A temperature compensation method for hemispherical resonant gyroscopes based on fuzzy control and Gaussian process

Abstract

The present invention discloses a temperature compensation method for a hemispherical resonant gyroscope based on fuzzy control and Gaussian process. The working range of the hemispherical resonant gyroscope is divided into several different temperature ranges according to the temperature value and the temperature change rate. Gaussian process models are respectively established in each temperature range. The resonant frequency of the resonator of the hemispherical resonant gyroscope at the current moment is collected, and the change rate of the resonant frequency of the resonator is calculated according to the resonant frequency. The membership degrees of the current moment to each temperature range are calculated according to the resonant frequency and the change rate of the resonant frequency, and the first predicted zero bias value corresponding to each Gaussian process model is determined. The second predicted zero bias value at the current moment is calculated according to each first predicted zero bias value and its corresponding membership degree, and the output angle of the hemispherical resonant gyroscope is optimized based on the second predicted zero bias value. By establishing a Gaussian process model and predicting the gyro zero bias according to the maximum likelihood estimation, the present invention can achieve a better prediction effect.

Description

Technical Field

[0001] The present invention belongs to the technical field of temperature compensation of hemispherical resonant gyroscopes, and particularly relates to a temperature compensation method for hemispherical resonant gyroscopes based on fuzzy control and Gaussian process. Background Art

[0002] A hemispherical resonant gyroscope is a component used to measure the angular velocity of a carrier. During use, the change in the external environmental temperature acts on the hemispherical resonant gyroscope, and the resulting drift is very complex. The material properties of the hemispherical resonant gyroscope, the resonant structure size of the resonator, and the natural frequencies of components (including exciters, capacitive sensors, resonators, etc.) will all undergo slight changes, which will all cause the output of the hemispherical resonant gyroscope to drift, ultimately resulting in a decrease in the detection accuracy of the hemispherical resonant gyroscope. Therefore, it is very necessary to model and compensate for the temperature drift of the hemispherical resonant gyroscope.

[0003] In the temperature compensation of hemispherical resonant gyroscopes, the traditional regression modeling method combines least squares modeling and piecewise modeling. The least squares method aims to establish a least squares model of the gyro zero bias and temperature-related variables (such as temperature and the rate of change of temperature) through the least squares method, and then predict the zero bias of the gyro under different temperature conditions according to the obtained model, and further compensate for the zero bias.

[0004] However, the least squares method is a linear fitting method and cannot well characterize the complex non-linear relationship between the zero bias of the hemispherical resonant gyroscope and temperature, resulting in a large error. Summary of the Invention

[0005] The purpose of the present invention is to provide a temperature compensation method for hemispherical resonant gyroscopes based on fuzzy control and Gaussian process, which uses the modeling method of Gaussian process regression to replace the least squares method, reduces the zero bias of the hemispherical resonant gyroscope, and reduces the detection error.

[0006] The present invention adopts the following technical solutions: A temperature compensation method for hemispherical resonant gyroscopes based on fuzzy control and Gaussian process, comprising the following steps:

[0007] Divide the working range of the hemispherical resonant gyroscope into several different temperature ranges according to the temperature value and the rate of change of temperature;

[0008] Establish a Gaussian process model in each temperature range respectively;

[0009] Collect the resonant frequency of the resonator of the hemispherical resonant gyroscope at the current moment, and calculate the rate of change of the resonant frequency of the resonator according to the resonant frequency;

[0010] Calculate the membership degrees of the current moment for each temperature range according to the resonance frequency and the rate of change of the resonance frequency, and based on the Gaussian process models for each temperature range, determine the first predicted zero bias values corresponding to each Gaussian process model with the resonance frequency and the rate of change of the resonance frequency as input information;

[0011] Calculate the second predicted zero bias value of the current moment according to each first predicted zero bias value and its corresponding membership degree, and optimize the output angle of the hemispherical resonator gyroscope based on the second predicted zero bias value.

[0012] Furthermore, divide the working range of the hemispherical resonator gyroscope into several different temperature ranges according to the temperature value and the rate of change of the temperature, including:

[0013] Divide the working range of the hemispherical resonator gyroscope into a low-temperature fast-drop section, a low-temperature slow-drop section, a low-temperature slow-rise section, a low-temperature fast-rise section, a high-temperature fast-drop section, a high-temperature slow-drop section, a high-temperature slow-rise section, and a high-temperature fast-rise section according to the temperature value and the rate of change of the temperature.

