Method for positioning air target TDOA (time difference of arrival) by ground unmanned platform system

Abstract

The invention provides a TDOA (time difference of arrival) positioning method for an air target by a ground unmanned platform system, which comprises the following steps of: obtaining a nonlinear positioning equation set based on a TDOA positioning measurement value, and solving the nonlinear positioning equation set based on a likelihood function to obtain a target function; obtaining an estimated value of a target position according to a Chan method to determine a three-dimensional space search area, initializing a five-element ring population, generating remaining elements based on first 20% of elements, and substituting the remaining elements into a target function to calculate a target function value; the acting force borne by each element is obtained, the current element is replaced based on the positive and negative properties of the acting force, and multiple replaced elements are obtained; iterating the replaced element based on the target function value minimization until the current iteration number reaches the preset maximum iteration number, and outputting the updated optimal element; and taking the updated optimal element as an aerial target position monitored by the ground unmanned platform, and obtaining a final target position estimation value of TDOA three-dimensional cooperative positioning of the ground unmanned platform.

Description

Technical Field

[0001] The present invention relates to the field of ground unmanned platform information interaction, and in particular to a TDOA positioning method for an aerial target by a ground unmanned platform system. Background Art

[0002] Ground unmanned platform, referred to as UGV, usually refers to an unmanned platform that is completely remote-controlled or autonomously operated according to pre-programmed procedures and can adapt to different tasks including reconnaissance detection, target capture, communication relay, logistics support, fire rescue and medical evacuation according to needs, including ground unmanned vehicles and ground robots. Ground unmanned platforms have the characteristics of strong sustained action capability, low cost and good stealth, and ground unmanned vehicles do not need people to drive. Therefore, ground unmanned platforms are one of the main equipment for future land exploration and have unlimited development and application space.

[0003] Ground unmanned platforms have great advantages in implementing diverse tasks. Faced with complex environments, such as unmanned areas such as deserts and wilderness, ground unmanned platforms equipped with positioning systems can accurately locate aerial targets, and have good concealment, and can effectively complete tasks such as target reconnaissance and detection. Collaborative positioning of ground unmanned platforms is one of the key technologies for ground unmanned systems to achieve positioning of aerial targets. Time Different of Arrival (TDOA), TDOA positioning of ground unmanned platform systems refers to multiple ground unmanned platforms acting as ground mobile base stations, obtaining the three-dimensional position estimate of the target to be located based on the received TDOA information, in order to implement the next plan.

[0004] However, when faced with complex environments, the TDOA positioning accuracy of the ground unmanned platform system is low, and in order to achieve high-precision three-dimensional TDOA collaborative positioning estimation for aerial targets, the real-time performance of the method and the layout of the ground unmanned platform also need to be considered.

[0005] Therefore, it is urgent to provide a solution to improve the above problems. Summary of the invention

[0006] The purpose of the present invention is to provide a TDOA positioning method for an aerial target by a ground unmanned platform system, so as to improve the problem of low accuracy of three-dimensional TDOA collaborative positioning in complex environments in the prior art.

[0007] The present invention provides a TDOA positioning method for aerial targets by a ground unmanned platform system, which adopts the following technical solutions:

[0008] A nonlinear positioning equation group is obtained based on the measurement value of TDOA positioning performed by the ground unmanned platform, and a target function is obtained by solving the nonlinear positioning equation group based on a likelihood function;

[0009] The estimated value of the target position is obtained according to the Chan method to determine the three-dimensional space search area, the five-element ring population is randomly initialized, the remaining 80% of the elements are generated based on the first 20% of the elements and substituted into the objective function to calculate the objective function value;

[0010] Obtaining the force exerted on each element based on the objective function value, and replacing the current element based on the positive or negative nature of the force to obtain a plurality of replaced elements;

[0011] Iteratively updating the replaced elements based on minimization of the objective function value until the current number of iterations reaches a preset maximum number of iterations, and then outputting the updated optimal element;

[0012] The updated optimal element is used as the position of the aerial target monitored by the ground unmanned platform to obtain the final target position estimation value of the TDOA three-dimensional collaborative positioning of the ground unmanned platform.

