Joint compensation method for delay and damping asymmetric error of all-angle hemispherical gyroscope

Abstract

The invention relates to an all-angle hemispherical gyroscope delay and damping asymmetric error joint compensation method, which belongs to the technical field of inertial navigation, and comprises the following steps: S1, obtaining a self-precession excitation signal and an angular velocity measurement value signal output by a gyroscope; s2, preliminarily estimating the time delay of the gyroscope by adopting a maximum likelihood weighted cross-correlation time delay estimation method; s3, estimating the damping asymmetry error of the gyroscope through a recursive least square method by utilizing the estimated time delay; s4, re-estimating the time delay of the gyroscope by using the estimated damping asymmetric error to obtain the updated estimated time delay; judging whether the updated estimated delay is converged or not; if not, returning to the step S3, and re-estimating the damping asymmetric error of the gyroscope through the recursive least square method by utilizing the updated estimated delay; if the time delay is converged, the finally estimated time delay is obtained; and S5, compensating the finally estimated delay and damping asymmetric error into a control system of the gyroscope. According to the invention, the measurement precision and long-term stability of the gyroscope are improved.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of inertial navigation, and particularly relates to a joint compensation method for delay and damping asymmetry errors of a full-angle hemispherical gyro. BACKGROUND

[0002] The hemispherical resonator gyro (HRG) is a high-precision inertial sensor based on the Coriolis vibration principle, widely used in aerospace, marine navigation, land positioning, and space exploration. The HRG measures angular velocity by detecting the precession effect of the standing wave in the resonant cavity, with high precision, long service life, no wearing parts, strong environmental adaptability, and excellent reliability. The HRG has two main working modes: force balance mode and full-angle mode. Among them, the full-angle mode has direct angular rate output, wide dynamic range, and high stability of the proportional factor, becoming an important research direction in the field of HRG.

[0003] In the full-angle mode, the measurement accuracy of the HRG is significantly affected by the structural asymmetry of the resonator, especially the damping asymmetry and the delay. The damping asymmetry is caused by the uneven distribution of the resonator damping, leading to angle-dependent drift and affecting the long-term stability of the system. The delay is mainly caused by the lag effect in the signal sampling and data processing process, causing a time sequence deviation between the input angular velocity and the measured signal, further exacerbating the measurement error of the system. Although existing research has proposed various methods to compensate for damping asymmetry errors, these methods mostly do not consider the impact of delay, resulting in limited compensation effect. In the prior art, the invention patent with publication number CN112504258A proposes an adaptive circuit to control the quartz hemispherical resonator gyro in full-angle mode, the invention patent with publication number CN115031713A proposes a method for self-calibration of detection signal nonlinearity to identify and self-calibrate the angle calculation error caused by the detection signal nonlinearity of the full-angle mode hemispherical resonator gyro, and the invention patent with publication number CN113587954A provides a damping uneven compensation control method and system to solve the technical problem of drift error caused by damping unevenness in the full-angle mode hemispherical resonator gyro. However, these methods do not fully consider the impact of delay on system performance, especially in high-precision measurement, where delay can cause the parameter update of the adaptive algorithm to lag, further affecting the compensation effect of damping asymmetry errors.

[0004] Therefore, the existing HRG error compensation methods have obvious deficiencies in dealing with the joint impact of delay and damping asymmetry errors, and a method that can simultaneously compensate for delay and damping asymmetry errors is needed to improve the measurement accuracy and long-term stability of the HRG system. SUMMARY

[0005] In view of the deficiencies of the prior art, the purpose of the present application is to provide a full-angle hemispherical gyro delay and damping asymmetric error joint compensation method, which can improve the measurement accuracy and long-term stability of the hemispherical resonator gyro system.

[0006] To achieve the above-mentioned purpose, the present application adopts the following technical solution: a full-angle hemispherical gyro delay and damping asymmetric error joint compensation method, comprising the following steps: S1, setting a self-precession excitation signal to excite the hemispherical gyro vibration, and obtaining the angular velocity measurement value signal of the self-precession excitation signal and the gyro output; S2, using a maximum likelihood weighted cross-correlation delay estimation method to preliminarily estimate the delay of the gyro, and obtaining the estimated delay; S3, using the estimated delay, estimating the damping asymmetric error of the gyro by recursive least squares method, and obtaining the estimated damping asymmetric error; S4, using the estimated damping asymmetric error, re-estimating the delay of the gyro, obtaining the updated estimated delay, judging whether the updated estimated delay converges, if not, returning to step S3, using the updated estimated delay to re-estimate the damping asymmetric error of the gyro by recursive least squares method, if it has converged, obtaining the final estimated delay; S5, compensating the final estimated delay and the damping asymmetric error to the control system of the gyro.