[0014] Furthermore, establish Gaussian process models respectively within each temperature range, including:

[0015] Collect several groups of data sets within each temperature range; among them, each group of data sets includes the resonance frequency of the resonator and the rate of change of the resonance frequency;

[0016] Establish Gaussian process models according to several groups of data sets.

[0017] Furthermore, before establishing Gaussian process models according to several groups of data sets, it also includes:

[0018] Perform z-score normalization and moving average filtering on each group of data sets in turn.

[0019] Furthermore, calculating the membership degrees of the current moment for each temperature range according to the resonance frequency and the rate of change of the resonance frequency includes:

[0020] U X,y =m X ×n y ,

[0021] where, U X,y is the membership degree of the current moment for each temperature range, X∈{A,B}, y∈{a,b,c,d}, m X is the membership degree of the current moment for the high-temperature section and the low-temperature section, n y is the membership degree of the current moment for the fast-drop section, the slow-drop section, the slow-rise section, and the fast-rise section.

[0022] Furthermore, determining the first predicted zero bias values corresponding to each Gaussian process model includes:

[0023]

[0024] Among them, m * is the first predicted zero bias value, k(x n , x * ) represents the Gaussian kernel, x n represents the resonance frequency and the resonance frequency change rate of the nth sampling point, represents the resonance frequency at the current moment, represents the resonance frequency change rate at the current moment, K n represents the kernel function, represents the Gaussian white noise of the nth sampling point, I n is the n-order identity matrix, and y is the zero bias value vector of the sampling point set.

[0025] Furthermore, the Gaussian kernel is:

[0026]

[0027] Among them, x i (h) is the hth component of the vector x i , x j (h) is the hth component of the vector x j , d is the dimension of the independent variable, and l h are both hyperparameters, and l h includes two characteristic length scales, l1 and l2.

[0028] Furthermore, calculating the second predicted zero bias value at the current moment according to each first predicted zero bias value and its corresponding membership degree includes:

[0029]

[0030] Among them, is the second predicted zero bias value, U Aa is the membership degree of the low-temperature fast-drop section, is the first predicted zero bias value output by the Gaussian process model of the low-temperature fast-drop section, U Ab is the membership degree of the low-temperature slow-drop section, is the first predicted zero bias value output by the Gaussian process model of the low-temperature slow-drop section, U Bd is the membership degree of the high-temperature fast-rise section, is the first predicted zero bias value output by the Gaussian process model of the high-temperature fast-rise section.

[0031] Another technical solution of the present invention: A temperature compensation device for a hemispherical resonant gyroscope based on fuzzy control and Gaussian process, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, the above-mentioned temperature compensation method for a hemispherical resonant gyroscope based on fuzzy control and Gaussian process is realized.

[0032] The beneficial effects of the present invention are as follows: The working range of the hemispherical resonant gyroscope of the present invention is divided into several different temperature ranges. By uniformly sampling the data in each temperature range, a Gaussian process model is established, and the gyro zero bias is predicted according to the maximum likelihood estimation, which can achieve better prediction effects. Description of the Drawings

[0033] Figure 1 It is the schematic diagram of the moving average filtering principle in the embodiment of the present invention;

[0034] Figure 2 It is the schematic diagram of the membership degrees of the high-temperature section and the low-temperature section in the embodiment of the present invention;

[0035] Figure 3 It is the schematic diagram of the membership degrees of the fast-drop section, the slow-drop section, the slow-rise section, and the fast-rise section in the embodiment of the present invention;

[0036] Figure 4 It is the schematic diagram of the division result of dividing the temperature change rate into three stages: low-temperature fast rise, high-temperature slow rise, and slow drop in the verification embodiment of the present invention;

[0037] Figure 5 It is the schematic diagram of the temperature compensation effect of the hemispherical resonant gyroscope by the method of the verification embodiment of the present invention. Detailed Embodiments

[0038] The present invention will be described in detail below with reference to the drawings and specific embodiments.

