Aircraft penetration trajectory planning method and system

Abstract

The invention provides an aircraft penetration trajectory planning method and system, and relates to the technical field of aircraft trajectory planing.The aircraft penetration trajectory planning method comprises the steps that a three-dimensional penetration space is constructed, and the exposure probability is calculated based on scattering intensity to generate an initial path; collecting real-time meteorological data including turbulence intensity and wind speed to calculate a meteorological threat value, and repairing the path points with the threat value exceeding the limit in the optimization window by adopting a DDP back propagation algorithm to generate safe path points; and finally, verifying whether the RCS increment of the security path point meets a threshold requirement or not to ensure a low detection probability.

Description

Technical Field

[0001] The present invention relates to the technical field of aircraft trajectory planning, and in particular to an aircraft penetration trajectory planning method and system. Background Art

[0002] In modern air defense systems, radar networks are increasingly capable of detecting aircraft, posing significant challenges to penetration missions. Traditional penetration trajectory planning methods primarily rely on static stealth design or simple path optimization, making them incapable of coping with the combined threats of dynamic radar detection and complex meteorological environments. For example, existing technologies often overlook the dynamic impact of the real-time relative posture of an aircraft and multiple radar base stations on its radar cross section, resulting in unstable stealth performance. Furthermore, sudden threats from meteorological conditions are not fully incorporated into real-time path planning, potentially leading to loss of control or trajectory deviation. Therefore, a penetration trajectory planning method that integrates dynamic optimization of multiple radar RCSs with real-time meteorological threat avoidance is urgently needed to enhance aircraft survivability and mission success rates.

[0003] In the prior art, publication number CN108958292A discloses a method for aircraft penetration trajectory planning based on the RRT* algorithm. Based on the RCS data of the aircraft under different circumferential postures, a radar detection probability model is established to determine the probability of the aircraft being detected by the radar during the penetration process; an aircraft penetration trajectory planning model is established based on the Dubins path; and penetration trajectory planning is performed based on the RRT* algorithm and the aircraft penetration trajectory planning model. That is, penetration trajectory planning is performed by combining the asymptotic optimality of the RRT* algorithm and the shortest Dubins path characteristics. This can effectively reduce the cost of aircraft penetration trajectory planning, obtain the aircraft penetration trajectory, and achieve effective aircraft penetration.

[0004] The main problems with the above scheme are: it relies on pre-stored circumferential RCS static data, does not consider the impact of the dynamic changes in the actual relative posture of the aircraft and the radar on the RCS, resulting in delayed adjustment of stealth performance and difficulty in coping with dynamic detection scenarios of multiple radar base stations; it does not consider the threat assessment of the path caused by meteorological changes, has weak prevention of flight risks caused by bad weather, and has low trajectory safety.

[0005] The above information disclosed in this Background section is only for enhancement of understanding of the background of the present disclosure and therefore it may contain information that does not form the prior art that is already known to a person of ordinary skill in the art. Summary of the Invention

[0006] The purpose of the present invention is to provide an aircraft penetration trajectory planning method and system to solve the problems raised in the above background technology.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] A method for planning an aircraft penetration trajectory, comprising the following steps:

[0009] Step 1: Construct a three-dimensional penetration space based on the aircraft's penetration area. Randomly generate multiple penetration paths in the three-dimensional penetration space. Calculate the aircraft's exposure probability at each penetration path point based on the scattering intensity. The shortest penetration path that ensures that the exposure probability of each penetration path point does not exceed the exposure threshold is selected as the initial path.

[0010] Step 2: Collect real-time meteorological data for each initial path point, including the turbulence intensity field and the three-dimensional wind speed field. Generate the real-time meteorological value of the path point based on the turbulence intensity field and the three-dimensional wind speed field, and then calculate the meteorological threat value of each initial path point.

[0011] Step 3: Set a threat value threshold. When the meteorological threat value of an initial path point exceeds the threat value threshold, the initial path point is set as a threat point. A breakthrough time period of equal length is taken before and after the threat point. All initial path points within the breakthrough time period are combined to form an optimization window. Within the optimization window, the coordinates of the threat point are adjusted based on DDP back propagation to generate a safe path point.

[0012] Step 4: Calculate the line-of-sight angle between the aircraft and the nearest radar when the aircraft is at the threat point, and obtain the optimal line-of-sight angle corresponding to the minimum scattering intensity of the radar wave emitted by the aircraft relative to the nearest radar. Define an incremental threshold relative to the minimum scattering intensity, and calculate the difference in the scattering intensity of the radar wave relative to the optimal line-of-sight angle when the aircraft is at the safe path point. When the difference between the two is outside the incremental threshold range, recalculate the safe path point. Otherwise, retain the safe path point and replace the original threat point with the safe path point and add it to the initial path point sequence. After all the threat points in the initial path are replaced, generate the final path point sequence as the aircraft's penetration trajectory.

