A low-high-frequency composite calibration method for a MEMS and MHD combined gyroscope

Abstract

The present invention discloses a low- and high-frequency composite calibration method for a MEMS and MHD combined gyroscope, comprising: synchronously collecting vibration response data of a combined gyroscope sensor, separating low- and high-frequency signals, calculating low-frequency static error parameters and high-frequency dynamic error parameters, constructing a static orthogonal matrix based on an installation angle error, generating a normalized error transfer coefficient using a cross-response ratio and a rejection ratio of high-frequency dynamic error parameters, generating a dynamic error matrix based on the normalized error transfer coefficient, establishing an expression of an error-containing output of the sensor using the dynamic error matrix, inverting the dynamic error matrix to obtain a dynamic error transfer matrix, jointly constructing a composite error compensation model by combining the static orthogonal matrix and the dynamic error transfer matrix, evaluating the error parameters after dynamic compensation, generating a residual feedback signal based on the error evaluation results, iteratively correcting the calibration error parameters until convergence, and outputting the calibration parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of inertial navigation and sensor calibration, and in particular to a low- and high-frequency composite calibration method for a MEMS and MHD combined gyroscope. Background Art

[0002] With the increasing application of inertial navigation technology in high-precision motion control, spacecraft attitude stabilization, and other fields, the performance limitations of traditional single-type gyroscopes are becoming increasingly prominent. Microelectromechanical system (MEMS) gyroscopes, due to their small size and low cost, offer good stability in low-frequency bands. However, their high-frequency noise and narrow dynamic response bandwidth limit their application in micro-vibration detection. While magnetohydrodynamic (MHD) angular velocity sensors can achieve high-sensitivity measurements over a wide bandwidth, they suffer from significant bias drift in the low-frequency band. Combining the two gyroscopes can complement each other's strengths, but effectively calibrating this combined gyroscope, particularly achieving high-precision calibration over a wide bandwidth, remains a pressing technical challenge.

[0003] Currently, calibration methods for inertial sensors primarily focus on a single sensor type, and there is no corresponding calibration method for calibrating a combined gyroscope under wide-band vibration conditions. Therefore, a calibration method that can combine low and high frequencies, tailored to the characteristics of a combined MEMS and MHD gyroscope, is urgently needed to improve the measurement accuracy and stability of the combined gyroscope under wide-band vibration conditions. Summary of the Invention

[0004] The present invention proposes a low- and high-frequency composite calibration method for a MEMS and MHD combined gyroscope to solve the above technical problems, specifically including:

[0005] Synchronously collect vibration response data from the MEMS and MHD combined gyroscope sensors, separate low- and high-frequency signals, and calculate low-frequency static error parameters and high-frequency dynamic error parameters. Low-frequency static error parameters include sensor zero bias, scale factor, and installation angle error. High-frequency dynamic error parameters include cross-response ratio, rejection ratio, data dispersion, and power spectral density.

[0006] A static orthogonal matrix is ​​constructed based on the installation angle error. The static orthogonal matrix is ​​used to reflect the non-ideal installation deviation between each two axes of the combined gyroscope in a low-frequency or static state, and the actual installation angle error is compensated by the static orthogonal matrix;

[0007] A normalized error transfer coefficient is generated using the cross-response ratio and rejection ratio of high-frequency dynamic error parameters. The normalized error transfer coefficient is used to characterize the degree of interference of the excitation axis on the non-excitation axis when the dynamic quantization combined gyroscope is affected by multi-axis excitation, providing a parameter for real-time compensation between cross axes.

[0008] generating a dynamic error matrix based on the normalized error transfer coefficients, the dynamic error matrix being used to reflect and quantify the degree of interference between cross-axes in a high-frequency or dynamic environment, establishing an expression of the sensor's error-containing output using the dynamic error matrix, inverting the dynamic error matrix to obtain a dynamic error transfer matrix, and using the dynamic error transfer matrix to suppress interference between cross-axes and compensate for errors between cross-axes in a high-frequency or dynamic environment;

[0009] The static orthogonal matrix and the dynamic error transfer matrix are combined to construct a composite error compensation model for suppressing the installation angle error, zero bias drift and cross-axis interference;

[0010] Based on the differences in frequency response characteristics of the combined MEMS and MHD gyroscope sensors, the low and high frequency signals after composite error compensation are fused using dynamic data integration and adaptive weighting. The proportion of low and high frequency signals in the fusion is automatically allocated through a time-varying weight function, and the fusion weight is adjusted in real time to optimize the complementarity of the combined gyroscope data in different frequency bands and dynamically adjust the contribution ratio of low and high frequency signals.

[0011] Furthermore, the method further comprises:

[0012] Vibration response data of the MEMS and MHD combined gyroscope sensor are synchronously collected by receiving an external excitation source signal, wherein the external excitation source includes static excitation, dynamic excitation, and combined static and dynamic excitation. The static excitation is to maintain the gyroscope attitude at a preset multi-axis static position and stimulate zero bias and installation error parameters;

[0013] The dynamic excitation is to apply multi-degree-of-freedom motion to the combined gyroscope according to the set frequency, amplitude and direction, and to apply swept frequency vibration in a preset frequency space, so as to calibrate the dynamic error parameters;

[0014] The dynamic and static integrated excitation uses a composite vibration including a low-frequency sinusoidal signal and high-frequency random noise as an excitation source to simulate the random vibration of the combined gyroscope in a complex environment.

[0015] Furthermore, the separation of low-frequency and high-frequency signals and calculation of low-frequency static error parameters and high-frequency dynamic error parameters include:

[0016] Use a low-pass filter to perform low-pass filtering on the vibration response data to extract the low-frequency MEMS signal;

[0017] The vibration response data is high-pass filtered using a high-pass filter to extract the high-frequency MHD signal;

[0018] The low-frequency static error parameters and high-frequency dynamic error parameters are calculated based on the low-frequency MEMS signal and the high-frequency MHD signal.

