A magnetic field estimation method based on an adaptive algorithm

Abstract

The application discloses a magnetic field estimation method based on an adaptive algorithm, which comprises the following steps: step 1, model establishment, a spin evolution model, a process equation and a detection model in an atomic magnetometer are established; and step 2, an extended Kalman filter is established, and an adaptive extended Kalman filter is established on the basis of the extended Kalman filter to estimate a magnetic field. The traditional spin noise spectrum cannot solve the problem of time-varying magnetic field tracking, and the actual performance of the extended Kalman filter is highly dependent on accurate system modeling and sensitive to system noise changes. The application significantly reduces the requirement of manual parameter optimization, and improves the applicability and operation robustness of the Kalman filter in quantum metrology applications.

Description

Technical Field

[0001] This invention relates to the field of magnetic field measurement technology, and mainly applies adaptive extended Kalman filtering, specifically a magnetic field estimation method based on an adaptive algorithm. Background Technology

[0002] Atomic magnetometers, as highly sensitive magnetic field measurement devices, have been widely used in medical diagnostics (such as magnetoencephalography and magnetocardiography), biomagnetic measurement, and fundamental physics research. Compared to devices based on superconducting quantum interference devices (SQUIDs), atomic magnetometers not only possess comparable sensitivity but also do not require cryogenic cooling and have achieved chip-level miniaturization, thus demonstrating significant advantages in portable, low-power magnetic field sensing applications.

[0003] In practical applications of atomic magnetometers, the spin noise-based magnetic field estimation method has attracted much attention due to its non-invasiveness and high resolution. However, this method faces the following core challenges:

[0004] Extremely low signal-to-noise ratio and difficulty in signal extraction: The spin noise signal itself has a weak amplitude and is easily submerged by environmental noise and detection system noise during the detection process, making it extremely difficult to directly extract effective magnetic field information.

[0005] Traditional spectral analysis methods are ill-suited for dynamic magnetic fields: Currently used spin noise spectrum analysis methods are essentially spectral analysis techniques, and their output is static or time-averaged magnetic field information. This method cannot capture the dynamic characteristics of magnetic fields changing over time, thus severely limiting its applicability in time-varying magnetic field scenarios.

[0006] The noise environment is complex and non-stationary, with strong model dependence: In real-world working environments, noise sources are diverse (such as optical noise, electronic noise, and environmental magnetic noise), and their statistical characteristics often change over time, exhibiting non-stationary features. Traditional methods such as Kalman filtering rely on accurate prior information about the noise covariance matrix, but this matrix is ​​difficult to accurately represent or obtain in real-time in actual systems, leading to a decrease in filtering performance or even divergence.

[0007] Lack of adaptive tracking capability for unknown waveform magnetic fields: Existing methods usually assume that the magnetic field change pattern is known or changes slowly, which cannot adapt to the real-time tracking of sudden or complex waveform magnetic fields, thus limiting their practicality in dynamic scenarios.

[0008] Therefore, how to achieve high-precision, adaptive real-time magnetic field estimation without prior waveform information in real-world environments with low signal-to-noise ratios, uncertain noise statistical characteristics, and dynamically changing magnetic fields has become a key problem that urgently needs to be solved in this technical field. Summary of the Invention

[0009] To address the shortcomings of existing technologies, this invention proposes a magnetic field estimation method based on an adaptive algorithm. This scheme employs adaptive extended Kalman filtering technology, combined with parameter estimation, to successfully achieve adaptive estimation of the magnetic field even when the prior magnetic field waveform is unknown, and also adaptively estimates the observation noise parameters.

[0010] To achieve the above objectives, the technical solution specifically adopted by the present invention is as follows:

[0011] A magnetic field estimation method based on an adaptive algorithm includes the following steps:

[0012] S1. For an atomic ensemble located in a magnetic field along a set direction, establish an evolutionary model describing its spin dynamics.

[0013] S2. The intensity information of the magnetic field to be measured is parameterized into a Larmor frequency that is proportional to the magnetic field intensity, and the Larmor frequency and at least two transverse components of the atomic spin are used to construct an extended state vector; based on the spin evolution model, a discretization process equation describing the evolution of the state vector over time is established.

