A resonator gyroscope temperature compensation method based on stepwise regression and Gaussian process

Abstract

The application discloses a resonator gyroscope temperature compensation method based on stepwise regression and a Gaussian process, and comprises the following steps: screening significant independent variables from preset independent variables through a stepwise regression model; constructing a sample set based on the significant independent variables, training a temperature compensation model; collecting significant variables at a current moment, estimating a zero bias value of the gyroscope through the temperature compensation model; and correcting an output angular velocity of the gyroscope according to the zero bias value. The technical problem of how to effectively suppress the temperature influence on the output zero bias of the hemispherical resonator gyroscope is solved, the zero bias stability of the output result is improved, and the robustness of the temperature compensation model is enhanced.

Description

Technical Field

[0001] This invention belongs to the field of temperature compensation for hemispherical resonant gyroscopes, and particularly relates to a temperature compensation method for resonant gyroscopes based on stepwise regression and Gaussian processes. Background Technology

[0002] Inertial navigation technology plays a vital role in national life and national defense, characterized by high precision, good security, and strong concealment. It serves a crucial purpose in military fields such as aviation, aerospace, and navigation, as well as in production and daily life, including underground exploration and oil extraction, demonstrating immense development potential and application prospects. High-precision and high-reliability hemispherical resonant gyroscopes (HRGs) are currently a research hotspot in the field. These are novel solid-state vibrating gyroscopes based on the Coriolis effect, sensing external input angular velocity through the precession effect of radial vibration standing waves of the hemispherical shell. They possess advantages such as high precision, high reliability, strong shock resistance, and long service life.

[0003] However, the size, shape, and physical properties of a hemispherical resonator gyroscope are easily affected by the temperature field, which in turn affects the gyroscope's performance, causing temperature drift and resulting in a decrease in the accuracy of the output results.

[0004] The main existing models for HRG temperature compensation include polynomial models, neural network models, and ARMA models, among which polynomial models have the most extensive engineering applications.

[0005] Polynomial models employ stepwise regression or piecewise fitting to find an explicit expression of the relationship between gyroscope bias and temperature information. Polynomial models are generally nonlinear, typically using absolute temperature, the rate of temperature change, and their higher-order terms as independent variables, and the gyroscope bias output as the dependent variable. The least squares method is used to select the independent variables and calculate the regression coefficients for each. While this method is simple and easy to implement, its compensation accuracy is low because it cannot accurately identify fluctuations in the gyroscope bias error within a small range, and its compensation effect is poor when temperature changes drastically.

[0006] In neural networks, backpropagation (BP) networks are commonly used for identification. This algorithm propagates the signal forward and the error backward, with weights adjusted using gradient descent to minimize the neural network error. However, BP networks suffer from local optima and are slow and inefficient to train. Radial basis function (RBF) neural networks, on the other hand, overcome these problems to some extent. They use the sum of local approximations to achieve a global approximation of the training data, thus achieving global optima. However, their network structure is more complex, training time is longer, and computational costs are higher.

[0007] The ARMA (Auto-Regressive and Moving Average) model is an important method for studying time series data. It is a hybrid model based on the autoregressive (AR) model and the moving average (MA) model. This model can describe the statistical characteristics of random drift and provide filtering compensation. However, the ARMA model requires the modeled data to be a generalized stationary time series. Since many factors that cause gyroscope zero-point drift are random, the gyroscope output usually cannot meet the above conditions.

[0008] Therefore, the technical problems of how to effectively suppress the zero bias error of the hemispherical resonant gyroscope output, improve the zero bias stability of the output results, enhance the robustness of the temperature compensation model, and ultimately meet the inertial navigation system's calculation accuracy requirements need to be solved. Summary of the Invention

[0009] The purpose of this invention is to provide a temperature compensation method for resonant gyroscopes based on stepwise regression and Gaussian processes, in order to solve at least one of the technical problems of how to effectively suppress the zero bias error of the hemispherical resonant gyroscope output, improve the zero bias stability of the output results, and enhance the robustness of the temperature compensation model.

[0010] The present invention adopts the following technical solution:

[0011] Example 1 provides a temperature compensation method for resonant gyroscopes based on stepwise regression and Gaussian processes, including:

[0012] Significant independent variables were selected from the pre-defined independent variables using a stepwise regression model; the pre-defined independent variables included the resonant frequency of the resonant gyroscope.

[0013] A sample set is constructed based on significant independent variables to train the temperature compensation model; the sample set includes resonant frequency and zero bias value.

