Unmanned aerial vehicle formation trajectory optimization method based on reconnaissance positioning task

Abstract

The application discloses a kind of unmanned aerial vehicle formation trajectory optimization methods based on reconnaissance positioning task, comprising: based on two-dimensional plane rectangular coordinate system constructs airborne radar motion model and measurement data model;Based on measurement data model, the angle of arrival AOA of airborne radar is analyzed to CRLB, to deduce CRLB formula;Performance analysis is carried out to unmanned aerial vehicle, to determine the limiting condition that unmanned aerial vehicle trajectory planning is subjected;Based on CRLB formula, the objective function of unmanned aerial vehicle trajectory planning algorithm is determined;Based on limiting condition, the objective function is iteratively solved using particle swarm optimization algorithm, and the optimal position of formation trajectory of unmanned aerial vehicle group is obtained.The method can intelligently plan the trajectory route of unmanned aerial vehicle formation for target positioning, reconnaissance task unmanned aerial vehicle cooperation, greatly improve the positioning accuracy of unmanned aerial vehicle cooperative positioning multi-target task, and have better robustness to time-varying environment and target.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, specifically relating to a method for optimizing the formation trajectory of unmanned aerial vehicles (UAVs) based on reconnaissance and positioning tasks. Background Technology

[0002] Radar, as the main force in defense and early warning, is a key weapon for acquiring aerial intelligence and gaining information superiority. With the development of radar technology, a single radar can no longer complete its mission independently. Radar networking, through the rational combination and deployment of different types of radars, achieves complementarity in the airspace, frequency domain, and time domain, overcoming the individual shortcomings of a single radar. It is a major technical and tactical means to cope with complex detection environments.

[0003] To build high-performance network radars, most current research focuses on utilizing unmanned aerial vehicles (UAVs) as mobile platform resources. However, traditional UAV formations mostly follow preset trajectories during missions. This approach suffers from insufficient diversity in observation space and poor positioning accuracy, resulting in suboptimal radar network performance. A solution to address these issues is to optimize UAV flight paths using intelligent algorithms, thereby achieving high-performance radar networking. This method of optimizing UAV formation trajectories to manage radar network performance has been widely applied in the military field, primarily in target engagement, intelligence gathering, and UAV penetration trajectory planning.

[0004] Currently, research on UAV trajectory planning mainly focuses on target engagement and low-altitude flight, with little attention paid to target localization. For target engagement, domestic and international scholars have established planning space models for complex environments, using comprehensive strike performance indicators as the objective function to adaptively plan the trajectories of multiple UAVs coordinating to engage targets. For low-altitude penetration, some scholars have proposed a series of UCAV (Unmanned Combat Aerial Vehicles) penetration trajectory planning methods under the threat of anti-stealth radar network deployments by introducing the idea of ​​rapidly expanding random numbers. Based on heuristic sparse algorithms, scholars have proposed a hierarchical strategy-based penetration path planning algorithm to improve the accuracy, real-time performance, mission adaptability, and feasibility of three-dimensional penetration path planning for small swarm aircraft.

[0005] Therefore, designing a collaborative trajectory planning method for UAVs capable of target localization and reconnaissance missions is one of the urgent tasks to be addressed in modern intelligent UAV trajectory planning. Summary of the Invention

[0006] To address the issue of low positioning accuracy caused by the use of preset trajectories in traditional UAV formations during joint reconnaissance and positioning missions, this invention provides a UAV formation trajectory optimization method based on reconnaissance and positioning tasks. This algorithm uses CRLB as the objective function and establishes constraints considering factors such as UAV performance, threat area avoidance, and radar antenna angle coverage to achieve trajectory planning for the UAV formation, significantly improving the tracking and positioning accuracy of multi-target reconnaissance.

