Three-axis gradient magnetic field system design method for atomic inertial sensor

Abstract

A three-axis gradient magnetic field system design method for an atomic inertial sensor belongs to the field of micro inertial measurement atomic sensors, and comprises the following steps: presetting a target magnetic field area and coil parameters; establishing a relationship between the magnetic flux density and the current density; constructing a matrix equation and calculating a vector; simplifying the matrix equation to obtain an overdetermined equation, and obtaining a display solution through solving to obtain a boundary condition; constructing a mathematical model and a fitness function of the whale optimization algorithm based on the adaptive weight; initializing a population, calculating an individual fitness value and searching a global optimal solution; the optimal position and the fitness are updated under the boundary condition; judging whether the fitness function meets a search stopping condition or not; discretizing the stream function and drawing a coil structure. According to the whale optimization algorithm based on the adaptive weight, the algorithm is prevented from falling into local optimum, and the coil design efficiency and precision are improved; and by adopting an integrated design, the assembly error caused by independent installation is avoided, and the coil processing precision is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of micro-miniature inertial measurement atomic sensors, and in particular relates to a design method of a three-axis gradient magnetic field system for an atomic inertial sensor. Background Art

[0002] Micro-inertial measurement atomic sensors combine the high precision of quantum technology and the integrated characteristics of MEMS technology, becoming one of the important development trends of future miniaturized and high-performance inertial navigation systems.

[0003] Micro-inertial measurement atomic sensors are atomic gyroscopes based on the magnetic resonance effect. They obtain the carrier's angular velocity by measuring the frequency of the Larmor precession of noble gas atoms. Because the Larmor precession frequency is proportional to the magnetic field strength, magnetic field gradients can lead to uneven distribution of the Larmor precession frequency, increasing the full width at half maximum of the resonance signal, reducing the signal-to-noise ratio and the relaxation time of the noble gas, and increasing the angular random walk coefficient of the gyroscope. Therefore, magnetic field gradients are a significant source of error affecting the accuracy of micro-inertial measurement atomic sensors. To further improve the accuracy of micro-inertial measurement atomic sensors, measures must be taken to suppress magnetic field gradients.

[0004] The three-axis gradient magnetic field compensation coils of traditional miniature inertial measurement atomic sensors are usually designed with axial and radial gradient magnetic field compensation coils in a rectangular shape, which are formed into a cylindrical or saddle shape by adhering to the coil frame and have a large aspect ratio. In addition, the axial and radial gradient magnetic field compensation coils need to be designed and installed independently. Positioning and dimensional errors will be introduced in this process, resulting in a large deviation between the actual processing accuracy and the theoretical value, which limits the miniaturization development of atomic sensors for inertial measurement. Summary of the Invention

[0005] Aiming at the design defects of the three-axis gradient magnetic field compensation coil of the existing micro-inertial measurement atomic sensor, the present invention provides a three-axis gradient magnetic field system design method for the atomic inertial sensor.

[0006] This invention utilizes an integrated planar coil design approach and proposes a corresponding design solution based on a heuristic optimization algorithm. The integrated three-axis gradient magnetic field coil design eliminates the need for separate design and installation of the axial and radial gradient magnetic field compensation coils, eliminating positioning and dimensional errors. This reduces installation errors and improves coil design efficiency and machining accuracy.

[0007] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0008] The present invention provides an integrated three-axis gradient magnetic field coil system, comprising: a z-axis top gradient coil, a z-axis bottom gradient coil, an x-axis left gradient coil, an x-axis right gradient coil, a y-axis front gradient coil, and a y-axis rear gradient coil; the z-axis top gradient coil, the z-axis bottom gradient coil, the x-axis left gradient coil, the x-axis right gradient coil, the y-axis front gradient coil, and the y-axis rear gradient coil are respectively arranged on the upper, lower, left, right, front, and rear surfaces of a cube;

[0009] A light hole is provided at the center of the z-axis top plane, the center of the z-axis bottom plane, the center of the x-axis left plane and the center of the x-axis right plane of the cube;

[0010] Radius R of each coil c Both are limited to l<R c <L, the maximum radius L is half the length of the square side, and the minimum radius l is greater than the radius of the light hole;

[0011] The target magnetic field region formed by each coil is a cube, which is located at the center of the cube.

