Dynamic target TDOA positioning method and system based on quantum golden eagle optimization layout

Abstract

The present invention discloses a dynamic target TDOA positioning method and system based on quantum Golden Eagle optimized layout, and relates to the technical field of UAV cluster information interaction. The technical points of the present invention include: establishing an optimized layout model and objective function based on geometric precision factor for a multi-UAV positioning system; wherein the multi-UAV positioning system includes a main UAV and multiple auxiliary UAVs; optimizing the arrangement of multiple UAVs using the quantum Golden Eagle algorithm to select the optimal arrangement; observing dynamic targets using the optimized multi-UAV optimal arrangement to obtain the observed position of the dynamic targets. The present invention solves the problem of inaccurate positioning of aerial dynamic targets by existing TDOA positioning methods. The designed quantum Golden Eagle mechanism can solve the optimized layout model of the multi-UAV positioning system with high precision, and improves the accuracy of the Chan algorithm in positioning dynamic targets.

Description

Technical Field

[0001] The present invention relates to the technical field of unmanned aerial vehicle cluster information interaction, and in particular to a dynamic target TDOA positioning method and system based on quantum golden eagle optimized layout. Background Art

[0002] UAV is short for Unmanned Aerial Vehicle, which usually refers to an unmanned aircraft that can be remotely controlled or autonomously controlled by a program. The three-dimensional collaborative positioning of multiple drones in a drone cluster is one of the key tasks required for drone cluster combat and mission execution. Time Difference of Arrival (TDOA) is one of the common systems of passive positioning. The multi-drone TDOA positioning technology does not require strict synchronization of the drone and radiation source clocks, has low system complexity and high positioning accuracy, so the TDOA positioning system is relatively stable and reliable, and has been widely used in actual engineering.

[0003] The most important indicator of the TDOA positioning system is positioning accuracy. The geometric dilution precision is referred to as GDOP (Geometric Dilution Precision). GDOP is a coefficient to measure positioning accuracy. The smaller the value, the higher the positioning accuracy. Therefore, GDOP can be used to measure the performance of the positioning system.

[0004] Through the search of existing technical literature, it is found that Zhou Gongqian et al., in the article "Analysis of the influence of base station layout on positioning accuracy based on TDOA" published in "Command Control and Simulation" (2017, Vol. 39, No. 6, pp. 119-126), analyzed the positioning equation based on TDOA, solved the nonlinear function of positioning error with respect to the azimuth of the base station target by differential operation, and proposed a chaotic double perturbation particle swarm algorithm to solve the function, but it only considered the two-dimensional plane positioning method of three base stations and could not be effectively applied to three-dimensional positioning. Chen Tao et al., in the article "Passive time difference positioning based on salp swarm algorithm" published in "Journal of Electronics and Information Technology" (2018, Vol. 40, No. 7, pp. 1591-1597), applied the salp swarm algorithm to TDOA positioning. Although the convergence speed of the salp swarm algorithm is stable and the positioning accuracy is high, it is only suitable for the positioning of fixed targets. In the article "Optimization of Base Station Layout of Civil Aviation Multi-point Positioning System" published in "Computer Applications and Software" (2022, Vol. 39, No. 2, pp. 294-299+314), Zhao Xiangcheng et al. established a mathematical model for the layout of base stations based on the immune optimization algorithm. The GDOP geometric sparse accuracy was used as the positioning accuracy evaluation criterion, and the immune optimization algorithm was used to calculate the optimal base station layout. Although it provides a solution for the layout of base stations in ground civil aviation systems, it only considers ground fixed base stations and does not consider the positioning of targets by mobile base stations in the air.

[0005] The search results of existing literature show that traditional TDOA positioning methods are based on fixed preset base stations to locate targets, and the coordinate settings of the targets to be located are also fixed. There are still technical gaps in the location settings of dynamic aerial base stations and how to solve the engineering problems of three-dimensional TDOA positioning of dynamic aerial targets. At the same time, how to optimize the layout of aerial base stations in real time according to the observed positions of dynamic targets is also a problem that needs to be solved. Therefore, finding a new method for multiple aerial base station positioning of dynamic targets in three-dimensional space has great practical significance. Summary of the invention

[0006] In view of the above problems, the present invention proposes a dynamic target TDOA positioning method and system based on quantum golden eagle optimized layout, in an effort to solve or alleviate one or more of the above problems.

[0007] According to one aspect of the present invention, a dynamic target TDOA positioning method based on quantum golden eagle optimization layout is proposed, and the method comprises the following steps:

[0008] Establishing an optimization layout model and objective function based on geometric precision factor for a multi-UAV positioning system; wherein the multi-UAV positioning system includes a main UAV and multiple auxiliary UAVs;

[0009] Use the quantum Golden Eagle algorithm to optimize the arrangement of multiple drones to select the optimal arrangement;

[0010] The optimized multi-UAV optimal arrangement is used to observe dynamic targets and obtain the observation position of dynamic targets.

[0011] Furthermore, the optimized layout model based on geometric precision factor is expressed as:

[0012]

[0013] Where P d The covariance matrix representing the positioning error of the multi-UAV positioning system for dynamic targets; trace(P d ) represents the matrix P d The sum of the elements on the main diagonal of ;

[0014] The objective function is expressed as:

[0015]

[0016] In the formula, Indicates the position coordinates of multiple auxiliary drones; Indicates that Substitute the coordinates of the auxiliary drone of the drone system into the calculation matrix P d , and get the objective function value

[0017] Furthermore, the process of optimizing the arrangement of multiple drones using the quantum golden eagle algorithm to select the optimal arrangement includes:

[0018] Initialize the quantum position of each quantum golden eagle in the quantum golden eagle population, and use the Chan algorithm to obtain the first observed position of the dynamic target, calculate the fitness value based on the first observed position, and determine the historical optimal quantum position of each quantum golden eagle;

[0019] In each iteration, the quantum position of the quantum golden eagle is updated according to the following steps: the quantum position of the quantum golden eagle is updated according to the evolution of the attack and cruise coefficients; the quantum position of the updated quantum golden eagle is mapped to the position, the fitness value of the updated individual is calculated, and the historical optimal quantum position of each quantum golden eagle is updated according to the fitness value;

[0020] Determine whether the maximum number of iterations has been reached. If so, terminate the loop iteration and output the global optimal position of the quantum golden eagle population.

