Unmanned aerial vehicle group grouping obstacle avoidance path intelligent optimization method based on CRLB

Abstract

The invention discloses an unmanned aerial vehicle group grouping obstacle avoidance path intelligent optimization method based on CRLB, and relates to the technical field of unmanned aerial vehicle group multi-target passive positioning, and the method comprises the steps: initializing parameters, including targets, unmanned aerial vehicles and measurement parameters; calculating an estimated position of a target by using a Chan-TDOA positioning algorithm, and deducing a measurement error CRLB; unmanned aerial vehicle group nodes are selected, an unmanned aerial vehicle group is reasonably grouped, and each group positions different targets; a constraint condition is established, a deduced measurement error CRLB is used as a target function of unmanned aerial vehicle group adaptive obstacle avoidance path optimization, a dynamic trajectory model of the unmanned aerial vehicle is constructed to dynamically adjust the optimal position of the unmanned aerial vehicle at the next moment, and during the period, the optimal position of the unmanned aerial vehicle at the next moment is searched in an accelerated manner by using a PSO algorithm. The method can effectively improve the multi-target passive positioning precision under the conditions of self-adaptive obstacle avoidance and no-fly zone bypassing, optimizes the resource utilization, and is suitable for the multi-target passive positioning task of the unmanned aerial vehicle group in a complex dynamic environment.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-target passive positioning of unmanned aerial vehicle clusters, and in particular to a node selection algorithm for unmanned aerial vehicle clusters based on CRLB (Cramer-Rao Lower Bound) for multi-target passive positioning and an adaptive obstacle avoidance path optimization algorithm based on CRLB and Particle Swarm Optimization (PSO). Background Art

[0002] Unmanned aerial vehicle swarms (UAVs) have attracted much attention due to their enhanced capabilities in complex tasks, such as target tracking, localization, and detection. Generally speaking, UAVs can accomplish tasks through active systems or passive systems.

[0003] For active positioning systems, a locator (e.g., radar) actively transmits signals to detect and determine the location of a target. While this can provide real-time tracking and high accuracy, it also exposes the location of the locator itself. In addition, active positioning systems typically require higher energy consumption and more complex infrastructure, which can pose logistical challenges.

[0004] A passive positioning system does not involve transmitting a signal. Instead, it works by detecting and analyzing electromagnetic waves emitted by the target's own electronic devices. Its main advantage is that it does not reveal the location of the receiving system, making it inherently more covert and difficult to detect. In this case, passive positioning technology for drones provides a significant advantage in situations where concealment, resource efficiency and survivability are critical, with the ability to detect targets without transmitting a signal.

[0005] For passive positioning of targets by drones, path optimization is essential to improve the accuracy and efficiency of target positioning. Through path optimization, the drone can reach the appropriate position in each frame, obtain the right viewing angle and high-quality measurements, and thus achieve high positioning accuracy. Therefore, dynamic path optimization can ensure that the drone is optimally positioned to minimize positioning errors, thereby improving the drone's ability to locate targets.

[0006] From the perspective of path optimization for UAVs, the heuristic-based A* algorithm has been used for path optimization to efficiently find the shortest path. Genetic Algorithms (GAs) have been introduced for cooperative path planning for UAVs. The algorithm uses a set of potential solutions (paths) that evolve between generations according to a fitness function and combines crossover and mutation operations to explore the solution space, while the fitness function guides the search towards the best or near-optimal path to avoid collisions and optimize the mission objectives. Differential Evolution (DE) algorithms are well suited for UAV path optimization because they are able to efficiently search high-dimensional spaces while minimizing time and energy consumption. In addition, projection algorithms have been deployed to improve the positioning accuracy of UAVs, which guides the UAV towards waypoints closer to the target. This approach reduces the computational burden associated with numerical search by projecting the UAV onto more promising paths based on a prediction model, thereby improving the efficiency and effectiveness of the path optimization process. Although the algorithm considers the application of passive positioning of the target, it ignores the complex obstacle environment during the positioning process. Regarding existing research, path optimization methods mainly focus on shortest path search and minimizing energy consumption, with poor computational rate, ignoring the role of path optimization in positioning accuracy.

[0007] In general, passive positioning systems achieve positioning by detecting electromagnetic waves emitted by the target itself, which has the advantages of strong concealment and difficulty to be detected. However, the application of existing passive positioning technology in dynamic and complex environments still faces some problems, especially in the case of dense obstacles or no-fly zones. How to optimize the path of the drone to improve positioning accuracy and efficiency still needs in-depth research. Current path optimization methods, such as those based on A* algorithms and genetic algorithms, can efficiently find short paths, but often ignore the real-time adaptability and improvement of positioning accuracy in complex environments. Existing technologies mainly focus on shortest path search and minimization of energy consumption, and lack precise control in the multi-target positioning process and effective response to obstacle avoidance. Summary of the invention

[0008] The present invention provides a CRLB-based intelligent optimization method for obstacle avoidance paths of drone swarm groups, so as to improve the positioning accuracy of drone swarms and the efficiency of resource utilization of drone swarms. At the same time, the PSO intelligent optimization algorithm is used to quickly search for the optimal position of the drone swarm at the next moment, thereby improving the efficiency of the proposed algorithm and shortening the calculation time.

