A Passive Localization Path Planning Algorithm for UAV Swarms Based on Parsing Global CRLB

Abstract

This invention discloses a passive localization path planning algorithm for UAV swarms based on analytical global CRLB, comprising the following steps: initializing the target, UAVs, a position information uncertainty model, and measurement parameters; calculating the initial position information of the target using the Chan-TDOA algorithm; handling the uncertainty of the target position information by calculating the integral average of CRLB in the position information uncertainty region (global CRLB); and finding the optimal flight path point of the UAV swarm at the next moment by minimizing the positioning CRLB value at each moment, thereby obtaining the optimal flight trajectory and positioning accuracy. This invention incorporates the uncertainty of the target position information, uses the global CRLB algorithm to determine the flight position of the UAVs at the next moment, and derives and designs an analytical calculation method for global CRLB under a certain uncertainty distribution, greatly improving the algorithm efficiency and adapting to real-time requirements. This algorithm can adapt to complex electromagnetic environments, effectively optimize the flight trajectory of UAV swarms, and significantly improve the accuracy of target localization.

Description

Technical Field

[0001] This invention relates to the field of single-target localization technology for UAV swarms, and in particular to a passive localization path planning algorithm for UAV swarms based on analytical global CRLB. Background Technology

[0002] With the rapid development of drone technology, drones are widely used in military reconnaissance, raids, search and capture operations, as well as in general aviation fields such as civilian flight demonstrations, emergency rescue, and terrain surveying. However, individual drones have limited payload capacity, carry a limited variety of sensors, and have a small effective range. To overcome these limitations, multi-drone collaborative operations are gradually becoming a development trend. In passive positioning scenarios, multi-drone systems can expand their effective range to complete more complex tasks while improving system resilience; even if one or more drones are damaged, the others can still continue to operate.

[0003] However, multi-UAV cooperative localization still faces numerous challenges in complex electromagnetic environments. Objective factors such as UAV position and velocity errors and the unknown true state vector of the radiation source make real-time, accurate localization of moving radiation sources extremely difficult. Furthermore, existing passive UAV localization technologies are inadequate in handling the uncertainty of target source position information, failing to fully reflect the localization situation when both the receiving station and the UAV are in motion, thus hindering accurate localization.

[0004] To improve positioning accuracy and reliability, researchers have proposed various improvement methods. For example, Qu,X. and Liu,T., et al., proposed the CWLS approximate iterative algorithm in the paper "Multi-source Passive Localization Via Multiple Unmanned Aerial Vehicles[J], Scientia Sinica(Informationis), 2019, 49(5): 570-584." This algorithm transforms the nonlinear relationship between the target position and auxiliary variables into a constrained quadratic programming problem and solves iteratively through linear approximation, effectively addressing the TDOA observation noise and sensor position error problems in multi-target localization. However, these methods still suffer from decreased positioning accuracy in non-common-view environments with incomplete measurement information, making it difficult to achieve high-precision positioning. Therefore, how to effectively handle the uncertainty of target source position information in complex electromagnetic environments and optimize UAV path planning to improve positioning accuracy and system anti-interference performance has become an urgent problem to be solved. Summary of the Invention

[0005] The purpose of this invention is to provide a passive localization path planning algorithm for UAV swarms based on analytical global CRLB.

[0006] To achieve the above objectives, the present invention is implemented according to the following technical solution:

[0007] This invention includes the following steps:

[0008] Step 1: Initialize the multi-UAV system and target parameters;

[0009] Step 1.1: Set up the target location uncertainty model: Let the position coordinates of the target source be... Target's true location It follows a two-dimensional Gaussian distribution. ,in The position mean vector, Let covariance matrix be the variance matrix. , for , Orientation standard deviation;

[0010] Step 1.2: Initialize the drone swarm positions: drones ( ), position matrix , For the first The initial coordinates of the first drone are determined, and the first drone is designated as the reference drone.

[0011] Step 1.3: Set physical parameters: signal bandwidth speed of light Positioning time interval Drone flight speed ;

[0012] Step 1.4: Define flight constraints: minimum turning radius Minimum approach distance Maximum deflection angle .