[0014] S3. Based on the Faraday rotation effect, establish a functional relationship between the polarization rotation angle of the probe light and the spin component in the state vector as an observation model to obtain a spin observation signal containing measurement noise through the polarization change of the probe light.

[0015] S4. Based on the process equation, perform the time update step of extended Kalman filtering to obtain the prior estimate of the state vector and its error covariance matrix.

[0016] S5. Based on the observation model and historical observation data, the measurement noise intensity at the current moment is dynamically estimated by analyzing the statistical characteristics of the predicted observation error.

[0017] S6. Combining the dynamically estimated measurement noise intensity, perform the state update step of adaptive extended Kalman filtering to correct the prior estimated state vector and obtain the posterior estimated state vector. Then, calculate the Larmor frequency and magnetic field estimate from the posterior estimated state vector.

[0018] Preferably, in step S1, the spin evolution model is constructed based on the Bloch equation, wherein the evolution process of the spin vector is linear dynamic and includes a relaxation effect characterized by the transverse relaxation time, and the noise introduced during the evolution process is an increment that follows the statistics of Gaussian white noise.

[0019] Preferably, in step S2, the process equation is a nonlinear equation, and its state vector includes the x-component and z-component of the atomic spin and the Larmor frequency; the process equation is iterated at discrete time intervals, and the process noise is modeled as Wiener increments.

[0020] Preferably, in step S3, the observation model is a linear model, which is expressed as a linear function relationship between the polarization rotation angle of the probe light and the spin x component in the state vector, the proportionality coefficient is the coupling constant between the probe light and the atomic spin, and the observation signal is superimposed with measurement noise that follows a Gaussian distribution.

[0021] Preferably, in step S4, the time update step of the extended Kalman filter includes: predicting the prior estimate of the current state based on the posterior estimate of the state at the previous time step using a nonlinear state evolution function; and predicting the prior estimate of the error covariance at the current time step based on the Jacobian matrix of the state transition function, the posterior estimate of the error covariance at the previous time step, and the process noise covariance.

[0022] Preferably, in step S5, the dynamic estimation of measurement noise intensity specifically includes: calculating observation information at a series of consecutive time points, wherein the observation information is the difference between the actual observed value and the observed value predicted based on the prior state; and recursively estimating the covariance matrix of the measurement noise based on the sample covariance of the observation information, the observation model matrix, and the preset estimation window size.

[0023] Preferably, in step S6, the state update step of the adaptive extended Kalman filter includes: calculating the Kalman gain matrix using the prior estimates of the dynamically estimated measurement noise covariance matrix, observation model matrix, and error covariance; correcting the prior estimates of the state vector using the Kalman gain matrix to obtain posterior estimates; and updating the posterior estimates of the error covariance matrix.

[0024] Preferably, the state vector includes the x-component and z-component of the atomic spin and the Larmor frequency; the nonlinear state evolution function takes the state vector of the previous time step as input and outputs the predicted value of the state vector of the current time step.

[0025] Preferably, the Jacobian matrix of the state transition function is obtained by taking the partial derivative of the nonlinear state evolution function with respect to the state vector, and its matrix elements characterize the coupling and evolution sensitivity between state variables.

[0026] Preferably, the observation model matrix is ​​a row vector, and its only non-zero element is the coupling constant between the probe light and the atomic spin, which corresponds to the coefficient of the spin x component in the state vector.

[0027] This invention has the following characteristics and beneficial effects:

[0028] I. This invention improves the accuracy of system state estimation by introducing adaptive extended Kalman filtering in the magnetic field measurement process with low signal-to-noise ratio. The adaptive method reduces the difficulty of manually adjusting parameters in complex physical models.

[0029] Second, by utilizing the dynamic adjustment characteristics of the adaptive extended Kalman filter, the consistency between the filtering results and the true value is improved when the system noise modeling is inaccurate, and the robustness to noise statistical uncertainty is stronger.

[0030] Third, the adaptive extended Kalman filter effectively suppresses noise by updating the state estimation error covariance matrix in real time and combining theoretical model predictions with experimental observations, thus maintaining high-precision magnetic field estimation even when noise statistics change.