[0019] Furthermore, the method further comprises:

[0020] Fix the combined gyroscope on a precision turntable and tilt it around the positive / negative X / Y / Z axes in sequence at preset angles. The installation angle error is calculated by geometric projection:

[0021] ;

[0022] in express y The output voltage value of the MEMS and MHD combined gyroscope sensor at different tilt positions of the axis, express y The reference output voltage value of the MEMS and MHD combined gyroscope sensor when the axis is not tilted, is the lever arm length from the laser reflector to the rotation center of the MEMS and MHD combined gyroscope, is the angle change measured by the laser autocollimator;

[0023] Correspondingly, the static orthogonal matrix is:

[0024] ;

[0025] Among them, the main diagonal elements of the matrix are 1, which means that the scale factor of each axis has been normalized, and the non-main diagonal elements represent the installation angle error between the cross axes (for example: express x Axis and y The installation angle error between the two axes is the deviation between the actual angle between the two axes and the theoretical orthogonal angle;

[0026] Furthermore, the method further comprises:

[0027] Sensor zero bias calibration, obtain the static The sensor zero bias error is calculated by taking the average of the low-frequency MEMS signal output in the static state after filtering data in multiple positions in the positive and negative axis directions;

[0028] The scale factor is calibrated by performing a linear fit between the input physical quantity angular velocity and the sensor output data voltage signal using the least squares method to calculate the input-output slope. .

[0029] Furthermore, the method further comprises:

[0030] The cross-response ratio reflects the gain of the influence of the output of the non-excitation axis on the excitation axis, and is calculated as follows:

[0031] ;

[0032] in iFor the non-excited axis, j is the excitation axis, Indicates the excitation axis j When excitation is applied, the non-excited axis i The RMS response value of the test area, Indicates the non-excited axis before excitation i The RMS value of the noise floor;

[0033] The rejection ratio reflects the sensor's ability to suppress interference from the excitation axis to the non-excitation axis, and is calculated as follows:

[0034] ;

[0035] in i For the non-excited axis, j is the excitation axis, Indicates the excitation axis j When excitation is applied, the non-excited axis i The RMS response value of the test area, Indicates the excitation axis j The RMS response value of the test area;

[0036] Data dispersion is used to measure the signal fluctuation caused by vibration and to reflect the impact of vibration on the stability of the combined gyroscope output signal. The data dispersion is calculated as follows:

[0037] ;

[0038] in, m is the number of samples of a single movement, n is the number of repetitions of the same vibration, For the u Repeated v sampling points k Axis measurements, For all repetitions v sampling points k axis mean;

[0039] The power spectral density is used to characterize the distribution density of signal power in the frequency domain. The power spectral density of the signal is calculated by fast Fourier transform analysis. The target frequency band is selected and the power spectral density is integrated in the frequency band to obtain the dynamic noise power. The dynamic noise power is calculated using the following method:

[0040] ;

[0041] in, and Respectively represent the starting frequency and cutoff frequency of the target frequency band analysis, and the two together define the integration interval [ , ], used to determine the specific noise frequency band, is the signal power spectral density, if the dynamic noise power If the threshold is exceeded, the adaptive filter is triggered to suppress high-frequency interference.

[0042] Furthermore, the method further comprises:

[0043] The normalized error transfer coefficient is calculated as follows:

[0044] ;

[0045] in, j represents the excitation axis, i represents the non-excitation axis, and the above formula represents the excitation axis j For non-excited shaft i The normalized error transfer coefficient of ;

[0046] Correspondingly, the dynamic error matrix is:

[0047] ;

[0048] Among them, the non-main diagonal elements represent the normalized error transfer coefficients of the excitation axis to the non-excitation axis (for example: Indicates the excitation axis y Shaft to non-excited shaft x Normalized error transfer coefficient of the axis);

[0049] Using the dynamic error matrix, the output of the sensor is expressed as:

[0050] ;

[0051] in, Indicates the output of the sensor x axis, y Axis and z The measured value of the axis angular velocity, Indicates the output of the sensor x axis, y Axis and z The true value of the axis angular velocity;

[0052] By the dynamic error matrix Invert the matrix to get the dynamic error transfer matrix :

[0053] ;

[0054] Among them, the determinant .

[0055] Furthermore, the method further comprises:

[0056] The static orthogonal matrix and the dynamic error transfer matrix are combined to construct a composite error compensation model for suppressing the installation angle error, zero bias drift and cross-axis interference;

[0057] Correspondingly, the composite error compensation model is:

[0058] ;

[0059] Indicates the output of the sensor x axis, y Axis and z The compensation value of the axis angular velocity, Indicates the output of the sensor x axis, y Axis and z The measured value of the axis angular velocity;

[0060] The method may be further configured to adopt the following steps: adopting adaptive weight fusion to achieve full-band connection;

[0061] Based on the frequency response differences between MEMS and MHD combined gyroscope sensors, the low- and high-frequency signals after composite error compensation are dynamically integrated and adaptively weighted. The proportion of low- and high-frequency signals in the fusion is automatically allocated through a time-varying weight function. The fusion weight is adjusted in real time to optimize the complementarity of the combined gyroscope data in different frequency bands and dynamically adjust the contribution ratio of low- and high-frequency signals.

[0062] According to the characteristic time constants of the two sensors and , using the time-varying weight function to dynamically adjust the weights of low and high frequency signals,

[0063] in:

[0064] Low frequency signal weight: ;

[0065] High frequency signal weight: ;

[0066] in, t For time, and are the characteristic time constants of the two sensors, Used to characterize the response inertia of MEMS sensors to low-frequency signals. Used to characterize the dynamic response capability of MHD sensors to high-frequency signals, according to the characteristic time constant of the sensor and Dynamically adjust the contribution ratio of low-frequency and high-frequency signals;

[0067] According to the time-varying weight function, the angular velocity signal of the sensor after dynamic compensation can be calculated as: ;

[0068] in, For low frequency k axis (k = x, y, z) The angular velocity signal, At high frequency k axis (k = x, y, z) The angular increment signal;

[0069] According to the angular velocity signal after dynamic compensation, it is integrated at a certain moment, and the low-frequency angular velocity and high-frequency angular increment signals are adaptively integrated to calculate the angle deviation:

[0070] ;

[0071] in, represents the time element of the integral, is the difference between the upper and lower limits of the integral, indicating the time of the observed angle change. It means in time t The corresponding time constant Down k axis (k = x, y, z) The corresponding angular velocity after compensation;

[0072] The constraints that the adaptive weight fusion needs to meet are:

[0073] ;

[0074] The left side of the equation constrains the high-frequency angular velocity Angle deviation The instantaneous impact of high-frequency noise to prevent overload, is the objective function For variables The partial derivative of high-frequency angular velocity indicates the sensitivity of the angular deviation to high-frequency angular velocity. is the time derivative, which represents the dynamic rate of change at high frequency. is the saturation angle increment threshold of the MHD sensor.

