Rate integration hemispherical resonator gyroscope self-calibration method assisted by low-precision gyroscope

Abstract

The invention belongs to the technical field of inertial navigation, and particularly relates to a self-calibration method of a rate integration hemispherical resonator gyroscope assisted by a low-precision gyroscope, which is suitable for various application occasions of rate integration HRG. The low-precision gyroscope coaxial with the rate integral HRG is used for assisting, the damping mismatch error of the rate integral HRG is estimated in real time by using a Kalman filtering method and is compensated, and the self-calibration of the rate integral HRG is realized. The precision of the finally output (omega 'HRG) k is higher than the original precision of the rate integration HRG and is also higher than the measurement precision of the auxiliary gyroscope; according to the method, the low-precision gyroscope is used for assistance, real-time calibration and compensation of the damping mismatch error parameters of the HRG are achieved on the premise that the size and cost are not excessively increased, the influence of the damping mismatch errors on the HRG precision is greatly reduced, the damping mismatch error parameters of the HRG can be accurately calibrated under the dynamic condition, and the accuracy of the HRG is improved. The influence of environmental change on the compensation effect can be greatly reduced, and the environmental adaptability of the HRG is improved.

Description

Technical Field

[0001] The present invention relates to the field of inertial navigation technology, and particularly to a self-calibration method for a rate integrating hemispherical resonant gyroscope (HRG) assisted by a low-precision gyroscope, which is applicable to various application scenarios of rate integrating HRG. Background Art

[0002] In recent years, HRG has been rapidly developed in various application fields. Its working principle is based on the energy transfer caused by the Coriolis effect between two vibration modes of a hemispherical resonator. As a new type of inertial device, HRG has characteristics such as a large measurement range, long life, and high reliability, and has the ability to achieve a measurement accuracy comparable to or even higher than that of existing optical gyroscopes in a smaller volume, and is considered to be the next-generation gyroscope with the best comprehensive performance.

[0003] Currently, there are mainly two application modes for HRG: the force balance mode and the rate integration mode. The former has a high measurement accuracy, but its small measurement range and bandwidth limit its application in the navigation field; while the latter, the rate integration mode, has an infinite measurement range in theory and an extremely stable scale factor, so it is suitable for application in inertial navigation scenarios. However, in the actual application process, the working mode of rate integration requires the free precession of the resonator vibration mode within the full angle range, which also makes the damping mismatch caused by the circumferential non-uniformity of the resonator become an error factor that must be considered.

[0004] In existing research, there has not been a relatively perfect solution publicly available for the HRG damping mismatch error. The current mainstream error suppression method is: obtaining the error parameters of HRG damping mismatch through parameter identification before the gyro starts running, and applying a control force using electrodes during the running process to offset the gyro output bias caused by the damping mismatch. However, this method does not consider the change in the gyro physical parameters caused by environmental changes. Therefore, the HRG using this method for error suppression is extremely sensitive to environmental changes such as temperature and is difficult to be actually applied under the condition of no temperature control.

[0005] According to the above analysis, if the physical parameters related to the damping mismatch in HRG can be estimated in real time, the influence of environmental changes on the output of the rate integrating HRG can be reduced while suppressing the damping mismatch error, and the output accuracy of HRG can be greatly improved. Summary of the Invention

[0006] In order to suppress the damping mismatch error and reduce the influence of environmental factors such as temperature changes on the rate integrating HRG, the present invention proposes a self-calibration method for a rate integrating HRG assisted by a low-precision gyroscope. Another low-precision auxiliary gyroscope coaxial with the rate integrating HRG (note that this gyroscope itself does not have damping mismatch error, and the available gyroscopes include but are not limited to ring laser gyroscopes, fiber optic gyroscopes, or microelectromechanical gyroscopes, etc.) is used to provide an external angular velocity reference, and the physical parameters inside the rate integrating HRG are estimated in real time to achieve real-time compensation for the damping mismatch error of the rate integrating HRG, effectively improving the measurement accuracy of the rate integrating HRG.