[0012] The present invention provides a method for designing a three-axis gradient magnetic field system for an atomic inertial sensor, comprising the following steps:

[0013] S1: Preset the target magnetic field area and coil parameters;

[0014] S2: According to the Biot-Savart law, the relationship between the magnetic flux density and the current density of the coil is established;

[0015] S3: Construct the matrix equation and calculate the unknown vector to obtain the current density coefficient, and then determine the current density expression;

[0016] S4: Simplify the matrix equation to obtain an overdetermined equation, and obtain an explicit solution by solving the overdetermined equation;

[0017] S5: Set the displayed solution as a boundary condition to limit the scope of the search space;

[0018] S6: Whale optimization algorithm based on adaptive weights;

[0019] Construct a mathematical model and fitness function for the whale optimization algorithm based on adaptive weights; initialize the population, calculate individual fitness values, and search for the global optimal solution; update the optimal position and fitness under boundary conditions; determine whether the fitness function meets the stop search condition; if F ≤ 5%, output the optimal solution and execute S7; if F > 5%, re-initialize the population until the fitness function meets the stop search condition;

[0020] S7: Discretize the stream function and plot the coil structure.

[0021] Furthermore, in step S1, the specific spatial position and size range of the coil are given first, and a coil is set on each square plane of the cube, namely the z-axis bottom gradient coil, the z-axis top gradient coil, the x-axis left gradient coil, the x-axis right gradient coil, the y-axis rear gradient coil and the y-axis front gradient coil; a light hole is set at the center of the z-axis bottom plane, the center of the z-axis top plane, the center of the x-axis left plane and the center of the x-axis right plane of the cube; the coil radius R c Limited to l<R c <L, the maximum radius L of the coil is half the side length of the square, and the minimum radius l of the coil is greater than the radius of the light hole; the target magnetic field area is a cube, located at the center of the cube.

[0022] Furthermore, the specific implementation process of step S2 is as follows:

[0023] The magnetic field value at any field point r(x,y,z) in space is obtained from the curl of the magnetic vector potential:

[0024]

[0025] in, is the Nabra operator, which represents the first-order partial differential vector sum of the potential field in the xyz direction, B(r) is the magnetic field value at any field point r(x,y,z) in space, and A(r) is the magnetic vector potential generated by the current density J of the coil:

[0026]

[0027] Where μ0 is the vacuum permeability, r′ is the position vector of the source point on the coil surface, r is the position vector of the field point in the target magnetic field region, and V is the surface area where the current is distributed;

[0028] Since the current density of the z-axis bottom gradient coil and the z-axis top gradient coil is distributed on the xy plane, the z-axis component of the current density J z = 0 and satisfy the current continuity equation By defining the vector potential ψ(x, y) as the stream function to describe the distribution trajectory of the current density in the xy plane, we have From this we get:

[0029]

[0030] Among them, J x is the x-axis component of current density, J y is the y-axis component of current density;

[0031] Simplify formula (2) to:

[0032]

[0033] Where x′ and y′ are the horizontal and vertical coordinates of a source point in the current density distribution area on the coil plane;

[0034] In the polar coordinate system, J in the xy plane x 、J y J r 、 Instead, trigonometric functions are introduced as the basis functions of the plane current density for Fourier preprocessing:

[0035]

[0036] Among them, J r is the radial component of current density, is the tangential component of current density, P n is the expansion coefficient of each order of coil current density, N is the order of expansion term, k value determines the type of coil, when k = 0, J r =0, it is used to design radial gradient magnetic field compensation coils; when k=1, it is used to design transverse gradient magnetic field compensation coils;

[0037] Substituting equation (5) into equation (4), the magnetic field value at any field point r (x, y, z) in the polar coordinate system is obtained as follows:

[0038]

[0039] Where H is the distance between the two coils;

[0040] Simplify formula (6) to:

[0041]

[0042] Among them, B z is the magnetic field component in the z-axis direction at each target field point, Q n is a function of any field point r(x,y,z).

