Gyroscope temperature drift error compensation method based on VI-GMM

Abstract

The invention discloses a gyroscope temperature drift error compensation method based on VI-GMM, and relates to the technical field of gyroscope detection, and the method comprises the following steps: S1, collecting data of temperature and output angular velocity of three axes of a gyroscope; step S2, preprocessing the collected data; s3, establishing a three-dimensional joint Gaussian mixture model for the temperature drift error of the gyroscope based on the triaxial coupling characteristics of the gyroscope; s4, deriving parameters in the model through a variational inference algorithm (VI), wherein the parameters comprise the weight pi < k >, the model expectation k and the covariance matrix sigma < k > of each Gaussian distribution; and S5, calculating the temperature drift error generated by the gyroscope in actual use by using the temperature drift error model in the step S3, and subtracting the corresponding temperature drift error from the output of the gyroscope to obtain compensated output data. According to the error compensation method, the temperature drift error of the gyroscope can be effectively corrected, and a more accurate error compensation method is provided.

Description

Technical Field

[0001] The present invention relates to the technical field of gyroscope detection, and in particular to a gyroscope temperature drift error compensation method based on VI-GMM. Background Art

[0002] As an effective tool for measuring or maintaining the orientation and angular velocity of an object, gyroscopes are widely used in navigation, aviation, aerospace, electronic products, robotics, etc. The sensitive structure and signal processing circuit of the gyroscope are very sensitive to temperature changes. Ambient temperature changes and internal heating can cause zero drift and scale factor changes in the gyroscope, thus affecting the measurement accuracy.

[0003] In order to improve the measurement accuracy and stability of the gyroscope, the temperature drift of the gyroscope must be compensated. However, the traditional compensation method usually adopts an offline method, which is time-consuming in actual operation and difficult to adapt to the dynamically changing temperature environment. In order to improve the real-time and accuracy of temperature drift, it is necessary to develop a method that can estimate and compensate temperature drift online.

[0004] In order to ensure the feasibility of temperature drift error compensation, it is necessary to establish an accurate error model to describe the relationship between temperature and gyroscope output. For example, the error model is established by using the average value method to perform linear fitting of temperature and zero-point angular velocity (reference: Institute of Software, Chinese Academy of Sciences. A method for compensating gyroscope temperature drift: CN 201110104532.6[P].2012-11-28.), or the zero-bias temperature n-order error model is established by using Kalman filtering (reference: Tongji University. An online estimation and compensation method for gyroscope temperature drift error: CN 202110362582.8[P].2022-11-18.) However, the above methods still have the following problems: First, using the average value to fit the error to a straight line cannot adapt to complex data distribution. When the data distribution is complex and there are multiple modes, the average value method may not accurately capture the true characteristics of the data. In addition, its fitting straight line cannot directly quantify the uncertain relationship between the data points and the model.

[0005] Second, Kalman filtering is more suitable for linear or approximately linear systems, has limited effect on nonlinear error modeling, and cannot directly handle multimodal errors; moreover, its performance depends to a large extent on the accuracy of the initial parameters, and the selection of initial state estimation and noise covariance has a great influence on the filtering effect; in addition, in the scenario of multi-sensor data fusion, Kalman filtering usually requires complex joint modeling and state estimation of the error models of each sensor, which is a cumbersome process. Summary of the invention

[0006] In view of the above technical problems to be solved, the present invention provides a gyroscope temperature drift error compensation method based on VI-GMM, which can effectively correct the gyroscope temperature drift error and provide a more accurate error compensation method.

[0007] In order to solve the above technical problems, the technical solution proposed by the present invention is: A gyroscope temperature drift error compensation method based on VI-GMM includes the following steps: Step S1, collecting data on temperature and output angular velocity of three axes of the gyroscope within the operating temperature range of the three-axis gyroscope sensor; Step S2, preprocessing the collected data; Step S3, establishing a three-dimensional joint Gaussian mixture model for the gyroscope temperature drift error based on the three-axis coupling characteristics of the gyroscope; The temperature drift error model is: ; in, oh is the angular velocity measurement value of the gyroscope; Indicates k Gaussian sub-models for angular velocity measurements oh The probability density function of K is the number of single Gaussian models included in the Gaussian mixture model of temperature drift error, K is a hyperparameter; For the k Gaussian distribution weights satisfy and 0； is the model expectation of each Gaussian distribution, and the mean is used to represent the expectation in the calculation; S k is the model covariance matrix; i k ={ ， ,S k ,k=1,2,…,K},θ =( i 1 , i 2 ,... i k ) T are the parameters of all single Gaussian models; T represents the transpose of the matrix; Step S4, derive the parameters in the model through the variational inference algorithm, including the weight of each Gaussian distribution π k 、 Model Expectationsµ k , covariance matrix S k ; Step S5, using the temperature drift error model in step S3, calculates the temperature drift error generated by the gyroscope during actual use, and then subtracts the corresponding temperature drift error from the output of the gyroscope to obtain compensated output data.

