Iterative least squares artificial magnetic field positioning method and device not affected by attitude

Abstract

The present invention provides an iterative least squares artificial magnetic field positioning method and device that is not affected by attitude, which belongs to the field of indoor positioning. Aiming at the problem of increased complexity caused by the attitude of the carrier, a method for establishing an artificial magnetic field positioning observation equation that is not affected by attitude is adopted, and the introduction of attitude unknown quantities is avoided by using the method of finding the modulus by frequency, and a simplified observation equation based on the modulus value of magnetic induction intensity is established, thereby reducing the number of nonlinear unknown quantities in the equation group and reducing the search space and the number of local optimal solutions for subsequent optimization and solution ideas; for the problem of solving nonlinear equations in the position solution process, an algorithm for performing positioning inversion solution based on iterative least squares is provided, with the goal of minimizing the modulus of the difference between the state quantity and the real-time observation quantity, and continuously expanding linearly at the iteration point and using least squares iterative calculation. The present invention realizes high-precision position solution with global optimality and fast convergence speed.

Description

Technical Field

[0001] The present invention belongs to the field of indoor positioning, and specifically relates to an iterative least square artificial magnetic field positioning method and device that are not affected by posture, which can realize real-time and accurate positioning that is not affected by carrier posture. Background Art

[0002] Continuous and reliable positioning information is of great significance for the application of location services in scenarios where Beidou satellite signals are blocked. Due to the influence of building blockage and multipath effects, the Beidou satellite navigation system is difficult to extend to indoor and other shielded scenarios, and cannot provide high-precision positioning services. Among the current indoor positioning methods, the inertial navigation system can continuously and autonomously obtain the carrier position information, but because the inertial device error diverges seriously over time, it cannot guarantee long-term positioning accuracy; WiFi, Bluetooth, ultra-wideband and other radio positioning technologies have high positioning accuracy in indoor environments with good line-of-sight conditions, but are seriously affected by indoor non-line-of-sight blockage and multipath problems, and the positioning reliability is poor; the indoor geomagnetic field map matching method has the advantages of passive concealment, strong anti-interference performance, and no error divergence, but it requires the establishment of a geomagnetic reference map in advance, and the positioning accuracy may not be met. Among the many indoor positioning methods, the indoor positioning technology based on artificial magnetic field makes full use of the high penetration advantage of low-frequency magnetic field, and inverts the user's position in real time based on magnetic field intensity, without the need to establish a reference map in advance, and has great application potential in indoor shielded positioning scenarios.

[0003] The basic principle of the artificial magnetic field positioning system is to use the known magnetic field radiation model to measure the magnetic induction vector intensity at the location of the sensor, and then invert and calculate the relative position according to the magnetic field model formula. However, the existing positioning solution method mainly solves the observation equation by bringing the carrier posture as a rotation matrix, introducing three new nonlinear variables into the nonlinear equation containing three variables, which leads to a greater solution complexity of the observation equation, and easily causes the positioning solution to have large positioning errors and difficulty in solution convergence. At the same time, existing methods often do not pay attention to the position solution process. For example, direct search or genetic algorithms are used for position solution, which have problems such as high computational complexity, large positioning errors, and slow convergence speed, which affect the positioning accuracy and positioning performance. Summary of the invention

[0004] In order to solve the posture problems and solution problems existing in the prior art, the present invention provides an iterative least squares artificial magnetic field positioning method and device that are not affected by posture. On the one hand, in view of the problem of increased complexity caused by the carrier posture, a method for establishing an artificial magnetic field positioning observation equation that is not affected by posture is systematically modeled, and the introduction of posture unknown quantities is avoided by using the frequency modulus method, and a simplified observation equation based on the intensity modulus value is established, thereby reducing the number of nonlinear unknown quantities in the equation group and reducing the search space and the number of local optimal solutions for subsequent optimization and solution ideas; on the other hand, in view of the nonlinear equation solution problem in the position solution process, an algorithm for positioning inversion solution based on iterative least squares is given, with the goal of minimizing the modulus of the difference between the state quantity and the real-time observation quantity, and continuously expanding linearly at the iteration point and using the least squares iterative calculation to achieve global optimal, fast convergence speed and high-precision position solution.

