CN114580601A - Magnetic dipole target positioning method based on improved intelligent optimization algorithm - Google Patents

Abstract

The invention belongs to the technical field of magnetic target positioning, and discloses a magnetic dipole target positioning method based on an improved intelligent optimization algorithm, which comprises the following steps: describing the magnetic induction intensity of a target by adopting a magnetic dipole model under a far field condition; constructing a magnetic dipole target positioning nonlinear equation set based on an improved intelligent optimization algorithm; and optimizing by using an improved intelligent optimization algorithm to realize the magnetic dipole target positioning based on the improved intelligent optimization algorithm. The optimization process by using the improved intelligent optimization algorithm comprises the following steps: an initial population is generated through initialization of the good point set, so that the initial population position is more uniform; secondly, adding a particle swarm position updating formula to enhance the information exchange and cooperation mechanism among the particles; in addition, the change probability and the Levy flight are added, so that the activity and the diversity of the particles are enhanced, and the algorithm is prevented from falling into local optimization. The invention has higher positioning precision and higher convergence rate under the condition of low signal-to-noise ratio, and can be used for magnetic target detection.

Description

A Magnetic Dipole Target Localization Method Based on Improved Intelligent Optimization Algorithm

technical field

The invention belongs to the technical field of magnetic target positioning, in particular to a magnetic dipole target positioning method based on an improved intelligent optimization algorithm.

Background technique

At present, the magnetic target localization method has important value in the application fields of aerial magnetic detection, robot attitude detection, geomagnetic field navigation, geological exploration, and unexploded ordnance detection. When the magnetic target is far enough away from the magnetic sensor, the target can be equivalent to a magnetic dipole, and the magnetic dipole can be used to describe the magnetic induction intensity of the target. The magnetic dipole localization problem is mainly solved by three types of methods: analytical method, optimization method and sequential filtering method. Among them, the analytical method is more sensitive to observation noise, and the positioning performance is poor under the condition of low signal-to-noise ratio; the sequential filtering method is mainly aimed at the positioning problem of moving targets, and the optimization method is currently based on improved intelligent optimization algorithms. The main method of magnetic dipole target localization.

The optimization algorithm usually obtains the position information of the magnetic target through the measurement data of the magnetic sensor and using the optimized algorithm. In 2008, Wiegert et al. proposed a gradient directional derivative method based on the central potential field for the real-time point-by-point localization problem. In 2009, Li Hua et al. used the genetic algorithm to locate the magnetic target based on the single spheroid model, and realized the on-line magnetic target localization. The calculation results show that the method is accurate in positioning and reliable in judgment. In 2017, Zhang Dan et al. studied the search path optimization problem of airborne magnetic detectors based on genetic algorithm. According to the prior information of the target, the spatial range of the solution was constrained, and the initial population was generated according to the rule search formation and random search formation, so that the individual non-inferiority And diversity is guaranteed. In 2018, Gao et al. used the LM algorithm to achieve localization of moving magnetic targets.

The research status of the magnetic dipole target localization problem based on the improved intelligent optimization algorithm at home and abroad shows that for the three-component magnetic field localization problem with a relatively small range, it is easy to converge to the optimal value using the traditional optimization method, but for the parameter When the range is relatively large and the objective function is relatively complex, the traditional optimization algorithm is too sensitive to the initial value, and the target positioning performance is difficult to guarantee.

Through the above analysis, the existing problems and defects in the prior art are: in the case of a relatively large parameter range and a relatively complex objective function, the traditional optimization algorithm is too sensitive to the initial value, and the target positioning performance is difficult to guarantee.

The difficulty of solving the above problems and defects is that it is difficult to quickly and accurately locate the magnetic dipole target under the condition of low signal-to-noise ratio.

The significance of solving the above problems and defects is as follows: the purpose of the present invention is to propose a magnetic dipole positioning method, which is used to solve the problem of low signal-to-noise ratio based on improved intelligent optimization algorithm. Magnetic dipole target positioning accuracy decline, convergence speed The problem of slowness can quickly analyze the target magnetic induction intensity data measured by the magnetic sensor.

SUMMARY OF THE INVENTION

Aiming at the problems existing in the prior art, the present invention provides a magnetic dipole target localization method based on an improved intelligent optimization algorithm.

The present invention is implemented in this way, a magnetic dipole target localization method based on an improved intelligent optimization algorithm, and the magnetic dipole target localization method based on the improved intelligent optimization algorithm includes:

The first step is to use the magnetic dipole model to describe the magnetic induction intensity of the target under far-field conditions, which is the model basis of this scheme;

Step 2, constructing a non-linear equation system for magnetic dipole target positioning based on the improved intelligent optimization algorithm, and determining a fitness function for the intelligent optimization algorithm;

Step 3, using the improved intelligent optimization algorithm for optimization, and realizing the magnetic dipole target location based on the improved intelligent optimization algorithm is the key step of this scheme.