[0007] The technical solution adopted by the present invention is as follows: A self-calibration method for a rate integrating hemispherical resonator gyroscope assisted by a low-precision gyroscope, which is divided into the following steps:

[0008] S1 Install the rate integrating HRG (hereinafter referred to as HRG) and the auxiliary gyroscope on the base so that the sensitive axes of the two gyroscopes are parallel to each other. At the same time, connect them to the control circuit so that they output the following data to the calculation module:

[0009] The output data of the HRG includes: the azimuth angle θ of the resonator mode at time k k ;

[0010] It should be noted that the azimuth angle θ of the resonator mode at time k k represents the cumulative rotation angle of the resonator since the rate integrating HRG is powered on, that is, θ k = θ0 + 2π × the number of turns the standing wave has rotated: For example, the standing wave angle at time 0 (i.e., the angle between the resonator mode and the x-axis electrode in the rate integrating HRG at time 0) θ0 = π / 2. If the standing wave rotates forward 2 turns from time 0 to time i, then θ i = π / 2 + 2 × 2π = 4.5π. If the standing wave rotates backward 1 turn from time i to time j, then θ j = π / 2 + 2 × 2π - 1 × 2π = 3.5π;

[0011] The output data of the auxiliary gyroscope includes: the external angular velocity reference at time k It should be noted that since the auxiliary gyroscope used here has low precision, there must be a certain gap from the true external angular velocity.

[0012] In the above description, the subscript k represents the value of the corresponding variable at time k, and the same applies hereinafter.

[0013] S2 Control the HRG to perform a virtual rotation at a constant rate Ω0.

[0014] S3: Establish a continuous-time Kalman filter error equation:

[0015] In the HRG, if only the error caused by damping mismatch is considered and random noise is ignored, the azimuth angle θ of the resonator mode can be described by the following differential equation:

[0016]

[0017] where G is the angular gain in the rate integration mode; Ω is the angular rate applied to the gyroscope from the outside; Δ(1 / τ) = 1 / τ1 - 1 / τ2 is the anisotropic damping coefficient, where τ1 and τ2 are the decay times of the main mode and the secondary mode of the resonator respectively; θ is the azimuth angle of the resonator mode, represents the derivative of θ with respect to time; θ τ is the azimuth angle of the damping axis. From Equation (1), it can be seen that since θ is the known output of the gyroscope, if Δ(1 / τ) and θ τ can be estimated in real time, then the value of the second term in the equation (i.e., the error caused by damping mismatch) can be calculated and compensated, and there is no need to worry about changes in the environment causing Δ(1 / τ) and θ τ to change, resulting in inaccurate compensation.

[0018] By performing an identical transformation on Equation (1), Equation (2) can be obtained:

[0019]

[0020] where the intermediate variables a and b are expressed as follows:

[0021]

[0022] From Equation (2), it can be seen that if another coaxial auxiliary gyroscope is used to provide a reference for the angular rate Ω applied to the gyroscope from the outside, then only a and b in the equation are unknowns. At this time, the Kalman filter can be used to estimate the intermediate variables a and b in real time, achieving the same effect as estimating Δ(1 / τ) and θ τ in real time.

[0023] For the auxiliary gyroscope, since there is no damping mismatch error, considering the output of the external angular velocity reference Ω ref as the sum of the true angular rate Ω and a constant zero bias B ref and ignoring random noise, we have:

[0024] Ω ref = Ω - B ref (4)

[0025] From Equation (2) and Equation (4), we can obtain:

[0026]

[0027] On the other hand, since the intermediate variables a and b change slowly over time, a first-order Markov process can be used to describe the time-varying processes of a and b; since B ref basically does not change, it is considered that B ref the derivative with respect to time is 0. From the above analysis, the continuous-time Kalman filter error equation can be obtained:

[0028]

[0029] a′ represents the rate of change of the intermediate variable a, and b′ represents the rate of change of the intermediate variable b;

[0030] Furthermore, the continuous-time Kalman filter error equation in component form can be obtained:

[0031]

[0032] S4 Establish a Kalman filter

[0033] S4.1 Define the Kalman filter system state vector X k at time k as follows:

[0034] X k =[θ k a k b k a′ k b k ′B k ref T (8)

[0035] where a k and b k respectively represent the values of the intermediate variables a and b at time k; a′ k and b k ′ respectively represent the values of the rates of change of a and b at time k; represents the value of the constant zero bias of the auxiliary gyro at time k.

