Double-gyroscope self-calibration method suitable for rate integration hemispherical resonator gyroscope

Abstract

The invention belongs to the technical field of inertial navigation, and particularly relates to a double-gyroscope self-calibration method suitable for a rate integration hemispherical resonator gyroscope. According to the invention, two coaxial rate integration HRGs are used, and a damping mismatch error of the two rate integration HRGs is estimated in real time by using a Kalman filtering method and is compensated, so that double-gyroscope self-calibration of the rate integration HRGs is realized; due to the fact that the estimated value of the damping mismatch error is deducted, the precision of the final output # imgabs0 # is higher than the original precision of the two HRGs. The two HRGs are used, real-time calibration and compensation of the HRG damping mismatch error are achieved on the premise that the size is not excessively increased, the influence of the damping mismatch error on the HRG precision is greatly reduced, and compared with a traditional damping mismatch error compensation method which can only conduct calibration under the static condition, the method has the advantage that the calibration accuracy is greatly improved. According to the method, the HRG damping mismatch error parameter can be accurately calibrated under the dynamic condition, 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 belongs to the technical field of inertial navigation, and particularly relates to a dual-gyro self-calibration method applicable to a rate-integrating hemispherical resonant gyroscope (HRG), 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 service life, and high reliability, and has the ability to achieve measurement accuracy comparable to or even higher than that of existing optical gyroscopes in a smaller volume. It is considered to be the next-generation gyroscope with the best comprehensive performance.

[0003] Currently, HRG mainly has two application modes: the force balance mode and the rate integration mode. The former has higher 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 vibration mode of the resonator to precess freely within the full angle range, which also makes the damping mismatch caused by the circumferential non-uniformity of the resonator an error factor that must be considered.

[0004] In existing research, there has not been a relatively perfect solution publicly available for the damping mismatch error of HRG. 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 physical parameters of the gyro caused by environmental changes. Therefore, 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] Based on the above analysis, if the physical parameters related to damping mismatch in HRG can be estimated in real time, the influence of environmental changes on the output of 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 reduce the influence of environmental factor changes such as temperature on the compensation effect of the rate-integrating HRG damping mismatch error, the present invention proposes a dual-gyro self-calibration method applicable to the rate-integrating HRG. By using the outputs of two coaxial rate-integrating HRGs, the physical parameters inside the two rate-integrating HRGs are estimated in real time, and the real-time compensation of the HRG damping mismatch error is realized. This method can effectively improve the measurement accuracy of the rate-integrating HRG.

[0007] The technical solution adopted by the present invention is as follows: a dual-gyro self-calibration method applicable to a rate-integrating hemispherical resonator gyro, which is divided into the following steps:

[0008] S1 Install two rate-integrating HRGs of the same model on the base so that the sensitive axes of the two rate-integrating HRGs are parallel to each other, and connect the two HRGs to the control circuit to output the following data to the calculation module. Name the two rate-integrating HRGs as HRG_A and HRG_B respectively:

[0009] The azimuth angle of the resonator mode at time k in HRG_A

[0010] The azimuth angle of the resonator mode at time k in HRG_B

[0011] 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 at time 0 and the x-axis electrode in the rate-integrating HRG) θ0 = π / 2, and the standing wave rotates forward 2 turns from time 0 to time i, then θ i = π / 2 + 2×2π = 4.5π, and the standing wave rotates backward 1 turn from time i to time j, then θ j = π / 2 + 2×2π - 1×2π = 3.5π;

[0012] In the above description, the subscript k represents the value of the corresponding variable at time k; the superscripts A and B respectively represent that the corresponding variable is a parameter of HRG_A or HRG_B, and the same applies hereinafter.

[0013] S2 Control both rate-integrating HRGs to perform virtual rotation at a constant rate Ω0.

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

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

[0016]

[0017] Wherein, 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; denotes the derivative with respect to θ; θ τ is the azimuth angle of the damping axis. It can be seen from Equation (1) that since θ is the known gyroscope output, if Δ(1 / τ) and θ τ can be estimated in real time, 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 the environmental changes causing Δ(1 / τ) and θ τ to change, resulting in inaccurate compensation.

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

[0019]

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

[0021]

[0022] It can be seen from Equation (2) that since two coaxial HRGs both sense the same external angular rate Ω and perform a virtual rotation at a constant rate Ω0, the terms of Ω and Ω0 can be eliminated by taking the difference. At this time, only a and b in the equation are unknowns, and the intermediate variables a and b can be estimated in real time using the Kalman filter, achieving the same effect as estimating Δ(1 / τ) and θ τ in real time.