[0009] In order to solve the above problems, the technical solution adopted by the present invention is as follows:

[0010] The present invention provides a CRLB-based intelligent optimization method for obstacle avoidance paths of drone swarm groups, comprising the following steps:

[0011] Step 1, initialize the parameters, including the location and number of targets and drones, and the covariance matrix of TDOA measurements;

[0012] Step 2, using the Chan-TDOA positioning algorithm to calculate the estimated position of the target, and derive the measurement error CRLB based on the Chan-TDOA positioning algorithm;

[0013] Step 3: Use the derived measurement error CRLB to select the nodes of the drone swarm and divide the drone swarm into groups. Each group locates different targets, so that the average Cramer-Rao lower bound of each group of drones is minimized.

[0014] Step 4: Establish constraint conditions and use the derived measurement error CRLB as the objective function of the adaptive obstacle avoidance path optimization of the drone swarm. Construct a dynamic trajectory model of the drone to dynamically adjust the optimal position of the drone at the next moment. During this process, use the PSO algorithm to accelerate the search for the optimal position of the drone at the next moment.

[0015] As a further description of the above technical solution, step 1 specifically includes:

[0016] Step 1.1, set the target position coordinate to w j =[x j ,y j ] T ; j = 1, 2, ..., m; m is the number of targets; set n drones carrying passive radars, and their position coordinates are u i =[x i ,y i ] T ; i = 0, 1, ..., n-1; the 0th drone is the reference drone node, and its position coordinates are u0 = [x0, y0] T ;

[0017] Step 1.2, set the covariance matrix of TDOA measurements to in Represents the variance of the distance difference measurement between the ith UAV and the reference UAV.

[0018] As a further description of the above technical solution, step 2 specifically includes:

[0019] Step 2.1, construct the TDOA nonlinear time difference equations based on the parameters initialized in step 1;

[0020] Step 2.2, calculate the estimated position of the target using the Chan-TDOA positioning algorithm;

[0021] Step 2.3, derive the measurement error CRLB based on the Chan-TDOA positioning algorithm based on the TDOA measurement equation.

[0022] As a further description of the above technical solution, step 2.1 specifically includes:

[0023] Assume that the time delay difference between the signal sent by the jth target and the reference UAV and the i-th UAV is τ j,i,0 , then the relationship is satisfied

[0024]

[0025] Where c is the propagation speed of electromagnetic waves, τ j,i represents the time when the signal from the jth target reaches the i-th UAV, τ j,0 represents the time when the signal from the jth target reaches the reference UAV, r j,i represents the distance from the i-th UAV to the j-th target, r j,0 represents the distance from the reference UAV to the jth target; the measured arrival time difference contains the measurement error and satisfies

[0026] τ j,i,0 ′=τ j,i,0 +Δτ j,i,0

[0027] Among them, τ j,i,0 ′ represents τ j,i,0 The actual measured value, Δτ j,i,0 Represents the TDOA measurement error, satisfying

[0028]

[0029] The TDOA nonlinear time difference equations are constructed as follows:

[0030]

[0031] in

[0032]

[0033] As a further description of the above technical solution, step 2.2 specifically includes:

[0034] definition x i,0 =x i -x0,y i,0 =y i -y0,r i,0 =r i -r0,τ i,0 =τ i -τ0;

[0035] Construct the TDOA nonlinear equations in matrix form:

[0036] ψ=h-GZ 0

[0037] where ψ is the error vector due to TDOA measurement noise, and

[0038]

[0039]

[0040] The covariance matrix Ψ of the error vector ψ is

[0041] Ψ=E[ψψ T ]=BQB

[0042] Where Q is the covariance matrix of the TDOA measurement,

[0043] B=diag{r1,r2,…r n-1}

[0044] Using the first weighted least squares method for estimation, the maximum likelihood estimate is

[0045] Z = argmin{(h-GZ) T Ψ -1 (h-GZ)}≈(G T Q -1 G)G T Q -1 h

[0046] Constructing the residual vector

[0047] ψ′=h′-G′Z′

[0048] in

[0049]

[0050] The covariance matrix Ψ′ of the error vector is

[0051] Ψ′=E[ψ′ψ′ T ]=4B′cov(Z)B′

[0052] in

[0053] B′=diag(Z1-x1,Z2-y1,Z3)

