A method for locating magnetic targets based on the vertical difference of the total geomagnetic field

Abstract

The application discloses a magnetic target positioning method based on geomagnetic total field vertical difference, utilizes a rotor unmanned aerial vehicle to carry an inertial navigation system and two vertically distributed optical pumping magnetometers, simultaneously measures geomagnetic total field data containing magnetic anomalies and real-time position data of the unmanned aerial vehicle when flying along a survey line, regards the magnetic target as a static magnetic dipole, takes the centers of the two optical pumps at the initial position as a coordinate origin, uses the magnetic moment of the magnetic target, position coordinates, known geomagnetic inclination and geomagnetic declination and real-time position coordinates of the two optical pumps to respectively represent the magnetic anomaly fields generated by the magnetic target at the positions of the two optical pumps, calculates the geomagnetic total field vertical difference of each point on the survey line by using the measurement values of the two optical pumps, jointly constructs a target function by using the magnetic anomaly difference values generated by the magnetic target at the positions of the two optical pumps, and estimates the position of the magnetic target by using a cuckoo optimization algorithm.

Description

Technical Field

[0001] This invention belongs to the field of underground magnetic target location, and specifically refers to a method for locating magnetic targets based on the vertical difference of the total geomagnetic field. Background Technology

[0002] Magnetic detection technology, as a crucial component of geomagnetic field research, plays a vital role in energy exploration, underwater pipeline location, shipwreck rescue, anti-submarine warfare, and unexploded ordnance detection. In these applications, determining the target's location and size is critical for subsequent operations. Advances in magnetic detection equipment and technology have made obtaining high-precision magnetic anomaly data possible. Therefore, researching how to utilize magnetic detection technology for target tracking and location has significant academic and practical value.

[0003] Magnetometers used in magnetic measurement technology are divided into vector magnetometers and scalar magnetometers. Vector magnetometers mainly include fluxgate magnetometers and MEMS magnetometers. During installation, the three axes need to be strictly calibrated, and during use, the attitude information of the magnetometer needs to be strictly measured.

[0004] Total field magnetometers employ optically pumped magnetometers, offering higher resolution and accuracy, longer detection ranges for magnetic targets, and requiring only the avoidance of dead angles in their operating posture. Therefore, total field magnetometers offer advantages such as high positioning accuracy, long positioning distance, and convenience and reliability in target location measurement. However, current total field positioning methods typically employ at least four optically pumped magnetometers in a measurement array, with each pair of magnetometers requiring strict perpendicularity between their measurement axes. These stringent installation and operation requirements, along with the excessive number of magnetometers, severely limit their application. Furthermore, an excessive number of magnetometers introduces more complex sensor noise, impacting target positioning accuracy. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a magnetic target positioning method based on the vertical difference of the total geomagnetic field, which overcomes the limitations of existing target positioning methods, especially the problems of complex installation and operation, large data processing volume, and low positioning accuracy caused by the use of optically pumped magnetometer arrays in existing methods.

[0006] This invention is implemented as follows:

[0007] A method for locating magnetic targets based on the vertical difference of the total geomagnetic field, the method comprising:

[0008] The airborne magnetic measurement system is equipped with two optically pumped magnetometers arranged vertically. The inertial navigation system is installed above the axis of the total field magnetometer. The center point of the axes of the two optically pumped magnetometers at the initial position of the airborne magnetic measurement system is taken as the origin of the system coordinate system. The direction of the airborne magnetic measurement system along the measurement line is the positive X-axis, and the vertical downward direction is the positive Z-axis. According to the right-hand rule, the positive Y-axis is perpendicular to the xoy plane to the right. The coordinates of each measurement point on the measurement line are obtained by the positioning system. The real-time position coordinates of the two optically pumped magnetometers are determined based on the distance from the optically pumped magnetometer to the positioning system.

[0009] The magnetic target is regarded as a stationary magnetic dipole. The center of the two optically pumped magnetometers at the initial position is taken as the origin of the coordinate system. The magnetic moment, position coordinates, known geomagnetic tilt and declination, and real-time position coordinates of the two optically pumped magnetometers are used to represent the magnetic anomaly field generated by the magnetic target at the position of the two optically pumped magnetometers.

[0010] The vertical difference of the total geomagnetic field at each point on the survey line is calculated based on the measurements of the two optically pumped magnetometers. This difference is then combined with the difference in magnetic anomalies generated by the magnetic target at the two optically pumped magnetometers to construct an objective function. The objective function is minimized using the Cuckoo Search algorithm to obtain the position coordinates and magnetic moment modulus of the magnetic target.

