Proton magnetometer magnetic field gradient estimation method based on full waveform fid signals

Abstract

The method for estimating the magnetic field gradient of a proton magnetometer based on a full waveform FID signal comprises the following steps: sampling the FID signal output by the proton magnetometer to obtain a discrete signal sequence containing sampling time and voltage value; performing denoising processing on the obtained discrete signal sequence using an autocorrelation function; performing Hilbert transform on the signal after denoising processing, constructing an analytical signal and extracting envelope features; detecting minimum value points of the extracted envelope features to obtain a time sequence; performing linear fitting on the sequence of detected minimum value points, fitting the minimum value points by a least square method, and estimating the slope of the fitted straight line; and calculating the estimated value of the magnetic field gradient according to the mathematical model of the FID signal using the obtained slope parameter. The method is easy to implement. Compared with the traditional gradient measurement method, the method has higher estimation accuracy and stability, improves the magnetic field gradient tolerance of the system, and has strong practical value.

Description

Technical Field

[0001] This invention relates to the field of magnetic field measurement, and more specifically to a method for estimating the magnetic field gradient of a proton magnetometer based on a full-waveform FID signal. Background Technology

[0002] A proton magnetometer is a device based on the principle of nuclear magnetic resonance. It inverts the magnitude of an external magnetic field by exciting proton nuclei to output a free induction decay (FID) signal. The frequency of the FID signal is proportional to the strength of the magnetic field being measured, and its proportionality coefficient is the gyromagnetic ratio. Therefore, the strength of the magnetic field can be obtained by accurately measuring the frequency. It has wide and important applications in many fields such as aerospace, geological resource exploration, military reconnaissance, and underwater exploration.

[0003] However, in many complex application environments, the spatial distribution of magnetic fields is often not uniform, but rather exhibits a significant magnetic field gradient. When a proton magnetometer is placed in a gradient magnetic field, proton groups at different locations within the measurement area will possess Larmor frequencies corresponding to the spatial magnetic field. This causes the generated FID signals to exhibit frequency overlap and phase mismatch after superposition, forming beat interference and causing the signal to attenuate rapidly. Consequently, this results in: a. inaccurate magnetic field values; b. inability to obtain gradient information.

[0004] In complex gradient field environments, the conventional method is the dual-sensor differential method. This method places one magnetometer vertically above another, with a distance between them ranging from 0.5 to 1 meter. These two magnetometers can simultaneously measure the magnetic field strength at that location. The difference between the two magnetic field strengths is then divided by the sensor distance to obtain the frequency estimation result. However, since the gradient tolerance of a proton magnetometer is 5000 nT / m, its performance begins to degrade significantly in environments exceeding this tolerance, making the frequency estimation results unreliable and causing this method to fail.

[0005] Overall, while existing research has proposed methods for estimating non-uniform magnetic field gradients, it suffers from the following problems: 1) A unified theoretical model has not yet been established for the frequency diffusion mechanism of the proton population, the superposition characteristics of FID signals, and the beat interference mechanism under complex gradient magnetic fields; 2) Existing methods still have shortcomings in terms of strong gradient adaptability. Therefore, there is an urgent need for a magnetic field gradient estimation method for proton magnetometers based on full-waveform FID signals. Summary of the Invention

[0006] This invention proposes a method for estimating the magnetic field gradient of a proton magnetometer based on full-waveform FID signals. This method is easy to implement and offers higher estimation accuracy and stability compared to traditional gradient measurement methods. It also improves the magnetic field gradient tolerance of the system, making it highly practical.

[0007] The technical solution adopted in this invention is as follows:

[0008] The method for estimating the magnetic field gradient of a proton magnetometer based on full-waveform FID signals includes the following steps: Step 1: Sample the FID signal output by the proton magnetometer to obtain a discrete signal sequence containing the sampling time and voltage value; Step 2: Denoise the discrete signal sequence obtained in Step 1 using the autocorrelation function; Step 3: Perform Hilbert transform on the denoised signal from Step 2 to construct an analytical signal and extract envelope features; Step 4: Detect local minima of the envelope features extracted in Step 3 to obtain the time series; Step 5: Perform linear fitting on the sequence of minimum points detected in Step 4. Use the least squares method to fit the minimum points and estimate the slope of the fitted line. Step 6: Based on the mathematical model of the FID signal, calculate the estimated value of the magnetic field gradient using the slope parameter obtained in Step 5.

