrix;

[0018] The number of eigenvalues ​​of the relative position error matrix obtained is 3, and all of them are greater than 0.

[0019] In a possible implementation, the calculation formula for obtaining the collision probability is expressed as:

[0020]

[0021] in: is the integration interval constant, represents an algorithm for calculating the probability of collision less than or equal to a threshold, where P is the collision probability, is the generalized inverse matrix of the relative position error matrix, The non-centrality parameter is The chi-square distribution with three degrees of freedom is represents the relative position vector, A vector representing the transposed relative position vector.

[0022] In one possible implementation, we obtain the integration interval constant The calculation formula is expressed as:

[0023]

[0024] in, represents three different eigenvalues, Indicates the radius of the protection box.

[0025] In a second aspect, a device for acquiring aircraft collision probability based on non-central chi-square distribution is provided, and the device may include:

[0026] An acquisition unit is used to acquire a protection box radius of a spherical collision protection box with the mass center of any aircraft as the sphere center based on the area radius of the collision area of ​​the two aircraft; wherein the collision area is a minimum spherical area that wraps the aircraft; the spherical collision protection box represents the collision protection range of the corresponding aircraft; and the protection box radius is the sum of the area radii corresponding to the two aircraft;

[0027] a determination unit, for determining, for any aircraft, a relative position vector of the center of mass position of the aircraft relative to the center of mass position of another aircraft in a three-dimensional Cartesian coordinate system, and obtaining nominal track data and actual flight track data of the aircraft in a cruise phase;

[0028] and, determining a relative position error matrix of the two aircraft and an eigenvalue of the corresponding relative position error matrix based on an error value between the nominal track data and the actual flight track data corresponding to each aircraft;

[0029] The processing unit is used to process the relative position vector, the relative position error matrix and the eigenvalues ​​of the corresponding relative position error matrix using a preset three-degree-of-freedom non-central chi-square distribution algorithm to obtain the collision probability between the two aircraft.

[0030] In a third aspect, an electronic device is provided, the electronic device comprising a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory communicate with each other via the communication bus;

[0031] Memory, used to store computer programs;

[0032] The processor is used to implement any method step described in the first aspect when executing the program stored in the memory.

[0033] In a fourth aspect, a computer-readable storage medium is provided, wherein a computer program is stored in the computer-readable storage medium, and when the computer program is executed by a processor, any method step described in the first aspect is implemented.

[0034] The method for obtaining the probability of collision of aircraft based on non-central chi-square distribution includes: obtaining the radius of a spherical collision protection box with the center of mass of any aircraft as the center of the sphere based on the area radius of the collision area of ​​the two aircraft; the collision area is the smallest spherical area that wraps the aircraft; the spherical collision protection box represents the collision protection range of the corresponding aircraft; the radius of the protection box is the sum of the area radii corresponding to the two aircraft; for any aircraft, in a three-dimensional Cartesian coordinate system, determining the relative position vector of the center of mass position of the aircraft relative to the center of mass position of the other aircraft, and obtaining the nominal track data and actual flight track data of the aircraft in the cruise phase; based on the error values ​​between the nominal track data and the actual flight track data corresponding to each aircraft, determining the relative position error matrix of the two aircraft and the eigenvalues ​​of the corresponding relative position error matrix; using a preset three-degree-of-freedom non-central chi-square distribution algorithm, processing the relative position vector, the relative position error matrix and the eigenvalues ​​of the corresponding relative position error matrix, and obtaining the probability of collision between the two aircraft. This method avoids the complex integration process by using non-central chi-square distribution, significantly shortens the calculation time, and improves the accuracy of collision probability estimation. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings required for use in the embodiments of the present application will be briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without paying creative work.

[0036] Figure 1 A schematic diagram of a system architecture for applying a method for obtaining aircraft collision probability based on non-central chi-square distribution provided in an embodiment of the present application;

[0037] Figure 2 A flowchart of a method for obtaining aircraft collision probability based on non-central chi-square distribution provided in an embodiment of the present application;

[0038] Figure 3 A schematic diagram of the structure of a device for acquiring aircraft collision probability based on non-central chi-square distribution provided in an embodiment of the present application;

[0039] Figure 4 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0040] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments of the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present application. Unless otherwise defined, the technical terms or scientific terms used in this application should be the common meanings understood by people with ordinary skills in the field to which the present invention belongs. The "first", "second" and similar words used in this application do not indicate any order, quantity or importance, but are only used to distinguish different components. "Including" or "including" and other similar words mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connected", "coupled" or "connected" and other similar words are not limited to physical or mechanical connections, but may include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0041] For ease of understanding, the terms involved in the embodiments of the present application are explained below:

[0042] Covariance matrix and the corresponding generalized inverse matrix The following 4 equations should be satisfied:

[0043] ;

[0044] ;

[0045] ;

[0046] ;

[0047] in, Performs a matrix transpose operation.