[0011] Furthermore, the calculation process for the difference in magnetic anomalies generated by the magnetic target at the two optically pumped magnetometers includes:

[0012] Assuming the magnetic target is on one side of the survey line, its position coordinates are represented as (x... s ,y s ,z s At a distance R from the magnetic target, the magnetic anomaly field generated by the magnetic target is:

[0013]

[0014] In the formula It is the distance from the magnetic target to the measuring point, M = [M x M y M z ]′ is the magnetic moment vector of the magnetic target, μ0=4π×10 -7 Let R be the free permeability, then R = [x] s -x,y s -y,z s -z]′ represents the distance from the magnetic target to the measuring point (x). s ,y s ,z s The distance vector of );

[0015] Find the magnetic anomaly field B a The projection ΔB in the direction of the geomagnetic field is:

[0016]

[0017] In the formula, u is the unit vector of the geomagnetic field direction, and |M| is the magnitude of the magnetic moment of the magnetic target.

[0018] The position coordinates of the two optically pumped magnetometers are (x s1 ,y s1 ,z s1 ), (x s1 ,y s1 ,z s1 Then, the projections of the magnetic anomaly field generated by the magnetic target at the optically pumped magnetometer onto the direction of the geomagnetic field are calculated as follows:

[0019]

[0020]

[0021] In the formula, R1 and R2 are the distances from the magnetic target to the first optically pumped magnetometer and the second optically pumped magnetometer, respectively;

[0022] The difference in the projections of the magnetic anomalies generated by the magnetic target at the two optically pumped magnetometers onto the direction of the Earth's magnetic field is calculated as follows:

[0023] ΔB a,12 | Theory =ΔB a1 -ΔB a2 .

[0024] Furthermore, based on the measurements from the two optical pump magnetometers, the vertical difference in the total geomagnetic field at each point along the survey line is calculated, including:

[0025] The data obtained from the two optically pumped magnetometers are expressed as follows:

[0026] B d1 =B a +B b +ΔB a1 B d2 =B a +B b +ΔB a2

[0027] Subtracting the two optical pump measurements eliminates the effects of geomagnetic variation and spatial inhomogeneity of the geomagnetic field, i.e.:

[0028] ΔB d,12 | Mensure =B d1 -B d1 =ΔB a1 -ΔB a2 .

[0029] Furthermore, the objective function is constructed as follows:

[0030] in, Represents the i-th ΔBd ,12 | Mensure , Indicates the i-th ΔB a,12 | Theory .

[0031] Furthermore, by minimizing the objective function using the cuckoo search algorithm, the position coordinates and magnetic moment magnitude of the magnetic target are obtained, including:

[0032] The four parameters of the magnetic target are defined as a 4-dimensional variable bird's nest, namely the position coordinates (x, y, z) and the magnitude of the magnetic moment |M|. The population size n is set, the population is initialized, and the initial positions of the bird's nests are randomly generated.

[0033] The fitness value of each bird's nest is determined based on the objective function, and the bird's nest with the best fitness value is selected as the globally optimal bird's nest location. The location of the next-generation Bird's Nest stadium will be updated;

[0034] Calculate the fitness value of the objective function. If the value is better than the objective function of the previous generation, update the bird's nest position; otherwise, keep the original position unchanged.

[0035] After updating the location, a randomly generated value R, following a uniform distribution from 0 to 1, is compared with the probability pa of the nest director discovering the foreign bird's egg. If R > pa, then... The nest locations are randomly changed, or left unchanged otherwise. The set of nest locations with the best fitness value is then retained, denoted as... Update the location of the next generation of Bird's Nest according to the following formula.

[0036]

[0037] In the formula This represents the position of the i-th bird's nest, i = 1, 2, 3, ..., n, in generation t. Let represent point-to-point multiplication, α represent the step size control variable used to control the step size. Typically, α is 1. levy(λ) is the Levy random search path, which is a random walk using the Levy flight mechanism. Its step size follows a heavy-tailed stable distribution, while the random step size follows a Levy distribution.

[0038] Levy:μ=t -λ ,1≤λ≤3

[0039] Determine if the algorithm meets the set maximum number of iterations. If it does, end the iterative optimization and output the globally optimal Bird's Nest location. and optimal solution Otherwise, continue iterative optimization until the globally optimal bird's nest position is found, which is the position coordinates and magnetic moment magnitude of the magnetic target.