[0008] As a further improvement of the above technical solution: Preferably, in step S3, Indicates k Gaussian sub-models for angular velocity measurements oh The probability density function of is: ; in, oh is the angular velocity measurement, which is a column vector of dimension 3, containing the gyroscope x, y, z Three angular velocity data of the axis: ; in, oh x Indicates gyroscope x Axis angular velocity measurement value, oh y Indicates gyroscope y Axis angular velocity measurement value, oh z Indicates gyroscope z Axis direction angular velocity measurement value.

[0009] Preferably, in step S4, the variational inference algorithm deduces the parameters in the model, comprising the following steps: S4-1, Initialization: Use K-means clustering algorithm to cluster the samples, and use the cluster center of the final cluster as µ k0 , the covariance matrix of the final cluster is taken as S k0 , and take the proportion of the final cluster samples to the total number of samples as π k0 ; S4-2, Introducing Hidden Variables: Introducing Hidden Variables z i ,express oh i Belong to k An exponential variable of a distribution: P(z) i =k）= π k ; in,z i ∈ { 1，2，...，K}; The temperature drift error model is rewritten as: ; S4-3, define variational distribution: let variational posterior distribution q(θ) In factorized form: ; in, represents the variational distribution of the mixture weights, represents the variational distribution of the mean, represents the variational distribution of covariance; S4-4, Optimize variational parameters: Optimize variational distribution parameters by maximizing the evidence lower bound; S4-5, confirm the optimal solution: repeat step S4-4 until the variational distribution parameter F The change in is less than the threshold, and the final variational distribution parameters are obtained; S4-6, calculate the final model parameters: calculate the final parameters of the Gaussian mixture model based on the final variational distribution parameters obtained by variational inference optimization.

[0010] Preferably, when the K-means clustering algorithm clusters samples, the step of initializing data is: S4-1-1, determine the K' value: determine the number of clusters K' to be created, the number of clusters is numerically equal to the number of single Gaussian models K in the Gaussian mixture model, that is, K'=K; S4-1-2, Initialize cluster center: Randomly select K' data points as the initial center of the cluster , where the superscript (0) represents the initial iteration state, the subscript j represents the jth cluster, j∈{1,2,…,K′}; S4-1-3, assign data points: For each data point, calculate its distance to the center of each cluster and assign it to the cluster with the smallest distance; that is, calculate each angular velocity measurement value oh i With each cluster center The Euclidean distance of t Indicates the number of iterations and is assigned to the cluster with the smallest Euclidean distance middle: S4-1-4, Update cluster center: Update the center of each cluster, that is, use the average value of all data in the cluster as the new cluster center: S4-1-5, convergence judgment: repeat S4-1-3 and S4-1-4 until the cluster center no longer changes, the algorithm is considered to have converged, the cluster at this time is the final cluster, take the cluster center of the final cluster As initialization parameter ,Right now ; S4-1-6, calculate the covariance matrix of the final cluster , using the covariance matrix of the final cluster as the initial parameter S k0 ; S4-1-7, calculate the mixing weight: calculate the proportion of samples in the final cluster to the total samples as the initial mixing weight π k0 ; because i k0 ={π k0 ，µ k0 ,S k0 ,k=1,2,…,K'},θ 0 =( i 1 , i 2 ,... i k’ ) T , after calculation, the initial parameter θ0 of θ is obtained, and the data initialization is completed.

[0011] Preferably, in S4-3, q(π k ) is the variational distribution of the mixed weight, set to Dirichlet distribution: ; in is a mixing weight that satisfies and , are the parameters of the Dirichlet distribution, ; q(μ k ) is the variational distribution of the mean, assuming it is a normal distribution: ; in is the mean of the kth Gaussian distribution (i.e., model expectation), is the mean parameter of the normal distribution, are the covariance matrix parameters of the normal distribution; q(Σ k ) is the variational distribution of the covariance, set to the inverse Wishart distribution: ; is the covariance matrix of the kth Gaussian distribution, is the degrees of freedom of the inverse Wishart distribution, , is the scale matrix parameter of the inverse Wishart distribution, is a positive definite matrix.