[0048] The existing collision probability calculation method is difficult to apply in dynamic and real-time environments due to complex integral operations and error accumulation problems. Therefore, an efficient and accurate collision probability calculation method is urgently needed to ensure the operational safety of low-altitude airspace.

[0049] The method for obtaining the probability of aircraft collision based on non-central chi-square distribution provided in this application adopts a spherical collision box model: one drone is abstracted as a mass point, and its coordinates are defined as the center of mass (or geometric center) of the drone; the other drone is simplified as a sphere model, and its center corresponds to the center of mass (or geometric center) of the drone, and the radius of the sphere is , is the sum of the radii of the spherical protection ranges of the two drones. Based on this modeling method, the collision probability calculation problem between the two drones can be further transformed into: the probability calculation problem of judging whether a particle falls into the sphere. This mathematical modeling method can effectively simplify the complex three-dimensional space collision probability calculation, which is convenient for the implementation and optimization of subsequent algorithms.

[0050] Introducing non-central chi-square distribution: The position error is modeled using the covariance matrix and its eigenvalues, and the collision probability is calculated using the non-central chi-square distribution, which improves the efficiency and accuracy of the calculation. By introducing the non-central chi-square distribution, the complex three-dimensional collision probability calculation is simplified to a single definite integral operation, which significantly improves the calculation accuracy. The use of non-central chi-square distribution avoids the complex integration process, significantly shortens the calculation time, and facilitates real-time collision probability estimation. At the same time, this method is applicable to aircraft collision scenarios with intersections at any angle, providing an efficient and reliable technical means for the safe navigation of drones in low-altitude airspace in the future.

[0051] Adaptable to multi-scenario applications: It is suitable for aircraft collision probability assessment at any position and angle, aiming to improve the safety of low-altitude airspace operations, especially for urban low-altitude transportation tools such as drones and electric vertical take-off and landing aircraft (eVTOL).

[0052] This application can be widely used in urban low-altitude traffic management systems, providing scientific support for the safety of low-altitude aircraft operations, and laying a technical foundation for the coordinated development of future drones and urban infrastructure.

[0053] The method for obtaining the probability of aircraft collision based on non-central chi-square distribution provided in the embodiment of the present application can be applied in Figure 1 In the system architecture shown in Figure 1 As shown, the system architecture may include: two aircraft, namely a first aircraft and a second aircraft, and a processor for acquiring movement information of the two aircraft in real time.

[0054] Any of the two aircraft can be abstracted as a mass point, and the coordinates of the mass point are the center of mass (or geometric center) of the UAV. Since each aircraft has a collision zone, the collision zone is centered on the center of mass of the corresponding aircraft and is the smallest spherical area that encloses the corresponding aircraft (such as the area surrounded by line 1 in the figure). Therefore, based on the radius of the collision zone of the two aircraft, the other aircraft is regarded as a sphere (i.e., a spherical collision protection box, such as the area surrounded by line 2 in the figure). The center of the sphere is the center of mass (or geometric center) of this UAV, and the protection box radius of the spherical collision protection box is , which is the sum of the radii of the areas involved in the collision areas of the two aircraft.

[0055] The processor is used for acquiring the motion information of two aircrafts in real time and executing the method for acquiring the probability of aircraft collision based on non-central chi-square distribution.

[0056] This method is computationally simple and efficient, suitable for complex scenarios in urban low-altitude traffic, and can provide important theoretical support and practical application value for urban low-altitude UAV operations.

[0057] The preferred embodiments of the present application are described below in conjunction with the drawings in the specification. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present application, and are not used to limit the present application. In addition, the embodiments and features in the embodiments of the present application may be combined with each other if there is no conflict.