[0005] In order to achieve the above object, the present invention adopts the following technical solution:

[0006] An iterative least square artificial magnetic field positioning method that is not affected by posture comprises the following steps:

[0007] Step 1: Using the magnetic dipole model, a magnetic field free space radiation model is established according to the emission source conditions to obtain the model magnetic induction intensity;

[0008] Step 2: Perform frequency separation filtering. After the sensor completes the magnetic field measurement, use Fourier transform to obtain frequency domain information to obtain the magnetic induction intensity of each emission source frequency point in the three-axis direction of the sensor coordinate system;

[0009] Step 3, find the modulus of the magnetic induction intensity at the same frequency measured in step 2, calculate the modulus value of the magnetic induction intensity at the same frequency, avoid the problem of increased solution complexity and the number of optimal solutions introduced by the attitude, and construct a nonlinear observation equation group;

[0010] Step 4: For the nonlinear observation equations constructed in step 3, the nonlinear observation equations are linearized at the iteration points using Taylor expansion, and an iterative position inversion solution is performed;

[0011] Step 5: Take the model magnetic induction intensity in step 1 as the state quantity, minimize the sum of squares of the difference between the state quantity and the observation quantity as the objective function, and use the least square method to iterate and solve continuously until the iterative offset meets the threshold condition;

[0012] Step 6: Determine whether the iteration is to be stopped. If the iteration step does not meet the threshold condition, the iteration continues. If the threshold condition is met, the iteration stops to achieve high-precision positioning of the artificial magnetic field.

[0013] The present invention also provides an iterative least square artificial magnetic field positioning device that is not affected by posture, comprising the following modules:

[0014] The model magnetic induction intensity acquisition module uses the magnetic dipole model to establish a magnetic field free space radiation model according to the emission source conditions to obtain the model magnetic induction intensity;

[0015] The sensor magnetic induction intensity acquisition module performs frequency separation filtering. After the sensor completes the magnetic field measurement, it uses Fourier transform to obtain the frequency domain information and obtain the magnetic induction intensity of the sensor at each emission source frequency point in the three-axis direction of the sensor coordinate system;

[0016] The observation equation construction module modulos the measured magnetic induction intensity at the same frequency, calculates the modulus of the magnetic induction intensity at the same frequency, avoids the problem of increased solution complexity and the number of optimal solutions introduced by the attitude, and constructs a nonlinear observation equation group;

[0017] The inversion solution module uses Taylor expansion to linearize the constructed nonlinear observation equations at the iteration points and performs iterative position inversion solution.

[0018] In the solution module, the model magnetic induction intensity is used as the state quantity, and the objective function is to minimize the sum of squares of the difference between the state quantity and the observation quantity. The least square method is used to iterate and solve continuously until the iterative offset meets the threshold condition.

[0019] The iteration module determines whether to stop the iteration. If the iteration step does not meet the threshold condition, the iteration continues. If the threshold condition is met, the iteration stops to achieve high-precision positioning of the artificial magnetic field.

[0020] The present invention also provides an electronic device, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of the above-mentioned iterative least squares artificial magnetic field positioning method not affected by posture are implemented.

[0021] The present invention also provides a non-transitory computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of an iterative least squares artificial magnetic field positioning method that is not affected by posture are implemented.

[0022] Beneficial effects:

[0023] 1. Compared with the existing positioning method that takes the attitude as an unknown quantity into the observation equation solution, the present invention avoids the complexity problem caused by the carrier attitude by finding the modulus according to the frequency, which can simplify the observation equation construction process and solution process, and reduce the solution search space and the number of local optimal solutions in the subsequent optimization solution process;

[0024] 2. Compared with direct optimization solution or solution using optimization algorithms such as genetic algorithm, the present invention solves the position through iterative least squares optimization, takes the modulus of the difference between the state quantity and the observed magnetic induction intensity as the objective function, and uses nonlinear equation linearization, least squares and continuous iteration to achieve global optimal, high-precision and rapidly convergent position inversion. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 The present invention is a flow chart of an iterative least squares artificial magnetic field positioning method that is not affected by posture.