[0031] Fourth, in real-world environments, the magnetic field may change over time. Adaptive extended Kalman filtering can update the magnetic field state estimate in real time, track the dynamic changes of the magnetic field, and maintain the real-time nature of the measurement.

[0032] Fifth, by setting the magnetic field as an unknown parameter, the model dependence of magnetic field estimation is effectively reduced, and the tracking of arbitrary waveform magnetic fields can be achieved without remodeling the magnetic field change process. Attached Figure Description

[0033] Figure 1 This is a flowchart of a magnetic field estimation method based on an adaptive algorithm according to an embodiment of the present invention.

[0034] Figure 2 This is a comparison of the mean square estimation error of adaptive extended Kalman filtering and extended Kalman filtering with respect to the accuracy of the initial measurement noise in this embodiment of the invention. Detailed Implementation

[0035] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0036] A magnetic field estimation method based on an adaptive algorithm, such as Figure 1 As shown, it includes the following steps:

[0037] S1. For an atomic ensemble located in a magnetic field along a set direction, establish a spin evolution model that describes its spin dynamics.

[0038] The spin evolution model is constructed based on the Bloch equation, wherein the evolution of the spin vector is linear dynamic and includes a relaxation effect characterized by the transverse relaxation time, and the noise introduced during the evolution process is an increment that follows the statistical rules of Gaussian white noise.

[0039] In this embodiment, the atomic gas cell is located at the center of the magnetic shielding structure, and a magnetic field along the y-axis is applied. The spin evolution model is determined using Bloch's equations for atoms under magnetic field conditions. Specifically, the spin component evolution in this embodiment is obtained from Bloch's equations:

[0040] ;

[0041] Where the spin vector Following linear dynamics, and These represent the spin components along the x-axis and z-axis at time t, respectively. Larmor frequency, representing atomic spin The initial spin state, This represents the spin noise increment, which follows Gaussian white noise statistics. and T1 and T2 represent the spin noise increments in the x-axis and z-axis directions at time t, respectively, and T2 represents the transverse relaxation time.

[0042] S2. The intensity information of the magnetic field to be measured is parameterized into a Larmor frequency that is proportional to the magnetic field intensity, and the Larmor frequency and at least two transverse components of the atomic spin are used to construct an extended state vector; based on the spin evolution model, a discretized process equation describing the evolution of the state vector over time is established.

[0043] The process equation is a nonlinear equation, and its state vector includes the x-component and z-component of the atomic spin, as well as the Larmor frequency. The process equation is iterated at discrete time intervals, and the process noise is modeled as Wiener increments. Specifically, the process equation is:

[0044] ;

[0045] in, The discrete time interval is defined as the sampling interval of the detector, where k is an integer representing the discrete sampling time, and t is the sampling interval of the detector. k This represents the time over k discrete time intervals. and ω represents the spin components along the x-axis and z-axis at time k, respectively. k This represents the Larmor frequency of the atom's spin at time k. (Process noise vector) It is the discrete noise increment at time k. and These represent the discrete spin noise increments in the x-axis and z-axis directions at time k, respectively. This represents the noise increment of the Larmor frequency of the atomic spin.

[0046] S3. Based on the Faraday rotation effect, establish a functional relationship between the polarization rotation angle of the probe light and the spin component in the state vector as an observation model to obtain a spin observation signal containing measurement noise through the polarization change of the probe light.

[0047] The observation model is a linear model, expressed as a linear function of the polarization rotation angle of the probe light and the spin x component in the state vector. The scaling factor is the coupling constant between the probe light and the atomic spin. Furthermore, the observation signal is superimposed with measurement noise that follows a Gaussian distribution. Specifically:

[0048] ;

[0049] in, This represents the noisy spin signal actually observed at time k; It is the coupling constant for detecting the coupling between light and atomic spin. R represents the measurement noise introduced during the detection process that follows a Gaussian distribution. k This indicates the measured noise intensity.

[0050] S4. Based on the process equation, perform the time update step of extended Kalman filtering to obtain the prior estimate of the state vector and its error covariance matrix.