[0009] In step 1, the FID signal output by the proton magnetometer is sampled using an ADC, with a sampling frequency of... The frequency is set to be much higher than the actual frequency of the FID signal under test to ensure that its dynamic changes can be fully reflected. The discrete signal sequence of the target signal is obtained by sampling. ,in: Indicates the first The sampling time corresponding to each sampling point Indicates the first Voltage values ​​at each sampling point.

[0010] In step 2, the discrete signal sequence acquired in step 1 is subjected to autocorrelation processing to suppress noise in the discrete signal sequence, and the sampled discrete signal sequence is denoted as discrete signal. Calculate its autocorrelation function: (1); In formula (1): is the autocorrelation function of a discrete signal; Let be the amplitude of the signal at the nth sampling time; Let be the amplitude of the signal at the (n+k)th sampling time; k is the delay order; N is the total number of sampling points. Since random noise is uncorrelated under different delays, the contribution of random noise tends to zero when k>0.

[0011] In step 3, the target signal after autocorrelation processing in step 2 is... Perform a Hilbert transform to construct an analytic signal and extract envelope features: (2); In formula (2): For target signal; The result of the Hilbert transform; For Hilbert transformation operators.

[0012] Then, the analytical signal is constructed: (3); In formula (3): For constructing the analytical signal; For imaginary units; And further calculate the envelope function: (4); In equation (4): This is the envelope function.

[0013] In step 4, the minimum point of the envelope feature is detected: For the detection signal , For the first The time to reach a minimum point For the first Signal data at each of the minimum points.

[0014] If the following conditions are met: (5); In equation (5): They represent the first One signal data; This represents the number of data points selected to the left and right of the most recent signal data at the minimum time; then... The data is the closest to the minimum value. Use the method described above to detect all the local minima.

[0015] In step 5, the sequence of minimum values ​​is denoted as... , For 1, 2, 3..., n The time series of the minimum value is denoted as , For the 1st, 2nd, 3rd..., n The time corresponding to each local minimum point is used to fit a straight line using the least squares method: (6); In formula (6): The value of the fitted line, For the first The independent variable for each data point The slope of the fitted line, This is the intercept of the fitted line.

[0016] Actual measured value and They are not equal; the difference between them is called the residual. (7); In equation (7): This represents the residual between the actual measured value and the fitted value.

[0017] Take the partial derivatives of the sum of squared residuals with respect to a and b, and set the partial derivatives with respect to a and b to zero to minimize the sum of squared residuals: (8); Solving equation (8) yields: (9); In equation (9): The average of the sums of all x. Let y be the average of the sums of all y.

[0018] In step 6, the mathematical model of the FID signal in the gradient field is: (10); In formula (10): Here is the mathematical model for the FID signal in the gradient magnetic field, where A is the effective amplitude; For time variables, This refers to the lateral relaxation time; It is the gyromagnetic ratio; For magnetic field gradient; This refers to the length of the proton magnetometer probe. The precession frequency of the central proton; This is an exponentially decaying term.

[0019] when At that time, it was known ,therefore ,at this time therefore: (11); In equation (11): For the first There are a total of minimum time values. The time of the minimum value, then

[0020] and The parameters correspond one-to-one, therefore ; Therefore, the magnetic field gradient can be calculated: (12).

[0021] This invention provides a method for estimating the magnetic field gradient of a proton magnetometer based on full-waveform FID signals, with the following technical advantages: 1) Simple equipment: Traditional methods often use a dual-sensor differential method, employing two sensors to simultaneously measure the magnetic field strength at two locations, then subtracting the difference between the two magnetic field strengths and dividing by the sensor distance to obtain the gradient value. However, the proton magnetometer magnetic field gradient estimation method based on full-waveform FID signals only requires the FID signal generated by a single sensor to estimate the gradient value.