[0021] Furthermore, the fitness calculation formula is:

[0022]

[0023] In the formula, represents the position of the dth quantum golden eagle in the εth iteration, Represents the position coordinate matrix of the auxiliary drone.

[0024] Furthermore, the process of updating the quantum position of the quantum golden eagle according to the evolution of the attack and cruise coefficients includes:

[0025] Update the attack coefficient at the ε+1th iteration and cruise coefficient

[0026]

[0027]

[0028] In the formula, and Respectively represent the minimum and maximum values ​​of the attack coefficient, G max represents the maximum number of iterations, and Respectively represent the minimum and maximum values ​​of the cruise coefficient;

[0029] Update the attack vector of the dth quantum golden eagle in the ε+1th iteration

[0030]

[0031] In the formula, represents the historical optimal quantum position of a quantum golden eagle randomly selected from the quantum golden eagle population, f∈{1,2,...,D}, f≠d, D represents the number of individuals in the quantum golden eagle population; represents the quantum position of the d-th quantum golden eagle in the ε-th iteration, N is the dimension of each quantum golden eagle, N = 3 × (M-1), M is the number of drones in three-dimensional space; the k-th dimension variable of the attack vector of the d-th quantum golden eagle in the ε+1th iteration

[0032] Update the cruise vector of the dth quantum golden eagle in the ε+1th iteration Randomly select the i-th dimension variable from the N-dimensional variables of the cruise vector of the d-th quantum golden eagle in the ε+1th iteration Determine the i-th dimension variable of the attack vector of the d-th quantum golden eagle in the ε+1th iteration Is the value of 0? but like but The value of coefficient α is determined according to the attack vector and quantum position, Randomly generate the remaining dimensional variables of the cruise vector of the dth quantum golden eagle in the ε+1th iteration is a random number between 0 and 1 that follows a uniform distribution;

[0033] Normalize the attack vector and cruise vector of the dth quantum golden eagle in the ε+1th iteration to get and For the ε+1th iteration, the normalized attack vector of the dth quantum golden eagle is like ||·|| means finding the l2 norm of ·, then like but The normalized cruise vector of the dth quantum golden eagle in the ε+1th iteration

[0034] Update the k-dimensional quantum rotation angle of the d-th quantum golden eagle in the ε+1th iteration and quantum revolving door

[0035]

[0036]

[0037] In the formula, and Generates a random number between 0 and 1 that follows a uniform distribution. like Then the k-dimensional quantum position of the d-th quantum golden eagle in the ε+1th iteration is updated to like but

[0038] Furthermore, the process of mapping the quantum position of the updated quantum golden eagle to a position, calculating the fitness value of the updated individual, and updating the historical optimal quantum position of each quantum golden eagle according to the fitness value includes:

[0039] For the updated quantum position of the dth quantum golden eagle in the ε+1th iteration According to the mapping rule, we can get the position of the dth quantum golden eagle in the ε+1th iteration. Calculate the fitness value of the updated position Will The historical optimal fitness value F of the dth quantum golden eagle before the ε+1th iteration d Compare, d = 1, 2, ..., D, if but At the same time Determined as the historical optimal quantum position of the dth quantum golden eagle up to the ε+1th iteration Otherwise, do not update and F d .

[0040] According to another aspect of the present invention, a dynamic target TDOA positioning system based on quantum golden eagle optimization layout is proposed, the system comprising:

[0041] A model building module, which is configured to establish an optimized layout model and an objective function based on a geometric precision factor of a multi-UAV positioning system; wherein the multi-UAV positioning system includes a main UAV and a plurality of auxiliary UAVs;

[0042] A drone arrangement optimization module, which is configured to optimize the arrangement of multiple drones using the quantum golden eagle algorithm to select the optimal arrangement;

[0043] The target position observation module is configured to observe the dynamic target using the optimized optimal arrangement of multiple UAVs to obtain the observation position of the dynamic target.

[0044] Furthermore, the optimized layout model based on the geometric precision factor in the model building module is expressed as:

[0045]

[0046] Where P d Represents the covariance matrix of the positioning error of the multi-UAV positioning system for dynamic targets; trace(P d ) represents the matrix P d The sum of the elements on the main diagonal of ;

[0047] The objective function is expressed as:

[0048]

[0049] In the formula, Indicates the position coordinates of multiple auxiliary drones; Indicates that Substitute the coordinates of the auxiliary drone of the drone system into the calculation matrix P d , and get the objective function value

[0050] Furthermore, the process of optimizing the arrangement of multiple drones using the quantum golden eagle algorithm in the drone arrangement optimization module to select the optimal arrangement includes:

[0051] Initialize the quantum position of each quantum golden eagle in the quantum golden eagle population, and use the Chan algorithm to obtain the first observed position of the dynamic target, calculate the fitness value based on the first observed position, and determine the historical optimal quantum position of each quantum golden eagle;

[0052] In each iteration, the quantum position of the quantum golden eagle is updated according to the following steps: the quantum position of the quantum golden eagle is updated according to the evolution of the attack and cruise coefficients; the quantum position of the updated quantum golden eagle is mapped to the position, the fitness value of the updated individual is calculated, and the historical optimal quantum position of each quantum golden eagle is updated according to the fitness value;

[0053] Determine whether the maximum number of iterations has been reached. If so, terminate the loop iteration and output the global optimal position of the quantum golden eagle population.