[0039] Since the internal temperature field of the hemispherical resonant gyroscope is difficult to directly measure, but the resonant frequency will affect the temperature change, the zero bias and temperature models established in the present invention are all based on this. Due to the hysteresis effect of the parameters of the hemispherical resonant gyroscope on temperature, the gyro has different characteristics in the heating section and the cooling section. Therefore, a segmented modeling strategy needs to be adopted. For segmented modeling, on the basis of the least squares method, the working range of the gyro is divided into the heating section and the cooling section, so as to improve the accuracy of the model.

[0040] For the junction of each interval, a fuzzy discrimination method is adopted to make the zero drift smoothly transition between different temperature intervals. At the same time, due to the more precise division of the temperature intervals, the model of each section is more accurate.

[0041] For the piecewise modeling strategy, since there may be significant differences between the models of the heating section and the cooling section, there will be large errors in the zero-bias prediction for the process from the heating section to the cooling section. Especially when the temperature changes repeatedly, there will be large jumps in the predicted zero-bias.

[0042] To address the above drawbacks, the present invention adopts a fuzzy control strategy to distinguish between the heating section and the cooling section. On this basis, intervals with faster and slower changes are further distinguished according to the magnitude of the change rate. For the junction of each interval, a fuzzy discrimination method is used to enable a smooth transition of the zero drift in different temperature intervals. At the same time, due to a more precise division of the temperature intervals, the model of each section is more accurate.

[0043] The present invention discloses a temperature compensation method for a hemispherical resonant gyroscope based on fuzzy control and Gaussian process, comprising the following steps: dividing the working interval of the hemispherical resonant gyroscope into several different temperature intervals according to the temperature value and the temperature change rate; establishing a Gaussian process model in each temperature interval; collecting the resonant frequency of the resonator of the hemispherical resonant gyroscope at the current moment, and calculating the change rate of the resonant frequency of the resonator according to the resonant frequency; calculating the membership degree of the current moment to each temperature interval according to the resonant frequency and the change rate of the resonant frequency, and based on the Gaussian process model of each temperature interval, using the resonant frequency and the change rate of the resonant frequency as input information to determine the first predicted zero-bias value corresponding to each Gaussian process model; calculating the second predicted zero-bias value at the current moment according to each first predicted zero-bias value and its corresponding membership degree, and optimizing the output angle of the hemispherical resonant gyroscope based on the second predicted zero-bias value.

[0044] The working interval of the hemispherical resonant gyroscope of the present invention is divided into several different temperature intervals. By uniformly sampling the data of each temperature interval, a Gaussian process model is established, and the gyro zero-bias is predicted according to the maximum likelihood estimation, which can achieve better prediction results.

[0045] By uniformly sampling the data of each section, a Gaussian process model is established, and the gyro zero-bias is predicted according to the maximum likelihood estimation, which can achieve better prediction results. Since the internal temperature field of the hemispherical gyro is difficult to directly measure, but the resonant frequency will affect the temperature change, the zero-bias and temperature models established in the present invention are both.

[0046] Specifically, dividing the working interval of the hemispherical resonant gyroscope into several different temperature intervals according to the temperature value and the temperature change rate includes: dividing the working interval of the hemispherical resonant gyroscope into a low-temperature fast-drop section, a low-temperature slow-drop section, a low-temperature slow-rise section, a low-temperature fast-rise section, a high-temperature fast-drop section, a high-temperature slow-drop section, a high-temperature slow-rise section, and a high-temperature fast-rise section according to the temperature value and the temperature change rate.

[0047] As described above, the temperature range and the temperature change rate range are divided. According to the magnitude of the temperature, the high-temperature section and the low-temperature section can be distinguished. According to the relationship between the temperature change rate and zero, the temperature range is divided into a heating section and a cooling section. At the same time, according to the magnitude of the temperature change rate, the heating section is divided into a fast-rise section and a slow-rise section, and the cooling section is divided into a slow-fall section and a fast-fall section. The specific division principle is shown in Subscript 1 below.

[0048] Table 1

[0049]

[0050] After dividing the temperature range, it is necessary to establish a Gaussian process model in each temperature range, and then predict the zero-offset value for each temperature range according to the Gaussian process model.