[0051] Specifically, the prior estimate of the current state is predicted using a nonlinear state evolution function; and the prior estimate of the current error covariance is predicted based on the Jacobian matrix of the state transition function, the posterior estimate of the error covariance from the previous time step, and the process noise covariance. The specific execution update expression is as follows:

[0052] ;

[0053] in, The prior estimated state variables at time k; Let be the posterior estimated state variables at time k-1; The nonlinear state evolution equation at time k-1 is given. Let be the prior estimate of the covariance matrix at time k; Let be the posterior estimated covariance matrix at time k-1; Let K be the partial derivative matrix of the state transition at time k-1; Let be the transpose of the partial derivative matrix of the state transition at time k-1; Let be the covariance matrix of the state noise at time k-1.

[0054] Furthermore, the prior estimated state variables at time k and the posterior estimated state variables at time k-1 are expressed as follows:

[0055] , ;

[0056] in, and These are the prior estimated spin components in the x-axis and z-axis directions at time k, respectively; To estimate the Larmor frequency in the prior at time k; and These are the posterior estimated spin components in the x-axis and z-axis directions at time k-1, respectively. The posterior estimate of the Larmor frequency at time k-1 is given; T denotes the transpose of the vector. Furthermore, the nonlinear state evolution equation at time k-1 is expressed as follows:

[0057] ;

[0058] in, It is a 3×1 state vector.

[0059] S5. Based on the observation model and historical observation data, the measurement noise intensity at the current moment is dynamically estimated by analyzing the statistical characteristics of the predicted observation error.

[0060] Specifically, the dynamic estimation of measurement noise intensity includes: calculating observation information at a series of consecutive time points, wherein the observation information is the difference between the actual observed value and the observed value predicted based on the prior state; and recursively estimating the covariance matrix of the measurement noise based on the sample covariance of the observation information, the observation model matrix, and the preset estimation window size.

[0061] In this embodiment, an adaptive extended Kalman filter is obtained from the established extended Kalman filter in the atomic magnetometer. The Sage-Husa adaptive algorithm is integrated into the framework of the extended Kalman filter, thus forming the adaptive extended Kalman filter. The core principle of the adaptive extended Kalman filter lies in dynamically updating the measurement noise through information and using a sliding window. In this embodiment, the adaptive estimation method for the measurement noise intensity is as follows:

[0062] ;

[0063] in, For the new information at time k; The transpose of the information at time k; The observation model matrix; is the transpose of the observation model matrix; N is the estimation window size; Let be the true value observed at time k; The predicted observation value at time k.

[0064] Furthermore, the observation model matrix is ​​represented as follows:

[0065] ;

[0066] in, Let be the coupling coefficient between light and spin, and T denote the transpose of the vector.

[0067] S6. Combining the dynamically estimated measurement noise intensity, perform the state update step of adaptive extended Kalman filtering to correct the prior estimated state vector and obtain the posterior estimated state vector. Then, calculate the Larmor frequency and magnetic field estimate from the posterior estimated state vector.

[0068] The state update step of the adaptive extended Kalman filter includes: calculating the Kalman gain matrix using the dynamically estimated measurement noise covariance matrix, observation model matrix, and prior estimates of the error covariance; correcting the prior estimates of the state vector using the Kalman gain matrix to obtain posterior estimates; and updating the posterior estimates of the error covariance matrix. Specifically, the state update part of the adaptive extended Kalman filter is represented as follows:

[0069] ;

[0070] in, The Kalman gain at time k; The measurement noise is adaptively estimated at time k; The estimated observation value at time k; I represents the 3×3 identity matrix; T represents the transpose of the matrix; -1 represents the inverse of the matrix.

[0071] To verify the effectiveness of the method described in this invention, simulation experiments were conducted. The experiments simulated a time-varying magnetic field and a time-varying measurement noise environment. Magnetic field estimation was performed using both the standard Extended Kalman Filter (EKF, assuming a fixed and known noise covariance) and the Adaptive Extended Kalman Filter (AEKF) proposed in this invention.

[0072] Figure 2 The performance comparison of the two methods is presented, showing the relationship between the estimated mean squared error (MSE) and the measurement noise variance in EKF and AEKF. The blue curve corresponds to the EKF result, and the red curve corresponds to the AEKF result. The results show that EKF fails to track changes in the magnetic field when the measurement noise covariance is underestimated or overestimated; compared with EKF, AEKF can achieve accurate estimation even without an accurate noise model, which is verified by simulation to demonstrate the robustness of AEKF to measurement noise.

