A method for calculating the same-course dual-aircraft cooperative flight interval for improving dual-aircraft search and rescue efficiency

Abstract

The present application belongs to the technical field of unmanned aerial vehicle search and rescue, and particularly relates to a method for calculating the same-route dual-aircraft cooperative flight interval for improving dual-aircraft search and rescue efficiency. First, the target effective search leg length is calculated according to the aircraft position, the aircraft searchable distance, the aircraft flight speed and the distance length information of the target being captured by two aircrafts, and then the target effective search leg length is converted into the aircraft cooperative interval. Second, the target positioning accuracy is calculated according to the aircraft position, the aircraft direction-finding error and the distance from the aircraft to the target, and then the target positioning accuracy is converted into the aircraft cooperative interval. Finally, the optimal aircraft cooperative interval general model satisfying the positioning accuracy requirement is constructed, and the dual-aircraft cooperative optimal interval is obtained by solving the highest total value of the dual-aircraft cooperative search target. The present application can solve the dual-aircraft cooperative flight optimal interval for different routes, increase the probability of the target being simultaneously searched by the cooperative aircrafts, and improve the dual-aircraft cooperative search target efficiency.

Description

A method for calculating the spacing between two aircraft flying in tandem on the same flight path to improve the efficiency of dual-aircraft search and rescue. Technical Field

[0001] This invention belongs to the field of unmanned aerial vehicle (UAV) search and rescue technology, and in particular relates to a method for calculating the distance between two UAVs flying in coordination along the same flight path to improve the efficiency of dual-UAV search and rescue. Background Technology

[0002] Unmanned aerial vehicles (UAVs) are characterized by their flexibility, adaptability, and high level of intelligence, playing an increasingly important role in ground target detection, earthquake search and rescue, and disaster survivor retrieval. For example, after disasters such as missing persons or earthquakes, UAVs equipped with electronic signal search and monitoring capabilities can search for mobile phone signals, narrowing down the search and rescue area and saving rescue time. Compared to single-unit systems, dual- or multi-UAV collaborative systems offer advantages such as acquiring various information in complex environments, monitoring multiple targets, and finding targets faster. They can quickly monitor and assess the disaster situation, guide rescue forces to locate affected areas, search for and rescue trapped personnel, and provide strong support for disaster relief.

[0003] In single-aircraft search and rescue, fixed targets can be located through multi-point direction finding by a single aircraft. However, for moving targets, multiple direction finding operations cannot be performed simultaneously, making effective rendezvous and direction finding positioning impossible. In dual-aircraft collaborative search and rescue, two aircraft, maintaining a certain distance between them, simultaneously perform direction finding on the target, enabling the location of moving targets and the generation of their movement trajectories, effectively solving the problem of single-aircraft search and rescue's inability to locate moving targets. However, current traditional dual-aircraft collaborative search signals mostly employ two types of routes: shared runway routes and fixed-distance dual-runway routes. The distance between the two aircraft and the deviation of the direction finding system are the main factors affecting the positioning accuracy of dual-aircraft operations. The design of dual-aircraft collaborative routes mainly considers two aspects: first, the common line of sight and time; to ensure the probability of simultaneous interception by both aircraft, the smaller the distance between them, the better; second, positioning accuracy; to ensure accurate target location, the larger the distance between the two aircraft, the better. The distance between the two aircraft is often set based on the navigator's experience rather than the flight information of the two aircraft, resulting in the position and flight distance of the two collaborative aircraft simultaneously searching for the target potentially not being optimal. Summary of the Invention