[0058] Figure 2 The flowchart of a method for obtaining the probability of aircraft collision based on non-central chi-square distribution is provided in an embodiment of the present application. Figure 2 As shown, the method may include:

[0059] Step S210: Based on the area radius of the collision area of ​​the two aircraft, obtain the protection box radius of a spherical collision protection box with the center of mass of any aircraft as the sphere center.

[0060] Based on the area radius of the collision area of ​​the first aircraft and the area radius of the collision area of ​​the second aircraft, a protection box radius of a spherical collision protection box with the first mass center of the first aircraft as the sphere center or the second mass center of the second aircraft as the sphere center is determined. The collision area is the smallest spherical area that encloses the corresponding aircraft;

[0061] The spherical collision protection box indicates the collision protection range of the corresponding aircraft;

[0062] The protection box radius is the sum of the area radius corresponding to the first aircraft and the area radius corresponding to the second aircraft.

[0063] Step S220: for any aircraft, determine the relative position vector of the center of mass position of the aircraft relative to the center of mass position of another aircraft in a three-dimensional Cartesian coordinate system, and obtain the nominal track data and actual flight track data of the aircraft in the cruise phase.

[0064] In a specific implementation, after determining the position of the three-dimensional model of any aircraft in the three-dimensional Cartesian coordinate system, determine the coordinate vector of the center of mass position of the corresponding aircraft in the three-dimensional Cartesian coordinate system to obtain the relative position vector of the center of mass positions of the two aircraft in the three-dimensional Cartesian coordinate system;

[0065] In the UAV ground monitoring system, the timestamps of the flight trajectories of each aircraft at different stages (such as take-off, hovering, climbing, cruising, descending and landing), the latitude and longitude of the trajectories, the altitude above the ground, the speed and other information can be obtained to obtain the nominal track data and actual flight track data of each aircraft in the cruising stage. Among them, the nominal speed, the position of the nominal track points at different timestamps, that is, the longitude and latitude and the altitude above the ground, and the actual flight track data include the actual speed, the position of the actual flight track points at different timestamps, that is, the longitude and latitude and the altitude above the ground.

[0066] Step S230: Determine the relative position error matrix of the two aircraft and the eigenvalue of the corresponding relative position error matrix based on the error value between the nominal track data and the actual flight track data corresponding to each aircraft.

[0067] In a specific implementation, for any aircraft, when the actual speed is the nominal speed, the error values ​​and corresponding error covariances between the positions of the actual flight track points and the nominal track points in different coordinate axis directions and at different time stamps in a three-dimensional Cartesian coordinate system are obtained;

[0068] Among them, the error value may include the error value between the position of the actual flight trajectory point in the x-axis direction and the position of the nominal track point, the error value between the position of the actual flight trajectory point in the y-axis direction and the position of the nominal track point, and the error value between the position of the actual flight trajectory point in the z-axis direction and the position of the nominal track point.

[0069] For example, any aircraft The direction coordinates are used to extract n actual flight trajectory points: , , …, , and the corresponding n nominal track points: , , …, Therefore, the error between the position of the actual flight trajectory point and the nominal flight trajectory point in the x-axis direction is: Similarly, the error value between the position of the actual flight trajectory point in the y-axis direction and the position of the nominal track point and the error value between the position of the actual flight trajectory point in the z-axis direction and the position of the nominal track point can be obtained using the same algorithm, which will not be elaborated in this application.

[0070] The error covariance may include a first variance of the error value between the position of the actual flight trajectory point in the x-axis direction and the position of the nominal track point, a second variance of the error value between the position of the actual flight trajectory point in the y-axis direction and the position of the nominal track point, and a third variance of the error value between the position of the actual flight trajectory point in the z-axis direction and the position of the nominal track point; and a first covariance of the error value between the position of the actual flight trajectory point in the x-axis direction and the error value between the position of the actual flight trajectory point in the y-axis direction and the error value between the position of the actual flight trajectory point in the nominal track point, a second covariance of the error value between the position of the actual flight trajectory point in the x-axis direction and the error value between the position of the actual flight trajectory point in the z-axis direction and the error value between the position of the actual flight trajectory point in the z-axis direction, and a third covariance of the error value between the position of the actual flight trajectory point in the y-axis direction and the error value between the position of the actual flight trajectory point in the z-axis direction and the error value

[0071] Continuing with the above example, the first variance of the error between the position of the actual flight track point of the first aircraft in the two aircraft in the x-axis direction and the position of the nominal track point can be expressed as: , the first variance of the error value between the position of the actual flight track point of the corresponding second aircraft in the x-axis direction and the position of the nominal track point The first variance from the first aircraft The algorithm is the same as that of , which will not be described here. Similarly, the second variance corresponding to the first aircraft is Difference with third party , and the second variance corresponding to the second aircraft Difference with third party It can also be obtained by a similar algorithm, which will not be described in detail here. The first aircraft is any one of the two aircrafts, and the second aircraft is the aircraft of the two aircrafts except the first aircraft.

