Stealth aircraft maneuvering avoidance method and system under quasi six-degree-of-freedom assumption

Abstract

The invention discloses a stealth aircraft maneuvering avoidance method and system under a quasi six-degree-of-freedom assumption, and the method comprises the steps: S100: obtaining an azimuth angle theta corresponding to an RCS peak in an RCS curve, and determining a high RCS region of an azimuth angle domain as [theta-w / 2, theta + w / 2], where w is the width of the RCS peak; s200, determining a high RCS flight path segment on the initial flight path; s300, setting a first turning point, a second turning point and a third turning point, and taking the first turning point, the second turning point and the third turning point as sequentially adjacent track control points to generate a maneuvering track; and S400, the aircraft flies along the initial flight path, flies along the maneuvering flight path when reaching the first turning point, and returns to the initial flight path and continues to fly along the initial flight path when reaching the third turning point. According to the invention, the exposure risk of the aircraft in a real three-dimensional flight scene can be reduced.

Description

Technical Field

[0001] This application relates to the field of aircraft maneuver avoidance strategy technology, specifically to a stealth aircraft maneuver avoidance method and system under the quasi-six degrees of freedom assumption. Background Technology

[0002] In radar detection environments, the flight path of a stealth aircraft should have low observability, meaning it should reduce the probability of being detected by radar. A key characteristic of stealth aircraft is that their radar cross section (RCS) exhibits significant sensitivity to azimuth and pitch angles. During flight, the time-domain RCS value observed by radar dynamically changes with the relative attitude of the aircraft and the radar, and a high RCS value increases the risk of detection. For stealth aircraft, there is often a concentration of high RCS values ​​in certain angular regions; these angular regions are called high RCS regions. To minimize the risk of detection, the high RCS regions of the aircraft should be avoided from being exposed to radar during stealth penetration.

[0003] While maintaining a sufficient distance from radar can generally ensure that an aircraft remains undetected at a normal azimuth angle, a significant high RCS region can still create critical exposure points on the flight path, greatly increasing the risk of detection. Reference 1 (X.Lu, J.Huang, Y.Wu, and L.Song, “Influence of stealth aircraft dynamic RCS peak on radardetection probability,” Chinese Journal of Aeronautics, vol. 36, no. 3, pp.137–145, 2023) discloses an avoidance strategy: minimizing exposure time by performing rapid turning maneuvers when the aircraft approaches a high RCS region, thereby reducing the risk of detection in that region. However, this avoidance strategy only considers the impact of yaw angle on the detection probability, neglecting the impact of roll angle during the turn. In reality, roll angle also significantly affects the detection probability; therefore, the above avoidance strategy still carries a significant risk of detection in real-world 3D flight scenarios. Summary of the Invention

[0004] The purpose of this application is to provide a stealth aircraft maneuvering avoidance method and system under the quasi-six degrees of freedom assumption.

[0005] On the one hand, this application provides a stealth aircraft maneuvering avoidance method under a quasi-six-degree-of-freedom assumption, including: S100: Obtain the azimuth angle θ corresponding to the RCS peak in the RCS curve, and determine the high RCS region of the azimuth angle domain as [θ-w / 2, θ+w / 2], where w is the width of the RCS peak; the RCS curve refers to the curve of the RCS value of the stealth aircraft changing with the azimuth angle at a zero pitch angle; S200: Determine a high RCS track segment on the initial flight track, wherein the high RCS track segment refers to the track segment corresponding to the high RCS area; S300: Set a first turning point, a second turning point, and a third turning point, and use these three turning points as sequentially adjacent track control points to generate a maneuvering track. The overload coefficients of the first turning point, the second turning point, and the third turning point are set to 2g~4g, 2g~4g, and 1.064g~1.15g, respectively. The first turning point is located at the starting point of the high RCS track segment, and the turning angle of the first turning point is set so that the aircraft can avoid the high RCS area after completing the turning maneuver at the first turning point. The positions of the second and third turning points should satisfy the following: the angle between the line connecting the second and third turning points and the line connecting the second turning point and the radar is θ+w / 2, and the third turning point is located on the initial flight track but not on the high RCS track segment. S400: The aircraft flies along the initial flight path. When it reaches the first turning point, it flies along the maneuvering path. When it reaches the third turning point, it returns to the initial flight path and continues to fly along the initial flight path.

[0006] Specifically, the location of the second turning point is as follows: find the point corresponding to the azimuth angle θ of the initial flight track, draw a perpendicular line from this point to the initial flight track, and the second turning point is set on this perpendicular line.