[0043] Furthermore, in step S3, each target field point is first substituted into equation (7) to obtain the matrix equation system:

[0044]

[0045] Simplify formula (7) to:

[0046] Ax=b (9)

[0047] Among them, B M is the z-axis component of the Mth target field point, Q MN is the Nth order expansion coefficient of the Mth target field point, P Nis the Nth-order expansion coefficient of the coil current density, A is the design matrix, and b is the target magnetic field vector;

[0048] Solving the above equations for vectors A and b yields the coil current density coefficient, thereby determining the coil current density expression.

[0049] Furthermore, in step S4, according to the theory that the number of target field points M is much larger than the number of harmonics N, equation (9) is an overdetermined system of equations. By introducing the generalized inverse matrix to solve the overdetermined system of equations, the least squares solution x is obtained:

[0050] x=(A T A) -1 A T b (10)

[0051] Where T represents the matrix transpose.

[0052] Furthermore, the mathematical model of the adaptive weight-based whale optimization algorithm is:

[0053]

[0054] Among them, D is the enclosed step size, E and C are coefficients, X * (t) is the prey position vector, X(t) is the whale’s current position vector, X(t+1) is the whale’s position vector at the next moment, t is the number of iterations, t max is the maximum number of iterations, q is a random number between [0,1], a is the convergence factor, p is the probability of the whale between shrinking and updating the spiral position, f is the spiral shape parameter of the whale bubble, h is a random number between [-1,1], X rand It means randomly selecting a whale from the population, λ=3, μ=2, w is the adaptive weight, and w is a random number between [0,1].

[0055] Furthermore, the mathematical expression of the fitness function F is:

[0056]

[0057] Among them, B z (x, y, z) is the magnetic field value at any field point r(x, y, z) in the polar coordinate system; B z (0,0,z) is the magnetic field value at the center of the xy plane r(0,0,z) in the polar coordinate system.

[0058] Furthermore, in step S6, a fitness function F is defined according to the gradient requirement of the target magnetic field region: the fitness function F is constructed by taking the maximum error between the magnetic field value at r(x, y, z) in the target magnetic field region and the magnetic field value at r(0, 0, z) in the center of the xy plane.

[0059] Furthermore, in step S7, the stream function is discretized using contour lines to obtain a coil structure with optimized parameters.

[0060] The beneficial effects of the present invention are:

[0061] (1) The present invention uses a whale optimization algorithm based on adaptive weights in the coil design process, which avoids the algorithm from falling into local optimality and improves the efficiency and accuracy of coil design.

[0062] (2) The present invention adopts an integrated design, which avoids assembly errors introduced during independent installation and improves the coil processing accuracy.

[0063] (3) The integrated three-axis gradient magnetic field coil designed in the present invention introduces a gradient magnetic field from the outside to compensate for the unevenly distributed gradient magnetic field in the internal residual magnetism, thereby providing three-axis magnetic field gradient compensation for the micro-inertial measurement atomic sensor, achieving an internal high-uniformity magnetic field environment, solving the errors caused by magnetic field inhomogeneity, and improving the measurement accuracy of the micro-inertial measurement atomic sensor. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 This is a schematic diagram of an integrated three-axis gradient magnetic field coil system provided by the present invention.

[0065] Figure 2 This is a schematic diagram of the deployment of an integrated three-axis gradient magnetic field coil system provided by the present invention.

[0066] Figure 3 This is a flow chart of a design method for a three-axis gradient magnetic field system for an atomic inertial sensor provided by the present invention.

[0067] In the figure, there are the z-axis bottom gradient coil 1, the z-axis top gradient coil 2, the x-axis left gradient coil 3, the x-axis right gradient coil 4, the y-axis rear gradient coil 5, the y-axis front gradient coil 6 and four light holes 7. DETAILED DESCRIPTION

[0068] The present invention will be further described in detail below with reference to the accompanying drawings.

[0069] In a first aspect, the present invention provides an integrated three-axis gradient magnetic field coil system.

[0070] See also Figure 1 To illustrate, the integrated three-axis gradient magnetic field coil system of the present invention is mainly composed of a z-axis bottom gradient coil 1, a z-axis top gradient coil 2, an x-axis left gradient coil 3, an x-axis right gradient coil 4, a y-axis rear gradient coil 5, a y-axis front gradient coil 6 and a light hole 7.