[0075] Furthermore, the method further comprises:

[0076] Evaluate the error parameters after dynamic compensation, and perform quaternion attitude calculation on the data after dynamic compensation to obtain the residual error:

[0077] ;

[0078] in, is the current posture quaternion calculated by gradient descent method, is the reference quaternion output by the attitude meter under the action of the laser autocollimator, To perform the inverse operation on this reference quaternion, it is expressed as Rotation in opposite directions, represents the relative rotation deviation between the two, It means taking the absolute value of the scalar component of this relative rotation deviation;

[0079] When the residual Exceeding the threshold When , it triggers iterative correction of dynamic and static error parameters;

[0080] The triggering conditions of the residual feedback signal include:

[0081] when When , the solution process is immediately interrupted and all parameter calibration is forced to start;

[0082] when When , only the dynamic error transfer matrix is ​​updated ;

[0083] when When , the zero bias parameters are recursively smoothed and corrected through the Kalman filter.

[0084] Furthermore, the method further comprises:

[0085] Iteratively correcting the dynamic and static error parameters using the residual feedback signal includes:

[0086] The iterative correction of static error parameters is achieved in the following way:

[0087] ;

[0088] in, Indicates a combined gyroscope k axis (k = x, y, z) The zero-biased mean of is the proportional coefficient designed according to the residual component, n Indicates the n Static error parameter iterations, n+1 Indicates the n+1 Static error parameter iterations, represents the residual error of each axis of the combined gyroscope, is the inter-axis coupling coefficient, which is a quantitative coefficient of the error transmission relationship between the optical and mechanical benchmarks determined by the laser autocollimator and the reference attitude meter. For laser autocollimator k axis (k = x, y, z) The residual of the angle value output by the direction, the iterative correction of the static error parameter requires re-collecting static multi-position data and updating the zero bias average value;

[0089] The iterative correction of dynamic error parameters is achieved in the following way:

[0090] ;

[0091] in is the dynamic learning rate, n Indicates the n Dynamic error parameter iteration, n+1 Indicates the n+1 Dynamic error parameter iteration, represents the cross-response ratio, represents the dynamic noise power, Represents the objective function For variables The partial derivative of the dynamic error parameter is iteratively corrected by calculating the high-frequency residual through the dynamic noise power and adjusting the cross-response ratio;

[0092] The convergence condition of iterative correction of dynamic and static error parameters is determined as follows: when the residual change in three consecutive iterations is And dynamic noise power Less than the preset threshold When , the system is judged to be converged and the calibration parameters are output.

[0093] Compared with the existing technology, the present invention has the following advantages and beneficial effects:

[0094] By comprehensively exciting the combined gyroscope and performing frequency division calibration, the technical solution of the present invention can simultaneously calibrate the low-frequency static error and high-frequency dynamic error in the combined gyroscope, solving the problem that the traditional method can only perform low-frequency or high-frequency calibration; by using a dynamic compensation algorithm for the error parameters, the zero bias stability of the combined gyroscope at low frequencies is improved. , in the case of high frequency, improve the cross-axis interference suppression ratio of the combined gyroscope, so that the cross-axis interference suppression ratio At the same time, it can also cope with a variety of complex environments, and through the residual feedback mechanism, the long-term drift error of the calibration parameters is reduced to The following is suitable for real-time error correction of multi-band angular motion measurements in high-dynamic environments, which can significantly improve the measurement accuracy of the combined gyroscope in scenarios such as spacecraft attitude control and unmanned system navigation. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Other features, objects and advantages of the present invention will become more apparent upon reading the detailed description of non-limiting embodiments made with reference to the following drawings:

[0096] Figure 1 A flowchart of a low- and high-frequency composite calibration method for a MEMS and MHD combined gyroscope provided in an embodiment of the present invention;

[0097] Figure 2 A flowchart of separating low and high frequency signals in a low and high frequency composite calibration method for a MEMS and MHD combined gyroscope provided in an embodiment of the present invention;

[0098] Figure 3 A schematic structural diagram of a MEMS and MHD combined gyroscope broadband calibration device used in a low- and high-frequency composite calibration method for a MEMS and MHD combined gyroscope provided in an embodiment of the present invention;

[0099] Description of reference numerals:

[0100] 1. MEMS and MHD combined gyroscope; 2. Data acquisition system; 3. External excitation source; 4. Reference attitude meter; 5. Laser reflector; 6. Three-axis turntable; 61. X-axis; 62. Y-axis; 63. Z-axis; 7. Laser autocollimator; 8. Computer; 9. Experimental bench. DETAILED DESCRIPTION

[0101] The present invention will be further described in detail below with reference to the accompanying drawings and examples. It will be understood that the specific embodiments described herein are intended only to illustrate the present invention and are not intended to limit the present invention. It should also be noted that, for ease of description, the accompanying drawings only illustrate portions relevant to the present invention, not all structures.

[0102] Figure 1 A flow chart of a low-high frequency composite calibration method for a MEMS and MHD combined gyroscope provided in an embodiment of the present invention, see Figure 1 The embodiment of the present invention provides a low- and high-frequency composite calibration method for a MEMS and MHD combined gyroscope, comprising:

[0103] S1, applying an external excitation source to the MEMS and MHD combined gyroscope sensor.