[0013] The beneficial effects of the TDOA positioning method for aerial targets provided by the ground unmanned platform system are as follows:

[0014] (1) The present invention proposes a TDOA positioning method for aerial targets by a ground unmanned platform system. The Chan method is first used to calculate the approximate position of the target to be located. Then, the objective function is optimized using the designed five-element ring optimization algorithm based on the 80 / 20 rule. The optimal solution is used as the estimated target position. This solves the technical problem of accurate detection of aerial targets by ground unmanned platforms and breaks through the application limitations of swarm intelligence algorithms in the field of three-dimensional collaborative TDOA positioning of ground unmanned platforms.

[0015] (2) The present invention proposes an 80 / 20 rule to initialize the population, and creates an initial population generation strategy that selects the best first 20% elements in the population according to the 80 / 20 rule and combines them with sine and cosine operators to generate the remaining 80% of the elements. This solves the problem that the swarm intelligence algorithm is highly dependent on the quality of the initial population, and is beneficial to expanding the search range and improving the convergence speed and accuracy of the algorithm.

[0016] (3) The present invention comprehensively considers the layout method of ground unmanned stations, proposes a star layout of five ground unmanned platforms and a cross layout of five ground unmanned platforms, compares the effects of the star layout of five base stations and the cross layout of five base stations on positioning accuracy, selects a suitable layout method based on the measurement results, and improves positioning accuracy.

[0017] Optionally, the process of obtaining the objective function includes:

[0018] Based on M ground unmanned platforms, one of them is selected as the service base station, and the remaining M-1 ground unmanned platforms are used as ground base stations. The target is obtained based on the three-dimensional coordinates to the ground base station B.m and the distance difference measurement value to the ground service base station B1, and establish an objective function based on the distance difference measurement value.

[0019] Optionally, the process of the WLS primary solution and the WLS secondary solution includes:

[0020] When the number of ground base stations is less than the distance threshold, an initial target position estimate is obtained based on the Chan method, and a three-dimensional search area is generated based on the initial target position estimate;

[0021] When the number of ground base stations is greater than or equal to the distance threshold, the initial nonlinear equation group is linearly transformed to obtain a linear equation group, the linear equation group is solved once based on WLS to obtain an initial solution, and a WLS secondary solution is performed based on the first estimated coordinate value and the first constraint condition to obtain the final target position estimate.

[0022] Optionally, the process of obtaining the initial target position estimate includes:

[0023] Based on the Chan method, an approximate position (x b ,y b ,z b ), target to ground base station B m The difference between the distance to the ground service base station B1 is r m -R1, where

[0024]

[0025] Let X m,1 =X m -X1,Y m,1 =Y m -Y1,Z m,1 =Z m -Z1, We can get:

[0026] Among them, x, y, z are the three-dimensional coordinates of the target point, X m ,Y m ,Z m For ground base station B m X1, Y1, Z1 are the three-dimensional coordinates of the first ground base station, R m is the distance from the target point to the mth ground base station, and R1 is the distance from the target point to the first ground base station;

[0027] When the number of ground base stations M = 4, three TDOA measurement values ​​can be obtained, where R1 is known and the mathematical expression of the initial target position estimate is:

[0028]

[0029] Optionally, the process of obtaining an estimate of the final target position includes:

[0030] In the first WLS, let is an unknown vector, where z p =[z p,1 ,z p,2 ,z p,3 ] T For the estimated value of the target to be located, a linear equation with noise is established: ψ = hG a z a , where

[0031]

[0032] Among them, R m,1 =cd m =R m -R1+cn m,1 , X m,1 =X m -X1,Y m,1 =Y m -Y1,Z m,1 =Z m -Z1; Let Q be the covariance matrix in TDOA positioning. When the target location is far away from the ground base station, we can get:

[0033]

[0034] In the second WLS, the equation system ψ′=h′-G′ is established a z′ a , where ψ′ is z a The error vector is:

[0035]

[0036] Among them, there is an unknown quantity z′ with unknown target a The solution is:

[0037]

[0038] Where B′=diag{z a,1 -x1,z a,2 -y1,z a,3 -z1,z a,4}, diag{·} represents the diagonal matrix formation function, and all elements not on the diagonal are zero. The expression of the target position estimate can be obtained as:

[0039]

[0040] in,

[0041] Optionally, the process of determining the three-dimensional space search area according to the estimated value of the target position obtained by the Chan method includes:

[0042] An approximate position (x) is obtained by Chan method b ,y b ,z b ), and use the approximate position to determine the three-dimensional space search area. in,

[0043]

[0044] in,

[0045] Among them, r is the maximum distance between the air service base station and the air base station. When the noise in the environment is small, When the noise in the environment is large, If the search interval exceeds the required search interval, the search position is limited to the boundary value.