[0012] Preferably, in S4-4, optimizing the variational distribution parameters is specifically: S4-4-1, Calculate the expectation of hidden variables: Calculate the hidden variables according to the current variational distribution parameters z i The posterior probability ; S4-4-2, update the mixed weight parameters : ; in, is the Dirichlet prior parameter, let , indicating that the initial assumption for the mixing weights is uniform distribution; S4-4-3, Update mean parameters and : ; ; in, and is the prior parameter of the mean, let is the sample mean, ， This indicates that the initial assumption about the mean parameter is weak; I is the identity matrix; S4-4-4, Update covariance parameters and : ; ; in, and is the inverse Wishart prior parameter, let , d is the angular velocity measurement data dimension, which is 3 here; , I is the identity matrix; this indicates that the initial assumption on the covariance matrix is ​​weak.

[0013] Compared with the prior art, the VI-GMM-based gyroscope temperature drift error compensation method provided by the present invention has the following advantages: (1) The VI-GMM-based gyroscope temperature drift error compensation method of the present invention can flexibly adapt to the multi-peak distribution characteristics of the data. Even if there are multiple different temperature drift modes in the data, GMM can better model them. The VI-GMM-based gyroscope temperature drift error compensation method of the present invention assigns the probability of belonging to each Gaussian component to each data point, provides a clear clustering explanation, and can quantify the uncertainty of the data points under different temperature drift modes.

[0014] (2) The VI-GMM-based gyroscope temperature drift error compensation method of the present invention does not rely on the linear assumption of data, can handle complex distributions, effectively capture the nonlinear characteristics in the gyroscope temperature drift error, and provide a more accurate error model; in addition, in the multi-sensor data fusion scenario, GMM can be flexibly used to fuse the error distributions of different sensors, and the error characteristics of each sensor can be comprehensively considered by adjusting the weights and parameters of the mixed components. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 It is a flow chart of the error compensation method of the present invention.

[0016] Figure 2 A flow chart for establishing the error model parameters of the present invention. DETAILED DESCRIPTION

[0017] The specific embodiments of the present invention are described in detail below. It should be understood that the specific embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0018] When the three-axis gyroscope is completely still, the speeds on the three axes are theoretically zero. However, in practice, the output data of the three axes are not zero, and the data of the three axes are not the same. This is because random noise and temperature affect the zero point of the gyroscope. The VI-GMM-based gyroscope temperature drift error compensation method of the present invention compensates for the temperature drift of the gyroscope, thereby eliminating the temperature drift error of the gyroscope as much as possible.

[0019] like Figure 1 As shown, the VI-GMM-based gyroscope temperature drift error compensation method of the present invention comprises the following steps: Step S1, collecting data on temperature and output angular velocity of three axes of the gyroscope within the operating temperature range of the three-axis gyroscope sensor.

[0020] Construct a curve of the gyroscope zero point changing with temperature. When the gyroscope is in a stable and stationary state and only the temperature changes, collect temperature data and angular velocity data in the three axis directions. Multiple measurements are required to collect data.

[0021] Step S2, preprocessing the collected data.

[0022] First, convert the data into units, with the temperature in degrees Celsius (℃) and the angular velocity data in degrees per second (° / s) or radians per second (rad / s); then remove outliers, using standard deviation to assist in identifying and removing data values ​​with obvious anomalies; if there are missing values ​​in the data, use interpolation to fill in the missing values ​​to ensure data integrity; finally, use Kalman filtering to remove noise and uncertainty in the data.

[0023] After the data is preprocessed, the stable data of the gyroscope zero-point output value with respect to temperature is obtained, forming a change curve.

[0024] Step S3, constructing a temperature drift error model using a Gaussian mixture model (GMM).

[0025] The temperature drift modeling formula is: ; in, oh is the angular velocity measurement value of the gyroscope; K is the number of single Gaussian models included in the Gaussian mixture model of temperature drift error, K is a hyperparameter; For the k Gaussian distribution weights satisfy and 0；µ k is the model expectation of each Gaussian distribution, and the mean is used to represent the expectation in the calculation; S k is the model covariance matrix; i k ={π k ，µ k ,S k ，k=1， 2,…,K},θ =( i 1 , i 2 ,... i k ) T are the parameters of all single Gaussian models; T represents the transpose of the matrix.