[0007] To achieve the above-mentioned technical objectives, the present invention adopts the following technical solution:

[0008] A method for optimizing UAV formation trajectories based on reconnaissance and positioning tasks includes:

[0009] Step 1: Construct an airborne radar motion model and measurement data model based on a two-dimensional Cartesian coordinate system; wherein, the two-dimensional Cartesian coordinate system is an XOY Cartesian coordinate system with the centroid of each UAV as the origin O, the north direction as the Y-axis, and the east direction as the X-axis;

[0010] Step 2: Perform CRLB analysis on the airborne radar's angle of arrival (AOA) based on the measurement data model to derive the CRLB formula;

[0011] Step 3: Perform performance analysis on the UAV to determine the constraints on UAV trajectory planning; wherein the constraints include speed, maximum yaw angle, UAV flight distance, and threat area avoidance;

[0012] Step 4: Determine the objective function of the UAV trajectory planning algorithm based on the CRLB formula;

[0013] Step 5: Based on the aforementioned constraints, the objective function is iteratively solved using the particle swarm optimization algorithm to obtain the optimal position of the UAV swarm's formation trajectory.

[0014] In one embodiment of the present invention, in step 1, the radar motion model is represented by the following formula:

[0015] S i,k =AX i,k +Bu i,k ;

[0016] Among them, S i,k Let X represent the motion model of the i-th airborne radar at time k. i,k U represents the state of the i-th airborne radar at time k. i,k Let represent the maneuver resource control variable for the i-th airborne radar at time k;

[0017]

[0018]

[0019] Where Δt represents the time the airborne radar has been operating. Let represent the angle between the flight direction of the i-th drone at time k and the X-axis.

[0020] In one embodiment of the present invention, in step 1, the measurement data model is represented by the following measurement equation:

[0021]

[0022] in, This represents the observation result of the i-th airborne radar on the j-th target at time k;

[0023]

[0024] Among them, X j =[x j ,y j ] T Let x represent the position coordinates of the j-th target. i,k and y i,k Let be the GPS positioning coordinates of the i-th airborne radar at time k. Let represent the measurement noise of the i-th airborne radar at time k for the j-th target. This represents the azimuth information of the j-th target obtained by the i-th airborne radar at time k.

[0025] In one embodiment of the present invention, step 2 includes:

[0026] 21) Noise variance of computer-borne radar observations of targets in, Let represent the noise variance observed by the i-th airborne radar for the j-th target at time k;

[0027] 22) The noise of the target location observations based on the UAV follows a mean of 0 and a variance of . By utilizing the characteristics of the Gaussian distribution, the joint probability density of the UAV observation results can be obtained;

[0028] 23) Calculate the Fisher information matrix based on the joint probability density to obtain the CRLB formula.

[0029] In one embodiment of the present invention, in step 21), the noise variance observed by the i-th airborne radar on the j-th target at time k is... The calculation formula is:

[0030]

[0031] Where λ represents the wavelength of the transmitted signal, and D i This represents the aperture area of ​​the i-th airborne radar antenna. This represents the signal-to-noise ratio of the signal received by the i-th airborne radar at the j-th target at time k.

[0032] In one embodiment of the present invention, in step 22), the joint probability density of the UAV observation results is expressed as:

[0033]

[0034] in, This represents the observation result of the i-th airborne radar on the j-th target at time k. Let V represent the noise variance observed by the i-th airborne radar at time k for the j-th target, where 1 ≤ i ≤ N, and N represents the number of airborne radars.

[0035] In one embodiment of the present invention, step 23) includes:

[0036] The logarithm of the joint probability density of the UAV observations is taken, and the Fisher information matrix is ​​calculated based on the expectation of the measurement set equaling the true value. Its expression is as follows:

[0037]

[0038] in,

[0039]

[0040]

[0041]

[0042]

[0043] The CRLB formula is then expressed as:

[0044]

[0045] Where, d k =[v 1,k ,ω 1,k ,v 2,k ,ω 1,k ,……,v N,k ,ω N,k ] T It represents the maneuver control resources of N airborne radars at time k, and T represents the transpose.

[0046] In one embodiment of the present invention, step 4 includes:

[0047] 41) Construct a window function using the Chebyshev filter based on the maximum non-attenuation angle;

[0048] 42) Based on the constructed window function, the CRLB formula is improved, and the improved CRLB formula is expressed as:

[0049]

[0050] in, Represents the window function. This represents the angle between the i-th UAV flight path and the j-th target at time k;

[0051] 43) The objective function of the UAV trajectory planning algorithm is determined based on the improved CRLB formula, and its expression is:

[0052]

[0053] Where, f(d) k ) represents the objective function of the UAV trajectory planning algorithm, and M represents the number of targets within the positioning area.