[0072] The first covariance of the error value between the position of the actual flight track point of the first aircraft in the x-axis direction and the y-axis direction and the position of the nominal track point can be expressed as:

[0073]

[0074] The first covariance of the error value between the position of the actual flight track point of the corresponding second aircraft in the x-axis direction and the y-axis direction and the position of the nominal track point The first covariance with the first aircraft The algorithm is the same as that of , which will not be described here. Similarly, the second covariance corresponding to the first aircraft is and the third covariance , and the second variance corresponding to the second aircraft and the third covariance It can also be obtained by a similar algorithm, which will not be described here.

[0075] Afterwards, a relative position error matrix is ​​constructed based on the error covariances of the two aircrafts obtained, and the eigenvalues ​​of the relative position error matrix are obtained. The error covariances of the two aircrafts with the same coordinate axis are added together, and the sum is taken as the relative error covariance of the two aircrafts on the corresponding coordinate axis, such as, , represents the relative error covariance (or first relative variance) of the two aircraft in the x-axis direction; , represents the relative error covariance (or second relative variance) of the two aircraft in the y-axis direction, , represents the relative error covariance (or third relative variance) of the two aircraft in the z-axis direction; other covariances are processed in the same way, and we get , represents the first relative covariance; , represents the second relative covariance; , represents the third relative covariance.

[0076] Furthermore, the relative position error matrix is ​​a 3X3 covariance matrix; wherein, the first relative variance determined based on the first variance of the two aircraft, the second relative variance determined based on the second variance of the two aircraft, and the third relative variance determined based on the third variance of the two aircraft are the main diagonal elements of the covariance matrix; the first relative covariance determined based on the first covariance of the two aircraft, the second relative covariance determined based on the second covariance of the two aircraft, and the third relative covariance determined based on the third covariance of the two aircraft are the non-main diagonal elements of the covariance matrix; the number of eigenvalues ​​of the relative position error matrix obtained is 3, such as Three different eigenvalues, all greater than 0.

[0077] In one example, the relative position error matrix is ​​recorded as , as shown below:

[0078]

[0079] Step S240: Using a preset three-degree-of-freedom non-central chi-square distribution algorithm, the relative position vector, the relative position error matrix and the eigenvalues ​​of the corresponding relative position error matrix are processed to obtain the collision probability between the two aircraft.

[0080] The calculation formula for obtaining the collision probability is expressed as:

[0081]

[0082] in: is the integration interval constant, The algorithm for calculating the collision probability less than or equal to the threshold, P is the collision probability, is the relative position error matrix (or covariance matrix) The generalized inverse matrix of The non-centrality parameter is The chi-square distribution with three degrees of freedom.

[0083] The meaning of the above formula is: collision probability It can be expressed as the non-centralized parameter , a non-central chi-square random variable with 3 degrees of freedom is less than or equal to the threshold probability.

[0084] Further, obtain the integral interval constant The calculation formula is expressed as:

[0085]

[0086] in, represents three different eigenvalues, Indicates the radius of the protection box.

[0087] In some embodiments, if If any eigenvalue in is 0, If is 0, the formula Calculate , that is, remove the eigenvalues ​​of 0 and then calculate; if If there is no eigenvalue of 0 in , then the formula is used Calculate .