[0054] Perform a second WLS estimate

[0055] Z′=(G′ T Ψ′ -1 G′) -1 G′ T Ψ′ -1 h′

[0056] The final estimated position of the target is

[0057]

[0058] As a further description of the above technical solution, step 2.3 specifically includes:

[0059] Assume that the measured TDOA value is

[0060] s=c[τ 1,0 ,τ 2,0 ,…,τ n-1,0 ] T

[0061] The actual measurement value is

[0062] s′=s+m

[0063] Where m is the TDOA measurement error, which follows a normal distribution. The probability density function of TDOA measurement is expressed as

[0064]

[0065] The likelihood function calculated from this density function is

[0066]

[0067] Taking the second-order partial derivative of the likelihood function with respect to the position coordinate parameter gives

[0068]

[0069] Its expected value is

[0070]

[0071] The Fisher information matrix FIM(s) of the positioning parameters is expressed as

[0072]

[0073] The measurement error CRLB matrix of target position estimation is obtained by taking the inverse of the Fisher information matrix FIM(s), which is

[0074] CRLB(s)=FIM -1 (s).

[0075] As a further description of the above technical solution, step 3 specifically includes:

[0076] Step 3.1, define the optimization objective function of node selection, assume that m targets are grouped by n drones to complete positioning, and for the jth target, the set of drones assigned to it is G j , the optimization goal is to minimize the average CRLB trace of all targets:

[0077]

[0078] Among them, Tr(CRLB t ) j represents the trace of the CRLB matrix of the jth target;

[0079] Step 3.2, establish constraints, requiring that each target requires at least 3 drones to locate, that is, n ≥ 3m, and each drone can only be assigned to one target group;

[0080] Step 3.3, use the exhaustive method to generate all feasible drone grouping solutions;

[0081] Step 3.4, calculate the corresponding CRLB value for each grouping scheme, and select the grouping scheme with the smallest objective function value as the optimal node selection scheme. The mathematical model of drone node selection is described as

[0082]

[0083] As a further description of the above technical solution, step 4 specifically includes:

[0084] Step 4.1: Use the CRLB value derived in step 3 as the objective function of path optimization. The optimization goal is to minimize the lower limit of positioning accuracy at the next moment:

[0085]

[0086] in, represents the position set of the j-th target UAV group at the next moment;

[0087] Step 4.2, construct path optimization constraints, including UAV kinematic constraints, no-fly zone constraints, and minimum approach distance constraints;

[0088] The kinematic constraints of the drones are the turning radius of each drone. Greater than the minimum allowable radius L min ;

[0089] The no-fly zone constraint means that the flight trajectory of the drone cannot enter the no-fly zone;

[0090] The minimum approach distance constraint is the distance between the UAV and the target at time t Greater than or equal to the minimum approach distance d min ;

[0091] Step 4.3, construct the minimum turning radius constraint, that is, the turning radius of each drone at time t Must be greater than or equal to the minimum turning radius L min ;

[0092] Step 4.4, based on the path optimization constraints, construct the dynamic trajectory model of the UAV, which is described as

[0093]

[0094] Step 4.5, use the PSO algorithm to accelerate the path optimization process.

[0095] As a further description of the above technical solution, step 4.5 specifically includes:

[0096] Initialize the PSO algorithm parameters, including the individual optimal position p of the particle s , the global optimal position p g , speed u s ; Each particle represents a set of heading angles of a group of drones, that is

[0097]

[0098] Update particle velocity and position:

[0099] u s (k+1)=ω(k)×u s (k)+c1l1(k)(p s (k)-η s (k))+c2l2(k)(p g (k)-η s (k))

[0100] η s (k+1)=η s (k)+u s (k+1)

[0101] Where, ω(k) = 0.9-0.5(k / T max ) is the inertia weight, T max is the maximum number of iterations, c1 and c2 are acceleration factors, l1 and l2 are random numbers, η s is the current position of the particle; the path optimization objective function Tr(CRLB) is used as the fitness function of the PSO algorithm, that is,

[0102]

[0103] Among them, η s (k) represents the current position of the sth particle, p g (k) The update method is:

[0104]

[0105]

[0106] The PSO position is updated iteratively until the maximum number of iterations is reached or the fitness function converges.

[0107] Compared with the prior art, the present invention has the following beneficial effects:

[0108] 1) The Chan-TDOA positioning algorithm and the measurement error CRLB are used in combination with the grouping method of the drone swarm nodes to achieve the high-precision requirements of multi-target passive positioning, which can significantly reduce the positioning error in complex environments and improve the reliability of target positioning.