[0104] Figure 3 A schematic diagram of the structure of a MEMS and MHD combined gyroscope broadband calibration device used in a high-frequency composite calibration method of a MEMS and MHD combined gyroscope provided in an embodiment of the present invention, see Figure 3 , exemplarily, it may include: an experimental table 9, on which a three-axis turntable 6, a laser autocollimator 7 and a computer 8 are placed, a MEMS and MHD combined gyroscope 1 is fixed on the three-axis turntable 6, wherein the three axes of the turntable are respectively an x-axis 61, a y-axis 62 and a z-axis 63, and a data acquisition system 2, an external excitation source 3, a reference attitude meter 4 and a laser reflector 5 are installed on the shell of the MEMS and MHD combined gyroscope 1.

[0105] The usage process is as follows: power on, connect the wires, fix the MEMS and MHD combination gyroscope 1 to be calibrated on the three-axis turntable 6, align the laser reflector 5 with the optical path of the laser autocollimator 7, and apply excitation to the MEMS and MHD combination gyroscope 1 through the external excitation source 3 to simulate its random vibration in a complex environment. The external excitation source includes static excitation, dynamic excitation, and dynamic and static combined excitation; the computer 8 is used to control the three-axis turntable 6 and the laser autocollimator 7, and at the same time receive the data transmitted by the data acquisition system 2 and perform data processing.

[0106] The static excitation means that the turntable keeps the gyroscope attitude still for 60 seconds at multiple preset positions, namely the positive and negative directions of the X / Y / Z axes, to stimulate zero bias and installation errors.

[0107] The dynamic excitation refers to applying multi-degree-of-freedom motion to the gyroscope according to the set frequency, amplitude and direction. The multi-degree-of-freedom motion is:

[0108] Low-frequency sinusoidal vibration, that is, applying amplitude to the positive and negative axes of X / Y / Z in sequence ,frequency Sine sweep, sweep rate ;

[0109] High frequency sweep vibration, that is, Within the range Octave stepping, dwell time of 2 seconds per frequency point, amplitude of 0.1° (RMS), used to calibrate dynamic error parameters;

[0110] The dynamic and static integrated excitation adopts a composite vibration including a low-frequency sinusoidal signal and a high-frequency random noise to simulate the random vibration of the combined gyroscope in a complex environment.

[0111] S2, synchronously collects vibration response data of the MEMS and MHD combined gyroscope sensor.

[0112] For example, it may include: using a data acquisition system 2 with a 16-bit ADC module to synchronously acquire the data signal of the MEMS and MHD combined gyroscope 1, wherein all devices are time-stamp aligned through the PTP protocol, and the synchronization error is , through the data acquisition system to The following signals are recorded synchronously at the sampling rate:

[0113] The three-axis angular velocity is output in the low frequency band of 0-100Hz; the three-axis angular increment is output in the high frequency band of 10-1000Hz; the reference quaternion output by the reference attitude meter 4 has an update rate of ≥200Hz; the laser autocollimator 7 is controlled by the computer 8 to output high-precision angle data with a sampling rate of ≥200Hz.

[0114] S3, separate the low and high frequency signals and calculate the error parameters.

[0115] Figure 2 This is a flowchart of separating low and high frequency signals in a calibration method for a low and high frequency composite of a MEMS and MHD combined gyroscope provided by an embodiment of the present invention, see Figure 2 , calculate the low-frequency static error parameters and high-frequency dynamic error parameters.

[0116] S3-1, low-pass filtering is performed on the vibration response data using a low-pass filter to extract the low-frequency MEMS signal; high-pass filtering is performed on the vibration response data using a high-pass filter to extract the high-frequency MHD signal.

[0117] S3-2, calculating low-frequency static error parameters and high-frequency dynamic error parameters based on the low-frequency MEMS signal and the high-frequency MHD signal.

[0118] S3-2-1, low-frequency static error parameters include sensor zero bias, scale factor and installation angle error;

[0119] S3-2-1-1, construct a static orthogonal matrix based on the installation angle error.

[0120] For example, it can be implemented in the following way:

[0121] Fix the combined gyroscope on a precision turntable and tilt it around the positive / negative X / Y / Z axes in sequence at preset angles. The installation angle error is calculated by geometric projection:

[0122] ;

[0123] in Indicates the output voltage value of the MEMS and MHD combined gyroscope sensor at different tilt positions of the y-axis. Indicates the reference output voltage value of the MEMS and MHD combined gyroscope sensor when the y-axis is not tilted. is the lever arm length from the laser reflector to the rotation center of the MEMS and MHD combined gyroscope, is the angle change measured by the laser autocollimator;

[0124] Correspondingly, the static orthogonal matrix is:

[0125] ;

[0126] Among them, the diagonal elements of the matrix are 1, which means that the scale factor of each axis has been normalized, 1 means that the sensitivity of each axis has been standardized and the reference is unified to 1, and the non-main diagonal elements represent the installation angle error between the cross axes (unit: rad). (For example: expressx Axis and y The installation angle error between the two axes is the deviation between the actual angle between the two axes and the theoretical orthogonal angle;

[0127] Scale factor normalization usually uses the original output signals of MEMS and MHD sensors to normalize the original output signals by the scale factor Converted to standard physical quantities, the units of the two sensors are unified and comparable. The following formula is used to normalize the two sensors:

[0128] ;

[0129] in, Indicates the output signal of the sensor. represents the sensor scale factor, Represents the converted standard physical quantity, that is, the angular velocity signal, the unit is ( ).

[0130] S3-2-1-2, calibration of sensor zero bias.

[0131] For example, the calibration of the sensor zero bias is done in a static Collect filtered data at multiple positions in the positive and negative axis directions, and take the average of the low-frequency MEMS signal output in the static state to calculate the sensor zero bias error, which can be calculated using the following formula:

[0132] ;

[0133] in express k axis (k = x, y, z) The zero-biased mean of express k axis (k = x, y, z) In the u Output voltage value in static position;

[0134] S3-2-1-3, calibration of scale factor.

[0135] For example, the scale factor is calibrated by performing a linear fit between the input physical quantity angular velocity and the sensor output data voltage signal using the least squares method to calculate the input-output slope. , nonlinearity is less than or equal to , use the following formula to calculate the slope:

[0136] ;

[0137] express k axis (k = x, y, z) The scaling factor, Indicates the firstu The reference angular velocity value of the sampling point, express k axis In the u The output voltage value at the time of sampling is represents the average value of the reference angular velocity, express k axis (k = x, y, z) The average value of the output voltage, N is the total number of sampling points.