[0013] Step 2: TDOA measurement data processing and initial target positioning;

[0014] Step 2.1: Collect TDOA measurement data: At that moment, the benchmark drone and the first Time difference of drones Converted to distance difference , For measuring noise;

[0015] Step 2.2: Construct the linearized equations of the Chan algorithm: ,in,

[0016] , ( (Distance from target to baseline drone) ;

[0017] Step 2.3: First Weighted Least Squares (WLS): , This is the weight matrix. ;

[0018] Step 2.4: Preliminary estimation based on the first WLS Construct a new observation vector: New vector to be estimated: Coefficient matrix: .

[0019] Step 2.5: Calculate the weight matrix Calculate the covariance matrix of the new error vector using the error propagation law. ,in , ,make .

[0020] Step 2.6: Perform the second WLS calculation ,get , respectively corresponding and The optimal estimate.

[0021] Step 2.7: Restore the target location: For By extracting the root cause and combining preliminary estimations, screening, and understanding, the initial target location result is obtained. .

[0022] Step 3: Analyze the global CRLB calculation;

[0023] Step 3.1: Construct the dynamic integration region: , This represents the average distance from the drone to the target. and These are the preset minimum and maximum side lengths, and the scaling factor. Take a value of 0.1 to 0.2;

[0024] Step 3.2: Apply the properties of Gaussian moments:

[0025] a. Odd-order moments: ( (non-negative integers)

[0026] b. Even-order moments: It can be seen that the odd-order moments are zero, so only the even-order moments are retained, which further simplifies the calculation of the analytical solution.

[0027] Step 3.3: Perform a Taylor expansion on the trace of the CRLB matrix: , where F is the Fisher information matrix;

[0028] Step 3.4: Calculate the global CRLB: .

[0029] Among them, local items That is Correction item It includes complete second- and fourth-order correction terms, and all partial derivative terms are calculated using high-precision numerical differentiation methods.

[0030] Step 3.5: Subdomain Global Overlay: Based on the mean square error of the Gaussian distribution of the target source The size evaluation divides the integration region into A subfield of integration With the geometric center of each subdomain As a new expansion point, and because the subfield is small enough, the geometric center This is approximately the center of the Gaussian weight function within this subdomain. A local Taylor expansion is performed for each subdomain:

[0031] .

[0032] Calculate the local subdomain CRLB approximation polynomial of the above expression. The product of the original global Gaussian weight function in the corresponding sub-region Integral value within: .

[0033] Step 3.6: All subdomains The global contributions are summed to obtain the final high-precision approximation of the global CRLB: This yields the final analytical approximation of the global CRLB.

[0034] Step 4: Constrained Adaptive PSO Path Planning;

[0035] Step 4.1: Initialize the particle swarm: Particles are represented by heading angle vectors. ,quantity ,scope ;

[0036] Step 4.2: Calculate the constrained heading range:

[0037] Turning radius constraint: ;

[0038] Goal-oriented constraints: , , ;

[0039] Step 4.3: Define the fitness function: , , , ;

[0040] Step 4.4: Update PSO parameters:

[0041] Inertia weight: ;

[0042] Learning factors: , ;

[0043] Particle position: , ;

[0044] Step 4.5: Calculate candidate waypoints: .

[0045] Step 5: Waypoint verification and position update;

[0046] Step 5.1: Minimum forward distance verification: Calculate the distance between the candidate waypoint and the current position. ,like Then adjust to ;

[0047] Step 5.2: Turning angle constraint verification: Calculate the actual turning angle ,like Then adjust the heading angle to Recalculate ;

[0048] Step 5.3: Position Matrix Update: Determine the position matrix... Final position at time Update the drone location matrix .

[0049] Step 6: Convergence judgment and optimal trajectory output.

[0050] Step 6.1: Determine the convergence condition (any one of the following conditions must be met):

[0051] Condition 1: ,

[0052] Condition 2: ,

[0053] in ;

[0054] Condition 3: Number of convergences ;

[0055] Step 6.2: Output Results: If the convergence condition is met, output the optimal UAV swarm track points. ) and positioning accuracy report ( Otherwise, return to step 2.

[0056] The beneficial effects of this invention are:

[0057] The advantages of this invention are more accurate positioning precision quantification, higher computational efficiency, and stronger engineering adaptability. Using the global analytical CRLB method to evaluate the passive positioning accuracy of UAVs, the reliability of precision quantification is higher than that of the single-point CRLB method in various scenarios where target position uncertainty exists. The global analytical CRLB method based on Gaussian moments and Taylor expansion utilizes the odd and even moment characteristics of the Gaussian distribution of the target position (odd moments eliminate integral redundancy, even moments simplify calculation) to transform the multidimensional integral of the global CRLB into an analytical expression. Simultaneously, a fourth-order Taylor expansion covers nonlinear effects. Therefore, compared to the single-point CRLB method that only evaluates a single position, it can more comprehensively cover the range of target uncertainty, significantly reducing precision quantification bias. Furthermore, compared to the Monte Carlo method that relies on a large number of random samples, it eliminates the need to repeatedly calculate the accuracy of sampling points, completely eliminating random fluctuations, resulting in better determinism and reproducibility of the precision quantification results.