[0046] Optionally, the process of replacing the current element based on the positive or negative nature of the force and obtaining a plurality of replaced elements includes:

[0047] Randomly initialize the elements in the five-element ring population, divide all elements into multiple rings, each ring contains multiple elements, and sort the elements in the initial five rings based on the objective function value. Based on the 80 / 20 rule and the sine-cosine algorithm, use the first 20% of the elements with the smallest objective function value to generate the remaining 80% of the elements;

[0048] Randomly select one of the top 20% elements with the smallest objective function value and replace it with the coordinate estimated by the Chan method. If the force acting on the current element is positive, retain the current element. If the force acting on the current element is negative, update and replace the current element based on the preset random number and the preset selection update probability. Stop updating when the current number of iterations reaches the preset maximum number of iterations to obtain the updated optimal element.

[0049] Optionally, the process of updating and replacing the current element based on a preset random number and a preset selection update probability includes:

[0050]

[0051] Among them, p s is a scale factor, pm is the preset probability of selection update, r s is a preset random number that follows a uniform distribution between [-1,1], r m is a preset random number that follows a uniform distribution between [0,1], d=1,2,3, represents the d-dimensional value of the k′th element in the εth iteration, represents the d-dimensional value of the optimal element in the εth iteration, Represents the d-dimensional value of the best element in the q′th ring at the εth iteration.

[0052] Optionally, the process of obtaining the estimated value of the final target position includes:

[0053] The three-dimensional coordinate components within the optimal element of the last iteration are used as the three-dimensional coordinate components of the final target position estimation value. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is a flow chart of TDOA positioning of aerial targets by a ground unmanned platform system provided by the present invention;

[0055] Figure 2 It is a schematic diagram of a star-shaped layout of five base stations and a cross-shaped layout of five base stations provided by the present invention;

[0056] Figure 3 It is a comparative relationship curve diagram of the root mean square error and noise variance of Chan, Chan-FECO in two base station layout modes provided by the present invention;

[0057] Figure 4 It is a comparison diagram of the mean square error values ​​of Chan, Chan-FECO and GA under different noise variances when five base stations are arranged in a star shape provided by the present invention;

[0058] Figure 5 It is a comparative relationship curve diagram of the mean square error value between Chan-FECO and GA provided by the present invention when the number of iterations is 70 generations and the noise variance is -14dB. DETAILED DESCRIPTION

[0059] 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. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention. Unless otherwise defined, the technical terms or scientific terms used herein should be understood by people with general skills in the field to which the present invention belongs. "Including" and similar words used in this article mean that the elements or objects appearing before the word include the elements or objects listed after the word and their equivalents, without excluding other elements or objects.

[0060] The embodiment of the present invention provides a TDOA positioning method for an aerial target by a ground unmanned platform system, comprising:

[0061] S1. Obtaining a nonlinear positioning equation group based on the measurement value of TDOA positioning performed by the ground unmanned platform, and solving the nonlinear positioning equation group based on the likelihood function to obtain a target function;

[0062] S2. Determine the three-dimensional space search area according to the estimated value of the target position obtained by the Chan method, randomly initialize the five-element ring population, generate the remaining 80% of the elements based on the first 20% of the elements and substitute them into the objective function to calculate the objective function value;

[0063] S3, obtaining the force exerted on each element based on the objective function value, and replacing the current element based on the positive or negative nature of the force to obtain a plurality of replaced elements;

[0064] S4, iteratively updating the replaced element based on minimization of the objective function value, stopping the updating when the current iteration number reaches a preset maximum iteration number, and outputting the updated optimal element;

[0065] S5. Use the updated optimal element as the position of the aerial target monitored by the ground unmanned platform to obtain the final target position estimation value of the TDOA three-dimensional collaborative positioning of the ground unmanned platform.

[0066] In some embodiments, when executing step S1, the process of obtaining the objective function includes:

[0067] Based on M ground unmanned platforms, one of them is selected as the service base station, and the remaining M-1 ground unmanned platforms are used as ground base stations. The target is obtained based on the three-dimensional coordinates to the ground base station B. m and the distance difference measurement value to the ground service base station B1, and establish an objective function based on the distance difference measurement value.