[0109] 2) Through the CRLB-based node selection method, the drone swarm is grouped and the position is configured in real time, which effectively improves the resource utilization efficiency of the drone swarm, reduces the use of redundant nodes, and realizes efficient division of labor and collaboration of multi-objective tasks.

[0110] 3) The PSO intelligent optimization algorithm is introduced, and the derived measurement error CRLB is used as the objective function to realize the adaptive obstacle avoidance path optimization of the UAV dynamic trajectory model. It can quickly search and adjust the optimal position of the UAV at the next moment, which not only improves the target positioning accuracy, but also enhances the adaptability and safety of the UAV in complex environments.

[0111] 4) The PSO algorithm is used to accelerate the optimization calculation, eliminating the need for lengthy numerical searches, effectively shortening the calculation time and improving the calculation efficiency of the overall algorithm. At the same time, this method shows strong robustness and applicability under different environmental conditions, ensuring the stability of the algorithm in complex dynamic environments.

[0112] 5) The present invention is suitable for scenarios such as multi-target positioning and drone group path optimization in complex obstacle environments. It overcomes the limitation of traditional path optimization methods that cannot effectively balance positioning accuracy and obstacle avoidance, and has broad engineering application value and promotion prospects.

[0113] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the embodiments of the present invention are specifically cited below and described in detail with reference to the attached drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0114] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0115] Figure 1 A schematic diagram of a scenario in which a drone cluster locates multiple targets according to the present invention;

[0116] Figure 2 It is the overall algorithm flow chart of the present invention;

[0117] Figure 3 The positions of the UAV and the target in the simulation experiment scene of the present invention;

[0118] Figure 4 This is a diagram of the drone allocation of the drone swarm node selection algorithm based on CRLB of the present invention;

[0119] Figure 5 This is a comparison chart of the positioning RMSE between the drone swarm node selection algorithm based on CRLB and the random selection method of the present invention;

[0120] Figure 6 It is a schematic diagram of the trajectory of three groups of UAV swarm path optimization algorithms based on CRLB and PSO algorithms of the present invention;

[0121] Figure 7 This is a comparison chart of positioning CRLB and RMSE of three groups of UAV swarm path optimization algorithms based on CRLB and PSO algorithms and fixed configurations in the present invention;

[0122] Figure 8 This is a comparison chart of positioning CRLB and RMSE of three groups of drone group path optimization algorithms based on CRLB and PSO algorithms and the exhaustive method of the present invention;

[0123] Fig. 9 This is a comparison chart of the single calculation time of the three groups of drone swarm path optimization algorithms based on CRLB and PSO algorithms and the exhaustive method of the present invention. DETAILED DESCRIPTION

[0124] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0125] like Figure 1 As shown in the figure, a drone swarm equipped with radars locates and tracks multiple targets. UAV represents a drone, its subscript is the drone serial number, and Target represents a target. For this scenario, the present invention provides a multi-target drone swarm passive positioning algorithm based on CRLB-based drone swarm passive positioning node selection and drone swarm adaptive obstacle avoidance passive positioning path optimization based on CRLB and PSO algorithm. The overall algorithm flow is shown in the attached figure. Figure 2 shown.

[0126] The CRLB-based passive positioning node selection and path optimization method for a drone swarm provided in an embodiment of the present invention is specifically as follows:

[0127] Step 1, initialize the parameters, including the location and number of targets and drones, and the covariance matrix of TDOA measurements.

[0128] In this embodiment, the position coordinates of the target are set to w j =[x j ,y j ] T ; j = 1, 2, ..., m; m is the target number;

[0129] Set up n drones carrying passive radars, and their position coordinates are u i =[x i ,y i ] T ; i = 0, 1, ..., n-1;

[0130] The 0th drone is the reference drone node, and its position coordinates are u0 = [x0, y0] T ;

[0131] Set the covariance matrix of TDOA measurements to in Represents the variance of the distance difference measurement between the ith UAV and the reference UAV.

[0132] Step 2: Calculate the estimated position of the target using the Chan-TDOA positioning algorithm and derive the measurement error CRLB based on the Chan-TDOA positioning algorithm, which specifically includes:

[0133] Step 2.1, construct the TDOA nonlinear time difference equations based on the parameters initialized in step 1, as follows:

[0134] Assume that the time delay difference between the signal sent by the jth target and the reference UAV and the i-th UAV is τ j,i,0 , then the relationship is satisfied

[0135]

[0136] Where c is the propagation speed of electromagnetic waves, τ j,i represents the time when the signal from the jth target reaches the i-th UAV, τ j,0 represents the time when the signal from the jth target reaches the reference UAV, r j,i represents the distance from the i-th UAV to the j-th target, r j,0 represents the distance from the reference UAV to the jth target; the measured time difference of arrival (TDOA) value inevitably contains measurement errors, so there is