Further, in the first step, the specific process of using the magnetic dipole model to describe the magnetic induction intensity of the target under far-field conditions is as follows:

When the distance between the magnetic sensor and the target is more than 2.5 times the size of the magnetic target, the magnetic target object is regarded as a magnetic dipole;

为磁偶极子的磁矩矢量，m为目标磁矩大小，θ为地磁倾角，

为地磁偏角。此时B点处目标产生的磁感应强度B；在直角坐标系中，将磁感应强度B方程展开。The target position of the magnetic dipole in the coordinate system is A(x ₀ , y ₀ , z ₀ ), the coordinate of the fluxgate sensor is B(x, y, z), and r is the distance from the origin of the magnetic dipole to the magnetic sensor. vector diameter,

is the magnetic moment vector of the magnetic dipole, m is the target magnetic moment, θ is the geomagnetic inclination,

is the magnetic declination angle. At this time, the magnetic induction intensity B generated by the target at point B; in the Cartesian coordinate system, expand the magnetic induction intensity B equation.

Further, the B equation of the magnetic induction intensity generated by the target at the point B is:

Further, the magnetic induction intensity B equation is expanded as:

In the Cartesian coordinate system, the magnetic induction intensity B equation is expanded to get:

where μ ₀ is the permeability of free space, the size is 4π×10 ^-7 H/m, the above formula is a nonlinear equation system containing 6 unknowns, at least two measurement points must be given, and six equations can be constructed to estimate The unknown parameters of the target; in the actual measurement situation, there will be a certain error in the measurement of the magnetic induction value, and the results obtained only by relying on the data of the two monitoring points are not accurate. In order to reduce the error, it is necessary to increase the number of magnetic sensors and Transform it into a nonlinear optimization problem and solve it with an optimization algorithm. .

Further, in the second step, a nonlinear equation system for magnetic dipole target positioning based on an improved intelligent optimization algorithm is constructed, and the specific process is as follows:

然后以误差平方和最小为准则来评估该组未知数，从而得到如下方程：First, a set of unknowns are assumed and substituted into the right half of the expansion of the B equation for the magnetic induction to obtain a set of estimates of the magnetic induction

The set of unknowns is then evaluated with the minimum sum of squared error as the criterion, resulting in the following equation:

所对应的未知量

就是方程的最优解。the estimator that minimizes f

The corresponding unknown

is the optimal solution of the equation.

Further, in the third step, the optimization process using the improved intelligent optimization algorithm is as follows:

First, the initial population is generated through the initialization of the good point set, so that the initial population position is more uniform;

Secondly, the particle swarm position update formula is added to enhance the information exchange and cooperation mechanism between particles;

In addition, changing the probability and Levi's flight is added, so that some particles can change their position according to the Levi's flight, enhance the activity and diversity of the particles, and prevent the algorithm from falling into local optimum.

Further, the initial population is generated by initializing the good point set, and the specific process is:

偏差

的集合称作佳点集，r称为佳点；其中C(r,ε)为常数且只与r,ε(ε＞0)有关，取r_k＝{2cos(2πk/p)}，1≤k≤M，其中p是满足(p-D/2)≥D的最小素数，或r_k＝{exp(k)}，1≤k≤M，{a}是a的小数部分；当计算函数在G_D上积分时，取n个佳点得到的误差是最小的相对于用任意给定的n个点的函数值构成的加权和而已。Suppose G _D is a unit cube in D-dimensional space, suppose r∈G _D , the form is

deviation

The set of is called a good point set, and r is called a good point; where C(r,ε) is a constant and only related to r,ε(ε>0), take r _k ={2cos(2πk/p)}, 1 ≤k≤M, where p is the smallest prime number satisfying (pD/2)≥D, or r _k ={exp(k)}, 1≤k≤M, {a} is the fractional part of a; when the calculation function is in When integrating on G _D , the error obtained by taking n best points is the smallest relative to the weighted sum formed by the function values of any given n points.

Further, the adding change probability and Levi flight, the specific process is:

(1) Using the good point set initialization method to generate the initial position X, given the initial population size N, the maximum number of iterations max_iter, the population dimension D, the learning coefficients c ₁ , c ₂ and other parameters;

(2) Minimize the fitness function, and jump out of the loop after obtaining the optimal solution, the suboptimal solution and the quarterly optimal solution by the gray wolf algorithm;

和

根据PSO-GWO混合算法的位置更新公式更新速度和位置；同时按照概率P_c＝0.5随机选择粒子进行莱维飞行，按照位置更新公式跳出局部最优，来更新速度和位置；(3) Update every cycle

and

Update the speed and position according to the position update formula of the PSO-GWO hybrid algorithm; at the same time, randomly select particles to carry out Levi flight according to the probability P _c =0.5, and jump out of the local optimum according to the position update formula to update the speed and position;

(4) Determine whether the number of iterations is equal to the preset upper limit value, and if so, end the operation; otherwise, jump to (2).

Further, the position update formula of the PSO-GWO hybrid algorithm in the (3) is:

The position update formula in (3) is as follows:

By adding a change probability P _c =0.5, in each iteration, the random number A=rand( ) set in the iteration is compared to determine whether the Levi flight strategy needs to be performed.

Another object of the present invention is to provide a computer device, the computer device includes a memory and a processor, the memory stores a computer program, and when the computer program is executed by the processor, the processor causes the processor to execute the Steps of a magnetic dipole target localization method based on an improved intelligent optimization algorithm.

Another object of the present invention is to provide a computer-readable storage medium storing a computer program, which, when executed by a processor, enables the processor to execute the magnetic dipole target localization based on the improved intelligent optimization algorithm steps of the method.

Another object of the present invention is to provide an information data processing terminal for implementing the magnetic dipole target positioning method based on the improved intelligent optimization algorithm.