[0013] Furthermore, the principle for calculating the exposure probability of an aircraft at each penetration path point based on scattering intensity is as follows:

[0014] The scattering intensity of the radar wave at each penetration path point of the aircraft is:

[0015]

[0016] Among them, RCS[θ i (j),λ i ] represents the scattering intensity of the radar wave emitted by the i-th radar at the j-th penetration path point of the aircraft, i represents the index of the radar, and i∈[1,N], N represents the number of radars, j represents the index of the penetration path point, θ i (j) represents the line of sight angle of the aircraft relative to the i-th radar at the j-th penetration path point, λi represents the wavelength of the i-th radar, f i represents the operating frequency of the i-th radar, c represents the speed of light, S represents the effective reflection area of the aircraft, and h represents the height of the aircraft surface, that is, the straight-line height difference between the lowest point and the highest point;

[0017] The probability of an aircraft being detected by radar at a penetration path point is:

[0018]

[0019] Among them, K(j,i) represents the probability that the aircraft is detected by the i-th radar at the j-th penetration path point, P i represents the transmission power of the i-th radar, R(j,i) represents the straight-line distance between the j-th penetration path point and the i-th radar, and L atm (f i ) represents the operating frequency f i The corresponding atmospheric attenuation loss;

[0020] The exposure probability of the aircraft is:

[0021] K(j)=max{K(j,i)|i∈[1,N]}

[0022] Where K(j) represents the exposure probability of the aircraft at the jth penetration path point.

[0023] Furthermore, when constructing the three-dimensional penetration space, the three-dimensional spatial range of the aircraft's penetration area is determined, including longitude, latitude, and altitude. The locations of radar base stations, air defense facilities, and terrain obstacles are marked as no-fly zones. The minimum and maximum speeds of the aircraft, the maximum climb and dive angles of the aircraft, and the minimum turning radius are used as constraints to divide the penetration area into uniform three-dimensional grid cells, with each cell representing a potential path point.

[0024] The initial path is a set of initial path points:

[0025] A={A t |t∈[0,T]}

[0026] Among them, A represents the set of initial path points, A t It represents the coordinates of the position reached at time t during the process of the aircraft flying along the initial path, t represents the time variable when the aircraft flies along the initial path, and T represents the time spent by the aircraft flying along the initial path.

[0027] Furthermore, the principle for calculating the weather threat value of each initial path point is as follows:

[0028] The formula for generating the real-time weather values of the initial path points is:

[0029] W(A t )=α×T(A t )+β×|V(A t )|

[0030] Among them, W(A t ) represents the initial path point A t Real-time meteorological value at time t, T(A t ) represents the initial path point A t Turbulence intensity at time t, |V(A t )| represents the initial path point A t The wind speed at time t, α and β represent the weight coefficients of turbulence intensity and wind speed, respectively, α + β = 1 and α > β;

[0031] The formula for calculating the meteorological threat value of each initial path point is:

[0032]

[0033] Among them, M(A t ) represents the initial path point A t The weather threat value at time t, W safe represents the meteorological safety threshold, W dang Indicates the meteorological danger threshold.

[0034] Furthermore, the principle of adjusting the coordinates of threat points based on DDP back propagation and generating safe path points is as follows:

[0035] The cost function of the threat point is constructed based on the formula:

[0036]

[0037] u k =(Δx k ,Δy k ,Δz k )

[0038] Among them, J k represents the cost function of the threat point within the optimization window, k represents the time of the threat point within the optimization window, and the time range of the entire optimization window is [k-Δt, k+Δt], Δt represents the penetration time period, u k Indicates the initial path point A k The coordinate adjustment amount, v represents the smoothness weight, and v = 0.1, Δx k , Δy k , Δz k Represent the initial path point A kThe amount of adjustment of the point in the horizontal, vertical and vertical coordinates;

[0039] Iterate backward from the end point of the optimization window t = k + Δt to the starting point t = k - Δt, and update u through the Bellman equation k , based on the formula:

[0040]

[0041] in, Represents the initial path point A after update k The coordinate adjustment amount, J k+1 Represents the initial path point A within the optimization window k+1 The cost function of

[0042] Generate coordinate adjustment based on gradient descent method

[0043] Through the optimized Starting from the starting point of the optimization window t = k-Δt, until the end point of the optimization window t = k + Δt, the coordinates of the initial path points are updated forward according to the formula:

[0044]

[0045] in, Represents the initial path point A after update k coordinates of

[0046] Recalculate the cost function based on the updated threat point coordinates. If the cost function decreases, accept the update. Repeat the reverse iteration and forward update steps. When the decrease in the cost function calculated twice is less than 10 -3 When , stop the iteration and output the current This is the coordinate of the threat point after adjustment.

[0047] Furthermore, the principle for generating the final pathpoint sequence is as follows:

[0048] The formula for obtaining the optimal sight angle corresponding to the minimum scattering intensity of the aircraft relative to the radar wave emitted by the nearest radar is:

[0049]

[0050] Among them, RCS[θ min (k),λ min ] represents the scattering intensity of the radar wave emitted by the nearest radar relative to the position of the aircraft at time k, θ min (k) represents the line-of-sight angle of the aircraft relative to the nearest radar at time k;

[0051] When RCS[θ min (k),λ min ] takes the minimum value, the corresponding sight angle represents the optimal sight angle at time k, recorded as θ best (k);

[0052] The incremental threshold of the minimum scattering intensity is set to ΔRCS, and the deviation of the scattering intensity of the aircraft relative to the optimal line of sight angle to the radar wave at the safe path point is calculated based on the following formula:

[0053]

[0054] ΔRCS=0.3×RCS0

[0055] Among them, RCS[θ safe (k),λ min ] represents the scattering intensity deviation value, θ safe (k) The line-of-sight angle of the aircraft at the safe path point at time k relative to the nearest radar, ΔRCS represents the incremental threshold of the minimum scattering intensity, and RCS0 represents the RCS[θ min (k),λ min ];

[0056] When RCS[θ safe (k),λ min ]≤ΔRCS, keep the safe path point;

[0057] When RCS[θ safe (k),λ min ]>ΔRCS, the safe path points are regenerated based on DDP back propagation until the retention conditions of the safe path points are met.

