Amphibious weak magnetic field measuring device and error correction method thereof

Abstract

The invention discloses an amphibious weak magnetic field measuring device and an error control method thereof. The device comprises a probe and a circuit system, wherein the probe is composed of a coil structure, a silver-copper composite coating electromagnetic shielding layer, a proton-rich solution and an acrylic shell, and the circuit system is composed of a polarization circuit, a signal conditioning circuit and a control circuit. According to the method, an error calibration parameter is calculated through a nonlinear least square algorithm, so that a calibrated magnetic field measurement value is close to a true value. The magnetic field measurement device has the characteristics of high magnetic field measurement precision and strong anti-interference capability, and is suitable for multi-environment working conditions. The method can be widely applied to the field of magnetic field measurement.

Description

Technical Field

[0001] The present invention relates to the field of magnetic field measurement, and particularly to an amphibious weak magnetic field measurement device and an error correction method thereof. Background Art

[0002] With the development of society and technology, the precise measurement of weak magnetic fields has played an indispensable role in resource exploration, environmental monitoring, and the national defense field. Although there are various existing magnetic field sensors, most of them have problems such as being sensitive to electromagnetic interference, having weak anti-interference ability, and low measurement accuracy. In addition, in complex environments, such as underwater measurement, due to the pointing errors of gyroscopes and magnetometers, it is difficult to obtain accurate three-axis vector magnetic field measurement results.

[0003] Therefore, how to improve the magnetic field measurement accuracy, anti-interference ability, and magnetic field measurement equipment that can adapt to multi-environment working conditions has become a challenge in the current technical field. Summary of the Invention

[0004] In view of this, in order to solve the technical problem that the existing magnetic field measurement device cannot cope with the electromagnetic interference in complex environments, which leads to low magnetic field measurement accuracy, on the one hand, the present invention proposes an amphibious weak magnetic field measurement device, which includes a probe composed of a coil structure, a silver-copper composite coating electromagnetic shielding layer, a proton-rich solution, and an acrylic outer shell, and a circuit system composed of a polarization circuit, a signal conditioning circuit, and a control circuit.

[0005] Furthermore, considering the great role of the weak magnetic field measurement device in geomagnetic measurement and the simplicity of operation, the device is provided with a GPS positioning function and a one-key measurement and display function on the screen.

[0006] In order to further pursue the ultimate in measurement accuracy, the present invention sets the coil structure as a quasi-square symmetric double-coil reverse series structure.

[0007] In some embodiments, while having high sensitivity, the signal conditioning circuit must ensure that its inherent noise is small and has a certain amplification and anti-interference ability. The signal is amplified step by step by using a cascaded multi-stage amplifier, and at the same time, a narrowband filter is interspersed for filtering. In addition, a tuning circuit is added before the pre-amplification circuit to achieve the LC frequency selection amplification function for a specific frequency.

[0008] In order to meet the requirements of the device for underwater measurement, combined with the fact that the overall circuit power consumption of the device is low and the heating situation is not obvious, the present invention uses a structural waterproofing method and an epoxy resin potting adhesive waterproofing method to waterproof the circuit part.

[0009] Based on the above device, the present invention also proposes an error correction method, and the method includes the following steps:

[0010] Obtain geomagnetic reference data and measurement data;

[0011] Define an error model, including zero bias error, sensitivity error, and non-orthogonal error;

[0012] Define the residual function as the relative error between the total field after calibration and the true value, and transform it into a non-linear least squares problem for solution;

[0013] Iteratively solve the residual function based on the LM algorithm to obtain the optimal parameters.

[0014] In some embodiments, for the three-axis pointing error caused by the underwater towed measurement method, based on the plane constraint correction algorithm, the deviation caused by the pointing errors of the magnetometer and gyroscope is corrected, specifically including:

[0015] Construct a comprehensive error model for the three-component magnetic measurement system;

[0016] According to the ellipse fitting problem for transformation, generate a solution matrix and an objective function;

[0017] Through the least squares optimization method, minimize the objective function to obtain the three-axis pointing error coefficients;

[0018] Correct according to the three-axis pointing error coefficients.

[0019] Based on the above solution, the present invention provides an amphibious weak magnetic field measurement device and its error calibration method. An improved proton magnetometer based on the Larmor precession effect is used as the core measurement component. Through the self-designed square reverse series coil and multi-layer electromagnetic shielding structure, the measurement accuracy reaches 23 nT. At the same time, through the signal conditioning circuit: using cascaded multi-stage amplifiers and narrowband filter design, high-gain amplification of weak signals and noise suppression are realized. Finally, the LM (Levenberg-Marquardt) algorithm is used to correct the fluxgate sensor error. It can simultaneously realize three-axis vector magnetic field measurement underwater and on land. Brief Description of the Drawings

[0020] Figure 1 is a schematic structural diagram of an amphibious weak magnetic field measurement device of the present invention;

[0021] Figure 2 is a schematic diagram of a single-coil model;

[0022] Figure 3 is a schematic diagram of a double-coil reverse series structure;

[0023] Figure 4 and Figure 6 are schematic diagrams of simulation models of a quasi-square coil from different perspectives;

[0024] Figure 5 and Figure 7 are schematic diagrams of simulation models of different perspectives of a circular coil;

[0025] Figure 8 is a schematic diagram of the principle of electrical noise interference;

[0026] Figure 9 is a schematic diagram of the principle of electrical noise interference under multi-layer shielding conditions;

[0027] Figure 10 is a schematic diagram of the polarization circuit in a specific embodiment of the present invention;