[0007] Specifically, the turning angle at the first turning point is set to 10°~25°.

[0008] Specifically, the first turning point, the second turning point, and the third turning point are used as track control points to generate a maneuvering track. This includes sequentially connecting the first turning point, the second turning point, and the third turning point, and generating an arc-shaped turning segment at each turning point to obtain the maneuvering track.

[0009] Specifically, arc-shaped turning segments are generated at each turning point, including: determining the turning plane normal vector at each turning point; determining the centripetal acceleration at the turning point based on the arc coordination turning constraint and the overload coefficient and turning plane normal vector at the turning point; further determining the turning radius, turning angle and turning center position at the turning point; and then generating arc-shaped turning segments at the turning point based on the turning radius, turning angle and turning center position. The circular arc coordination turning constraint includes: the turning centripetal force is the resultant force of the aircraft's gravity and lift, and the direction of the turning centripetal force is perpendicular to the normal vector of the turning plane.

[0010] Specifically, step S400 further includes: the aircraft flying along the initial flight path, performing a first turning maneuver when reaching the first turning point, and flying along the maneuver path; performing a second turning maneuver when reaching the second turning point, and continuing to fly along the maneuver path; performing a third turning maneuver when reaching the third turning point, returning to the initial flight path and continuing to fly along the initial flight path.

[0011] On the other hand, this application provides a stealth aircraft maneuvering avoidance system under a quasi-six-degree-of-freedom assumption, comprising: The first module is used to obtain the azimuth angle θ corresponding to the RCS peak in the RCS curve, and to determine the high RCS region of the azimuth angle domain as [θ-w / 2, θ+w / 2], where w is the width of the RCS peak; the RCS curve refers to the curve of the RCS value of the stealth aircraft changing with the azimuth angle at a zero pitch angle; The second module is used to determine the high RCS track segment on the initial flight track, where the high RCS track segment refers to the track segment corresponding to the high RCS area; The third module is used to set the first, second, and third turning points and generate a maneuvering track using these three points as sequentially adjacent track control points. The overload coefficients for the first, second, and third turning points are set to 2g~4g, 2g~4g, and 1.064g~1.15g, respectively. The first turning point is located at the starting point of the high RCS track segment, and the turning angle of the first turning point is set so that the aircraft can avoid the high RCS area after completing the turning maneuver at the first turning point. The positions of the second and third turning points should satisfy the following: the angle between the line connecting the second and third turning points and the line connecting the second turning point and the radar is θ+w / 2, and the third turning point is located on the initial flight track but not on the high RCS track segment. The fourth module is used to allow the aircraft to fly along the initial flight path. When it reaches the first turning point, it will fly along the maneuvering path. When it reaches the third turning point, it will return to the initial flight path and continue flying along the initial flight path.

[0012] Compared with the prior art, this application has the following advantages and beneficial effects: This application determines the high RCS track segment on the initial flight track based on the high RCS region of the azimuth angle domain. When the aircraft flies to the high RCS track segment, it makes the actual flight track of the aircraft deviate from the high RCS track segment by turning maneuvering, that is, the aircraft flies along the maneuvering track, thereby realizing the avoidance of the high RCS region and reducing the exposure risk of the aircraft in the real three-dimensional flight scene.

[0013] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit the invention. Attached Figure Description

[0014] Figure 1 The RCS curve of the aircraft in rectangular coordinates; Figure 2 This diagram illustrates the radar detection probability of a flight path point when an aircraft flies along a straight path. In the diagram, 1 represents a straight path. Figure 3 Figure 1 is a schematic diagram of the evasion mechanism of existing evasion strategies. Figure 2 shows the actual flight path of the aircraft, and Figure 3 shows a magnified view of point A in Figure 2. Figure 4 A comparison of the exposure time of an aircraft in the high RCS region when flying along a straight path and a maneuvering path; Figure 5 A schematic diagram showing the setup of track control points; Figure 6 The simulation data for flight parameters during the flight process of the aircraft in the two-dimensional maneuver mode in the simulation experiment are shown in Figures (a), (c), (e), and (g), which are the curves of the change of angle of attack, pitch angle, roll angle, and yaw angle during the flight process, respectively. Figure (b) shows the detection probability of the aircraft in a single radar cycle during the flight process. and cumulative discovery probability Figure (d) shows the RCS change curve during the flight of the aircraft, and Figures (f) and (h) show the change curves of the radar relative azimuth angle and the radar relative elevation angle during the flight of the aircraft, respectively. Figure 7 The simulation data for flight parameters during the flight process of the aircraft in the three-dimensional maneuver mode in the simulation experiment are shown in Figures (a), (c), (e), and (g), which are the curves of the change of angle of attack, pitch angle, roll angle, and yaw angle during the flight process, respectively. Figure (b) shows the detection probability of the aircraft in a single radar cycle during the flight process. and cumulative discovery probability Figure (d) shows the RCS change curve during the flight of the aircraft, and Figures (f) and (h) show the change curves of the radar relative azimuth angle and the radar relative elevation angle during the flight of the aircraft, respectively. Figure 8 This is a schematic diagram of the deflection angle DA; Figure 9 The cumulative discovery probability of using the improved turning maneuver strategy and the unimproved turning strategy. contrast; Figure 10 This is a flowchart illustrating the method described in this application. Detailed Implementation