[0004] The purpose of this invention is to provide a method for calculating the optimal two-aircraft cooperative spacing along the same flight path that satisfies both target search accuracy requirements and optimal search time. First, based on the aircraft's position, searchable distance, flight speed, and the distance the target is captured by both aircraft, the effective search segment length is calculated, and then converted into the aircraft cooperative spacing. Second, based on the aircraft's position, direction-finding error, and distance from the aircraft to the target, the target positioning accuracy is calculated, and then converted into the aircraft cooperative spacing. Finally, a general model for the optimal aircraft cooperative spacing that meets the positioning accuracy requirements is constructed. By finding the solution that maximizes the total value of the two-aircraft cooperative target search, the optimal two-aircraft cooperative spacing is obtained. This invention can solve for the optimal two-aircraft cooperative flight spacing for different flight paths, increasing the probability of the target being simultaneously searched by the cooperating aircraft, and improving the efficiency of two-aircraft cooperative target search.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for calculating the spacing between two aircraft flying in tandem on the same flight path to improve the efficiency of dual-aircraft search and rescue includes the following steps:

[0007] S1. Calculate the effective search segment length of the target: Define the search and rescue value of a target as the segment length in which the target is effectively searched by two aircraft at the same time. With the aircraft speed as V km / min, the time for the target to be searched by two aircraft at the same time as Tmin, the search and rescue value of the target is P = V * T.

[0008] S2. Convert the effective search segment length into cooperative flight distance: Assuming two aircraft fly along the same route at the same speed, without loss of generality, let the coordinates of aircraft 1 and 2 be (x1, y1) and (x2, y1) respectively, and the cooperative flight distance Δh = x1 - x2 = Δt * V; the number of targets is n, and the position coordinates of target i are (x1, y1) and (x2, y1) respectively. ti ,y ti The effective search start and end positions of the first aircraft for target i are [hA]. is ,hA ie The effective search start and end positions of the second aircraft for target i are [hM]. is ,hM ie Assuming the first plane is in front and the second plane is behind;

[0009] The effective search path length for the first aircraft A to acquire the target is:

[0010] f A (h)={[hA 1s ,hA 1e ],[hA 2s ,hA 2e ],…,[hA ns ,hAne ]},

[0011] The effective search path length for the target acquired by the second aircraft M is:

[0012] f M (h)={[hM 1s ,hM 1e ],[hM 2s ,hM 2e ],…,[hM ns ,hM ne ]},

[0013] The relative distance between the second aircraft and the first aircraft is: f M (Δh+h)={[Δh+hM 1s ,Δh+hM 1e ],[Δh+hM 2s ,Δh+hM 2e ],…,[Δh+hM ns ,Δh+hM ne ]};

[0014] S3. Calculate the target positioning accuracy: The target's true coordinates are (x... t ,y t The theoretical direction-finding angles are θ1 and θ2, and the direction-finding deviations are Δ1 and Δ2, respectively. The intersection point is (x t1 ,y t1 The positioning error is the distance d from the actual target position to the intersection positioning position, and the positioning accuracy is defined as follows: Where R is the distance from the aircraft to the target;

[0015] S4. Convert target positioning accuracy into dual-aircraft cooperative flight distance:

[0016] According to plane geometry, the equation of the line is:

[0017] tgθ1·xy=tgθ1·x1

[0018] tgθ2·xy=tgθ2·x2

[0019] Target location obtained: Similarly, when a deviation occurs, the equation of the straight line is:

[0020] tg(θ1+Δ1)·xy=tg(θ1+Δ1)·x1

[0021] tg(θ2+Δ2)·xy=tg(θ2+Δ2)·x2

[0022] Target location obtained:

[0023]

[0024] The distance between the positioning point and the actual location of the target, i.e., the positioning error, is:

[0025]

[0026] From the above formula, it can be seen that the positioning error is related to Δ1 and Δ2, that is, to the direction-finding angle and the aircraft's direction-finding error. The direction-finding angles θ1 and θ2 are constants, and the values ​​of Δ1 and Δ2 are empirical values. This transforms the error d into a function that is only related to (x1-x2), defining the positioning accuracy. It is also converted into a function related to (x1-x2); (x1-x2) is the aircraft coordination distance, that is, the target positioning accuracy is converted into the aircraft's coordination flight distance;

[0027] S5. Calculate the optimal cooperative flight distance that meets the positioning accuracy requirements: based on f A (h) and f M (Δh+h) calculates the total flight distance of the two aircraft simultaneously capturing n targets, which is the total search and rescue value of the targets.