[0068] Specifically, one of the M ground unmanned platforms is selected as the ground base station B1 as the service base station, with coordinates (X1, Y1, Z1), M>4, and the remaining ground platforms are ground base stations V m , m=2,3,...,M, the coordinates are (X m ,Y m ,Z m ), the target position is set to (x, y, z), the target to the ground base station B m The distance is Target to ground base station B m The difference between the distance to the ground service base station B1 is R m,1 , R m,1 =cd m =R m -R1+cn m,1 , m = 2, 3, ..., M, where c is the electromagnetic wave propagation speed c = 3 × 10 5 km / s,d m is the TDOA measurement value, n m,1 is the error caused by noise when the mth ground base station measures TDOA, which satisfies independent and identical distribution and has a variance of σ 2 Gaussian distribution.

[0069] Furthermore, the coordinate values ​​of each ground base station and the target are substituted to obtain the measured value of the TDOA distance difference:

[0070]

[0071] Furthermore, let ΔR = [R 2,1 ,R 3,1 ,...,R M,1 ] T , R=[R2,R3,...,R M ] T , R1=[R1,R1,...,R1] T , n=[n 2,1 ,n 3,1 ,...,n M,1 ] T , ΔR, R, R1 and n are all matrices of size (M-1)×1, so

[0073] Furthermore, considering the case where the number of ground base stations M>4, since the target is m The distance difference between the distance to the ground service base station B1 and the measured value R m,1 The mean is μ=R m -R1, with variance σ2 Gaussian distribution, and each measurement value is independent of each other, the likelihood function is:

[0074]

[0075] Therefore, finding the maximum coordinate value of the likelihood function is equivalent to finding in, is the estimated position coordinate interval.

[0076] Construct the objective function f(e)=(ΔR-R+R1) based on the likelihood function T (ΔR-R+R1)| x,y,z , e = [x, y, z] is a vector consisting of coordinate variables of the position interval of the positioning target.

[0077] In some embodiments, the process of executing step S2 to obtain the final target position estimate includes:

[0078] S2-1, when the number of ground base stations is less than the distance threshold, obtaining an initial target position estimate based on the Chan method, and generating a three-dimensional search area based on the initial target position estimate;

[0079] S2-2. When the number of ground base stations is greater than or equal to the distance threshold, the initial nonlinear equation group is linearly transformed to obtain a linear equation group, the linear equation group is solved once based on WLS to obtain an initial solution, and a WLS secondary solution is performed based on the first estimated coordinate value and the first constraint condition to obtain the final target position estimate.

[0080] Specifically, the process of executing step S2-1 to obtain the initial target position estimate includes:

[0081] Based on the Chan method, an approximate position (x b ,y b ,z b ), target to ground base station B m The difference between the distance to the ground service base station B1 is R m -R1, where

[0082]

[0083] Let X m,1 =X m -X1,Y m,1 =Y m -Y1,Z m,1 =Z m -Z1, We can get:

[0084]

[0085] Where T represents the transpose of the matrix.

[0086] When the number of ground base stations M = 4, three TDOA measurement values ​​can be obtained, where R1 is known and the mathematical expression of the initial target position estimate is:

[0087]

[0088] Among them, x b ,y b 、z b The 3D coordinates representing the initial target position estimate.

[0089] Specifically, the process of generating a three-dimensional search area based on the initial target position estimation value in step S2-1 includes:

[0090] An approximate position (x) is obtained by Chan method b ,y b ,z b ), and use the approximate position to determine the three-dimensional space search area. in,

[0091]

[0092] Therefore, we can get:

[0093]

[0094] Among them, l can be selected according to the noise level in the actual environment, r is the farthest distance between the air service base station and the air base station, so when the noise in the environment is small, When the noise in the environment is large, If the search interval exceeds the required search interval, the search position is limited to the boundary value.

[0095] Specifically, when executing step S2-2, the WLS is solved once, including:

[0096] In the first WLS, let is an unknown vector, where As the estimated value of the target to be located, a linear equation ψ=hG with noise is established a z a , where

[0097]

[0098] Let Q be the covariance matrix in TDOA positioning. When the target location is far away from the ground base station, we can get:

[0099]

[0100] Among them, z a,1 ,z a,2 ,z a,3 ,z a,4 represents the unknown vector z a The four components of .