[0028] Figure 11 is a schematic diagram of the signal conditioning circuit in a specific embodiment of the present invention;

[0029] Figure 12 is a schematic diagram of the band-pass filter circuit in a specific embodiment of the present invention;

[0030] Figure 13 is a schematic diagram of non-orthogonal error;

[0031] Figure 14 is a schematic diagram of the coordinate system orientation of a three-component magnetic measurement system;

[0032] Figure 15 is a schematic diagram of a vector rotating around the z-axis of the coordinate system;

[0033] Figure 16 is a schematic diagram of the error of a three-axis magnetic sensor;

[0034] Figure 17 is a schematic diagram comparing the measured magnetic field curve and the theoretical curve in a test embodiment of the present invention;

[0035] Figure 18 is the measured fitting curve in a test embodiment of the present invention;

[0036] Figure 19 is a line graph of some data comparing the absolute error of the magnetic field before and after underwater test correction;

[0037] Figure 20 is a schematic diagram of the device of the present invention;

[0038] Reference numerals: 1, probe; 2, six-axis gyroscope; 3, display and operation screen; 4, polarization circuit; 5, signal conditioning circuit; 7, device battery. Detailed implementation manners

[0039] Next, the technical solutions in the embodiments of the present application will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present application without creative efforts belong to the scope of protection of the present application.

[0040] It should be noted that for the convenience of description, only the parts related to the relevant invention are shown in the drawings. Without conflict, the embodiments in the present application and the features in the embodiments can be combined with each other.

[0041] It should be understood that the "system", "device", "unit" and / or "module" used in the present application is a method for distinguishing different components, elements, parts, portions or assemblies at different levels. However, if other words can achieve the same purpose, the word can be replaced by other expressions.

[0042] As shown in the present application and the claims, unless the context clearly indicates an exception, words such as "a", "an", "one" and / or "the" are not specifically singular and may also include the plural. Generally speaking, the terms "comprising" and "including" only indicate the steps and elements that have been clearly identified, and these steps and elements do not constitute an exclusive list. The method or device may also include other steps or elements. An element defined by the statement "comprising one..." does not exclude the existence of another identical element in the process, method, commodity or device including the element.

[0043] In the description of the embodiments of the present application, "a plurality" means two or more than two. The following terms "first" and "second" are only used for descriptive purposes and cannot be understood as indicating or implying relative importance or implicitly indicating the quantity of the indicated technical features. Thus, the features defined with "first" and "second" may explicitly or implicitly include one or more of such features.

[0044] In addition, flowcharts are used in the present application to illustrate the operations performed by the system according to the embodiments of the present application. It should be understood that the operations before or after may not be executed precisely in sequence. On the contrary, the steps can be processed in reverse order or simultaneously. At the same time, other operations can also be added to these processes, or one or several steps can be removed from these processes.

[0045] Referring to Figure 1 , which is a schematic structural diagram of an optional example of the amphibious weak magnetic field measurement device proposed by the present invention. The device includes a probe, a circuit system, a GPS module and a screen display module, wherein:

[0046] The probe consists of a quasi-square symmetric double-coil reverse series structure, a silver-copper composite coating electromagnetic shielding layer, a proton-rich solution, and an acrylic shell. The silver-copper composite coating electromagnetic shielding layer covers the coil structure, and the coil structure is placed inside the acrylic shell. The acrylic shell is filled with a proton-rich solution. Through this setting, it is possible to accurately capture the free exponential decay signal generated by Larmor precession while effectively reducing the signal-to-noise ratio.

[0047] The circuit system includes a polarization circuit, a signal conditioning circuit, and a control circuit.

[0048] The physical schematic diagram of the device is referred to Figure 20 。

[0049] In some feasible embodiments, the coil structure is designed as a quasi-square symmetric double-coil reverse series structure. By optimizing the coil shape, this structure increases the cross-sectional area of the inner coil, thereby greatly improving the magnetic field induction signal strength.

[0050] As the core component in the sensor, the design of the coil needs to take into account both the size limitation of the device and the influence of the magnetic field gradient on the measurement accuracy. Therefore, a single coil is usually used to perform two key tasks simultaneously: one is to polarize the proton-rich solution, and the other is to receive the Larmor signal. This design requires the coil configuration to precisely balance two major requirements: First, it must be able to generate a sufficiently strong and stable polarization magnetic field that is perpendicular to the external magnetic field to ensure that the protons in the proton-rich solution can be fully aligned and form a significant macroscopic magnetic moment; second, the coil also needs to have high sensitivity to capture the weak Larmor signal released by the protons during relaxation, ensuring that the signal strength and clarity meet the measurement requirements. By optimizing the coil configuration and parameters, these two functions can be efficiently and accurately completed within a limited space.

[0051] The simple coil model diagram is referred to Figure 2 , as can be seen from the figure, although the single-coil configuration has a simple structure and is easy to manufacture, it significantly exposes the weakness of being vulnerable to external environmental interference. In the context of weak magnetic field measurement, even a weak external interference will greatly affect the measurement accuracy, such as electromagnetic noise generated when surrounding electronic components work, various communication signal interferences, etc. The single-coil structure cannot cancel or reduce the noise interference, which directly leads to a significant reduction in the signal-to-noise ratio.