Combined with all the above technical solutions, the advantages and positive effects of the present invention are as follows: the present invention selects a hybrid algorithm of two intelligent optimization algorithms, that is, the particle swarm-grey wolf hybrid optimization algorithm based on Levy flight to study the improved intelligent optimization algorithm. Algorithm for the magnetic dipole target localization problem. Aiming at the shortcomings of particle swarm optimization and gray wolf algorithm that are easy to fall into local optimum, an improved particle swarm optimization algorithm is proposed, which improves the defect of particle swarm optimization and gray wolf algorithm falling into local optimum. Introduce the initialization of good point sets when generating the initial population to enhance the diversity and uniformity of the initial population, and introduce adaptive weights when the group position is updated to meet the optimization requirements in different periods. Adding Levi flight can optimize the particle swarm and grayscale. The vitality and jumping ability of the particles in the wolf optimization algorithm are conducive to the particles jumping out of the local optimum.

Description of drawings

FIG. 1 is a flowchart of a method for locating a magnetic dipole target based on an improved intelligent optimization algorithm provided by an embodiment of the present invention.

FIG. 2 is a schematic diagram of a magnetic dipole model provided by an embodiment of the present invention.

FIG. 3 is a schematic diagram of the social level of a gray wolf population provided by an embodiment of the present invention.

FIG. 4 is a schematic diagram of a two-dimensional population distribution generated by initialization of a good point set provided by an embodiment of the present invention.

FIG. 5 is a schematic diagram of a two-dimensional population distribution generated by random initialization according to an embodiment of the present invention.

FIG. 6 is a flowchart of an algorithm provided by an embodiment of the present invention.

FIG. 7 is a schematic diagram of a 1×4 node detection array provided by an embodiment of the present invention.

FIG. 8 is a schematic diagram of a target moving to a position A according to an embodiment of the present invention.

FIG. 9 is a schematic diagram illustrating a comparison of positioning errors of different algorithms under different signal-to-noise ratios provided by an embodiment of the present invention.

FIG. 10 is a schematic diagram of the change trend of the convergence curves of the three algorithms under the condition that the signal-to-noise ratio is changed from -5dB to 35dB when the number of iterations is 100 according to an embodiment of the present invention.

In Figure 10: Figure a, the convergence curve of experiment 1; Figure b, the convergence curve of experiment 2; Figure c, the convergence curve of experiment 3; Figure d, the convergence curve of experiment 4; Figure e, the convergence curve of experiment 5.

Detailed ways

In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention, but not to limit the present invention.

In view of the problems existing in the prior art, the present invention provides a magnetic dipole target positioning method based on an improved intelligent optimization algorithm. The present invention is described in detail below with reference to the accompanying drawings.

The magnetic dipole target localization method based on the improved intelligent optimization algorithm provided by the present invention can also be implemented by those skilled in the industry by other steps. The magnetic dipole target localization method based on the improved intelligent optimization algorithm provided by the present invention in FIG. 1 Just one specific example.

As shown in FIG. 1, the magnetic dipole target positioning method based on the improved intelligent optimization algorithm provided by the embodiment of the present invention includes:

S101: Use the magnetic dipole model to describe the magnetic induction intensity of the target under far-field conditions;

S102: Construct a nonlinear equation system for magnetic dipole target positioning based on an improved intelligent optimization algorithm;

S103: Use the improved intelligent optimization algorithm to perform optimization, and realize the magnetic dipole target localization based on the improved intelligent optimization algorithm.

In S101 provided by the embodiment of the present invention, the specific process of using the magnetic dipole model to describe the magnetic induction intensity of the target under far-field conditions is as follows:

When the distance between the magnetic sensor and the target is more than 2.5 times the size of the magnetic target, the magnetic target object is regarded as a magnetic dipole;

为地磁偏角。The target position of the magnetic dipole in the coordinate system is A(x ₀ , y ₀ , z ₀ ), the coordinate of the fluxgate sensor is B(x, y, z), and r is the distance from the origin of the magnetic dipole to the magnetic sensor. vector radius, m is the magnetic moment vector of the magnetic dipole, θ is the geomagnetic dip,

is the magnetic declination angle.

At this time, the B equation of the magnetic induction intensity generated by the target at point B is:

In the Cartesian coordinate system, the magnetic induction intensity B equation is expanded to get:

where μ ₀ is the permeability of free space, the size is 4π×10 ^-7 H/m, the above formula is a nonlinear equation system containing 6 unknowns, at least two measurement points must be given, and six equations can be constructed to estimate The unknown parameters of the target; in the actual measurement situation, there will be a certain error in the measurement of the magnetic induction value, and the results obtained only by relying on the data of the two monitoring points are not accurate. In order to reduce the error, it is necessary to increase the number of magnetic sensors and Transform it into a nonlinear optimization problem and solve it with an optimization algorithm.

In S102 provided by the embodiment of the present invention, a nonlinear equation system for magnetic dipole target positioning based on an improved intelligent optimization algorithm is constructed, and the specific process is as follows:

然后以误差平方和最小为准则来评估该组未知数，从而得到如下方程：First, a set of unknowns are assumed and substituted into the right half of the expansion of the B equation for the magnetic induction to obtain a set of estimates of the magnetic induction

The set of unknowns is then evaluated with the minimum sum of squared error as the criterion, resulting in the following equation:

所对应的未知量

就是方程的最优解。the estimator that minimizes f

The corresponding unknown

is the optimal solution of the equation.