[0014] Collect significant variables at the current moment and estimate the real-time zero bias value of the resonant gyroscope using the trained temperature compensation model;

[0015] The output angular velocity of the resonant gyroscope is corrected based on the real-time zero bias value.

[0016] Furthermore, significant independent variables are selected from the predefined independent variables using a stepwise regression model, including:

[0017] 1) Construct a training dataset based on the preset independent variables, and determine the regression coefficients of the following linear regression equation based on the training dataset:

[0018]

[0019] Where β0 is the regression constant, β1,β2,…,β m Here are the regression coefficients, and ε represents the coefficients that follow a regression pattern with a mean of zero and a variance of σ.2 Random error of normal distribution, x m , where is the m-th preset independent variable, and y is a zero bias value;

[0020] 2) Perform an F-test on each pre-defined independent variable according to the following formula:

[0021]

[0022] in, For the i-th zero bias value y i The estimated values, i = 1, 2, ..., n, y is the average value of the zero bias, y is the measured value of the zero bias, and n is the number of training samples in the sample set.

[0023] 3) Filter each regression coefficient according to the following formula to determine the significant independent variables:

[0024]

[0025] Where j = 1, 2, ..., m, and α is a given significance level, when When selecting independent variable x j It is a significant independent variable.

[0026] Furthermore, the method includes: testing the correlation between significant independent variables and the linear regression equation based on the following goodness-of-fit test:

[0027]

[0028] When the goodness of fit R 2 If the value is within a predetermined range, it indicates that the significant independent variable and the linear regression equation are correlated. The estimated value is the zero-bias value.

[0029] Furthermore, a sample set is constructed based on significant independent variables to train a temperature compensation model, including:

[0030] Construct a univariate GPR model based on Gaussian white noise using the following formula:

[0031] y(X)=f(X)+ε,

[0032] in, f(·) and y(·) represent multiple inputs X respectively. i ∈R d The latent input and output functions, i = 1, 2, ..., n, are used to define the significant independent variable X at time i. i and zero bias y i Construct training samples and generate a sample set. Where n is the number of training samples, X = {X1, X2, ..., X}n} represents the set of n inputs.

[0033] Furthermore, the n potential input function values ​​f(X1), f(X2), ..., f(X) in the temperature compensation model were determined. n Expressions of type ), including:

[0034] Based on n potential output function values ​​f(X1), f(X2), ..., f(X n Given a Gaussian process, determine the latent input function values ​​f(X1), f(X2), ..., f(X). n The mean function in ).

[0035] Furthermore, this also includes determining k(X,X') in the temperature compensation model as a Gaussian kernel function based on the covariance function formula, with the specific calculation method as follows:

[0036]

[0037] Where h = 1, 2, ..., d, represents the current dimension of the significant independent variable X, and x h ,x′ h Let represent the h-th dimension data of the significant independent variable X and its transpose, respectively. The signal variance of the covariance function is represented by l. h This represents the feature length scale of the h-th dimension input.

[0038] Furthermore, the method also includes: estimating the hyperparameter θ in the temperature compensation model based on maximum likelihood estimation.

[0039] Furthermore, significant variables at the current moment are collected, and the zero bias value of the gyroscope is estimated using a temperature compensation model, including:

[0040] The significant variables collected at the current moment are used as input to the temperature compensation model, and the output of the model is predicted and fitted to obtain the zero bias value of the gyroscope.

[0041] Example 2 provides a resonant gyroscope temperature compensation device based on stepwise regression 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 a resonant gyroscope temperature compensation method based on stepwise regression and Gaussian process as described in any of the above examples.

[0042] The beneficial effects of this invention are as follows: First, this invention first uses a stepwise regression model to quickly screen out significant independent variables that have a significant impact on the output of the gyroscope from multiple self-reported energies, and removes independent variables with low correlation, thereby reducing the amount of data processing in the model and improving data processing efficiency; furthermore, a Gaussian process is used to optimize the model, thereby achieving the technical effect of improving the zero-bias stability of the model output gyroscope. Attached Figure Description

[0043] Figure 1 This is a flowchart illustrating the steps of a resonant gyroscope temperature compensation method based on stepwise regression and Gaussian process according to an embodiment of the present invention.

[0044] Figure 2 This is a flowchart of a stepwise regression analysis method for a stepwise regression model according to an embodiment of the present invention;

[0045] Figure 3 This is a flowchart illustrating the steps involved in establishing a temperature compensation model according to an embodiment of the present invention.