[0028]

[0029] Adjust Δh to maximize P(Δh) while ensuring the positioning accuracy is within 5%R;

[0030]

[0031] Adjust Δh to maximize P(Δh) while ensuring positioning accuracy is within 5%R; use the Harris Eagle optimization algorithm to search for the optimal solution of P(Δh), and simultaneously determine the optimal cooperative flight spacing Δh; assume Δh min Δh represents the minimum coordinated flight spacing. max The initial solution X for the Harris Eagle optimization algorithm is Δh, representing the maximum cooperative flight spacing. min and Δh max The fitness function is f(X) = P(X).

[0032] Furthermore, the Harris Eagle optimization algorithm includes the following steps:

[0033] (1) Initialize the population, including the upper and lower bounds of the search space, the maximum number of iterations of the algorithm, the dimension of the solution equals the number of objectives D, the number of solutions is the size of the population NP, and randomly initialize the population pop(1:NP,1:D).

[0034] (2) Calculate the fitness value of each individual based on the fitness function and save the best individual in the population;

[0035] (3) Update the prey escape energy E and the prey escape probability r;

[0036] (4) Compare the escape energy, update the position according to the position update formula or the four strategies to hunt prey, and update the position; (5) Calculate the fitness of each individual and update the optimal fitness value of the population.

[0037] (6) Repeat steps 3-5 until the maximum number of iterations is reached and the accuracy requirement is met. The final optimal solution is the optimal effective capture segment length, and thus the cooperative flight distance is obtained.

[0038] Furthermore, the four strategies include a soft encirclement strategy, a hard encirclement strategy, a gradual rapid dive soft encirclement strategy, and a gradual rapid dive hard encirclement strategy.

[0039] The advantages of this invention are as follows: First, based on the aircraft's position, effective search range, flight speed, and the distance between the target and the target simultaneously captured by two aircraft, the effective search segment length is calculated (at a constant cruise speed, a longer effective search segment length results in a longer search time). This effective segment length is then converted into aircraft coordination spacing. Second, based on the aircraft's position, direction-finding error, and distance from the aircraft to the target, the target positioning accuracy is calculated. This accuracy is then converted into aircraft coordination spacing. Finally, a general model for the target's search and rescue value is established, mapping this value to the target's positioning accuracy and aircraft coordination spacing. By solving the optimization function that maximizes the sum of the target's value in dual-aircraft coordinated search and rescue, the optimal aircraft coordination spacing that satisfies the positioning accuracy requirements is determined. Compared to traditional methods that rely on operators' experience to set coordinated flight paths, the dual-aircraft coordinated flight spacing calculated by this invention ensures target positioning accuracy while maintaining maximum common line-of-sight and time, providing strong data support for subsequent sensor planning and increasing the search efficiency of this coordinated mission. Attached Figure Description

[0040] Figure 1 is a schematic diagram of the overall technical process of the present invention.

[0041] Figure 2 is a schematic diagram of the coordinated flight path and dual-aircraft coordinated search and rescue target location in this invention.

[0042] Figure 3 is a schematic diagram showing the location of the target on the flight path and the distance at which it is simultaneously captured by two aircraft in this invention.

[0043] Figure 4 is a schematic diagram of the dual-machine rendezvous and positioning principle in this invention.

[0044] Figure 5 is a flowchart of the Harris Eagle optimization algorithm in this invention.

[0045] Figure 6 shows the positioning error distribution during a 20km interval in dual-aircraft cooperative flight.

[0046] Figure 7 shows the positioning error distribution when the distance between the two aircraft during cooperative flight is 30 km.

[0047] Figure 8 shows the positioning error distribution when the distance between the two aircraft during cooperative flight is 40 km.

[0048] Figure 9 shows the positioning error distribution when the distance between the two aircraft during cooperative flight is 50 km.

[0049] Figure 10 shows the positioning error distribution when the distance between the two aircraft during cooperative flight is 60 km.