In S103 provided by the embodiment of the present invention, the optimization process using the improved intelligent optimization algorithm is as follows:

First, the initial population is generated through the initialization of the good point set, so that the initial population position is more uniform;

Secondly, the particle swarm position update formula is added to enhance the information exchange and cooperation mechanism between particles;

In addition, changing the probability and Levi's flight is added, so that some particles can change their position according to the Levi's flight, enhance the activity and diversity of the particles, and prevent the algorithm from falling into local optimum.

The initial population is generated through the initialization of the good point set, and the specific process is as follows:

偏差

的集合称作佳点集，r称为佳点；其中C(r,ε)为常数且只与r,ε(ε＞0)有关，取r_k＝{2cos(2πk/p)}，1≤k≤M，其中p是满足(p-D/2)≥D的最小素数，或r_k＝{exp(k)}，1≤k≤M，{a}是a的小数部分。当计算函数在G_D上积分时，取n个佳点得到的误差是最小的相对于用任意给定的n个点的函数值构成的加权和而已。Suppose G _D is a unit cube in D-dimensional space, suppose r∈G _D , the form is

deviation

The set of is called a good point set, and r is called a good point; where C(r,ε) is a constant and only related to r,ε(ε>0), take r _k ={2cos(2πk/p)}, 1 ≤k≤M, where p is the smallest prime number satisfying (pD/2)≥D, or r _k ={exp(k)}, 1≤k≤M, and {a} is the fractional part of a. When the computing function is integrated over G _D , the error obtained by taking n optimal points is the smallest relative to the weighted sum formed by the function values of any given n points.

The adding change probability and Levi flight, the specific process is:

(1) Using the good point set initialization method to generate the initial position X, given the initial population size N, the maximum number of iterations max_iter, the population dimension D, the learning coefficients c ₁ , c ₂ and other parameters;

(2) Minimize the fitness function, and jump out of the loop after obtaining the optimal solution, the suboptimal solution and the quarterly optimal solution by the gray wolf algorithm;

和

根据PSO-GWO混合算法的位置更新公式更新速度和位置；同时按照概率P_c＝0.5随机选择粒子进行莱维飞行，按照位置更新公式跳出局部最优，来更新速度和位置；(3) Update every cycle

and

Update the speed and position according to the position update formula of the PSO-GWO hybrid algorithm; at the same time, randomly select particles to carry out Levi flight according to the probability P _c =0.5, and jump out of the local optimum according to the position update formula to update the speed and position;

(4) If the iteration stop condition is not reached, update the speed and position of the particle according to the third step, and then start the calculation from the second step, and perform (3) after the loop is completed until the end condition is reached.

The position update formula of the PSO-GWO hybrid algorithm in (3) is:

The position update formula in (3) is as follows:

By adding a change probability P _c =0.5, in each iteration, the random number A=rand( ) set in the iteration is compared to determine whether the Levi flight strategy needs to be performed.

The technical solutions of the present invention will be described in detail below with reference to specific embodiments.

1 Magnetic dipole target localization model based on improved intelligent optimization algorithm

1.1 Magnetic Dipole Model

For a magnetic target object, when the distance between the magnetic sensor and the target is greater than 2.5 times the size of the magnetic target, the magnetic target object can be regarded as a magnetic dipole.

As shown in Figure 2, the target position of the magnetic dipole in the coordinate system is A(x ₀ , y ₀ , z ₀ ), the coordinate of the fluxgate sensor is B(x, y, z), and r is the magnetic dipole From the origin to the vector radius of the magnetic sensor, m is the magnetic moment vector of the magnetic dipole. At this time, the magnetic induction intensity B generated by the target at point B is:

In the Cartesian coordinate system, formula (1) can be expanded to get:

where μ ₀ is the permeability of free space, and the size is 4π×10 ^-7 H/m. Equation (2) is a nonlinear equation system containing 6 unknowns. Obviously, at least two measurement points must be given, so at least There are six equations. However, in the actual measurement situation, there will be a certain error in the measurement of the magnetic induction intensity value. Secondly, the results obtained only by relying on the data of two monitoring points are not accurate. In order to reduce the error, the number of magnetic sensors should be appropriately increased, assuming that there are 4 magnetic sensor, convert it into a nonlinear optimization problem and solve it using an optimization algorithm.

1.2 Determination of the objective function

然后以误差平方和最小为准则来评估该组未知数，从而得到如下方程：For the system of equations in the previous section, you can think of it as a nonlinear least squares problem. First, a set of unknowns is assumed and substituted into the right half of equation (2) to obtain a set of estimates of the magnetic induction

The set of unknowns is then evaluated with the minimum sum of squared error as the criterion, resulting in the following equation:

所对应的未知量

就是方程的最优解。the estimator that minimizes f

The corresponding unknown

is the optimal solution of the equation.