[0138] S3-2-2, high-frequency dynamic error parameters include cross-response ratio, rejection ratio, data dispersion and power spectral density.

[0139] Exemplary ones include:

[0140] The cross-response ratio reflects the gain (in dB) of the output of the non-excitation axis on the excitation axis. The cross-response ratio is calculated as follows:

[0141] ;

[0142] in i For the non-excited axis, j is the excitation axis, Indicates the excitation axis j When excitation is applied, the non-excited axis i The RMS response value of the test area, Indicates the non-excited axis before excitation i The RMS value of the noise floor;

[0143] The rejection ratio reflects the sensor's ability to suppress interference from the excitation axis to the non-excitation axis (unit: dB). The rejection ratio is calculated as follows:

[0144] ;

[0145] in i For the non-excited axis, j is the excitation axis, Indicates the excitation axis j When excitation is applied, the non-excited axis i The RMS response value of the test area, Indicates the excitation axis j The RMS response value of the test area;

[0146] The data dispersion is used to measure the signal fluctuation caused by vibration and reflect the impact of vibration on the stability of the combined gyroscope output signal. The data dispersion is calculated as follows:

[0147] ;

[0148] in, m is the number of samples of a single movement, n is the number of repetitions of the same vibration, For the u Repeated v sampling points k axis (k = x, y, z) Measurement value, For all repetitions v sampling points k axis (k = x, y, z) mean;

[0149] The power spectral density (PSD) is used to characterize the distribution density of signal power in the frequency domain and is calculated using the following formula:

[0150] ;

[0151] in, The frequency domain representation of the signal is obtained by sampling the time domain signal to obtain a discrete time series, and then performing fast Fourier transform (FFT) on the discrete time series to calculate the frequency domain representation. , N represents the number of discrete data points sampled, Indicates the sampling rate;

[0152] By performing Fast Fourier Transform (FFT) analysis on the high-frequency signal, the power spectral density of the signal is calculated. The target frequency band is selected, and the power spectral density (PSD) is integrated in the frequency band to obtain the dynamic noise power. The dynamic noise power is calculated using the following method:

[0153] ;

[0154] in, and Respectively represent the starting frequency and cutoff frequency of the target frequency band analysis, and the two together define the integration interval [ , ], used to determine the specific noise frequency band, is the signal power spectral density, if the dynamic noise power If the threshold is exceeded, the adaptive filter is triggered to suppress high-frequency interference.

[0155] S3-2-2-1, generating a normalized error transfer coefficient based on the cross-response ratio and the rejection ratio, and generating a dynamic error matrix according to the normalized error transfer coefficient.

[0156] Optionally, the normalized error transfer coefficient may be calculated in the following manner:

[0157] ;

[0158] in, j represents the excitation axis, i represents the non-excitation axis, and the above formula represents the excitation axis j For non-excited shaft i The normalized error transfer coefficient of ;

[0159] Correspondingly, the dynamic error matrix is:

[0160] ;

[0161] Among them, the non-main diagonal elements represent the normalized error transfer coefficients of the excitation axis to the non-excitation axis (for example: Indicates the excitation axis y Shaft to non-excited shaft x Normalized error transfer coefficient of the axis);

[0162] S3-2-2-2, using the dynamic error matrix to establish an expression of the sensor's error-containing output, inverting the dynamic error matrix to obtain a dynamic error transfer matrix.

[0163] Exemplarily, using the above dynamic error matrix, the output of the sensor is expressed as:

[0164] ;

[0165] in, Indicates the output of the sensor x axis, y Axis and z The measured value of the axis angular velocity, Indicates the output of the sensor x axis, y Axis and z The true value of the axis angular velocity;

[0166] By the dynamic error matrix Invert the matrix to get the dynamic error transfer matrix ,

[0167] ;

[0168] Among them, the determinant .

[0169] S4, a composite error compensation model is constructed based on the static orthogonal matrix and the dynamic error transfer matrix.

[0170] Exemplarily, a composite error compensation model is constructed based on the static orthogonal matrix obtained in S3-2-1-1 and the dynamic error transfer matrix obtained in S3-2-2-2, so as to suppress the installation angle error, zero bias drift and cross-axis interference;

[0171] Correspondingly, the composite error compensation model is:

[0172] ;

[0173] Indicates the output of the sensor x axis, y Axis and z The compensation value of the axis angular velocity, Indicates the output of the sensor x axis, y Axis and z The measured value of the axis angular velocity;

[0174] In this embodiment, the method may add the following steps, using adaptive weight fusion to achieve full-band connection;

[0175] Based on the frequency response differences between MEMS and MHD combined gyroscope sensors, the low- and high-frequency signals after composite error compensation are dynamically integrated and adaptively weighted. The proportion of low- and high-frequency signals in the fusion is automatically allocated through a time-varying weight function. The fusion weight is adjusted in real time to optimize the complementarity of the combined gyroscope data in different frequency bands and dynamically adjust the contribution ratio of low- and high-frequency signals.

[0176] The difference in frequency response characteristics between the MEMS and MHD combined gyroscope sensors is that the MEMS sensor is more sensitive to angular vibrations at low frequencies (0-30 Hz) and has a more precise response, i.e., output signal, whereas the MHD sensor is more sensitive to angular vibrations at high frequencies (10-1000 Hz) and has a more precise response.

[0177] According to the characteristic time constants of the two sensors and , using the time-varying weight function to dynamically adjust the weights of low and high frequency signals, where:

[0178] Low frequency signal weight: ;

[0179] High frequency signal weight: ;

[0180] in, t For time, and are the characteristic time constants of the two sensors, Used to characterize the response inertia of MEMS sensors to low-frequency signals. Used to characterize the dynamic response capability of MHD sensors to high-frequency signals, according to the characteristic time constant of the sensor and Dynamically adjust the contribution ratio of low-frequency and high-frequency signals;

[0181] The low-frequency signal weight, i.e., its change over time, reflects the long-term stability advantage of the MEMS sensor in the low-frequency band. The high-frequency signal weight, i.e., its rapid approach to steady state over time, reflects the MHD sensor's ability to respond quickly to high-frequency transient signals.