[0007] Preferably, the specific method of step S1 is: S11, using an elliptical orbit to represent the control principle of the full-angle mode, and introducing measurement noise to obtain the gyro angular velocity of the hemispherical resonator gyro at a certain time; S12, in the absence of external inertial angular velocity input, setting a self-precession excitation signal to make the gyro in working condition, and recording the complete self-precession excitation signal and collecting the complete angular velocity measurement value signal of the gyro output; cutting the angular velocity measurement value signal of the gyro output from time k to time k+t to obtain a first angular velocity measurement value signal with a time length of t; cutting the self-precession excitation signal from time k to time k+t to obtain a first self-precession excitation signal with a time length of t.

[0008] Preferably, the specific method of step S2 is: S21, using the maximum likelihood weighted cross-correlation delay estimation method to calculate the weighted cross-correlation function of the first angular velocity measurement value signal and the first self-precession excitation signal; S22, calculating the estimated delay: performing inverse fast Fourier transform on the weighted cross-correlation function of the first angular velocity measurement value signal and the first self-precession excitation signal, and then finding the position of the inverse transform maximum value, which corresponds to the horizontal coordinate time, that is, the estimated delay .

[0009] Preferably, the specific method of step S3 is: S31, using the estimated delay , intercept the self-advance excitation signal from time to time, to obtain a second self-advance excitation signal with a time length of t; S32, using the first angular velocity measurement signal and the second self-advance excitation signal, and using the least square method to solve the estimated damping asymmetry error.

[0010] Preferably, the specific method of step S32 is: S321, initializing the estimated parameter vector; S322, for each time k, constructing a regression vector on the estimated delay ; S323, based on the gyro angular velocity, the estimated parameter vector and the regression vector, calculating the error between the actual measurement value and the predicted value of the gyro angular velocity at time k; S324, based on the regression vector, the covariance matrix and the error between the actual measurement value and the predicted value of the gyro angular velocity at time k, re-estimating the estimated parameter vector to obtain the updated estimated parameter vector at time k; S325, updating the covariance matrix.

[0011] Preferably, the specific method of step S4 is: S41, using the estimated damping asymmetry error to obtain the compensated gyro angular velocity at a certain time; S42, using the compensated gyro angular velocity at a certain time to update the angular velocity at each time in the first angular velocity measurement signal to obtain a second angular velocity measurement signal; S43, using the maximum likelihood weighted cross-correlation delay estimation method to calculate the weighted cross-correlation function of the second angular velocity measurement signal and the second self-advance excitation signal; S44, re-calculating the estimated delay: performing inverse fast Fourier transform on the weighted cross-correlation function of the second angular velocity measurement signal and the second self-advance excitation signal, and then finding the position of the maximum value of the inverse transform, which corresponds to the time of the abscissa, i.e. the updated estimated delay ; S45, judging whether the updated estimated delay converges: setting a delay convergence threshold, judging whether the difference between the updated estimated delay and the last estimated delay is less than the delay convergence threshold; if not, returning to step S3 to re-estimate the damping asymmetry error using the updated estimated delay ; if yes, updating the estimated delay and the damping asymmetric error is the final estimated result.

[0012] Compared with the prior art, the present application has the following beneficial effects: the present application firstly preliminarily estimates the time delay of the system through the maximum likelihood weighted cross-correlation time delay estimation, and dynamically compensates the damping asymmetric error in combination with the recursive least square algorithm, so as to realize high-precision joint compensation of the time delay and the damping asymmetric error. Through multiple iteration optimization, the present application significantly reduces the angle-dependent drift error, and improves the measurement precision and long-term stability of the hemispherical resonator gyro. The present application has high result reliability, strong universality, simple operation, high precision after compensation of the full-angle hemispherical resonator gyro, good practicability, and is suitable for high-precision inertial navigation systems in the fields of aerospace, marine navigation, land positioning and space exploration. The present application solves the problem of insufficient consideration of the coupling influence of the time delay and the damping asymmetric error in the prior art, and leads to insufficient compensation precision and poor system stability. BRIEF DESCRIPTION OF DRAWINGS

[0013] In order to more clearly illustrate the technical solutions in the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or the prior art description. Obviously, the drawings in the following description can also be obtained by those skilled in the art without creative labor on the basis of the drawings.