[0015] To enable those skilled in the art to better understand the present application, the present application will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are merely some embodiments of the present application, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present application without creative effort are within the scope of protection of the present application.

[0016] To facilitate understanding of this application and its differences and advantages compared to the circumvention strategy in Document 1, the following will first refer to the appendix. Figures 1-4 The avoidance strategies in Reference 1 will be explained in detail.

[0017] Please see Figure 1 This shows the RCS curve of an aircraft in Cartesian coordinates. Cartesian coordinates, also known as rectangular coordinates, are a commonly used coordinate system for describing physical positions in space. This RCS curve shows the change in the aircraft's RCS value as a function of the radar wave incident azimuth angle, determined by the aircraft's stealth characteristics. Specifically... Figure 1 The RCS curve shown is the RCS curve obtained at a 0° pitch angle. Azimuth is a fundamental concept in radar aircraft detection principles; it represents the angle between the projection of the radar wave's illumination direction onto the xy-plane of the aircraft's coordinate system and the aircraft's nose, and can also be called the radar relative azimuth. From Figure 1 The RCS curve shows a significant peak at 35° azimuth. Therefore, the azimuth range of 30° to 40° is defined as the high RCS region of the azimuth angle domain.

[0018] Please see Figure 2 This shows the radar detection probability of a flight path point when the aircraft flies along a preset straight flight path. , Figure 2 The coordinate system in the diagram is a ground reference coordinate system, which represents the relative position of the aircraft and the radar. From... Figure 2 It can be seen that trackpoints in the high RCS region have a relatively high probability of radar detection. This means there is a significant risk of exposure. Trackpoint radar detection probability. The specific calculation method will be described in detail later.

[0019] Please see Figure 3 Figure 1 illustrates the evasion mechanism of the evasion strategy described in Reference 1. The aircraft initiates a turning maneuver when approaching the high RCS region and quickly crosses the high RCS region before returning to a straight trajectory. Figure (a) shows a schematic diagram of the aircraft's actual flight trajectory, and Figure (b) shows a magnified view of point A in Figure (a). The red arrow in Figure (b) represents the instantaneous relative position vector between the radar and the aircraft.

[0020] Please see Figure 4 This figure shows a comparison of the exposure time of an aircraft in the high RCS region when flying along a straight path and a maneuvering path. The dashed lines represent the straight path, i.e., the preset flight path, which can be understood as the initial path; the solid lines represent the maneuvering path, which is the path obtained after applying a maneuvering evasion strategy to the initial path, i.e., the actual flight path of the aircraft after applying the maneuvering evasion strategy. The light red area represents the high RCS region in the azimuth angle domain. Figure 4 It can be seen that, compared with a straight path, a maneuvering path can significantly shorten the exposure time of the aircraft in the high RCS region.

[0021] However, the evasion strategy disclosed in Reference 1 is based on two-dimensional space. Directly applying it to real three-dimensional flight scenarios still carries a significant risk of detection. The following simulation experiments will be conducted to demonstrate the detection risk of the aircraft during flight in two-dimensional and three-dimensional maneuvering modes, in order to verify the shortcomings of the evasion strategy disclosed in Reference 1 in real three-dimensional flight scenarios.

[0022] The two-dimensional maneuvering mode refers to using the evasion strategy in reference 1 in two-dimensional space, while the three-dimensional maneuvering mode refers to using the evasion strategy in reference 1 in three-dimensional space. That is, the flight of the aircraft is simulated under the quasi-six degrees of freedom assumption. The main difference between the two maneuvering modes is that in the two-dimensional maneuvering mode, the turning maneuver of the aircraft only considers the yaw of the aircraft; while in the three-dimensional maneuvering mode, the turning maneuver of the aircraft is consistent with the real three-dimensional flight scenario and also considers the rolling action of the aircraft.