[0054] Furthermore, the fitness calculation formula in the drone arrangement optimization module is:

[0055]

[0056] In the formula, represents the position of the dth quantum golden eagle in the εth iteration, Represents the position coordinate matrix of the auxiliary drone;

[0057] The process of updating the quantum position of the quantum golden eagle according to the evolution of the attack and cruise coefficients includes:

[0058] Update the attack coefficient at the ε+1th iteration and cruise coefficient

[0059]

[0060]

[0061] In the formula, and Respectively represent the minimum and maximum values ​​of the attack coefficient, G max represents the maximum number of iterations, and Respectively represent the minimum and maximum values ​​of the cruise coefficient;

[0062] Update the attack vector of the dth quantum golden eagle in the ε+1th iteration

[0063]

[0064] In the formula, represents the historical optimal quantum position of a quantum golden eagle randomly selected from the quantum golden eagle population, f∈{1,2,...,D}, f≠d, D represents the number of individuals in the quantum golden eagle population; represents the quantum position of the d-th quantum golden eagle in the ε-th iteration, N is the dimension of each quantum golden eagle, N = 3 × (M-1), M is the number of drones in three-dimensional space; the k-th dimension variable of the attack vector of the d-th quantum golden eagle in the ε+1th iteration

[0065] Update the cruise vector of the dth quantum golden eagle in the ε+1th iteration Randomly select the i-th dimension variable from the N-dimensional variables of the cruise vector of the d-th quantum golden eagle in the ε+1th iteration Determine the i-th dimension variable of the attack vector of the d-th quantum golden eagle in the ε+1th iteration Is the value of 0? but like but The value of coefficient α is determined according to the attack vector and quantum position, Randomly generate the remaining dimensional variables of the cruise vector of the dth quantum golden eagle in the ε+1th iteration is a random number between 0 and 1 that follows a uniform distribution;

[0066] Normalize the attack vector and cruise vector of the dth quantum golden eagle in the ε+1th iteration to get and For the ε+1th iteration, the normalized attack vector of the dth quantum golden eagle is like ||·|| means finding the l2 norm of ·, then like but The normalized cruise vector of the dth quantum golden eagle in the ε+1th iteration

[0067] Update the k-dimensional quantum rotation angle of the d-th quantum golden eagle in the ε+1th iteration and quantum revolving door

[0068]

[0069]

[0070] In the formula, and Generates a random number between 0 and 1 that follows a uniform distribution. like Then the k-dimensional quantum position of the d-th quantum golden eagle in the ε+1th iteration is updated to like but

[0071] Compared with the prior art, the present invention has the following technical effects:

[0072] The present invention proposes a dynamic target TDOA positioning method and system based on quantum Golden Eagle optimization layout, designs a multi-UAV positioning system optimization layout model based on geometric precision factor, fills the technical gap in the dynamic layout of aerial base stations, solves the engineering problem of inaccurate positioning of aerial dynamic targets by existing TDOA positioning methods, and improves the accuracy of Chan algorithm for dynamic target positioning; based on quantum optimization theory and Golden Eagle optimization mechanism, a quantum Golden Eagle optimization mechanism is proposed, and a new search strategy is designed based on quantum rotation angle and quantum revolving door, which further improves the convergence performance of the algorithm. The designed quantum Golden Eagle mechanism can optimize the layout model of multi-UAV positioning system High-precision solutions are obtained, and the optimized layout is used to locate dynamic targets to improve positioning accuracy. A four-base station Y-type layout is proposed as the initial arrangement of multiple UAVs, and points in three-dimensional space are preset as backup coordinates of auxiliary UAVs. The designed quantum Golden Eagle optimization mechanism is used to optimize the layout of the multi-UAV positioning system to obtain the optimized coordinates of the auxiliary UAVs. The optimized coordinates of the auxiliary UAVs are used to form a new arrangement to perform three-dimensional TDOA positioning of aerial targets, which solves the engineering problem of optimizing the layout of aerial base stations according to the target observation position to further realize target positioning, and breaks through the application limitations of swarm intelligence algorithms in TDOA positioning and optimizing base station layout. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] The present invention can be better understood by referring to the description given below in conjunction with the accompanying drawings, which together with the following detailed description are included in this specification and form a part of this specification, and are used to further illustrate the preferred embodiments of the present invention and explain the principles and advantages of the present invention.

[0074] Figure 1 It is a flow chart of a dynamic target TDOA positioning method based on quantum Golden Eagle optimization layout described in an embodiment of the present invention.

[0075] Figure 2 It is another flow chart of a dynamic target TDOA positioning method based on quantum Golden Eagle optimization layout described in an embodiment of the present invention.

[0076] Figure 3It is a schematic diagram of the initial position and backup position of the multi-UAV positioning system in three-dimensional space in an embodiment of the present invention.

[0077] Figure 4 It is a comparison diagram of mean square error values ​​of QGEO-Chan and Chan algorithms of the method of the present invention under different noise variances when the secondary observation target is a dynamic target in an embodiment of the present invention.

[0078] Figure 5 It is a comparison diagram of mean square error values ​​of QGEO-Chan and Chan algorithms of the method of the present invention under different noise variances when the secondary observation target is a fixed target in an embodiment of the present invention. DETAILED DESCRIPTION

[0079] In order to enable those skilled in the art to better understand the scheme of the present invention, exemplary implementations or embodiments of the present invention will be described below in conjunction with the accompanying drawings. Obviously, the described implementations or embodiments are only implementations or embodiments of a part of the present invention, not all of them. Based on the implementations or embodiments of the present invention, all other implementations or embodiments obtained by ordinary technicians in the field without creative work should fall within the scope of protection of the present invention.

[0080] In view of the shortcomings and deficiencies of the prior art, the present invention provides a dynamic target TDOA positioning method and system based on quantum Golden Eagle optimized layout to achieve high-precision three-dimensional dynamic TDOA positioning of aerial targets, filling the technical gap of optimizing the aerial base station layout according to the target observation position to further achieve target positioning, and designs a quantum Golden Eagle mechanism for solving the problem, which has a fast convergence speed and breaks through the application limitations of the swarm intelligence algorithm to optimize the base station layout method.

[0081] The embodiment of the present invention proposes a dynamic target TDOA positioning method based on quantum golden eagle optimization layout, such as Figure 1 As shown, the method comprises the following steps:

[0082] Step 1: Establishing an optimization layout model and objective function based on geometric precision factor of a multi-UAV positioning system; wherein the multi-UAV positioning system includes a main UAV and multiple auxiliary UAVs;

[0083] Step 2: Use the quantum golden eagle algorithm to optimize the arrangement of multiple drones to select the optimal arrangement;

[0084] Step 3: Use the optimized multi-UAV optimal arrangement method to observe the dynamic target and obtain the observation position of the dynamic target.