[0137] τ j,i,0 ′=τ j,i,0 +Δτ j,i,0 (2)

[0138] Among them, τ j,i,0 ′ represents τ j,i,0 The actual measured value, Δτ j,i,0 Represents the TDOA measurement error, satisfying

[0139]

[0140] The TDOA nonlinear time difference equations are constructed as follows:

[0141]

[0142] in

[0143]

[0144] Step 2.2, use the Chan-TDOA positioning algorithm to calculate the estimated position of the target, as follows:

[0145] Ignoring the subscript j, define x i,0 =x i -x0,y i,0 =y i -y0,r i,0 =r i -r0,τ i,0 =τ i -τ0, where x i represents the x-coordinate and y-coordinate of the i-th drone i represents the y coordinate of the i-th drone, x i,0 represents the x-direction distance from the reference UAV to the i-th UAV, y i,0 represents the y-direction distance from the reference UAV to the i-th UAV, τ i,0 represents the time when the signal from the i-th UAV reaches the reference UAV, r i,0 Represents the distance from the reference UAV to the i-th UAV.

[0146] Construct the TDOA nonlinear equations in matrix form:

[0147] ψ=h-GZ 0 (6)

[0148] where ψ is the error vector due to TDOA measurement noise, and

[0149]

[0150] The covariance matrix Ψ of the error vector ψ is

[0151]

[0152] Where Q is the covariance matrix of the TDOA measurement,

[0153] B=diag{r1,r2,…r n-1} (11)

[0154] Using the first weighted least squares method for estimation, the maximum likelihood estimate is

[0155] Z = argmin{(h-GZ) T Ψ -1 (h-GZ)}≈(G T Q -1 G)G T Q -1 h (12)

[0156] Constructing the residual vector

[0157] ψ′=h′-G′Z′ (13)

[0158] in

[0159]

[0160] The covariance matrix Ψ′ of the error vector is

[0161] ψ′=E[ψ′ψ′ T ]=4B′cov(Z)B′ (17)

[0162] in

[0163] B′=diag(Z1-x1,Z2-y1,Z3) (18)

[0164] Perform a second WLS estimate

[0165] Z′=(G′ T Ψ′ -1 G′) -1 G′ T Ψ′ -1 h′ (19)

[0166] The final estimated position of the target is

[0167]

[0168] Step 2.3, derive the measurement error CRLB based on the Chan-TDOA positioning algorithm based on the TDOA measurement equation, as follows:

[0169] Assume that the measured TDOA value is

[0170] s=c[τ 1,0 ,τ 2,0 ,…,τn-1,0 ] T (twenty one)

[0171] The actual measurement value is

[0172] s′=s+m (22)

[0173] Where m is the TDOA measurement error, which follows a normal distribution Where Q is the covariance matrix of the TDOA measurement given above. The probability density function of the TDOA measurement can be expressed as

[0174]

[0175] The likelihood function calculated from this density function is

[0176]

[0177] Taking the second-order partial derivative of the above formula with respect to the position coordinate parameter, we get

[0178]

[0179]

[0180] Its expected value is

[0181]

[0182] Then, the Fisher information matrix FIM(s) of the localization parameters can be expressed as

[0183]

[0184] Therefore, the measurement error CRLB matrix of the target position estimation is obtained by taking the inverse of the Fisher information matrix FIM(s), which is

[0185] CRLB(s)=FIM -1 (s) (32)

[0186] Step 3: Use the derived measurement error CRLB to select the nodes of the drone group, group the drone group reasonably, and locate different targets in each group, so that the average Cramer-Rao lower bound of each group of drones is minimized, the multi-target passive positioning accuracy is improved, and the resource utilization efficiency is improved, as follows:

[0187] Step 3.1, define the optimization objective function of node selection, assume that m targets are grouped by n drones to complete positioning, and the set of drones assigned to each target j is G j The optimization goal is to minimize the average CRLB trace (Trace, Tr) of all targets:

[0188]

[0189] Where Tr(CRLB t ) j represents the trace of the CRLB matrix of target j;

[0190] Step 3.2, establish constraints, requiring that each target requires at least 3 drones to locate, that is, n ≥ 3m, and each drone can only be assigned to one target group;

[0191] Step 3.3, use the exhaustive method to generate all feasible drone grouping solutions;

[0192] Step 3.4, calculate the corresponding CRLB value for each grouping scheme, and select the grouping scheme with the smallest objective function value as the optimal node selection scheme, thereby improving the target positioning accuracy and optimizing the resource utilization efficiency. The mathematical model of drone node selection can be described as

[0193]