2 Magnetic dipole target localization method based on improved intelligent optimization algorithm

2.1 Localization algorithm based on gray wolf optimization

The gray wolf optimization algorithm is a swarm intelligence optimization algorithm proposed by Mirjalili et al. in 2014. The algorithm is a heuristic algorithm proposed to simulate the social hierarchy and hunting behavior of gray wolves in nature. There is a social hierarchy representing power and domination in gray wolves. The system divides wolves into α wolves, β wolves, δ wolves, and ω wolves, as shown in Figure 3, where α wolves are the highest-ranked wolf group, other wolves need to obey the orders of α wolves, and β wolves obey α wolves The wolf also assists the alpha wolf in decision-making, while the delta wolf is the subordinate wolf of the beta wolf and must obey the orders of the alpha wolf and the beta wolf. In addition to being strictly hierarchical, gray wolves also have hunting characteristics, which mainly include surrounding prey, chasing prey, and attacking prey.

(1) Surrounding the prey

The six parameters of the optimal solution of the fitness function are used as the prey. When the gray wolf group finds the prey, it will quickly approach and surround the prey. The position of the gray wolf is updated as follows (6) (assuming the search space is d-dimensional):

X(t)={X _i (t)|i=1,2,...,d} (4)

X(t+1) ⁼ XP(t)-AD(6)

where X(t) represents the location of the t-th generation gray wolf population, X ^P (t) represents the location of the t-th generation prey, D represents the distance vector between the gray wolf population and the prey, and A and C represent the coefficient vectors.

A=2ar ₁ -a (7)

C=2r ₂ (8)

In formulas (7) (8) (9): r ₁ , r ₂ are uniformly distributed random numbers from 0 to 1, a is a convergence factor, which decreases linearly from 2 to 0, and max_iter is the maximum number of iterations.

(2) Pursue prey

When the gray wolf surrounds the prey, the hunting behavior begins. During hunting, since the alpha wolf, beta wolf, and delta wolf are more sensitive to the prey, other gray wolves will The distances between them are D _α , D _β , D _δ , calculate the moving distances X ₁ , X ₂ , X ₃ of the self toward α wolf, β wolf, and δ wolf respectively, and move toward the encircling circle of the three, update the formula Such as (10)(11)(12):

X ₁ =X ^α -AD ^α

X ₂ =X ^β -AD ^β (11)

X ₃ =X ^δ -AD ^δ

where i=1,2,3...,d, X(t+1) represents the position update of ω wolf.

(3) Attack the prey

When the prey stops moving, the gray wolf starts to attack the prey. The mathematical description of this process is that when the value of A is outside the range of [-1, 1], the search agent randomly conducts the search agent at the current position of the gray wolf and the optimal solution. Search, when the value of A is within the range of [-1,1], the optimal solution must be found

2.2 PSO-based positioning algorithm

越小时，取得位置精度越好，定位越准确。当种群规模为N，维度为D时，粒子X的位置可以表示为X_i＝(x_i1,x_i2,...,x_id,...,x_iD)，其中x_id表示第i维的第d个分量，粒子X的速度为V_i＝(v_i1,v_i2,...,v_id,...,v_iD)，其中v_id表示第i维的第d个速度，粒子的位置和速度更新公式如下(13)(14)：The PSO algorithm is an optimization algorithm of swarm intelligent random search proposed by the foraging behavior of birds. Each particle can be regarded as an individual in the d-dimensional search space, and the current position of the particle corresponds to an optimization nonlinear problem. The candidate solution, the flight process of the particle in the search space is the search process of the individual. When the particle is initialized, it has two properties: position and speed. The particles in the initialization have an initial speed and position. Each time the algorithm iterates, the particle determines the value of itself and its neighbors according to its own experience and the experience of adjacent particles. The optimal position of the particle to update its position. In addition, each particle has a fitness value corresponding to its own position. When the fitness function

The smaller the value, the better the obtained position accuracy and the more accurate the positioning. When the population size is N and the dimension is D, the position of particle X can be expressed as X _i =(x _i1 ,x _i2 ,...,x _id ,...,x _iD ), where x _id represents the i-th dimension The d-th component of , the velocity of particle X is _Vi = (v _i1 ,v _i2 ,...,v _id ,...,v _iD ), where v _id represents the d-th velocity of the i-th dimension, the particle The position and velocity update formulas of are as follows (13) (14):

w=wmax-(t/max_iter)*(wmax-wmin) (15)

表示个体极值，

表示全局极值，t表示当前的迭代次数，c₁,c₂为学习因子，通常设置c₁＝c₂＝2，r₁，r₂为0到1的均匀分布的随机数，式(15)w为惯性权值，权重的取值越大，全局搜索能力越强，取值越小，局部搜索能力越强，取值范围一般为(0,4)。where j=1,2,...,d,

represents the individual extreme value,

represents the global extreme value, t represents the current number of iterations, c ₁ , c ₂ are learning factors, usually set c ₁ =c ₂ =2, r ₁ , r ₂ are uniformly distributed random numbers from 0 to 1, formula (15 )w is the inertia weight, the larger the value of the weight, the stronger the global search ability, the smaller the value, the stronger the local search ability, the value range is generally (0,4).

2.3 Levi flight

The Levy flight is a random search walk method used to describe the Levy distribution. Many studies have shown that the behavior of many insects and animals in nature conforms to the Levy distribution. The Levy flight mainly uses the Mantegna algorithm, which is used to generate a random step size that conforms to the Levy distribution. local optimum.

