An indoor local magnetic field modeling method and device based on a magnetic source equivalence principle

Abstract

The application provides an indoor local magnetic field modeling method and device based on a magnetic source equivalence principle, and belongs to the technical field of indoor positioning. The method comprises the following steps: collecting triaxial magnetometer data in a space range by using an array magnetic sensor to obtain original measurement information of an indoor magnetic field; modeling the indoor magnetic field into an equivalent magnetic dipole model composed of multiple equivalent magnetic dipoles based on the magnetic source equivalence principle, and setting magnetic moment and position parameters of the magnetic dipoles to make the magnetic field generated by the model consistent with the real magnetic field in an observation area; establishing an observation model for describing the relationship between the measurement values and the model parameters according to the measurement values of the array magnetic sensor and the equivalent magnetic dipole model; and solving the parameters of the equivalent magnetic dipole model to obtain the equivalent magnetic dipole model of the indoor magnetic field by using a nonlinear least square optimization method, wherein the parameters include the magnetic moment and the position of the magnetic dipoles. The application significantly improves the accuracy and reliability of the model.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of indoor positioning, and particularly relates to an indoor local magnetic field modeling method and device based on a magnetic source equivalence principle. BACKGROUND

[0002] The geomagnetic field as a natural vector field is widely used in the heading reference correction of an inertial navigation system due to its time-space stability and quasi-uniform distribution in unobstructed outdoor space. By fusing three-axis magnetometer and gyroscope data, the heading angle error can be effectively suppressed, and the reliability of the inertial navigation system can be significantly improved. However, in indoor and other enclosed spaces, the magnetic field environment changes dramatically due to factors such as building structure and electrical radiation, and the magnetic field gradient fluctuates dramatically, resulting in the failure of traditional geomagnetic-based correction algorithms, which becomes a bottleneck for indoor application of magnetic navigation technology.

[0003] Due to the high non-uniformity of the indoor magnetic field, its spatial distribution has unique "magnetic fingerprint" characteristics, which are encoded by the ferromagnetic distribution of building materials and the operating state of electromagnetic equipment, and can be used for positioning in satellite-denied environments (such as inside buildings, underground facilities, underwater spaces, etc.).

[0004] The existing Gaussian process model models the magnetic field by designing a covariance kernel function, which can incorporate physical laws but has the following problems: the design of the kernel function depends on prior knowledge, and the extrapolation error is significant; the calculation cost is high in high-dimensional scenarios; and the traditional isotropic kernel is difficult to capture the directionality and heterogeneity of the magnetic field. The existing magnetic field polynomial model fits the magnetic field strength by a polynomial, which is simple in structure but has the following shortcomings: it is difficult to describe local mutations or high-dimensional nonlinear relationships; and the extrapolation performance is limited. Although these two models satisfy Maxwell's equations, they essentially rely on mathematical fitting and interpolation, lack a deep understanding of the mechanism of generating the magnetic field, and are difficult to maintain high-precision modeling in complex local magnetic field anomaly scenarios. SUMMARY

[0005] To solve the above technical problems, the application provides an indoor local magnetic field modeling method and device based on a magnetic source equivalence principle, which introduces an equivalent magnetic dipole model. The model generates a magnetic field that is consistent with the real magnetic field in the observation area by constructing a virtual equivalent magnetic dipole; the equivalent magnetic source is constructed using magnetic dipole parameters (such as magnetic moment and position) to reflect the physical characteristics of the magnetic field source, and the model is simple in structure, efficient in calculation, and supports fast inversion. By superimposing multiple magnetic dipoles, the model can approximate complex magnetic field distribution and realize high-precision magnetic field prediction, providing a lightweight and effective solution for real-time magnetic field positioning and navigation in large-scale complex environments.