[0046] Figure 4 This is a comparison diagram of the original angular velocity and the compensated angular velocity results according to an embodiment of the present invention;

[0047] Figure 5 This is a diagram of zero-bias residual error after compensation, according to an embodiment of the present invention. Detailed Implementation

[0048] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0049] Example 1 provides a temperature compensation method for resonant gyroscopes based on stepwise regression and Gaussian processes, including:

[0050] Significant independent variables are selected from the preset independent variables using a stepwise regression model. The preset independent variables include the resonant frequency of the resonant gyroscope. A sample set is constructed based on the significant independent variables to train the temperature compensation model. The sample set includes the resonant frequency and the zero bias value. The significant variables at the current moment are collected, and the real-time zero bias value of the resonant gyroscope is estimated through the trained temperature compensation model. The output angular velocity of the resonant gyroscope is corrected based on the real-time zero bias value.

[0051] It should be noted that in practice, many factors influence the independent variables of a gyroscope, such as the resonant frequency, the rate of change of the resonant frequency, and its higher-order terms. Therefore, it is necessary to select one or more of the most significant independent variables as inputs for compensation. This can improve the accuracy of the model's zero-bias compensation and enhance the model's adaptability under different conditions. Generally, the independent variables that influence the gyroscope's zero bias are as follows: resonant frequency, first derivative of the resonant frequency, square of the resonant frequency, square of the first derivative of the resonant frequency, second derivative of the resonant frequency, and square of the second derivative of the resonant frequency.

[0052] In one embodiment, combined with Figure 1 The model takes multiple preset independent variables, such as resonant frequency, first derivative of resonant frequency, square of resonant frequency, square of first derivative of resonant frequency, second derivative of resonant frequency, square of second derivative of resonant frequency, and measurement data such as the actual output of the pre-acquired gyroscope as input. Before these measurement data are input into the model, they need to be normalized according to the normalization formula to eliminate the dimensional effect of each measurement data and improve the calculation accuracy of the model.

[0053] The model first performs stepwise regression analysis on all possible independent variables as input to the stepwise regression model to screen out significant independent variables. Then, it performs Gaussian process regression analysis on the significant independent variables, specifically including: constructing a sample set of significant independent variables as input to the GPR model for model training, outputting the fitted data of the gyroscope's zero bias value, and then performing temperature compensation on the gyroscope's zero bias value to output the gyroscope's output angular velocity; while the insignificant independent variables are finally discarded.

[0054] Among them, combined Figure 2 The stepwise regression model is used to perform stepwise regression analysis on the preset independent variables to screen for significant independent variables, specifically including:

[0055] 1) Construct a training dataset based on the preset independent variables, and determine the regression coefficients of the following linear regression equation based on the training dataset:

[0056]

[0057] Where β0 is the regression constant, β1,β2,…,β m Here are the regression coefficients, and ε represents the coefficients that follow a regression pattern with a mean of zero and a variance of σ. 2 Random error of normal distribution, x m , where is the m-th preset independent variable, and y is a zero bias value;

[0058] Written in matrix form:

[0059] Y=Xβ+ε (2)

[0060] in,

[0061] The unknown parameters of the multiple linear regression equation are estimated using the least squares method as follows:

[0062]

[0063] in, This is the least squares estimate of the unknown parameter β.

[0064] 2) Perform an F-test on the linear regression equation using the following formula:

[0065] This step is used to perform a significance test on the linear regression equation, that is, to examine all regression variables x1, x2, ..., x... m Does it have a significant impact on the overall random variable y? To this end, the null hypothesis is proposed:

[0066] H0: β1=β2=…β m =0, (5)

[0067] Furthermore, the linear regression equation is tested using the sum of squared residuals according to formula (6).

[0068]

[0069] in, Regarding the actual result y i The estimated values ​​for i = 1, 2, ..., n It is the average of the actual results, and n is the number of data sample points.

[0070] If the assumption is true, it indicates that the linear regression equation is not significant; otherwise, it is significant.

[0071] 3) This includes screening each regression coefficient and the preset independent variables according to the following formula to determine the significant independent variables:

[0072]

[0073] Where j = 1, 2, ..., m, and α is a given significance level, when When selecting independent variable x j It is a significant independent variable.