[0052] When delving deeper into signal detection and enhancement techniques, the configuration of using symmetric double coils in reverse series exhibits unique advantages, such as Figure 3As shown. The core of this configuration lies in the symmetry of its physical structure and the precise consistency of the coil parameters. This design feature enables interference signals generated by the external environment to induce responses with equal amplitudes but opposite phases in the respective coils. Conversely, the target Larmor precession signal remains phase-synchronized in these two coils, which provides a solid foundation for signal processing.

[0053] By implementing a differential output mechanism, this structure ingeniously utilizes the phase consistency of the Larmor-induced signals, causing the effective signals to be superimposed at the output end, thereby achieving a doubling effect of the signal amplitude. The enhancement amplitude is equivalent to the direct addition of the output signals of two individual coils. At the same time, the interference noise that is prevalent in the environment, as a common-mode signal, cancels each other out during the differential processing due to the opposite phases. This characteristic significantly reduces the noise and thus greatly improves the signal-to-noise ratio of the output signal.

[0054] Although the symmetric double-coil reverse series structure has significantly improved the signal-to-noise ratio of the output signal of traditional circular coils, in order to further pursue the ultimate measurement accuracy, it is urgently necessary to construct a detection platform based on an initial induction signal with a higher signal-to-noise ratio.

[0055] To verify the effectiveness of this design, in this embodiment, an advanced multi-physics simulation software COMSOL was used to simulate and analyze the excitation magnetic field of the coil. The simulation process starts with a geometric model constructed according to the precise dimensions of the coil, and then a constant 1A excitation current is applied to the model. On the premise of ensuring that all coil geometric dimension parameters, wire diameters, and excitation current intensities are consistent, a direct comparison was made between the excitation magnetic field intensities generated by the square-like coil and the circular coil.

[0056] The simulation results are as Figures 4 - 7 shown. From Figures 4 - 7 the simulation results, it can be clearly seen that the excitation magnetic field intensity B s at the center position of the square-like coil reaches 11.7 mT, while the excitation magnetic field intensity B c corresponding to the center of the circular coil is 11.5 mT. This comparison shows that under the same physical constraints, the excitation magnetic field intensity of the circular coil is slightly lower than that of the square-like coil. Based on the previous detailed calculations of the coil geometric parameters, we also know that there is a clear proportional relationship between the internal volume V of the square-like coil and the cross-sectional area V c of the inner circle of the circular coil. The square-like coil is based on a square structure with curved arcs at the intersections of the sides. Given a set of specific parameter settings, the final physical dimensions are: inner diameter 40.4 mm, coil thickness 10.1 mm, and coil height 34.04 mm.

[0057] Furthermore, considering the direct influence of magnetic field strength on the degree of proton polarization and the macroscopic magnetic moment, we set the macroscopic magnetic moment exhibited by the polarized protons in the quasi-square coil as M s , while the macroscopic magnetic moment of the corresponding protons in the circular coil is M c . Since the degree of proton polarization is proportional to the magnetic field strength, it can be reasonably inferred that under the same conditions, the degree of proton polarization in the quasi-square coil is higher, resulting in an increase in its macroscopic magnetic moment M s relative to M c in the circular coil.

[0058] Finally, we derive the ratio formula between these two macroscopic magnetic moments, that is, the ratio of M s to M c can be expressed as:

[0059]

[0060] Given the difference in macroscopic magnetic moments, according to the derivation of the above formula, it is known that under the same conditions, the signal amplitude induced by the quasi-square inductor is about 1.3 times higher than that of the circular inductor. Based on the above analysis, when considering the differences in the internal area (the quasi-square is the volume V, and the circular is the cross-sectional area V c ) and macroscopic magnetic moments of the two coils, this design optimization enables the quasi-square inductor to achieve 1.65 times the signal amplitude of the circular inductor, realizing a significant improvement in the output signal amplitude. This improvement not only enhances the signal strength but also effectively improves the signal-to-noise ratio of the system by reducing the relative influence of background noise.

[0061] In some embodiments, to improve the anti-interference ability, the device adopts a double-layer shielding structure of a silver-copper composite coating and copper foil. By repeatedly reflecting and absorbing electromagnetic waves, it effectively shields external electromagnetic interference, significantly improving the quality of the Larmor precession signal.

[0062] The frequency range of the proton precession signal driven by the geomagnetic field mainly concentrates in the very low frequency band of 1 kHz to 3 kHz. In this frequency band, the signal characteristics show that the magnetic component dominates, while the electric component is relatively minor. Therefore, when designing the shielding scheme, the effectiveness of magnetic shielding measures should be given priority to maximize the suppression of magnetic interference, and electrical shielding means should be supplemented to achieve a more comprehensive noise suppression effect.

[0063] Specifically, in this embodiment, a double-layer shielding structure scheme is selected for magnetic shielding. The inner layer shielding directly uses conductive paint to coat the surface of the coil to achieve efficient use of space. In the selection of conductive paint, factors such as cost, conductivity, adhesion, and stability are comprehensively considered. Finally, a silver-copper composite conductive paint is selected. This paint not only has a conductivity close to that of the high-cost silver-based paint, maintaining a good shielding effect, but also has good stability, which is an optimized choice in terms of cost performance. The outer layer shielding uses ordinary copper foil material to further consolidate the shielding effect.

[0064] For electrical shielding, a strategy of reducing the grounding impedance of the shielding structure is mainly adopted. Specifically, it can be achieved by adding multi-strand copper wires or optimizing the grounding of the center point of the shielding layer, thereby further reducing electromagnetic wave leakage and improving the overall shielding efficiency. Specifically, due to physical proximity or layout characteristics between conductors, a coupling capacitance will be formed, and this coupling capacitance becomes a key channel for electrical noise to invade the signal path of the sensor coil. As Figure 8 shown, electrical noise is coupled into the coil signal through this coupling capacitance mechanism, thereby having an adverse impact on the performance of the sensor.

