Unmanned aerial vehicle adaptive site selection and TDOA passive positioning method based on fixed receiving station

Abstract

The invention relates to the technical field of passive positioning, and particularly discloses an unmanned aerial vehicle adaptive site selection and TDOA passive positioning method based on a fixed receiving station, and the method comprises the steps: building a TDOA measurement model: setting a target position as p = (x, y, z), setting the position of an ith receiver as si = (xi, yi, zi), i = 1,..., 6, and setting a first receiver as a reference receiver; a time difference observation equation: # imgabs0 # is established, i = 2,..., 6, c is signal propagation speed, and ni1 is measurement noise; the initial position is solved through a Chan algorithm, a time difference equation is linearized and then written into a matrix form Ap = d1b + c, and a matrix A, vectors b and c are all obtained through calculation of receiver coordinates and observation time difference; an initial position estimation p0 is obtained through weighted least square solution, and a closed-form solution is obtained through correction by using a constraint p-s1 = d1; and optimizing a positioning result based on Newton iteration: taking p0 as an initial value, and iterating to a high-precision solution p * through a Gaussian-Newton iteration formula pk + 1 = pk-[J (pk) TJ (pk)]-1J (pk) Tf (pk). According to the technical scheme, stability and flexibility can be considered, and positioning precision, real-time performance and robustness are improved.

Description

Technical Field

[0001] The present invention relates to the field of passive positioning technology, and in particular to a UAV adaptive site selection and TDOA passive positioning method based on a fixed receiving station. Background Art

[0002] In the field of target positioning, time difference of arrival (TDOA) passive positioning technology has been widely used due to its unique advantages. This technology constructs a hyperbolic equation based on the time difference between signals arriving at different receiving stations and determines the target position by solving a system of nonlinear equations. Among classic algorithms, the Chan algorithm, as a non-iterative closed-form solution, offers low computational complexity and high positioning accuracy when line-of-sight conditions and Gaussian measurement noise are present, and can approach the optimal estimate. Newton-based methods, such as the Taylor algorithm, require iterative optimization of the initial estimate to improve accuracy, but these methods rely heavily on the initial value, and their convergence performance is significantly affected by the initial estimate.

[0003] When it comes to base station site selection, the location of sensors (receiving stations) significantly impacts positioning accuracy. Theoretically, the optimal base station layout can be determined by maximizing Fisher information or minimizing the Cramér-Rao lower bound (CRLB). However, fixed base station placement schemes struggle to cope with changes in viewing angle due to target maneuvering, and positioning accuracy is easily affected by the geometric distribution of the array. Traditional positioning node selection often translates into a non-convex optimization problem of minimizing the error covariance or CRLB. While approaches such as semidefinite programming can provide approximate solutions, these problems suffer from high exhaustive search complexity, slow response, and difficulty in real-time application.

[0004] In recent years, research on reconfiguring formations using drones as signal receiving nodes has gained momentum. This approach theoretically enables dynamic target tracking and optimized deployment, offering high maneuverability and flexibility. However, drones are limited by speed, energy consumption, and airspace constraints, resulting in delayed response times for deployment adjustments, a bottleneck in practical applications.

[0005] Although the academic community has tried to introduce swarm intelligence optimization methods, such as genetic algorithms and particle swarm algorithms, for receiving station layout optimization to minimize positioning error or CRLB, and these heuristic methods can find better solutions in complex search spaces, existing work mostly assumes that base stations are fixed and lacks the adaptability to dynamic target tracking. There is still room for improvement in positioning accuracy, algorithm convergence, and other aspects.

[0006] In summary, traditional fixed base stations have problems such as slow response, low positioning accuracy and slow algorithm convergence. The full UAV receiving array is limited by the platform's maneuvering speed and airspace restrictions, making it difficult to quickly change formations, resulting in insufficient emergency response capabilities. There is an urgent need for a UAV adaptive site selection and TDOA passive positioning method based on fixed receiving stations that can balance stability and flexibility and improve positioning accuracy, real-time performance and robustness. Summary of the Invention

[0007] The present invention provides a UAV adaptive site selection and TDOA passive positioning method based on fixed receiving stations, which can balance stability and flexibility and improve positioning accuracy, real-time performance and robustness.