[0006] To achieve the above purpose, the application adopts the following technical solutions:

[0007] An indoor local magnetic field modeling method based on magnetic source equivalence principle, comprising the following steps:

[0008] Step 1, acquiring triaxial magnetometer data in a space range by using an array magnetic sensor to obtain original measurement information of the indoor magnetic field;

[0009] Step 2, modeling the indoor magnetic field as an equivalent magnetic dipole model composed of multiple equivalent magnetic dipoles based on the magnetic source equivalence principle, and setting the magnetic moment and position parameters of the magnetic dipoles to make the magnetic field generated by the equivalent magnetic dipole model consistent with the real magnetic field in the observation area;

[0010] Step 3, establishing an observation model for describing the relationship between the triaxial magnetometer data and the parameters of the equivalent magnetic dipole model according to the triaxial magnetometer data collected by the array magnetic sensor and combining the equivalent magnetic dipole model;

[0011] Step 4, solving the parameters of the equivalent magnetic dipole model according to the observation model by a nonlinear least squares optimization method to obtain the equivalent magnetic dipole model of the indoor magnetic field, wherein the parameters include the magnetic moment and position of the magnetic dipoles.

[0012] The application also provides an indoor local magnetic field modeling device based on the magnetic source equivalence principle, comprising the following modules:

[0013] An original measurement information acquisition module acquires triaxial magnetometer data in a space range by using an array magnetic sensor to obtain original measurement information of the indoor magnetic field;

[0014] A model construction module models the indoor magnetic field as an equivalent magnetic dipole model composed of multiple equivalent magnetic dipoles based on the magnetic source equivalence principle, and sets the magnetic moment and position parameters of the magnetic dipoles to make the magnetic field generated by the equivalent magnetic dipole model consistent with the real magnetic field in the observation area;

[0015] A relationship description module establishes an observation model for describing the relationship between the triaxial magnetometer data and the parameters of the equivalent magnetic dipole model according to the triaxial magnetometer data collected by the array magnetic sensor and combining the equivalent magnetic dipole model;

[0016] A parameter solving module solves the parameters of the equivalent magnetic dipole model according to the observation model by a nonlinear least squares optimization method to obtain the equivalent magnetic dipole model of the indoor magnetic field, wherein the parameters include the magnetic moment and position of the magnetic dipoles.

[0017] The application also provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned indoor local magnetic field modeling method based on the magnetic source equivalence principle when executing the program.

[0018] The application further provides a non-transitory computer-readable storage medium, which stores a computer program, and the computer program is executed by a processor to implement the steps of the indoor local magnetic field modeling method based on the equivalent principle of magnetic source.

[0019] Advantages:

[0020] The equivalent magnetic dipole model can overcome the shortcomings of the Gaussian model and the polynomial model. The Gaussian model has the problems of sensitive kernel function design and difficulty in identifying local magnetic anomalies, and the polynomial model is difficult to describe local mutations and high-dimensional nonlinear relationships and has insufficient extrapolation ability. Although the two models satisfy the Maxwell equation set, they are only mathematical fitting in nature and lack a deep understanding of the mechanism of generating a magnetic field. In contrast, the equivalent magnetic dipole model directly reflects the physical characteristics of the magnetic source, can more accurately describe the spatial variation of the magnetic field and capture the influence of local magnetic sources, the model parameters have clear physical meaning, can be traced back to the actual magnetic source distribution, have good physical interpretability, and significantly improve the accuracy and reliability of the model. BRIEF DESCRIPTION OF DRAWINGS

[0021] Figure 1 A flowchart of the indoor local magnetic field modeling method based on the equivalent principle of magnetic source of the application;

[0022] Figure 2 A schematic diagram of the indoor local magnetic field modeling device based on the equivalent principle of magnetic source of the application;

[0023] Figure 3 An error diagram of the equivalent magnetic dipole model for estimating a three-axis magnetic field; wherein a represents the X-axis estimated magnetic field error, b represents the Y-axis estimated magnetic field error, and c represents the Z-axis estimated magnetic field error. DETAILED DESCRIPTION

[0024] In order to make the purpose, technical scheme and advantages of the application clearer, the application will be further described in detail below in combination with the drawings and examples. It should be understood that the specific examples described herein are only used to explain the application and not to limit the application. In addition, the technical features involved in each embodiment of the application described below can be combined with each other as long as they do not conflict with each other.