[0051] Specifically, first, data sampling is performed to obtain a data set for constructing the Gaussian process model, that is, several groups of data sets are collected in each temperature range; among them, each group of data sets includes the resonant frequency of the harmonic oscillator and the change rate of the resonant frequency.

[0052] After obtaining the data set, each group of data sets is sequentially subjected to z-score normalization and moving average filtering. Z-score normalization is to perform z-score normalization on the data (i.e., the resonant frequency and the change rate of the resonant frequency), and the processing is carried out according to the following formula:

[0053]

[0054] Among them, mean, n' is the number of data sets, x is the resonant frequency and the change rate of the resonant frequency, S is the sample variance,

[0055] Regarding the moving average filtering, the data is subjected to moving average filtering, which can filter out the noise in the signal. The formula is as follows:

[0056]

[0057] Among them, the filtered result, H is the width of the filtering window, x m is the m-th data after z-score normalization. As Figure 1 shown, it is necessary to calculate the average value of the H / 2 data before and after centered on x i as the filtering result of the i-th point. Only in this way can the noise be filtered out.

[0058] Next, it is necessary to establish a Gaussian process model in each temperature range according to the data set, and establish a Gaussian process model based on several groups of data sets. As a specific implementation, a section of data is uniformly sampled to obtain n sampling points. Specifically, n is taken as 100 in this embodiment. Then, a Gaussian process model of zero offset, resonance frequency, and resonance frequency change rate is established based on the above sampling points.

[0059] Specifically, the Gaussian process model is as follows:

[0060]

[0061] Among them, f(X) is the zero offset value vector of the sampling point set, X = [x1, x2] T is a two-dimensional column vector, and the two components respectively represent the resonance frequency and the resonance frequency change rate. K n is a kernel function used to measure the generalized distance between any two points. The subscript n represents the number of data sets. The kernel function uses a Gaussian kernel, that is:

[0062]

[0063] Among them, x i (h) is the h-th component of the vector x i , x j (h) is the h-th component of the vector x j , d is the dimension of the independent variable, and l h are both hyperparameters. l h includes two characteristic length scales, l1 and l2, which reflect the dependence degree of the Gaussian regression process on the resonance frequency and the resonance frequency change rate in the independent variable. I is the n-order identity matrix. represents the Gaussian white noise in the model.

[0064] Then, according to the maximum likelihood estimation, the hyperparameters of the Gaussian process model are optimized to obtain the following function:

[0065]

[0066] Among them,

[0067] Finally, find the maximum value of this function to obtain the hyperparameters l1, l2, σ f , σ n , and then the Gaussian process functions of each temperature range are obtained.

[0068] In one embodiment, when the resonance frequency and the resonance frequency change rate at a moment are obtained, calculate the predicted value at this moment under each model. Assume that the known data is y, and the data to be predicted is y * ,

[0069] Specifically, the posterior probability density is obtained according to Bayes' formula:

[0070] p(y * |x * , x, y) ~ N(y * |m * , Σ * ) (5)

[0071] Next, determining the first prediction zero bias value corresponding to each Gaussian process model includes:

[0072]

[0073]

[0074] where m * is the first prediction zero bias value, k(x n , x * ) represents the Gaussian kernel, x n represents the resonance frequency and the resonance frequency change rate of the nth sampling point, represents the resonance frequency at the current moment, represents the resonance frequency change rate at the current moment, Kn represents the kernel function, represents the Gaussian white noise at the nth sampling point, I n is the n-order identity matrix, y is the zero bias value vector of the sampling point set, and the Gaussian kernel is shown in formula (4).

[0075] Finally, calculating the membership degree of the current moment to each temperature interval according to the resonance frequency and the resonance frequency change rate includes:

[0076] U X,y = m X × n y ,

[0077] where U X,y is the membership degree of the current moment to each temperature interval, X ∈ {A, B}, y ∈ {a, b, c, d}, as Figure 2 and Figure 3 shown, the membership degree can be calculated respectively through the resonance frequency and its change rate, m X and n y , m X is the membership degree of the current moment to the high temperature section and the low temperature section, n y is the membership degree of the current moment to the fast drop section, the slow drop section, the slow rise section and the fast rise section.