[0071] like Figure 1 and Figure 2 As shown, a coil is installed on each square plane of the cube. These coils are: z-axis bottom gradient coil 1, z-axis top gradient coil 2, x-axis left gradient coil 3, x-axis right gradient coil 4, y-axis rear gradient coil 5, and y-axis front gradient coil 6. A light hole 7 is also installed at the center of the z-axis bottom plane, z-axis top plane, x-axis left plane, and x-axis right plane of the cube. Light hole 7 is mainly used to allow laser light in the x- and z-axis directions to pass through. The z-axis bottom gradient coil 1, z-axis top gradient coil 2, x-axis left gradient coil 3, x-axis right gradient coil 4, y-axis rear gradient coil 5, and y-axis front gradient coil 6 provide a gradient magnetic field inside the cube, compensating for the uneven magnetic field distribution inside.

[0072] In a second aspect, the present invention provides a method for designing a three-axis gradient magnetic field system for an atomic inertial sensor.

[0073] See also Figure 3 To illustrate, the present invention provides a design method for a three-axis gradient magnetic field system for an atomic inertial sensor, and its specific implementation process is as follows:

[0074] Step S1: Preset the target magnetic field area and coil parameters (maximum radius L, minimum radius l, coil radius R c );

[0075] Before designing the coil, the specific spatial location and size range of the coil must be determined. In the present invention, a coil is positioned on each square plane of the cube. These coils are: z-axis bottom gradient coil 1, z-axis top gradient coil 2, x-axis left gradient coil 3, x-axis right gradient coil 4, y-axis rear gradient coil 5, and y-axis front gradient coil 6. Furthermore, a light aperture 7 is positioned at the center of the z-axis bottom plane, z-axis top plane, x-axis left plane, and x-axis right plane of the cube.

[0076] The light hole 7 is preferably circular, and its diameter is preferably 5 mm. The side length of each square of the cube is preferably 16 mm, and the coil radius R c Limited to l<R c <L, the maximum radius L of the coil is preferably 8 mm, which is half the side length of the square. The minimum radius l of the coil is larger than the radius of the light hole 7, and the minimum radius of the coil is preferably 3 mm. At the same time, the target magnetic field area is a cube with a side length of preferably 4 mm, located at the center of the cube.

[0077] In the present invention, the integrated three-axis gradient magnetic field coil can specifically use polyimide or polyester film as a base material and be manufactured using a flexible circuit board process, so it has high reliability and is easy to install.

[0078] The following describes the design of the z-axis bottom gradient coil 1 and the z-axis top gradient coil 2 as examples. The design process of other coils, such as the x-axis left gradient coil 3, the x-axis right gradient coil 4, the y-axis rear gradient coil 5, and the y-axis front gradient coil 6, is similar.

[0079] Step S2: According to the Biot-Savart law, the relationship between the magnetic flux density and the current density of the coil is established;

[0080] The magnetic field value at any field point r(x,y,z) in space can be obtained from the curl of the magnetic vector potential:

[0081]

[0082] in, is the Nabra operator, which represents the first-order partial differential vector sum of the potential field in the xyz direction, B(r) is the magnetic field value at any field point r(x,y,z) in space, and A(r) is the magnetic vector potential generated by the current density J of the coil, which can be expressed as:

[0083]

[0084] Where μ0 is the vacuum permeability, r′ is the position vector of the source point on the coil surface, r is the position vector of the field point in the target magnetic field region, and V is the surface area where the current is distributed.

[0085] Since the current density of the z-axis bottom gradient coil 1 and the z-axis top gradient coil 2 is distributed on the xy plane, the z-axis component of the current density J z = 0 and satisfy the current continuity equation

[0086] By defining the vector potential ψ(x, y) as the stream function to describe the distribution trajectory of the current density in the xy plane, we have You can get:

[0087]

[0088] Among them, J x is the x-axis component of current density, J y is the y-axis component of current density.

[0089] Therefore, formula (2) can be simplified as:

[0090]

[0091] Among them, x′ and y′ are the horizontal and vertical coordinates of a source point in the current density distribution area on the coil plane.