The position update formula of Levi's flight is as follows (16):

是表示第i个粒子在迭代第t次的位置，为初始位置，

表示更新后的位置，

表示点乘运算，α代表步长控制量，Levy(λ)表示随机搜索路径，并且Levy(λ)满足下式(17)：where: i∈[1,2,...,N], where

is the position of the i-th particle at the t-th iteration, which is the initial position,

represents the updated location,

represents the point multiplication operation, α represents the step size control amount, Levy(λ) represents the random search path, and Levy(λ) satisfies the following formula (17):

Levy(λ)～μ=t ^-λ , 1<λ≤3 (17)

The step size of the Levy flight belongs to the Levy distribution, and the formula for the step size s is Equation (18):

Among them, μ, v belong to the normal distribution as follows:

Among them, σ _μ , σ _v are respectively the following formulas (21) (22):

_σv = 1 (22)

The value of β is usually 1.5.

2.4 Magnetic Dipole Localization Algorithm Based on PSO-GWO Hybrid

Since the gray wolf group of the gray wolf algorithm follows the commands of alpha wolves, beta wolves, and delta wolves to hunt, but each individual is independent, there is no useful information exchange between gray wolves and the group, so useful information is not used. , causing the algorithm to converge too slowly and the accuracy is not high, so the position update formula in the particle swarm algorithm is introduced into the position update formula of the gray wolf algorithm, so as to make use of useful information, this hybrid algorithm has memory and cooperation mechanism . In addition, the inertia constant w is introduced to adjust the local optimization ability and global optimization ability of the hybrid algorithm of gray wolf particle swarm. Therefore, the position update and gray wolf distance formula of the hybrid algorithm are as follows (23) (24):

2.5 Improved PSO-GWO Algorithm

2.5.1 Best point set initialization

偏差

的集合称作佳点集，r称为佳点。其中C(r,ε)为常数且只与r,ε(ε＞0)有关，取r_k＝{2cos(2πk/p)}，1≤k≤M，其中p是满足(p-D/2)≥D的最小素数，或r_k＝{exp(k)}，1≤k≤M，{a}是a的小数部分。理论证明，当计算函数在G_D上积分时，取n个佳点得到的误差是最小的相对于用任意给定的n个点的函数值构成的加权和而已。The definition of good point set is: Suppose G _D is a unit cube of D-dimensional space, and suppose r∈G _D , the form is

deviation

The set of is called the good point set, and r is called the good point. where C(r,ε) is a constant and is only related to r,ε(ε>0), take r _k ={2cos(2πk/p)}, 1≤k≤M, where p is satisfying (pD/2) The smallest prime number ≥D, or r _k ={exp(k)}, 1≤k≤M, and {a} is the fractional part of a. Theoretically, when the calculation function is integrated on G _D , the error obtained by taking n optimal points is the smallest relative to the weighted sum formed by the function values of any given n points.

Figure 4 and Figure 5 respectively show the two-dimensional initial population distribution diagrams with a population size of 100 generated by using the good point set initialization method and the random initialization method.

It can be seen from the figure that in the case of taking 100 points, the optimal point set initialization is more uniform than the population distribution generated by random initialization. Secondly, the population distribution of the good point set has nothing to do with the dimension, which can be well adapted to high-dimensional problems; In addition, when the optimal point set is initialized, the population distribution effect is the same every time, and it has high stability. Therefore, by mapping the best points of _GD to the target solution space, a more uniform point selection method can be obtained. Since the PSO-GWO hybrid algorithm obtains the optimal solution by moving the particles in the solution space, after iteration, the local optimum is constantly approaching the global optimum, so if the population falls into premature convergence at this time, the algorithm will not be able to find the global optimum. However, through the optimal point set initialization method, the particles can be evenly distributed in the solution space around the current optimal position of the population, which can more effectively characterize the solution space characteristics, so that the initial population maintains a good diversity, so as to avoid the algorithm falling into the local optimum. , and eventually converge to the global optimum.

2.5.2 Adding Individual Optimal Memory and Levi's Flight

Since the gray wolf algorithm is easy to fall into the local optimum, adding the experience of individual particle historical optimum into the GWO algorithm can improve the distribution of particles, but the improved PSO-GWO still has the disadvantage of falling into the local optimum. Levy flight takes into account the short-distance search and the occasional long-distance step size, which can break the particle "clustering" situation, improve the activity and jumping ability of the population particles, and fundamentally improve the PSO-GWO hybrid algorithm. optimal defect. Based on the Levi flight strategy, the position update formula is expressed as the following formula (25):

By adding a change probability P _c =0.5, in each iteration, the random number A=rand( ) set in the iteration is compared to determine whether the Levi flight strategy needs to be performed.

The specific steps of the whole improved PSO-GWO algorithm are as follows:

(1) Using the good point set initialization method to generate the initial position X, given the initial population size N, the maximum number of iterations max_iter, the population dimension D, the learning coefficients c ₁ , c ₂ and other parameters;

(2) Minimize the fitness function, and jump out of the loop after obtaining the optimal solution, the suboptimal solution and the quarterly optimal solution by the gray wolf algorithm;

和

根据式子(23)更新速度和位置；同时按照概率P_c＝0.5随机选择粒子进行莱维飞行，按照式(25)跳出局部最优，来更新速度和位置；(3) Update every cycle

and

Update speed and position according to formula (23); at the same time randomly select particles to carry out Levi flight according to probability P _c =0.5, and jump out of the local optimum according to formula (25) to update speed and position;

(4) Determine whether the number of iterations is equal to the preset upper limit value, and if so, end the operation; otherwise, jump to (2).

The technical solution of the present invention is described in detail below in conjunction with simulation experiments.