[0182] According to the time-varying weight function, the angular velocity signal of the sensor after dynamic compensation can be calculated as:

[0183] ;

[0184] in, For low frequency k axis (k = x, y, z) The angular velocity signal, At high frequency k axis (k = x, y, z) When the weight ratio of low and high frequency signals is different, the angular velocity signal after dynamic compensation will also change.

[0185] According to the angular velocity signal after dynamic compensation, it is integrated at a certain moment, and the low-frequency angular velocity and high-frequency angular increment signals are adaptively integrated to calculate the angle deviation:

[0186] ;

[0187] in, represents the time element of the integral, is the difference between the upper and lower limits of the integral, indicating the time of the observed angle change. If the angle increases, it means that the angle changes slowly, that is, the signal is at a low frequency. , so that its low-frequency weight increases to fully accumulate the low-frequency stable signal of MEMS. If it decreases, it means that the angle changes quickly, that is, the signal is at high frequency. , the high-frequency weights saturate quickly, reflecting the high-frequency transient response of MHD, Refers to the time constant corresponding to time t Down k axis (k = x, y, z) The corresponding angular velocity after compensation;

[0188] The constraints that the adaptive weight fusion needs to meet are:

[0189] ;

[0190] The left side of the equation constrains the high-frequency angular velocity Angle deviation The instantaneous impact of high-frequency noise to prevent overload, is the objective function For variables The partial derivative of high-frequency angular velocity indicates the sensitivity of the angular deviation to high-frequency angular velocity. The time derivative represents the dynamic rate of change at high frequency. The right side of the equation introduces Threshold, when the angle deviation approaches the saturation limit of the MHD sensor, the low-frequency weight is automatically reduced to avoid integral overflow. is the saturation angle increment threshold of the MHD sensor. In practical applications, it is dynamically adjusted value to achieve full-band connection.

[0191] S5, evaluating the error parameters after dynamic compensation.

[0192] The residual norm obtained by performing quaternion attitude calculation on the dynamically compensated data is:

[0193] ;

[0194] in, is the current posture quaternion calculated by gradient descent method, is the reference quaternion output by the attitude meter under the action of the laser autocollimator, To perform the inverse operation on this reference quaternion, it is expressed as Rotation in opposite directions, represents the relative rotation deviation between the two, It means taking the absolute value of the scalar component of this relative rotation deviation;

[0195] When the residual Exceeding the threshold When , it triggers iterative correction of dynamic and static error parameters;

[0196] The triggering conditions of the residual feedback signal include:

[0197] when When , the solution process is immediately interrupted and all parameter calibration is forced to start;

[0198] when When , only the dynamic error transfer matrix is ​​updated ;

[0199] when When , the zero bias parameters are recursively smoothed and corrected through the Kalman filter.

[0200] S6, generating a residual feedback signal based on the error evaluation result, iteratively correcting the calibration error parameters until convergence, and outputting the calibration parameters.

[0201] Exemplary ones include:

[0202] The iterative correction of static error parameters is achieved in the following way:

[0203] ;

[0204] in, Indicates a combined gyroscope k axis (k = x, y, z) The zero-biased mean of is the proportional coefficient designed according to the residual component, n Indicates the n Static error parameter iterations, n+1 Indicates the n+1 Static error parameter iterations, represents the residual error of each axis of the combined gyroscope, is the inter-axis coupling coefficient, which is a quantitative coefficient of the error transmission relationship between the optical and mechanical benchmarks determined by the laser autocollimator and the reference attitude meter. For laser autocollimator k axis (k = x, y, z) (k = x, y, z) The residual of the angle value output by the direction, the iterative correction of the static error parameter requires re-collecting static multi-position data and updating the zero bias average value;

[0205] The iterative correction of dynamic error parameters is achieved in the following way:

[0206] ;

[0207] in is the dynamic learning rate, n Indicates the n Dynamic error parameter iteration, n+1 Indicates the n+1 Dynamic error parameter iteration, represents the cross-response ratio, represents the dynamic noise power, Represents the objective function For variables The partial derivative of the dynamic error parameter is iteratively corrected by calculating the high-frequency residual through the dynamic noise power and adjusting the cross-response ratio;

[0208] The convergence condition of iterative correction of dynamic and static error parameters is determined as follows: when the residual change in three consecutive iterations is And dynamic noise power Less than the preset threshold When , the system is judged to be converged and the calibration parameters are output.

[0209] Compared with the current state of the art, the present invention has the following beneficial effects:

[0210] By comprehensively exciting the combined gyroscope and performing frequency division calibration, the technical solution of the present invention can simultaneously calibrate the low-frequency static error and high-frequency dynamic error in the combined gyroscope, solving the problem that the traditional method can only perform low-frequency or high-frequency calibration; by using a dynamic compensation algorithm for the error parameters, the zero bias stability of the combined gyroscope at low frequencies is improved. , in the case of high frequency, improve the cross-axis interference suppression ratio of the combined gyroscope, so that the cross-axis interference suppression ratio At the same time, it can also cope with a variety of complex environments, and through the residual feedback mechanism, the long-term drift error of the calibration parameters is reduced to The following is suitable for real-time error correction of multi-band angular motion measurements in high-dynamic environments, which can significantly improve the measurement accuracy of the combined gyroscope in scenarios such as spacecraft attitude control and unmanned system navigation.

[0211] Note that the above are only preferred embodiments of the present invention and the technical principles employed. Those skilled in the art will appreciate that the present invention is not limited to the specific embodiments described herein, and that various obvious changes, readjustments, and substitutions are possible for those skilled in the art without departing from the scope of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments and may include many other equivalent embodiments without departing from the scope of the present invention. The scope of the present invention is determined by the scope of the appended claims.