[0014] Figure 1 A flowchart of the joint compensation method of the time delay and the damping asymmetric error of the full-angle hemispherical gyro is provided for the present application.

[0015] Figure 2 The mode angle of the gyro and the change of the spin excitation signal in embodiment one of the present application.

[0016] Figure 3 The damping parameter estimated by the joint compensation method of the present application and the convergence process of the gain with time in embodiment one of the present application.

[0017] Figure 4 The angle drift deviation result diagrams of a certain full-angle hemispherical resonator gyro before compensation, only using damping asymmetric compensation and using the compensation method provided by the present application in embodiment one of the present application. DETAILED DESCRIPTION

[0018] In order to make the objects, technical solutions and advantages of the present application clearer, the technical solutions in the present application will be clearly and completely described below with reference to the drawings in the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative work fall within the protection scope of the present application. In order to make the above-mentioned features and advantages of the present application more obvious and easy to understand, the following specific embodiments are described in detail below, and the drawings are referenced.

[0019] As shown in Figure 1 , the embodiment of the present application provides a joint compensation method for time delay and damping asymmetry error of a full-angle hemispherical gyro, comprising the following steps: S1, setting a self-precession excitation signal to excite the hemispherical gyro to vibrate, and obtaining a self-precession excitation signal and an angular velocity measurement value signal output by the gyro; S2, preliminarily estimating the time delay of the gyro by using a maximum likelihood weighted cross-correlation time delay estimation method, to obtain an estimated time delay; S3, estimating the damping asymmetry error of the gyro by using the estimated time delay through a recursive least square method, to obtain an estimated damping asymmetry error; S4, re-estimating the time delay of the gyro by using the estimated damping asymmetry error, to obtain an updated estimated time delay; judging whether the updated estimated time delay converges; if not, returning to step S3, re-estimating the damping asymmetry error of the gyro by using the updated estimated time delay through the recursive least square method; if yes, obtaining a final estimated time delay; S5, compensating the final estimated time delay and the damping asymmetry error to a control system of the gyro.

[0020] In the embodiment, the specific method of step S1 is: S11, using an elliptical orbit to represent the control principle of the full-angle mode, and introducing a measurement noise, to obtain a gyro angular velocity of the hemispherical resonator gyro at a certain time : ; Wherein, κ represents a gyro scale factor, Ω represents an external input angular rate, ω0 represents a resonant frequency, θ represents a mode angle of the gyro, Q represents a quality factor of the gyro, γ1 and γ2 represent two orthogonal components of the damping asymmetry error, a represents a long axis of the orbit, P(θ) represents a self-precession excitation signal at a certain time, and w is the introduced measurement noise; S12, in the absence of external inertial angular velocity input, i.e. Ω is 0, artificially setting the self-precession excitation signal to make the gyro in a working state, and recording a complete self-precession excitation signal and collecting a complete angular velocity measurement value signal output by the gyro; The angular velocity measurement signals output by the gyroscope from time k to time k+t are extracted to obtain the first angular velocity measurement signal T with a duration of t. a1 ; By extracting the precession excitation signal from time k to time k+t, a first precession excitation signal T with a duration of t is obtained. a2 .