[0085] The method starts from step 1. In step 1, an optimization layout model and an objective function based on geometric precision factor of a multi-UAV positioning system are established; wherein the multi-UAV positioning system includes a main UAV and a plurality of auxiliary UAVs.

[0086] According to an embodiment of the present invention, Figure 2 As shown, firstly, an optimization layout model of multi-UAV positioning system is established and the objective function is constructed.

[0087] Assume that there are M drones in three-dimensional space, and the position coordinates of the target to be determined are (x, y, z). The target position can be estimated using the known position coordinates of each drone and the measured TDOA observation value. Select one of the M drones as the main drone B1 with coordinates (x1, y1, z1), and the rest as auxiliary drones B m , m=2,3,...,M, the coordinates are (x m ,y m ,z m ), locate the target to be sought, and the target to be sought arrives at the auxiliary UAV B m The distance is Target to be requested to auxiliary drone B m The difference between the distance to the main drone 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 measuring TDOA; the coordinates of each UAV and the target to be determined are brought in to obtain the distance difference between the target radiation source signal and the mth auxiliary UAV and the main UAV 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 Since the geometric relationship between the aerial base station and the target has a great influence on the positioning accuracy of the multi-UAV positioning system, the layout of the base station will change the relative position of the target, and the calculation parameters of the TDOA equation will also change, which will eventually affect the positioning accuracy of the target. Therefore, GDOP is selected as the standard for evaluating the positioning accuracy to optimize the base station layout.

[0088] Assume that the target positioning error is dx, dy and dz, and the measurement error of each UAV and its error component dx m ,dy m and dz m There is no correlation between them. The distance difference r between the target and the mth auxiliary UAV and the main UAV is m,1 =r m -r1 Differentiate and simplify to get: k m =F mx dx m +F my dy m +F mz dz m , m=2,3,...,M, let H be the coefficient matrix, is the error caused by the TDOA positioning method to the target measurement, ΔX = [k1-k2, k1-k3, …, k1-k M ] T is the error caused by the state of each drone itself, Δs represents the positioning error of the target radiation source, Δs=[dx,dy,dz] T ,but The least square method is used to solve the positioning error of the radiation source, and the positioning error of the target is The covariance matrix of the positioning error is In the formula, F=(H T H) -1 H T , Where σ rm,1 represents the standard deviation of TDOA measurement error, η ij represents the correlation coefficient of TDOA measurement error, Assume that the standard deviations of the components of the site error vector are the same, that is, because but The TDOA positioning accuracy is expressed by the geometric precision factor:

[0089]

[0090] Where GDOP is the optimized layout model based on geometric precision factor; Pd The covariance matrix trace(P d ) represents the matrix P d The sum of the elements on the main diagonal of .

[0091] If a multi-UAV positioning system consisting of 4 UAVs is considered, then Optimize the position of the auxiliary drones to get a better layout, Indicates the mth auxiliary drone The new position coordinates obtained after optimization, m = 2, 3, 4, are used to form the auxiliary drone coordinate matrix Each row represents the position coordinates of an auxiliary drone, and the objective function is constructed based on the geometric precision factor. Indicates that Substitute the coordinates of the auxiliary drone of the drone system into the calculation matrix P d , and get the objective function value

[0092] Then, step 2 is executed. In step 2, the arrangement of multiple drones is optimized using the quantum golden eagle algorithm to select the optimal arrangement. The specific process includes:

[0093] Step 21: Initialize the quantum position of each quantum golden eagle in the quantum golden eagle population, and use the Chan algorithm to obtain the first observed position of the dynamic target, calculate the fitness value based on the first observed position, and determine the historical optimal quantum position of each quantum golden eagle;

[0094] Step 22. In each iteration, the quantum position of the quantum golden eagle is updated according to the following steps: the quantum position of the quantum golden eagle is updated according to the evolution of the attack and cruise coefficients; the quantum position of the updated quantum golden eagle is mapped to a position, the fitness value of the updated individual is calculated, and the historical optimal quantum position of each quantum golden eagle is updated according to the fitness value;

[0095] Step 2 and 3: Determine whether the maximum number of iterations has been reached. If reached, terminate the loop iteration and output the global optimal position of the quantum golden eagle population.

[0096] According to an embodiment of the present invention, Figure 2 As shown, first, in step 21, the quantum position of each quantum golden eagle in the quantum golden eagle population is initialized, the Chan algorithm is used to obtain the first observed position of a dynamic target, and the fitness value is calculated according to the first observed position to determine the historical optimal quantum position of each quantum golden eagle.

[0097] There are D quantum golden eagles in the quantum golden eagle population. The dimension of each quantum golden eagle is N, N = 3 × (M-1), and the maximum number of iterations is G. max , ε represents the number of iterations. The quantum position of the dth quantum golden eagle in the εth iteration is Randomly initialize the initial quantum position of the quantum golden eagle in the search space.

[0098] Set the initial coordinates of the dynamic target to (x a ,y a ,z a ), x a =γ1+0.5,y a =1.5γ2+2.5,z a =1.5γ3+0.5, γ1, γ2 and γ3 are all random numbers between 0 and 1 that obey uniform distribution. At this time, the target reaches the auxiliary drone base station B. m The difference between the distance to the main UAV base station B1 is r m -r1, then there is Simplify this formula and let x m,1 =x m -x1,y m,1 =y m -y1,z m,1 =z m -z1, Available The Chan algorithm is a non-recursive hyperbolic equations solution method with an analytical expression solution. Consider a multi-UAV positioning system when the number of aerial base stations M = 4. At this time, three TDOA measurement values ​​can be obtained. Assuming that r1 is known, the estimated value of the target position is Bring this formula into A quadratic equation about r1 can be obtained. The positive root of r1 can be taken back to obtain the first observed position of the dynamic target (x′ a ,y′ a ,z′ a ), which is the first observed position of the dynamic target obtained by the Chan algorithm; in some cases, r1 may have two positive roots, and this ambiguity can be selected based on the relevant prior information.