[0194] Step 4: Establish constraint conditions, use the derived measurement error CRLB as the objective function of the UAV swarm adaptive obstacle avoidance path optimization, build a dynamic trajectory model of the UAV to dynamically adjust the optimal position of the UAV at the next moment, and use the PSO algorithm to accelerate the search for the optimal position of the UAV at the next moment. The details are as follows:

[0195] Step 4.1: Use the CRLB value derived in step 3 as the objective function of path optimization. The optimization goal is to minimize the lower limit of positioning accuracy at the next moment:

[0196]

[0197] in represents the position set of the drone group of target j at the next moment (time t+1);

[0198] Step 4.2, construct path optimization constraints:

[0199] UAV kinematic constraints: turning radius L of each UAV t i Must be larger than the minimum allowable radius L min ;

[0200] No-fly zone restrictions: The flight trajectory of the drone cannot enter the no-fly zone (NFZ) NFZ ,Right now

[0201]

[0202] Where S NFZ is the union of all no-fly zones p is the number of single no-fly zones;

[0203] Minimum approach distance constraint: the distance between the drone and the target at time t Must be greater than or equal to the minimum approach distance d min ,Right now

[0204]

[0205] Step 4.3, construct the minimum turning radius constraint: the turning radius L of each drone at time t t i Must be greater than or equal to the minimum turning radius L min ;

[0206] Step 4.4, based on the path optimization constraints, construct the dynamic trajectory model of the UAV to ensure that the UAV meets the set constraints during the path optimization process. The mathematical model of UAV path optimization can be described as

[0207]

[0208] Step 4.5, use the PSO algorithm to accelerate the path optimization process, as follows:

[0209] Initialize the PSO algorithm parameters, including the individual optimal position p of the particle s , the global optimal position p g , speed u s ; Each particle represents a set of heading angles of a group of drones, that is

[0210]

[0211] Update particle speed and position by the following formula:

[0212] u s (k+1)=ω(k)×u s (k)+c1l1(k)(p s (k)-η s (k))+c2l2(k)(p g (k)-η s (k)) (40)

[0213] η s (k+1)=η s (k)+u s (k+1) (41)

[0214] Where ω(k)=0.9-0.5(k / T max ) is the inertia weight, T maxis the maximum number of iterations, c1 and c2 are acceleration factors, l1 and l2 are random numbers, η s is the current position of the particle. The path optimization objective function Tr(CRLB) is used as the fitness function of the PSO algorithm, that is,

[0215]

[0216] where η s (k) represents the current position of the sth particle, p g (k) can be updated by:

[0217]

[0218] Iterate and update the PSO position until the maximum number of iterations is reached, that is, k = T max When or the fitness function converges.

[0219] By executing steps 1 to 4, the entire process of passive positioning node selection and path optimization of drone swarm using the target drone passive positioning algorithm based on CRLB for drone swarm passive positioning node selection and adaptive obstacle avoidance passive positioning path optimization of drone swarm based on CRLB and PSO algorithm can be obtained.

[0220] The following is a computer simulation experiment on the CRLB-based drone swarm node selection for multi-target passive positioning and the CRLB-based PSO-based drone swarm adaptive obstacle avoidance path optimization algorithm:

[0221] 1) When initializing the targets, drones, and measurement parameters, assume that there are 9 drones (n=9) and 3 targets (m=3) in the two-dimensional plane. The positions of the drones are (0, 10000) m, (2500, 9000) m, (4000, 8500) m, (5000, 7500) m, (7000, 6200) m, (7800, 5000) m, (9000, 4200) m, (9500, 2500) m, (9000, 1000) m. The positions of the targets are (10000, 32000) m, (23000, 23000) m, and (30000, 10000) m. Set the minimum turning radius of the drone to L. min =100m, the minimum approach distance is d min =5000m, the initial topology is as shown in the attached Figure 3 shown.

[0222] 2) When the UAV is positioned, the Chan-TDOA algorithm is used to solve the target position estimate, which is implemented using equations (1) to (19).

[0223] 3) According to the node selection constraint conditions, all possible grouping situations of the drone swarm are traversed, and the CRLB of each situation is calculated according to the method of formula (20)~(32), and the grouping scheme is found according to the optimization objective of formula (34).

[0224] In order to evaluate the node selection performance, the root mean square error (RMSE) is used to characterize the positioning accuracy. When the Monte Carlo number is K = 800, the RMSE of random grouping and CRLB-based node selection grouping is calculated. The calculation method is:

[0225]

[0226] The simulation results show that if three drones are assigned to one target, the drones will be divided into three groups to locate the three targets respectively. The node selection results based on CRLB are shown in the attached figure. Figure 4 As shown; from the attached Figure 5 It can be seen that the RMSE of the proposed algorithm is significantly lower than that of the traditional algorithm. The RMSE of the three targets based on the proposed algorithm is reduced by about 20%-30% compared with the traditional algorithm. This result shows that the target positioning accuracy can be greatly improved through efficient node selection.