[0021] In this embodiment, the specific method of step S2 is as follows: S21, First angular velocity measurement signal T a1 With the first self-precession excitation signal T a2 Due to the system's sluggishness, a certain time delay is inevitable. Therefore, the maximum likelihood weighted cross-correlation delay estimation method is used to calculate the first angular velocity measurement signal T. a1 With the first self-precession excitation signal T a2 The weighted cross-correlation function G a as follows: ; Where, ψ a (f) is the first maximum likelihood weighting function, G af The signal T represents the first angular velocity measurement value. a1 and the first self-precession excitation signal T a2 The cross power spectrum, j represents the imaginary number, f represents the sampling frequency, h represents the delay in gyroscope signal transmission, and N is the number of discrete points in the signal; ; ; ; ; ; Among them, T a1f and T a2f The first angular velocity measurement signal T is respectively a1 and the first self-precession excitation signal T a2 The Fourier transform function is a function of frequency; Indicates T a1f The complex conjugate, Indicates T a2f The complex conjugate of G; a1f The first angular velocity measurement signal T a1 The self-power spectral density, given by T a1f Multiply by its complex conjugate; G a2f The first self-precession excitation signal T a2 The self-power spectral density, given by T a2f Multiply by its complex conjugate; C aThe signal T represents the first angular velocity measurement value. a1 and the first self-precession excitation signal T a2 The coherence function; S22. Calculate the estimated delay: for the first angular velocity measurement signal T a1 With the first self-precession excitation signal T a2 The weighted cross-correlation function G a Perform an inverse fast Fourier transform, then find the location of the maximum value of the inverse transform. The time corresponding to this location on the horizontal axis is the estimated delay. : ; Here, IFFT|| represents the inverse fast Fourier transform.

[0022] In this embodiment, the specific method of step S3 is as follows: S31. Utilizing the estimated delay , cut Time to The precession excitation signal at time t is used to obtain the second precession excitation signal T of duration t. b2 ; S32, using the first angular velocity measurement signal T a1 Second self-precession excitation signal T b2 The two orthogonal components of the estimated damping asymmetry error are obtained by using the least squares method. and The value.

[0023] In this embodiment, the second self-precession excitation signal T b2 Actually, it is the timing signal of the self-precession excitation signal P(θ), and the first angular velocity measurement signal T. a1 In reality, it is the angular velocity of the gyroscope. The timing signals satisfy the gyro angular velocity formula in S11. The second self-precession excitation signal T... b2 With the first angular velocity measurement signal T a1 Alignment; First angular velocity measurement signal T a1 The sample points can be denoted as θ(0), θ(1), ..., θ(N-1), corresponding to times k, k+1, ..., k+N-1; the second self-precession excitation signal T b2 The sample points can be denoted as P(0), P(1), ..., P(N-1), corresponding to time points P(0, P(1), ..., P(N-1)). , , ..., ; Therefore, the specific method for step S32 is as follows: S321. Initialize the estimated parameter vector : ; wherein, represents the gain of the estimated self-precession excitation signal, and respectively represent two orthogonal components of the estimated damping asymmetry error, T represents the transpose of a matrix; S322, for each time instant k, a regression vector Φ(k) is constructed on the estimated time delay as follows: ; S323, based on the gyro angular velocity, the estimated parameter vector and the regression vector, an error ε(k) between the actual measurement value and the predicted value of the gyro angular velocity at time instant k is calculated: ; wherein, is the actual measurement value of the gyro angular velocity at time instant k, is the predicted value of the gyro angular velocity at time instant k. Since the sampled signal is discrete, k-1 represents a time point before time instant k, represents the estimated parameter vector at time instant k-1; S324, based on the regression vector, the covariance matrix and the error between the actual measurement value and the predicted value of the gyro angular velocity at time instant k, the estimated parameter vector is re-estimated to obtain an updated estimated parameter vector at time instant k : ; wherein, D(k-1) represents the covariance matrix at time instant k-1, a larger positive diagonal matrix can be taken initially, and λ represents a forgetting factor; and respectively represent the second term and the third term of the updated estimated parameter vector at time instant k; the damping angle θ γ is: ; wherein, atan2() represents a four-quadrant inverse tangent function; S325, the covariance matrix is updated as follows: ; wherein, D(k) represents the covariance matrix at time instant k.