Claims

1. A low- and high-frequency composite calibration method for a MEMS and MHD combined gyroscope, characterized in that: include: Synchronously collect vibration response data from the MEMS and MHD combined gyroscope sensors, separate low- and high-frequency signals, and calculate low-frequency static error parameters and high-frequency dynamic error parameters. Low-frequency static error parameters include sensor zero bias, scale factor, and installation angle error. High-frequency dynamic error parameters include cross-response ratio, rejection ratio, data dispersion, and power spectral density. A static orthogonal matrix is ​​constructed based on the installation angle error. The static orthogonal matrix is ​​used to reflect the non-ideal installation deviation between each two axes of the combined gyroscope in a low-frequency or static state, and the actual installation angle error is compensated by the static orthogonal matrix; A normalized error transfer coefficient is generated using the cross-response ratio and rejection ratio of high-frequency dynamic error parameters. The normalized error transfer coefficient is used to characterize the degree of interference of the excitation axis on the non-excitation axis when the dynamic quantization combined gyroscope is affected by multi-axis excitation, providing a parameter for real-time compensation between cross axes. generating a dynamic error matrix based on the normalized error transfer coefficients, the dynamic error matrix being used to reflect and quantify the degree of interference between cross-axes in a high-frequency or dynamic environment, establishing an expression of the sensor's error-containing output using the dynamic error matrix, inverting the dynamic error matrix to obtain a dynamic error transfer matrix, and using the dynamic error transfer matrix to suppress interference between cross-axes and compensate for errors between cross-axes in a high-frequency or dynamic environment; The static orthogonal matrix and the dynamic error transfer matrix are combined to construct a composite error compensation model for suppressing the installation angle error, zero bias drift and cross-axis interference; Based on the differences in frequency response characteristics of the combined MEMS and MHD gyroscope sensors, the low and high frequency signals after composite error compensation are fused using dynamic data integration and adaptive weighting. The proportion of low and high frequency signals in the fusion is automatically allocated through a time-varying weight function, and the fusion weight is adjusted in real time to optimize the complementarity of the combined gyroscope data in different frequency bands and dynamically adjust the contribution ratio of low and high frequency signals.

2. The calibration method for low- and high-frequency composite of MEMS and MHD combined gyroscope according to claim 1, characterized in that: The method further comprises: Vibration response data of the MEMS and MHD combined gyroscope sensor are synchronously collected by receiving an external excitation source signal, wherein the external excitation source includes static excitation, dynamic excitation, and combined static and dynamic excitation. The static excitation is to maintain the gyroscope attitude at a preset multi-axis static position and stimulate zero bias and installation error parameters; The dynamic excitation is to apply multi-degree-of-freedom motion to the combined gyroscope according to the set frequency, amplitude and direction, and to apply swept frequency vibration in a preset frequency space, so as to calibrate the dynamic error parameters; The dynamic and static integrated excitation uses a composite vibration including a low-frequency sinusoidal signal and high-frequency random noise as an excitation source to simulate the random vibration of the combined gyroscope in a complex environment.

3. The calibration method for a low- and high-frequency composite MEMS and MHD gyroscope according to claim 1, characterized in that: The separation of low-frequency and high-frequency signals and calculation of low-frequency static error parameters and high-frequency dynamic error parameters include: Use a low-pass filter to perform low-pass filtering on the vibration response data to extract the low-frequency MEMS signal; The vibration response data is high-pass filtered using a high-pass filter to extract the high-frequency MHD signal; The low-frequency static error parameters and high-frequency dynamic error parameters are calculated based on the low-frequency MEMS signal and the high-frequency MHD signal.

4. The calibration method for a low- and high-frequency composite MEMS and MHD gyroscope according to claim 1, characterized in that: The method further comprises: Fix the combined gyroscope on a precision turntable and tilt it around the positive / negative X / Y / Z axes in sequence at preset angles. The installation angle error is calculated by geometric projection: ； in express y The output voltage value of the MEMS and MHD combined gyroscope sensor at different tilt positions of the axis, express y The reference output voltage value of the MEMS and MHD combined gyroscope sensor when the axis is not tilted, is the lever arm length from the laser reflector to the rotation center of the MEMS and MHD combined gyroscope, is the angle change measured by the laser autocollimator; Correspondingly, the static orthogonal matrix is: ； The main diagonal elements of the matrix are 1, which means that the scale factors of each axis have been normalized. The non-main diagonal elements represent the installation angle error between the cross axes, that is, the deviation between the actual angle between the two axes and the theoretical orthogonal angle.

5. The calibration method for low- and high-frequency composite of MEMS and MHD combined gyroscope according to claim 4, characterized in that: The method further comprises: Sensor zero bias calibration, obtain the static The sensor zero bias error is calculated by taking the average of the low-frequency MEMS signal output in the static state after filtering data in multiple positions of the positive and negative axes. The scale factor is calibrated by performing a linear fit between the input physical quantity angular velocity and the sensor output data voltage signal using the least squares method to calculate the input-output slope. .

6. The low-high frequency composite calibration method of the MEMS and MHD combined gyroscope according to claim 1, characterized in that: The method further comprises: The cross-response ratio reflects the gain of the influence of the output of the non-excitation axis on the excitation axis, and is calculated as follows: ； in i For the non-excited axis, j is the excitation axis, Expressing motivation j When excitation is applied, the non-excited axis i The RMS response value of the test area, Indicates the non-excited axis before excitation i The RMS value of the noise floor; The rejection ratio reflects the sensor's ability to suppress interference from the excitation axis to the non-excitation axis. The rejection ratio is calculated as follows: ； in i For the non-excited axis, j is the excitation axis, Indicates the excitation axis j When excitation is applied, the non-excited axis i The RMS response value of the test area, Indicates the excitation axis j The RMS response value of the test area; Data dispersion is used to measure the signal fluctuation caused by vibration and to reflect the impact of vibration on the stability of the combined gyroscope output signal. The data dispersion is calculated as follows: ； in, m is the number of samples of a single movement, n is the number of repetitions of the same vibration, For the u Repeated v sampling points k Axis measurements, For all repetitions v sampling points k axis mean; The power spectral density is used to characterize the distribution density of signal power in the frequency domain. The power spectral density of the signal is calculated by fast Fourier transform analysis. The target frequency band is selected and the power spectral density is integrated in the frequency band to obtain the dynamic noise power. The dynamic noise power is calculated using the following method: ； in, and Respectively represent the starting frequency and cutoff frequency of the target frequency band analysis, and the two together define the integration interval [ , ], used to determine the specific noise frequency band, is the signal power spectral density, if the dynamic noise power If the threshold is exceeded, the adaptive filter is triggered to suppress high-frequency interference.