[0023] In the simulation test, the initial trajectories for both maneuver modes were the same and were both straight trajectories. The aircraft flew along the initial trajectory until it approached the high RCS track segment. The aircraft then initiated a turning maneuver based on an evasive strategy until it deviated from the high RCS track segment, after which it returned to the initial trajectory and continued to fly along the initial trajectory.

[0024] Given a fixed radar position, the aircraft flies along its initial track. The azimuth angle is related to the aircraft's position on the initial track. The track segment corresponding to the azimuth angle range of the high RCS region on the initial track is the high RCS track segment, which also corresponds to the track segment with the most dangerous azimuth angle. In this simulation, the azimuth angle range of the high RCS region is 30° to 40°. Because the risk of detection increases significantly when the aircraft flies in the high RCS track segment, it performs a turning maneuver when approaching it to deviate from the high RCS track segment and thus reduce the risk of detection.

[0025] The track control points set in this simulation test are shown in Table 1 and... Figure 5 , Figure 5 The dashed line segment represents the high RCS track segment, where the track control point is located. , , The three turning points of the maneuver are denoted as the first turning point. Second turning point Third turning point The turning angle TA for the first turn is set to 20°, the overload at each turning point is maintained at 2g, and the flight speed is constant at 246m / s; the radar threat model uses a radar power coefficient K=2×10 21 The radar is located 100 kilometers away from the origin of the coordinate system (0, 0, 0). In Table 1, the letter R represents the distance of the radar from the origin of the coordinate system. The radar has a scanning cycle of 4 seconds and a sampling interval of 0.05 seconds. In the three-dimensional maneuvering mode, the flight altitude is set to 8000 meters.

[0026] Table 1. Coordinates of track control points in the ground coordinate system In Table 1, the starting point End point These represent the starting and ending points of the initial straight track, and the first turning point, respectively. The point corresponding to the 30° azimuth angle above the straight flight path, the third turning point. The point corresponding to a 40° azimuth angle on the straight flight path, the first turning point. and the third turning point That is, the starting and ending points of the high RCS track segment; the second turning point. The geometric meaning is: determine the point corresponding to the 35° azimuth angle above the straight track, draw a perpendicular line to the straight track through that point, and the second turning point. It is then set on that vertical line. It should be understood that the point corresponding to the azimuth angle ψ on the straight track refers to the point where the radar wave is incident at the azimuth angle ψ when the aircraft is located at that point.

[0027] Please also see Figure 5 Track control points , , The turning point is used to guide the aircraft's turning maneuvers in the high RCS region. In this simulation, the aircraft has a significant peak at 35° azimuth angle, and the high RCS region is the azimuth angle range of 30° to 40°. Therefore, the turning point is determined based on the azimuth angle range corresponding to the high RCS region to reduce exposure risk.

[0028] The basic principle for determining the turning point in this simulation is to initiate the turning maneuver when the aircraft is about to reach the high RCS track segment, in order to avoid the high RCS area as much as possible. During the simulation, the aircraft first flies along the initial track, and upon reaching the high RCS track segment, it moves along the first turning point. Second turning point Third turning point The determined maneuvering path is used to perform a turning maneuver, then the path returns to the initial path and continues to fly along the initial path.

[0029] The simulated flight parameters of the aircraft during flight are obtained by combining the aircraft dynamics model. Please refer to [link / reference]. Figures 6-7 The simulated flight parameters for the aircraft's flight process in two-dimensional and three-dimensional maneuvering modes are shown respectively in the simulation test. Figure 6 (g) Figure 7 (g) The radar relative azimuth angle is the azimuth angle mentioned above. Figure 6 (h) Figure 7 In (h), the radar relative elevation angle refers to the angle between the radar-aircraft relative position vector and the xy plane of the aircraft coordinate system. The detection probability within a single radar cycle... and cumulative discovery probability It can be used to quantify the exposure risk and detection probability of an aircraft. and cumulative discovery probability The specific calculation method will be described in detail later.

[0030] Combination Figures 5-7 It can be seen that in both two-dimensional and three-dimensional maneuvering modes, the aircraft at the first turning point All turning maneuvers at the point of intersection effectively avoid high RCS zones, thus preventing RCS peak exposure during the initial maneuver phase. At the second turning point... The turning maneuver is designed to quickly traverse the high RCS zone, minimizing exposure time in the high RCS zone by accelerating during turns. In both two-dimensional and three-dimensional maneuver modes, the second turning point... All of these correspond to the high RCS zone, making them particularly suitable for high overload maneuvers and helping to quickly pass through the high RCS zone.