[0078] Then, calculating the second predicted zero offset at the current moment according to each first predicted zero offset and its corresponding membership degree includes:

[0079]

[0080] Wherein, is the second predicted zero offset, U Aa is the membership degree of the low-temperature fast-drop section, is the first predicted zero offset output by the Gaussian process model of the low-temperature fast-drop section, U Ab is the membership degree of the low-temperature slow-drop section, is the first predicted zero offset output by the Gaussian process model of the low-temperature slow-drop section, U Bd is the membership degree of the high-temperature fast-rise section, is the first predicted zero offset output by the Gaussian process model of the high-temperature fast-rise section.

[0081] In order to verify the method of the present invention, the following verification examples were carried out. As shown in Table 2, the data of the hemispherical resonant gyroscope for 7.7 hours are known. The data includes the resonant frequency and the output angle. The angular velocity and the temperature change rate signal with smaller noise are obtained through moving average filtering, and the length of the moving window is 500 s. The stable value of the angular velocity is taken as 6.52678, and the zero offset and zero offset stability are calculated based on this. For the temperature interval, it is divided into a high-temperature section and a low-temperature section. For the temperature change rate, it is divided into three stages: fast rise, slow rise, and slow drop. The division results are as Figure 4 shown.

[0082] Table 2

[0083]

[0084] As Figure 5 shown, by using Gaussian process regression based on fuzzy control, a good compensation effect is obtained. The zero offset stability drops from 0.0142133 to 0.000368. The zero offset stability is improved by two orders of magnitude. At the same time, the zero offset stability in each time period is shown in Table 2. It can be concluded that the Gaussian process regression based on fuzzy control has a particularly significant effect on suppressing the zero offset in the startup section, which is due to the separate modeling of the startup section, improving the model accuracy.

[0085] The present invention also discloses a hemispherical resonant gyro temperature compensation device based on fuzzy control and Gaussian process, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the above-mentioned hemispherical resonant gyro temperature compensation method based on fuzzy control and Gaussian process.

[0086] The above-mentioned device can be a computing device such as a desktop computer, a notebook, a palm computer, and a cloud server. The device may include, but is not limited to, a processor and a memory. Those skilled in the art can understand that the device may include more or fewer components, or combine certain components, or different components. For example, it may also include input / output devices, network access devices, etc.

[0087] The processor can be a Central Processing Unit (CPU), and the processor can also be other general-purpose processors, Digital Signal Processors (DSPs), Application Specific Integrated Circuits (ASICs), Field-Programmable Gate Arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor can be a microprocessor or the processor can also be any conventional processor, etc.

[0088] In some embodiments, the memory can be an internal storage unit of the device, such as the hard disk or memory of the device. In other embodiments, the memory can also be an external storage device of the device, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) card, a Flash Card, etc. equipped on the device. Further, the memory can also include both the internal storage unit and the external storage device of the device. The memory is used to store an operating system, application programs, a BootLoader, data, and other programs, such as the program code of the computer program, etc. The memory can also be used to temporarily store data that has been output or will be output.

[0089] It should be noted that for the specific content of the above-mentioned device, since it is based on the same concept as the method embodiment of the present invention, for its specific functions and the technical effects brought, reference can be specifically made to the method embodiment section, and details will not be elaborated here.

Claims

1. A temperature compensation method for a hemispherical resonant gyroscope based on fuzzy control and Gaussian process, characterized in that, It includes the following steps: Divide the working range of the hemispherical resonant gyroscope into several different temperature ranges according to the temperature value and the temperature change rate; Establish a Gaussian process model in each of the said temperature ranges; Collect the resonant frequency of the resonator of the hemispherical resonant gyroscope at the current moment, and calculate the change rate of the resonant frequency of the resonator according to the said resonant frequency; Calculate the membership degree of the current moment to each of the said temperature ranges according to the said resonant frequency and the change rate of the resonant frequency, and based on the Gaussian process model of each temperature range, use the said resonant frequency and the change rate of the resonant frequency as input information to determine the first predicted zero bias value corresponding to each of the said Gaussian process models; Calculate the second predicted zero bias value at the current moment according to each of the said first predicted zero bias values and their corresponding membership degrees, and optimize the output angle of the hemispherical resonant gyroscope based on the second predicted zero bias value.