[0050] Figure 11 is a distribution of positioning errors when the distance between the two aircraft during cooperative flight is 70 km.

[0051] Figure 12 is a distribution of positioning errors when the distance between the two aircraft during cooperative flight is 80 km.

[0052] Figure 13 is a distribution of positioning errors when the distance between the two aircraft during cooperative flight is 90 km.

[0053] Figure 14 is a distribution of positioning errors when the distance between the two aircraft during cooperative flight is 100 km. Detailed Implementation

[0054] Example 1

[0055] This invention first calculates the effective search segment length of the target based on the aircraft's position, effective search range, flight speed, and the distance between the target and two simultaneously acquired by the two aircraft (at a constant cruise speed, a longer effective search segment results in a longer search time), and then converts this effective search segment length into aircraft coordination spacing. Secondly, it calculates the target positioning accuracy based on the aircraft's position, direction-finding error, and distance from the aircraft to the target, and then converts this target positioning accuracy into aircraft coordination spacing. Finally, it calculates the target's search and rescue value based on the effective search segment length, and by calculating the maximum total value achieved through dual-aircraft coordinated search and rescue, it determines the optimal aircraft coordination spacing that satisfies the positioning accuracy requirements. The technical flowchart is shown in Figure 1.

[0056] 1.1 Calculate the effective search segment length of the target

[0057] The search and rescue value of a target is defined as the length of the flight segment in which the target is effectively searched by two aircraft simultaneously. The longer the search segment, the longer the search time, and thus the higher the search and rescue value. Assuming the aircraft's average flight speed is V km / min, the time it takes for the target to be searched by two aircraft simultaneously is T min, and the target's search and rescue value is P = V * T.

[0058] 1.2 Effective search segment length converted into cooperative spacing

[0059] Assuming they fly along the same route at the same speed, without loss of generality, let the coordinates of aircraft 1 and 2 be (x1, y1) and (x2, y1) respectively, and the cooperative flight distance Δh = x1 - x2 = Δt * V. The number of targets is n, and the position coordinates of target i are (x1, y1) and (x2, y1) respectively. ti ,y ti The effective search start and end positions of the first aircraft for target i are [hA]. is ,hA ie The effective search segment length, i.e., the starting and ending positions of the target, is calculated using the search and rescue value formula. The effective search starting and ending positions of the second aircraft for target i are [hM]. is ,hM ie Assuming the first aircraft is in front and the second aircraft is behind, the cooperative search route is illustrated in Figures 2 and 3.

[0060] The effective search path length for the first aircraft N to acquire the target is:

[0061] f A (h)={[hA 1s ,hA 1e ],[hA 2s ,hA 2e ],…,[hA ns ,hA ne ]},

[0062] The effective search path length for the target acquired by the second aircraft M is:

[0063] f M (h)={[hM 1s ,hM 1e ],[hM 2s ,hM 2e ],…,[hM ns ,hM ne ]},

[0064] The relative distance (i.e., the cooperative flight distance) between the second aircraft and the first aircraft is: f M (Δh+h)={[Δh+hM 1s ,Δh+hM 1e ],[Δh+hM 2s ,Δh+hM 2e ],…,[Δh+hM ns ,Δh+hM ne In this formula, the cooperative flight spacing is converted into a function related to the effective search segment length.

[0065] 1.3 Calculate the target positioning accuracy

[0066] The two-aircraft rendezvous and positioning method uses the direction-finding information of two aircraft, combined with simple trigonometric operations, to estimate the position of the radiation source target. The coordinates of aircraft 1 and 2 are (x1, y1) and (x2, y1) respectively, and the true coordinates of the target are (x...). t ,y t The theoretical direction-finding angles are θ1 and θ2, and the direction-finding deviations are Δ1 and Δ2, respectively. The intersection point is (x t1 ,y t1 See Appendix 4 for a diagram illustrating the rendezvous and positioning.

[0067] The positioning error is the distance d from the actual target position to the intersection positioning position, and the positioning accuracy is defined as... Where R is the distance from the aircraft to the target.