[0008] In order to solve the above technical problems, this application provides the following technical solutions:

[0009] The UAV adaptive site selection and TDOA passive positioning method based on fixed receiving stations includes:

[0010] Construct a TDOA measurement model: set the target position to p = (x, y, z), and the position of the i-th receiver to s i =(x i ,y i ,z i ), where i = 1,…,6, and the first receiver is the reference receiver; establish the time difference observation equation: Where i = 2,…,6, c is the signal propagation speed, n i1 To measure noise;

[0011] The Chan algorithm is used to solve the initial position: the time difference equation is linearized and written into the matrix form Ap = d1b + c, where the matrix A and the vectors b and c are calculated from the receiver coordinates and the observed time difference; the initial position estimate p0 is solved by weighted least squares, and the closed-form solution is corrected using the constraint ||p-s1||=d1;

[0012] Based on Newton iteration optimization positioning results: Taking p0 as the initial value, through the Gauss-Newton iteration formula p k+1 =p k -[J(p k ) T J(p k )] -1 J(p k ) T f(p k ) Iterate to a high-precision solution p * ; where J(p) is the Jacobian matrix of the residual function with respect to p.

[0013] Furthermore, a fixed base station and dual UAV collaborative station structure is adopted, combined with an adaptive differential evolution algorithm to optimize the three-dimensional position of the UAV, with the average GDOP minimization as the objective function. And meet the maximum flight speed, airspace boundaries and no-fly zone constraints, among which GDOP i is the GDOP value of the i-th radiation source position, and N is the number of radiation source positions.

[0014] Through the above method, a joint optimized deployment scheme of fixed base stations and auxiliary UAVs can be obtained, which can minimize the GDOP in the target area, thereby improving the geometric robustness and overall accuracy of the TDOA positioning system.

[0015] Furthermore, the linearization process of the Chan algorithm includes: squaring both sides of the time difference equation and sorting them to obtain in d1=||p-s1||; the residual function f(p) in the Newton iteration is the sum of the squares of the residuals of each time difference equation, and the Jacobian matrix J(p) is the first-order partial derivative matrix of the residual function with respect to p.

[0016] Furthermore, in the structure of collaborative deployment of the fixed base station and the dual UAVs, the fixed base station serves as the main structure to form a stable receiving framework, and the dual UAVs serve as mobile nodes to adjust their positions in real time to assist in deployment.

[0017] Furthermore, the optimization variables of the adaptive differential evolution algorithm are the three-dimensional coordinates (x i ,y i ,z i ), the individual is encoded as a 6-dimensional vector [x1, y1, z1, x2, y2, z2], and the initial population is uniformly randomly generated in the preset spatial domain.

[0018] Furthermore, the mutation operation of the adaptive differential evolution algorithm adopts the "DE / rand / 1" strategy, and the scaling factor F is adaptively adjusted to F=F min +(F max -F min )·rand1(), where F min =0.4, F max =0.9, rand l ()∈[0,1] is a uniformly distributed random number.

[0019] Furthermore, the crossover operation of the adaptive differential evolution algorithm adopts an adaptive crossover rate CR~N(0.5,0.1 2 ), dynamically adjust the crossover probability through normal distribution to ensure that at least one dimension of genes crosses over.

[0020] Furthermore, the fitness function of the adaptive differential evolution algorithm is The current station layout plan at the target point x i The geometric dilution of precision at .

[0021] Furthermore, the physical constraints include:

[0022] Maximum flight speed constraint: ||S i (t+1)-S i(t)||≤V max Δt, where V max is the maximum flight speed of the UAV, Δt is the interval between consecutive decision times;

[0023] Airspace boundary constraints: UAV 3D coordinates (x i ,y i ,z i ) is located within the preset airspace where flight is allowed, and avoids geometric polygonal areas such as the no-fly zones S1 and S2. When crossing the boundary, the boundary rebound method is used to correct the coordinates.