[0099] Pre-set the layout of the aerial base stations. and They represent the position coordinates when all dimensions of the quantum golden eagle are all 0 and all 1, respectively. That is, when the k-th dimension variable of the d-th quantum golden eagle is iterated When the corresponding k-th dimension position for when The k-th dimension position corresponding to According to the above rules, the quantum position of the dth quantum golden eagle in the εth iteration is mapped to the position Convert the position of the quantum golden eagle into the position coordinate matrix of the auxiliary drone Constructing the fitness function According to the first observation position (x′) of the dynamic target obtained by Chan algorithm a ,y′ a ,z′ a ), calculate the fitness value of the dth quantum golden eagle in the εth iteration Will and the historical optimal fitness value F of the dth quantum golden eagle before the εth iteration d Compare, d = 1, 2, ..., D, if but At the same time Determined as the historical optimal quantum position of the dth quantum golden eagle up to the εth iteration Otherwise, do not update and F d .

[0100] Then, if Figure 2 As shown, in step 22, the quantum position of the quantum golden eagle is updated in each iteration according to the following steps: first, the quantum position of the quantum golden eagle is updated according to the evolution of the attack coefficient and the cruise coefficient. The details are as follows.

[0101] Update the attack coefficient at the ε+1th iteration and cruise coefficient and Respectively represent the minimum and maximum values ​​of the attack coefficient, and Represent the minimum and maximum values ​​of the cruise coefficient respectively; for the dth quantum golden eagle in the ε+1th iteration, a quantum golden eagle is randomly selected from the quantum golden eagle population to obtain the historical optimal quantum position Get the attack vector of the dth quantum golden eagle in the ε+1th iteration The k-th dimension variable of the attack vector of the d-th quantum golden eagle in the ε+1th iteration The cruising vector of the dth quantum golden eagle in the ε+1th iteration is Randomly select the i-th dimension variable from the N-dimensional variables of the cruise vector of the d-th quantum golden eagle in the ε+1th iteration Determine the i-th dimension variable of the attack vector of the d-th quantum golden eagle in the ε+1th iteration Is the value of 0? but like but The value of coefficient α is determined according to the attack vector and quantum position. Randomly generate the remaining dimensional variables of the cruise vector of the dth quantum golden eagle in the ε+1th iteration is a random number between 0 and 1 that follows a uniform distribution; normalize the attack vector and cruise vector of the dth quantum golden eagle in the ε+1th iteration to obtain and For the ε+1th iteration, the normalized attack vector of the dth quantum golden eagle is like ||·|| means finding the l2 norm of ·, then like but The normalized cruise vector of the dth quantum golden eagle in the ε+1th iteration Update the k-dimensional quantum rotation angle of the d-th quantum golden eagle in the ε+1th iteration to and are all random numbers between 0 and 1 that obey uniform distribution. The k-dimensional quantum revolving door of the d-th quantum Golden Eagle in the ε+1th iteration is Generate a random number between 0 and 1 that follows a uniform distribution like Then the k-dimensional quantum position of the d-th quantum golden eagle in the ε+1th iteration is updated to like but

[0102] Then, the quantum position of the updated quantum golden eagle is mapped to the position, the fitness value of the updated individual is calculated, and the historical optimal quantum position of each quantum golden eagle is updated according to the fitness value. The details are as follows.

[0103] For the updated quantum position of the dth quantum golden eagle in the ε+1th iteration According to the mapping rule, we can get the position of the dth quantum golden eagle in the ε+1th iteration. Calculate the fitness value of the updated position Will The historical optimal fitness value F of the dth quantum golden eagle before the ε+1th iteration d Compare, d = 1, 2, ..., D, if but At the same time Determined as the historical optimal quantum position of the dth quantum golden eagle up to the ε+1th iteration Otherwise, do not update and F d .

[0104] Finally, if Figure 2 As shown, in steps 2 and 3, it is determined whether the maximum number of iterations has been reached. If so, the loop iteration is terminated and the global optimal position of the quantum golden eagle population is output; otherwise, the iteration continues. The details are as follows.

[0105] Determine whether the maximum number of iterations G has been reached max If it is not reached, set ε = ε + 1 and return to step 3; if it is reached, terminate the loop iteration and select the one with the smallest fitness value from the historical optimal quantum position of the quantum golden eagle as the global optimal quantum position of the quantum golden eagle population. After mapping, it is transformed into the global optimal position Convert the global optimal position of the quantum golden eagle population into the position coordinate matrix of the auxiliary drone This is the optimized layout of base stations of the multi-UAV positioning system.

[0106] Finally, step three is executed. In step three, the dynamic target is observed using the optimized optimal arrangement of multiple UAVs to obtain the observation position of the dynamic target.

[0107] According to an embodiment of the present invention, Figure 2 As shown in the figure, the dynamic target is observed by the Chan algorithm according to the optimized base station layout, and the secondary observation position of the dynamic target is obtained. The multi-UAV positioning system base station layout output after iteration is used as the base station layout of the Chan algorithm to perform secondary positioning of the dynamic target. At this time, the position of the dynamic target is (x b ,y b ,z b ), x b =λ1+0.5,y b =1.5λ2+2.5,z b =1.5λ3+0.5, λ1, λ2 and λ3 are all random numbers between 0 and 1 that obey uniform distribution. The dynamic target secondary positioning coordinates obtained by Chan algorithm are (x b ′,y b ′,z b ′).

[0108] The technical effect of the present invention is further verified through experiments.

[0109] The dynamic target TDOA positioning method based on the quantum Golden Eagle optimization layout designed by the present invention is denoted as QGEO-Chan, and the TDOA positioning method for dynamic targets in the air based on the Chan algorithm is denoted as Chan, and a comparative experiment is carried out.