[0040] Compared with the prior art, the beneficial effects of this invention are as follows:

[0041] This invention provides a method for locating magnetic targets based on the vertical difference of the total geomagnetic field. Compared with traditional methods, this method reduces the number of optically pumped magnetometers to two, simplifies the complex and stringent requirements of instrument installation, reduces application costs while improving work efficiency, makes full use of the data from each measuring point on the survey line, reduces the adverse effects of sensor noise from multiple magnetometers, and improves the positioning accuracy of magnetic targets.

[0042] This invention employs the Cuckoo Search algorithm to solve the objective function, which offers higher optimization efficiency compared to numerical iterative optimization algorithms and commonly used algorithms such as Differential Evolution (DE) and Particle Swarm Optimization (PSO). By utilizing the Levy flight search mechanism to update the optimization parameters, it effectively addresses the problem of DE and PSO algorithms easily getting trapped in local optima during iterative optimization. Attached Figure Description

[0043] Figure 1 This is a schematic diagram illustrating the principle of the magnetic target positioning method described in this invention. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0045] This invention provides a magnetic target localization method based on the vertical difference of the total geomagnetic field. It utilizes a rotary-wing UAV equipped with an inertial navigation system (SPAN) and two vertically distributed optically pumped magnetometers. While flying along the survey line, it simultaneously measures the total geomagnetic field data, including magnetic anomalies, and the UAV's real-time position data. The magnetic target is considered a stationary magnetic dipole. The center of the two optically pumps at the initial position is taken as the origin of the coordinate system. The magnetic anomaly field generated by the magnetic target at the locations of the two optically pumps is represented by the magnetic moment of the magnetic target, its position coordinates, the known geomagnetic tilt and declination, and the real-time position coordinates of the two optically pumps. The vertical difference of the total geomagnetic field at each point on the survey line is calculated using the measurements from the two optically pumps. This difference, combined with the difference in magnetic anomalies generated by the magnetic target at the two optically pumps, constructs an objective function. A cuckoo search algorithm is then used to estimate the position of the magnetic target. This invention reduces the number of sensors to two, fully utilizes the data from each measurement point on the survey line, and achieves precise localization of the magnetic target.

[0046] like Figure 1As shown, the airborne magnetic measurement system is equipped with two total field optically pumped magnetometers, sensor1 and sensor2, arranged vertically, 2 meters apart. The inertial navigation system (SPAN) is positioned directly above the axis of the total field magnetometers. Assuming the magnetic target is located at a depth of z on the left (or right) below the system, with a magnetic moment of |M|, the origin of the system coordinate system is taken as the center point of the axes of the two optically pumped magnetometers at the initial position of the airborne magnetic system. The direction of movement of the airborne magnetic measurement system along the measurement line is the positive X-axis, and the vertical downward direction is the positive Z-axis. The airborne magnetic measurement system travels in a straight line along the measurement line in the XOY plane. The coordinates of each measurement point on the measurement line are obtained by the inertial navigation system. Given the distance from the optically pumped magnetometers to the positioning system, the real-time position coordinates of the two optically pumped magnetometers can be determined. Based on the above information, a measurement model of the measurement system during operation is established, and the measured data is saved.

[0047] Assuming the magnetic target is on one side of the survey line, its position coordinates can be represented as (x... s ,y s ,z s At a distance R from the magnetic target, the magnetic anomaly field generated by the magnetic target is:

[0048]

[0049] In the formula It is the distance from the magnetic target to the measuring point, M = [M x M y M z ]′ is the magnetic moment vector of the target body, μ0=4π×10 -7 Let R be the free permeability, then R = [x] s -x,y s -y,z s -z]′ represents the distance from the magnetic target to the measuring point (x). s ,y s ,z s The distance vector of );

[0050] When the hard magnetic field of the target is very small, and the induced magnetic field of the soft magnetic material is the main component, the direction of the target's magnetic moment is the same as the direction of the geomagnetic vector, and the magnetic anomaly field R a The projection ΔB in the direction of the geomagnetic field is expressed as:

[0051]

[0052] In the formula, u is the unit vector of the geomagnetic field direction, and |M| is the magnitude of the magnetic moment of the magnetic target.