[0024] Furthermore, the adaptive differential evolution algorithm introduces an elite guidance mechanism, saves the best individuals of each generation to form an elite library to guide the mutation direction, and adopts a boundary reflection strategy to deal with out-of-bounds individuals; the algorithm termination condition is to reach the maximum iteration number G max Or there is no significant improvement in the optimal solution of M consecutive generations. The optimal individual finally output is the joint optimized station layout plan of fixed base stations and dual UAVs, which minimizes the average GDOP value in the surveillance airspace.

[0025] The principle and beneficial effects of the scheme are as follows: The TDOA measurement model is constructed based on the basic principle of time difference positioning. The time difference between the target signal reaching different receivers is used to establish a nonlinear hypersurface equation system. By introducing a reference receiver (No. 1), the geometric relationship between the target position and the position of each receiver is converted into a time difference observation equation, providing a mathematical basis for subsequent positioning solution. The model takes into account the measurement noise n i1 to ensure the consistency between the model and the actual physical scene.

[0026] In the closed-form solution for the initial position using the Chan algorithm, the nonlinear time difference equation is squared and linearized, transforming it into the matrix form Ap = d1b + c. The weighted least squares (WLS) method is then used to solve the linear equations, quickly obtaining the initial estimate p0 of the target position. This approach eliminates iterations and offers low computational complexity, making it suitable for scenarios with high real-time requirements. The constraint ‖p - s1‖ = d1 eliminates error accumulation during the linearization process, ensuring the geometric rationality of the initial solution.

[0027] In the Newton iteration optimization positioning accuracy, the initial solution p0 of the Chan algorithm is used as the starting point of the Newton iteration. By constructing the residual function f(p) (the sum of the squares of the residuals of the time difference equation), the Jacobian matrix J(p) is used to describe the gradient information of the residual to the position, and the position estimate is iteratively updated based on the Gauss-Newton method: p k+1 =p k -[J(p k ) T J(p k )] -1 J(p k) T f(p k ); converge to a higher precision solution p through iteration * , which overcomes the defect of Newton's method being sensitive to initial values ​​and improves the positioning robustness in complex environments.

[0028] Combining the speed of the Chan algorithm with the high precision of Newton iteration significantly reduces positioning error compared to using either the Chan algorithm or Newton method (such as the Taylor algorithm) alone. Experiments show that the combined algorithm outperforms either algorithm in terms of average positioning error and maximum positioning error.

[0029] By combining weighted least squares and the noise covariance matrix W, the interference of measurement noise on the initial solution is suppressed, improving noise immunity. Using the closed-form solution of the Chan algorithm as the initial value for the Newton iteration avoids the slow convergence or local optimality problems associated with the traditional Newton method due to random initial values, significantly accelerating iterative convergence and making it suitable for real-time positioning of dynamic targets. The combination of nonlinear models and iterative optimization ensures stable performance in both line-of-sight (LOS) and non-line-of-sight (NLOS) scenarios, effectively addressing complex interference factors in real-world environments.

[0030] This solution achieves a balance between stability and flexibility through the synergy of structural design, algorithm fusion and optimization strategy, and improves positioning accuracy, real-time performance and robustness.

[0031] Using fixed ground base stations as the primary structure, a stable receiving framework is formed, providing fundamental positioning geometric support and avoiding the formation fluctuation risks associated with a fully mobile array. Dual drones are introduced as mobile receiving nodes, leveraging their mobility to adjust the formation in real time and dynamically respond to changes in target position, addressing the inherent inability of fixed base stations to adapt to target maneuvers.

[0032] Fixed base stations and drones form a complementary "basic framework + dynamic adjustment" model, ensuring basic system stability while enabling adaptive formation reconstruction through real-time drone position optimization. Using the drones' three-dimensional coordinates as optimization variables, an optimal station layout is generated in real time through iterative calculations, ensuring the formation's geometry consistently approaches the optimal layout for the target area, balancing stability and dynamic adaptability.

[0033] Leveraging the ability of non-iterative closed-form solutions to approximate optimal estimates under line-of-sight conditions, this approach quickly provides an initial position with minimal error, laying the foundation for subsequent optimization. Newton iterative refinement optimization uses the Chan solution as the initial value and iteratively solves the nonlinear equations to correct for the effects of measurement noise and non-line-of-sight errors, significantly improving positioning accuracy.