[0022] 2) High Accuracy: In magnetic field environments with gradients, the FID signal output by a proton magnetometer exhibits beat phenomena, leading to rapid signal attenuation and significant errors in the estimation of magnetic field strength. Consequently, the gradient obtained through differential estimation also suffers from substantial errors. However, the proton magnetometer magnetic field gradient estimation method based on the full-waveform FID signal is grounded in principle. It doesn't simply perform differential estimation between two points; instead, it directly establishes a mathematical model within the gradient field, obtaining the mapping relationship between the gradient and the waveform. This avoids the error accumulation and differential amplification effects inherent in the traditional "estimate field strength first, then differential" approach. It can still obtain stable and reliable gradient estimation results even in gradient environments with beats and rapid attenuation, thereby improving measurement accuracy.

[0023] 3) High speed: The implementation process of the method of the present invention only requires the analog FID signal to be converted into a digital signal by an analog-to-digital converter (ADC), and the microcontroller (MCU) to complete the steps of denoising, envelope extraction, minimum point detection and least squares fitting in sequence according to the processing flow proposed in the present invention, so as to quickly estimate the geomagnetic field gradient. The overall computation is low and the processing speed is fast. Attached Figure Description

[0024] The present invention will be further described below with reference to the accompanying drawings and examples; Figure 1 This is a schematic diagram illustrating the principle of the proton magnetometer of the present invention generating the FID signal.

[0025] Figure 2(a) shows the original FID signal waveform; Figure 2(b) shows the signal waveform after autocorrelation processing of the original FID signal.

[0026] Figure 3 This is a diagram illustrating the effect of extracting the FID signal envelope according to the present invention.

[0027] Figure 4 This is a diagram showing the effect of detecting the minimum point of the envelope and performing least-squares fitting according to the present invention.

[0028] Figure 5 The figure shows the results of one hundred experiments when the magnetic field gradient of the present invention is 5000 nT / m. Detailed Implementation

[0029] A method for estimating the magnetic field gradient of a proton magnetometer based on full-waveform FID signals is proposed. This method samples the FID signal output by the proton magnetometer; performs noise reduction using an autocorrelation function; extracts the envelope using Hilbert transform; detects the envelope minima; performs least-squares fitting on the minima; and estimates the gradient value of the magnetic field. The method includes the following steps: Step 1: Sample the FID signal affected by noise. Set the sampling frequency to several times greater than the actual frequency of the FID signal to obtain a discrete signal sequence containing the sampling time and voltage value for subsequent digital processing.

[0030] Step 2: Calculate the autocorrelation function of the discrete signal obtained in Step 1. Since random noise is uncorrelated at different delays, autocorrelation processing can significantly suppress noise components and preserve the decaying oscillation characteristics of the FID signal, making the signal structure clearer.

[0031] Step 3: Perform Hilbert transform on the signal after autocorrelation processing in Step 2 to construct an analytical signal and calculate its envelope function, which is used to obtain the attenuation envelope characteristics of the entire FID signal waveform.

[0032] Step 4: Detect each minimum point of the envelope extracted in Step 3 and obtain its time series for further processing.

[0033] Step 5: Perform linear fitting on the sequence of minimum points detected in Step 4. Use the least squares method to fit the minimum points and estimate the slope of the fitted line.

[0034] Step 6: Based on the mathematical model of the FID signal, and with known physical parameters such as gyromagnetic ratio and probe length, calculate the estimated value of the magnetic field gradient using the slope parameter obtained in Step 5.