[0092] In the polar coordinate system, J in the xy plane x 、J yWill be J r 、 (J r is the radial component of current density, is replaced by the tangential component of the current density), and the trigonometric function is introduced as the basis function of the plane current density for Fourier preprocessing:

[0093]

[0094] Among them, P n is the expansion coefficient of the current density series, N is the order of the expansion term, where N is 4, and the k value determines the type of coil. When k = 0, J r =0, used to design radial gradient magnetic field compensation coils (referring to 1 and 2 in the present invention); when k=1, used to design transverse gradient magnetic field compensation coils (referring to 3, 4, 5, 6 in the present invention), here k=0 is selected.

[0095] Substituting formula (5) into formula (4), the magnetic field value at any field point r (x, y, z) in the polar coordinate system can be obtained as follows:

[0096]

[0097] Where, H is the distance between the two coils.

[0098] Formula (6) can be simplified as:

[0099]

[0100] Among them, B z is the magnetic field component in the z-axis direction at each target field point, Q n is a function of any field point r(x,y,z).

[0101] Step S3: construct a matrix equation and calculate the unknown vector to obtain the current density coefficient, and then determine the current density expression;

[0102] Substituting each target field point into formula (7) yields the following matrix equations:

[0103]

[0104] Among them, B M is the z-axis component of the Mth target field point, Q MN is the Nth order expansion coefficient of the Mth target field point, P N is the Nth-order expansion coefficient of the coil current density.

[0105] Formula (7) can be simplified as:

[0106] Ax=b (9)

[0107] Where A is the design matrix and b is the target magnetic field vector.

[0108] Solving the above equations for vectors A and b can yield the line current density coefficient, thereby determining the coil current density expression, which is Formula (6).

[0109] Step S4: Solve the overdetermined equation and obtain the explicit solution to provide boundary conditions for the subsequent optimization algorithm;

[0110] Since the number of target field points M is much larger than the harmonic order N, formula (9) is an overdetermined system of equations. By introducing the generalized inverse matrix to solve the overdetermined system of equations, the least squares solution x is obtained:

[0111] x=(A T A) -1 A T b (10)

[0112] Where T represents the matrix transpose.

[0113] Step S5: determining search boundary conditions;

[0114] The explicit solution x obtained according to formula (10) is the boundary condition to limit the scope of the search space.

[0115] Step S6: whale optimization algorithm based on adaptive weights;

[0116] The optimal stream function is determined by optimizing the current density coefficient using the whale optimization algorithm. The whale optimization algorithm mainly achieves the optimization purpose by simulating the spiral bubble net feeding method of whales. However, during the iterative process of the whale optimization algorithm, the population diversity will decrease due to the increase in the number of iterations, causing the algorithm to fall into a local optimal solution. In response to this. The present invention introduces adaptive weights to change the way whales update their positions. This whale optimization algorithm based on adaptive weights can expand the search range of prey locations, and at the same time, it can search for more optimal solutions around the prey while updating the position, thereby improving the optimization efficiency and accuracy.

[0117] The specific implementation process is as follows:

[0118] S6.1: Construct a mathematical model of the whale optimization algorithm based on adaptive weights;

[0119] In the present invention, the mathematical model involved in the whale optimization algorithm based on adaptive weights is as follows:

[0120]

[0121] Among them, D is the enclosed step size, E and C are coefficients, X *(t) is the prey position vector, X(t) is the whale’s current position vector, X(t+1) is the whale’s position vector at the next moment, t is the number of iterations, t max is the maximum number of iterations, q is a random number between [0,1], a is the convergence factor, p is the probability of the whale between shrinking and updating the spiral position, f is the spiral shape parameter of the whale bubble, h is a random number between [-1,1], X rand It means randomly selecting a whale from the population, λ=3, μ=2, w is the adaptive weight, and w is a random number between [0,1].

[0122] S6.2: Construct fitness function;

[0123] The explicit solution x obtained according to formula (10) is used as a boundary condition to limit the search space range, and the fitness function F is defined according to the gradient requirements of the target magnetic field region. In the present invention, the maximum error between the magnetic field value at the target magnetic field region r(x,y,z) and the magnetic field value at the center of the xy plane r(0,0,z) is taken to construct the fitness function F, and F ≤ 5% is set as the stop condition for the search:

[0124]

[0125] Among them, B z (x, y, z) is the magnetic field value at any field point r(x, y, z) in the polar coordinate system; B z (0,0,z) is the magnetic field value at the center of the xy plane r(0,0,z) in the polar coordinate system.