[0227] 6) Simulation results of CRLB-based path optimization algorithm: Through the node selection method, the UAVs have been divided into multiple groups to locate different targets. In this section, the performance of the CRLB-based path optimization algorithm is analyzed for each UAV group. A total of 800 independent Monte Carlo simulation experiments were conducted to compare the performance of the proposed CRLB-based path optimization algorithm with the fixed formation method. For the convenience of description, the proposed CRLB-based path optimization algorithm is referred to as the "proposed algorithm" and the fixed formation method is referred to as the "traditional algorithm".

[0228] 7) When executing the proposed algorithm, according to the node selection constraints and the optimization target, i.e., equation (38), equations (39) to (44) are used for path optimization.

[0229] As attached Figure 7 ,The comparison results of RMSE and CRLB between the proposed path optimization algorithm and the traditional algorithm are as follows:

[0230] In the first group of drones, the average RMSE of the proposed method is reduced by about 43.37% compared with the traditional method, and the average CRLB is reduced by about 62.99%; in the second group of drones, the average RMSE of the proposed method is reduced by about 47.59% compared with the traditional method, and the average CRLB is reduced by about 68.65%; in the third group of drones, the average RMSE of the proposed method is reduced by about 45.01% compared with the traditional method, and the average CRLB is reduced by about 66.68%. The proposed method can adaptively avoid NFZ, while the fixed formation method cannot avoid NFZ.

[0231] In order to improve the efficiency of the proposed path optimization method, this paper uses the PSO algorithm to accelerate the search for the optimal location configuration solution. Fig. 9 The efficiency comparison between PSO algorithm and exhaustive algorithm is shown. Fig. 9 As can be seen from the figure, the average search time of the PSO algorithm is reduced by about 62.5% compared with the exhaustive algorithm. Figure 8 It can be seen that the average positioning accuracy of the two algorithms is almost the same.

[0232] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A CRLB-based intelligent optimization method for obstacle avoidance paths of drone swarms, characterized in that: The following steps are involved: Step 1, initialize the parameters, including the location and number of targets and drones, and the covariance matrix of TDOA measurements; Step 2, using the Chan-TDOA positioning algorithm to calculate the estimated position of the target, and derive the measurement error CRLB based on the Chan-TDOA positioning algorithm; Step 3: Use the derived measurement error CRLB to select the nodes of the drone swarm and divide the drone swarm into groups. Each group locates different targets, so that the average Cramer-Rao lower bound of each group of drones is minimized. Step 4: Establish constraint conditions and use the derived measurement error CRLB as the objective function of the adaptive obstacle avoidance path optimization of the drone swarm. Construct a dynamic trajectory model of the drone to dynamically adjust the optimal position of the drone at the next moment. During this process, use the PSO algorithm to accelerate the search for the optimal position of the drone at the next moment.

2. The method according to claim 1, characterized in that Step 1 specifically includes: Step 1.1, set the target position coordinate to w j =[x j ,y j ] T ; j = 1, 2, ..., m; m is the number of targets; set n drones carrying passive radars, and their position coordinates are u i =[x i ,y i ] T ; i = 0, 1, ..., n-1; the 0th drone is the reference drone node, and its position coordinates are u0 = [x0, y0] T ; Step 1.2, set the covariance matrix of TDOA measurements to in Represents the variance of the distance difference measurement between the ith UAV and the reference UAV.

3. The method according to claim 2, characterized in that Step 2 specifically includes: Step 2.1, construct the TDOA nonlinear time difference equations based on the parameters initialized in step 1; Step 2.2, calculate the estimated position of the target using the Chan-TDOA positioning algorithm; Step 2.3, derive the measurement error CRLB based on the Chan-TDOA positioning algorithm based on the TDOA measurement equation.