[0110] Randomly select one of the multiple drones as the main drone B1, and establish a three-dimensional coordinate system with the main drone as the origin. Randomly or according to a certain rule, select M-1 drones around the main drone as auxiliary drones B m , m=2,3,...,M. The total number of base stations M=4 is selected, and the four base stations are arranged in a Y shape with the main UAV as the origin. The base station coordinates of the initial layout of the UAV system are shown in Table 1, in km:

[0111] Table 1 Initial coordinates of base station Y-type layout

[0112]

[0113] Figure 3 The figure is a schematic diagram of the initial position of the multi-UAV positioning system in three-dimensional space and the preset backup position of the UAV. In the dynamic target TDOA positioning method QGEO-Chan based on the quantum golden eagle optimization layout proposed in the present invention, the population size of the quantum golden eagle is D = 40, the dimension of each quantum golden eagle is N = 3 × (M-1), that is, N = 9, and the maximum number of iterations G max =50, and The values ​​of are Attack coefficient and cruise coefficient The standard deviation of the site error σ s =0.005km, standard deviation of time difference error The simulation parameters of Chan algorithm can be found in reference [1].

[0114] 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 method 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 and (x′, y′, z′) is the estimated position of the aerial target.

[0115] Figure 4 This is a comparison chart of the mean square error values ​​of QGEO-Chan and Chan under different noise variances when the secondary observation target is a dynamic target. The mean square error MSE under different noise variances is the statistical average of 1000 experiments. It can be seen from the figure that the QGEO-Chan proposed in the present invention performs better in the positioning problem of dynamic targets than the traditional Chan algorithm with a fixed base station layout, and overcomes the problem of inaccurate positioning of random targets by the Chan algorithm.

[0116] Figure 5 This is a comparison chart of the mean square error values ​​of QGEO-Chan and Chan under different noise variances when the secondary observation target is a fixed target. At this time, the secondary observation target is a fixed value, (x b ,y b ,z b ) is set to (1,3,1.5), that is, x b =1,y b =3, z b =1.5.

[0117] from Figure 5 It can be seen that when the secondary observation target is a fixed target, the QGEO-Chan algorithm that optimizes the layout of the UAV base station according to the first observation target has a smaller mean square error value and higher positioning accuracy under different noise variance conditions than the Chan algorithm that uses a fixed base station layout. The mean values ​​of the multi-UAV TDOA positioning estimates obtained using different methods under different noise variances are shown in Table 2. The average estimated coordinate MV is the statistical average of 1000 experiments, in km.

[0118] Table 2 Comparison of the mean positioning estimates of QGEO-Chan and Chan algorithms when the secondary observation target is a fixed target

[0119]

[0120] Another embodiment of the present invention provides a dynamic target TDOA positioning system based on the quantum golden eagle optimization layout, the system comprising:

[0121] A model building module, which is configured to establish an optimized layout model and an objective function based on a geometric precision factor of a multi-UAV positioning system; wherein the multi-UAV positioning system includes a main UAV and a plurality of auxiliary UAVs;

[0122] A drone arrangement optimization module, which is configured to optimize the arrangement of multiple drones using the quantum golden eagle algorithm to select the optimal arrangement;

[0123] The target position observation module is configured to observe the dynamic target using the optimized optimal arrangement of multiple UAVs to obtain the observation position of the dynamic target.

[0124] In this embodiment, preferably, the optimized layout model based on the geometric precision factor in the model building module is expressed as:

[0125]

[0126] Where P d The covariance matrix representing the positioning error of the multi-UAV positioning system for dynamic targets; trace(Pd ) represents the matrix P d The sum of the elements on the main diagonal of ;

[0127] The objective function is expressed as:

[0128]

[0129] In the formula, Indicates the position coordinates of multiple auxiliary drones; Indicates that Substitute the coordinates of the auxiliary drone of the drone system into the calculation matrix P d , and get the objective function value

[0130] In this embodiment, preferably, the process of optimizing the arrangement of multiple drones using the quantum golden eagle algorithm in the drone arrangement optimization module to select the optimal arrangement includes:

[0131] Initialize the quantum position of each quantum golden eagle in the quantum golden eagle population, and use the Chan algorithm to obtain the first observed position of the dynamic target, calculate the fitness value based on the first observed position, and determine the historical optimal quantum position of each quantum golden eagle;

[0132] In each iteration, the quantum position of the quantum golden eagle is updated according to the following steps: the quantum position of the quantum golden eagle is updated according to the evolution of the attack and cruise coefficients; the quantum position of the updated quantum golden eagle is mapped to the position, the fitness value of the updated individual is calculated, and the historical optimal quantum position of each quantum golden eagle is updated according to the fitness value;

[0133] Determine whether the maximum number of iterations has been reached. If so, terminate the loop iteration and output the global optimal position of the quantum golden eagle population.

[0134] In this embodiment, preferably, the fitness calculation formula in the drone arrangement optimization module is:

[0135]

[0136] In the formula, represents the position of the dth quantum golden eagle in the εth iteration, Represents the position coordinate matrix of the auxiliary drone;

[0137] The process of updating the quantum position of the quantum golden eagle according to the evolution of the attack and cruise coefficients includes:

[0138] Update the attack coefficient at the ε+1th iteration and cruise coefficient

[0139]

[0140]

[0141] In the formula, and Respectively represent the minimum and maximum values ​​of the attack coefficient, G max represents the maximum number of iterations, and Respectively represent the minimum and maximum values ​​of the cruise coefficient;

[0142] Update the attack vector of the dth quantum golden eagle in the ε+1th iteration

[0143]

[0144] In the formula, represents the historical optimal quantum position of a quantum golden eagle randomly selected from the quantum golden eagle population, f∈{1,2,...,D}, f≠d, D represents the number of individuals in the quantum golden eagle population; represents the quantum position of the d-th quantum golden eagle in the ε-th iteration, N is the dimension of each quantum golden eagle, N = 3 × (M-1), M is the number of drones in three-dimensional space; the k-th dimension variable of the attack vector of the d-th quantum golden eagle in the ε+1th iteration

