A magnetic field estimation method applied to an atomic magnetometer

Abstract

The application discloses a magnetic field estimation method applied to an atomic magnetometer, and comprises the following steps: step 1, model establishment, establishing a nonlinear system evolution model and a detection model applied to the atomic magnetometer; step 2, establishing an extended Kalman filter estimator; and step 3, estimating a spin sensing magnetic field through the extended Kalman filter estimator. The application generalizes the extended Kalman filter method to the atomic magnetometer, can estimate a static magnetic field, a Wiener process magnetic field and an Ornstein-Uhlenbeck process magnetic field in a more general atomic magnetometer, greatly widens the limitation of the existing magnetic field estimation in the atomic magnetometer, and is extremely inspiring in the application of filtering engineering.

Description

Technical Field

[0001] This invention relates to the field of magnetic field detection using atomic magnetometers, specifically to a magnetic field estimation method applied in atomic magnetometers. Background Technology

[0002] Existing theories divide atomic magnetometers into two parts: a sensing part and a detection part. The sensing part describes how external magnetic field signals are sensed through interaction with the outermost electron spins of alkali metals in the magnetometer's gas chamber. The detection part describes how the outermost electron spins of alkali metals are detected through interaction with linearly polarized light. Generally, both sensing and detection processes are affected by additive white Gaussian noise. This necessitates a suitable algorithm for estimating the magnetic field.

[0003] The linear Kalman filter method was first used for static magnetic field estimation, stemming from studies of spin compression that occurs during continuous probes. It provides a limit to static magnetic field estimation. However, this method is only suitable for atomic magnetometers with system dissipation much greater than the Larmor frequency. Therefore, how to perform magnetic field estimation (filtering) in more general atomic magnetometers has become a problem to be solved. Summary of the Invention

[0004] In view of the shortcomings of the prior art, this invention proposes a magnetic field estimation method for use in atomic magnetometers, which can be applied to magnetic field estimation in more general atomic magnetometers.

[0005] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:

[0006] A magnetic field estimation method applied in an atomic magnetometer includes the following steps:

[0007] Step 1: Establish the model

[0008] Step 1.1 Establish an evolution model of spin under the action of a magnetic field in an atomic magnetometer, using spin sensing magnetic field information.

[0009] Step 1.2 Establish an evolution model of the magnetic field to be estimated in the atomic magnetometer.

[0010] Step 1.3 Considering the influence of the evolution of the magnetic field on the spin, establish a nonlinear system evolution model in the atomic magnetometer.

[0011] Step 1.4 establishes the detection model in the atomic magnetometer. Information about the mean value of the spin operator is detected using probe light.

[0012] Step 2: Establish an extended Kalman filter to estimate the magnetic field.

[0013] Step 2.1 Based on the models in Steps 1.3 and 1.4, establish the extended Kalman filter predictor in the atomic magnetometer to obtain the predicted information of the spin operator mean and the magnetic field. Obtain the mean square error of the spin operator mean and the magnetic field prediction. Obtain the Kalman gain.

[0014] Step 2.2 Establish the extended Kalman filter estimator in the atomic magnetometer to obtain the optimal estimates of the spin operator mean and the magnetic field. Obtain the mean square error of the optimal estimates of the spin operator mean and the magnetic field.

[0015] Preferably, in the static magnetic field estimation, the nonlinear system evolution model of the atomic magnetometer in step 1.3 is as follows:

[0016]

[0017] DJ in the model y dj represents the average of the total spin components along the y-direction; z This represents the average of the total spin components along the z-direction; dB t T2 represents the increment of the magnetic field change, and T2 represents the relaxation time; ω l The Larmor frequency is represented by ω, which is related to the magnetic field. l =γB t ε(t) represents the waveform of the current driving the pump light.

[0018] Preferably, in the Wiener process magnetic field estimation, the nonlinear system evolution model of the atomic magnetometer in step 1.3 is as follows:

[0019]

[0020] Preferably, in the Ornstein-Uhlenbeck process magnetic field estimation, the nonlinear evolution model of the atomic magnetometer in step 1.3 is as follows:

[0021]

[0022] This invention has the following characteristics and beneficial effects:

[0023] This invention innovatively applies the Extended Kalman Filter (EKF) method to magnetic field estimation in atomic magnetometers, overcoming the limitation of previous estimation methods that could only be used in atomic magnetometers with high dissipation. The EKF method is more general and can be applied to a wider range of atomic magnetometers for magnetic field estimation. Attached Figure Description

[0024] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0025] Figure 1 Flowchart for estimating magnetic fields in an atomic magnetometer using extended Kalman filtering; Detailed Implementation

[0026] It should be noted that, unless otherwise specified, the embodiments and features described in the present invention can be combined with each other.