7. The calibration method for a low- and high-frequency composite MEMS and MHD gyroscope according to claim 4, characterized in that: The method further comprises: The normalized error transfer coefficient is calculated as follows: ； in, j represents the excitation axis, i represents the non-excited axis, and the normalized error transfer coefficient represents the excited axis j For non-excited shaft i The normalized error transfer coefficient of ; Correspondingly, the dynamic error matrix is: ； Among them, the non-main diagonal elements represent the excitation axis j For non-excited shaft i The normalized error transfer coefficient of ; Using the dynamic error matrix, the output of the sensor is expressed as: ； in, Indicates the output of the sensor x axis, y Axis and z The measured value of the axis angular velocity, Indicates the output of the sensor x axis, y Axis and z The true value of the axis angular velocity; By the dynamic error matrix Invert the matrix to get the dynamic error transfer matrix , ； Among them, the determinant .

8. The low-high frequency composite calibration method of the MEMS and MHD combined gyroscope according to claim 7, characterized in that: The method further comprises: The static orthogonal matrix and the dynamic error transfer matrix are combined to construct a composite error compensation model for suppressing the installation angle error, zero bias drift and cross-axis interference; Correspondingly, the composite error compensation model is: ； Indicates the output of the sensor x axis, y Axis and z The compensation value of the axis angular velocity, Indicates the output of the sensor x axis, y Axis and z The measured value of the axis angular velocity; Based on the frequency response differences between MEMS and MHD combined gyroscope sensors, the low- and high-frequency signals after composite error compensation are dynamically integrated and adaptively weighted. The proportion of low- and high-frequency signals in the fusion is automatically allocated through a time-varying weight function. The fusion weight is adjusted in real time to optimize the complementarity of the combined gyroscope data in different frequency bands and dynamically adjust the contribution ratio of low- and high-frequency signals. According to the characteristic time constants of the two sensors and , using the time-varying weight function to dynamically adjust the weights of low and high frequency signals, where: Low frequency signal weight: ; High frequency signal weight: ; in, t For time, and are the characteristic time constants of the two sensors, Used to characterize the response inertia of MEMS sensors to low-frequency signals. Used to characterize the dynamic response capability of MHD sensors to high-frequency signals, according to the characteristic time constant of the sensor and Dynamically adjust the contribution ratio of low-frequency and high-frequency signals; According to the time-varying weight function, the angular velocity signal of the sensor after dynamic compensation can be calculated as: ； in, For low frequency k The angular velocity signal of the axis, At high frequency k The incremental angle signal of the axis; According to the angular velocity signal after dynamic compensation, it is integrated at a certain moment, and the low-frequency angular velocity and high-frequency angular increment signals are adaptively integrated to calculate the angle deviation: ； in, represents the time element of the integral, is the difference between the upper and lower limits of the integral, indicating the time of the observed angle change. It means in time t The corresponding time constant Down k The magnitude of the compensated angular velocity corresponding to the axis; The constraints that the adaptive weight fusion needs to meet are: ； The left side of the equation constrains the high-frequency angular velocity Angle deviation The instantaneous impact of high-frequency noise to prevent overload, is the objective function For variables The partial derivative of high-frequency angular velocity indicates the sensitivity of the angular deviation to high-frequency angular velocity. is the time derivative, which represents the dynamic rate of change at high frequency. is the saturation angle increment threshold of the MHD sensor.

9. The low-high frequency composite calibration method of the MEMS and MHD combined gyroscope according to claim 8, characterized in that: The method further comprises: Evaluate the error parameters after dynamic compensation, and perform quaternion attitude calculation on the data after dynamic compensation to obtain the residual error: ； in, is the current posture quaternion calculated by gradient descent method, is the reference quaternion output by the attitude meter under the action of the laser autocollimator, To perform the inverse operation on this reference quaternion, it is expressed as Rotation in opposite directions, represents the relative rotation deviation between the two, It means taking the absolute value of the scalar component of this relative rotation deviation; When the residual Exceeding the threshold When , it triggers the iterative correction of dynamic and static error parameters; The triggering conditions of the residual feedback signal include: when When , the solution process is immediately interrupted and all parameter calibration is forced to start; when When , only the dynamic error transfer matrix is ​​updated ; when When , the zero bias parameters are recursively smoothed and corrected through the Kalman filter.

10. The low-high frequency composite calibration method of the MEMS and MHD combined gyroscope according to claim 9, characterized in that: The method further comprises: Iteratively correcting the dynamic and static error parameters using the residual feedback signal includes: The iterative correction of static error parameters is achieved by the following method: ； in, Indicates a combined gyroscope k The mean bias of the axis, is the proportional coefficient designed according to the residual component, n Indicates the n Static error parameter iterations, n+1 Indicates the n+1 Static error parameter iterations, Indicates a combined gyroscope k The residual of the axis, is the inter-axis coupling coefficient, which is a quantitative coefficient of the error transmission relationship between the optical and mechanical benchmarks determined by the laser autocollimator and the reference attitude meter. For laser autocollimator k The residual of the angle value output in the axial direction, the iterative correction of the static error parameter requires re-collecting static multi-position data and updating the zero bias average value; The iterative correction of dynamic error parameters is achieved by the following method: ； in is the dynamic learning rate, n Indicates the n Dynamic error parameter iteration, n+1 Indicates the n+1 Dynamic error parameter iteration, represents the cross-response ratio, represents the dynamic noise power, Represents the objective function For variables The partial derivative of the dynamic error parameter is iteratively corrected by calculating the high-frequency residual through the dynamic noise power and adjusting the cross-response ratio; The convergence condition of iterative correction of dynamic and static error parameters is determined as follows: when the residual change in three consecutive iterations is And dynamic noise power Less than the preset threshold When , the system is judged to be converged and the calibration parameters are output.

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