[0023] From the above analysis, for HRG_A and HRG_B, respectively:

[0024]

[0025] Taking the difference between Equation (4) and Equation (5) gives:

[0026]

[0027] Since the intermediate variables a and b change slowly with time, the time-varying process of a and b can be described using a first-order Markov process; from the above analysis, the continuous-time Kalman filter error equation can be obtained:

[0028]

[0029] Wherein, is the intermediate variable, representing and The difference; δa A and δb A respectively represent the A rates of change of a A and b; δa B and δb B respectively represent the B rates of change of a B and b; Furthermore, the continuous-time Kalman filter error equation in component form can be obtained:

[0030]

[0031] S4 Establish a Kalman filter

[0032] S4.1 Define the state vector X of the Kalman filter system at time k k as follows:

[0033]

[0034] All variables in Equation (9) are the values of the corresponding variables in S3 at time k.

[0035] S4.2 The one-step prediction calculation formula for the Kalman filter state is as follows:

[0036]

[0037] where represents the estimated value of the state quantity X at time k - 1, and its initial value is set to k-1 0 at k = 0 0 1×9 represents a 1×9 zero matrix; 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:

[0038]

[0039] In Equation (11), I is the identity matrix, T is the sampling interval, and F k-1 is the value of the continuous-time state transition matrix F of the Kalman filter at time k - 1. It can be seen from Equation (8) that:

[0040]

[0041] S4.3 The one-step predicted mean square error matrix P of the state from time k - 1 to time k k / k-1 is calculated as follows:

[0042]

[0043] The P in Equation (13) 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 gyroscope (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 gyroscope and engineering experience.

[0044] S4.4 Filter gain K at time k k The calculation formula is as follows:

[0045] K k = P k / k-1 H T (HP k / k-1 H T + R) -1 (14)

[0046] In Equation (14), H is the measurement matrix:

[0047] H = [1 0 0 0 0 0 0 0 0] (15)

[0048] In Equation (14), R is the observation noise covariance matrix, and the specific value is obtained from the actual performance of the gyroscope and engineering experience. S4.5 Estimated value of the state quantity at time k The calculation formula is as follows:

[0049]

[0050] In Equation (16), Z k is the observed quantity at time k:

[0051]

[0052] S4.6 State estimation mean square error matrix P at time k k The calculation formula is as follows:

[0053]

[0054] S5 Perform HRG damping mismatch error parameter estimation and compensation:

[0055] S5.1 Initialize the timer and set k = 0;

[0056] 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 as the estimated value of Take the third element in as the estimated value of Take the fourth element in as the estimated value of Take the fifth element in as the estimated value of

[0057] S5.3 If k ≥ 1, perform compensation for the HRG damping mismatch error:

[0058] S5.3.1 Calculate the angular increments of HRG_A and HRG_B from time k - 1 to time k before compensation and

[0059]

[0060]

[0061] S5.3.2 Calculate the angular increments of HRG_A and HRG_B from time k - 1 to time k after compensation and

[0062]

[0063] S5.4 Take and the mean value of as the output of the dual - gyro system at time k

[0064]

[0065] S5.5 Let k = k + 1;

[0066] S5.6 Loop through S5.2 - S5.5 until the current measurement ends, then exit the loop.

[0067] The present invention uses two coaxial rate - integrating HRGs, and uses the Kalman filtering method to estimate and compensate the damping mismatch error of the two rate - integrating HRGs in real time, realizing the dual - gyro self - calibration of the rate - integrating HRG. Since the estimated value of the damping mismatch error is deducted, the final output has a higher accuracy than the original accuracy of the two HRGs.

[0068] The present invention has the following technical effects:

[0069] 1. The present invention uses two HRGs to achieve real-time calibration and compensation of the damping mismatch error of the HRG without excessive increase in volume, significantly reducing the impact of the damping mismatch error on the accuracy of the HRG.

[0070] 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 HRG damping mismatch error parameters under dynamic conditions.

[0071] 3. Compared with the traditional HRG damping mismatch error compensation method, the present invention can significantly reduce the impact of environmental changes on the compensation effect and improve the environmental adaptability of the HRG. BRIEF DESCRIPTION OF THE DRAWINGS

[0072] Figure 1 : Flow chart of the self-calibration method proposed by the present invention

[0073] Figure 2 : Graph of the applied external angular rate varying with time

[0074] Figure 3 : Estimated value of the intermediate parameter a A

[0075] Figure 4 : Estimated value of the intermediate parameter a B

[0076] Figure 5 : Estimated value of the intermediate parameter b A

[0077] Figure 6 : Estimated value of the intermediate parameter b B

[0078] Figure 7 : Angular rate error of the HRG before and after compensation DETAILED DESCRIPTION OF THE INVENTION

[0079] The content not described in detail in this specification belongs to the prior art well-known to those skilled in the art.