[0026] Figure 2 is a flow chart of the iterative least squares position solution method. DETAILED DESCRIPTION

[0027] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.

[0028] like Figure 1 As shown, an iterative least square artificial magnetic field positioning method of the present invention that is not affected by posture includes the following steps:

[0029] Step 1: Using the magnetic dipole model, a magnetic field free space radiation model is established according to the emission source conditions to obtain the model magnetic induction intensity;

[0030] Step 2: Perform frequency separation filtering. After the sensor completes the magnetic field measurement, use Fourier transform to obtain frequency domain information to obtain the magnetic induction intensity of each emission source frequency point in the three-axis direction of the sensor coordinate system;

[0031] Step 3, find the modulus of the magnetic induction intensity at the same frequency measured in step 2, calculate the modulus value of the magnetic induction intensity at the same frequency, avoid the problem of increased solution complexity and the number of optimal solutions introduced by the attitude, and construct a nonlinear observation equation group;

[0032] Step 4: For the nonlinear observation equations constructed in step 3, the nonlinear observation equations are linearized at the iteration points using Taylor expansion, and an iterative position inversion solution is performed;

[0033] Step 5: Take the model magnetic induction intensity in step 1 as the state quantity, minimize the sum of squares of the difference between the state quantity and the observation quantity as the objective function, and use the least square method to iterate and solve continuously until the iterative offset meets the threshold condition;

[0034] Step 6: Determine whether the iteration is to be stopped. If the iteration step does not meet the threshold condition, the iteration continues. If the threshold condition is met, the iteration stops to achieve high-precision positioning of the artificial magnetic field.

[0035] Specifically, the step 1 includes:

[0036] The basic principle of artificial magnetic field positioning is to measure the magnetic induction intensity with the sensor and substitute it into the known magnetic field model to solve the position. A rectangular coordinate system (source coordinate system) is established with the center of the emission source as the origin. The center is located at the origin and the direction is along the The space-time variation model of the artificial magnetic field emission source of the axis in the Cartesian coordinate system is as follows (1):

[0037] (1)

[0038] in, is the magnetic induction intensity, is the coordinate of the magnetic measuring point; is the free space permeability; is along The magnetic moment of the energized coil of the shaft; is the distance from the magnetic measuring point to the energized coil; They refer to the unit direction vectors along the three coordinate axes of the emission source coordinate system.

[0039] The magnetic induction intensity of the three-axis orthogonal artificial magnetic field source along the source coordinate system The components of the three axes are expressed by the free space radiation model of the magnetic dipole magnetic field shown in equation (2):

[0040] (2)

[0041] in, is the coordinate system along the emission source The magnetic induction intensity components of the three axes; is along the source coordinate system The magnetic moment of the energized coil in three axes;

[0042] The magnetic field has vector characteristics, so the magnetic induction intensity measured by the sensor is not only related to the magnetic field intensity at the point where it is located, but also to the sensor posture. Assume that the carrier coordinate system can be rotated along the X-axis by the emission source reference system , Y rotation , Z-axis rotation According to Faraday's law of electromagnetic induction, the induced voltage value of the magnetic sensor coil is given by formula (3):

[0043] (3)

[0044] in, is the triaxial induced voltage measured by the sensor under the load system; is the operating angular frequency; is the number of turns of the sensor coil, is the coil area; is the magnetic induction intensity of the magnetic measuring point where the sensor is located along the three-axis directions of the sensor coordinate system; is the rotation matrix, and its form is as follows:

[0045] (4)

[0046] in, is the rotation angle from the sensor carrier system to the emission source reference system; sin and cos are the sine and cosine trigonometric operation symbols.