[0145] Update the cruise vector of the dth quantum golden eagle in the ε+1th iteration Randomly select the i-th dimension variable from the N-dimensional variables of the cruise vector of the d-th quantum golden eagle in the ε+1th iteration Determine the i-th dimension variable of the attack vector of the d-th quantum golden eagle in the ε+1th iteration Is the value of 0? but like but The value of coefficient α is determined according to the attack vector and quantum position, Randomly generate the remaining dimensional variables of the cruise vector of the dth quantum golden eagle in the ε+1th iteration is a random number between 0 and 1 that follows a uniform distribution;

[0146] Normalize the attack vector and cruise vector of the dth quantum golden eagle in the ε+1th iteration to get and For the ε+1th iteration, the normalized attack vector of the dth quantum golden eagle is like ||·|| means finding the l2 norm of ·, then like but The normalized cruise vector of the dth quantum golden eagle in the ε+1th iteration

[0147] Update the k-dimensional quantum rotation angle of the d-th quantum golden eagle in the ε+1th iteration and quantum revolving door

[0148]

[0149]

[0150] In the formula, and Generates a random number between 0 and 1 that follows a uniform distribution. like Then the k-dimensional quantum position of the d-th quantum golden eagle in the ε+1th iteration is updated to like but

[0151] In this embodiment, preferably, the process of mapping the updated quantum position of the quantum golden eagle to a position, calculating the fitness value of the updated individual, and updating the historical optimal quantum position of each quantum golden eagle according to the fitness value in the drone arrangement optimization module includes:

[0152] For the updated quantum position of the dth quantum golden eagle in the ε+1th iteration According to the mapping rule, we can get the position of the dth quantum golden eagle in the ε+1th iteration. Calculate the fitness value of the updated position Will The historical optimal fitness value F of the dth quantum golden eagle before the ε+1th iteration d Compare, d = 1, 2, ..., D, if but At the same time Determined as the historical optimal quantum position of the dth quantum golden eagle up to the ε+1th iteration Otherwise, do not update and F d .

[0153] The functions of a dynamic target TDOA positioning system based on the quantum Golden Eagle optimized layout in an embodiment of the present invention can be described by the aforementioned dynamic target TDOA positioning method based on the quantum Golden Eagle optimized layout. Therefore, for the parts not described in detail in the system embodiment, please refer to the above method embodiment and will not be repeated here.

[0154] Although the present invention has been described according to a limited number of embodiments, it will be apparent to those skilled in the art, with the benefit of the above description, that other embodiments are contemplated within the scope of the invention thus described. The disclosure of the present invention is intended to be illustrative rather than restrictive of the scope of the invention, which is defined by the appended claims.

[0155] The documents cited in the present invention are as follows:

[0156] [1] Li Zhaohua, Wang Yuduo, Shao Qing. TDOA three-dimensional positioning algorithm based on Chan[J]. Modern Telecommunications Technology, 2014(11):36-40.

Claims

1. A dynamic target TDOA positioning method based on the quantum golden eagle optimized layout is characterized by: The following steps are involved: Establishing an optimization layout model and objective function based on geometric precision factor for a multi-UAV positioning system; wherein the multi-UAV positioning system includes a main UAV and multiple auxiliary UAVs; The quantum golden eagle algorithm is used to optimize the arrangement of multiple drones to select the optimal arrangement; the quantum position of each quantum golden eagle in the quantum golden eagle population is initialized, and the first observed position of the dynamic target is obtained by using the Chan algorithm, and the fitness value is calculated based on the first observed position to determine the historical optimal quantum position of each quantum golden eagle; in each iteration, the quantum position of the quantum golden eagle is updated according to the following steps: the quantum position of the quantum golden eagle is updated according to the evolution of the attack and cruise coefficients; the quantum position of the updated quantum golden eagle is mapped to the position, the fitness value of the updated individual is calculated, and the historical optimal quantum position of each quantum golden eagle is updated according to the fitness value; it is determined whether the maximum number of iterations has been reached, and if so, the loop iteration is terminated, and the global optimal position of the quantum golden eagle population is output; The optimized multi-UAV optimal arrangement is used to observe dynamic targets and obtain the observation position of dynamic targets.

2. The dynamic target TDOA positioning method based on quantum golden eagle optimization layout according to claim 1 is characterized in that: The optimized layout model based on geometric precision factor is expressed as: Where P d The covariance matrix representing the positioning error of the multi-UAV positioning system for dynamic targets; trace(P d ) represents the matrix P d The sum of the elements on the main diagonal of ; The objective function is expressed as: In the formula, Indicates the position coordinates of multiple auxiliary drones; Indicates that Substitute the coordinates of the auxiliary drone of the drone system into the calculation matrix P d , and get the objective function value 3. The dynamic target TDOA positioning method based on quantum golden eagle optimization layout according to claim 1 is characterized in that: The fitness value calculation formula is: In the formula, represents the position of the dth quantum golden eagle in the εth iteration, Represents the position coordinate matrix of the auxiliary drone.