[0026] Indicates k Gaussian sub-models for angular velocity measurements oh The probability density function of is: ; in, oh is the angular velocity measurement, which is a column vector of dimension 3, containing the gyroscope x, y, z Three angular velocity data of the axis: ; in, oh x Indicates gyroscope x Axis angular velocity measurement value, oh y Indicates gyroscope y Axis angular velocity measurement value, oh z Indicates gyroscope z Axis direction angular velocity measurement value.

[0027] Step S4, derive the parameters in the model through the variational inference algorithm, including the weight of each Gaussian distribution 、 Model Expectations , covariance matrix .

[0028] After the modeling is completed in step S3, in order to quickly and easily obtain the accurate parameters of the temperature drift error model, the present invention uses a variational inference algorithm to calculate the parameters. The calculation process is as follows: Figure 2 .

[0029] S4-1, Initialization: Use K-means clustering algorithm to cluster the samples, and use the cluster center of the final cluster as µ k0 , the covariance matrix of the final cluster is taken as S k0 , and take the proportion of the final cluster samples to the total number of samples as π k0 .

[0030] Furthermore, the steps of initializing data for the K-means clustering algorithm are: S4-1-1, determine the K' value: determine the number of clusters K' to be created. The number of clusters is numerically equal to the number of single Gaussian models K in the Gaussian mixture model, that is, K'=K.

[0031] S4-1-2, Initialize cluster center: Randomly select K' data points as the initial center of the cluster , where the superscript (0) represents the initial iteration state, and the subscript j represents the jth cluster, j∈{1,2,…,K′}.

[0032] S4-1-3, assign data points: For each data point, calculate its distance from the center of each cluster and assign it to the cluster with the smallest distance. That is, calculate each angular velocity measurement value oh iWith each cluster center The Euclidean distance of the cluster is t, where t represents the number of iterations, and it is assigned to the cluster with the smallest Euclidean distance. middle: ; in, represents the Euclidean distance, It is t The iteration k The center of a cluster.

[0033] S4-1-4, Update cluster center: Update the center of each cluster, that is, use the average value of all data in the cluster as the new cluster center: ; in, express The number of data points in .

[0034] S4-1-5, Convergence judgment: Repeat S4-1-3 and S4-1-4 until the cluster center no longer changes or When , the algorithm is considered to have converged, where ε is a small positive number, which is determined according to the actual situation. The cluster at this time is the final cluster, and the cluster center of the final cluster is taken as As initialization parameter ,Right now ;

[0035] S4-1-6, calculate the covariance matrix of the final cluster : ; The covariance matrix of the final cluster is used as the initial parameter S k0 : .

[0036] S4-1-7, calculate the mixing weight: calculate the proportion of samples in the final cluster to the total samples as the initial mixing weight π k0 : ; Where N is the total number of samples.

[0037] because i k0 ={π k0 ，µ k0 ,S k0 ,k=1,2,…,K'},θ 0 =( i 1 , i 2 ,... i k’ ) T , through the above steps, the initial parameter θ0 of θ can be obtained and the data initialization is completed.

[0038] S4-2, introduce hidden variables.

[0039] Since each angular velocity measurement oh i It is uncertain which Gaussian distribution it belongs to, so when using the variational inference algorithm to calculate the model parameters, it is necessary to introduce hidden variables z i , used to indicate oh i Belong to k An indicator variable for a distribution: P(z) i =k）=π k ； in, z i ∈ { 1，2，...，K}.

[0040] Then the joint probability in the temperature drift error model can be written as: ; The temperature drift error model is rewritten as: .

[0041] S4-3, define variational distribution.

[0042] Assume variational posterior distribution In factorized form (mean field approximation): ; in, represents the variational distribution of the mixture weights, represents the variational distribution of the mean, represents the variational distribution of the covariance.

[0043] is the variational distribution of the mixture weight, assuming a Dirichlet distribution: ; in is a mixing weight that satisfies and . are the parameters of the Dirichlet distribution, .

[0044] The probability density function of is: ; in is the multivariate beta function: ; Where Γ represents the Gamma function.

[0045] is the variational distribution of the mean, assuming a normal distribution: ; in is the mean of the kth Gaussian distribution (i.e., model expectation), is the mean parameter of the normal distribution, are the covariance matrix parameters of the normal distribution.

[0046] The probability density function of is: ; in, d is the data dimension, d =3.

[0047] in, The mean of the kth Gaussian distribution, is the mean parameter of the normal distribution, are the covariance matrix parameters of the normal distribution.