[0047] The present invention provides a method for establishing an observation equation that is not affected by posture, avoiding the influence of unknown posture to reduce the equation search space and the number of local optimal solutions.

[0048] Specifically, step 2 includes:

[0049] Frequency division multiplexing is used to increase the number of observation equations to achieve position solution. In the frequency division multiplexing system, the transmitting source is used along three axes. The sensor coil can simultaneously measure the magnetic field of three frequencies along the three axes. The observation equation can be constructed by separation filtering, as shown in formula (5):

[0050] (5)

[0051] in, Represents the sensor coordinate system Shaft frequency The induced voltage value obtained by measuring the magnetic induction intensity is Represents the sensor coordinate system Shaft frequency The induced voltage value obtained by measuring the magnetic induction intensity is Represents the sensor coordinate system Shaft frequency An induced voltage value obtained by measuring the magnetic induction intensity; Indicates along the source coordinate system The shaft frequency is The magnetic moment of Indicates along the source coordinate system The shaft frequency is The magnetic moment of Indicates along the source coordinate system The shaft frequency is The magnetic moment of

[0052] Expanding formula (5), 3 Each variable of the 3-matrix can constitute an observation equation. By solving the set of equations simultaneously, the values ​​of the six unknown quantities of position and attitude can be obtained, thereby realizing position solution.

[0053] In the measurement coordinate system, measure the magnetic induction vector There is the following relationship with the magnetic induction intensity vector in space:

[0054] (6)

[0055] in, is the three-dimensional magnetic induction intensity vector at the magnetic measurement point along the direction of the emission source coordinate system.

[0056] Assume that the three axes of the source coordinate system are The frequency of the magnetic field is radiated. At this time, the magnetic induction intensity vector at the magnetic measuring point in the space along the direction of the reference coordinate system of the transmitting source Contains the frequency information shown in the following formula (7):

[0057] (7)

[0058] After obtaining the magnetic induction intensity information in the frequency domain through Fourier transform, the relationship between the magnetic induction intensity of the sensor in each direction at each frequency point is obtained:

[0059] (8)

[0060] in, Represents the sensor coordinate system at the magnetic measuring point Three-way measurement Three-frequency magnetic induction intensity matrix; matrix elements Indicates along the sensor coordinate system The frequency in the axial direction is The magnetic induction intensity component, Indicates along the sensor coordinate system The frequency in the axial direction is The magnetic induction intensity component, Indicates along the sensor coordinate system The frequency in the axial direction is The magnetic induction intensity components of is the magnetic measuring point along the source coordinate system The frequency in the axial direction is The magnetic induction intensity component, is the magnetic measuring point along the source coordinate system The frequency in the axial direction is The magnetic induction intensity component, is the magnetic measuring point along the source coordinate system The frequency in the axial direction is The magnetic induction intensity component.

[0061] The present invention provides a method for establishing an observation equation that is not affected by posture, avoiding the influence of unknown posture to reduce the equation search space and the number of local optimal solutions.

[0062] Specifically, step 3 includes:

[0063] By transposing the matrix, multiplying it and taking the diagonal elements, we can find the modulus of magnetic induction intensity at the same frequency:

[0064] (9)

[0065] Among them, diag() means extracting the diagonal elements of the matrix, and the superscript T means the transpose of the matrix.

[0066] At this time, according to the emission source The frequency is separated and filtered and a nonlinear observation equation group is constructed, as shown in the following equation (10):

[0067] (10)

[0068] in, Indicates that in the source coordinate system, the frequency at the magnetic measurement point is The modulus of magnetic induction intensity; Indicates that in the sensor coordinate system, the frequency at the magnetic measuring point is The modulus of magnetic induction intensity.

[0069] At this time, compared with the 9-dimensional equation group containing the unknown quantity of attitude, the equation is simplified in form and solution, and can be solved by linearization and optimization. This method uses frequency information to calculate the modulus of magnetic induction intensity at different frequencies, avoids the complexity caused by the sensor attitude, realizes the construction of observation equations that are not affected by attitude, and solves the complexity problem introduced by attitude.