2. The temperature compensation method for a hemispherical resonant gyroscope based on fuzzy control and Gaussian process according to claim 1, characterized in that, Dividing the working range of the hemispherical resonant gyroscope into several different temperature ranges according to the temperature value and the temperature change rate includes: Divide the working range of the hemispherical resonant gyroscope into a low-temperature fast-drop section, a low-temperature slow-drop section, a low-temperature slow-rise section, a low-temperature fast-rise section, a high-temperature fast-drop section, a high-temperature slow-drop section, a high-temperature slow-rise section, and a high-temperature fast-rise section according to the temperature value and the temperature change rate.

3. The temperature compensation method for a hemispherical resonant gyroscope based on fuzzy control and Gaussian process according to claim 2, characterized in that, Establishing a Gaussian process model in each of the said temperature ranges includes: Collect several groups of data sets in each of the said temperature ranges; wherein, each group of data sets includes the resonant frequency of the resonator and the change rate of the resonant frequency; Establish the said Gaussian process model according to several groups of the said data sets.

4. The temperature compensation method for a hemispherical resonant gyroscope based on fuzzy control and Gaussian process according to claim 3, characterized in that, Before establishing the said Gaussian process model according to several groups of the said data sets, it further includes: Perform z-score normalization and moving average filtering on each group of the said data sets in sequence.

5. The temperature compensation method for a hemispherical resonant gyroscope based on fuzzy control and Gaussian process according to claim 3, characterized in that, Calculating the membership degree of the current moment to each of the said temperature ranges according to the said resonant frequency and the change rate of the resonant frequency includes: U X,y = m X × n y , Among them, U X,y′ is the membership degree of each of the temperature ranges at the current moment, X ∈ {A, B}, A represents the low-temperature section, B represents the high-temperature section, y ∈ {a, b, c, d}, a represents the rapid descent section, b represents the slow descent section, c represents the slow ascent section, d represents the rapid ascent section, m X is the membership degree of the high-temperature section and the low-temperature section at the current moment, n y is the membership degree of the rapid descent section, the slow descent section, the slow ascent section, and the rapid ascent section at the current moment.

6. The temperature compensation method for a hemispherical resonant gyroscope based on fuzzy control and Gaussian process according to claim 4, characterized in that, Determining the first predicted zero bias value corresponding to each of the said Gaussian process models includes: where m * is the first predicted zero offset value, k(x n , x * ) represents the Gaussian kernel, x n represents the resonance frequency and the resonance frequency change rate of the nth sampling point, represents the resonance frequency at the current moment, represents the resonance frequency change rate at the current moment, K n represents the kernel function, represents the Gaussian white noise of the nth sampling point, I n is the nth order identity matrix, and y is the zero offset value vector of the sampling point set.

7. The temperature compensation method for a hemispherical resonant gyroscope based on fuzzy control and Gaussian process according to claim 6, characterized in that, The Gaussian kernel is: where x i (h) is the h-th component of the vector x i , x j (h) is the h-th component of the vector x j , d is the dimension of the independent variable, and l h are both hyperparameters, l h includes two characteristic length scales l1 and l2.

8. The temperature compensation method for a hemispherical resonant gyroscope based on fuzzy control and Gaussian process according to any one of claims 2-7, characterized in that, Calculating the second predicted zero bias value at the current moment according to each of the said first predicted zero bias values and their corresponding membership degrees includes: Among them, is the second predicted zero offset value, U Aa is the membership degree of the low-temperature rapid descent section, is the first predicted zero offset value output by the Gaussian process model of the low-temperature rapid descent section, U Ab is the membership degree of the low-temperature slow descent section, is the first predicted zero offset value output by the Gaussian process model of the low-temperature slow descent section, U Bd is the membership degree of the high-temperature rapid ascent section, is the first predicted zero offset value output by the Gaussian process model of the high-temperature rapid ascent section.

9. A temperature compensation device for a hemispherical resonant gyroscope based on fuzzy control and Gaussian process, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the said processor executes the said computer program, it realizes a temperature compensation method for a hemispherical resonant gyroscope based on fuzzy control and Gaussian process as described in any one of claims 1-8.

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