[0036] S4.2 The Kalman filter state one-step prediction calculation formula is as follows:

[0037]

[0038] where represents the estimated value of the state quantity X k-1 at time k - 1, and its initial value is set to 0 1×6 when k = 0; represents the one-step predicted value of the state quantity from time k - 1 to time k; Φ k / k-1 ​is the one-step state transition matrix from time k-1 to time k:

[0039]

[0040] In Equation (10), I is the identity matrix, T is the sampling interval, and F k-1 is the value of the Kalman filter continuous-time state transition matrix F at time k-1. As can be seen from Equation (7):

[0041]

[0042] In Equation (9), U k represents the control matrix at time k, as shown in Equation (12):

[0043]

[0044] where u k represents the value of the continuous-time control matrix u at time k. As can be seen from Equation (7):

[0045]

[0046] S4.3 One-step prediction mean square error matrix P of the state from time k-1 to time k k / k-1 The calculation formula is as follows:

[0047]

[0048] In Equation (14), P k-1 represents the one-step prediction mean square error matrix of the state at time k-1. When k = 0, its initial value is set to P 0-1 , P 0-1 The specific value is obtained from the actual performance of the gyro (such as bias instability and random walk, etc.) and engineering experience; Q is the system noise covariance matrix, and the specific value is also obtained from the actual performance of the gyro and engineering experience.

[0049] S4.4 Filter gain K at time k k The calculation formula is as follows:

[0050] K k = P k / k-1 H T (HP k / k-1 H T + R) -1 (15)

[0051] In Equation (15), H is the measurement matrix:

[0052] H = [1 0 0 0 00] (16)

[0053] In Equation (15), R is the observation noise covariance matrix, and its specific value is obtained from the actual performance of the gyroscope and engineering experience.

[0054] S4.5 Estimated value of the state quantity at time k The calculation formula is as follows:

[0055]

[0056] In Equation (17), Z k is the observed quantity at time k:

[0057] Z k = θ k (18)

[0058] S4.6 Mean square error matrix P of the state estimate at time k k The calculation formula is as follows:

[0059]

[0060] S5 Perform HRG damping mismatch error parameter estimation and compensation:

[0061] S5.1 Initialize the timer and set k = 0;

[0062] S5.2 Sequentially execute S4.2 - S4.6 to perform a round of Kalman filter parameter estimation and obtain the estimated value of the state vector X k at time k Take the second element in it as the estimated value of a k at time k Take the third element in it as the estimated value of b k at time k

[0063]

[0064] S5.3 If k ≥ 1, perform compensation for the HRG damping mismatch error:

[0065] S5.3.1 Calculate the angular increment (ω HRG ) k of the HRG from time k - 1 to time k before compensation:

[0066]

[0067] S5.3.2 Calculate the angular increment (ω′ HRG ) k of the HRG from time k - 1 to time k after compensation:

[0068]

[0069] Use (ω′ HRG ) k as the angular increment output of the HRG at time k.

[0070] S5.4 Let k = k + 1;

[0071] S5.5 Loop through S5.2 - S5.4 until the end of this measurement, then exit the loop.

[0072] The present invention uses a low-precision gyro coaxial with the rate-integrating HRG for assistance, and uses the Kalman filtering method to estimate and compensate the damping mismatch error of the rate-integrating HRG in real time, achieving self-calibration of the rate-integrating HRG. The final output (ω′ HRG ) k has a higher precision than the original precision of the rate-integrating HRG and also higher than the measurement precision of the assisting gyro.

[0073] The present invention has the following technical effects:

[0074] 1. By using a low-precision gyro for assistance, the present invention realizes the real-time calibration and compensation of the damping mismatch error parameter of the HRG without excessive increase in volume and cost, and greatly reduces the influence of the damping mismatch error on the precision of the HRG.

[0075] 2. Compared with the traditional damping mismatch error compensation method that can only be calibrated under static conditions, the present invention can accurately calibrate the damping mismatch error parameter of the HRG under dynamic conditions.

[0076] 3. Compared with the traditional HRG damping mismatch error compensation method, the present invention can greatly reduce the influence of environmental changes on the compensation effect and improve the environmental adaptability of the HRG. BRIEF DESCRIPTION OF THE DRAWINGS

[0077] Figure 1 : Flow chart of the self-calibration method proposed by the present invention

[0078] Figure 2 : Diagram of the applied external angular rate varying with time

[0079] Figure 3 : Estimated value of the intermediate parameter a

[0080] Figure 4 : Estimated value of the intermediate parameter b

[0081] Figure 5 : Angular rate error of the HRG before and after compensation DETAILED DESCRIPTION OF THE INVENTION

[0082] Contents not detailedly described in this specification belong to the prior art well-known to those skilled in the art.