[0034] Weighted least squares (WLS) combines the noise covariance matrix W to perform weighted processing on the measurement noise and reduce the interference of noise on the solution results.

[0035] Taking the average geometric dilution of precision (GDOP) as the objective function, the geometric sources of positioning error are directly optimized. By minimizing the global GDOP value, the positioning accuracy of the station structure in the entire monitoring area is ensured to be balanced and optimal, avoiding the local error amplification problem caused by poor geometric distribution of traditional fixed stations.

[0036] The Chan algorithm can obtain the initial solution without multiple iterations, and the computational complexity is significantly lower than that of pure iterative algorithms (such as the Taylor algorithm), meeting real-time requirements.

[0037] Incorporate the maximum flight speed constraint of the UAV||S i (t+1)-S i (t)||≤V max Δt ensures that the optimized formation adjustment is within the physically reachable range, avoids computational waste caused by infeasible solutions, and improves real-time performance.

[0038] The Newton iteration's correction of the Chan solution reduces the algorithm's sensitivity to measurement noise and non-line-of-sight errors, allowing it to converge to a highly accurate solution even when the time difference measurement error is large. The adaptive DE algorithm's boundary reflection strategy and elite retention mechanism ensure stable optimization under complex airspace constraints (such as no-fly zones), avoiding falling into local optima or generating invalid solutions. Adaptive control parameters (such as the scaling factor F and the crossover rate CR) and an elite guidance mechanism accelerate the algorithm's convergence speed, reducing the number of iterations by over 30% compared to traditional swarm intelligence algorithms (such as genetic algorithms), ensuring real-time response to drone formation adjustments.

[0039] The hybrid station structure is suitable for long-term monitoring of static targets (dominated by fixed base stations) and can also cope with the rapid tracking of dynamic targets (drone-assisted formation reconstruction), maintaining stable performance in multiple scenarios such as military reconnaissance and emergency response.

[0040] By organically combining the above technologies, this solution overcomes the limitations of traditional fixed and fully mobile positioning systems, achieving comprehensive performance improvements in stability and flexibility, accuracy and real-time performance, and environmental adaptability. It is particularly suitable for complex positioning scenarios with high dynamics and strong interference. This achieves the goal of balancing stability and flexibility while improving positioning accuracy, real-time performance, and robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Flowchart of the adaptive site selection and TDOA passive positioning method for UAVs based on fixed receiving stations;

[0042] Figure 2 This is a schematic diagram of the layout structure of fixed base stations, drones, and target trajectories in the scene;

[0043] Figure 3 The following is a schematic diagram of the distribution of positioning errors under each strategy. DETAILED DESCRIPTION

[0044] The following is further described in detail through specific implementation methods:

[0045] Adaptive site selection and TDOA passive positioning method for UAVs based on fixed receiving stations (such as Figure 1 shown), including,

[0046] TDOA measurement model: Assume the target drone position is p = (x, y, z), and the position of the i-th receiver is s i =(x i ,y i ,z i ), (i=1,…,6), assuming that receiver No. 1 is the reference. The distance from the target to receiver No. i is Then the time difference observation between receiver No. i and receiver No. 1 is

[0047]

[0048] Where c is the signal propagation speed, n i1 is the measurement noise. The above equation can be rewritten as the hypersurface equation:

[0049] ‖ps i ‖-‖p-s1‖=cΔt i1 (i=2,…,6)

[0050] This set of equations is nonlinear and will form the basis for subsequent positioning solutions.

[0051] Chan algorithm solves the initial position: define Δ i1 =cΔt i1 , by squaring both sides of the i=2,…,6 hypersurface equations and sorting them, we can get the linearized expression:

[0052]

[0053] in The above equation is written in matrix form as Ap=d1b+c, where the matrix A and vectors b and c are calculated from the receiver coordinates and the observed time difference. The weighted least squares method is used to solve this linear system of equations to obtain the initial position estimate p0:

[0054] p0=(A T WA) -1 A T W(d1b+c),W=Cov{n i1} -1

[0055] Where W is the covariance matrix of the time difference measurement noise. The above formula is similar to the classical weighted least squares solution X = (G T WG) -1 G T Ws, where W represents the covariance matrix of the TDOA measurement. Finally, by substituting p0 into the constraint ‖p-s1‖=d1 to solve for d1 and correct p, the closed-form solution of the Chan algorithm is obtained as the target initial position estimate.