[0025] The application provides an indoor local magnetic field modeling method based on a magnetic source equivalent principle, which models an indoor local magnetic field by using an equivalent magnetic dipole model. The method realizes accurate solution of model parameters by constructing an equivalent magnetic dipole model represented by parameters such as a magnetic moment vector and a spatial position and combining a nonlinear optimization algorithm, thereby effectively approximating a complex indoor magnetic field distribution. The method has the advantages of simple model structure, efficient real-time calculation and fast inversion of a magnetic field, and the model can approximate a complex magnetic field distribution by superposition of multiple magnetic dipoles, thereby realizing a high-precision magnetic field modeling overall process.

[0026] Specifically, as shown in the drawings, Figure 1 An indoor local magnetic field modeling method based on a magnetic source equivalent principle provided by the application comprises the following steps:

[0027] Step 1: Collecting triaxial magnetometer data in a space range by using an array type magnetic sensor;

[0028] Step 2: Constructing an equivalent magnetic dipole model;

[0029] Step 3: Constructing an observation model;

[0030] Step 4: Solving the magnetic field equivalent magnetic dipole model parameters to obtain an indoor magnetic field equivalent magnetic dipole model.

[0031] Specifically, the step 1 comprises:

[0032] A tester holds a planar array type magnetic sensor to collect triaxial magnetic field data of each magnetic sensor in a range covered by the array.

[0033] Specifically, the step 2 comprises:

[0034] An indoor magnetic field is formed by the joint action of multiple scattered magnetic sources, mainly including electronic devices, metal structures, pipelines and other magnetic materials. According to classical electromagnetic theory, Helmholtz theorem points out that any static magnetic field distribution can be uniquely decomposed into the superposition of an irrotational field (described by a magnetic scalar potential ) and a divergence-free field (described by a magnetic vector potential ), and the specific expression is:

[0035] ;

[0036] Meanwhile, the magnetic field satisfies Ampere's law:

[0037]

[0038] wherein, is a vacuum permeability, denotes a gradient operator, Gradient of magnetic scalar potential, Rotation of magnetic vector potential, Rotation of magnetic vector potential, in the absence of free current region (J=0), J represents the current density vector, magnetic field degenerates into irrotational field, namely . At this time, the magnetic field distribution is only determined by the boundary conditions and the medium magnetization characteristics, and has nothing to do with the physical structure of the real source.

[0039] In the complex indoor magnetic environment, the physical structure and spatial distribution of the real magnetic source (such as building reinforcement, electronic equipment, etc.) are difficult to accurately model, but according to the equivalent theory, no matter how complex the real magnetic source is, there is always a set of equivalent magnetic dipole, which produces the magnetic field consistent with the real field distribution in the observation area. Therefore, the invention introduces the equivalent magnetic dipole model, and constructs a virtual magnetic dipole, so that the magnetic field generated by the virtual magnetic dipole is consistent with the real magnetic field in the observation area.

[0040] Suppose that the real magnetic field at the indoor observation point is determined by the superposition of all current elements around it, which follows the Biot-Savart law, and the real current density vector is , represents the position of the magnetic source, and the magnetic field of the magnetic source at the indoor observation point is:

[0041] ;

[0042] wherein, represents the position vector of the indoor observation point, represents the real magnetic field vector at the indoor observation point; represents the relative position vector of the indoor observation point to the th magnetic dipole position ; represents the three-dimensional volume differential element. (The invention uses magnetic dipole to approximate the magnetic source, so the position of the i th magnetic source is , and the position of the th magnetic dipole is also ).

[0043] According to the multipole expansion theory of static magnetic field, the magnetic field of any local current distribution (or magnetized body) in the far field region can be expanded as:

[0044] ;

[0045] wherein, is the magnetic dipole moment, represents the relative position vector between the observation point and the magnetic dipole, when the observation distance is much larger than the size of the magnetic dipole, the dipole term decays with , and the dipole dominates in the far field condition, express It is a higher-order infinitesimal. Therefore, in an indoor environment, if the magnetometer is placed at a certain distance from the magnetic source (not in close contact with the magnet surface), the magnetic dipole approximation has physical plausibility.

[0046] By discretizing the integral, the above equation can be approximated by a superposition field of a finite number of magnetic dipoles:

[0047] ;

[0048] in, This represents the magnetic field vector predicted by the equivalent model at the indoor observation point; N represents the number of magnetic dipoles. This represents the magnetic moment vector of the i-th equivalent magnetic dipole; Indicates the distance from the observation point to the th Magnetic dipole position The relative position vector at the location; Indicates the distance from the observation point to the th The distance between magnetic dipoles. For the summation sign, as N→∞, the discrete superposition converges to the true integral.