[0080] To make the technical method and advantages of this application clearer, the present invention will be further described below with reference to the accompanying drawings. The specific embodiments described herein are only used to explain this application and are not used to limit this application.

[0081] The flow chart of the dual-axis self-calibration method for the rate integrating hemispherical resonator gyro proposed by the present invention is as Figure 1 shown.

[0082] To prove the feasibility of the present invention, a simulation experiment was conducted. During the experiment, the two HRGs were shaken together, and the applied angular rate varied with time as Figure 2As shown. It is set that the zero-bias instabilities of both HRGs are 0.1° / h, and the random walks are both The virtual rotation angular rates of the two HRGs are both Ω0 = 12° / s; meanwhile, it is assumed that due to environmental changes and other reasons, the azimuth angle θ of the damping axis of the HRG τ changes slowly with time.

[0083] 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 (24), where diag represents a diagonal matrix:

[0084]

[0085] The system noise covariance matrix is set as shown in Equation (25):

[0086] Q = diag[0 0 0 0 0 (5×10 -4 ° / h) 2 (5×10 -4 ° / h) 2 (5×10 -4 ° / h) 2 (5×10 -4 ° / h) 2 (25)

[0087] The observation noise covariance matrix is set as shown in Equation (26):

[0088] R = diag[(5×10 -4 °) 2 (26)

[0089] The error calibration is carried out using the method proposed in the present invention. During the calibration process, the estimated values of the intermediate parameters a A and a B are as Figure 3 and Figure 4 shown; the estimated values of b A and b B are as Figure 5 and Figure 6 shown; it can be seen that although the true values of a and b in the two HRGs change slowly with time, the estimated values basically fluctuate around the true values, indicating 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 7 shown, and 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 dual gyro self-calibration method suitable for a rate-integrating hemispherical resonant gyro, characterized in that: The method is divided into the following steps: S1 installs two rate-integrating HRGs of the same model on the base so that the sensitive axes of the two rate-integrating HRGs are parallel to each other, and connects the two HRGs to the control circuit so that it outputs the following data to the calculation module. The two rate-integrating HRGs are named HRG_A and HRG_B respectively: The azimuth of the vibration mode of the resonator in HRG_A at time k The azimuth of the vibration mode of the resonator in HRG_B at time k The subscript k indicates the value of the corresponding variable at time k; the superscripts A and B indicate that the corresponding variable is a parameter of HRG_A or HRG_B, respectively; S2 controls both rate-integrated HRGs to perform virtual rotation at a constant rate Ω0; S3 establishes the continuous-time Kalman filter error equation: In the rate-integrated 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; 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 HRG_A and HRG_B, respectively: Subtracting equation (4) from equation (5) yields: Continuous-time Kalman filter error equation: in, is an intermediate variable, indicating and The difference between A and δb A Respectively represent a A and b A The rate of change of B and δb B Respectively represent a B and b B The rate of change; the continuous time Kalman filter error equation can be further quantified: S4 establishes the Kalman filter: S4.1 Define the state vector X of the Kalman filter system at time k k as follows: Each variable in formula (9) is the value of the corresponding variable in S3 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 (11), 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 (8), we can know that: 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 (13), 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 (14) In formula (14), H is the measurement matrix: H＝[1 0 0 0 0 0 0 0 0] (15) In formula (14), 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 (16), Z k is the observed value at time k: S4.6 The mean square error matrix P of the state estimation at time k k The calculation formula is as follows: 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 Estimated value of Pick The third element in Estimated value of Pick The fourth element in Estimated value of Pick The fifth element in Estimated value of S5.3 If k ≥ 1, compensate for HRG damping mismatch error: S5.3.1 Calculate the angular increment of HRG_A and HRG_B from time k-1 to time k before compensation and S5.3.2 Calculate the angular increment of HRG_A and HRG_B from time k-1 to time k after compensation and S5.4 Take and The mean value of is taken as the output of the dual gyro system at time k S5.5 Let k=k+1; S5.6 executes S5.2-S5.5 in a loop until the current measurement is completed and then exits the loop.

2. The dual gyro self-calibration method for a rate-integrating hemispherical resonant gyro 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 1×9 Represents a 1×9 dimensional zero matrix.

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

4. The dual gyro self-calibration method for a rate-integrating hemispherical resonant gyro 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 dual gyro self-calibration method for a rate-integrating hemispherical resonant gyro 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.

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