[0035] The present invention will be further described with reference to the accompanying drawings: like Figure 1 The diagram illustrates the principle of the proton magnetometer generating the FID signal according to this invention. The proton magnetometer probe contains a large number of hydrogen protons, and a polarization coil is wound around its container, with the coil axis perpendicular to the external geomagnetic field B to be measured. First, the switch is switched to s1, generating an induced magnetic field, denoted as H, in the coil. This magnetic field is much stronger than the Earth's magnetic field, causing the macroscopic magnetic moment of the protons to tend towards the artificial magnetic field. Then, the switch is switched to s2, the artificial magnetic field disappears, and the polarized protons will undergo Larmor precession around the direction of the Earth's magnetic field, thus outputting the FID signal.

[0036] Figure 2(a) shows the waveform of the original FID signal acquired in this invention. Due to the combined effects of external environmental noise, circuit thermal noise, and quantization error, the original signal exhibits obvious random fluctuation characteristics. The noise amplitude is not negligible compared to the effective signal, resulting in its oscillation structure being severely masked, making it difficult to directly use for parameter extraction of the magnetic field gradient in this invention. Figure 2(b) shows the waveform of the original FID signal after autocorrelation processing. By performing autocorrelation on the original sequence, the non-correlation of random noise at different delays significantly weakens its contribution, while the oscillation period and exponential decay characteristics of the true FID signal are enhanced in the autocorrelation results. The denoised signal waveform is smooth and regular, and its decay envelope and periodic characteristics are clearly presented, making it reliable input data for subsequent Hilbert transform envelope extraction and minimum point detection.

[0037] like Figure 3 The image shows the result of extracting the envelope from the signal using the Hilbert transform. Compared to the original oscillation waveform, the envelope curve more clearly characterizes the energy decay pattern of the FID signal. This step plays a crucial role in signal feature enhancement and gradient inversion.

[0038] like Figure 4 The figure shows the results of minimum point detection of the envelope signal and least squares fitting based on the minimum point sequence. The least squares method uses the information of all data points to jointly determine the slope of the fitted line. The positive and negative disturbances of random noise will cancel each other out, thus making the final fitting result stable and reliable. It improves the robustness of parameter extraction in noisy environments and effectively enhances the accuracy and stability of magnetic field gradient estimation.

[0039] like Figure 5 The figure shows the results of one hundred repeated measurements of the target signal and estimation of the magnetic field gradient under the same experimental conditions. Each experiment independently acquired the original FID signal and sequentially performed autocorrelation denoising, Hilbert envelope extraction, minimum point detection, and least squares fitting according to the method of this invention, thereby obtaining the gradient estimate corresponding to each experimental result. The results show that this invention can stably output magnetic field gradient estimation results close to the true value, significantly reducing the impact of random noise on the accuracy of a single measurement and improving the reliability of the overall measurement system.

[0040] This invention presents a method for estimating the magnetic field gradient of a proton magnetometer based on full-waveform FID signals. It can efficiently achieve signal denoising, feature extraction, and gradient inversion using only software algorithms without the need for additional hardware. It has the advantages of simple implementation, low computational cost, strong anti-interference ability, and high estimation accuracy.

Claims

1. A method for estimating the magnetic field gradient of a proton magnetometer based on full-waveform FID signals, characterized in that... Includes the following steps: Step 1: Sample the FID signal output by the proton magnetometer to obtain a discrete signal sequence containing the sampling time and voltage value; Step 2: Denoise the discrete signal sequence obtained in Step 1 using the autocorrelation function; Step 3: Perform Hilbert transform on the denoised signal from Step 2 to construct an analytical signal and extract envelope features; Step 4: Detect local minima of the envelope features extracted in Step 3 to obtain the time series; Step 5: Perform linear fitting on the sequence of minimum points detected in Step 4. Use the least squares method to fit the minimum points and estimate the slope of the fitted line. Step 6: Based on the mathematical model of the FID signal, calculate the estimated value of the magnetic field gradient using the slope parameter obtained in Step 5.

2. The method for estimating the magnetic field gradient of a proton magnetometer based on full-waveform FID signals according to claim 1, characterized in that: In step 1, the FID signal output by the proton magnetometer is sampled using an ADC, with a sampling frequency of... The frequency is set to be much higher than the actual frequency of the FID signal under test to ensure that its dynamic changes can be fully reflected. The discrete signal sequence of the target signal is obtained by sampling. ,in: Indicates the first The sampling time corresponding to each sampling point Indicates the first Voltage values ​​at each sampling point.