[0049] Under static magnetic field and linear isotropic medium conditions, the magnetic field satisfies the superposition principle: (1) Linear superposition: The total magnetic field generated by multiple independent magnetic sources is the vector sum of the magnetic fields of each source. (2) Spatial independence: The magnetic field generated by each magnetic source is only related to its own parameters and relative position, and is not affected by other sources. Under these conditions, the total magnetic field in a complex magnetic environment... It can be decomposed into a background field (such as the Earth's magnetic field) and the magnetic fields of all local magnetic sources. The linear superposition of (steel bars, equipment, etc.) is represented as follows:

[0050] ;

[0051] in, This represents the background magnetic field vector, typically the Earth's magnetic field.

[0052] The problem of finding the equivalent magnetic dipole is essentially a nonlinear least squares optimization problem. The existence of its solution depends on the sufficiency of the observation data. Based on the relationship between the number of parameters and the degrees of freedom of measurement, each magnetic dipole requires 6 parameters, including the position of the magnetic dipole. and magnetic moment and background magnetic field There are a total of ( There are ) unknowns, among which , , These represent the background magnetic field at... axis, axis, Axis components, subscripts , , Representing the local coordinate system axis, axis, Axis components, subscript Indicates the first One magnetic dipole. A triaxial magnetometer provides three independent measurements, therefore a minimum of ( This invention employs an array of magnetic sensors integrated at fixed intervals to measure spatial magnetic field information and solve for the magnetic field model parameters. The superscript T denotes the transpose of the matrix.

[0053] Specifically, step 3 includes:

[0054] Assume the measured value of the array magnetic sensor is , This indicates the label of each magnetometer in the array magnetic sensor. This indicates the number of magnetometers in an array-type magnetic sensor. The magnetic field measurement model is represented as follows:

[0055] ;

[0056] in,

[0057] ;

[0058] ;

[0059] in, This represents the measurement value of the spatial magnetic array. , ,…, This represents the measured value of each magnetic sensor in the magnetometer of an array-type magnetic sensor. Indicates measurement noise. , , ..., This represents the measurement error of each magnetic sensor in the magnetometer of an array-type magnetic sensor. This represents the magnetic field predicted by the equivalent magnetic dipole model. , , ..., This represents the magnetic field measured at an indoor observation point using an equivalent magnetic dipole model. , , ..., This represents the position vector of each indoor observation point. Assuming the magnetometer is calibrated, we can assume the measurement error is a zero-mean Gaussian distribution, and the covariance matrix... , This represents the variance of the measurement noise; , indicating the number of magnetic dipoles. represents the position of the th magnetic dipole; , represents the sensor label in the spatial magnetic array, represents the position of the sensor with label in the spatial magnetic array, represents the measured value at ; and represents the spatial distance from the sensor with label to the th magnetic dipole.

[0060] In particular, the step 4 comprises:

[0061] The magnetic field model parameters can be solved using a nonlinear least squares method:

[0062] .

[0063] wherein argmin represents a parameter function that makes the objective function take the minimum value, and the result obtained by the function is the argument (parameter) value when the objective function reaches the minimum value; r represents the magnetic dipole position, m represents the magnetic moment vector of the equivalent magnetic dipole, represents the background magnetic field.

[0064] Embodiment:

[0065] A planar array magnetic sensor composed of 42 magnetic sensors with a layout of 6 rows and 7 columns and an interval of 10 cm between each magnetic sensor is adopted to collect magnetic field data. The collected magnetic field data Y is:

[0066] ;

[0067] wherein , ,…, respectively represent the three-axis magnetic field data collected by the 42 magnetic sensors.

[0068] The equivalent magnetic dipole model parameters (magnetic source position, magnetic moment) and the background magnetic field are solved by using the collected magnetic field data and through a nonlinear least squares optimization method, and the equivalent magnetic dipole model is obtained. The equivalent magnetic dipole model can be used to predict the magnetic field intensity information at the next moment.