[0027] In the description of this invention, it should be understood that the terms "center," "longitudinal," "lateral," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," and "outer," etc., indicating orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of the invention. Furthermore, the terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. Thus, features defined with "first," "second," etc., may explicitly or implicitly include one or more of that feature. In the description of this invention, unless otherwise stated, "a plurality of" means two or more.

[0028] In the description of this invention, it should be noted that, unless otherwise explicitly specified and limited, the terms "installation," "connection," and "linking" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral connection; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; and they can refer to the internal connection of two components. Those skilled in the art will understand the specific meaning of the above terms in this invention based on the specific circumstances.

[0029] Example 1:

[0030] This invention provides a magnetic field estimation method applied in atomic magnetometers, such as... Figure 1 As shown, it includes the following steps:

[0031] Step 1: Establish the model

[0032] Step 1.1 Establish a model of spin evolution under the influence of a magnetic field in an atomic magnetometer. This model utilizes spin-sensing magnetic field information. The specific model used in this embodiment is as follows.

[0033]

[0034] Step 1.2 Establish an evolution model of the magnetic field to be estimated in the atomic magnetometer. This invention estimates the static magnetic field.

[0035] dB t =0

[0036] Step 1.3 Considering the influence of the evolution of the magnetic field on the spin, a nonlinear system evolution model is established in the atomic magnetometer.

[0037] In the estimation of the static magnetic field, the nonlinear system evolution model of the atomic magnetometer in this embodiment is as follows:

[0038]

[0039] DJ in the model y dj represents the average of the total spin components along the y-direction; z This represents the average of the total spin components along the z-direction; dB t T2 represents the increment of the magnetic field change, and T2 represents the relaxation time; ω l The Larmor frequency is represented by ω, which is related to the magnetic field. l =γB t ε(t) represents the waveform of the current driving the pump light.

[0040] Therefore, in this embodiment, f[X(t)] k-1 ),t k-1 Specifically:

[0041]

[0042] in, Specifically

[0043] Step 1.4: The mean value of the spin operator in the spin-sensing magnetic field is detected by probe light, and a detection model is established in the atomic magnetometer. In this embodiment, the detection model is specifically in the following form.

[0044] I k =g D j z +ξ D

[0045] Among them, I k It is the intensity of the probe light at time k, g D ξ represents the optical-spin coupling coefficient. DThis represents the observation noise introduced at time k.

[0046] Step 2: Establish an extended Kalman filter to estimate the magnetic field.

[0047] Step 2.1 Based on the models in Steps 1.3 and 1.4, an extended Kalman filter predictor is established in the atomic magnetometer to obtain the predicted information of the spin operator mean and the magnetic field. The mean square error of the spin operator mean and the magnetic field prediction is obtained. This invention uses a method commonly used in engineering, namely linearization followed by discretization, to establish the predictor. The predictor is as follows:

[0048]

[0049]

[0050] in, The prediction at time k is specifically written as The optimal estimate at time k-1 is expressed as follows: f[·] represents a function of system evolution, the specific form of which varies depending on the estimation of different evolutionary magnetic fields; u(t) k-1 Let ε(t) represent the control term at time k-1, specifically written as [0 ε(t) 0]. T ;P k|k-1 φ represents the mean square error matrix of the prediction at time k; k,k-1 This represents the discrete state deviation transition matrix, specifically in this embodiment as follows: Its specific form also varies depending on the estimation of different evolving magnetic fields. Q k-1 Let be the covariance matrix of the process noise at time k-1.

[0051] Step 2.2 Establishes an extended Kalman filter estimator in the atomic magnetometer to obtain the optimal estimates of the spin operator mean and magnetic field. Obtains the Kalman gain. Obtains the mean square error of the optimal estimates of the spin operator mean and magnetic field. In this embodiment, the commonly used engineering method of linearization followed by discretization is used to establish the optimal estimator.

[0052]

[0053]

[0054] R k =(IK k H k )P k|k-1 (IK k H k ) T +K k R k K k

[0055] Among them, Z k H represents the observations in the experiment at time k; k Specifically written as

[0056]

[0057] In this invention, the observation equation is linear, where H k Similar to h[·], both are [0, g D ] T ;R k Let be the covariance matrix of the observation noise.

[0058] Example 2

[0059] The difference between this embodiment and Embodiment 1 is that in step 1.2, an evolution model of the magnetic field to be estimated is established in the atomic magnetometer to estimate the Wiener process magnetic field.

[0060] dB t =dw B

[0061] In step 1.3, in the Wiener process magnetic field estimation, the nonlinear system evolution model of the atomic magnetometer is as follows:

[0062]

[0063] Example 3

[0064] The difference between this embodiment and Embodiment 1 is that in step 1.2, an evolution model of the magnetic field to be estimated is established in the atomic magnetometer to estimate the magnetic field of the Ornstein-Uhlenbeck process.