[0058] The present invention also provides an aircraft penetration trajectory planning system, which is used to implement the above-mentioned aircraft penetration trajectory planning method, specifically comprising:

[0059] The initial path planning module is used to construct a three-dimensional penetration space based on the aircraft's penetration area, randomly generate multiple penetration paths in the three-dimensional penetration space, calculate the aircraft's exposure probability at each penetration path point based on the scattering intensity, and select the shortest penetration path that satisfies the exposure probability of each penetration path point not exceeding the exposure threshold as the initial path;

[0060] The meteorological impact analysis module is used to collect real-time meteorological data for each initial path point, specifically including the turbulence intensity field and the three-dimensional wind speed field. Based on the turbulence intensity field and the three-dimensional wind speed field, the real-time meteorological value of the path point is generated, and the meteorological threat value of each initial path point is calculated.

[0061] The path optimization module is used to set a threat value threshold. When the meteorological threat value of an initial path point exceeds the threat value threshold, the initial path point is set as a threat point. A breakthrough time period of equal length is taken before and after the threat point, and all initial path points within the breakthrough time period are combined to form an optimization window. Within the optimization window, the coordinates of the threat point are adjusted based on DDP back propagation to generate a safe path point.

[0062] The penetration trajectory generation module is used to calculate the line of sight angle between the aircraft and the nearest radar when the aircraft is at the threat point position, and obtain the optimal line of sight angle corresponding to the minimum scattering intensity of the radar wave emitted by the aircraft relative to the nearest radar, define the incremental threshold relative to the minimum scattering intensity, and calculate the difference in the scattering intensity of the radar wave relative to the optimal line of sight angle when the aircraft is at the safe path point position. When the difference between the two is outside the incremental threshold range, the safe path point is recalculated. Otherwise, the safe path point is retained, and the original threat point is replaced by the safe path point and added to the initial path point sequence. After all the threat points in the initial path are replaced, the final path point sequence is generated as the aircraft penetration trajectory.

[0063] Compared with the prior art, the present invention has the following beneficial effects:

[0064] The present invention generates the probability of an aircraft being detected by multiple radars in combination with the aircraft's real-time flight attitude, and generates initial path points based on the lowest probability of being detected by radar, ensuring that the aircraft is always in a low-detection state in a multi-radar environment, reducing the risk of detection and improving the concealment of the path.

[0065] The present invention also uses airborne radar to collect environmental data including turbulence intensity and three-dimensional wind speed in real time, and calculates the meteorological threat value, thereby avoiding flight risks caused by bad weather, improving the safety of the penetration trajectory and the applicability of the planning method; for path points whose meteorological threat values exceed the threshold, an optimization window is generated, and a cost function is constructed within the optimization window based on the DDP back propagation algorithm to perform local repair. According to the repaired safe path points, their deviation from the minimum scattering intensity is calculated. The safe path points are retained only when the deviation is within the incremental threshold range. The repaired path points avoid meteorological threats and maintain a low detection state, thereby achieving high adaptability of the solution in a dynamic environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] Figure 1 This is a schematic diagram of a method flow in accordance with an embodiment of the present invention;

[0067] Figure 2 This is a graph analyzing changes in the detection probability of an aircraft according to an embodiment of the present invention;

[0068] Figure 3 Schematic diagram of a fitting curve of the detection probability and scattering intensity of an aircraft according to an embodiment of the present invention;

[0069] Figure 4 This is a diagram showing changes in meteorological threat values according to an embodiment of the present invention;

[0070] Figure 5 Schematic diagram of a fitting curve of a meteorological threat value and a meteorological value according to an embodiment of the present invention;

[0071] Figure 6 Schematic diagram of system modules according to an embodiment of the present invention. DETAILED DESCRIPTION

[0072] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to specific embodiments.

[0073] It should be noted that, unless otherwise defined, the technical or scientific terms used in the present invention should have the usual meanings understood by people with ordinary skills in the field to which the present invention belongs. The "first", "second" and similar words used in the present invention do not indicate any order, quantity or importance, but are only used to distinguish different components. "Include" or "comprise" and 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. "Connect" or "connected" and 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 position relationships. When the absolute position of the object being described changes, the relative position relationship may also change accordingly.

[0074] Example:

[0075] See also Figures 1 to 6 , the present invention provides a technical solution:

[0076] A method for planning an aircraft penetration trajectory, comprising the following steps:

[0077] Step 1: Construct a three-dimensional penetration space based on the aircraft's penetration area. Randomly generate multiple penetration paths in the three-dimensional penetration space. Calculate the aircraft's exposure probability at each penetration path point based on the scattering intensity. The shortest penetration path that ensures that the exposure probability of each penetration path point does not exceed the exposure threshold is selected as the initial path.

[0078] In this embodiment, the principle for calculating the exposure probability of the aircraft at each penetration path point based on the scattering intensity is as follows:

[0079] The scattering intensity of the radar wave at each penetration path point of the aircraft is:

[0080]

[0081] Among them, RCS[θ i (j),λ i ] represents the scattering intensity of the radar wave emitted by the i-th radar at the j-th penetration path point of the aircraft, i represents the index of the radar, and i∈[1,N], N represents the number of radars, j represents the index of the penetration path point, θ i (j) represents the line of sight angle of the aircraft relative to the i-th radar at the j-th penetration path point, λ i represents the wavelength of the i-th radar, f i represents the operating frequency of the i-th radar, c represents the speed of light, S represents the effective reflection area of the aircraft, and h represents the height of the aircraft surface, that is, the straight-line height difference between the lowest point and the highest point;

[0082] RCS reflects the ability of the aircraft surface to reflect radar waves. The smaller the RCS value, the lower the probability of the aircraft being detected by radar. The aircraft surface can be regarded as a smooth conductive surface. Based on the physical optics method, the RCS value is related to the incident angle. For an aircraft, its effective reflection area and surface undulation height are fixed, so it is necessary to adjust the aircraft attitude and change the aircraft's line of sight angle relative to the radar, thereby changing the aircraft's scattering intensity of radar waves.