[0054] In one embodiment of the present invention, step 5 includes:

[0055] The particle swarm optimization algorithm is used to initialize the particle swarm and parameter settings, including initial position and initial velocity; the fitness of each particle is evaluated, and the velocity and position of the particles are continuously updated and adjusted in each iteration by tracking two extreme values; the objective function f(d) is then applied. k The optimal position of the drone swarm that satisfies the constraints at each time step is obtained through iterative solutions. After multiple solutions, the optimal trajectory of the drone formation can be obtained.

[0056] The beneficial effects of this invention are:

[0057] 1. The UAV formation trajectory optimization method provided by this invention, based on various practical constraints, can intelligently plan the trajectory route of UAV formation for target positioning and reconnaissance missions, which greatly improves the positioning accuracy of UAV cooperative positioning of multiple targets and has better robustness to time-varying environments and targets.

[0058] 2. The UAV formation trajectory optimization method proposed in this invention adopts the particle swarm optimization algorithm and combines constraints such as UAV performance, radar antenna constraints, and threat area control, which improves the speed and convergence value of the algorithm and helps it escape local optima.

[0059] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0060] Figure 1 This is a flowchart illustrating a method for optimizing UAV formation trajectories based on reconnaissance and positioning tasks, provided by an embodiment of the present invention.

[0061] Figure 2 This is a schematic diagram of the UAV motion model provided in an embodiment of the present invention;

[0062] Figure 3 This is a schematic diagram of a window function constructed based on the maximum non-attenuation angle, provided in an embodiment of the present invention;

[0063] Figure 4 This is a schematic diagram of the optimal trajectory of the UAV formation obtained by simulation using the algorithm of this invention;

[0064] Figure 5 This is a schematic diagram of the default trajectory of a traditional formation drone;

[0065] Figure 6 This is a comparison chart of the CRLB variation curves of the traditional route and the route optimized by the algorithm of this invention. Detailed Implementation

[0066] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0067] Example 1

[0068] Please see Figure 1 , Figure 1 This is a flowchart illustrating a method for optimizing UAV formation trajectories based on reconnaissance and positioning tasks, provided in an embodiment of the present invention. The method includes:

[0069] Step 1: Construct an airborne radar motion model and measurement data model based on a two-dimensional Cartesian coordinate system.

[0070] First, initialize the algorithm, specifically including:

[0071] Suppose there are N drones performing reconnaissance missions within a target area, each drone carrying an active radar. Let i be the i-th airborne radar, 1≤i≤N, with i initialized to 1, and N being an integer greater than 1.

[0072] Then, the problem of UAV angle measurement and positioning is simplified to be discussed in a two-dimensional plane. Specifically, an XOY plane rectangular coordinate system is established with the centroid of each UAV as the origin O, the north direction as the Y-axis, and the east direction as the X-axis.

[0073] Finally, based on the aforementioned two-dimensional Cartesian coordinate system, an airborne radar motion model and a measurement data model are constructed.

[0074] Specifically, constructing drone motion models, such as Figure 2 As shown, let X i,kThis represents the state of the i-th airborne radar at time k. x i,k and y i,k Let be the GPS positioning coordinates of the i-th airborne radar at time k. This indicates the angle between the drone's flight direction and the X-axis.

[0075] Using the linear velocity v of the i-th airborne radar i,k and angular velocity ω i,k As a control variable for mobile resources u i,k u i,k =[v i,k ,ω i,k ] T The flight of the airborne radar is affected by the maximum horizontal flight speed v of the i-th UAV platform. imax Minimum horizontal flight speed v imin and maximum angular velocity ω imax The limitation, i.e., v imin ≤v ik ≤v imax , -ω imax ≤ω ik ≤ω imax .

[0076] Therefore, the airborne radar motion model, that is, the discrete kinematic model of the UAV, can be expressed as:

[0077] S i,k =AX i,k +Bu i,k (1)

[0078] in,

[0079]

[0080]

[0081] Where Δt represents the time the airborne radar has been operating, which is also the time the UAV has been operating. Let represent the angle between the flight direction of the i-th drone at time k and the X-axis.