[0126] S6.3: Initialize the population, calculate individual fitness values ​​and find the global optimal solution;

[0127] S6.4: Update the optimal position and fitness under boundary conditions;

[0128] S6.5: Determine whether the fitness function meets the stop search condition; if F≤5%, output the optimal solution and then execute step S7; if F>5%, return to execute step S6.3.

[0129] Step S7: Discretize the stream function and draw the coil structure.

[0130] The flow function is discretized using contour lines to obtain the coil structure after parameter optimization.

[0131] The present invention completes the design of an integrated three-axis gradient magnetic field coil system by designing a whale optimization algorithm based on adaptive weights. The transverse gradient magnetic field compensation coil and radial gradient magnetic field compensation coil constants obtained are both 100pT / (mm·mA).

[0132] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present invention. These improvements and modifications should also be regarded as within the scope of protection of the present invention.

Claims

1. A design method for a three-axis gradient magnetic field system for an atomic inertial sensor, characterized in that: The following steps are involved: S1: Preset the target magnetic field area and coil parameters; S2: According to the Biot-Savart law, the relationship between the magnetic flux density and the current density of the coil is established; S3: Construct the matrix equation and calculate the unknown vector to obtain the current density coefficient, and then determine the current density expression; S4: Simplify the matrix equation to obtain an overdetermined equation, and obtain an explicit solution by solving the overdetermined equation; S5: Set the displayed solution as a boundary condition to limit the scope of the search space; S6: Whale optimization algorithm based on adaptive weights; Construct a mathematical model and fitness function for the whale optimization algorithm based on adaptive weights; initialize the population, calculate individual fitness values, and search for the global optimal solution; update the optimal position and fitness under boundary conditions; determine whether the fitness function meets the stop search condition; if F ≤ 5%, output the optimal solution and execute S7; if F > 5%, re-initialize the population until the fitness function meets the stop search condition; S7: Discretize the stream function and plot the coil structure.

2. The method for designing a three-axis gradient magnetic field system for an atomic inertial sensor according to claim 1, characterized in that: In step S1, the specific spatial position and size range of the coil are first given. A coil is set on each square plane of the cube, namely the z-axis bottom gradient coil, the z-axis top gradient coil, the x-axis left gradient coil, the x-axis right gradient coil, the y-axis rear gradient coil and the y-axis front gradient coil; a light hole is set at the center of the z-axis bottom plane, the z-axis top plane, the x-axis left plane center and the x-axis right plane center of the cube; the coil radius R c Limited to l<R c <L, the maximum radius L of the coil is half the side length of the square, and the minimum radius l of the coil is greater than the radius of the light hole; the target magnetic field area is a cube, located at the center of the cube.

3. The method for designing a three-axis gradient magnetic field system for an atomic inertial sensor according to claim 1, wherein: The specific implementation process of step S2 is as follows: The magnetic field value at any field point r(x,y,z) in space is obtained from the curl of the magnetic vector potential: in, is the Nabra operator, which represents the first-order partial differential vector sum of the potential field in the xyz direction, B(r) is the magnetic field value at any field point r(x,y,z) in space, and A(r) is the magnetic vector potential generated by the current density J of the coil: Where μ0 is the vacuum permeability, r′ is the position vector of the source point on the coil surface, r is the position vector of the field point in the target magnetic field region, and V is the surface area where the current is distributed; Since the current density of the z-axis bottom gradient coil and the z-axis top gradient coil is distributed on the xy plane, the z-axis component of the current density J z = 0 and satisfy the current continuity equation By defining the vector potential ψ(x, y) as the stream function to describe the distribution trajectory of the current density in the xy plane, we have From this we get: Among them, J x is the x-axis component of current density, J y is the y-axis component of current density; Simplify formula (2) to: Where x′ and y′ are the horizontal and vertical coordinates of a source point in the current density distribution area on the coil plane; In the polar coordinate system, J in the xy plane x 、J y J r 、 Instead, trigonometric functions are introduced as the basis functions of the plane current density for Fourier preprocessing: Among them, J r is the radial component of current density, is the tangential component of current density, P n is the expansion coefficient of each order of coil current density, N is the order of expansion term, k value determines the type of coil, when k = 0, J r =0, it is used to design radial gradient magnetic field compensation coils; when k=1, it is used to design transverse gradient magnetic field compensation coils; Substituting equation (5) into equation (4), the magnetic field value at any field point r (x, y, z) in the polar coordinate system is obtained as follows: Where H is the distance between the two coils; Simplify formula (6) to: Among them, B z is the magnetic field component in the z-axis direction at each target field point, Q n is a function of any field point r(x,y,z).