[0069] As shown in Figure 3 , the horizontal axis represents the label of each magnetic sensor in the array magnetic sensor, and the vertical axis represents the error of the estimated magnetic field, with the unit of microtesla, wherein Figure 3 a of the first subgraph represents the X-axis estimated magnetic field error, Figure 3b is the Y-axis estimated magnetic field error, Figure 3 c is the Z-axis estimated magnetic field error. As can be seen from the figure, the three-axis magnetic field errors estimated by the equivalent magnetic dipole model are all less than 0.4uT, wherein the X-axis magnetic field error is less than 0.013uT, the Y-axis magnetic field error is less than 0.003uT, and the Z-axis magnetic field error is less than 0.04uT. It can be seen that the equivalent magnetic dipole model can accurately predict the local magnetic field strength.

[0070] As shown in Figure 2 The application further provides an indoor local magnetic field modeling device based on the equivalent principle of magnetic sources, comprising the following modules:

[0071] An original measurement information acquisition module acquires triaxial magnetometer data in a space range by using an array type magnetic sensor, and acquires original measurement information of an indoor magnetic field;

[0072] A model construction module models the indoor magnetic field into an equivalent magnetic dipole model composed of multiple equivalent magnetic dipoles based on the equivalent principle of magnetic sources, and sets magnetic moment and position parameters of the magnetic dipoles so that the magnetic field generated by the equivalent magnetic dipole model is consistent with the real magnetic field in the observation area;

[0073] A relationship description module establishes an observation model for describing the relationship between triaxial magnetometer data and parameters of the equivalent magnetic dipole model according to the triaxial magnetometer data collected by the array type magnetic sensor and in combination with the equivalent magnetic dipole model;

[0074] A parameter solving module solves the parameters of the equivalent magnetic dipole model according to the observation model by a nonlinear least square optimization method, and obtains the equivalent magnetic dipole model of the indoor magnetic field, wherein the parameters include the magnetic moment and the position of the magnetic dipoles.

[0075] The application further provides an electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor implements the steps of the above-mentioned indoor local magnetic field modeling method based on the equivalent principle of magnetic sources when executing the program.

[0076] The application further provides a non-transitory computer readable storage medium having a computer program stored thereon, wherein the computer program implements the steps of the above-mentioned indoor local magnetic field modeling method based on the equivalent principle of magnetic sources when executed by a processor.

[0077] Those skilled in the art will appreciate that embodiments of the present application can be readily used as software, hardware, or a combination of software and hardware. In a software embodiment, the methods can be tangibly embodied in a machine-readable storage medium having stored thereon instructions that can be used to program a computer to perform any of the methods. The software implementation can be initialized by loading and executing a set of instructions arranged to perform one of the methods into the computer's memory. Alternatively, hard-wired circuitry can be used in place of, or in combination with, software instructions. Thus, the

[0078] The present application is described in reference to the flowchart and / or block diagrams of the methods, apparatus (systems) and computer program products according to embodiments of the application. It will be understood that each block of the flowchart and / or block diagrams, and combinations of blocks in the flowchart and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general purpose computer, special purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions specified in the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in one or more of the flowchart and / or block diagram block or blocks. Figure 1 means for performing one or more functions specified in one or more of the flowchart and / or block diagram block or blocks.

[0079] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instructions which implement the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in one or more of the flowchart and / or block diagram block or blocks. Figure 1 means for performing one or more functions specified in one or more of the flowchart and / or block diagram block or blocks.

[0080] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the flowchart and / or block diagram block or blocks. Figure 1 one or more functions specified in one or more of the flowchart and / or block diagram block or blocks. Figure 1 means for performing one or more functions specified in one or more of the flowchart and / or block diagram block or blocks.

[0081] While preferred embodiments of the application have been described, modifications and variations can be apparent to those skilled in the art once aware of the general underlying concepts. Accordingly, the appended claims are intended to encompass all modifications and variations as falling within the scope of the application.

[0082] It will be apparent to those skilled in the art that various modifications and variations can be made to the present application without departing from the spirit or scope of the application. Thus, it is intended that the present application cover modifications and variations of this application provided they come within the scope of the appended claims and their equivalents.