[0065] dB t =-χB t dt+dw B

[0066] In step 1.3, in the Ornstein-Uhlenbeck process magnetic field estimation, the nonlinear evolution model of the atomic magnetometer is as follows:

[0067]

[0068] Therefore, in this embodiment, f[X(t)] k-1 ),t k-1 Specifically:

[0069]

[0070] Specifically

[0071] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings, but the present invention is not limited to the described embodiments. For those skilled in the art, various changes, modifications, substitutions, and variations can be made to these embodiments, including components, without departing from the principles and spirit of the present invention, and these variations still fall within the protection scope of the present invention.

Claims

1. A magnetic field estimation method applied in an atomic magnetometer, characterized in that, Includes the following steps: Step 1: Establish the model Establish a nonlinear system evolution model and a detection model for use in an atomic magnetometer; Step 2: Establish the extended Kalman filter estimator Step 2.1 Based on the nonlinear system evolution model, establish an extended Kalman filter predictor in the atomic magnetometer; Step 2.2 Obtain the predicted values ​​of the spin operator mean and the spin sensing magnetic field through the extended Kalman filter predictor, and at the same time obtain the mean square error of the spin operator mean and the spin sensing magnetic field prediction. Step 2.3 Obtain the Kalman gain based on the mean value of the spin operator and the mean square error of the spin sensing magnetic field prediction; Step 2.4 Based on the detection model, the mean value of the spin operator and the predicted value of the spin sensing magnetic field, the prediction mean square error, and the Kalman gain, establish the extended Kalman filter estimator; Step 3: Estimate the spin-sensing magnetic field using an extended Kalman filter estimator. Step 3.1 Obtain the best estimates of the spin operator mean and the spin-sensing magnetic field using an extended Kalman filter estimator; Step 3.2 Obtain the mean square error between the spin operator mean and the best estimate of the spin sensing magnetic field using an extended Kalman filter estimator.

2. The magnetic field estimation method applied to an atomic magnetometer according to claim 1, characterized in that, Step 1 includes the following sub-steps: Step 1.1 Establish a spin evolution model under the action of a magnetic field in an atomic magnetometer based on the spin sensing magnetic field information; Step 1.2 Establish a model for the evolution of the magnetic field to be estimated in the atomic magnetometer; Step 1.3 Based on the spin evolution model and the magnetic field evolution model to be estimated, establish a nonlinear system evolution model in the atomic magnetometer; Step 1.4 The mean value of the spin operator in the spin sensing magnetic field is detected by probe light, and a detection model is established in the atomic magnetometer.

3. The magnetic field estimation method applied to an atomic magnetometer according to claim 1, characterized in that, In step 2.1, the expression for the extended Kalman filter predictor is as follows: in, This represents the prediction at time k; The optimal estimate at time k-1 is represented by f[·], which represents the system evolution function; u(t) k-1 ) represents the control term at time k-1; P k|k-1 φ represents the mean square error matrix of the prediction at time k; k,k-1 Q represents the discrete state deviation transition matrix; k-1 Let be the covariance matrix of the process noise at time k-1.

4. The magnetic field estimation method applied to an atomic magnetometer according to claim 1, characterized in that, In step 2.4, the expression for the extended Kalman filter estimator is as follows: R k =(I-K k H k )P k|k-1 (I-K k H k ) T +K k R k K k Among them, Z k H represents the observations in the experiment at time k; k Specifically written as Where H k Similar to h[·], both are [0, g D ] T ;R k Let be the covariance matrix of the observation noise.

5. The magnetic field estimation method applied to an atomic magnetometer according to claim 2, characterized in that, In step 1.3, the expression for the nonlinear system evolution model in the static magnetic field estimation is as follows: DJ in the model y dj represents the average of the total spin components along the y-direction; z This represents the average of the total spin components along the z-direction; dB t T2 represents the increment of the magnetic field change, and T2 represents the relaxation time; ω l The Larmor frequency is represented by ω, which is related to the magnetic field. l =γB t ε(t) represents the waveform of the current driving the pump light.

6. The magnetic field estimation method applied to an atomic magnetometer according to claim 2, characterized in that, In the Wiener process magnetic field estimation, the nonlinear system evolution model of the atomic magnetometer in step 1.3 is as follows: 。 7. The magnetic field estimation method applied to an atomic magnetometer according to claim 2, characterized in that, In the Ornstein-Uhlenbeck process magnetic field estimation, the nonlinear evolution model of the atomic magnetometer in step 1.3 is as follows:

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