[0058] Based on the global analytical CRLB method, the UAV path planning is combined with the constrained adaptive PSO algorithm. The adaptability of the planning results to flight constraints and the improvement in positioning accuracy are both higher than those of traditional path planning algorithms without precision guidance. The path planning algorithm based on global analytical CRLB not only obtains the global theoretical upper limit of positioning accuracy through analytical methods (providing a precise target for path optimization), but also adapts to different distance scenarios by dynamically adjusting the integral region and disturbance amplitude. Therefore, it has a greater information gain in the balance between "precision optimization and safety constraints". The UAV trajectory obtained can not only meet physical constraints such as minimum turning radius and maximum deflection angle, but also guide the continuous improvement of positioning accuracy. Moreover, the computation time is much lower than that of the Monte Carlo method, which adapts to the real-time needs of real-world positioning. Attached Figure Description

[0059] Figure 1 This is a schematic diagram illustrating a scenario where a drone swarm, according to the present invention, locates a target with an uncertain position.

[0060] Figure 2 This is a flowchart of the overall passive positioning path planning algorithm for unmanned aerial vehicle swarms in this invention;

[0061] Figure 3 The positions of the drone and the target in the simulation experiment scenario of this invention;

[0062] Figure 4 The diagram shows the CRLB effect of the passive localization path planning algorithm for UAV swarms based on parsed global CRLB of this invention.

[0063] Figure 5 The diagram shows the RMSE performance of the passive localization path planning algorithm for UAV swarms based on parsed global CRLB of this invention.

[0064] Figure 6 This is a complete comparison and optimization table of the results of the passive localization path planning algorithm for UAV swarms based on parsed global CRLB of this invention. Detailed Implementation

[0065] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. The illustrative embodiments and descriptions herein are used to explain the present invention, but are not intended to limit the present invention.

[0066] like Figure 1 As shown: This illustrates how a swarm of UAVs equipped with radar can locate targets with uncertain positions. Indicates the first A drone is deployed to the unpredictable area surrounding the target. The delineation is indicated. For this scenario, the present invention provides a passive localization path planning algorithm for UAV swarms based on parsed global CRLB, the overall algorithm flow of which is attached. Figure 2 As shown.

[0067] The passive localization path planning algorithm for UAV swarms based on parsed global CRLB described in this invention has the following specific operation steps:

[0068] Step 1: Establish a Gaussian model for the uncertainty of the target position, configure the initial position matrix of the UAV swarm, and set physical parameters and flight constraints.

[0069] Step 1.1: Set up the target location uncertainty model: Let the position coordinates of the target source be... Target's true location It follows a two-dimensional Gaussian distribution. ,in The position mean vector, Let covariance matrix be the variance matrix. , for , Orientation standard deviation;

[0070] Step 1.2: Initialize the drone swarm positions: drones ( ), position matrix , For the first The initial coordinates of the first drone are determined, and the first drone is designated as the reference drone.

[0071] Step 1.3: Set physical parameters: signal bandwidth speed of light Positioning time interval Drone flight speed ;

[0072] Step 1.4: Define flight constraints: minimum turning radius Minimum approach distance Maximum deflection angle .

[0073] Step 2: Collect time difference measurement data and convert it into distance difference. Apply the Chan algorithm to solve for the target's initial position estimate using the weighted least squares method twice.

[0074] Step 2.1: Collect TDOA measurement data: At that moment, the benchmark drone and the first Time difference of drones Converted to distance difference , For measuring noise;

[0075] Step 2.2: Construct the linearized equations of the Chan algorithm:

[0076] (1)

[0077] in,

[0078] (2)

[0079] (3)

[0080] (4)

[0081] ( (The distance from the target to the baseline drone).