[0056] Newton iteration:

[0057] Using the result p0 of the Chan algorithm as the initial value, the residual function f(p) of TDOA positioning is constructed, and the position is updated step by step. Specifically, the objective function is defined as the sum of the squares of the residuals of each time difference equation, and the gradient and Jacobian matrix are used for iteration:

[0058] p l+1 =p l -[J(p k ) T J(p k )] -1 J(p k ) T f(p k ),

[0059] Where J(p) is the Jacobian matrix of the residual function for p. This iterative process (Gauss-Newton method) can quickly converge to a higher precision solution. Through iteration, the positioning accuracy of the Chan solution can be significantly improved, and finally a fine position estimate p is obtained. *

[0060] Formation optimization objective function:

[0061] To further improve the geometric accuracy of the TDOA positioning system, the Geometric Dilution of Precision (GDOP) is used as a measure of the quality of the receiving node deployment. GDOP directly reflects the impact of the station geometry on positioning accuracy. A smaller GDOP value indicates a better positioning system geometry, stronger noise immunity, and higher positioning accuracy.

[0062] Specifically, let the receiver array be R = {r1, r2, ..., r M}, construct the measurement matrix (i.e., Jacobian matrix) of TDOA measurement at the target position x, then GDOP is defined as the function of the trace and variance of the positioning error covariance matrix corresponding to the measurement model. This paper chooses the following form of GDOP as the optimization objective function:

[0063]

[0064] Where J is the Jacobian matrix of the TDOA measurement equation at the target point. In order to meet the requirements of multi-target / multi-region positioning, this embodiment uses multiple candidate target points {x i The weighted sum of GDOP is used as the overall evaluation index:

[0065]

[0066] By minimizing the above objective function, it is expected to obtain a receiving array layout with optimal geometric structure and stable positioning accuracy in the entire target area.

[0067] Improved differential evolution algorithm design:

[0068] To solve the receiver placement optimization problem with the goal of minimizing GDOP, this paper proposes an improved adaptive differential evolution algorithm. Based on the standard differential evolution (DE), this algorithm introduces adaptive control parameter adjustment, an elite guidance mechanism, and a boundary reflection strategy to significantly improve the algorithm's convergence speed and solution quality.

[0069] 1. Individual representation and population initialization

[0070] There are M receiving nodes (including fixed base stations and auxiliary drones), and the position of each node in three-dimensional space is represented by r i =(x i ,y i ,z i ), each individual is encoded as a 3M-dimensional vector:

[0071]

[0072] Where G represents the current evolutionary generation, NP is the population size, and the initial population is generated uniformly and randomly within the set spatial range.

[0073] 2. Differential mutation operation

[0074] The “DE / rand / 1” strategy is used for basic mutation, and an adaptive scaling factor F∈(0,1) is introduced:

[0075]

[0076] where r1, r2, r3∈{1,…, NP} are random individual indices that are different from each other and from j. Scaling factor F G Dynamically adjust according to the following adaptive rules:

[0077] F 1 =F min +(F max -F min )·rand1()

[0078] Among them, rand1()∈[0,1] is a uniformly distributed random number, and F min =0.4,F max =0.9.

[0079] 3. Crossover operation (adaptive crossover rate)

[0080] The mutation vector is crossed with the current individual to generate a test individual:

[0081]

[0082] Among them CR G ∈[0,1] is the crossover probability, rand2(i) is the random value of the i-th dimension, and rand_idx is a randomly selected index to ensure that at least one dimension crosses. The crossover rate is also updated adaptively, for example:

[0083] CR 2 =N(0.5,0.1 2 )

[0084] That is, it follows a normal distribution with a mean of 0.5 and a standard deviation of 0.1.

[0085] 4. Fitness function design (with GDOP as indicator)

[0086] The fitness function is calculated based on the geometric dilution of precision (GDOP) at several representative points in the target area:

[0087]

[0088] in Calculated from the current position.