[0101] Furthermore, when executing step S2-2, the WLS secondary solution includes:

[0102] In the second WLS, the equation system ψ′=h′-G′ is established a z′ a , where ψ′ is z a The error vector is:

[0103]

[0104] Among them, there is an unknown quantity z′ with unknown target a The solution is:

[0105]

[0106] Where B′=diag{z a,1 -x1,z a,2 -y1,z a,3 -z1,z a,4}, diag{·} represents the diagonal matrix formation function, all elements not on the diagonal are zero, z′ a,1 ,z′ a,2 ,z′ a,3 ,z′ a,4 Represents the unknown quantity z′ a The four components of .

[0107] Furthermore, the target position estimate z can be obtained p The expression is:

[0108]

[0109] in,

[0110] In some embodiments, the process of replacing the current element based on the positive and negative properties of the force in step S3 to obtain multiple replaced elements includes:

[0111] S3-1, randomly initialize the elements in the five-element ring population, divide all elements into multiple rings, each ring contains multiple elements, and sort the elements in the initial five rings based on the objective function value, and use the first 20% of the elements with the smallest objective function value to generate the remaining 80% of the elements based on the 80 / 20 rule and the sine-cosine algorithm;

[0112] Specifically, randomly initialize the elements in the five-element ring population, divide all elements into q rings, each ring contains L elements, that is, the population size is N = L × q, and the maximum number of iterations is G max ,but

[0113] At this time, the number of iterations is 0, the population dimension d = 1, 2, 3, and rand is a preset random number between 0 and 1 that follows a uniform distribution. represents the lower limit of the population position, represents the upper limit of the population position, Represents the initial value of dimension d of the kth element.

[0114] Calculate the objective function value based on the constructed objective function for: They represent the initial values ​​of the three dimensions of the kth element respectively.

[0115] S3-2. Randomly select one of the top 20% elements with the smallest objective function value and replace it with the coordinate estimated by the Chan method. If the force acting on the current element is positive, retain the current element. If the force acting on the current element is negative, update and replace the current element based on a preset random number and a preset selection update probability. Stop updating when the current number of iterations reaches the preset maximum number of iterations, and obtain the updated optimal element.

[0116] Specifically, the elements in the initial five-element ring are sorted according to the objective function value, and the 80 / 20 rule is combined with the sine and cosine operators to generate the remaining 80% of the elements using the first 20% of the elements with the smallest objective function value; one of the first 20% of the elements with the smallest objective function value is randomly selected and the coordinate (x b ,y b ,z b ) instead, that is Generate a preset random number r1 between 0 and 2 that follows a uniform distribution, and choose the update probability to be but:

[0117]

[0118] Wherein, i=1,2,…,0.2N, t=0.2N+4×(i-1)+j, j=1,2,…,4, r2 is a preset random number between 0 and 1 that follows a uniform distribution, r3 is a preset random number between 0 and 2 that follows a uniform distribution, Represents the updated element value, represents the top 20% of element values, Represents the remaining 80% of the element values.

[0119] Furthermore, the objective function value is calculated The element with the smallest objective function value is determined as the optimal element in the new initial population obtained by the 80 / 20 rule. is the optimal element up to the εth iteration.

[0120] In some embodiments, the process of iteratively updating the replaced element in step S4 includes:

[0121] The L′th element in the q′th ring in the ε+1th iteration The force from the other L-1 elements in the ring is recorded as q′=1,2,…q, L′=1,2,…L, k′=L×(q′-1)+L′, The mass corresponding to the L′th element in the q′th ring at the ε+1th iteration is the objective function value, that is and is the weight coefficient.

[0122] When L′=1, use “L” instead of “L′-1”, and use “L-1” instead of “L′-2”; when L′=2, use “L” instead of “L′-2”; when L′=L-1, use “1” instead of “L′+2”; when L′=L, use “1” instead of “L′+1”, and use “2” instead of “L′+2”.