[0031] Although the basic principle of "avoiding direct exposure to high RCS through turning maneuvers" is consistent in both maneuvering modes, the three-dimensional maneuvering mode also includes roll maneuvers, resulting in a coupling effect between roll angle and azimuth angle changes. Therefore, at the third turning point... This introduces additional complexity. This coupling causes azimuth back-off, which can be seen in [reference needed]. Figure 7 The red dashed circle in the image indicates that the aircraft has re-entered the high RCS region. For example... Figures 6-7 As shown in the RCS curves, only one RCS peak appears in the two-dimensional maneuver mode, but two distinct RCS peaks appear in the three-dimensional maneuver mode. The second RCS peak is caused by the azimuth backtracking phenomenon. Furthermore, according to... Figures 6-7The radar detection probability curves show that the radar detection probability of the flight path in the two-dimensional maneuver mode is 11.83%, while the radar detection probability of the flight path in the three-dimensional maneuver mode rises to 58.14%, further indicating that the azimuth retreat phenomenon significantly increases the risk of being detected.

[0032] The inventors analyzed that the azimuth regression phenomenon might be caused by the following: the flight paths are the same in both two-dimensional and three-dimensional maneuvering modes. The main difference between the two maneuvering modes stems from the introduction of the roll angle. Specifically, compared to the two-dimensional maneuvering mode, the three-dimensional maneuvering mode, based on the quasi-six degrees of freedom assumption, introduces a roll angle. Considering that the horizontal distance along the y-axis of the aircraft's axis is much greater than the radar's altitude along the z-axis, when the aircraft rolls, the change in the cosine of the roll angle causes the azimuth angle to decrease rapidly. This rapid decrease in azimuth angle leads to re-entry into the high RCS region, resulting in a sudden increase in radar detection risk and potentially introducing new exposure risks during maneuvering.

[0033] Therefore, the third turning point This is a key factor in determining whether to re-enter the high RCS zone. To avoid azimuth regression in three-dimensional maneuvering mode, this application optimizes the overload coefficient, the position of the third turning point, and the turning angle TA, and proposes a turning maneuvering strategy applicable to three-dimensional maneuvering mode.

[0034] In this application, a deflection angle DA is introduced when determining the location of the third turning point. The deflection angle DA is defined as the angle formed by the first and second connecting lines. The first connecting line is the line connecting the second turning point to the radar, and the second connecting line is the line connecting the second turning point and the third turning point. The deflection angle DA can be used to approximate the azimuth angle of the radar wave incident at the end of the second turn, see [reference needed]. Figure 8 As shown in the figure. Through multiple simulation experiments, it can be seen that for each set turning angle TA, there exists a range of deflection angles DA that keeps the radar detection probability at a low level; and as the turning angle TA increases, this range of low radar detection probability gradually expands.

[0035] In this simulation, the high RCS zone is defined as the azimuth angle range of 30° to 40°. Therefore, when the deflection angle DA is 40°, the high RCS zone can be completely avoided, and the occurrence of azimuth retraction can be delayed to the greatest extent. Moreover, when the deflection angle DA is 40°, further increasing the turning angle TA also helps to delay the occurrence of azimuth retraction, thereby effectively preventing the azimuth angle from re-entering the high RCS zone.

[0036] Therefore, based on this simulation test, the specific improved turning maneuver strategy proposed in this application is: third turning point A relatively small overload factor of 1.064g was adopted to minimize the azimuth retraction; simultaneously, the third turning point Located on the initial track with a deflection angle DA of 40°; and the first turning point. Second turning point The positions are consistent with those in Table 1, and the overload factor is set to 2g for all of them.

[0037] To verify the technical effectiveness of the improved turning maneuver strategy proposed in this application, simulation experiments were conducted in three-dimensional maneuvering modes under different turning angles (TA) and different radar threat coefficients, using both the improved and unimproved turning maneuver strategies, and the cumulative detection probability during flight was obtained. Please see Figure 9 .from Figure 9 It can be seen that, under different turning angles (TA) and different radar power coefficients, the improved turning maneuver strategy can effectively reduce the risk of being detected.

[0038] It should be noted that the difference between the improved and unimproved turning maneuvering strategies lies only in the third turning point. Overload coefficient and location. In the unimproved turning maneuvering strategy, the third turning point... The overload factor is 2g, and the third turning point This is the end point of the high RCS track segment.