[0070] Specifically, the step 4 includes:

[0071] The observation equations established by formula (10) are all nonlinear equations and cannot be solved directly. Therefore, the present invention uses iterative least squares to optimize and solve. The general idea of ​​iterative least squares solution is to set the search space and state points, and use optimization to continuously iterate the state points until the iteration step meets the accuracy requirements. The iteration step along the three dimensions is determined by the least squares solution of the difference between the linearized state quantity and the observation value.

[0072] Next, we derive the least square method to determine the iteration step size. In each iteration, assume that the coordinates of the lth iteration point are , at this time, the magnetic induction intensity calculated by the iterative point coordinates is:

[0073] (11)

[0074] in, is the coordinate system of the emission source at the lth iteration point The function calculated in the three-axis direction, i.e. the state quantity, is equal to the value of the coordinate system of the emission source at this iteration point. Magnetic induction intensity in three axes The square of the modulus; is a constant, is the magnitude of the magnetic moment.

[0075] At this time Linearization at:

[0076] (12)

[0077] in, Represents the sensor along the source coordinate system The observed magnetic induction intensity in three directions, For the state quantity Along the source coordinate system Partial derivatives in direction. is the difference between the iterative point coordinates and the real position coordinates. and the iteration point coordinates The relationship between them satisfies:

[0078] (13)

[0079] Specifically, the step 5 includes:

[0080] By shifting the terms in equation (12), we can obtain the difference between the observed value of magnetic induction intensity and the state quantity: The linear relationship between the position offset to be solved is:

[0081] (14)

[0082] in, For the direction The difference between the observed value of magnetic induction intensity and the state quantity is expressed in matrix form as:

[0083] (15)

[0084] in, The source coordinate system The difference vector between the observed value of magnetic induction intensity and the state quantity in the three-axis direction has the dimension ; G is the partial derivative matrix composed of partial derivatives of the state quantity at the iteration point, and its dimension is ,element Represents the source coordinate system Axis direction state At the iteration point coordinates Along the source coordinate system Partial derivatives in direction, elements Represents the source coordinate system Axis direction state At the iteration point coordinates Along the source coordinate system The partial derivative of the direction, Represents the source coordinate system Axis direction state exist Along the source coordinate system Partial derivatives of direction; is the position offset, and its dimension is When the accurate position offset is solved in the position optimization solution process When , the accurate position can be obtained by summing it with the state quantity. Position offset It can be expressed as:

[0085] (16)

[0086] Among them, argmin is a mathematical operation, which means to find The coordinates of the iteration point when the square of the modulus reaches the minimum value in the domain. The least squares solution of equation (16) is:

[0087] (17)

[0088] Using the above least squares, the position offset of each iteration can be obtained ,Through continuous iteration, the position offset that meets the threshold is found, and the global optimal, fast-converging high-precision position solution can be achieved.

[0089] like Figure 2 As shown, the steps of the iterative process are as follows:

[0090] Step 1: System initialization, giving the estimated position and initial coordinate values ;

[0091] Step 2: Linearization, using Taylor expansion, at the state point of this iteration (i.e., the iteration coordinate point) to linearize the nonlinear observation equation and construct the linearized equation for this iteration;

[0092] Step 3: Use the least squares solution to obtain the position offset of this iteration ;

[0093] Step 4: Determine the convergence of the iteration. If the position offset of the iterative solution If the following formula (18) is satisfied, the error introduced by this iterative solution is judged to be within an acceptable range, and the output state point is as the solved position.

[0094] (18)

[0095] in, For the The position coordinates of the iteration, is the preset threshold, that is, the threshold condition.