[0083] To make the technical methods and advantages of this application clearer, the present invention will be further described below in conjunction with the accompanying drawings. The specific embodiments described herein are only used to explain this application and are not used to limit this application.

[0084] The implementation process of the dual-axis self-calibration method for a rate-integrating hemispherical resonator gyroscope proposed by the present invention is as Figure 1 shown.

[0085] To prove the feasibility of the present invention, a simulation experiment was conducted. During the experiment, the HRG and RLG were shaken together, and the applied angular rate changed with time as Figure 2 shown. The performance parameters of the set HRG and RLG are shown in Table 1; the virtual rotation angular rate of the HRG, Ω0 = 3° / s; at the same time, it is assumed that due to reasons such as environmental changes, the azimuth angle θ τ of the damping axis of the HRG changes slowly with time.

[0086] Table 1 Performance parameters of HRG and RLG

[0087]

[0088] The filtering period of the Kalman filter is set to 200 Hz. The initial value of the state estimation mean square error matrix is set as shown in Equation (22), where diag represents a diagonal matrix:

[0089] P 0-1 = diag[(1°) 2 (0.1° / h) 2 (0.1° / h) 2 (0.001° / h 2 ) 2 (0.001°h 2 ) 2 (1° / h) 2 (22)

[0090] Set the system noise covariance matrix as shown in Equation (23):

[0091] Q = diag[(1×10 -10 °) 2 0 0 (5×10 -6 ° / h) 2 (5×10 -6 ° / h) 2 0] (23)

[0092] Set the observation noise covariance matrix as shown in Equation (24):

[0093] R = diag[(2×10 -6 °) 2(24)

[0094] The error calibration is carried out using the method proposed by the present invention. During the calibration process, the estimated values of the intermediate parameters a and b are as Figure 3 and Figure 4 shown. It can be seen that although the true values of a and b change slowly with time, the estimated values basically fluctuate around the true values. It can be known that this method has the ability of real-time calibration and compensation; the angular rate errors of the HRG before and after compensation are as Figure 4 shown. It can be observed that this method has an obvious inhibitory effect on the damping mismatch error and can effectively improve the measurement accuracy of the HRG.