[0083] The probability of an aircraft being detected by radar at a penetration path point is:

[0084]

[0085] Among them, K(j,i) represents the probability that the aircraft is detected by the i-th radar at the j-th penetration path point, P i represents the transmission power of the i-th radar, R(j,i) represents the straight-line distance between the j-th penetration path point and the i-th radar, and L atm (f i ) represents the operating frequency f i The corresponding atmospheric attenuation loss;

[0086] The exposure probability of the aircraft is:

[0087] K(j)=max{K(j,i)|i∈[1,N]}

[0088] Where K(j) represents the exposure probability of the aircraft at the jth penetration path point;

[0089] The probability of an aircraft being detected by radar reflects the probability of an aircraft being detected by different radars when the aircraft is at a certain location. The probability of an aircraft being detected by radar is mainly determined by the radar transmission power, the straight-line distance between the aircraft and the radar, the atmospheric attenuation loss of the radar, and the real-time RCS value of the aircraft. 10 [RCS[θ i (j),λ i ]×P i ] reflects the direct detection effect of the signal emitted by the radar on the aircraft and describes the target echo intensity received by the radar, 10log 10 [RCS[θ i (j),λ i ]×P i The higher the value, the more directly the radar can detect the aircraft. The dynamic range of radar echo power is extremely large, so a logarithmic transformation is used to ensure computability. The probability of an aircraft being detected by radar is proportional to the aircraft's real-time RCS value and the radar transmit power. 10 R(j,i) reflects the signal attenuation of the radar wave transmitted in space during the radar detection process. The radar wave will attenuate when it goes back and forth, and the attenuation each time is The double decay is Convert to logarithmic form The signal attenuation of radar waves transmitted in space is proportional to the distance between the radar and the aircraft; -L atm (f i ) represents the effect of the atmospheric attenuation coefficient on the radar detection effect, which is related to the real-time weather conditions. Severe weather conditions will affect the radar detection effect. The worse the weather conditions, the higher the atmospheric attenuation coefficient and the worse the radar detection effect. The radar power density decays with the square of the distance. The logarithm is used in the numerator to measure the signal attenuation, which retains the gradient information of the long-range radar. The denominator uses R 2 (j,i) compensates for attenuation so that detection by long-range radars will not be overlooked. The probability of an aircraft being detected by radar is proportional to the aircraft's RCS value and radar transmit power, and inversely proportional to the distance between the aircraft and the radar and atmospheric attenuation loss. The same aircraft will be detected by multiple radars, and in order to successfully penetrate, it must ensure that it is not detected by any radar. Therefore, the probability with the highest detection probability among all radars is taken as the aircraft's exposure probability. Table 1 reflects the probability of an aircraft being detected by radar under different scattering intensities, and associates key parameters such as radar transmit power, distance between radar and aircraft, and atmospheric attenuation loss, reflecting the impact of each parameter on the detection probability.

[0090] Table 1

[0091]

[0092]

[0093] The lower the exposure threshold, the higher the requirement for the concealment of the penetration mission. The exposure threshold is set based on the concealment of the penetration mission. The exposure threshold K0 of the penetration mission is determined through expert evaluation. When K(j)≤K0, the j-th penetration path point can be added to the initial path as the initial path point.

[0094] When constructing the three-dimensional penetration space, the three-dimensional spatial range of the aircraft's penetration area is determined, including longitude, latitude, and altitude. The locations of radar base stations, air defense facilities, and terrain obstacles are marked as no-fly zones. The minimum and maximum speeds of the aircraft, the maximum climb and dive angles of the aircraft, and the minimum turning radius are used as constraints. The penetration area is divided into uniform three-dimensional grid cells, with each cell representing a potential path point.

[0095] The initial path is a set of initial path points:

[0096] A={A t |t∈[0,T]}

[0097] Among them, A represents the set of initial path points, A t It represents the coordinates of the position reached at time t during the process of the aircraft flying along the initial path, t represents the time variable when the aircraft flies along the initial path, and T represents the time spent by the aircraft flying along the initial path.

[0098] Step 2: Collect real-time meteorological data for each initial path point, including the turbulence intensity field and the three-dimensional wind speed field. Generate the real-time meteorological value of the path point based on the turbulence intensity field and the three-dimensional wind speed field, and then calculate the meteorological threat value of each initial path point.