[0096] If the condition is not met, the fifth step of position state update is completed and then the second step is entered for iterative calculation;

[0097] Step 5: Update the location status and obtain the location offset After that, the coordinates are updated. After the update, the sensor coordinates are :

[0098] (19)

[0099] The position solution is performed by iterative least squares, which takes advantage of the least squares solution to nonlinear problems and can make comprehensive use of the information of each observation equation; the iterative idea continues to calculate the state quantity until it approaches the true solution. The position solution using iterative least squares can effectively utilize the observation data information to achieve fast and optimal position solution. The experimental results of the iterative least squares positioning method without being affected by the attitude are shown in Table 1, and the experimental results of the attitude matrix + direct optimization positioning method are shown in Table 2.

[0100] Table 1 Experimental results of the positioning method without being affected by posture + iterative least squares positioning method

[0101]

[0102] Table 2 Experimental results of posture matrix + direct optimization positioning method

[0103]

[0104] The average measurement error of the present invention in the X-axis is 0.31 m, the standard deviation is 0.24 m, the average error of the Y-axis is 0.32 m, the standard deviation is 0.09 m, and the average error of the two-dimensional level is 0.48 m, the standard deviation is 0.18 m. The average measurement error of the X-axis of other methods is 0.85 m, the standard deviation is 0.40 m, the average error of the Y-axis is 0.33 m, the standard deviation is 0.26 m, and the average horizontal error is 1.0 m, the standard deviation is 0.29 m. Compared with the present invention, the errors of other methods are increased in all aspects and the accuracy is reduced.

[0105] The present invention also provides an iterative least square artificial magnetic field positioning device that is not affected by posture, comprising the following modules:

[0106] The model magnetic induction intensity acquisition module uses the magnetic dipole model to establish a magnetic field free space radiation model according to the emission source conditions to obtain the model magnetic induction intensity;

[0107] The sensor magnetic induction intensity acquisition module performs frequency separation filtering. After the sensor completes the magnetic field measurement, it uses Fourier transform to obtain the frequency domain information and obtain the magnetic induction intensity of the sensor at each emission source frequency point in the three-axis direction of the sensor coordinate system;

[0108] The observation equation construction module modulos the measured magnetic induction intensity at the same frequency, calculates the modulus of the magnetic induction intensity at the same frequency, avoids the problem of increased solution complexity and the number of optimal solutions introduced by the attitude, and constructs a nonlinear observation equation group;

[0109] The inversion solution module uses Taylor expansion to linearize the constructed nonlinear observation equations at the iteration points and performs iterative position inversion solution.

[0110] In the solution module, the model magnetic induction intensity is used as the state quantity, and the objective function is to minimize the sum of squares of the difference between the state quantity and the observation quantity. The least square method is used to iterate and solve continuously until the iterative offset meets the threshold condition.

[0111] The iteration module determines whether to stop the iteration. If the iteration step does not meet the threshold condition, the iteration continues. If the threshold condition is met, the iteration stops to achieve high-precision positioning of the artificial magnetic field.

[0112] The present invention also provides an electronic device, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the steps of the above-mentioned iterative least squares artificial magnetic field positioning method not affected by posture are implemented.

[0113] The present invention also provides a non-transitory computer-readable storage medium on which a computer program is stored. When the computer program is executed by a processor, the steps of the above-mentioned iterative least squares artificial magnetic field positioning method that is not affected by posture are implemented.

[0114] It should be understood by those skilled in the art that the embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes. The solutions in the embodiments of the present invention may be implemented in various computer languages, for example, object-oriented programming language Java and interpreted scripting language JavaScript, etc.

[0115] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0116] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0117] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0118] Although the preferred embodiments of the present invention have been described, those skilled in the art may make other changes and modifications to these embodiments once they have learned the basic creative concept. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention.