[0039] The following will combine the above and Figure 10 The methodology of this application can be summarized as follows: S100: Determines the high RCS region of the azimuth angle domain; Specifically, the RCS curve of the aircraft at a pitch angle of 0° is obtained, that is, the curve showing the relationship between the RCS value of the aircraft and the azimuth angle of the aircraft. The azimuth angle θ corresponding to the RCS peak in the RCS curve is determined. Then the high RCS region of the azimuth angle domain is [θ-w / 2, θ+w / 2], where w is the width of the RCS peak.

[0040] S200: Determine a high RCS track segment on the initial flight track. The high RCS track segment refers to the track segment corresponding to the high RCS area. Specifically, the azimuth range corresponding to the high RCS track segment is [θ-w / 2, θ+w / 2].

[0041] S300: Set a first turning point, a second turning point, and a third turning point, and use these three turning points as sequentially adjacent track control points to generate a maneuvering track. The overload coefficients of the first turning point, the second turning point, and the third turning point are set to 2g~4g, 2g~4g, and 1.064g~1.15g, respectively. The first turning point is located at the starting point of the high RCS track segment, and the turning angle of the first turning point is set so that the aircraft can avoid the high RCS area after completing the turning maneuver at the first turning point. The positions of the second and third turning points should satisfy the following: the angle between the line connecting the second and third turning points and the line connecting the second turning point and the radar is θ+w / 2, and the third turning point is located on the initial flight track but not on the high RCS track segment. Based on the generated maneuver trajectory, it is imperative that: the turning angle at the second turning point should be set to ensure that after completing the turning maneuver at the second turning point, the aircraft can fly straight to the third turning point; the turning angle at the third turning point should be set to ensure that after completing the turning maneuver at the third turning point, the aircraft returns to the initial flight path.

[0042] In some specific implementations, the turning angle of the first turning point is set to 10°~25°.

[0043] One specific method for determining the location of the second turning point in this application is as follows: Find the point corresponding to the 35° azimuth angle on the initial flight track, draw a perpendicular line from this point to the initial flight track, and set the second turning point on this perpendicular line. When the turning angle of the first turning point is known and the second turning point must be on the flight track after the aircraft turns, the intersection of the flight track after the turn and the perpendicular line is the location of the second turning point.

[0044] Because the risk of detection increases significantly when an aircraft flies along a high RCS track, a turning maneuver is performed just before the aircraft enters the high RCS track to deviate from it and reduce the risk of detection. Therefore, turning points need to be set in advance, and a turning maneuver track needs to be generated based on these points. The aircraft can then fly along the maneuver track.

[0045] One specific implementation method for generating a maneuvering track by using the first turning point, the second turning point, and the third turning point as track control points is as follows: connect the first turning point, the second turning point, and the third turning point in sequence, and generate an arc-shaped turning segment at each turning point to obtain the maneuvering track.

[0046] Furthermore, a specific implementation method for generating arc-shaped turning segments at each turning point is as follows: determine the normal vector of the turning plane at each turning point, determine the centripetal acceleration at the turning point based on the arc coordination turning constraint and the overload coefficient and the normal vector of the turning plane at the turning point, and further determine the turning radius, turning angle and turning center position at the turning point, and then generate an arc-shaped turning segment at the turning point based on the turning radius, turning angle and turning center position.

[0047] The above constraints for coordinated circular turning include: the centripetal force during turning is the resultant force of the aircraft's gravity and lift, and the direction of the centripetal force is perpendicular to the normal vector of the turning plane. Therefore, based on the triangle rule of the resultant force between the centripetal force F, gravity G, and lift L, Newton's second law is used to determine the centripetal acceleration at the turning point.

[0048] centripetal acceleration The calculation formula is expressed as follows: (1) In equation (1), It is the acceleration due to gravity; , This represents the angle between the centripetal force during turning and the horizontal plane, which is also the angle between the turning plane and the horizontal plane. It can be obtained from the normal vector of the turning plane. This indicates the overload coefficient at the turning point.

[0049] Calculate the turning radius at the turning point using the basic formula for centripetal force and Newton's second law. : (2) In formula (2): The flight speed scalar of the aircraft, i.e. the flight speed at the turning point, is given in advance.

[0050] The location of the turning center is determined based on the turning radius, turning angle, and the spatial position of the turning point. The turning segment is a circular arc, and the turning point is a point on that arc. Given the turning radius, turning angle, and the position of a point on the arc, the location of the turning center can be determined. : (3) In equation (3), Indicates the spatial location of the turning point. and These represent the flight speed directions before and after the turn. Indicates the turning angle.