[0073] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely preferred examples and are not intended to limit the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. A magnetic field estimation method based on an adaptive algorithm, characterized in that, Includes the following steps: S1. For an atomic ensemble located in a magnetic field along a set direction, establish a spin evolution model that describes its spin dynamics. S2. The intensity information of the magnetic field to be measured is parameterized into a Larmor frequency that is proportional to the magnetic field intensity, and the Larmor frequency and at least two transverse components of the atomic spin are used to construct an extended state vector; based on the spin evolution model, a process equation describing the evolution of the state vector over time is established. S3. Based on the Faraday rotation effect, establish a functional relationship between the polarization rotation angle of the probe light and the spin component in the state vector as an observation model to obtain a spin observation signal containing measurement noise through the polarization change of the probe light. S4. Based on the process equation, perform the time update step of extended Kalman filtering to obtain the prior estimate of the state vector and its error covariance matrix. S5. Based on the observation model and historical observation data, the measurement noise intensity at the current moment is dynamically estimated by analyzing the statistical characteristics of the predicted observation error. In step S5, dynamically estimating the measurement noise intensity specifically includes: calculating observation information at a series of consecutive time points, wherein the observation information is the difference between the actual observed value and the observed value predicted based on the prior state; and recursively estimating the covariance matrix of the measurement noise based on the sample covariance of the observation information, the observation model matrix, and the preset estimation window size. The expression is as follows: ； in, For the new information at time k; The transpose of the information at time k; The observation model matrix; is the transpose of the observation model matrix; N is the estimation window size; Let be the true value observed at time k; The predicted observation value at time k; The observation model matrix is ​​represented as follows: ； in, Let T be the coupling coefficient between light and spin, and T denote the transpose of the vector. S6. Combining the dynamically estimated measurement noise intensity, perform the state update step of adaptive extended Kalman filtering to correct the prior estimated state vector and obtain the posterior estimated state vector. Then, calculate the Larmor frequency and magnetic field estimate from the posterior estimated state vector.

2. The method according to claim 1, characterized in that, In step S1, the spin evolution model is constructed based on the Bloch equation, wherein the evolution process of the spin vector is linear dynamic and includes a relaxation effect characterized by the transverse relaxation time, and the noise introduced during the evolution process is an increment that follows the statistics of Gaussian white noise.

3. The method according to claim 1, characterized in that, In step S2, the process equation is a nonlinear equation, and its state vector includes the x-component, z-component, and Larmor frequency of the atomic spin; the process equation is iterated at discrete time intervals, and the process noise is modeled as Wiener increments.

4. The method according to claim 1, characterized in that, In step S3, the observation model is a linear model, which is expressed as a linear function relationship between the polarization rotation angle of the probe light and the spin x component in the state vector. The proportionality coefficient is the coupling constant between the probe light and the atomic spin, and the observation signal is superimposed with measurement noise that follows a Gaussian distribution.

5. The method according to claim 1, characterized in that, In step S4, the time update step of the extended Kalman filter includes: predicting the prior estimate of the current state based on the posterior estimate of the state at the previous time step using a nonlinear state evolution function; and predicting the prior estimate of the error covariance at the current time step based on the Jacobian matrix of the state transition function, the posterior estimate of the error covariance at the previous time step, and the process noise covariance.

6. The method according to claim 1, characterized in that, In step S6, the state update step of the adaptive extended Kalman filter includes: calculating the Kalman gain matrix using the dynamically estimated measurement noise covariance matrix, observation model matrix, and prior estimate of error covariance; correcting the prior estimate of the state vector using the Kalman gain matrix to obtain the posterior estimate, and updating the posterior estimate of the error covariance matrix.

7. The method according to claim 5, characterized in that, The state vector includes the x-component and z-component of the atomic spin and the Larmor frequency; the nonlinear state evolution function takes the state vector of the previous time step as input and outputs the predicted value of the state vector of the current time step.

8. The method according to claim 5, characterized in that, The Jacobian matrix of the state transition function is obtained by taking the partial derivative of the nonlinear state evolution function with respect to the state vector, and its matrix elements characterize the coupling and evolution sensitivity between state variables.

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