[0065] Figure 8 In, C NC is the coupling capacitance value between the noise source and the coil, C c is the coupling capacitance value between the coil and the ground, C N is the coupling capacitance between the noise source and the ground. Assuming the noise amplitude of the noise source is V N , then the noise value coupled into the coil is:

[0066]

[0067] In the formula, V C is the noise amplitude coupled into the coil. It can be seen from the formula that under the condition that the amplitude of the noise source remains unchanged, reducing the coupling capacitance value C NC between the noise source and the coil and increasing the coupling capacitance value between the coil and the ground can reduce the noise amplitude in the coil.

[0068] When a shielding structure is added to the coil, assuming the shielding structure has n layers, its equivalent diagram of being interfered by the noise source is as Figure 9 shown. It can be seen that when a multi-layer shielding structure is adopted, the more grounding impedance terms in the formula, the smaller the noise amplitude coupled from the noise source to the coil. Secondly, reducing the grounding impedance of the shielding layer can also reduce the noise coupling value.

[0069] In some embodiments, as the core excitation and reception part, the polarization circuit mainly realizes the function of injecting direct current into the probe, thereby generating an excitation magnetic field hundreds of times stronger than the geomagnetic field. This magnetic field changes the motion state of the hydrogen protons in the hydrogen-rich solution in the probe, causing them to precess around the excitation magnetic field.

[0070] The excitation magnetic field is a primary alternating magnetic field established by an excitation current flowing through a probe coil, and its direction is perpendicular to the original geomagnetic field. Its main function is to align the moving magnetic moments of hydrogen protons along the direction of the excitation magnetic field to form a macroscopic magnetic moment, and this process is called the polarization process. When the polarization is completed, usually within 2 - 4 seconds, the macroscopic magnetic moments of hydrogen protons in the hydrogen-rich solution will tend towards the direction of the excitation magnetic field. Subsequently, the system quickly turns off the current and switches to the excitation and reception mode, using the same coil to receive the induced electromotive force generated by the change in the secondary field (i.e., the relaxation magnetic field), namely the proton precession signal, thereby completing the signal conditioning, acquisition, storage, and measurement.

[0071] During the polarization process, the circuit design has strict requirements for the on-resistance and turn-off speed, and at the same time, the timing control needs to be precise and error-free. To avoid mis-triggering, a snubber resistor is set between the drain and the gate to protect the circuit. The switching circuit design requires the coil current to quickly decay to zero after polarization is completed and avoid oscillation phenomena to ensure the accuracy of subsequent signal reception.

[0072] In specific operations, when a 12V DC voltage is applied between pins 1 and 16 and pins 13 and 9 are made conductive, the system will be excited by a DC pulse for 2 - 4 seconds. Subsequently, the polarization circuit quickly turns off the DC voltage through the relay ZXMP7A17K, and at the same time keeps pins 13 and 9 conductive for 10 ms so that the energy release resistor connected to pin 9 can absorb the instantaneous high voltage generated by the coil. Subsequently, the voltage between pins 1 and 16 is removed, and it is switched to the signal reception mode. The coil is connected to the signal reception end to perform conditioning such as amplifying and filtering the proton precession signal. The schematic diagram of the relay switching module is as Figure 10 shown, and the devices applied include resistors, capacitors, diodes, DB125 - 3.81 - 3P - GN - S, DB128L - 5.08 - 2P - GN - S, DB128L - 5.08 - 2P - GN - S, HK19F - DC12V - SHG, and interface circuits, etc.

[0073] In some alternative embodiments, the signal conditioning module includes a tuning module, a preamplifier, a band - pass filter, and a post - amplifier. Since the signal coming out of the probe is submerged in noise, a tuning circuit is added before the pre - amplification circuit to achieve the LC frequency - selection amplification function for a specific frequency. The signal is amplified step by step by using a cascaded multi - stage amplifier method, and at the same time, a narrow - band filter is interspersed for filtering. The block diagram of the signal conditioning circuit is as Figure 11 shown.

[0074] On the basis of ensuring electromagnetic shielding of the coil part, considering that the amplitude of the detected rotational precession signal is extremely small, reaching the microvolt level, it is necessary to amplify the gain of the signal conditioning circuit to accurately capture its frequency characteristics. However, this amplification process is prone to noise interference generated by electrical components, especially the front-end circuit of the system, such as the tuning circuit and the preamplifier, which contribute far more to the overall noise figure than the rear-end part. In view of this, a band-pass filtering link is particularly embedded between the preamplifier and the postamplifier to reduce noise interference. Considering that the frequency range of the target signal falls between 1 kHz and 4 kHz, the design of the band-pass filter also focuses on this frequency band.

[0075] For this reason, this paper uses a Butterworth-type band-pass filter with a low rectangularity coefficient, as Figure 12 shown. The devices used include signal amplifiers, resistors, and capacitors, etc. This filter cleverly combines the advantages of an eighth-order high-pass filter and a fourth-order low-pass filter and is constructed by cascading, showing extremely flat characteristics within the passband. The eighth-order high-pass design is selected to shorten the starting transition band and achieve a steeper rising edge to effectively eliminate low-frequency noise; while the high-frequency noise is relatively low, so the fourth-order low-pass design can meet the requirements. This circuit design also incorporates a strategy of alternating multi-stage amplification and filtering layout, greatly suppressing the adverse effects of internal component noise and external power frequency interference on signal quality.