[0082] Step 2.3: First Weighted Least Squares (WLS):

[0083] (5)

[0084] This is the weight matrix. ;

[0085] Step 2.4: Preliminary estimation based on the first WLS

[0086] (6)

[0087] Construct new observation vectors:

[0088] (7)

[0089] New vector to be estimated:

[0090] (8)

[0091] Coefficient matrix:

[0092] (9)

[0093] Step 2.5: Calculate the weight matrix Calculate the covariance matrix of the new error vector using the error propagation law. ,in

[0094] (10)

[0095] (11)

[0096] make .

[0097] Step 2.6: Perform the second WLS calculation ,get , respectively corresponding and The optimal estimate.

[0098] Step 2.7: Restore the target location: For By extracting the root cause and combining preliminary estimations, screening, and understanding, the initial target location result is obtained.

[0099] (12)

[0100] Step 3: Construct a dynamic integration region, utilize the Gaussian moment property and Taylor expansion, and calculate the global CRLB analytical approximation value through a subdomain partitioning strategy.

[0101] Step 3.1: Construct the dynamic integration region:

[0102] (13)

[0103] in

[0104] (14)

[0105] This represents the average distance from the drone to the target. and These are the preset minimum and maximum side lengths, and the scaling factor. Take a value of 0.1 to 0.2;

[0106] Step 3.2: Apply the properties of Gaussian moments:

[0107] a. Odd-order moments:

[0108] (15)

[0109] b. Even-order moments:

[0110] (16)

[0111] It can be seen that the odd-order moments are zero, so only the even-order moments are retained, which further simplifies the calculation of the analytical solution.

[0112] Step 3.3: Perform a Taylor expansion on the trace of the CRLB matrix:

[0113] (17)

[0114] Where F is the Fisher information matrix;

[0115] Step 3.4: Calculate the global CRLB:

[0116] (18)

[0117] Among them, local items That is Correction item It includes complete second- and fourth-order correction terms, and all partial derivative terms are calculated using high-precision numerical differentiation methods.

[0118] Step 3.5: Subdomain Global Overlay: Based on the mean square error of the Gaussian distribution of the target source The size evaluation divides the integration region into A subfield of integration With the geometric center of each subdomain As a new expansion point, and because the subfield is small enough, the geometric center This is approximately the center of the Gaussian weight function within this subdomain. A local Taylor expansion is performed for each subdomain:

[0119] (19)

[0120] Calculate the local subdomain CRLB approximation polynomial of the above expression. The product of the original global Gaussian weight function in the corresponding sub-region Integral value within:

[0121] (20)

[0122] Step 3.6: All subdomains The global contributions are summed to obtain the final high-precision approximation of the global CRLB:

[0123] (twenty one)

[0124] This yields the final analytical approximation of the global CRLB.

[0125] Step 4: Initialize the particle swarm heading angle, calculate the turning radius and target guidance constraint range, define the fitness function and iteratively update the particle positions.

[0126] Step 4.1: Initialize the particle swarm: Particles are represented by heading angle vectors. ,quantity ,scope ;

[0127] Step 4.2: Calculate the constrained heading range:

[0128] Turning radius constraint:

[0129] (twenty two)

[0130] Goal-oriented constraints:

[0131] (twenty three)

[0132] (twenty four)

[0133] (25)

[0134] Step 4.3: Define the fitness function:

[0135] (26)

[0136] , , ;

[0137] Step 4.4: Update PSO parameters:

[0138] Inertia weight:

[0139] (27)

[0140] Learning factors:

[0141] (28)

[0142] (29)

[0143] Particle position:

[0144] (30)

[0145] in ;

[0146] Step 4.5: Calculate candidate waypoints:

[0147] (31)

[0148] Step 5: Verify that the candidate waypoints meet the minimum forward distance and turning angle constraints, adjust waypoints that do not meet the conditions, and update the UAV position matrix.

[0149] Step 5.1: Minimum forward distance verification: Calculate the distance between the candidate waypoint and the current position.

[0150] (32)

[0151] like Then adjust to

[0152] (33)

[0153] Step 5.2: Turning angle constraint verification: Calculate the actual turning angle

[0154] (34)

[0155] like Then adjust the heading angle to Recalculate ;

[0156] Step 5.3: Position Matrix Update: Determine the position matrix... Final position at time Update the drone location matrix

[0157] (35)

[0158] Step 6: Determine the convergence conditions such as CRLB threshold, continuous change, or maximum number of iterations, and output the optimal waypoint sequence and positioning accuracy report.