[0068] 1.4 Target positioning accuracy converted into cooperative spacing

[0069] According to plane geometry, the equation of the line is:

[0070] tgθ1·xy=tgθ1·x1

[0071] tgθ2·xy=tgθ2·x2

[0072] Target location obtained:

[0073] Similarly, when a deviation occurs, the equation of the straight line is:

[0074] tg(θ1+Δ1)·xy=tg(θ1+Δ1)·x1

[0075] tg(θ2+Δ2)·xy=tg(θ2+Δ2)·x2

[0076] Target location obtained:

[0077]

[0078] The distance between the positioning point and the actual location of the target, i.e., the positioning error, is:

[0079]

[0080] From the above formula, it can be seen that the positioning error is related to Δ1 and Δ2, that is, to the direction-finding angle and the aircraft's direction-finding error, where the direction-finding angles θ1 and θ2 are constants. The values ​​of Δ1 and Δ2 are obtained from the table below, thus transforming the error d into a function that is only related to (x1-x2), defining the positioning accuracy. It is also converted into a function related to (x1-x2). (x1-x2) is the aircraft coordination distance, that is, the target positioning accuracy is converted into the aircraft coordination distance.

[0081] Direction finding error settings:

[0082] The rendezvous and positioning accuracy of two aircraft is related to the direction finding accuracy of a single aircraft. Assuming that the direction finding of the two aircraft is a phase interferometer system, the selection of various errors is shown in the table below based on engineering experience.

[0083] Table 1 Sources of Direction Finding Error

[0084]

[0085] 1.5 Calculate the optimal cooperative flight spacing to meet positioning accuracy requirements

[0086] The search and rescue value of a target is defined as the length of the flight path in which the target is effectively searched by two aircraft simultaneously. The longer the effective search segment, the higher the search and rescue value. The total search and rescue value of a target is defined as the total length of the entire flight path in which all targets are effectively searched by two aircraft simultaneously.

[0087] According to f A (h) and f M (Δh+h) calculates the total flight distance of the two aircraft simultaneously capturing n targets, which is the total search and rescue value of the targets.

[0088] Adjust Δh to maximize P(Δh) while ensuring the positioning accuracy is within 5% of R.

[0089]

[0090] and

[0091] Where R is the distance from the aircraft to the target.

[0092] Adjust Δh to maximize P(Δh) while ensuring the positioning accuracy is within 5% of R.

[0093] The Harris Eagle optimization algorithm is used to search for the optimal solution of P(Δh), and the optimal cooperative flight distance Δh can also be obtained. Assume Δh... min Δh represents the minimum coordinated flight spacing. max The initial solution X for the Harris Eagle optimization algorithm is Δh, representing the maximum cooperative flight spacing. min and Δh max The fitness function is f(X) = P(X), where X is a random number between X and P(X). The steps of the Harris Eagle optimization algorithm are shown below, and its flowchart is shown in Figure 5:

[0094] The algorithm consists of three phases: the global exploration phase, the global exploration to local exploration transition phase, and the local exploration phase. In the HHO algorithm, the position of the Harris Eagle is considered as a candidate solution, and the best candidate solution in the iteration is the prey.

[0095] (1) Global search phase

[0096] During the exploration phase, the Harris Eagle employs two strategies to search for prey, with both strategies having equal probability. The two search strategies are as follows:

[0097]

[0098]

[0099] Where t is the current iteration number. This represents the position of individual i after the t-th iteration. This indicates that the individual position is randomly selected after the t-th iteration. r1, r2, r3, r4, and q are random numbers in the range [0,1]. Let represent the optimal position after the t-th iteration, i.e., the prey position. Ub and Lb are the upper and lower bounds of the search space, respectively. The average position of the population after t iterations is represented by the following formula:

[0100]

[0101] (2) The transition from global exploration to local development stage

[0102] The HHO algorithm can switch between global exploration and local exploitation strategies based on the prey's escape energy. The prey's escape energy decreases dynamically, that is, it decreases as the number of iterations increases. Its escape energy is defined as:

[0103]

[0104] Where E0 is the initial escape energy of the prey, a random number between [-1, 1], which is automatically updated after each iteration. t is the current iteration number. T is the maximum number of iterations. A global exploration strategy is executed when |E| ≥ 1. A local exploration strategy is executed when |E| < 1.