[0099] The principle for calculating the meteorological threat value of each initial path point is:

[0100] The formula for generating the real-time weather values of the initial path points is:

[0101] W(A t )=α×T(A t )+β×|V(A t )|

[0102] Among them, W(A t ) represents the initial path point A t Real-time meteorological value at time t, T(A t ) represents the initial path point A t Turbulence intensity at time t, |V(A t )| represents the initial path point A tThe wind speed at time t, α and β represent the weight coefficients of turbulence intensity and wind speed, respectively, α + β = 1 and α > β;

[0103] During flight, the aircraft is mainly affected by meteorological conditions such as turbulence intensity field and three-dimensional wind speed field. Turbulence is mainly caused by wind shear, terrain effect or thermal convection, which can lead to unstable aircraft attitude, structural fatigue or even loss of control. The lower the value, the more stable the aircraft is, and the higher the value, the more unstable the aircraft attitude is. The three-dimensional wind speed field describes the vector distribution of wind speed in space, including the size and direction of the wind. T(A t ) represents the initial path point A t The turbulence intensity at time t is used to reflect the instability of the airflow, V(A t ) is the initial path point A t The three-dimensional wind speed vector, whose modulus |V(A t )| reflects the initial path point A t The wind speed at time t jointly affects the meteorological conditions during the flight of the aircraft. Both turbulence intensity and wind speed are proportional to the real-time meteorological value. The higher the real-time meteorological value, the higher the risk faced by the aircraft. During high-altitude penetration, turbulence has a more significant impact on the safety of the aircraft, while wind speed mainly affects the speed of the aircraft. Therefore, the weight coefficient of turbulence intensity is higher, taking α = 0.7 and β = 0.3.

[0104] The formula for calculating the meteorological threat value of each initial path point is:

[0105]

[0106] Among them, M(A t ) represents the initial path point A t The weather threat value at time t, W safe represents the meteorological safety threshold, W dang Indicates the meteorological danger threshold.

[0107] The weather threat value is determined based on the real-time weather value of the path point and the weather value threshold, reflecting the impact of weather conditions on the aircraft trajectory. The larger the weather threat value, the more significant the impact of weather conditions on the aircraft trajectory. safe represents the meteorological safety threshold, W dang Indicates the meteorological danger threshold. When the real-time meteorological value is lower than W safeWhen the real-time meteorological value is higher than the meteorological danger threshold, the threat of the current meteorological condition reaches its highest level, and the meteorological threat value is 1. When the real-time meteorological value is within the range of the meteorological safety threshold and the meteorological danger threshold, the meteorological threat value is determined according to the deviation between the real-time meteorological value and the meteorological safety threshold. The lower the deviation, the smaller the meteorological threat value, and the smaller the impact of the meteorological conditions. The higher the deviation, the larger the meteorological threat value, and the greater the impact of the meteorological conditions. Table 2 reflects the impact of wind speed and turbulence intensity on the meteorological threat value at different times, reflecting the size of the meteorological threat encountered by the aircraft, W safe =15,W dang =35.

[0108] Table 2

[0109]

[0110]

[0111] Step 3: Set a threat value threshold. When the meteorological threat value of an initial path point exceeds the threat value threshold, the initial path point is set as the threat point. Five path points closest to the time variable of the threat point are selected before and after the threat point to form an optimization window. Within the optimization window, the coordinates of the threat point are adjusted based on DDP back propagation to generate a safe path point.

[0112] In this embodiment, the principle of adjusting the coordinates of threat points based on DDP back propagation and generating safe path points is as follows:

[0113] The cost function of the threat point is constructed based on the formula:

[0114]

[0115] u k =(Δx k ,Δy k ,Δz k )

[0116] Among them, J k represents the cost function of the threat point within the optimization window, k represents the time of the threat point within the optimization window, and the time range of the entire optimization window is [k-Δt, k+Δt], Δt represents the penetration time period, u k Indicates the initial path point A k The coordinate adjustment amount, v represents the smoothness weight, and v = 0.1, Δx k , Δy k , Δz k Represent the initial path point A k The amount of adjustment of the point in the horizontal, vertical and vertical coordinates;

[0117] The cost function of the threat point consists of two parts, including the meteorological threat cost and the smoothness cost. The meteorological threat cost reflects the sum of the meteorological threat values of all initial path points in the optimization window. By adjusting the path point coordinates, M(A k ) as low as possible to avoid strong turbulence and high wind speed areas; v×|u k | 2 It represents the smoothness cost and is the trajectory adjustment penalty. When adjusting the threat point, the coordinates of other initial path points in the optimization window will also be adjusted accordingly, where u k =(Δx k ,Δy k ,Δz k ) is the coordinate adjustment of the threat point. A smaller value of the smoothness weight v focuses more on reducing the threat and allows a larger adjustment of the coordinate position. k | 2 The purpose is to keep the trajectory as smooth as possible while reducing threats and avoid frequent and violent fluctuations of the aircraft. By adjusting the coordinates of the threat point and other initial path points in the optimization window, the meteorological threat value of all initial path points in the optimization window is minimized. However, directly avoiding the threat point may cause path mutations, which does not conform to the actual flight situation of the aircraft. k | 2 Limit the adjustment range to balance the avoidance of threat points and the smoothness of the trajectory;

[0118] Iterate backward from the end point of the optimization window t = k + Δt to the starting point t = k - Δt, and update u through the Bellman equation k , based on the formula:

[0119]

[0120] in, Represents the initial path point A after update k The coordinate adjustment amount, J k+1 Represents the initial path point A within the optimization window k+1 The cost function of

[0121] Generate coordinate adjustment based on gradient descent method

[0122] Through the optimized Starting from the starting point of the optimization window t = k-Δt, until the end point of the optimization window t = k + Δt, the coordinates of the initial path points are updated forward according to the formula:

[0123]

[0124] in, Represents the initial path point A after update k coordinates of

[0125] Recalculate the cost function based on the updated threat point coordinates. If the cost function decreases, accept the update. Repeat the reverse iteration and forward update steps. When the decrease in the cost function calculated twice is less than 10 -3 When , stop the iteration and output the current This is the coordinate of the threat point after adjustment.