[0024] In the embodiment, the specific method of step S4 is as follows: S41, the gyro angular velocity after compensation at a certain time instant is obtained by using the estimated damping asymmetry error. ; S42. Using the compensated gyroscope angular velocity at a certain moment The formula is used to measure the first angular velocity signal T. a1 The angular velocity at each moment is updated to obtain the second angular velocity measurement signal T. b1 ; S43. Using the maximum likelihood weighted cross-correlation delay estimation method, calculate the second angular velocity measurement signal T. b1 With the second self-precession excitation signal T b2 The weighted cross-correlation function G b as follows: ; Where, ψ b (f) is the second maximum likelihood weighting function, G bf The signal T represents the second angular velocity measurement value. b1 Second self-precession excitation signal T b2 The cross power spectrum, where j represents the imaginary number, f represents the frequency, and h is the time delay variable; ; ; ; ; ; Among them, T b1f and T b2f The second angular velocity measurement signal T is respectively b1 Second self-precession excitation signal T b2 The Fourier transform function is a function of frequency; Indicates T b1f The complex conjugate, Indicates T b2f The complex conjugate of G; b1f The second angular velocity measurement signal T b1 The self-power spectral density, given by T b1f Multiply by its complex conjugate; G b2f The second self-precession excitation signal T b2 The self-power spectral density, given by T b2f Multiply by its complex conjugate; C b The signal T represents the second angular velocity measurement value. b1 Second self-precession excitation signal T b2 The coherence function; S44. Recalculate the estimated delay: for the second angular velocity measurement signal T b1With the second self-precession excitation signal T b2 The weighted cross-correlation function G b Perform an inverse Fast Fourier Transform (IFFT) and find the location of the maximum value of the inverse transform. The time interval corresponding to this location on the x-axis is the estimated delay for updating. ; S45. Determine the delay of the update estimate. Convergence status: Set a delay convergence threshold (threshold) to determine the estimated delay for updating. Compared with the previous estimated delay Is the difference less than the delay convergence threshold? If not, return to step S3 and use the updated estimated delay. Re-estimate the damping asymmetry error; if so, update the estimated delay. Two orthogonal components of damping asymmetry error and This is the final estimated result.

[0025] Experimental Example: To verify the correctness of this invention, a combined compensation for delay and damping asymmetry errors was performed on a full-angle hemispherical resonator gyroscope according to the method provided in this invention. The quality factor of this full-angle hemispherical resonator gyroscope is approximately 10 million, and the frequency split is approximately 2.5 mHz.

[0026] Figure 2 The experiment shows the changes in the mode angle of the gyroscope and the spin-precession excitation signal. Figure 3 The convergence process of the damping parameters and gain over time estimated using the joint compensation method of the present invention is shown. The final estimated damping parameters and delay results obtained using the method provided by the present invention are listed in Table 1.

[0027] Table 1. Damping parameters and delay results of a full-angle hemispherical resonant gyroscope obtained using the method of the present invention:

[0028] The estimated gyroscope parameters were compensated into the gyroscope's control system. By changing the mode angle, the effects of damping asymmetry error and delay error on the angular drift deviation of the hemispherical resonator gyroscope were analyzed. (See [link to relevant documentation]). Figure 4, the radial coordinate unit is an elliptical orbit parameter, that is, the short axis b of the harmonic oscillator elliptical motion trajectory divided by the long axis a. In the case where the damping asymmetry error and the delay error are not compensated, the maximum deviation of the angle drift deviation of the hemispherical resonator gyro is 62.52; in the case where only the damping asymmetry error is compensated, the maximum deviation of the angle drift deviation is reduced to 9.72; after the damping asymmetry error and the delay error are compensated at the same time, the maximum deviation of the angle drift deviation is further reduced to 1.2132, which is reduced by 51.5 times compared with the case where the errors are not compensated, and is further reduced by 8 times compared with the case where only the damping asymmetry error is compensated, verifying the correctness and effectiveness of the method proposed in the application.

[0029] In the description of the application, it should be understood that the terms "first", "second" are only for the purpose of description, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of indicated technical features. Therefore, the features defined with "first", "second" can be explicitly or implicitly included one or more of the features.

[0030] The part of the application not disclosed in detail belongs to the known technology in the art.

[0031] Although the above describes the specific embodiments of the application for the purpose of understanding the application by those skilled in the art, it should be clear that the application is not limited to the scope of the specific embodiments, and for those skilled in the art, it is obvious that various changes are within the spirit and scope of the application defined and determined by the appended claims, and all the application and creation using the concept of the application are protected.