[0159] Step 6.1: Determine the convergence condition (any one of the following conditions must be met):

[0160] Condition 1: ,

[0161] Condition 2: ,

[0162] in ;

[0163] Condition 3: Number of convergences ;

[0164] Step 6.2: Output Results: If the convergence condition is met, output the optimal UAV swarm track points. ) and positioning accuracy report ( Otherwise, return to step 2.

[0165] By executing steps 1 to 6, the entire process of locating the target using the passive localization path planning algorithm for UAV swarms based on parsing global CRLB can be obtained.

[0166] The following is a computer simulation experiment to demonstrate the passive localization path planning algorithm for UAV swarms based on analytical global CRLB described in this invention:

[0167] 1) When initializing the target, UAVs, and measurement parameters, three UAVs carrying positioning devices are set as shown in Figure (3). Their positions in the rectangular coordinate system are (0, 0) m, (8660, 0) m, and (4330, 7500) m, respectively. The position of the fixed radiation source target is set to (25000, 15000) m. The signal bandwidth is set to 300MHz, the electromagnetic wave propagation speed is the speed of light, and the sampling time is 10⁻ 8 The drone's flight speed is 800 m / s; flight constraint parameters are set as follows: minimum turning radius 300 m, minimum forward distance 200 m, maximum deflection angle π / 3; the TDOA measurement signal-to-noise ratio is set to 5 ± 0.1, and the experimental iteration time step is 20.

[0168] 2) The initial estimate of the target position is calculated using the Chan algorithm, that is, Gaussian perturbation is added to the target source signal using equations (1)-(4) to construct the TDOA nonlinear equation system. Then, the first weighted least squares method is used to solve the problem using equation (5), and the second weighted least squares method is used to solve the problem using equations (6)-(12) to obtain the initial estimate of the target position.

[0169] 3) Calculate the theoretical upper limit of positioning accuracy using the analytical global CRLB method, that is, construct the dynamic integration region using equations (13)-(14), simplify the integration by combining the Gaussian moment property equations (15)-(16), perform Taylor expansion on the trace of the CRLB matrix using equation (17), and finally calculate the analytical approximation of the global CRLB value using equations (18)-(21).

[0170] 4) Based on the analytical global CRLB value, constrained adaptive PSO path planning is carried out. That is, the particle swarm constraint range is determined by equation (22)-(25), the fitness function is defined by equation (26), and the global optimal heading angle is obtained by combining the parameter update rules of equation (27)-(30). Then, the candidate position of the UAV at the next moment is calculated by equation (31).

[0171] 5) Post-process and verify the accuracy of the planning results, that is, use equations (32)-(34) to correct waypoints and headings, and use equation (35) to calculate and update the optimal position of the UAV swarm at the next moment.

[0172] 6) Perform a planning termination judgment, that is, use several termination conditions to terminate the algorithm execution or restart the loop. If the loop terminates, output the optimal drone swarm position and the corresponding optimal global CRLB and RMSE (root-mean square error) results.

[0173] like Figures 4-6 As shown in the figure, the analytical global CRLB algorithm represents the passive localization path planning algorithm for UAV swarms based on analytical global CRLB proposed in this method, while the single-point CRLB algorithm represents the traditional CRLB estimation path planning algorithm for deterministic targets. Figures 4-6 As can be seen, the CRLB value of the parsed global CRLB algorithm is significantly lower, reduced by about 15%. Furthermore, the RMSE is lower, by more than 30%, indicating higher positioning accuracy.

[0174] The technical solutions of the present invention are not limited to the specific embodiments described above. Any technical modifications made in accordance with the technical solutions of the present invention fall within the protection scope of the present invention.

Claims

1. A passive localization path planning algorithm for UAV swarms based on analytical global CRLB, characterized in that, Includes the following steps: Step 1: Initialize the multi-UAV system, target, and measurement parameters; Step 2: TDOA measurement data processing and initial target positioning; Step 3: Global CRLB parsing calculation; Step 4: Constrained Adaptive PSO Path Planning; Step 5: Waypoint verification and position update; Step 6: Convergence judgment and optimal trajectory output.