[0123] The L′th element in the q′th ring in the ε+1th iteration The update depends on if illustrate It is a good element, from the perspective of system balance. The smaller, The greater the force, the stronger the element becomes, thus making the quality of each element more similar. In this case, should be retained, so if illustrate It may not be a good element because of its stress Negative, indicating that the system expects the element to become weaker, and also indicates that its own quality is relatively large. In this case, The replacement should generate new elements in a better neighborhood, so the d-dimensional variable of the L′th element in the q′th ring in the ε+1th iteration is updated as:

[0124]

[0125] Among them, p s is a scale factor, p m is the preset probability of selection update, r s is a preset random number that follows a uniform distribution between [-1,1], r m is a preset random number that follows a uniform distribution between [0,1], d=1,2,3, represents the d-dimensional value of the k′th element in the εth iteration, represents the d-dimensional value of the optimal element in the εth iteration, Represents the d-dimensional value of the best element in the q′th ring at the εth iteration.

[0126] Furthermore, the L′th element in the q′th ring of the ε+1th iteration is calculated Updates obtained Objective function value After updating the elements in each ring, the element with the smallest objective function value is determined as the optimal element of the ε+1th iteration. The updated optimal objective function value The objective function value of the optimal element before the ε+1th iteration update Compare, if Then confirm is the optimal element after the ε+1th iteration, and the corresponding objective function value is Otherwise, let

[0127] Furthermore, it is determined whether the current number of iterations has reached the maximum number of iterations G. max If it is not reached, set ε = ε + 1 and continue iterating; if the maximum number of iterations is reached, terminate the iteration and output the optimal element of the last iteration

[0128] In some embodiments, the process of executing step S5 to obtain the final target position estimate includes:

[0129] The best element of the last iteration will be obtained As the estimated target position after iteration

[0130] For the convenience of description, the TDOA positioning method for aerial targets by the ground unmanned platform system combined with the Chan method designed by the present invention is recorded as Chan-FECO, the TDOA positioning method for aerial targets by the ground unmanned platform system based on the genetic optimization method is recorded as GA, and the TDOA positioning method for aerial targets by the ground unmanned platform system based on the Chan method is recorded as Chan.

[0131] Randomly select one of the multiple ground unmanned platforms as the ground service base station B1, and establish a three-dimensional coordinate system with the ground service base station as the origin. Randomly or according to a certain rule, select M-1 ground unmanned platforms as ground base stations B around the ground service base station. m , m=2,3,...,M. Select the total number of base stations M=5, the star layout of five ground unmanned platforms and the cross layout of five ground unmanned platforms with the ground service base station as the origin, Figure 2 Figure 1 is a schematic diagram of a star-shaped layout of five base stations and a cross-shaped layout of five base stations. The base station coordinates of the two layouts are shown in Table 1.

[0132] Table 1 Base station coordinates for five-base station star layout and five-base station cross layout

[0133]

[0134] In the Chan-FECO TDOA positioning method for aerial targets by the ground unmanned platform system proposed in the present invention, the search area l = 0.5, the total number of five-element rings q = 20, the number of elements in each ring L = 5, the population size N = q × L = 100, and the maximum number of iterations G max , when using the 80 / 20 rule to generate the remaining 80% of the elements in the population, choose to update the probability Weight coefficient when calculating the resultant force Scale factor p s =1, probability value p m =0.9.

[0135] The accuracy of positioning requires a series of indicators to evaluate. The average estimated coordinates MV and mean square error MSE of the positioning solution are used as the evaluation criteria for the algorithm performance. The formula for calculating MV and MSE in three-dimensional positioning estimation is MV = E[(x * ,y * ,z * )],MSE=E[(xx * ) 2 +(yy * ) 2 +(zz * ) 2], where (x, y, z) is the actual position of the aerial target, (x * ,y * ,z * ) is the estimated position of the aerial target, and E is the mean calculation.

[0136] Assume the coordinates of the aerial target are (1,2.5,2) in km. Figure 3 Figure 3 is the comparison curve of the root mean square error and noise variance of Chan and Chan-FECO under two base station layout methods. It can be seen that the accuracy of the two methods of the five-base station star layout is better than that of the five-base station cross arrangement.

[0137] The star arrangement of five base stations is selected as the optimal layout of ground base stations, and the positioning accuracy of the three methods of Chan-FECO, GA and Chan is compared. Figure 4 The figure is a comparison of the mean square error values ​​of Chan, Chan-FECO and GA under different noise variances. It can be seen that in the TDOA positioning of aerial targets by ground unmanned platform systems, the closer the positioning estimate is to the actual position and the smaller the mean square error value is, the higher the positioning accuracy and the better the performance is. As the noise variance increases, the mean square error increases, and the positioning accuracy decreases, but the Chan-FECO method performs best, with a lower mean square error value, higher positioning accuracy and better performance.