[0088] Corresponding to the above method, the embodiment of the present application also provides a device for obtaining the probability of aircraft collision based on non-central chi-square distribution, such as Figure 3 As shown, the device comprises:

[0089] The acquisition unit 310 is used to acquire the protection box radius of a spherical collision protection box with the mass center of any aircraft as the sphere center based on the area radius of the collision area of ​​the two aircraft; wherein the collision area is the smallest spherical area that wraps the aircraft; the spherical collision protection box represents the collision protection range of the corresponding aircraft; and the protection box radius is the sum of the area radii corresponding to the two aircraft;

[0090] The determination unit 320 is used to determine, for any aircraft, a relative position vector of the center of mass position of the aircraft relative to the center of mass position of another aircraft in a three-dimensional Cartesian coordinate system, and obtain the nominal track data and actual flight track data of the aircraft in the cruise phase;

[0091] and, determining a relative position error matrix of the two aircraft and an eigenvalue of the corresponding relative position error matrix based on an error value between the nominal track data and the actual flight track data corresponding to each aircraft;

[0092] The processing unit 330 is used to process the relative position vector, the relative position error matrix and the eigenvalues ​​of the corresponding relative position error matrix using a preset three-degree-of-freedom non-central chi-square distribution algorithm to obtain the collision probability between the two aircraft.

[0093] The functions of each functional unit of the aircraft collision probability acquisition device based on non-central chi-square distribution provided in the above-mentioned embodiment of the present application can be realized through the above-mentioned method steps. Therefore, the specific working process and beneficial effects of each unit in the aircraft collision probability acquisition device based on non-central chi-square distribution provided in the embodiment of the present application will not be repeated here.

[0094] The present application also provides an electronic device, such as Figure 4 As shown, it includes a processor 410 , a communication interface 420 , a memory 430 and a communication bus 440 , wherein the processor 410 , the communication interface 420 , and the memory 430 communicate with each other via the communication bus 440 .

[0095] Memory 430, for storing computer programs;

[0096] The processor 410 is used to execute the program stored in the memory 430 to implement the following steps:

[0097] Based on the area radius of the collision area of ​​the two aircraft, the protection box radius of a spherical collision protection box with the center of mass of any aircraft as the sphere center is obtained; wherein the collision area is the smallest spherical area that wraps the aircraft; the spherical collision protection box represents the collision protection range of the corresponding aircraft; the protection box radius is the sum of the area radii corresponding to the two aircraft;

[0098] For any aircraft, determine the relative position vector of the center of mass position of the aircraft relative to the center of mass position of another aircraft in a three-dimensional Cartesian coordinate system, and obtain the nominal track data and actual flight track data of the aircraft in the cruise phase;

[0099] Determine the relative position error matrix of the two aircraft and the eigenvalue of the corresponding relative position error matrix based on the error value between the nominal track data and the actual flight track data corresponding to each aircraft;

[0100] The relative position vector, the relative position error matrix and the eigenvalues ​​of the corresponding relative position error matrix are processed using a preset three-degree-of-freedom non-central chi-square distribution algorithm to obtain the collision probability between the two aircraft.

[0101] The communication bus mentioned above can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The communication bus can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, only one thick line is used in the figure, but it does not mean that there is only one bus or one type of bus.

[0102] The communication interface is used for communication between the above electronic device and other devices.

[0103] The memory may include a random access memory (RAM) or a non-volatile memory (NVM), such as at least one disk memory. Optionally, the memory may also be at least one storage device located away from the aforementioned processor.

[0104] The above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0105] The implementation methods and beneficial effects of the components of the electronic device in the above embodiments to solve the problems can be seen in Figure 2 The various steps in the illustrated embodiment are implemented, therefore, the specific working process and beneficial effects of the electronic device provided by the embodiment of the present application are not repeated here.

[0106] In another embodiment provided in the present application, a computer-readable storage medium is also provided, in which instructions are stored. When the computer-readable storage medium is executed on a computer, the computer executes the method for obtaining the aircraft collision probability based on the non-central chi-square distribution as described in any of the above embodiments.

[0107] In another embodiment provided in the present application, a computer program product including instructions is also provided. When the computer program product is executed on a computer, the computer executes the method for obtaining the aircraft collision probability based on the non-central chi-square distribution described in any one of the above embodiments.

[0108] Those skilled in the art will appreciate that the embodiments in the present application can be provided as methods, systems, or computer program products. Therefore, the embodiments in the present application can be in the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the embodiments in the present application can be in the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0109] The embodiments of the present application are described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the process. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0110] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0111] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process in the computer or other programmable device. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0112] Although the preferred embodiments of the present application have been described, those skilled in the art may make additional changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications falling within the scope of the embodiments of the present application.

[0113] Obviously, those skilled in the art can make various changes and modifications to the embodiments in the present application without departing from the spirit and scope of the embodiments in the present application. Thus, if these modifications and variations of the embodiments in the present application fall within the scope of the claims and their equivalents in the embodiments of the present application, the embodiments of the present application are also intended to include these modifications and variations.