Claims

1. A low-precision gyro-assisted rate-integrating hemispherical resonant gyro self-calibration method, characterized in that: The method is divided into the following steps: S1 installs the rate-integrating HRG and the auxiliary gyro on the base so that the sensitive axes of the two gyro are parallel to each other. At the same time, they are connected to the control circuit so that it outputs the following data to the calculation module: The output data of HRG includes: the azimuth angle θ of the resonator vibration mode at time k k , represents the angle between the vibration mode of the resonator and the x-axis electrode in the HRG at time k; The output data of the auxiliary gyroscope include: external angular velocity reference at time k The subscript k indicates the value of the corresponding variable at time k; S2 controls HRG to perform virtual rotation at a constant rate Ω0; S3: Establish the continuous-time Kalman filter error equation: In HRG, only the error caused by damping mismatch is considered, and random noise is ignored. The azimuth angle θ of the resonator vibration mode can be described by the following differential equation: Where G is the angular gain in rate integration mode; Ω is the angular rate applied to the gyroscope by the outside world; Δ(1 / τ)=1 / τ1-1 / τ2 is the anisotropic damping coefficient, where τ1 and τ2 are the decay times of the main mode and the secondary mode of the resonator, respectively; θ is the azimuth angle of the resonator vibration mode, represents the derivative of θ; θ τ is the azimuth of the damping axis; By transforming equation (1) into an identity, we can get equation (2): Among them, the intermediate variables a and b are expressed as follows: For the auxiliary gyro, consider the external angular velocity reference Ω output by it ref is the true angular rate Ω and the constant zero bias B ref and ignoring random noise, we have: Oh ref =Ω-B ref (4) From formula (2) and formula (4), we can get: Continuous-time Kalman filter error equation: a′ represents the rate of change of the intermediate variable a, and b′ represents the rate of change of the intermediate variable b; The continuous-time Kalman filter error equation can be further expressed in quantitative form: S4 establishes Kalman filter S4.1 Define the state vector X of the Kalman filter system at time k k as follows: X k =[θ k a k b k a′ k b′ k B k ref ] T (8) Among them, a k and b k Respectively represent the values ​​of intermediate variables a and b at time k; a′ k and b′ k They represent the values ​​of the rates of change of a and b at time k respectively; represents the value of the constant zero bias of the auxiliary gyro at time k; S4.2 Kalman filter state one-step prediction calculation formula is as follows: in Represents the state quantity X at time k-1 k-1 An estimated value of represents the one-step prediction value of the state quantity from time k-1 to time k; Φ k / k-1 is the state one-step transfer matrix from time k-1 to time k: In formula (10), I is the unit matrix, T is the sampling interval, and F k-1 is the value of the Kalman filter continuous-time state transfer matrix F at time k-1; from formula (7), we can know that: In formula (9), U k represents the control matrix at time k, as shown in formula (12): where u k represents the value of the continuous-time control matrix u at time k. From equation (7), we can know that: u=[G(Ω ref +Ω0) 0 0 0 0 0] T (13) S4.3 One-step prediction mean square error matrix P from time k-1 to time k k / k-1 The calculation formula is as follows: In formula (14), P k-1 represents the one-step prediction mean square error matrix of the state at time k-1; Q is the system noise covariance matrix; S4.4 Filter gain K at time k k The calculation formula is as follows: K k =P k / k-1 H T (HP k / k-1 H T +R) -1 (15) In formula (15), H is the measurement matrix: H＝[1 0 0 0 0 0] (16) In formula (15), R is the observation noise covariance matrix; S4.5 Estimated value of state quantity at time k The calculation formula is as follows: In formula (17), Z k is the observed value at time k: WITH k =θ k (18) S4.6 The mean square error matrix P of the state estimation at time k k The calculation formula is as follows: P k =(I-K k H)P k / k-1 (I-K k H) T +K k RK k T ; (19) S5 performs HRG damping mismatch error parameter estimation and compensation: S5.1 Initialize the timer, set k = 0; S5.2 executes S4.2-S4.6 in sequence, performs a round of Kalman filter parameter estimation, and obtains the state vector X at time k k Estimated value of Pick The second element in is a k Estimated value of Pick The third element in b k Estimated value of S5.3 If k ≥ 1, compensate for HRG damping mismatch error: S5.3.1 Calculate the angular increment (ω) of HRG from time k-1 to time k before compensation HRG ) k : S5.3.2 Calculate the angular increment (ω′) of the HRG from time k-1 to time k after compensation. HRG ) k : Use (ω′ HRG ) k As the angular increment output of HRG at time k; S5.4 Let k = k + 1; S5.5 executes S5.2-S5.4 in a loop until the current measurement is completed and then exits the loop.

2. The low-precision gyro-assisted rate-integrating hemispherical resonant gyro self-calibration method according to claim 1, characterized in that: Set the state quantity X at time k-1 k-1 Estimated value of The initial value when k = 0 is 0 1×6 Represents a 1×6 dimensional zero matrix.

3. The low-precision gyro-assisted rate-integrating hemispherical resonant gyro self-calibration method according to claim 1, characterized in that: Set the state one-step prediction mean square error matrix P at time k-1 k-1 When k = 0, the initial value is P 0-1 , P 0-1 The specific value is obtained from the actual performance of the gyroscope and engineering experience.

4. The low-precision gyro-assisted rate-integrating hemispherical resonant gyro self-calibration method according to claim 1, characterized in that: The specific value of the system noise covariance matrix Q is obtained from the actual performance of the gyroscope and engineering experience.

5. The low-precision gyro-assisted rate-integrating hemispherical resonant gyro self-calibration method according to claim 1, characterized in that: The specific value of the observation noise covariance matrix R is obtained from the actual performance of the gyroscope and engineering experience.

6. The low-precision gyro-assisted rate-integrating hemispherical resonant gyro self-calibration method according to any one of claims 1 to 5, characterized in that: The low-precision auxiliary gyroscope is a laser gyroscope, a fiber optic gyroscope or a micromechanical gyroscope, and the gyroscope itself does not have a damping mismatch error.

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