[0126] Step 4: Calculate the line-of-sight angle between the aircraft and the nearest radar when the aircraft is at the threat point, and obtain the optimal line-of-sight angle corresponding to the minimum scattering intensity of the radar wave emitted by the aircraft relative to the nearest radar. Define an incremental threshold relative to the minimum scattering intensity, and calculate the difference in the scattering intensity of the radar wave relative to the optimal line-of-sight angle when the aircraft is at the safe path point. When the difference between the two is outside the incremental threshold range, recalculate the safe path point. Otherwise, retain the safe path point and replace the original threat point with the safe path point and add it to the initial path point sequence. After all the threat points in the initial path are replaced, generate the final path point sequence as the aircraft's penetration trajectory.

[0127] In this embodiment, the principle for generating the final path point sequence is as follows:

[0128] The formula for obtaining the optimal sight angle corresponding to the minimum scattering intensity of the aircraft relative to the radar wave emitted by the nearest radar is:

[0129]

[0130] Among them, RCS[θ min (k),λ min ] represents the scattering intensity of the radar wave emitted by the nearest radar relative to the position of the aircraft at time k, θ min (k) represents the line-of-sight angle of the aircraft relative to the nearest radar at time k;

[0131] When RCS[θ min (k),λ min ] takes the minimum value, the corresponding sight angle represents the optimal sight angle at time k, recorded as θ best (k);

[0132] RCS[θ min (k),λ min ] takes the minimum value, indicating that the aircraft's reflection of radar waves is the weakest at this time, the stealth effect is the best, the probability of being detected is the lowest, and the corresponding angle is the optimal line of sight angle;

[0133] The incremental threshold of the minimum scattering intensity is set to ΔRCS, and the deviation of the scattering intensity of the aircraft relative to the optimal line of sight angle to the radar wave at the safe path point is calculated based on the following formula:

[0134]

[0135] ΔRCS=0.3×RCS0

[0136] Among them, RCS[θ safe (k),λ min ] represents the scattering intensity deviation value, θ safe (k) The line-of-sight angle of the aircraft at the safe path point at time k relative to the nearest radar, ΔRCS represents the incremental threshold of the minimum scattering intensity, and RCS0 represents the RCS[θ min (k),λ min ];

[0137] When RCS[θ safe (k),λ min ]≤ΔRCS, keep the safe path point;

[0138] When RCS[θ safe (k),λ min ]>ΔRCS, the safe path points are regenerated based on DDP back propagation until the retention conditions of the safe path points are met.

[0139] After repairing the threat point through DDP back propagation, it is necessary to confirm that the repaired safe path point still meets the radar stealth requirements. The DDP back propagation algorithm repairs the threat point according to the meteorological threat value, but the adjusted coordinates may change the relative attitude between the aircraft and the radar, resulting in an increase in the RCS value. By comparing the adjusted RCS value with the minimum RCS value, it is determined whether the adjusted safe path point can meet the radar stealth requirements. The cosine square function is used to describe the change of RCS with the line of sight angle. The influence of the actual sight angle on RCS due to the deviation of the optimal sight angle is safe (k)-θ best When (k) = 0°, RCS[θ safe (k),λ min ]=RCs0, at this time the aircraft's line of sight angle relative to the radar is the optimal angle, its RCS value is RCS0, the aircraft's stealth effect is the best, when θ safe (k)-θ best When (k) = 180°, RCS[θ safe (k),λ min] = RCS0 × 1.4. The RCS value at this point is maximum. The aircraft's dynamic RCS value relative to a single radar is proportional to the deviation of the aircraft's line of sight angle relative to the radar from the optimal angle. The greater the deviation of the radar's line of sight angle from the optimal angle, the easier it is to be detected by the radar. The minimum scattering intensity increment threshold is set to 0.3 × RCS0. The RCS value of the safe path point is allowed to increase by no more than 30% compared to the optimal angle to ensure that the aircraft's exposure probability and meteorological influences are reduced.

[0140] See also Figure 6 The present invention also provides an aircraft penetration trajectory planning system, which is used to implement the above-mentioned aircraft penetration trajectory planning method, specifically comprising:

[0141] The initial path planning module is used to construct a three-dimensional penetration space based on the aircraft's penetration area, randomly generate multiple penetration paths in the three-dimensional penetration space, calculate the aircraft's exposure probability at each penetration path point based on the scattering intensity, and select the shortest penetration path that satisfies the exposure probability of each penetration path point not exceeding the exposure threshold as the initial path;

[0142] The meteorological impact analysis module is used to collect real-time meteorological data for each initial path point, specifically including the turbulence intensity field and the three-dimensional wind speed field. Based on the turbulence intensity field and the three-dimensional wind speed field, the real-time meteorological value of the path point is generated, and the meteorological threat value of each initial path point is calculated.

[0143] The path optimization module is used to set a threat value threshold. When the meteorological threat value of an initial path point exceeds the threat value threshold, the initial path point is set as the threat point. Five path points closest to the time variable of the threat point are selected before and after the threat point to form an optimization window. Within the optimization window, the coordinates of the threat point are adjusted based on DDP back propagation to generate a safe path point.