[0053] The position coordinates of optically pumped magnetometer sensor1 and optically pumped magnetometer sensor1 are (xs1, ys1) and (ys1) respectively. s1 ,zs1),(x s1,y s1 ,z s1 Then, the projections of the magnetic anomaly field generated by the magnetic target at the optically pumped magnetometer onto the direction of the geomagnetic field are as follows:

[0054]

[0055]

[0056] In the formula, R1 and R2 are the distances from the magnetic target to optically pumped magnetometer 1 and optically pumped magnetometer 2, respectively;

[0057] Theoretically, the difference in the projection of the magnetic anomalies generated by the magnetic target at the two optically pumped magnetometers onto the direction of the Earth's magnetic field is:

[0058] ΔB a,12 | Theory =ΔB a1 -ΔB a2

[0059] In addition to the magnetic anomaly ΔB generated by the target, the data measured by the total field magnetometer also include the geomagnetic field B. b and geomagnetic diurnal variation B n Therefore, the data measured by the two optically pumped magnetometers can be expressed as follows:

[0060] B d1 =B a +B b +ΔB a1 B d2 =B a +B b +ΔB a2

[0061] The geomagnetic field varies over time and is spatially uneven, which can affect target positioning. Subtracting two optical pump measurements can eliminate the effects of geomagnetic variation and spatial inhomogeneity of the geomagnetic field, i.e., ΔB. d,12 | Mensure =B d1 -B d1 =ΔB a1 -ΔB a2

[0062] In the formula ΔB d,12 | Mensure This represents the difference between the measurements taken by the two optically pumped magnetometers.

[0063] To facilitate letting ΔB d,12 | Mensure =ΔB 12,M ΔB a,12 | Theory =ΔB 12,T We can obtain: ΔB12,M =ΔB 12,T ;

[0064] As the aerial survey system moves along the survey line, assuming there are a total of n measurement points, the optically pumped magnetometer will collect n sets of data. At measurement point n, the difference between the measurements from the two optically pumped magnetometers is... The theoretical value of the difference between the projections of the magnetic anomalies generated by the magnetic target at the two optically pumped magnetometers onto the direction of the Earth's magnetic field is...

[0065] Based on the difference between the measured and theoretical values ​​of the magnetic anomaly difference, an objective function is constructed as follows:

[0066]

[0067] By minimizing the objective function using the Cuckoo algorithm, the position coordinates (x, y, z) of the magnetic target and the magnitude of the magnetic moment |M| are obtained.

[0068] The position coordinates and magnetic moment magnitude of the magnetic target are obtained by minimizing the objective function using the cuckoo search algorithm, as follows:

[0069] The four parameters of the desired magnetic target (position coordinates (x, y, Z) and the magnitude of the magnetic moment |M|) are defined as a 4-dimensional variable, representing a bird's nest. The population size is set to n, the population is initialized, and the initial positions of several bird nests are randomly generated. The fitness value of each bird nest is determined according to the objective function, and the bird nest with the optimal fitness value is selected as the globally optimal bird nest position. The location of the next generation of bird nests is updated, and the fitness value of the objective function is calculated. If the fitness value is better than that of the previous generation, the nest location is updated; otherwise, the original location is kept unchanged. After the location update, a randomly generated random value R, which follows a uniform distribution from 0 to 1, is compared with the probability pa of the nest owner discovering the foreign bird egg. If R > pa, then the nest location is updated. The nest locations are randomly changed, or left unchanged otherwise. The set of nest locations with the best fitness value is then retained, denoted as... Update the location of the next generation of Bird's Nest according to the following formula.

[0070]

[0071] In the formula This represents the position of the i-th (i = 1, 2, 3, ..., α) nest in generation t. Let represent point-to-point multiplication, α represent the step size control variable used to control the step size. Typically, α is 1. levy(λ) is the Levy random search path, which is a random walk using the Levy flight mechanism. Its step size follows a heavy-tailed stable distribution, while the random step size follows a Levy distribution.

[0072] Levy:μ=t -λ ,1≤λ≤3

[0073] Determine if the algorithm meets the set maximum number of iterations. If it does, end the iterative optimization and output the globally optimal Bird's Nest location. and optimal solution Otherwise, continue iterative optimization until the globally optimal bird's nest position is found, which is the position coordinates and magnetic moment magnitude of the magnetic target.