Claims

1. A method for modeling indoor local magnetic field based on the principle of magnetic source equivalence, characterized in that, The method comprises the following steps: Step 1: collecting tri-axial magnetometer data in a spatial range by using an array magnetic sensor to obtain original measurement information of an indoor magnetic field; Step 2: modeling the indoor magnetic field as an equivalent magnetic dipole model composed of multiple equivalent magnetic dipoles based on the equivalent principle of magnetic sources, and setting the magnetic moment and position parameters of the magnetic dipoles to make the magnetic field generated by the equivalent magnetic dipole model consistent with the real magnetic field in the observation area; Step 3: establishing an observation model based on the tri-axial magnetometer data collected by the array magnetic sensor and the equivalent magnetic dipole model to describe the relationship between the tri-axial magnetometer data and the parameters of the equivalent magnetic dipole model; Step 4: solving the parameters of the equivalent magnetic dipole model according to the observation model by using a nonlinear least squares optimization method to obtain the equivalent magnetic dipole model of the indoor magnetic field, wherein the parameters include the magnetic moment and position of the magnetic dipoles.

2. The indoor local magnetic field modeling method based on the magnetic source equivalence principle according to claim 1, characterized in that, In the step 1, the array magnetic sensor is integrated at fixed intervals to measure spatial magnetic field information.

3. The indoor local magnetic field modeling method based on the magnetic source equivalence principle according to claim 1, characterized in that, In the step 2, the equivalent magnetic dipole model uses the superposition field of a finite number of magnetic dipoles to approximate the real magnetic field distribution by means of discrete integration, and when the number of magnetic dipoles tends to infinity, the discrete superposition converges to the real integral.

4. The indoor local magnetic field modeling method based on the magnetic source equivalence principle of claim 1, wherein, In the step 3, the influence of measurement noise is considered, the measurement error is assumed to be zero-mean Gaussian distribution, and the tri-axial magnetometer data collected by the array magnetic sensor is connected to the parameters of the equivalent magnetic dipole model through the observation model.

5. The indoor local magnetic field modeling method based on the magnetic source equivalence principle according to claim 1, characterized in that, In the step 4, the nonlinear least squares optimization method solves the parameters of the equivalent magnetic dipole model according to the observation model and the tri-axial magnetometer data collected by the array magnetic sensor to minimize the error between the tri-axial magnetometer data collected by the array magnetic sensor and the model prediction value.

6. The indoor local magnetic field modeling method based on the magnetic source equivalence principle according to claim 1, characterized in that, The equivalent magnetic dipole model approximates complex magnetic field distribution by superimposing multiple magnetic dipoles, and is suitable for real-time magnetic field positioning and navigation in large-scale complex environments.

7. The indoor local magnetic field modeling method based on the magnetic source equivalence principle according to claim 1, characterized in that, The parameters of the equivalent magnetic dipole model are traced back to the actual magnetic source distribution.

8. An indoor local magnetic field modeling device based on the magnetic source equivalence principle, characterized in that, The method comprises the following modules: An original measurement information acquisition module acquires tri-axial magnetometer data in a spatial range by using an array magnetic sensor to obtain original measurement information of an indoor magnetic field; A model construction module models the indoor magnetic field as an equivalent magnetic dipole model composed of multiple equivalent magnetic dipoles based on the equivalent principle of magnetic sources, and sets the magnetic moment and position parameters of the magnetic dipoles to make the magnetic field generated by the equivalent magnetic dipole model consistent with the real magnetic field in the observation area; A relationship description module establishes an observation model based on the tri-axial magnetometer data collected by the array magnetic sensor and the equivalent magnetic dipole model to describe the relationship between the tri-axial magnetometer data and the parameters of the equivalent magnetic dipole model; A parameter solving module solves the parameters of the equivalent magnetic dipole model according to the observation model by using a nonlinear least squares optimization method to obtain the equivalent magnetic dipole model of the indoor magnetic field, wherein the parameters include the magnetic moment and position of the magnetic dipoles.

9. An electronic device comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, The processor executes the program to implement the steps of the indoor local magnetic field modeling method based on the equivalent principle of magnetic sources according to any one of claims 1 to 7. 10.A non-transitory computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program, when executed by the processor, implements the steps of a method for modeling an indoor local magnetic field based on a magnetic source equivalence principle as claimed in any one of claims 1 to 7.

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