[0076] In some feasible embodiments, in order to meet the requirements of underwater measurement of the device, considering that the overall circuit power consumption of this device is relatively low and the heating situation is not obvious, this paper adopts the methods of structural waterproofing and epoxy potting adhesive waterproofing to waterproof the circuit part. Structural waterproofing is the most traditional mode of waterproofing for electronic products. The main idea is to hydrophobic, divert water, and effectively isolate the external package and the internal electrical part. Here, in this embodiment, all electrical parts are integrated into a waterproof box to isolate the entry of water from the external structure. However, the circuit board is used in an environment with heavy water vapor, and there is also a risk of deformation during use. The gaps at the appearance joints will also deform accordingly, or the appearance may be damaged artificially or non-artificially at any time, becoming potential concerns. On the basis of structural waterproofing, the method of epoxy potting adhesive waterproofing is added, which can wrap the entire PCB board, thus playing the roles of waterproofing, moisture-proofing, salt spray-proofing, mildew-proofing, earthquake-proofing, and anti-external impact, etc. Epoxy resin is a saturated resin, and the epoxy potting adhesive produced with it has characteristics such as high body strength, strong adhesion, good weather resistance, low shrinkage rate, high insulation strength, non-toxic and environmental protection, etc. After potting, it can have stable mechanical and electrical properties between -45 - 120 °C. It can protect the circuit board in all directions and greatly improve the service life of the circuit board.

[0077] In some feasible embodiments, the control circuit uses STM32F102VCT6 as the MCU of the system. The chip has a working frequency as high as 120 MHz, meeting the requirements of timing control and frequency measurement. Considering the great role of the weak magnetic field measurement device in geomagnetic measurement and the simplicity of operation, a one-key measurement and display function for the screen is provided for the device, both of which are driven by STM32.

[0078] Based on the above device, the present invention also provides an error correction method, which is applied to the above device and includes the following steps:

[0079] Obtain geomagnetic reference data and measurement data to obtain the original data matrix of the fluxgate sensor and the corresponding true value vector B of the total geomagnetic field M =[B M1 ,B M2 ,...,B MN ;

[0080] Define an error model, including zero-offset error, sensitivity error, and non-orthogonal error;

[0081] Define the residual function as the relative error between the calibrated total field and the true value, and transform it into a non-linear least squares problem for solution;

[0082] Based on the LM algorithm, iterate and solve the residual function to obtain the optimal parameters.

[0083] Specifically, based on the different mechanisms of error formation, the errors of the three-axis magnetic sensor can be divided into three categories: zero-offset error, non-orthogonal error, and sensitivity error.

[0084] The zero-offset error originates from the deviation introduced by each axis of the three-axis magnetometer in the signal processing circuit and the A / D conversion process. This deviation causes the magnetic field measurement values of each axis to be non-zero even under the condition that the external magnetic field is zero, thus generating an error.

[0085] The non-orthogonal error is closely related to the process accuracy in the manufacturing process of the magnetometer. Due to manufacturing inaccuracies, the three axes of the three-axis magnetometer may not be completely perpendicular (orthogonal) to each other. This non-orthogonal state directly leads to the generation of measurement errors. The specific manifestations of the non-orthogonal error are as Figure 13 shown.

[0086] The sensitivity error is due to the accuracy limitation of the three-axis magnetometer in the signal processing circuit, resulting in differences in sensitivity between the axes, and thus introducing errors in the measurement process. This error is caused by the inconsistent response of each axis to magnetic field changes.

[0087] Set up a theoretical orthogonal coordinate system of a three-axis magnetic sensor composed of the x, y, and z coordinate axes. In contrast, there is a non-orthogonal coordinate system in practical applications composed of the x', y', and z' coordinate axes. To quantify the difference between the two, we assume that the origins of the two coordinate systems coincide, and the x-axis coincides exactly with the x'-axis, while the y-axis and the y'-axis are in the same plane. Based on this setting, the non-orthogonal error angles (α1, α2, α3) can be derived, and these angles reflect the degree of deviation of the actual coordinate system from the ideal orthogonal coordinate system.

[0088] Introduce a transformation matrix O, which can represent the transformation relationship between the ideal orthogonal coordinate system and the actual non-orthogonal coordinate system. Through the matrix O, the measured values in the ideal coordinate system can be transformed to the actual coordinate system.

[0089]

[0090] The following is the mathematical model description of the sensitivity error K and the zero-bias error b, where Kx, Ky, and Kz respectively represent the sensitivity errors of the three-axis magnetic sensor on the x, y, and z measurement axes, while bx, by, and bz respectively correspond to the zero-bias errors on these three axes. Each axis has its unique sensitivity and zero-bias values, and these parameters together constitute the error characteristics of the sensor in these axial directions.

[0091]

[0092] Assume that the measured magnetic field vector value of the three-axis magnetometer under ideal conditions is B t =[B t x B t y B t z T , and the magnetic field vector value in the actual situation is B c =[B c x B c y B c z T , then the relationship between the two is as follows:

[0093] B c =KOB t +b+n

[0094] Let C=b+n, then we have:

[0095] B t =O -1 K -1 (B c -C)=DB c ​​-E

[0096] In this formula, D and E are defined as error calibration parameters. Once these parameters are accurately solved, they can be used to correct and obtain the accurate magnetic field vector in the coordinate system of the three-axis magnetic sensor, denoted as B t . A calibration method for three-axis magnetic sensors based on the improved LM algorithm.