[0051] S400: The aircraft flies along the initial flight path. When it reaches the first turning point, it uses a turning maneuver to make the aircraft fly along the maneuvering path. When it reaches the third turning point, it returns to the initial flight path and continues to fly along the initial flight path.

[0052] The aircraft flies along the initial flight path. When it reaches the first turning point, it performs the first turning maneuver and flies along the maneuver path. When it reaches the second turning point, it performs the second turning maneuver and continues to fly along the maneuver path. When it reaches the third turning point, it performs the third turning maneuver, returns to the initial flight path, and continues to fly along the initial flight path.

[0053] In this application, based on the high RCS region of the azimuth angle domain, a high RCS track segment is determined on the initial flight track. When the aircraft flies to the high RCS track segment, it deviates from the high RCS track segment by turning maneuver and flies along the maneuver track, thereby avoiding the high RCS region and reducing the risk of exposure.

[0054] It should be noted that the radar detection probability of the above-mentioned aircraft at the waypoints is... And the detection probability within a single radar cycle during flight. and cumulative discovery probability The calculation is performed using the following method: First, under the assumption of no sideslip, the attitude parameters of the aircraft at the waypoint are solved based on the aircraft dynamics model constructed in the airflow coordinate system: The aircraft dynamics model is constructed based on the premise that "the resultant force acting on the aircraft is the resultant force of the aircraft's gravity, thrust, and aerodynamic force." To express the aircraft's dynamic equations in the airflow coordinate system, the aircraft's gravity, thrust, and aerodynamic force need to be projected onto this system. Therefore, constructing the aircraft dynamics model in the airflow coordinate system involves transformations between multiple coordinate reference systems, including the airflow coordinate system, the body coordinate system, and the flight path coordinate system.

[0055] Then, based on the spatial positions of the radar and the waypoint in the ground coordinate system, and based on the aircraft's attitude parameters at the waypoint, the relative attitude of the aircraft relative to the radar at the waypoint in the body coordinate system is solved: Given the spatial positions of the radar and waypoints in the ground coordinate system, we need to solve for the relative attitude of the aircraft relative to the radar at the waypoints in the aircraft's body coordinate system. Since the body coordinate system is related to the aircraft's attitude parameters at the waypoints, we can perform a transformation between the ground and body coordinate systems based on these attitude parameters. Specifically, we construct a transformation matrix from the body coordinate system to the ground coordinate system based on the aircraft's attitude parameters at the waypoints. Then use the transformation matrix Transform the relative position vector from the radar to the waypoint to the aircraft coordinate system, and solve for the relative attitude of the aircraft relative to the radar at the waypoint.

[0056] Next, based on the radar's signal-to-noise ratio and the given false alarm probability Solve for the radar detection probability of the aircraft at each waypoint. Among them, the false alarm probability in engineering It has a specific value; signal-to-noise ratio Related to the relative distance between the aircraft and the radar, and the aircraft's RCS value, it can be calculated using radar equations. Where R represents the relative distance between the aircraft and the radar; This represents the RCS value of the aircraft at the waypoint. Specifically, it involves first determining the azimuth of the aircraft at the waypoint, and then... Figure 1 The RCS value corresponding to the azimuth angle is obtained, which is the RCS value of the aircraft at the track point; K represents the radar power coefficient, which is determined by the characteristics of the radar system.

[0057] Finally, based on the radar detection probability of the aircraft at each waypoint Calculate the detection probability of the aircraft within a single radar scan cycle. and the cumulative detection probability of the aircraft throughout its flight path : Within a single radar scan cycle, the aircraft will pass through multiple waypoints. The probability of radar detection of the aircraft at each waypoint is summed and divided by the radar scan cycle to obtain the probability of detection of the aircraft within a single radar scan cycle. ,in, This represents the expected probability of radar detection of the flight path points of the aircraft within a single radar scan cycle; T represents the radar scan cycle, and at any given moment, the probability of the radar beam intercepting the aircraft is 1 / T. This represents the time integral variable.

[0058] Based on the detection probability of the aircraft in each radar scan cycle Calculate the cumulative detection probability of the aircraft throughout its flight path. ,in, This represents the detection probability in the i-th radar scan cycle. Cumulative detection probability. It can be used to quantify the exposure risk of an aircraft throughout its flight path.

[0059] Although embodiments of this application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting this application. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of this application.