[0105] (3) Partial Development Phase

[0106] When |E| < 1, the population enters the local development phase. Based on the predation strategy of the Harris Eagle, various position update strategies are designed for the local development phase. Let r be a random number between [0, 1] used to select different position update strategies. Let r be the escape probability of the prey; r ≥ 0.5 represents escape failure, and r < 0.5 represents escape success.

[0107] soft surround

[0108] When 0.5 ≤ |E| < 1 and r ≥ 0.5, the algorithm uses a soft-encirclement strategy for position update. The position update formula is as follows:

[0109]

[0110]

[0111] Where, Δx t It is the distance between the prey's location and the current individual's location. J is a random number between [0, 2].

[0112] hard surround

[0113] When |E| < 0.5 and r ≥ 0.5, the Harris Hawk employs a hard encirclement strategy for position updates. The position update formula is as follows:

[0114]

[0115] A gradual, rapid, soft encirclement

[0116] When 0.5 ≤ |E| < 1 and r < 0.5, a gradual, rapid dive soft encirclement strategy is adopted for position update. The position update formula is as follows:

[0117]

[0118]

[0119] Z = Y + S·LF(D)

[0120] Where f() is the fitness function, D is the dimension of the problem, S is a random vector of size 1×D, and LF is the Lévy flight function, whose formula is:

[0121]

[0122]

[0123] Where μ and ν are random values ​​within (0,1), and β is a random constant.

[0124] A progressive, rapid dive with a hard encirclement

[0125] When |E| < 0.5 and r < 0.5, a gradual, rapid dive hard encirclement strategy is adopted for position update. The position update formula is as follows:

[0126]

[0127]

[0128] Z = Y + S·LF(D)

[0129] The algorithm implementation steps are as follows:

[0130] (1) Initialize the population, including the upper and lower bounds of the search space, the maximum number of iterations of the algorithm, the dimension of the solution equals the number of objectives D, the number of solutions is the size of the population NP, and randomly initialize the population pop(1:NP,1:D).

[0131] (2) Calculate the fitness value of each individual based on the fitness function and save the best individual in the population;

[0132] (3) Update prey escape energy E;

[0133] (4) Compare the magnitude of escape energy, update the position according to the position update formula or four strategies to hunt prey, and update the position;

[0134] (5) Calculate the fitness of each individual and update the optimal fitness value of the population;

[0135] (6) Repeat steps 3-5 until the maximum number of iterations is reached and the accuracy requirement is met. The final optimal solution is the optimal effective capture segment length, and thus the cooperative aircraft spacing is obtained.

[0136] For targets 50 to 300 kilometers away, if the positioning accuracy is to be within 5%R, the calculation method provided by this invention can be used to solve for a distance of 60-100 km between the two machines.

[0137] Application simulation verification

[0138] According to the calculation method provided by this invention, for targets at a distance of 50–300 km, the required distance between the two aircraft is 60–100 km to ensure a positioning accuracy within 5%R. To verify the validity of the results, simulations were performed on the target positioning error distribution for different cooperative flight distances to check whether it is consistent with the calculation results of this invention.

[0139] The simulated airspace for dual-aircraft cooperative flight is a rectangular area of ​​-175km to 175km in the X direction and 5km to 355km in the Y direction. The simulation grid is divided into 10km sections, and each grid point is simulated 500 times. The positioning error is calculated with a 50% circular probability.

[0140] Figure 6-14 shows the error distribution of simulations with a dual-machine cooperative spacing of 20km to 100km (10km interval). The contour lines in the figure indicate the positioning error values; for example, 5 represents a CEP (50%) error of 5%. The distance between the green and red dots represents the dual-machine cooperative spacing. Simulation results also demonstrate that for targets 50-300km away, to ensure positioning accuracy within 5%R, a dual-machine spacing of 60-100km is recommended, as this results in better search and rescue performance, consistent with the calculation results of this invention.