[0074] In one embodiment, assume H0: β j =0, using the resonant frequency of the acquired resonant gyroscope as the model input, and after calculation and verification, if the assumption holds, then the selected independent variable x j If a variable is significant, then remove it; otherwise, remove the independent variable x. j .

[0075] It should be noted that in multiple linear regression analysis, a significant linear regression equation does not necessarily mean that every independent variable has a significant impact on the result y. When the linear regression equation contains insignificant variables, it presents problems such as inconvenience in using the regression equation for prediction and control, and increased variance, affecting prediction accuracy. Therefore, it is necessary to perform a significance test on each regression coefficient, eliminate unnecessary independent variables, and re-establish a more accurate and simpler regression equation to overcome the aforementioned problems.

[0076] Furthermore, the correlation between significant independent variables and the linear regression equation is tested according to the following goodness-of-fit test:

[0077]

[0078] When the goodness of fit R 2 If the value is within a predetermined range, it indicates that the significant independent variable and the linear regression equation are correlated. The estimated value with zero bias

[0079] In one feasible embodiment, the goodness of fit R 2 The value of R is between [0,1]. 2 The closer R is to 1, the better the regression fit; 2 The closer the goodness of fit is to 0, the worse the fit. For example, according to statistical principles, if the goodness of fit is in the range of 0.8 to 1, it can be concluded that there is a strong correlation between the independent variable and the regression model.

[0080] Furthermore, combined Figure 3 A sample set is constructed based on significant independent variables, and a temperature compensation model is trained, including:

[0081] 1) Construct a univariate GPR model based on Gaussian white noise according to the following formula:

[0082] y(X)=f(X)+ε, (9)

[0083] in, f(·) and y(·) represent multiple inputs X respectively. i ∈R d The latent input and output functions, i = 1, 2, ..., n, are used to define the significant independent variable X at time i. i and zero bias y i Construct training samples and generate a sample set. Where n is the number of training samples, X = {X1, X2, ..., X} n} represents the set of n inputs.

[0084] Furthermore, the n potential input function values ​​f(X1), f(X2), ..., f(X) in the temperature compensation model are determined. n The expression includes: based on n potential output function values ​​f(X1), f(X2), ..., f(X... n A Gaussian process, f(X) ~ GP(m(X), k(X, X′)), is defined, and the values ​​of f(X1), f(X2), ..., f(X′) are determined. n The mean function in ).

[0085] In one embodiment, based on n latent output function values ​​f(X1), f(X2), ..., f(X... n If a process satisfies a Gaussian process, then with m(X) = 0, the output is:

[0086] f(X)~N(0,k(X,Y′)), (10)

[0087] Where k(X, X′) is an n×n covariance matrix, which is composed of the covariances k(X1, X′) among the n samples. j The sequence is composed of i, j = 1, 2, ..., n.

[0088] Furthermore, this also includes determining k(X,X') in the temperature compensation model as a Gaussian kernel function based on the covariance function formula, with the specific calculation method as follows:

[0089]

[0090] Where h = 1, 2, ..., d represents the current dimension of the input significant independent variable X, and x h ,x′ h Let represent the h-th dimension data of the significant independent variable X and its transpose, respectively. The signal variance of the covariance function is represented by l. h This represents the feature length scale of the h-th dimension input.

[0091] 2) Estimate the hyperparameter θ in the temperature compensation model based on maximum likelihood estimation. include:

[0092] In one feasible embodiment, the hyperparameter θ in the temperature compensation model can be estimated using gradient descent or particle swarm optimization. The specific calculation method is as follows:

[0093] ①Maximum Likelihood (ML) estimation

[0094] To estimate X, we observe Z. If the observed value is z, the probability density of that value is L(x) = p(z|x). We introduce the likelihood function L(x) = p(z|x), and the x that maximizes the likelihood function is taken as the optimal estimate of X.

[0095]

[0096]

[0097]

[0098]

[0099] Under the assumption of a Gaussian process (normal distribution), it is easy to obtain the joint density function p(x,z) or conditional probability density function p(x|z), p(z|x) of variables X and Z, that is, it is easy to obtain the likelihood function required for maximum likelihood estimation.

[0100] ②Maximum A Posterior (MAP) estimation

[0101] Given an observation Z = z, the value of x that maximizes the conditional probability density p(x|z) is the most likely estimate.

[0102]

[0103]

[0104]

[0105]

[0106] ③ Bayes' Theorem

[0107]

[0108] Here, assuming x is the independent variable and z is the dependent variable, then p(z|x) represents the probability, p(x) and p(z) represent prior information about the variables, and p(x|z) represents posterior information.