[0089] 5. Selection Mechanism and Elite Retention

[0090] Adopt the "winner-retains" strategy: if the fitness of the test individual is better than that of the parent individual, replace it:

[0091]

[0092] At the same time, the individuals with the best fitness in each generation are saved to form an elite library, which is used to guide the direction of subsequent mutations.

[0093] 6. Boundary processing and convergence judgment

[0094] If a dimension of an individual exceeds the boundary, the boundary rebound method is used for correction:

[0095]

[0096] The algorithm iteration termination condition can be set as the maximum algebra G maxOr there is no obvious improvement in the optimal solution for several consecutive generations.

[0097] 7. Optimal solution output

[0098] The optimal individual X is finally output * That is, the joint optimized deployment plan of fixed base stations and auxiliary UAVs can minimize the GDOP in the target area, thereby improving the geometric robustness and overall accuracy of the TDOA positioning system.

[0099] Specific usage: Verification was performed using test data generated through simulation. The following scenario was constructed: Four fixed base stations (rectangular layout) were deployed in a two-dimensional area (1000m, 1000m) and equipped with two coordinated drones. The enemy drone target moved along a circular trajectory near the center of the area. The comparison targets included the "fixed base station deployment strategy" and the "fixed base station + one drone strategy," and were compared with this method. Table 1 shows the average GDOP, maximum positioning error, and average positioning error comparison results for different strategies.

[0100]

[0101] Table 1 Comparison of positioning performance under different station layout strategies

[0102] Figure 2 This diagram illustrates the layout of fixed base stations, drones, and target trajectories in this scenario. Figure 3 The distribution of positioning errors for each strategy is presented. Comparison shows that this method achieves lower GDOP and positioning error in multi-target areas. In particular, compared to the fixed base station strategy alone, this method significantly reduces the average positioning error. Compared to the single-UAV strategy, the addition of a cooperative UAV further optimizes the measurement geometry. In summary, this method offers superior positioning accuracy, greater maneuverability, and adaptability in multi-target environments, meeting the requirements of highly dynamic military reconnaissance and possessing significant military application value.

[0103] Comparative simulations show that this method outperforms traditional methods in terms of average GDOP and positioning error, indicating that the adaptive DE and dual-UAV collaborative strategy significantly improves positioning accuracy and adaptability, further demonstrating the effectiveness and practical value of this method.

[0104] The above are only embodiments of the present invention. The invention is not limited to the fields involved in this implementation case. Common knowledge such as the known specific structures and characteristics in the scheme is not described in detail here. Ordinary technicians in the relevant field are aware of all common technical knowledge in the technical field to which the invention belongs before the application date or priority date, can obtain all existing technologies in the field, and have the ability to apply conventional experimental means before that date. Ordinary technicians in the relevant field can improve and implement this scheme in combination with their own abilities under the inspiration given by this application. Some typical known structures or known methods should not become obstacles for ordinary technicians in the relevant field to implement this application. It should be pointed out that for those skilled in the art, without departing from the structure of the present invention, several variations and improvements can be made, which should also be regarded as the scope of protection of the present invention. These will not affect the effect of the implementation of the present invention and the practicality of the patent. The scope of protection required by this application shall be based on the content of its claims, and the specific implementation methods and other records in the specification can be used to interpret the content of the claims.

Claims

1. The UAV adaptive site selection and TDOA passive positioning method based on fixed receiving stations is characterized by: include: Construct a TDOA measurement model: set the target position to p = (x, y, z), and the position of the i-th receiver to s i =(x i ,y i ,z i ), where i = 1,…,6, and the first receiver is the reference receiver; establish the time difference observation equation: Where i = 2,…,6, c is the signal propagation speed, n i1 To measure noise; The Chan algorithm is used to solve the initial position: the time difference equation is linearized and written into the matrix form Ap = d1b + c, where the matrix A and the vectors b and c are calculated from the receiver coordinates and the observed time difference; the initial position estimate p0 is solved by weighted least squares, and the closed-form solution is corrected using the constraint ||p-s1||=d1; Based on Newton iteration optimization positioning results: Taking p0 as the initial value, through the Gauss-Newton iteration formula p k+1 =p k -[J(p k ) T J(p k )] -1 J(p k ) T f(p k ) Iterate to a high-precision solution p * ; where J(p) is the Jacobian matrix of the residual function with respect to p.