[0097] Regarding the total geomagnetic field value BM measured by the proton magnetic sensor as the accurate true value of the total geomagnetic field, the problem of solving the error calibration parameters of the three-axis magnetic sensor can be transformed into a nonlinear least squares problem, and its mathematical expression is as follows.

[0098]

[0099] In this equation, F(B c , x) represents the objective function, which is used to quantify the calibration effect; while r(B c , x) represents the residual function, which calculates the relative error between the total geomagnetic field B t measured by the three-axis magnetic sensor and processed by error calibration and the true value B M , reflecting the degree of deviation of Bt from BM after calibration, that is:

[0100]

[0101] The parameter vector to be estimated is x = [b x b y b z K x K y K z α1α2α3] contains nine key parameters, which respectively correspond to the zero-offset error, sensitivity error of the three-axis magnetic sensor, and each component in the non-orthogonal error model. By using the total geomagnetic field value measured by the proton magnetic sensor as a reference, we define the residual function as the relative error between the output after calibration of the three-axis magnetic sensor and the output of the proton magnetic sensor. Based on this residual function, we use the nonlinear least squares method to solve the error calibration parameters, aiming to make the total output of the three-axis magnetic sensor as close as possible to the accurate output of the proton magnetic sensor.

[0102] The significant advantage of this method lies in that once the estimated parameter x is obtained by the non - linear least - squares method, the sensitivity error matrix K, the non - orthogonal error matrix O, and the bias vector b can be directly calculated according to the error model. Without the need for complex matrix decomposition steps, the error calibration parameter matrices D and E of the three - axis magnetic sensor can be directly constructed. This method not only avoids the uncertainty brought by the arbitrary rotation matrix R that may be introduced in the ellipsoid fitting method due to matrix decomposition, but also, thanks to the high - precision proton magnetic sensor as the calibration reference, significantly improves the accuracy of the calibrated three - axis magnetic sensor in measuring the total geomagnetic field.

[0103] The LM (Levenberg - Marquardt) algorithm adopted in this embodiment is an optimization strategy that cleverly combines the advantages of the Newton - Gauss method and the steepest - descent method. Its iterative formula is as shown in the equation. This algorithm shows high flexibility by adjusting the parameter λ: when λ takes a large value, the iterative process tends to the steepest - descent method, and can achieve a faster descent speed in the region far from the extreme point, effectively avoiding falling into local minima; while when λ gradually decreases, the iterative process gradually approaches the characteristics of the Newton - Gauss method, showing excellent convergence performance near the extreme point, ensuring that the algorithm can accurately and efficiently approach the global optimal solution.

[0104]

[0105] Adaptive damping factor adjustment: If the residual decreases, accept the update and decrease λ (towards the Gauss - Newton method); if the residual increases, reject the update and increase λ (towards the steepest - descent method).

[0106] Termination condition: Stop the iteration when the parameter change amount ‖δx‖ < ∈ or the residual change rate is lower than the threshold.

[0107] Output: Optimal parameter estimate x * 。

[0108] In some feasible embodiments, for the three - axis pointing error caused by the underwater towed measurement method, based on the plane - constraint correction algorithm, the deviation caused by the pointing errors of the magnetometer and the gyroscope is corrected. By introducing the calculation of the pitch angle and the roll angle in the inertial navigation system, the accuracy of underwater magnetic field measurement is ensured.

[0109] Obtain geomagnetic reference data;

[0110] Construct a comprehensive error model for the three - component magnetic measurement system;

[0111] According to the conversion of the ellipse - fitting problem, generate a solution matrix and an objective function;

[0112] Through the least - squares optimization method, minimize the objective function to obtain the three - axis pointing error coefficient;

[0113] Perform correction according to the said three-axis pointing error coefficients.

[0114] The pointing error of the three-component magnetic measurement system coordinate system is shown as the error generated by the non-parallelism between the corresponding sensitive axes of the three-axis magnetic sensor and the inertial navigator. Figure 14 As shown, it is the error generated by the non-parallelism between the corresponding sensitive axes of the three-axis magnetic sensor and the inertial navigator.

[0115] The deviation between coordinate systems can be obtained from the rotation matrix formed by Euler angles. Parameterize the coordinate system pointing error as a rotation matrix to get:

[0116]

[0117] The errors of the three-axis sensor have been corrected in the previous LM algorithm and will not be elaborated here. Finally, the comprehensive error model of the three-component magnetic measurement system can be set as:

[0118]

[0119] Where h m is the measurement vector of the three-axis magnetic sensor, K sf is the sensitivity error matrix of the three-axis magnetic sensor, K0 is the orthogonal error matrix of the three-axis magnetic sensor, R c is the coordinate system pointing error matrix in the magnetic measurement system, h b is the zero-bias error vector of the axis magnetic sensor, is the projection of the external magnetic field in the inertial navigation system coordinate system.

[0120] After the change of the system comprehensive error model, the attitude expansion form can be obtained as:

[0121]

[0122] The plane constraint method is based on the parameterization theory of spatial vector rotation. As Figure 15 shown, it is a method to construct the constraint for solving the error coefficients of the magnetic measurement system by compressing the three-component magnetic measurement data into a plane.