[0144] The penetration trajectory generation module is used to calculate the line of sight angle between the aircraft and the nearest radar when the aircraft is at the threat point position, and obtain the optimal line of sight angle corresponding to the minimum scattering intensity of the radar wave emitted by the aircraft relative to the nearest radar, define the incremental threshold relative to the minimum scattering intensity, and calculate the difference in the scattering intensity of the radar wave relative to the optimal line of sight angle when the aircraft is at the safe path point position. When the difference between the two is outside the incremental threshold range, the safe path point is recalculated. Otherwise, the safe path point is retained, and the original threat point is replaced by the safe path point and added to the initial path point sequence. After all the threat points in the initial path are replaced, the final path point sequence is generated as the aircraft penetration trajectory.

[0145] The above formulas are all dimensionless and numerical calculations. The formulas are obtained by collecting a large amount of data and performing software simulation to obtain the most recent real situation. The preset parameters in the formulas are set by technicians in this field according to actual conditions.

[0146] The above embodiments can be implemented in whole or in part by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented in whole or in part in the form of a computer program product. Those skilled in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented by electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed by hardware or software depends on the specific application and design constraints of the technical solution.

[0147] The units described as separate components may or may not be physically separate, and the components shown as units may or may not be physical units, and may be located in one place or distributed across multiple network units. Some or all of these units may be selected to achieve the purpose of this embodiment as needed.

[0148] The above is only a specific implementation method of the present application, but the scope of protection of the present application is not limited thereto. Any technician familiar with this technical field can easily think of changes or replacements within the technical scope disclosed in this application, which should be covered by the scope of protection of the present application.

Claims

1. A method for planning an aircraft penetration trajectory, characterized in that: The specific steps include: Step 1: Construct a three-dimensional penetration space based on the aircraft's penetration area. Randomly generate multiple penetration paths in the three-dimensional penetration space. Calculate the aircraft's exposure probability at each penetration path point based on the scattering intensity. The shortest penetration path that ensures that the exposure probability of each penetration path point does not exceed the exposure threshold is selected as the initial path. Step 2: Collect real-time meteorological data for each initial path point, including the turbulence intensity field and the three-dimensional wind speed field. Generate the real-time meteorological value of the path point based on the turbulence intensity field and the three-dimensional wind speed field, and then calculate the meteorological threat value of each initial path point. Step 3: Set a threat value threshold. When the meteorological threat value of an initial path point exceeds the threat value threshold, the initial path point is set as a threat point. A breakthrough time period of equal length is taken before and after the threat point. All initial path points within the breakthrough time period are combined to form an optimization window. Within the optimization window, the coordinates of the threat point are adjusted based on DDP back propagation to generate a safe path point. Step 4: Calculate the line-of-sight angle between the aircraft and the nearest radar when the aircraft is at the threat point, and obtain the optimal line-of-sight angle corresponding to the minimum scattering intensity of the radar wave emitted by the aircraft relative to the nearest radar. Define an incremental threshold relative to the minimum scattering intensity, and calculate the difference in the scattering intensity of the radar wave relative to the optimal line-of-sight angle when the aircraft is at the safe path point. When the difference between the two is outside the incremental threshold range, recalculate the safe path point. Otherwise, retain the safe path point and replace the original threat point with the safe path point and add it to the initial path point sequence. After all the threat points in the initial path are replaced, generate the final path point sequence as the aircraft's penetration trajectory.

2. The method for planning an aircraft penetration trajectory according to claim 1, wherein: The principle for calculating the exposure probability of the aircraft at each penetration path point based on the scattering intensity in step 1 is: The scattering intensity of the radar wave at each penetration path point of the aircraft is: Among them, RCS[θ i (j),λ i ] represents the scattering intensity of the radar wave emitted by the i-th radar at the j-th penetration path point of the aircraft, i represents the index of the radar, and i∈[1,N], N represents the number of radars, j represents the index of the penetration path point, θ i (j) represents the line of sight angle of the aircraft relative to the i-th radar at the j-th penetration path point, λ i represents the wavelength of the i-th radar, f i represents the operating frequency of the i-th radar, c represents the speed of light, S represents the effective reflection area of the aircraft, and h represents the height of the aircraft surface, that is, the straight-line height difference between the lowest point and the highest point; The probability of an aircraft being detected by radar at a penetration path point is: Among them, K(j,i) represents the probability that the aircraft is detected by the i-th radar at the j-th penetration path point, P i represents the transmission power of the i-th radar, R(j,i) represents the straight-line distance between the j-th penetration path point and the i-th radar, and L atm (f i ) represents the operating frequency f i The corresponding atmospheric attenuation loss; The exposure probability of the aircraft is: K(j)=max{K(j,i)|i∈[1,N]} Where K(j) represents the exposure probability of the aircraft at the jth penetration path point.

3. The method for planning an aircraft penetration trajectory according to claim 1, wherein: When constructing the three-dimensional penetration space in step 1, the three-dimensional spatial range of the aircraft penetration area is determined, including longitude, latitude, and altitude, and the locations of radar base stations, air defense facilities, and terrain obstacles are marked as no-fly zones. The minimum and maximum speeds of the aircraft, the maximum climb and dive angles of the aircraft, and the minimum turning radius of the aircraft are used as constraints to divide the penetration area into uniform three-dimensional grid cells, each cell representing a potential path point; The initial path is a collection of a series of initial path points: A={A t |t∈[0,T]} Among them, W represents the set of initial path points, W t It represents the coordinates of the position reached at time t during the process of the aircraft flying along the initial path, t represents the time variable when the aircraft flies along the initial path, and T represents the time spent by the aircraft flying along the initial path.