[0082] Furthermore, assume the position coordinates of the j-th target are X j =[x j ,y j ] T Assuming that the measurement data obtained by the airborne radar includes the direction angle of the target and its own GPS positioning information, the measurement equation of the i-th airborne radar for the j-th target at time k can be expressed as:

[0083]

[0084]

[0085] in, Let x represent the observation result of the i-th airborne radar on the j-th target at time k. i,k and y i,k Let be the GPS positioning coordinates of the i-th airborne radar at time k. Let represent the measurement noise of the i-th airborne radar at time k for the j-th target. This represents the azimuth information of the j-th target obtained by the i-th airborne radar at time k.

[0086] Step 2: Based on the measurement data model, perform CRLB (Cramer-Rao Lower Bound) analysis on the airborne radar's angle of arrival (AOA) to derive the CRLB formula.

[0087] 21) Standard deviation of noise in computer-borne radar observations of targets.

[0088] Specifically, Let represent the measurement noise of the i-th airborne radar at time k for the j-th target, which follows a Gaussian distribution with a mean of 0. The covariance is:

[0089]

[0090] Where blkdiag(g) denotes the diagonalization of the matrix. Let represent the noise variance observed by the i-th airborne radar for the j-th target at time k. This represents the variance of the error in the measurement of the target's X-axis coordinate by the i-th airborne radar at time k. Let represent the variance of the error in the measurement of the target's Y-axis coordinate by the i-th airborne radar at time k.

[0091] Assuming the AOA positioning model in two-dimensional space is within a line-of-sight environment, the power of the signal received by the airborne radar can be determined using a propagation loss model of electromagnetic waves in free space:

[0092]

[0093] in, Let P be the signal power of the j-th target received by the i-th airborne radar. t j Let J be the transmitted signal power of the j-th target. Let the transmit antenna gain of the j-th target be... Let λ be the gain of the i-th airborne radar receiving antenna, and λ be the wavelength of the transmitted signal. Let L be the distance between target j and airborne radar i at time k, and L be the feeder loss.

[0094] Assuming the power of the noise signals is equal, the gain of the transmitting and receiving antennas is equal, and the power of the target's transmitted signal is equal, the signal-to-noise ratio (SNR) of the signal received by the i-th airborne radar at the j-th target at time k can be calculated using the following formula:

[0095]

[0096] Where SNR is the signal-to-noise ratio of the reference point at a distance r.

[0097] Therefore, the noise variance observed by the i-th airborne radar for the j-th target at time k is:

[0098]

[0099] Among them, D i It is the aperture area of ​​the i-th airborne radar antenna.

[0100] 22) The noise of the target location observations based on the UAV follows a mean of 0 and a variance of . By utilizing the characteristics of the Gaussian distribution, the joint probability density of the UAV observation results can be obtained.

[0101] Specifically, in passive localization problems, the target's localization accuracy is typically quantified using CRLB, and the target's localization performance is also measured using this method. Based on the above description, the noise of the UAV's target localization observations follows a mean of 0 and a variance of... The Gaussian distribution, i.e.

[0102] Since the observations from each UAV are independent, the joint probability density of the observations from N UAVs is:

[0103]

[0104] 23) Calculate the Fisher information matrix based on the joint probability density to obtain the CRLB formula.

[0105] Specifically, taking the logarithm of the joint probability density of the UAV observation results yields:

[0106]

[0107] The Fisher information matrix is ​​then represented as:

[0108]

[0109] Since the measurement set is an unbiased estimator of the truth, its expected value is equal to the truth value. Therefore, the information matrix can be written as:

[0110]

[0111] in,

[0112]

[0113]

[0114]

[0115]

[0116] The CRLB formula is then expressed as:

[0117]

[0118] Where, d k =[v 1,k ,ω 1,k ,v 2,k ,ω 1,k ,……,v N,k ,ω N,k ] T It represents the maneuver control resources of N airborne radars at time k, and T represents the transpose.