[0123] By transposing the attitude expansion formula, we can get:

[0124]

[0125] According to the previous Euler rotation formula, the expressions of the coordinates of points T1 and T2 based on point T can be obtained as follows:

[0126]

[0127] Using the pairwise differences of the three vectors T, T1, and T2 to form vectors TT1, TT2, and TT3, their expressions are as follows:

[0128]

[0129] From the derivation of linear algebra, it can be known that if the three vectors TT1, TT2, and TT3 in the schematic diagram are coplanar, the determinant of the matrix formed by them is always 0, that is

[0130] det(TT1, TT2, TT3) = 0

[0131] Since this equation is always equal to zero, it indicates that the coplanarity of TT1, TT2, and TT3 always holds.

[0132] Based on this, two characteristics of the spatial magnetic vector can be obtained:

[0133] (1) When any point rotates around the z-axis, its trajectory forms a plane, and the magnetic field vector h at the measurement point does not affect the coplanar relationship of the data.

[0134] (2) The normal vector of the trajectory plane is a vector parallel to the z-axis.

[0135] Applying the above two key characteristics to the processing of three-component magnetic measurement data, we can deduce that: after completing the error correction of the triaxial magnetic sensor and the precise adjustment of the coordinate system pointing error, by using the pitch angle and roll angle information provided by the inertial navigation system, performing corresponding rotation operations on the γ-axis and x-axis of the triaxial magnetic sensor can effectively compress the magnetic measurement data originally scattered in three-dimensional space into a plane. This plane has a significant characteristic, that is, it is perpendicular to the z-axis of the local horizontal coordinate system. Based on this principle, this embodiment constructs an objective function aimed at solving the error correction coefficient in order to further optimize and precise the processing flow of magnetic measurement data.

[0136] The plane constraint form of the magnetic measurement data is as follows:

[0137]

[0138] Use a triaxial magnetic sensor and an attitude instrument to construct a plane vector:

[0139]

[0140] Since all vectors in any plane are perpendicular to the normal vector of the plane, let the normal vector of the constructed plane in the figure be the z-axis direction vector and set it as [0, 0, 1]. Then the following equation holds:

[0141]

[0142] After simplification, it can be obtained that:

[0143]

[0144] It conforms to the equation of any ellipsoidal surface in the three-dimensional coordinate system:

[0145] f(x) = (x - x c ) T ·G·(x - x c ) = 1

[0146] The scalar invariance principle is applied to the calibration method of a triaxial magnetic sensor, which relies on the relatively stable characteristics of the geomagnetic field in a short period of time. Specifically, by collecting the measurement data of the triaxial sensor in different rotation states and plotting its data trajectory, and then using the ellipsoid surface fitting technology, the ellipsoid coefficient matrix is extracted from these data trajectories. This process aims to correct and restore the magnetic measurement data trajectory distorted due to sensor errors (including zero offset, sensitivity difference, and non-orthogonality) to an ideal spherical shape. During this calibration process, the zero offset error is manifested as the offset of the origin position of the fitted sphere relative to the theoretical origin; while the sensitivity error and non-orthogonal error directly cause changes in the size and shape of the fitted sphere, turning it into an ellipse. As Figure 16 shown.

[0147] The ellipsoid fitting problem can be transformed into an optimization problem:

[0148]

[0149] After simplification and arrangement, the following formula can be obtained

[0150]

[0151] From this, it can be concluded that this is the solution of the matrix

[0152]

[0153] Finally, the objective function of this problem can be obtained:

[0154]

[0155] Substitute the N groups of observed three-component magnetic measurement system data into the objective function, thereby establishing the connection between the unknown error correction coefficient and the known observed quantity. Theoretically, when all error coefficients are accurately solved, the determinant is 0. Based on this property, the solution of the matrix problem is converted into the solution of a system of linear equations. The least squares optimization method can be used to minimize the objective function to obtain the estimated values of all unknown coefficients. When using the parameters of the fitted triaxial fluxgate and the self-made probe, the LM nonlinear least squares optimization method is used to solve this equation, and the unknown coefficients in the error coefficients can be obtained, thereby correcting the error.

[0156] Based on the above device, the present invention also gives a set of test comparison data:

[0157] Test method:

[0158] Step 1: Connect the YL2410 DC regulated power supply and the Helmholtz coil, and place them in a self-made magnetic shielding cover.

[0159] Step 2: Place a self-made magnetic field probe in the center of the Helmholtz coil, and connect the control circuit and the upper computer system.

[0160] Step 3: Adjust the YL2410 DC regulated power supply and set the initial current value to 100 mA.

[0161] Step 4: Increase the output current of the current source in steps of 100 mA, read out the measured frequency and the corresponding magnetic field strength value given by the self-made probe, and record them.

[0162] Step 5: Import the simulated value of the magnetic field distribution of the Helmholtz coil into Python, and at the same time import the recorded magnetic field strength values into Python.

[0163] Step 6: Compare the theoretical data and the measured data, and analyze the data to obtain the accuracy of the self-made probe.

[0164] The magnetic field generation device used is a Helmholtz coil. The magnetic field generated inside the Helmholtz coil is uniform and linearly related to the current in the input coil, B = 200I. In this article, the theoretical total magnetic field generated by the Helmholtz coil can be obtained. According to the relationship between the magnetic field and the current, the relationship curve between the theoretical magnetic field and the current can be drawn. By measuring the data of the actual magnetic field obtained under the theoretical magnetic field, the error of the current sensor can be obtained. After error correction, the accuracy of the sensor can be obtained, as Figure 17 shown.