2. The UAV swarm passive localization path planning algorithm based on analytical global CRLB according to claim 1, characterized in that: Step 1 specifically includes: Step 1.1: Set up the target location uncertainty model: Let the position coordinates of the target source be... Target's true location It follows a two-dimensional Gaussian distribution. ,in The position mean vector, Let covariance matrix be the variance matrix. , for , Orientation standard deviation; Step 1.2: Initialize the drone swarm positions: drones ( ), position matrix , For the first The initial coordinates of the first drone are determined, and the first drone is designated as the reference drone. Step 1.3: Set physical parameters: signal bandwidth speed of light Positioning time interval Drone flight speed ; Step 1.4: Define flight constraints: minimum turning radius Minimum approach distance Maximum deflection angle .

3. The passive localization path planning algorithm for UAV swarms based on analytical global CRLB as described in claim 2, characterized in that: Step 2 specifically includes: Step 2.1: Collect TDOA measurement data: At that moment, the benchmark drone and the first Time difference of drones Converted to distance difference , For measuring noise; Step 2.2: Construct the linearized equations of the Chan algorithm: ,in, , ( (Distance from target to baseline drone) ; Step 2.3: First Weighted Least Squares (WLS): , This is the weight matrix. ; Step 2.4: Preliminary estimation based on the first WLS Construct a new observation vector: New vector to be estimated: Coefficient matrix: ; Step 2.5: Calculate the weight matrix Calculate the covariance matrix of the new error vector using the error propagation law. ,in , ,make ; Step 2.6: Perform the second WLS calculation ,get , respectively corresponding and The optimal estimate; Step 2.7: Restore the target location: For By extracting the root cause and combining preliminary estimations, screening, and understanding, the initial target location result is obtained. .

4. The passive localization path planning algorithm for UAV swarms based on analytical global CRLB as described in claim 3, characterized in that: Step 3 specifically includes: Step 3.1: Construct the dynamic integration region: , This represents the average distance from the drone to the target. and These are the preset minimum and maximum side lengths, and the scaling factor. Take a value of 0.1 to 0.2; Step 3.2: Apply the properties of Gaussian moments: a. Odd-order moments: ( (non-negative integers) b. Even-order moments: It can be seen that the odd-order moments are zero, so only the even-order moments are retained, which further simplifies the calculation of the analytical solution. Step 3.3: Perform a Taylor expansion on the trace of the CRLB matrix: Where F is the Fisher information matrix; Step 3.4: Calculate the global CRLB: ; Among them, local items That is Correction item It includes complete second- and fourth-order correction terms, and all partial derivative terms are calculated using high-precision numerical differentiation methods; Step 3.5: Subdomain Global Overlay: Based on the mean square error of the Gaussian distribution of the target source The size evaluation divides the integration region into A subfield of integration With the geometric center of each subdomain As a new expansion point, and because the subfield is small enough, the geometric center Approximately the center of the Gaussian weight function within this subdomain, perform a local Taylor expansion for each subdomain: Calculate the local subdomain CRLB approximation polynomial of the above expression. The product of the original global Gaussian weight function in the corresponding sub-region Integral value within: Step 3.6: All subdomains The global contributions are summed to obtain the final high-precision approximation of the global CRLB: This yields the final analytical approximation of the global CRLB.

5. The UAV swarm passive localization path planning algorithm based on parsing global CRLB according to claim 4, characterized in that: Step 4 specifically includes: Step 4.1: Initialize the particle swarm: Particles are represented by heading angle vectors. ,quantity ,scope ; Step 4.2: Calculate the constrained heading range: Turning radius constraint: ; Goal-oriented constraints: , , ; Step 4.3: Define the fitness function: , , , ; Step 4.4: Update PSO parameters: Inertia weight: ; Learning factors: , ; Particle position: , ; Step 4.5: Calculate candidate waypoints: .

6. The UAV swarm passive localization path planning algorithm based on parsing global CRLB according to claim 5, characterized in that: Step 5 specifically includes: Step 5.1: Minimum forward distance verification: Calculate the distance between the candidate waypoint and the current position. ,like Then adjust to ; Step 5.2: Turning angle constraint verification: Calculate the actual turning angle ,like Then adjust the heading angle to Recalculate ; Step 5.3: Position Matrix Update: Determine the position matrix... Final position at time Update the drone location matrix .

7. The passive localization path planning algorithm for UAV swarms based on analytical global CRLB as described in claim 6, characterized in that: Step 6 specifically includes: Step 6.1: Determine the convergence condition (any one of the following conditions must be met): Condition 1: , Condition 2: , in ; Condition 3: Number of convergences ; Step 6.2: Output Results: If the convergence condition is met, output the optimal UAV swarm track points. ) and positioning accuracy report ( Otherwise, return to step 2.

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