[0138] Figure 5 The figure shows the comparison relationship curve of Chan-FECO and GA when the iteration number is 70 generations and the noise variance is -14dB. It can be seen that compared with the GA method, the Chan-FECO method has a faster convergence speed and higher convergence accuracy, indicating that the performance of the Chan-FECO method is better.

[0139] The mean values ​​of TDOA positioning estimation of aerial targets by the ground unmanned platform system obtained by Chan and Chan-FECO with five base stations in a cross-shaped layout under different noise variances are shown in Table 2.

[0140] Table 2 Comparison of the mean positioning estimates of Chan-FECO and Chan algorithms for a five-base station cross layout

[0141]

[0142] The mean values ​​of TDOA positioning estimation of aerial targets by the ground unmanned platform system obtained by Chan-FECO, GA and Chan with five base stations in a star layout under different noise variances are shown in Table 3.

[0143] Table 3 Comparison of the mean positioning estimates of Chan-FECO, GA and Chan algorithms for five-base station star layout

[0144]

[0145]

[0146] See also Figure 1 First, establish the TDOA positioning estimation model of the ground unmanned system and construct the objective function. Then, obtain the estimated value of the target position according to the Chan method, initialize the five-element ring population, combine the 80 / 20 rule with the sine and cosine operators, and use the first 20% of the elements with the smallest objective function value to generate the remaining 80% of the elements. Then, each element is subjected to the combined force F of other elements in the ring to determine whether to update the element. If the combined force F>0, keep the element. If F<0, update the element, calculate the objective function value of the updated element, and determine the current optimal element. Finally, determine whether the current number of iterations reaches the maximum number of iterations. If so, output the optimal element of the last iteration as the target estimated value of the TDOA positioning of the ground unmanned platform. If not, re-determine whether to keep the current element or update the current element based on the combined force.

[0147] Although the embodiments of the present invention are described in detail above, it is obvious to those skilled in the art that various modifications and variations can be made to these embodiments. However, it should be understood that such modifications and variations are within the scope and spirit of the present invention as described in the claims. Moreover, the present invention described herein may have other embodiments and may be implemented or realized in a variety of ways.

Claims

1. A TDOA positioning method for an aerial target by a ground unmanned platform system, characterized in that: include: A nonlinear positioning equation group is obtained based on the measurement value of TDOA positioning performed by the ground unmanned platform, and a target function is obtained by solving the nonlinear positioning equation group based on a likelihood function; The estimated value of the target position is obtained according to the Chan method to determine the three-dimensional space search area, the five-element ring population is randomly initialized, the remaining 80% of the elements are generated based on the first 20% of the elements and substituted into the objective function to calculate the objective function value; Obtaining the force exerted on each element based on the objective function value, and replacing the current element based on the positive or negative nature of the force to obtain a plurality of replaced elements; Iteratively updating the replaced elements based on minimization of the objective function value until the current number of iterations reaches a preset maximum number of iterations, and then outputting the updated optimal element; The updated optimal element is used as the position of the aerial target monitored by the ground unmanned platform to obtain the final target position estimation value of the TDOA three-dimensional collaborative positioning of the ground unmanned platform.

2. The TDOA positioning method for aerial targets by a ground unmanned platform system according to claim 1, characterized in that: The process of obtaining the objective function includes: Based on M ground unmanned platforms, one of them is selected as the service base station, and the remaining M-1 ground unmanned platforms are used as ground base stations. The target is obtained based on the three-dimensional coordinates to the ground base station B. m and the distance difference measurement value to the ground service base station B1, and establish an objective function based on the distance difference measurement value.

3. The TDOA positioning method for aerial targets by a ground unmanned platform system according to claim 1, characterized in that: The process of obtaining the estimated value of the final target position includes: When the number of ground base stations is less than the distance threshold, an initial target position estimate is obtained based on the Chan method, and a three-dimensional search area is generated based on the initial target position estimate; When the number of ground base stations is greater than or equal to the distance threshold, the initial nonlinear equation group is linearly transformed to obtain a linear equation group, the linear equation group is solved once based on WLS to obtain an initial solution, and a WLS secondary solution is performed based on the first estimated coordinate value and the first constraint condition to obtain the final target position estimate.