In order to verify the magnetic dipole localization performance of the PSO-GWO hybrid algorithm based on Levy flight, the magnetic dipole target localization simulation system based on the improved intelligent optimization algorithm is used for analysis. As shown in Figure 7, a Cartesian coordinate system is established with the No. 1 sensor node as the origin, and the positions of the remaining three magnetic sensors are shown in Figure 7. Assuming that the magnetic dipole moves to point A (see Figure 8), its position and angle information (see Table 1) is given, and then the three-component value of the magnetic induction intensity at each node is deduced by substituting the formula, and these coordinate values are used as the algorithm's Entry parameters, the parameter estimation accuracy can be measured by the mean square error, the formula is:

It is assumed that the actual parameter of the magnetic target is x, x _i is the estimated result of the ith experiment, and N is the total number of Monte Carlo simulations.

学习因子c₁＝c₂＝c₃＝0.5，PSO算法的参数设置为c₁＝c₂＝2，w＝0.8，PSO-GWO算法的参数设置为wmax＝0.9，wmin＝0.2，其中莱维飞行中的beta＝1.5，随机跳出的概率P_c＝0.5，因为实际传感器测量数据中包含噪声，所以设置信噪比SNR从-5dB每隔10dB变换到35dB，最大迭代次数max_iter为100次，种群规模N为60。蒙特卡洛仿真次数为50次，计算均方根误差值用于不同算法的性能比较。The algorithm parameters are set as follows: There are four magnetic sensors and the positions of the sensors are as shown in the figure above. The control ranges of the parameters are: x∈[0,10], y∈[0,10], z∈[0,10] ,m∈[0,2000],θ∈[0,π/2],

The learning factor c ₁ =c ₂ =c ₃ =0.5, the parameters of the PSO algorithm are set as c ₁ =c ₂ =2,w=0.8,the parameters of the PSO-GWO algorithm are set as wmax=0.9,wmin=0.2, where Levy beta=1.5 in flight, the probability of random jumping out P _c =0.5, because the actual sensor measurement data contains noise, so set the signal-to-noise ratio SNR from -5dB every 10dB to 35dB, the maximum number of iterations max_iter is 100 times, the population The scale N is 60. The number of Monte Carlo simulations is 50, and the root mean square error value is calculated for the performance comparison of different algorithms.

Table 1 The parameter values of the target moving to point A

The target localization results under different signal-to-noise ratios obtained by applying PSO, GWO and the improved PSO-GWO algorithm proposed in the present invention are shown in Figure 9. It can be seen from Figure 9 that in the case of a very low signal-to-noise ratio, it is different from GWO and GWO. Compared with the PSO algorithm, the PSO-GWO algorithm can maintain high precision, and when the signal-to-noise ratio SNR=35, the positioning error of the PSO-GWO algorithm can be reduced to 0.01. Whether it is low SNR or high SNR, the solution performance of PSO-GWO algorithm is better than that of PSO algorithm and GWO algorithm.

In addition, Fig. 10(a)-Fig. 10(e) clearly show the changing trend of the convergence curves of the three algorithms when the SNR is changed from -5dB to 35dB when the number of iterations is 100. For each SNR case, the convergence speed of the PSO-GWO algorithm is better than the other two algorithms. From the above results, it can be seen that the proposed PSO-GWO is better than the other two algorithms in terms of solution accuracy and convergence speed.

Conclusion: The present invention studies a magnetic dipole target location method based on an improved intelligent optimization algorithm. By using the good point set initialization method to initialize the gray wolf particle swarm population, and then adding the particle cooperation mechanism of the PSO algorithm to improve the information utilization rate of the gray wolf algorithm, adding change probability and Levi flight to improve the activity of particles and maintain the diversity of particles Compared with the positioning results of the PSO algorithm and the GWO algorithm, the improved algorithm has a great improvement in the convergence speed and solution accuracy. It is verified that Improving the effectiveness of PSO-GWO algorithm at low signal-to-noise ratio.

It should be noted that the embodiments of the present invention may be implemented by hardware, software, or a combination of software and hardware. The hardware portion may be implemented using special purpose logic; the software portion may be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or specially designed hardware. Those of ordinary skill in the art will appreciate that the apparatus and methods described above may be implemented using computer-executable instructions and/or embodied in processor control code, for example on a carrier medium such as a disk, CD or DVD-ROM, such as a read-only memory Such code is provided on a programmable memory (firmware) or a data carrier such as an optical or electronic signal carrier. The device and its modules of the present invention can be implemented by hardware circuits such as very large scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, etc., or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., It can also be implemented by software executed by various types of processors, or by a combination of the above-mentioned hardware circuits and software, such as firmware.

The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited to this. Any person skilled in the art is within the technical scope disclosed by the present invention, and all within the spirit and principle of the present invention Any modifications, equivalent replacements and improvements made within the scope of the present invention should be included within the protection scope of the present invention.

Claims (10)

1. A magnetic dipole target positioning method based on an improved intelligent optimization algorithm is characterized by comprising the following steps:

step one, describing the magnetic induction intensity of a target by adopting a magnetic dipole model under a far field condition;

constructing a magnetic dipole target positioning nonlinear equation set based on an improved intelligent optimization algorithm;

and step three, optimizing by using an improved intelligent optimization algorithm, and realizing magnetic dipole target positioning based on the improved intelligent optimization algorithm.