[0119] Step 3: Perform performance analysis on the UAV to determine the constraints on the UAV trajectory planning; wherein the constraints include speed, maximum yaw angle, UAV flight distance, and threat area avoidance.

[0120] a) Speed: Due to limitations in UAV performance, its straight-line flight speed is restricted to a certain range, among which... and These are the minimum and maximum flight speeds of the drone:

[0121]

[0122] b) Maximum Yaw Angle: The maximum yaw angle refers to the maximum angle between the initial direction and the turning direction when the UAV makes a horizontal turn at its rated speed, and is constrained by its own performance parameters. It is one of the main evaluation indicators for whether a UAV can fly normally. If the UAV's turning angle in the horizontal direction is greater than the maximum yaw angle, the UAV's flight speed must be reduced to ensure the safety of the aircraft. The formula for calculating the yaw angle is:

[0123]

[0124] Therefore, the maximum yaw angle constraint is:

[0125]

[0126] in, It is the maximum yaw angle of the drone.

[0127] c) Flight range of drones: Due to limitations in fuel capacity and consumption, the flight range of drones is restricted.

[0128]

[0129] Among them, L max For the maximum distance, L i Let the distance traveled by the i-th drone be:

[0130]

[0131] Here we remind the reader that (x) i,k ,y i,k (x) represents the position of the i-th drone at time k, and its position at the previous time is (x). i,k-1 ,y i,k-1 ).

[0132] d) Threat Area Avoidance: During flight operations, drones may encounter insurmountable areas, such as impassable mountains, which they must avoid. To simplify the model, this embodiment equates the threat area to a circle with a finite area. The constraints on the threat area are as follows:

[0133]

[0134] Assume the center of the j-th threat region is x. d j =[x j ,y j ] T R i,k j M is the distance between the i-th drone and the j-th threat area at time k. d It refers to the number of threat areas.

[0135] Step 4: Determine the objective function of the UAV trajectory planning algorithm based on the CRLB formula.

[0136] 41) Construct a window function using the Chebyshev filter based on the maximum non-attenuation angle.

[0137] Specifically, a window function is constructed using a Chebyshev filter based on the maximum non-attenuated angle. This is applied when the angle between the UAV's flight path and the target... When the target signal received by the airborne radar reaches a certain range, the signal-to-noise ratio will decrease accordingly; where, it is assumed that the maximum non-attenuation angle is η. max =π / 3.

[0138] Due to the directivity of radar antennas, the angle between the drone's flight path and the target... When a certain range is reached, the signal-to-noise ratio of the target signal received by the airborne radar will decrease accordingly. Assume the maximum non-attenuation angle is η. max =π / 3, use Chebyshevfilter to construct the window function h(η), as follows Figure 3 As shown.

[0139] 42) Based on the constructed window function, the CRLB formula is improved, and the improved CRLB formula is expressed as:

[0140]

[0141] in, Represents the window function. Let represent the angle between the i-th UAV flight path and the j-th target at time k.

[0142] 43) The objective function of the UAV trajectory planning algorithm is determined based on the improved CRLB formula, and its expression is:

[0143]

[0144] Where, f(d) k ) represents the objective function of the UAV trajectory planning algorithm, and M represents the number of targets within the positioning area.

[0145] Step 5: Based on the aforementioned constraints, the objective function is iteratively solved using the particle swarm optimization algorithm to obtain the optimal position of the UAV swarm's formation trajectory.

[0146] Specifically, a particle swarm optimization algorithm is used to initialize the particle swarm and parameter settings, including initial position and initial velocity; the fitness of each particle is evaluated, and in each iteration, the velocity and position of the particles are continuously updated and adjusted by tracking two extreme values ​​(pbest and gbest); the objective function f(d) is then applied. k The optimal position of the drone swarm that satisfies the constraints at each time step is obtained through iterative solutions. After multiple solutions, the optimal trajectory of the drone formation can be obtained.

[0147] For details on the implementation of the particle swarm optimization algorithm, please refer to existing related technologies; this invention will not provide a detailed description here.