4. The dynamic target TDOA positioning method based on quantum golden eagle optimization layout according to claim 3 is characterized in that: The process of updating the quantum position of the quantum golden eagle according to the evolution of the attack and cruise coefficients includes: Update the attack coefficient at the ε+1th iteration and cruise coefficient In the formula, and Respectively represent the minimum and maximum values ​​of the attack coefficient, G max represents the maximum number of iterations, and Respectively represent the minimum and maximum values ​​of the cruise coefficient; Update the attack vector of the dth quantum golden eagle in the ε+1th iteration In the formula, represents the historical optimal quantum position of a quantum golden eagle randomly selected from the quantum golden eagle population, f∈{1,2,...,D}, f≠d, D represents the number of individuals in the quantum golden eagle population; represents the quantum position of the dth quantum golden eagle in the εth iteration, d=1,2,...,D,k=1,2,...,N,N is the dimension of each quantum golden eagle, N=3×(M-1), M is the number of drones in three-dimensional space; the k-th dimension variable of the attack vector of the d-th quantum golden eagle in the ε+1th iteration Update the cruise vector of the dth quantum golden eagle in the ε+1th iteration Randomly select the i-th dimension variable from the N-dimensional variables of the cruise vector of the d-th quantum golden eagle in the ε+1th iteration i∈{1,2,...,N}, determines the i-th dimension variable of the attack vector of the d-th quantum golden eagle in the ε+1th iteration Is the value of 0? but like but The value of coefficient α is determined according to the attack vector and quantum position, Randomly generate the remaining dimensional variables of the cruise vector of the dth quantum golden eagle in the ε+1th iteration is a random number between 0 and 1 that follows a uniform distribution; Normalize the attack vector and cruise vector of the dth quantum golden eagle in the ε+1th iteration to get and For the ε+1th iteration, the normalized attack vector of the dth quantum golden eagle is like ||·|| means finding the e2 norm of ·, then like but The normalized cruise vector of the dth quantum golden eagle in the ε+1th iteration Update the k-dimensional quantum rotation angle of the d-th quantum golden eagle in the ε+1th iteration and quantum revolving door In the formula, and Generates a random number between 0 and 1 that follows a uniform distribution. like Then the k-dimensional quantum position of the d-th quantum golden eagle in the ε+1th iteration is updated to like but 5. The dynamic target TDOA positioning method based on quantum golden eagle optimization layout according to claim 4 is characterized in that: The process of mapping the quantum position of the updated quantum golden eagle to a position, calculating the fitness value of the updated individual, and updating the historical optimal quantum position of each quantum golden eagle according to the fitness value includes: For the updated quantum position of the dth quantum golden eagle in the ε+1th iteration According to the mapping rule, we can get the position of the dth quantum golden eagle in the ε+1th iteration. Calculate the fitness value of the updated position Will The historical optimal fitness value F of the dth quantum golden eagle before the ε+1th iteration d Compare, d = 1, 2, ..., D, if but At the same time Determined as the historical optimal quantum position of the dth quantum golden eagle up to the ε+1th iteration Otherwise, do not update and F d .

6. Dynamic target TDOA positioning system based on quantum golden eagle optimized layout, characterized by: include: A model building module, which is configured to establish an optimized layout model and an objective function based on a geometric precision factor of a multi-UAV positioning system; wherein the multi-UAV positioning system includes a main UAV and a plurality of auxiliary UAVs; The UAV arrangement optimization module is configured to optimize the arrangement of multiple UAVs using the quantum golden eagle algorithm to select the optimal arrangement; initialize the quantum position of each quantum golden eagle in the quantum golden eagle population, and use the Chan algorithm to obtain the first observed position of the dynamic target, calculate the fitness value according to the first observed position, and determine the historical optimal quantum position of each quantum golden eagle; update the quantum position of the quantum golden eagle according to the following steps in each iteration: update the quantum position of the quantum golden eagle according to the evolution of the attack and cruise coefficients; map the quantum position of the updated quantum golden eagle to a position, calculate the fitness value of the updated individual, and update the historical optimal quantum position of each quantum golden eagle according to the fitness value; determine whether the maximum number of iterations has been reached, and if so, terminate the loop iteration and output the global optimal position of the quantum golden eagle population; The target position observation module is configured to observe the dynamic target using the optimized optimal arrangement of multiple UAVs to obtain the observation position of the dynamic target.

7. The dynamic target TDOA positioning system based on quantum golden eagle optimized layout according to claim 6 is characterized in that: The optimized layout model based on geometric precision factor in the model building module is expressed as: Where P d The covariance matrix representing the positioning error of the multi-UAV positioning system for dynamic targets; trace(P d ) represents the matrix P d The sum of the elements on the main diagonal of ; The objective function is expressed as: In the formula, Indicates the position coordinates of multiple auxiliary drones; Indicates that Substitute the coordinates of the auxiliary drone of the drone system into the calculation matrix P d , and get the objective function value 8. The dynamic target TDOA positioning system based on quantum golden eagle optimized layout according to claim 6 is characterized in that: The fitness value calculation formula in the drone arrangement optimization module is: In the formula, represents the position of the dth quantum golden eagle in the εth iteration, Represents the position coordinate matrix of the auxiliary drone; The process of updating the quantum position of the quantum golden eagle according to the evolution of the attack and cruise coefficients includes: Update the attack coefficient at the ε+1th iteration and cruise coefficient In the formula, and Respectively represent the minimum and maximum values ​​of the attack coefficient, G max represents the maximum number of iterations, and Respectively represent the minimum and maximum values ​​of the cruise coefficient; Update the attack vector of the dth quantum golden eagle in the ε+1th iteration In the formula, represents the historical optimal quantum position of a quantum golden eagle randomly selected from the quantum golden eagle population, f∈{1,2,...,D}, f≠d, D represents the number of individuals in the quantum golden eagle population; represents the quantum position of the dth quantum golden eagle in the εth iteration, N is the dimension of each quantum golden eagle, N = 3 × (M-1), M is the number of drones in three-dimensional space; the k-th dimension variable of the attack vector of the d-th quantum golden eagle in the ε+1th iteration Update the cruise vector of the dth quantum golden eagle in the ε+1th iteration Randomly select the i-th dimension variable from the N-dimensional variables of the cruise vector of the d-th quantum golden eagle in the ε+1th iteration Determine the i-th dimension variable of the attack vector of the d-th quantum golden eagle in the ε+1th iteration Is the value of 0? but like but The value of coefficient α is determined according to the attack vector and quantum position, Randomly generate the remaining dimensional variables of the cruise vector of the dth quantum golden eagle in the ε+1th iteration is a random number between 0 and 1 that follows a uniform distribution; Normalize the attack vector and cruise vector of the dth quantum golden eagle in the ε+1th iteration to get and For the ε+1th iteration, the normalized attack vector of the dth quantum golden eagle is like ||·|| means finding the l2 norm of ·, then like but The normalized cruise vector of the dth quantum golden eagle in the ε+1th iteration Update the k-dimensional quantum rotation angle of the d-th quantum golden eagle in the ε+1th iteration and quantum revolving door In the formula, and Generates a random number between 0 and 1 that follows a uniform distribution. like Then the k-dimensional quantum position of the d-th quantum golden eagle in the ε+1th iteration is updated to like but

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