4. The method according to claim 3, characterized in that Step 2.1 specifically includes: Assume that the time delay difference between the signal sent by the jth target and the reference UAV and the i-th UAV is τ j,i,0 , then the relationship is satisfied Where c is the propagation speed of electromagnetic waves, τ j,i represents the time when the signal from the jth target reaches the i-th UAV, τ j,0 represents the time when the signal from the jth target reaches the reference UAV, r j,i represents the distance from the i-th UAV to the j-th target, r j,0 represents the distance from the reference UAV to the jth target; the measured arrival time difference contains the measurement error and satisfies t j,i,0 ′=τ j,i,0 +Δτ j,i,0 Among them, τ j,i,0 ′ represents τ j,i,0 The actual measured value, Δτ j,i,0 Represents the TDOA measurement error, satisfying The TDOA nonlinear time difference equations are constructed as follows: in 5. The method according to claim 4, characterized in that Step 2.2 specifically includes: definition x i,0 =x i -x0,y i,0 =y i -y0,r i,0 =r i -r0,τ i,0 =τ i -τ0; Construct the TDOA nonlinear equations in matrix form: ψ=h-GZ 0 where ψ is the error vector due to TDOA measurement noise, and The covariance matrix ψ of the error vector ψ is ψ=E[ψψ T ]=BQB Where Q is the covariance matrix of the TDOA measurement, B=diag{r1,r2,…r n-1 } Using the first weighted least squares method for estimation, the maximum likelihood estimate is Z=argmin{(h-GZ) T Ψ -1 (h-GZ)}≈(G T Q -1 G)G T Q -1 h Constructing the residual vector ψ′=h′-G′Z′ in The covariance matrix Ψ′ of the error vector is Ψ′=E[ψ′ψ′ T ]=4B′cov(Z)B′ in B′=diag(Z1-x1, Z2-y1, Z3) Perform a second WLS estimate Z′=(G′ T P′ -1 G′) -1 G′ T P′ -1 h′ The final estimated position of the target is 6. The method according to claim 5, characterized in that Step 2.3 specifically includes: Assume that the measured TDOA value is s=c[τ 1，0 ,t 2，0 ,…,t n-1，0 ] T The actual measurement value is S′=S+m Where m is the TDOA measurement error, which obeys the normal distribution N(0, Q). The probability density function of TDOA measurement is expressed as The likelihood function calculated from this density function is Taking the second-order partial derivative of the likelihood function with respect to the position coordinate parameter gives Its expected value is The Fisher information matrix FIM(s) of the positioning parameters is expressed as The measurement error CRLB matrix of target position estimation is obtained by taking the inverse of the Fisher information matrix FIM(s), which is CRLB(s)=FIM -1 (s)。 7. The method according to claim 6, characterized in that Step 3 specifically includes: Step 3.1, define the optimization objective function of node selection, assume that m targets are grouped by n drones to complete positioning, and for the jth target, the set of drones assigned to it is G j , the optimization goal is to minimize the average CRLB trace of all targets: Among them, Tr(CRLB t ) j represents the trace of the CRLB matrix of the jth target; Step 3.2, establish constraints, requiring that each target requires at least 3 drones to locate, that is, n ≥ 3m, and each drone can only be assigned to one target group; Step 3.3, use the exhaustive method to generate all feasible drone grouping solutions; Step 3.4, calculate the corresponding CRLB value for each grouping scheme, and select the grouping scheme with the smallest objective function value as the optimal node selection scheme. The mathematical model of drone node selection is described as 8. The method according to claim 7, characterized in that Step 4 specifically includes: Step 4.1: Use the CRLB value derived in step 3 as the objective function of path optimization. The optimization goal is to minimize the lower limit of positioning accuracy at the next moment: in, represents the position set of the j-th target UAV group at the next moment; Step 4.2, construct path optimization constraints, including UAV kinematic constraints, no-fly zone constraints, and minimum approach distance constraints; The kinematic constraints of the drones are the turning radius of each drone. Greater than the minimum allowable radius L min ; The no-fly zone constraint means that the flight trajectory of the drone cannot enter the no-fly zone; The minimum approach distance constraint is the distance between the UAV and the target at time t Greater than or equal to the minimum approach distance d min ; Step 4.3, construct the minimum turning radius constraint, that is, the turning radius of each drone at time t Must be greater than or equal to the minimum turning radius L min ; Step 4.4, based on the path optimization constraints, construct the dynamic trajectory model of the UAV, which is described as Step 4.5, use the PSO algorithm to accelerate the path optimization process.

9. The method according to claim 8, characterized in that Step 4.5 specifically includes: Initialize the PSO algorithm parameters, including the individual optimal position p of the particle s , the global optimal position p g , speed u s ; Each particle represents a set of heading angles of a group of drones, that is Update particle velocity and position: u s (k+1)=ω(k)×u s (k)+c1l1(k)(p s (k)-η s (k))+c2l2(k)(p g (k)-η s (k)) or s (k+1)=η s (k)+u s (k+1) Where, ω(k) = 0.9-0.5(k / T max ) is the inertia weight, T max is the maximum number of iterations, c1 and c2 are acceleration factors, l1 and l2 are random numbers, η s is the current position of the particle; the path optimization objective function Tr(CRLB) is used as the fitness function of the PSO algorithm, that is, Among them, η s (k) represents the current position of the sth particle, p g (k) The update method is: The PSO position is updated iteratively until the maximum number of iterations is reached or the fitness function converges.

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