4. The TDOA positioning method for aerial targets by a ground unmanned platform system according to claim 3 is characterized in that: The process of obtaining the initial target position estimate includes: Based on the Chan method, an approximate position (x b ,y b , z b ), target to ground base station B m The difference between the distance to the ground service base station B1 is R m -R1, where Let X m，1 =X m -X1,Y m，1 =Y m -Y1,Z m，1 =Z m -Z1, We can get: Among them, x, y, z are the three-dimensional coordinates of the target point, X m , Y m , Z m For ground base station B m X1, Y1, Z1 are the three-dimensional coordinates of the first ground base station, R m is the distance from the target point to the mth ground base station, and R1 is the distance from the target point to the first ground base station; When the number of ground base stations M = 4, three TDOA measurement values ​​can be obtained, where R1 is known and the mathematical expression of the initial target position estimate is:

5. The TDOA positioning method for aerial targets by a ground unmanned platform system according to claim 3, characterized in that: The WLS primary solution and WLS secondary solution process include: In the first WLS, let is an unknown vector, where z p =[z p,1 , z p,2 , z p,3 ] T For the estimated value of the target to be located, a linear equation with noise is established: ψ = hG a z a , where Among them, R m，1 =cd m =R m -R1+cn m，1 , X m，1 =X m -X1,Y m，1 =Y m -Y1,Z m，1 =Z m -Z1; Let Q be the covariance matrix in TDOA positioning. When the target location is far away from the ground base station, we can get: In the second WLS, the equation system ψ′=h′-G′ is established a z′ a , where ψ′ is z a The error vector is: Among them, there is an unknown quantity z′ with unknown target a The solution is: Where B′=diag{z a，1 -x1,z a，2 -y1,z a，3 -z1,z a，4 }, diag{·} represents the diagonal matrix formation function, and all elements not on the diagonal are zero. The expression of the target position estimate can be obtained as: in, 6. The TDOA positioning method for aerial targets by a ground unmanned platform system according to claim 1, characterized in that: The process of determining the three-dimensional space search area by obtaining an estimated value of the target position according to the Chan method includes: An approximate position (x) is obtained by Chan method b ,y b , z b ), and use the approximate position to determine the three-dimensional space search area. in, in, Among them, r is the maximum distance between the air service base station and the air base station. When the noise in the environment is small, When the noise in the environment is large, If the search interval exceeds the required search interval, the search position is limited to the boundary value.

7. A method for TDOA positioning of aerial targets by a ground unmanned platform system according to claim 1, characterized in that: The process of replacing the current element based on the positive or negative nature of the force and obtaining a plurality of replaced elements includes: Randomly initialize the elements in the five-element ring population, divide all elements into multiple rings, each ring contains multiple elements, and sort the elements in the initial five rings based on the objective function value. Based on the 80 / 20 rule and the sine-cosine algorithm, use the first 20% of the elements with the smallest objective function value to generate the remaining 80% of the elements; Randomly select one of the top 20% elements with the smallest objective function value and replace it with the coordinate estimated by the Chan method. If the force acting on the current element is positive, retain the current element. If the force acting on the current element is negative, update and replace the current element based on the preset random number and the preset selection update probability. Stop updating when the current number of iterations reaches the preset maximum number of iterations to obtain the updated optimal element.

8. A method for TDOA positioning of aerial targets by a ground unmanned platform system according to claim 7, characterized in that: The process of updating and replacing the current element based on a preset random number and a preset selection update probability includes: Among them, p s is a scale factor, p m is the preset probability of selection update, r s is a preset random number that follows a uniform distribution between [-1,1], r m is a preset random number that follows a uniform distribution between [0,1], d = 1, 2, 3, represents the d-dimensional value of the k′th element in the εth iteration, represents the d-dimensional value of the optimal element in the εth iteration, Represents the d-dimensional value of the best element in the q′th ring at the εth iteration.

9. The TDOA positioning method for aerial targets by a ground unmanned platform system according to claim 1, characterized in that: The process of obtaining the estimated value of the final target position includes: The three-dimensional coordinate components within the optimal element of the last iteration are used as the three-dimensional coordinate components of the final target position estimation value.

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