Claims

1. A stealth aircraft maneuvering avoidance method under a quasi-six-degree-of-freedom assumption, characterized in that, include: S100: Obtain the azimuth angle θ corresponding to the RCS peak in the RCS curve, and determine the high RCS region of the azimuth angle domain as [θ-w / 2, θ+w / 2], where w is the width of the RCS peak; the RCS curve refers to the curve of the RCS value of the stealth aircraft changing with the azimuth angle at a zero pitch angle; S200: Determine a high RCS track segment on the initial flight track, wherein the high RCS track segment refers to the track segment corresponding to the high RCS area; S300: Set a first turning point, a second turning point, and a third turning point, and use these three turning points as sequentially adjacent track control points to generate a maneuvering track. The overload coefficients of the first turning point, the second turning point, and the third turning point are set to 2g~4g, 2g~4g, and 1.064g~1.15g, respectively. The first turning point is located at the starting point of the high RCS track segment, and the turning angle of the first turning point is set so that the aircraft can avoid the high RCS area after completing the turning maneuver at the first turning point. The positions of the second and third turning points should satisfy the following: the angle between the line connecting the second and third turning points and the line connecting the second turning point and the radar is θ+w / 2, and the third turning point is located on the initial flight track but not on the high RCS track segment. S400: The aircraft flies along the initial flight path. When it reaches the first turning point, it flies along the maneuvering path. When it reaches the third turning point, it returns to the initial flight path and continues to fly along the initial flight path.

2. The stealth aircraft maneuvering evasion method as described in claim 1, characterized in that: The location of the second turning point is as follows: find the point corresponding to the azimuth angle θ of the initial flight track, draw a perpendicular line from this point to the initial flight track, and set the second turning point on this perpendicular line.

3. The stealth aircraft maneuvering evasion method as described in claim 1, characterized in that: The turning angle at the first turning point is set to 10°~25°.

4. The stealth aircraft maneuvering evasion method as described in claim 1, characterized in that: The step of generating a maneuvering trajectory by using the first turning point, the second turning point, and the third turning point as track control points includes: By sequentially connecting the first turning point, the second turning point, and the third turning point, and generating arc-shaped turning segments at each turning point, the maneuvering track is obtained.

5. The stealth aircraft maneuvering evasion method as described in claim 4, characterized in that: The step of generating arc-shaped turning segments at each turning point includes: The normal vector of the turning plane at the turning point is determined. Based on the arc coordination turning constraint and the overload coefficient and normal vector of the turning plane at the turning point, the centripetal acceleration at the turning point is determined. The turning radius, turning angle and turning center position at the turning point are further determined. Then, an arc-shaped turning segment is generated at the turning point based on the turning radius, turning angle and turning center position. The circular arc coordination turning constraint includes: the turning centripetal force is the resultant force of the aircraft's gravity and lift, and the direction of the turning centripetal force is perpendicular to the normal vector of the turning plane.

6. The stealth aircraft maneuvering evasion method as described in claim 1, characterized in that: Step S400 further includes: the aircraft flying along the initial flight path, performing a first turning maneuver when reaching the first turning point, and flying along the maneuver path; performing a second turning maneuver when reaching the second turning point, and continuing to fly along the maneuver path; performing a third turning maneuver when reaching the third turning point, returning to the initial flight path and continuing to fly along the initial flight path.

7. A stealth aircraft maneuvering avoidance system under a quasi-six-degree-of-freedom assumption, characterized in that, include: The first module is used to obtain the azimuth angle θ corresponding to the RCS peak in the RCS curve, and to determine the high RCS region of the azimuth angle domain as [θ-w / 2, θ+w / 2], where w is the width of the RCS peak; the RCS curve refers to the curve of the RCS value of the stealth aircraft changing with the azimuth angle at a zero pitch angle; The second module is used to determine the high RCS track segment on the initial flight track, where the high RCS track segment refers to the track segment corresponding to the high RCS area; The third module is used to set the first, second, and third turning points and generate a maneuvering track using these three points as sequentially adjacent track control points. The overload coefficients for the first, second, and third turning points are set to 2g~4g, 2g~4g, and 1.064g~1.15g, respectively. The first turning point is located at the starting point of the high RCS track segment, and the turning angle of the first turning point is set so that the aircraft can avoid the high RCS area after completing the turning maneuver at the first turning point. The positions of the second and third turning points should satisfy the following: the angle between the line connecting the second and third turning points and the line connecting the second turning point and the radar is θ+w / 2, and the third turning point is located on the initial flight track but not on the high RCS track segment. The fourth module is used to allow the aircraft to fly along the initial flight path. When it reaches the first turning point, it will fly along the maneuvering path. When it reaches the third turning point, it will return to the initial flight path and continue flying along the initial flight path.

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