3. The method for estimating the magnetic field gradient of a proton magnetometer based on full-waveform FID signals according to claim 2, characterized in that: In step 2, the discrete signal sequence acquired in step 1 is subjected to autocorrelation processing to suppress noise in the discrete signal sequence, and the sampled discrete signal sequence is denoted as discrete signal. Calculate its autocorrelation function: （1）； In formula (1): is the autocorrelation function of the discrete signal; Let be the amplitude of the signal at the nth sampling time; Let be the amplitude of the signal at the (n+k)th sampling time; k is the delay order; N is the total number of sampling points. Since random noise is uncorrelated under different delays, the contribution of random noise tends to zero when k>

0.

4. The method for estimating the magnetic field gradient of a proton magnetometer based on full-waveform FID signals according to claim 3, characterized in that: In step 3, the target signal after autocorrelation processing in step 2 is... Perform a Hilbert transform to construct an analytic signal and extract envelope features: （2）； In formula (2): For target signal; The result of the Hilbert transform; For Hilbert transform operators; Then, the analytical signal is constructed: （3）； In formula (3): For constructing the analytical signal; For imaginary units; And further calculate the envelope function: （4）； In equation (4): This is the envelope function.

5. The method for estimating the magnetic field gradient of a proton magnetometer based on full-waveform FID signals according to claim 4, characterized in that: In step 4, the minimum points of the envelope features are detected: For the detection signal , For the first The time to reach a minimum point For the first Signal data at each minimum point; If the following conditions are met: （5）； In equation (5): They represent the first One signal data; This represents the number of data points selected to the left and right of the most recent signal data at the minimum time; then... The data is the closest to the minimum value. Use the method described above to detect all the local minima.

6. The method for estimating the magnetic field gradient of a proton magnetometer based on full-waveform FID signals according to claim 5, characterized in that: In step 5, the sequence of minimum values ​​is denoted as... , For 1, 2, 3..., n The time series of the minimum value is denoted as , For the 1st, 2nd, 3rd..., n The time corresponding to each local minimum point is used to fit a straight line using the least squares method: （6）； In formula (6): The value of the fitted line, For the first The independent variable for each data point The slope of the fitted line, This is the intercept of the fitted line.

7. The method for estimating the magnetic field gradient of a proton magnetometer based on full-waveform FID signals according to claim 6, characterized in that: Actual measured value and They are not equal, and the difference between them is called the residual: （7）； In equation (7): This represents the residual between the actual measured value and the fitted value.

8. The method for estimating the magnetic field gradient of a proton magnetometer based on full-waveform FID signals according to claim 7, characterized in that: Take the partial derivatives of the sum of squared residuals with respect to a and b, and set the partial derivatives with respect to a and b to zero to minimize the sum of squared residuals: （8）； Solving equation (8) yields: （9）； In equation (9): The average of the sums of all x. Let y be the average of the sums of all y.

9. The method for estimating the magnetic field gradient of a proton magnetometer based on full-waveform FID signals according to claim 8, characterized in that: In step 6, the mathematical model of the FID signal in the gradient field is: （10）； In formula (10): Here is the mathematical model for the FID signal in the gradient magnetic field, where A is the effective amplitude; For time variables, This refers to the lateral relaxation time; It is the gyromagnetic ratio; For magnetic field gradient; This refers to the length of the proton magnetometer probe. The precession frequency of the central proton; This is an exponentially decaying term.

10. The method for estimating the magnetic field gradient of a proton magnetometer based on full-waveform FID signals according to claim 9, characterized in that: when At that time, it was known ,therefore ,at this time therefore: （11）； In equation (11): For the first There are a total of minimum time values. The time of the minimum value, then and The parameters correspond one-to-one, therefore ; Therefore, the magnetic field gradient can be calculated: （12）。

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