4. The method for planning an aircraft penetration trajectory according to claim 3, wherein: The principle for calculating the meteorological threat value of each initial path point in step 2 is: The formula for generating the real-time weather values of the initial path points is: W(A t )=α×T(A t )+β×|V(A t )| Among them, W(A t ) represents the initial path point A t Real-time meteorological value at time t, T(A t ) represents the initial path point A t Turbulence intensity at time t, |V(A t )| represents the initial path point A t The wind speed at time t, α and β represent the weight coefficients of turbulence intensity and wind speed, respectively, α + β = 1 and α > β; The formula for calculating the meteorological threat value of each initial path point is: Among them, M(A t ) represents the initial path point A t The weather threat value at time t, W safe represents the meteorological safety threshold, W dang Indicates the meteorological danger threshold.

5. The method for planning an aircraft penetration trajectory according to claim 4, characterized in that: The principle of adjusting the threat point coordinates based on DDP back propagation in step 3 to generate safe path points is as follows: The cost function of the threat point is constructed based on the formula: u k =(Δx k ,Δy k ,Δz k ) Among them, J k represents the cost function of the threat point within the optimization window, k represents the time of the threat point within the optimization window, and the time range of the entire optimization window is [k-Δt, k+Δt], Δt represents the penetration time period, u k Indicates the initial path point A k The coordinate adjustment amount, v represents the smoothness weight, and v = 0.1, Δx k , Δy k , Δz k Represent the initial path point A k The amount of adjustment of the point in the horizontal, vertical and vertical coordinates; Iterate backward from the end point of the optimization window t = k + Δt to the starting point t = k - Δt, and update u through the Bellman equation k , based on the formula: in, Represents the initial path point A after update k The coordinate adjustment amount, J k+1 Represents the initial path point A within the optimization window k+1 The cost function of Generate coordinate adjustment based on gradient descent method Through the optimized Starting from the starting point of the optimization window t = k-Δt, until the end point of the optimization window t = k + Δt, the coordinates of the initial path points are updated forward according to the formula: in, Represents the initial path point A after update k coordinates of Recalculate the cost function based on the updated threat point coordinates. If the cost function decreases, accept the update. Repeat the reverse iteration and forward update steps. When the decrease in the cost function calculated twice is less than 10 -3 When , stop the iteration and output the current This is the coordinate of the threat point after adjustment.

6. The method for planning an aircraft penetration trajectory according to claim 5, characterized in that: The principle for generating the final path point sequence in step 4 is: The formula for obtaining the optimal line of sight angle corresponding to the minimum scattering intensity of the aircraft relative to the radar wave emitted by the nearest radar is: Among them, RCS[θ min (k),λ min ] represents the scattering intensity of the radar wave emitted by the nearest radar relative to the position of the aircraft at time k, θ min (k) represents the line-of-sight angle of the aircraft relative to the nearest radar at time k; When RCS[θ min (k),λ min ] takes the minimum value, the corresponding sight angle represents the optimal sight angle at time k, recorded as θ best (k); The incremental threshold of the minimum scattering intensity is set to ΔRCS, and the deviation of the scattering intensity of the aircraft at the safe path point relative to the optimal line of sight angle to the radar wave is calculated based on the following formula: ΔRCS=0.3×RCS0 Among them, RCS[θ safe (k),λ min ] represents the scattering intensity deviation value, θ safe (k) The line-of-sight angle of the aircraft at the safe path point at time k relative to the nearest radar, ΔRCS represents the incremental threshold of the minimum scattering intensity, and RCS0 represents the RCs[θ min (k),λ min ]; When RCS[θ safe (k),λ min ]≤ΔRCS, retain the safe path point; When RCS[θ safe (k),λ min ]>ΔRCS, the safe path points are regenerated based on DDP back propagation until the retention conditions of the safe path points are met.

7. An aircraft penetration trajectory planning system, characterized by: The system is used to implement the aircraft penetration trajectory planning method according to any one of claims 1 to 6, specifically comprising: The initial path planning module is used to construct a three-dimensional penetration space based on the aircraft's penetration area, randomly generate multiple penetration paths in the three-dimensional penetration space, calculate the aircraft's exposure probability at each penetration path point based on the scattering intensity, and select the shortest penetration path that satisfies the exposure probability of each penetration path point not exceeding the exposure threshold as the initial path; The meteorological impact analysis module is used to collect real-time meteorological data for each initial path point, specifically including the turbulence intensity field and the three-dimensional wind speed field. Based on the turbulence intensity field and the three-dimensional wind speed field, the real-time meteorological value of the path point is generated, and the meteorological threat value of each initial path point is calculated. The path optimization module is used to set a threat value threshold. When the meteorological threat value of an initial path point exceeds the threat value threshold, the initial path point is set as a threat point. A breakthrough time period of equal length is taken before and after the threat point, and all initial path points within the breakthrough time period are combined to form an optimization window. Within the optimization window, the coordinates of the threat point are adjusted based on DDP back propagation to generate a safe path point. The penetration trajectory generation module is used to calculate the line of sight angle between the aircraft and the nearest radar when the aircraft is at the threat point position, and obtain the optimal line of sight angle corresponding to the minimum scattering intensity of the radar wave emitted by the aircraft relative to the nearest radar, define the incremental threshold relative to the minimum scattering intensity, and calculate the difference in the scattering intensity of the radar wave relative to the optimal line of sight angle when the aircraft is at the safe path point position. When the difference between the two is outside the incremental threshold range, the safe path point is recalculated. Otherwise, the safe path point is retained, and the original threat point is replaced by the safe path point and added to the initial path point sequence. After all the threat points in the initial path are replaced, the final path point sequence is generated as the aircraft penetration trajectory.

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