[0148] The UAV formation trajectory optimization method provided by this invention, based on various practical constraints, can intelligently plan the trajectory route of UAV formations for target positioning and reconnaissance missions, which greatly improves the positioning accuracy of UAV cooperative positioning of multiple targets and has better robustness to time-varying environments and targets.

[0149] Furthermore, the UAV formation trajectory optimization method proposed in this invention adopts the particle swarm optimization algorithm and combines constraints such as UAV performance, radar antenna constraints, and threat area control, which improves the speed and convergence value of the algorithm and helps it escape local optima.

[0150] Example 2

[0151] To verify the effectiveness of the algorithm proposed in Embodiment 1 above, this embodiment sets up a special scenario, namely, establishing the objective function of UAV formation in a multi-target reconnaissance and localization task, and using the trajectory planning algorithm in this invention to derive the change of CRLB. The algorithm is analyzed and verified, and the effect of this invention is further illustrated by the following simulation.

[0152] 1. Simulation parameter settings

[0153] See Table 1 below for details.

[0154] Table 1

[0155]

[0156] 2. Simulation Content

[0157] This simulation compares the UAV formation trajectory optimization algorithm and the traditional trajectory route for reconnaissance and positioning missions.

[0158] This simulation is modeled on a two-dimensional plane. Assume the XOY plane has dimensions of 1800 × 1600, and contains five airborne radars with initial positions of (1200, 870), (600, -500), (400, 1200), (-300, 900), and (-300, -500). Three targets are located near the center, and the radius of each of the five threat zones is 100 meters.

[0159] 3. Simulation Result Analysis

[0160] Substituting the above initialization parameters into the trajectory planning algorithm of this invention, and using the MATLAB R2021b programming environment, a simulation analysis was performed on the above-mentioned UAV formation reconnaissance and positioning multi-target scenario. The simulation results are as follows: Figure 4 As shown.

[0161] Figure 4In the diagram, five lines represent the trajectories of the formation drones calculated by a trajectory optimization algorithm. The circles surrounding each trajectory represent threat areas, and the three lines near the center of each area are marked as targets to be located by the formation drones. From a constraint perspective, the algorithm's trajectories satisfy both the constraint of bypassing threat areas and the performance requirements of the drones, with the drones' headings as close to the target as possible. This improves positioning accuracy. From a positioning accuracy perspective, the trajectories planned by the algorithm enable the drone formation to move towards the target.

[0162] Assuming the default trajectory of a traditional formation drone is as follows Figure 5 As shown. By comparing the CRLB value curves corresponding to the traditional route and the optimized route of this invention, the correctness of the algorithm of this invention can be verified, as follows. Figure 6 As shown.

[0163] from Figure 6 As can be seen, when the formation of UAVs travels along the route planned by the algorithm, the CRLB value decreases linearly and is lower than the CRLB value corresponding to the traditional route. Therefore, the trajectory optimization algorithm in this invention can greatly improve the positioning accuracy of multi-target tasks in UAV cooperative localization.

[0164] In conclusion, the simulation experiments verified the correctness, effectiveness, and reliability of the present invention.

[0165] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for optimizing UAV formation trajectories based on reconnaissance and positioning tasks, characterized in that, include: Step 1: Construct an airborne radar motion model and measurement data model based on a two-dimensional Cartesian coordinate system; wherein, the two-dimensional Cartesian coordinate system is an XOY Cartesian coordinate system with the centroid of each UAV as the origin O, the north direction as the Y-axis, and the east direction as the X-axis; Step 2: Perform CRLB analysis on the airborne radar's angle of arrival (AOA) based on the measurement data model to derive the CRLB formula; Step 3: Perform performance analysis on the UAV to determine the constraints on UAV trajectory planning; wherein the constraints include speed, maximum yaw angle, UAV flight distance, and threat area avoidance; Step 4: Determine the objective function of the UAV trajectory planning algorithm based on the CRLB formula; Step 5: Based on the aforementioned constraints, the objective function is iteratively solved using the particle swarm optimization algorithm to obtain the optimal position of the UAV swarm's formation trajectory.