2. The method for positioning the magnetic dipole target based on the improved intelligent optimization algorithm according to claim 1, wherein in the step one, the specific process of describing the magnetic induction intensity of the target by using the magnetic dipole model under the far-field condition is as follows:

when the distance between the magnetic sensor and the target is more than 2.5 times of the size of the magnetic target, the magnetic target object is regarded as a magnetic dipole;

the target position of the magnetic dipole in the coordinate system is A (x)₀,y₀,z₀) The coordinates of the fluxgate sensor are B (x, y, z), r is the vector from the origin of the magnetic dipole to the magnetic sensor,

is the magnetic moment vector of the magnetic dipole, m is the target magnetic moment, theta is the geomagnetic inclination angle,

is the magnetic declination. The magnetic induction intensity B generated by the target at the point B; and in a rectangular coordinate system, developing a magnetic induction intensity B equation.

3. The improved intelligent optimization algorithm-based magnetic dipole target positioning method as claimed in claim 2, wherein the magnetic induction intensity B equation generated by the target at the B point is as follows:

4. the improved intelligent optimization algorithm-based magnetic dipole target positioning method according to claim 2, wherein the magnetic induction intensity B equation is developed as follows:

in a rectangular coordinate system, developing a magnetic induction intensity B equation to obtain:

wherein mu₀A free space permeability of 4 π × 10^-7H/m, the above formula is a nonlinear equation set containing 6 unknowns, and at least two measurement points are required to be provided, six equations are constructed, and the target parameters can be solved; under the actual measurement condition, certain errors exist in the measurement of the magnetic induction intensity value, the result obtained by only depending on the data of two monitoring points is not accurate, in order to reduce the errors, the number of the magnetic sensors needs to be increased, the magnetic sensors are converted into a nonlinear optimization problem, and then an optimization algorithm is utilized to solve the problem.

5. The method for positioning the magnetic dipole target based on the improved intelligent optimization algorithm of claim 1, wherein in the second step, the specific process of constructing the magnetic dipole target positioning nonlinear equation set based on the improved intelligent optimization algorithm comprises the following steps:

first, a set of possible target parameters are substituted into the magnetic dipole model to obtain a set of estimates of the magnetic induction intensity

The set of unknowns is then evaluated on the criterion of least sum of squared errors, resulting in the following equation:

so that f takes the minimum value

Corresponding unknown quantity

Is the optimal solution of the equation.

6. The method for positioning magnetic dipole targets based on the improved intelligent optimization algorithm of claim 1, wherein in the third step, the optimization process by using the improved intelligent optimization algorithm comprises:

firstly, initializing to generate an initial population through a good point set, so that the position of the initial population is more uniform;

secondly, adding a particle swarm position updating formula to enhance the information exchange and cooperation mechanism among the particles;

in addition, the probability change and the Levy flight are added, so that a part of particles can change the positions of the particles according to the Levy flight.

7. The method for positioning the magnetic dipole target based on the improved intelligent optimization algorithm according to claim 6, wherein the specific process of generating the initial population through the initialization of the optimal point set comprises the following steps: g_DIs a unit cube of D-dimensional space, assuming r ∈ G_DIn the shape of

Deviation of

The set of (a) is called a set of vertices, r is called a vertex; wherein C (r, epsilon) is constant and is only related to r, epsilon (epsilon > 0), taking r_k1 ≦ k ≦ M where p is the smallest prime number that satisfies (p-D/2) ≧ D, or r_k1 ≦ k ≦ M, and { a } is the fractional portion of a; when the calculation function is in G_DWhen the integration is carried out, the error obtained by taking n optimal points is the smallest relative to the weighted sum formed by the function values of any given n points;

the specific process of adding the change probability and the Levy flight is as follows:

(1) generating an initial position X by using a good point set initialization method, setting an initial population scale N, a maximum iteration number max _ iter, a population dimension D and a learning coefficient c₁,c₂The like;

(2) the fitness function is minimized, and the cycle is skipped after the optimal solution, the suboptimal solution and the quarterly optimal solution are obtained by the gray wolf algorithm;

(3) update at each cycle

And

updating the speed and the position of the population according to a position updating formula of a PSO-GWO hybrid algorithm; according to the probability P at the same time_cRandomly selecting particles to carry out Levin flight according to 0.5, and jumping out the local optimum according to a position updating formula to update the speed and the position;

(4) judging whether the iteration times are equal to a preset upper limit value or not, and if so, ending the operation; otherwise, jumping to (2);

the position updating formula of the PSO-GWO hybrid algorithm in the step (3) is as follows:

the position update formula in (3) is as follows:

by adding change probability P_cAnd (0.5), comparing the random number A (rand () set in iteration) at each iteration to judge that the Laey flight strategy is not needed.

8. A computer arrangement, characterized in that the computer arrangement comprises a memory and a processor, the memory storing a computer program, which when executed by the processor causes the processor to carry out the steps of the improved intelligent optimization algorithm based magnetic dipole target localization method according to any one of claims 1 to 7.

9. A computer readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of the improved intelligent optimization algorithm-based magnetic dipole target location method according to any one of claims 1 to 7.

10. An information data processing terminal, characterized in that the information data processing terminal is used for implementing the magnetic dipole target positioning method based on the improved intelligent optimization algorithm of any one of claims 1 to 7.

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