Claims

1. A method for calculating the spacing between two aircraft operating on the same flight path to improve the efficiency of dual-aircraft search and rescue, characterized in that, Includes the following steps: S1. Calculate the effective search segment length of the target: Define the search and rescue value of a target as the segment length in which the target is effectively searched by two aircraft simultaneously. Let the aircraft speed be V km / min, the time it takes for the target to be simultaneously searched by two aircraft be T min, and the target's search and rescue value be... ； S2. Convert the effective search segment length into cooperative flight distance: Assuming both aircraft fly along the same route at the same speed, let the coordinates of aircraft 1 and 2 be respectively... Coordinated flight distance The number of targets is n, and the position coordinates of target i are... The effective search start and end positions of the first aircraft for target i are: The effective search start and end positions of the second aircraft for target i are... Assuming the first plane is in front and the second plane is behind; The effective search path length for the first aircraft A to acquire the target is: The effective search path length for the second aircraft M to acquire the target is: The relative distance between the second aircraft and the first aircraft is: ； S3. Calculate the target positioning accuracy: The target's true coordinates are... The theoretical direction finding angles are respectively and Let the direction finding deviations be respectively and The intersection point is The positioning error is the distance d from the actual target position to the intersection positioning position; the positioning accuracy is defined as... Where R is the distance from the aircraft to the target; S4. Convert the target positioning accuracy into the distance between the two aircraft in cooperative flight: According to plane geometry, the equation of the straight line is: Target location obtained: Similarly, when a deviation occurs, the equation of the straight line is: Target location obtained: ， The distance between the positioning point and the actual location of the target, i.e., the positioning error, is: From the above formula, it can be seen that the positioning error is related to... ， It is related to the direction-finding angle and the aircraft's direction-finding error, among which the direction-finding angle... ， For a constant value, ， The value is taken as an empirical value, thus transforming the error d into one that only relates to... Related functions, positioning accuracy definition Also converted to Related functions; S5. Calculate the optimal cooperative flight distance that satisfies the positioning accuracy requirements: based on... and Calculate the total flight distance of two aircraft simultaneously capturing n targets, which is the total search and rescue value of the targets. ;Adjustment This ensures that the positioning accuracy is within 5%R. maximum; Search using Harris Hawk optimization algorithm The optimal solution can be obtained, and the cooperative flight distance can also be calculated. Optimal; Assumption This represents the minimum interval between coordinated flights. The initial solution X of the Harris Eagle optimization algorithm represents the maximum cooperative flight interval. and Random numbers between these ranges, with the fitness function being... 。 2. The method for calculating the distance between two aircraft flying in coordinated flight on the same route to improve the efficiency of dual-aircraft search and rescue as described in claim 1, characterized in that: The Harris Eagle optimization algorithm includes the following steps: (1) Initialize the population, including the upper and lower limits of the search space, the maximum number of iterations of the algorithm, the dimension of the solution equals the number of objectives D, the number of solutions, i.e. the size of the population, is NP, and randomly initialize the population. (2) Calculate the fitness value of each individual according to the fitness function and save the best individual in the population; (3) Update the prey escape energy E and the prey escape probability r; (4) Compare the magnitude of the escape energy, and chase the prey according to the position update formula or four strategies, and update the position; (5) Calculate the fitness of each individual and update the fitness value of the best individual in the population; (6) Repeat steps 3-5 until the maximum number of iterations is reached and the accuracy requirement is met. The final optimal solution is the optimal effective capture segment length, and then the cooperative flight distance is obtained.

3. The method for calculating the spacing between two aircraft traveling on the same flight path to improve the efficiency of dual-aircraft search and rescue as described in claim 2, characterized in that: The four strategies include soft encirclement strategy, hard encirclement strategy, gradual rapid dive soft encirclement strategy, and gradual rapid dive hard encirclement strategy.

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