4. The method for designing a three-axis gradient magnetic field system for an atomic inertial sensor according to claim 3, wherein: In step S3, first substitute each target field point into equation (7) to obtain the matrix equation system: Simplify formula (7) to: Ax=b (9) Among them, B M is the z-axis component of the Mth target field point, Q MN is the Nth order expansion coefficient of the Mth target field point, P N is the Nth-order expansion coefficient of the coil current density, A is the design matrix, and b is the target magnetic field vector; Solving the above equations for vectors A and b yields the coil current density coefficient, thereby determining the coil current density expression.

5. The method for designing a three-axis gradient magnetic field system for an atomic inertial sensor according to claim 4, characterized in that: In step S4, according to the theory that the number of target field points M is much larger than the number of harmonics N, equation (9) is an overdetermined system of equations. By introducing the generalized inverse matrix to solve the overdetermined system of equations, the least squares solution x is obtained: x=(A T A) -1 A T b (10) Where T represents the matrix transpose.

6. The method for designing a three-axis gradient magnetic field system for an atomic inertial sensor according to claim 1, characterized in that: The mathematical model of the adaptive weight-based whale optimization algorithm is: Among them, D is the enclosed step size, E and C are coefficients, X * (t) is the prey position vector, X(t) is the whale’s current position vector, X(t+1) is the whale’s position vector at the next moment, t is the number of iterations, t max is the maximum number of iterations, q is a random number between [0,1], a is the convergence factor, p is the probability of the whale between shrinking and updating the spiral position, f is the spiral shape parameter of the whale bubble, h is a random number between [-1,1], X rand It means randomly selecting a whale from the population, λ=3, μ=2, w is the adaptive weight, and w is a random number between [0,1].

7. The method for designing a three-axis gradient magnetic field system for an atomic inertial sensor according to claim 1, characterized in that: The mathematical expression of the fitness function F is: Among them, B z (x, y, z) is the magnetic field value at any field point r(x, y, z) in the polar coordinate system; B z (0,0,z) is the magnetic field value at the center of the xy plane r(0,0,z) in the polar coordinate system.

8. The method for designing a three-axis gradient magnetic field system for an atomic inertial sensor according to claim 1, characterized in that: In step S6, the fitness function F is defined according to the gradient requirement of the target magnetic field region: the fitness function F is constructed by taking the maximum error between the magnetic field value at r(x, y, z) in the target magnetic field region and the magnetic field value at r(0, 0, z) in the xy plane center.

9. The method for designing a three-axis gradient magnetic field system for an atomic inertial sensor according to claim 1, characterized in that: In step S7, the stream function is discretized using contour lines to obtain a coil structure with optimized parameters.

10. An integrated three-axis gradient magnetic field coil system designed using the three-axis gradient magnetic field system design method for an atomic inertial sensor according to any one of claims 1 to 9, characterized in that: include: The z-axis top gradient coil, the z-axis bottom gradient coil, the x-axis left gradient coil, the x-axis right gradient coil, the y-axis front gradient coil, and the y-axis rear gradient coil are respectively arranged on the upper, lower, left, right, front, and rear surfaces of the cube; A light hole is provided at the center of the z-axis top plane, the center of the z-axis bottom plane, the center of the x-axis left plane and the center of the x-axis right plane of the cube; Radius R of each coil c Both are limited to l<R c <L, the maximum radius L is half the length of the square side, and the minimum radius l is greater than the radius of the light hole; The target magnetic field region formed by each coil is a cube, which is located at the center of the cube.

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