Claims

1. A method for obtaining aircraft collision probability based on non-central chi-square distribution, characterized in that: The method comprises: Based on the area radius of the collision area of ​​the two aircraft, the protection box radius of a spherical collision protection box with the center of mass of any aircraft as the sphere center is obtained; wherein the collision area is the smallest spherical area that wraps the aircraft; the spherical collision protection box represents the collision protection range of the corresponding aircraft; the protection box radius is the sum of the area radii corresponding to the two aircraft; For any aircraft, determine the relative position vector of the center of mass position of the aircraft relative to the center of mass position of another aircraft in a three-dimensional Cartesian coordinate system, and obtain the nominal track data and actual flight track data of the aircraft in the cruise phase; Determine the relative position error matrix of the two aircraft and the eigenvalue of the corresponding relative position error matrix based on the error value between the nominal track data and the actual flight track data corresponding to each aircraft; Using a preset three-degree-of-freedom non-central chi-square distribution algorithm, the relative position vector, the relative position error matrix and the eigenvalues ​​of the corresponding relative position error matrix are processed to obtain a collision probability between the two aircraft; The nominal track data includes the nominal speed, the longitude and latitude of the nominal track points at different timestamps, and the altitude above the ground; the actual flight track data includes the actual speed, the longitude and latitude of the actual flight track points at different timestamps, and the altitude above the ground; Based on the error values ​​between the nominal track data and the actual flight track data corresponding to each aircraft, the relative position error matrix of the two aircraft and the eigenvalues ​​of the corresponding relative position error matrix are determined, including: For any aircraft, when the actual speed is the nominal speed, obtain the error value and corresponding error covariance between the position of the actual flight track point and the position of the nominal track point in different coordinate axis directions and at different time stamps in the three-dimensional Cartesian coordinate system; Based on the error covariance of the two aircrafts obtained, a relative position error matrix is ​​constructed; Obtaining eigenvalues ​​of the relative position error matrix; The error values ​​include the error value between the position of the actual flight trajectory point in the x-axis direction and the position of the nominal track point, the error value between the position of the actual flight trajectory point in the y-axis direction and the position of the nominal track point, and the error value between the position of the actual flight trajectory point in the z-axis direction and the position of the nominal track point; The error covariance includes a first variance of the error value between the position of the actual flight trajectory point in the x-axis direction and the position of the nominal track point, a second variance of the error value between the position of the actual flight trajectory point in the y-axis direction and the position of the nominal track point, and a third variance of the error value between the position of the actual flight trajectory point in the z-axis direction and the position of the nominal track point; and a first covariance of the error value between the position of the actual flight trajectory point in the x-axis direction and the position of the nominal track point and the position of the actual flight trajectory point in the y-axis direction, a second covariance of the error value between the position of the actual flight trajectory point in the x-axis direction and the position of the nominal track point and the position of the actual flight trajectory point in the z-axis direction, and a third covariance of the error value between the position of the actual flight trajectory point in the y-axis direction and the position of the nominal track point and the position of the actual flight trajectory point in the z-axis direction; The relative position error matrix is ​​a 3X3 covariance matrix; wherein a first relative variance determined based on a first variance of the two aircraft, a second relative variance determined based on a second variance of the two aircraft, and a third relative variance determined based on a third variance of the two aircraft are main diagonal elements of the covariance matrix; a first relative covariance determined based on the first covariance of the two aircraft, a second relative covariance determined based on the second covariance of the two aircraft, and a third relative covariance determined based on the third covariance of the two aircraft are non-main diagonal elements of the covariance matrix; The number of eigenvalues ​​of the relative position error matrix obtained is 3, and all are greater than 0; The calculation formula for obtaining the collision probability is expressed as: in: is the integration interval constant, represents an algorithm for calculating the probability of collision less than or equal to a threshold, where P is the collision probability, is the generalized inverse matrix of the relative position error matrix, The non-centrality parameter is The chi-square distribution with three degrees of freedom is represents the relative position vector, Represents the vector after the relative position vector is transposed; Get the integration interval constant The calculation formula is expressed as: in, represents three different eigenvalues, Indicates the radius of the protection box.