[0109] In the absence of any prior information about the state (or independent variable) x, the maximum a posteriori estimation (MAP) is equivalent to the maximum likelihood estimation (ML).

[0110]

[0111]

[0112]

[0113] (assuming no prior information about state x, its distribution mean is m) x =0, variance C x →∞)

[0114]

[0115] Maximizing the log-posterior function is equivalent to maximizing the log-likelihood function, which yields the best estimate.

[0116] In the estimation of the hyperparameter θ of a Gaussian process, considering the maximum a posteriori estimate of θ, according to Bayesian theory...

[0117]

[0118] Since θ has little prior information, it is usually assumed that its prior distribution is uniform.

[0119]

[0120]

[0121]

[0122] m can be considered θ =0,C θ As θ approaches infinity, the maximum a posteriori estimate of θ is equivalent to its maximum likelihood estimate.

[0123]

[0124] here, To estimate the optimal hyperparameters, ln(p(y|x,θ)) is the log-likelihood function for estimating θ. Find the optimal hyperparameters. It can be transformed into an optimization problem of the log-likelihood function ln(p(y|x,θ)).

[0125] From the preceding analysis, we can conclude that Then ln(p(y|x,θ))=ln(L(θ)) can be transformed into

[0126]

[0127] Where, m y =0 n×1 ,

[0128] Based on the log-likelihood equation The optimal hyperparameters can be obtained using gradient descent or particle swarm optimization. Complete parameter estimation.

[0129] 3) After obtaining the hyperparameters of the temperature compensation model using the training samples, prediction can be performed. Assume there are n samples to be predicted. * n * y * From n * Given an n-dimensional Gaussian process v, and n values ​​y in the training set derived from this process, based on the additivity of the Gaussian distribution... Obey n+n * Gaussian distribution, i.e. in

[0130] Assuming that random vectors X and Z both follow a normal distribution (Gaussian distribution), based on the additivity of the normal distribution...

[0131] That is, Y ~ N(m) y C y ), (twenty three)

[0132] Where X is an n-dimensional vector and Z is an m-dimensional vector.

[0133]

[0134]

[0135]

[0136]

[0137]

[0138]

[0139] make Then there is

[0140]

[0141] make Then there is

[0142]

[0143] in,

[0144]

[0145]

[0146] The unpredicted y is performed using a Gaussian process. * When estimating, construct For the variance of the joint Gaussian distribution The calculation is performed using the following method:

[0147]

[0148] achievable

[0149] p(y * |x * ,x,y)~N(y * |m * ,Σ * )

[0150]

[0151] Where, m * is n * Predicted value y * The mean vector formed, Σ * This represents the uncertainty of the prediction.

[0152] Furthermore, significant variables at the current moment are collected, and the zero bias value of the gyroscope is estimated using a temperature compensation model, including:

[0153] The significant variables collected at the current moment are used as input to the temperature compensation model, and the output of the model is predicted and fitted to obtain the zero bias value of the gyroscope.

[0154] In one feasible embodiment, after determining the various unknown parameters of the temperature compensation model, the significant variables collected at the current moment are used as the input of the temperature compensation model, and prediction fitting is performed on all the data. That is, for each frequency information that changes over time, the predicted zero bias value of the gyroscope is obtained through the temperature compensation model.

[0155] After obtaining all the zero-bias prediction fitting data through the temperature compensation model using the resonant frequency, these zero-bias data are used to compensate the output angular velocity of the gyroscope, ultimately achieving temperature compensation.

[0156] The effectiveness of this invention can be further illustrated by the following experiments.

[0157] Taking a set of actual output data from a hemispherical resonant gyroscope with a sampling time of 8 hours and a sampling frequency of 20Hz as an example, a stepwise regression + Gaussian process regression model is established using the retained resonant frequency, derivative term and its higher-order term after screening as input to perform temperature compensation on the gyroscope angular velocity data, and the compensation results are displayed and analyzed.