[0074] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for locating a magnetic target object based on the vertical difference of the geomagnetic total field, characterized in that, The method comprises: The system is equipped with two optical pumping magnetometers arranged in vertical direction, and an inertial navigation system installed above the total field magnetometer axis. The center point of the two optical pumping magnetometer axis at the initial position of the system is taken as the origin of the system coordinate system. The positive direction of the X axis is the moving direction of the system along the survey line, the positive direction of the Z axis is vertically downward, and the positive direction of the Y axis is vertically right according to the right-hand rule The coordinates of each survey point on the survey line are obtained by the positioning system. According to the distance between the optical pumping magnetometer and the positioning system, the real-time position coordinates of the two optical pumping magnetometers are determined. The magnetic target body is regarded as a static magnetic dipole, the center of the two optical pumping magnetometers at the initial position is regarded as the coordinate origin, the magnetic moment, the position coordinates, the known geomagnetic inclination and the geomagnetic declination of the magnetic target body and the real-time position coordinates of the two optical pumping magnetometers are used to respectively represent the magnetic anomaly field generated by the magnetic target body at the positions of the two optical pumping magnetometers; The vertical difference of the geomagnetic total field at each point of the survey line is calculated according to the measurement values of the two optical pumping magnetometers, a target function is constructed in combination with the magnetic anomaly difference generated by the magnetic target body at the positions of the two optical pumping magnetometers, the target function is minimized by using the cuckoo search algorithm, and the position coordinates and the magnetic moment module value of the magnetic target body are obtained.

2. The method for locating a magnetic target object based on the vertical difference of geomagnetic total field according to claim 1, characterized in that, The calculation process of the magnetic anomaly difference generated by the magnetic target body at the positions of the two optical pumping magnetometers comprises: Suppose the magnetic target is on one side of the survey line, and its position coordinates are represented as , at a distance from the magnetic target, the magnetic anomaly field generated by the magnetic target is: ， wherein is the distance of the magnetic target to the measuring point, is the magnetic moment vector of the magnetic target, is the vacuum permeability, is the distance vector of the magnetic target to the measuring point; Finding a magnetic anomaly field Projection in the direction of the geomagnetic field Is: ， In the formula is a unit vector of the direction of the geomagnetic field, is a modulus value of the magnetic moment of the magnetic target body; The position coordinates of the two optical pumping magnetometers are respectively , The projections of the magnetic anomaly field generated by the magnetic target body at the optical pumping magnetometer in the direction of the geomagnetic field are respectively ， ， ， ， In the formula , are the distances of the magnetic target to the first and second optical pumping magnetometers, respectively. The difference between the projections of the magnetic anomalies generated by the magnetic target body at the positions of the two optical pumping magnetometers in the direction of the geomagnetic field is calculated as: 。 3. The magnetic target body positioning method based on the vertical difference of the geomagnetic total field according to claim 2, characterized in that, The vertical difference of the geomagnetic total field at each point of the survey line is calculated according to the measurement values of the two optical pumping magnetometers, and comprises: The data measured by the two optical pumping magnetometers are respectively represented as: ， The influence of the magnetic daily variation and the spatial non-uniformity of the geomagnetic field is eliminated by subtracting the measurement values of the two optical pumping magnetometers, that is: 。 4. The method according to claim 3, wherein the magnetic target body is located based on the vertical difference of the geomagnetic total field. The target function is constructed as: wherein denotes the ith , denotes the ith .

5. The magnetic target body positioning method based on the vertical difference of the geomagnetic total field according to claim 4, characterized in that, The cuckoo search algorithm is used to minimize the target function, and the position coordinates and the magnetic moment module value of the magnetic target body are obtained, and the method comprises: Four parameters of the magnetic target are defined as a 4-dimensional variable bird nest, the four parameters being position coordinates and a modulus value of a magnetic moment A population size n is set, a colony is initialized, and initial positions of the bird nests are randomly generated According to the target function, a fitness value of each bird nest is determined, and a bird nest with an optimal fitness value is selected as a global optimal bird nest position updating the next generation bird nest position; The fitness value of the target function is calculated, if the value is better than that of the last generation of the target function, the bird nest position is updated, otherwise the original position remains unchanged. After updating the location, a randomly generated value following a uniform distribution from 0 to 1 is compared with the probability that the nest owner discovers the foreign bird's egg. If the random value is greater than the probability that the nest owner discovers the foreign bird's egg, then... The nest locations are randomly changed, or left unchanged otherwise. The set of nest locations with the best fitness value is then retained, denoted as... The location of the next generation of Bird's Nest will be updated according to the following formula. : ， In the formula represents the first , bird's nest in the first generation position, represents point-to-point multiplication, represents a step control quantity, used to control the step size, usually, take 1, Levy random search path, belongs to random walk, uses the Levy flight mechanism, and the step length of the walk satisfies a heavy-tailed stable distribution, and the random step length is a Levy distribution: ， determine whether the algorithm meets the set maximum number of iterations, if yes, end the iteration optimization, and output the global optimal nest position and the optimal solution , otherwise continue the iteration optimization, and the global optimal nest position is the global optimal solution, i.e. the position coordinates and magnetic moment modulus value of the magnetic target body.

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