2. A device for obtaining aircraft collision probability based on non-central chi-square distribution, characterized in that: The device comprises: An acquisition unit is used to acquire a protection box radius of a spherical collision protection box with the mass center of any aircraft as the sphere center based on the area radius of the collision area of ​​the two aircraft; wherein the collision area is a minimum spherical area that wraps the aircraft; the spherical collision protection box represents the collision protection range of the corresponding aircraft; and the protection box radius is the sum of the area radii corresponding to the two aircraft; a determination unit, for determining, for any aircraft, a relative position vector of the center of mass position of the aircraft relative to the center of mass position of another aircraft in a three-dimensional Cartesian coordinate system, and obtaining nominal track data and actual flight track data of the aircraft in a cruise phase; and, determining a relative position error matrix of the two aircraft and an eigenvalue of the corresponding relative position error matrix based on an error value between the nominal track data and the actual flight track data corresponding to each aircraft; a processing unit, configured to process the relative position vector, the relative position error matrix and the eigenvalues ​​of the corresponding relative position error matrix using a preset three-degree-of-freedom non-central chi-square distribution algorithm to obtain a collision probability between the two aircraft; The nominal track data includes the nominal speed, the longitude and latitude of the nominal track points at different timestamps, and the altitude above the ground; the actual flight track data includes the actual speed, the longitude and latitude of the actual flight track points at different timestamps, and the altitude above the ground; Based on the error values ​​between the nominal track data and the actual flight track data corresponding to each aircraft, the relative position error matrix of the two aircraft and the eigenvalues ​​of the corresponding relative position error matrix are determined, including: For any aircraft, when the actual speed is the nominal speed, obtain the error value and corresponding error covariance between the position of the actual flight track point and the position of the nominal track point in different coordinate axis directions and at different time stamps in the three-dimensional Cartesian coordinate system; Based on the error covariance of the two aircrafts obtained, a relative position error matrix is ​​constructed; Obtaining eigenvalues ​​of the relative position error matrix; The error values ​​include the error value between the position of the actual flight trajectory point in the x-axis direction and the position of the nominal track point, the error value between the position of the actual flight trajectory point in the y-axis direction and the position of the nominal track point, and the error value between the position of the actual flight trajectory point in the z-axis direction and the position of the nominal track point; The error covariance includes a first variance of the error value between the position of the actual flight trajectory point in the x-axis direction and the position of the nominal track point, a second variance of the error value between the position of the actual flight trajectory point in the y-axis direction and the position of the nominal track point, and a third variance of the error value between the position of the actual flight trajectory point in the z-axis direction and the position of the nominal track point; and a first covariance of the error value between the position of the actual flight trajectory point in the x-axis direction and the position of the nominal track point and the position of the actual flight trajectory point in the y-axis direction, a second covariance of the error value between the position of the actual flight trajectory point in the x-axis direction and the position of the nominal track point and the position of the actual flight trajectory point in the z-axis direction, and a third covariance of the error value between the position of the actual flight trajectory point in the y-axis direction and the position of the nominal track point and the position of the actual flight trajectory point in the z-axis direction; The relative position error matrix is ​​a 3X3 covariance matrix; wherein a first relative variance determined based on a first variance of the two aircraft, a second relative variance determined based on a second variance of the two aircraft, and a third relative variance determined based on a third variance of the two aircraft are main diagonal elements of the covariance matrix; a first relative covariance determined based on the first covariance of the two aircraft, a second relative covariance determined based on the second covariance of the two aircraft, and a third relative covariance determined based on the third covariance of the two aircraft are non-main diagonal elements of the covariance matrix; The number of eigenvalues ​​of the relative position error matrix obtained is 3, and all are greater than 0; The calculation formula for obtaining the collision probability is expressed as: in: is the integration interval constant, represents an algorithm for calculating the probability of collision less than or equal to a threshold, where P is the collision probability, is the generalized inverse matrix of the relative position error matrix, The non-centrality parameter is The chi-square distribution with three degrees of freedom is represents the relative position vector, Represents the vector after the relative position vector is transposed; Get the integration interval constant The calculation formula is expressed as: in, represents three different eigenvalues, Indicates the radius of the protection box.

3. An electronic device, characterized in that: The electronic device comprises a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory communicate with each other via the communication bus; Memory, used to store computer programs; The processor is used to implement the method of claim 1 when executing the program stored in the memory.

4. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method of claim 1 is implemented.

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