2. The method for optimizing UAV formation trajectories based on reconnaissance and positioning tasks according to claim 1, characterized in that, In step 1, the radar motion model is represented by the following formula: S i,k =AX i,k +Bu i,k 4 Among them, S i,k Let X represent the motion model of the i-th airborne radar at time k. i,k U represents the state of the i-th airborne radar at time k. i,k Let represent the maneuver resource control variable for the i-th airborne radar at time k; Where Δt represents the time the airborne radar has been operating. Let represent the angle between the flight direction of the i-th drone at time k and the X-axis.

3. The method for optimizing UAV formation trajectories based on reconnaissance and positioning tasks according to claim 1, characterized in that, In step 1, the measurement data model is represented by the following measurement equation: in, This represents the observation result of the i-th airborne radar on the j-th target at time k; Among them, X j =[x j ,y j ] T Let x represent the position coordinates of the j-th target. i,k and y i,k Let be the GPS positioning coordinates of the i-th airborne radar at time k. Let represent the measurement noise of the i-th airborne radar at time k for the j-th target. This represents the azimuth information of the j-th target obtained by the i-th airborne radar at time k.

4. The method for optimizing UAV formation trajectories based on reconnaissance and positioning tasks according to claim 1, characterized in that, Step 2 includes: 21) Noise variance of computer-borne radar observations of targets in, Let represent the noise variance observed by the i-th airborne radar for the j-th target at time k; 22) The noise of the target location observations based on the UAV follows a mean of 0 and a variance of . By utilizing the characteristics of the Gaussian distribution, the joint probability density of the UAV observation results can be obtained; 23) Calculate the Fisher information matrix based on the joint probability density to obtain the CRLB formula.

5. The method for optimizing UAV formation trajectories based on reconnaissance and positioning tasks according to claim 4, characterized in that, In step 21), the noise variance observed by the i-th airborne radar on the j-th target at time k is... The calculation formula is: Where λ represents the wavelength of the transmitted signal, and D i This represents the aperture area of ​​the i-th airborne radar antenna. This represents the signal-to-noise ratio of the signal received by the i-th airborne radar at the j-th target at time k.

6. The method for optimizing UAV formation trajectories based on reconnaissance and positioning tasks according to claim 5, characterized in that, In step 22), the joint probability density of the UAV observation results is expressed as: in, This represents the observation result of the i-th airborne radar on the j-th target at time k. Let V represent the noise variance observed by the i-th airborne radar at time k for the j-th target, where 1 ≤ i ≤ N, and N represents the number of airborne radars.

7. The method for optimizing UAV formation trajectories based on reconnaissance and positioning tasks according to claim 6, characterized in that, Step 23) includes: The logarithm of the joint probability density of the UAV observations is taken, and the Fisher information matrix is ​​calculated based on the expectation of the measurement set equaling the true value. Its expression is as follows: in, The CRLB formula is then expressed as: Where, d k =[v 1,k ,ω 1,k ,v 2,k ,ω 1,k ,……,v N,k ,ω N,k ] T It represents the maneuver control resources of N airborne radars at time k, and T represents the transpose.

8. The method for optimizing UAV formation trajectories based on reconnaissance and positioning tasks according to claim 7, characterized in that, Step 4 includes: 41) Construct a window function using the Chebyshev filter based on the maximum non-attenuation angle; 42) Based on the constructed window function, the CRLB formula is improved, and the improved CRLB formula is expressed as: in, Represents the window function. This represents the angle between the i-th UAV flight path and the j-th target at time k; 43) The objective function of the UAV trajectory planning algorithm is determined based on the improved CRLB formula, and its expression is: Where, f(d) k ) represents the objective function of the UAV trajectory planning algorithm, and M represents the number of targets within the positioning area.

9. The method for optimizing UAV formation trajectories based on reconnaissance and positioning tasks according to claim 1, characterized in that, Step 5 includes: The particle swarm optimization algorithm is used to initialize the particle swarm and parameter settings, including initial position and initial velocity; the fitness of each particle is evaluated, and the velocity and position of the particles are continuously updated and adjusted in each iteration by tracking two extreme values; the objective function f(d) is then applied. k The optimal position of the drone swarm that satisfies the constraints at each time step is obtained through iterative solutions. After multiple solutions, the optimal trajectory of the drone formation can be obtained.

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