[0119] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. An iterative least squares artificial magnetic field positioning method that is not affected by posture, characterized in that: The steps include: Step 1: Using the magnetic dipole model, a magnetic field free space radiation model is established according to the emission source conditions to obtain the model magnetic induction intensity; Step 2: Perform frequency separation filtering. After the sensor completes the magnetic field measurement, use Fourier transform to obtain frequency domain information to obtain the magnetic induction intensity of the sensor at each emission source frequency point in the three-axis direction of the sensor coordinate system; Step 3, find the modulus of the magnetic induction intensity at the same frequency measured in step 2, calculate the modulus value of the magnetic induction intensity at the same frequency, avoid the problem of increased solution complexity and the number of optimal solutions introduced by the attitude, and construct a nonlinear observation equation group; Step 4: For the nonlinear observation equations constructed in step 3, the nonlinear observation equations are linearized at the iteration points using Taylor expansion, and an iterative position inversion solution is performed; Step 5: Take the model magnetic induction intensity in step 1 as the state quantity, minimize the sum of squares of the difference between the state quantity and the magnetic induction intensity observation quantity as the objective function, and use the least square method to iterate and solve continuously until the iterative offset meets the threshold condition; Step 6: Determine whether the iteration is to be stopped. If the iteration step does not meet the threshold condition, the iteration continues. If the threshold condition is met, the iteration stops to achieve high-precision positioning of the artificial magnetic field.

2. The iterative least square artificial magnetic field positioning method not affected by posture according to claim 1, characterized in that: The step 1 comprises: A rectangular coordinate system is established with the center of the transmitting source as the origin. The magnetic induction intensity of the three-axis orthogonal artificial magnetic field transmitting source is along The components of the three axes are expressed by the magnetic field free space radiation model of a magnetic dipole as shown in equation (2): (2) in, is the coordinate system along the emission source The magnetic induction intensity components of the three axes; is the free space permeability; is the spatial distance from the spatial magnetic measurement point to the emission source, is the three-dimensional coordinate of the magnetic measuring point in the direction of the coordinate axis; is along the source coordinate system Magnetic moment of the powered coil in three axes.

3. The iterative least square artificial magnetic field positioning method not affected by posture according to claim 2, characterized in that: The step 2 comprises: Take the center of the sensor coil as the origin and the three-axis orthogonal coils of the sensor as the direction. After completing the magnetic field measurement, the frequency domain information is obtained by Fourier transform to obtain the sensor coordinate system of the magnetic measuring point where the sensor is located. The frequencies in the three directions are The magnetic induction intensity is constructed, and the observation equation is shown in formula (8): （8） in, Indicates the sensor coordinate system at the magnetic measuring point The frequency obtained by three-directional measurement is The magnetic induction intensity matrix of Indicates along the sensor coordinate system The frequency in the axial direction is The magnetic induction intensity component, Indicates along the sensor coordinate system The frequency in the axial direction is The magnetic induction intensity component, Indicates along the sensor coordinate system The frequency in the axial direction is The magnetic induction intensity component; is a rotation matrix, which is in the form , is the rotation angle from the sensor carrier system to the emission source reference system; the matrix element is the magnetic measuring point along the source coordinate system The frequency in the axial direction is The magnetic induction intensity component, is the magnetic measuring point along the source coordinate system The frequency in the axial direction is The magnetic induction intensity component, is the magnetic measuring point along the source coordinate system The frequency in the axial direction is The magnetic induction intensity component.

4. The iterative least square artificial magnetic field positioning method not affected by posture according to claim 3, characterized in that: In step 3, the nonlinear observation equations constructed are: （10） in, Indicates that in the source coordinate system, the frequency at the magnetic measurement point is The modulus of magnetic induction intensity; Indicates that in the sensor coordinate system, the frequency at the magnetic measuring point is The modulus of magnetic induction intensity.

5. The iterative least square artificial magnetic field positioning method not affected by posture according to claim 4, characterized in that: The step 4 comprises: In each iterative solution, assume that the coordinates of the lth iteration point are , its distance from the emission source is , using the square of the magnetic induction intensity modulus as the function of the iteration value, the function obtained by the iteration point is for: （11） in, is the coordinate system of the emission source at the lth iteration point The function calculated in the three-axis direction, i.e. the state quantity, is equal to the value of the coordinate system of the emission source at this iteration point. Magnetic induction intensity in three axes The square of the modulus; is a constant, is the magnitude of the magnetic moment; At this time, the function At the iteration point coordinates Linear expansion is performed at: （12） in, Represents the sensor along the source coordinate system The observed magnetic induction intensity in three directions, is the coordinate of the state quantity at the iteration point Along the source coordinate system Partial derivatives of direction; is the difference between the iterative point coordinates and the real position coordinates. and the iteration point coordinates The relationship between .