2. The method for adaptive site selection and TDOA passive positioning of unmanned aerial vehicles based on fixed receiving stations according to claim 1 is characterized in that: A fixed base station and dual UAV collaborative station structure are used, combined with an adaptive differential evolution algorithm to optimize the three-dimensional position of the UAV, with the average GDOP minimization as the objective function. And meet the maximum flight speed, airspace boundaries and no-fly zone constraints, among which GDOP i is the GDOP value of the i-th radiation source position, and N is the number of radiation source positions.

3. The method for adaptive site selection and TDOA passive positioning of unmanned aerial vehicles based on fixed receiving stations according to claim 2 is characterized in that: The linearization process of the Chan algorithm includes: squaring both sides of the time difference equation and sorting them to obtain in d1=||p-s1||; the residual function f(p) in the Newton iteration is the sum of the squares of the residuals of each time difference equation, and the Jacobian matrix J(p) is the first-order partial derivative matrix of the residual function with respect to p.

4. The method for adaptive site selection and TDOA passive positioning of unmanned aerial vehicles based on fixed receiving stations according to claim 3 is characterized in that: In the structure of coordinated deployment of fixed base stations and dual UAVs, the fixed base station serves as the main structure to form a stable receiving framework, and the dual UAVs serve as mobile nodes to adjust their positions in real time to assist in deployment.

5. The method for adaptive site selection and TDOA passive positioning of unmanned aerial vehicles based on fixed receiving stations according to claim 4 is characterized in that: The optimization variables of the adaptive differential evolution algorithm are the three-dimensional coordinates of the dual UAVs (x i ,y i ,z i ), the individual is encoded as a 6-dimensional vector [x1, y1, z1, x2, y2, z2], and the initial population is uniformly randomly generated in the preset spatial domain.

6. The method for adaptive site selection and TDOA passive positioning of unmanned aerial vehicles based on fixed receiving stations according to claim 5, characterized in that: The mutation operation of the adaptive differential evolution algorithm adopts the "DE / rand / 1" strategy, and the scaling factor F is adaptively adjusted to F=F min +(F max -F min )·rand1(), where F min =0.4, F max =0.9, rand1()∈[0,1] is a uniformly distributed random number.

7. The method for adaptive site selection and TDOA passive positioning of unmanned aerial vehicles based on fixed receiving stations according to claim 6, characterized in that: The crossover operation of the adaptive differential evolution algorithm adopts an adaptive crossover rate CR~N(0.5,0.1 2 ), dynamically adjust the crossover probability through normal distribution to ensure that at least one dimension of genes crosses over.

8. The method for adaptive site selection and TDOA passive positioning of unmanned aerial vehicles based on fixed receiving stations according to claim 7, characterized in that: The fitness function of the adaptive differential evolution algorithm is The current station layout plan at the target point x i The geometric dilution of precision at .

9. The method for adaptive site selection and TDOA passive positioning of unmanned aerial vehicles based on fixed receiving stations according to claim 8, characterized in that: The physical constraints include: Maximum flight speed constraint: ||S i (t+1)-S i (t)||≤V max Δt, where V max is the maximum flight speed of the UAV, Δt is the interval between consecutive decision times; Airspace boundary constraints: UAV 3D coordinates (x i ,y i ,z i ) is located within the preset airspace where flight is allowed, and avoids geometric polygonal areas such as the no-fly zones S1 and S2. When crossing the boundary, the boundary rebound method is used to correct the coordinates.

10. The method for adaptive site selection and TDOA passive positioning of unmanned aerial vehicles based on fixed receiving stations according to claim 9, characterized in that: The adaptive differential evolution algorithm introduces an elite guidance mechanism, saves the best individuals in each generation to form an elite library to guide the direction of mutation, and adopts a boundary reflection strategy to deal with out-of-bounds individuals; The algorithm termination condition is to reach the maximum iteration number G max Or there is no significant improvement in the optimal solution of M consecutive generations. The optimal individual finally output is the joint optimized station layout plan of fixed base stations and dual UAVs, which minimizes the average GDOP value in the surveillance airspace.

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