Claims

1. A method for jointly compensating for delay and damping asymmetry errors in a full-angle hemispherical gyroscope, characterized in that, Includes the following steps: S1. Set the self-precession excitation signal to excite the hemispherical gyroscope to vibrate, and obtain the self-precession excitation signal and the angular velocity measurement value signal output by the gyroscope; S2. The delay of the gyroscope is initially estimated using the maximum likelihood weighted cross-correlation delay estimation method to obtain the estimated delay; S3. Using the estimated delay, estimate the damping asymmetry error of the gyroscope through the recursive least squares method to obtain the estimated damping asymmetry error. S4. Using the estimated damping asymmetry error, re-estimate the gyroscope's delay to obtain the updated estimated delay; determine whether the updated estimated delay converges. If convergence fails, return to step S3 and use the updated estimated delay to re-estimate the damping asymmetry error of the gyroscope using the recursive least squares method; if convergence has been achieved, the final estimated delay is obtained. S5. The final estimated delay and damping asymmetry errors are compensated into the gyroscope's control system.

2. The method for joint compensation of delay and damping asymmetry error of a full-angle hemispherical gyroscope according to claim 1, characterized in that, The specific method for step S1 is as follows: S11. The control principle of the full-angle mode is represented by an elliptical orbit, and measurement noise is introduced to obtain the gyro angular velocity of the lower hemispherical resonant gyroscope at a certain moment. S12. Without external inertial angular velocity input, set the precession excitation signal to put the gyroscope into working state, and record the complete precession excitation signal and collect the complete angular velocity measurement signal output by the gyroscope. The angular velocity measurement signal output by the gyroscope from time k to time k+t is extracted to obtain the first angular velocity measurement signal with a duration of t; The precession excitation signal from time k to time k+t is extracted to obtain the first precession excitation signal with a duration of t.

3. The method for joint compensation of delay and damping asymmetry error of a full-angle hemispherical gyroscope according to claim 2, characterized in that, The specific method for step S2 is as follows: S21. Using the maximum likelihood weighted cross-correlation delay estimation method, calculate the weighted cross-correlation function between the first angular velocity measurement signal and the first self-precession excitation signal; S22. Calculate the estimated delay: Perform an inverse fast Fourier transform on the weighted cross-correlation function of the first angular velocity measurement signal and the first self-precession excitation signal, and then find the position of the maximum value of the inverse transform. The time corresponding to this position on the horizontal axis is the estimated delay. .

4. The method for joint compensation of delay and damping asymmetry error of a full-angle hemispherical gyroscope according to claim 3, characterized in that, The specific method for step S3 is as follows: S31. Utilizing the estimated delay , cut Time to The precession excitation signal at time t is used to obtain the second precession excitation signal with a duration of t; S32. Using the first angular velocity measurement signal and the second self-precession excitation signal, the estimated damping asymmetry error is solved by the least squares method.

5. The method for joint compensation of delay and damping asymmetry error of a full-angle hemispherical gyroscope according to claim 4, characterized in that, The specific method for step S32 is as follows: S321. Initialize the estimated parameter vector; S322. For each time k, in the estimated delay Above, construct the regression vector; S323. Based on the gyroscope angular velocity, the estimated parameter vector, and the regression vector, calculate the error between the actual measured value and the predicted value of the gyroscope angular velocity at time k. S324. Based on the regression vector, covariance matrix, and the error between the actual measured value and the predicted value of the gyroscope angular velocity at time k, the estimated parameter vector is re-estimated to obtain the updated estimated parameter vector at time k. S325, Update the covariance matrix.

6. The method for joint compensation of delay and damping asymmetry error of a full-angle hemispherical gyroscope according to claim 4, characterized in that, The specific method for step S4 is as follows: S41. Using the estimated damping asymmetry error, obtain the compensated gyro angular velocity at a certain moment; S42. Using the compensated gyroscope angular velocity at a certain moment, update the angular velocity of the first angular velocity measurement signal at each moment to obtain the second angular velocity measurement signal. S43. Using the maximum likelihood weighted cross-correlation delay estimation method, calculate the weighted cross-correlation function between the second angular velocity measurement signal and the second self-precession excitation signal; S44. Recalculate the estimated delay: Perform an inverse fast Fourier transform on the weighted cross-correlation function of the second angular velocity measurement signal and the second self-precession excitation signal, and then find the position of the maximum value of the inverse transform. The time corresponding to this position on the horizontal axis is the updated estimated delay. ; S45. Determine the delay of the update estimate. Convergence: Set a delay convergence threshold to determine the delay for updating the estimated delay. Compared with the previous estimated delay Is the difference less than the delay convergence threshold? If not, return to step S3 and use the updated estimated delay. Re-estimate the damping asymmetry error; if so, update the estimated delay. The damping asymmetry error is the final estimated result.

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