[0158] First, the data was smoothed for 500 seconds. Then, normalization was performed, taking into full account the resonant frequency-related independent variables that might affect the gyroscope's zero bias. Next, stepwise regression analysis was used to screen for significant independent variables, retaining four variables with high correlation to the zero bias: the resonant frequency term, the first derivative term of the resonant frequency, the square term of the first derivative term of the resonant frequency, and the second derivative term of the resonant frequency. 100 sample points were extracted at equal intervals from these four variables and used as input to a stepwise regression + Gaussian process regression model for model training. Finally, the model was used to perform temperature compensation on all angular velocity data over 8 hours. The compensation results after using the temperature compensation method proposed in this invention are as follows:

[0159] When the constant external angular velocity is 9.8643° / h, the zero-bias stability of the original data is 0.740921° / h. A comparison of the original angular velocity and the compensated angular velocity is shown below. Figure 4As shown, the zero-bias stability after compensation is as follows: Figure 5 As shown, the zero-bias stability after compensation is 0.006446° / h, which improves the zero-bias stability of the data by two orders of magnitude, ultimately achieving a precision of thousands of degrees, which can meet the requirements of high-precision inertial navigation calculation.

[0160] Example 2 provides a resonant gyroscope temperature compensation device based on stepwise regression 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 a resonant gyroscope temperature compensation method based on stepwise regression and Gaussian process as described in any of the above examples.

Claims

1. A temperature compensation method for resonant gyroscopes based on stepwise regression and Gaussian processes, comprising: Significant independent variables are selected from the pre-defined independent variables using a stepwise regression model; The preset independent variable includes the resonant frequency of the resonant gyroscope; A sample set is constructed based on the aforementioned significant independent variables, and a temperature compensation model is trained; the sample set includes the resonant frequency and the zero bias value. Collect significant variables at the current moment, and estimate the real-time zero bias value of the resonant gyroscope through the trained temperature compensation model; The output angular velocity of the resonant gyroscope is corrected based on the real-time zero bias value; Significant independent variables are selected from the predefined independent variables using a stepwise regression model, including: 1) Construct a training dataset based on the preset independent variables, and determine the regression coefficients of the following linear regression equation based on the training dataset: ， in, For the regression constant, For regression coefficients, To conform to a mean of zero and a variance of Random error of normal distribution Let m be the preset independent variable. It has zero bias. 2) Perform an F-test on each of the preset independent variables according to the following formula: ， in, For the i-th zero bias value The estimated value, , y is the average value of the zero bias, y is the measured value of the zero bias, and n is the number of training samples in the sample set. 3) Filter each regression coefficient according to the following formula to determine the significant independent variables: ， in, , where α is a given significance level, when When selecting independent variables The significant independent variable is; The correlation between the significant independent variables and the linear regression equation is tested using the following goodness-of-fit test: ， When goodness of fit If the value is within a predetermined range, it is determined that the significant independent variable and the linear regression equation are correlated. The estimated value with zero bias; Based on the aforementioned significant independent variables, a sample set is constructed, and a temperature compensation model is trained, including: Construct a univariate GPR model based on Gaussian white noise using the following formula: ， in, , These represent multiple inputs respectively. The latent input function and latent output function, and the significant independent variables at time i. and zero bias Construct training samples and generate a sample set. ,in, The number of training samples. express A set of inputs.

2. The temperature compensation method for resonant gyroscopes based on stepwise regression and Gaussian processes as described in claim 1, wherein the temperature compensation model is determined in... The potential input function values The expressions include: according to Potential output function values The latent input function value is determined by satisfying a Gaussian process. The mean function in [the context].

3. The resonant gyroscope temperature compensation method based on stepwise regression and Gaussian process as described in claim 2 further includes determining the temperature compensation model according to the covariance function formula. The Gaussian kernel function is calculated as follows: ， in, , representing the significant independent variable The current dimension, They respectively represent the significant independent variables. The Dimensional data and its transpose, This represents the signal variance of the covariance function. Indicates the first The feature length scale of the dimension input.

4. The resonant gyroscope temperature compensation method based on stepwise regression and Gaussian process as described in any one of claims 1-3, further comprising: The hyperparameters in the temperature compensation model are estimated based on maximum likelihood. , .

5. A temperature compensation method for a resonant gyroscope based on stepwise regression and Gaussian process as described in claim 4, comprising collecting significant variables at the current moment and estimating the zero bias value of the gyroscope through the temperature compensation model, including: The significant variable at the current time of acquisition is used as the input of the temperature compensation model, and the output of the model is predicted and fitted to obtain the zero bias value of the gyroscope.

6. A resonant gyroscope temperature compensation device based on stepwise regression and Gaussian process, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor, when executing the computer program, implements a resonant gyroscope temperature compensation method based on stepwise regression and Gaussian process as described in any one of claims 1-5.

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