[0165] The measured values are as Figure 18 shown, and the change trend is approximately linear. Therefore, a linear regression model is used here to fit the measured curve, and then the obtained regression curve is transformed into a theoretical curve by a linear transformation method to achieve data correction. It can be obtained from the Matlab simulation that the measured B = 2.078I + 440. The theoretical magnetic field curve is B = 2I. Therefore, the measured value is first subtracted by 440, and then multiplied by 0.96 to obtain the magnitude of the current magnetic field. The data is shown in Table 1.

[0166] Table 1 Partial data of the accuracy test of the self-made magnetometer

[0167]

[0168]

[0169] Measure the uncertainty multiple times at 400 mA, and obtain: Type A 73.3, Type B 11.25, Type C 74.9.

[0170] In an underwater environment, the device successfully corrected the errors of the gyroscope and magnetometer during towed measurement through a plane constraint correction algorithm, ensuring the accuracy of underwater magnetic field data. The device also achieved an underwater measurement accuracy of 20nT.

[0171] The ground simulation test system consists of an inertial navigation system and a three-axis magnetic sensor. A land simulation model similar to the underwater towed three-component structure is used to evaluate the performance of the planar constraint correction method. The main test is to use the spatial freedom three-component data collected without a special trajectory under towing conditions to correct the three-component magnetic survey data and test the accuracy of the corrected magnetic survey data.

[0172] The land model mainly needs to consider the mutual influence of magnetic fields between devices. A six-axis inertial navigation module with low power and low noise is selected as the inertial navigation system, and it is separated from the three-axis magnetic sensor by more than 50 cm and placed in a sub-

[0173] On the acrylic board, a land simulation model is formed.

[0174] 250 sampling points were randomly selected for sampling, and the current data were recorded. The experimental underwater algorithm was used for correction and compared with the values ​​measured by the three-axis magnetometer at these points to confirm the accuracy after correction.

[0175] Step 1: Place the probe and gyroscope on the turntable and make sure both can work normally;

[0176] Step 2: Rotate 30 degrees each time and record the magnetic field measurement data and gyroscope data;

[0177] Step 3: Use the plane constraint method to correct and compare the magnetic data with the corrected data during measurement.

[0178] Reference Figure 19 The experimental results in Table 2 show that the drag measurement accuracy is greatly improved. The error in measuring the total geomagnetic field before error calibration is large. The root mean square error of the total geomagnetic field before calibration is 1406.6nT. After calibration, the root mean square error is smaller and reduced to 162.2nT. The uncertainty is: x-axis: 46.31, y-axis: 32.70, z-axis: 43.64.

[0179] Table 2 Comparison of data before and after correction of land simulation experiment

[0180]

[0181] The above is a specific description of the preferred implementation of the present invention, but the invention is not limited to the embodiments. Those skilled in the art may make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. An amphibious weak magnetic field measuring device, characterized in that: The invention comprises a probe and a circuit system, wherein the probe is connected to the circuit system, wherein: The probe comprises a coil structure, a silver-copper composite coating electromagnetic shielding layer, a proton-rich solution and an acrylic shell; The silver-copper composite coating electromagnetic shielding layer covers the coil structure, the coil structure is placed in the acrylic shell, and the acrylic shell is filled with the proton-rich solution; The circuit system includes a polarization circuit, a signal conditioning circuit and a control circuit.

2. The amphibious weak magnetic field measuring device according to claim 1, characterized in that: It also includes a GPS module and a screen display module.

3. The amphibious weak magnetic field measuring device according to claim 2, characterized in that: The coil structure is a square-like symmetrical double-coil reverse series structure.

4. The amphibious weak magnetic field measuring device according to claim 2, characterized in that: The polarization circuit is used to excite the probe to generate an excitation magnetic field.

5. The amphibious weak magnetic field measuring device according to claim 4, characterized in that: The signal conditioning circuit includes a tuning module, a preamplifier, a bandpass filter and a post-amplifier in sequence, wherein: The bandpass filter adopts a Butterworth bandpass filter with a low rectangular coefficient.

6. The amphibious weak magnetic field measuring device according to claim 5, characterized in that: The circuit system is integrated in a waterproof box, and the waterproof box is filled with epoxy resin potting glue.

7. An error correction method applied to the amphibious weak magnetic field measurement device as claimed in claim 1, characterized in that: include: Obtain geomagnetic reference data and measurement data; Define the error model, including bias error, sensitivity error, and non-orthogonality error; The residual function is defined as the relative error between the total field after calibration and the true value, and is converted into a nonlinear least squares problem for solution; The residual function is iteratively solved based on the LM algorithm to obtain the optimal parameters.

8. The error correction method according to claim 7, characterized in that: The non-orthogonal error matrix in the error model is expressed as follows: Among them, α1, α2 and α3 represent the non-orthogonality errors on the x-axis, y-axis and z-axis respectively.

9. The error correction method according to claim 7, characterized in that: Also includes: Based on the plane constraint correction algorithm, the three-axis pointing error is corrected.

10. The error correction method according to claim 9, characterized in that: The step of correcting the three-axis pointing error based on the plane constraint correction algorithm specifically includes: Obtain geomagnetic benchmark data; Construct a comprehensive error model for a three-component magnetic measurement system; Collect the measurement data of the three-axis sensor in different rotation states, draw its data trajectory, and use the ellipsoid surface fitting technology to extract the ellipsoid coefficient matrix from these data trajectories; Transform the problem according to the ellipse fitting problem to generate the solution matrix and objective function; By using the least squares optimization method, the objective function is minimized to obtain the three-axis pointing error coefficient; Correction is performed according to the three-axis pointing error coefficients.

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