6. The iterative least square artificial magnetic field positioning method not affected by posture according to claim 5, characterized in that: The step 5 comprises: By transposing equation (12) and expressing it in matrix form, we can obtain: （15） in, The source coordinate system The difference vector between the observed value of magnetic induction intensity and the state quantity in the three-axis direction has the dimension ; G is the partial derivative matrix composed of partial derivatives of the state quantity at the iteration point, and its dimension is ,element Represents the source coordinate system Axis direction state At the iteration point coordinates Along the source coordinate system Partial derivatives in direction, elements Represents the source coordinate system Axis direction state exist Along The partial derivative of the direction, express Axis direction state At the iteration point coordinates Along Partial derivatives of direction; is the position coordinate offset vector, dimension is ; When the accurate position offset is solved in the position optimization solution process When , the accurate position is obtained by summing with the state quantity; the position offset It is expressed as: （16） Among them, argmin is a mathematical operation, which means to find The coordinates of the iteration point when the square of the modulus reaches the minimum value in the domain of definition; the least squares solution of equation (16) is: , the superscript T represents the transpose of the matrix; the position offset of each iteration is obtained by using the above least squares method , through continuous iteration, find the position offset that meets the threshold condition , thereby achieving global optimal, rapidly converging high-precision position solution.

7. The iterative least square artificial magnetic field positioning method not affected by posture according to claim 6, characterized in that: The step 6 comprises: If the position offset of the iterative solution If the following formula is satisfied, the error introduced by this iterative solution is judged to be within an acceptable range, and the coordinates of the iterative points are output. As the solution position; （18） in, is a preset threshold, i.e., a threshold condition; If the threshold condition is not met, the position status is updated and the iterative calculation is performed again; The process of updating the position status includes: obtaining the position offset After that, the coordinates are updated, and the updated iterative point coordinates The sensor coordinates are: （19）。 8. An iterative least square artificial magnetic field positioning device that is not affected by posture, characterized in that: Includes the following modules: The model magnetic induction intensity acquisition module uses the magnetic dipole model to establish a magnetic field free space radiation model according to the emission source conditions to obtain the model magnetic induction intensity; The sensor magnetic induction intensity acquisition module performs frequency separation filtering. After the sensor completes the magnetic field measurement, it uses Fourier transform to obtain the frequency domain information and obtain the magnetic induction intensity of the sensor at each emission source frequency point in the three-axis direction of the sensor coordinate system; The observation equation construction module modulos the measured magnetic induction intensity at the same frequency, calculates the modulus of the magnetic induction intensity at the same frequency, avoids the problem of increased solution complexity and the number of optimal solutions introduced by the attitude, and constructs a nonlinear observation equation group; The inversion solution module uses Taylor expansion to linearize the constructed nonlinear observation equations at the iteration points and performs iterative position inversion solution. In the solution module, the model magnetic induction intensity is used as the state quantity, and the objective function is to minimize the sum of squares of the difference between the state quantity and the observation quantity. The least square method is used to iterate and solve continuously until the iterative offset meets the threshold condition. The iteration module determines whether to stop the iteration. If the iteration step does not meet the threshold condition, the iteration continues. If the threshold condition is met, the iteration stops to achieve high-precision positioning of the artificial magnetic field.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that: When the processor executes the program, the steps of an iterative least squares artificial magnetic field positioning method that is not affected by posture are implemented as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the steps of an iterative least square artificial magnetic field positioning method not affected by attitude as claimed in any one of claims 1 to 7 are implemented.

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