[0048] q(Σ k ) is the variational distribution of the covariance, assuming an inverse Wishart distribution: ; is the covariance matrix of the kth Gaussian distribution, is the degrees of freedom of the inverse Wishart distribution, , is the scale matrix parameter of the inverse Wishart distribution, is a positive definite matrix.

[0049] q(Σ k ) is: ; in, is the multivariate Gamma function: .

[0050] S4-4, Optimize variational parameters.

[0051] The variational distribution parameters are optimized by maximizing the evidence lower bound (ELBO), specifically: S4-4-1, Calculate the expectation of hidden variables: Calculate the hidden variables according to the current variational distribution parameters z i The posterior probability of: ; in, is the angular velocity measurement value oh i The posterior probability (i.e., responsibility) of belonging to the kth distribution, , ; .

[0052] S4-4-2, update the mixed weight parameters : ; in, is the Dirichlet prior parameter, let , The value of indicates that the initial assumption for the mixing weights is a uniform distribution.

[0053] S4-4-3, Update mean parameters and : ; .

[0054] in and is the prior parameter of the mean, let is the sample mean, ， and A value of indicates a weak initial assumption about the mean parameter. I is the identity matrix.

[0055] S4-4-4, Update covariance parameters and : ; .

[0056] in, and is the inverse Wishart prior parameter, let , d is the angular velocity measurement data dimension, which is 3 here; , I is the identity matrix. and A value of indicates a weak initial assumption about the covariance matrix.

[0057] S4-5, confirm the optimal solution.

[0058] Repeat step S4-4 until the variational distribution parameter F The change in is less than the threshold, that is When , we get the final variational distribution parameters , , , and .

[0059] in is the variational distribution parameter of the tth iteration, represents the Euclidean distance of the parameter vector, Take 10 -5 .

[0060] S4-6, calculate the final model parameters: the final variational distribution parameters obtained by variational inference optimization , , , and , calculate the final parameters of the Gaussian mixture model i k ={ ， ,S k ，k=1， 2，…，K}。

[0061] Furthermore, the step of calculating the final model parameters is: 4-6-1, Calculate the mixed weight : ; 4-6-2, calculate the mean : ; 4-6-3, Calculate covariance : ; in, d is the angular velocity measurement data dimension, take d=3 .

[0062] Step S5, using the temperature drift error model in step S3, calculates the temperature drift error generated by the gyroscope during actual use, and then subtracts the corresponding temperature drift error from the output of the gyroscope to obtain compensated output data.

[0063] The above implementation cases are only preferred embodiments of the present invention and are not intended to limit the present invention in any form. Although the present invention has been disclosed as above with preferred embodiments, they are not intended to limit the present invention. Therefore, any simple modification, equivalent changes and modifications made to the above embodiments according to the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the scope of protection of the technical solution of the present invention.

Claims

1. A gyroscope temperature drift error compensation method based on VI-GMM, characterized in that: The following steps are involved: Step S1, collecting data on temperature and output angular velocity of three axes of the gyroscope within the operating temperature range of the three-axis gyroscope sensor; Step S2, preprocessing the collected data; Step S3, establishing a three-dimensional joint Gaussian mixture model for the gyroscope temperature drift error based on the three-axis coupling characteristics of the gyroscope; The temperature drift error model is: ； in, ω is the angular velocity measurement value of the gyroscope; Indicates k Gaussian sub-models for angular velocity measurements ω The probability density function of K is the number of single Gaussian models included in the Gaussian mixture model of temperature drift error, K is a hyperparameter; For the k Gaussian distribution weights satisfy and 0； is the model expectation of each Gaussian distribution, and the mean is used to represent the expectation in the calculation; Σ k is the model covariance matrix; θ k ={ ， ,Σ k , k = 1, 2, …, K}, θ =( θ 1 , θ 2 ,... θ k ) T are the parameters of all single Gaussian models; T represents the transpose of the matrix; Step S4, derive the parameters in the model through the variational inference algorithm, including the weight of each Gaussian distribution π k 、 Model Expectations µ k , covariance matrix Σ k ; Step S5, using the temperature drift error model in step S3, calculates the temperature drift error generated by the gyroscope during actual use, and then subtracts the corresponding temperature drift error from the output of the gyroscope to obtain compensated output data.

2. The VI-GMM-based gyroscope temperature drift error compensation method according to claim 1, characterized in that: In the step S3, Indicates k Gaussian sub-models for angular velocity measurements ω The probability density function of is: ； in, ω is the angular velocity measurement, a column vector of dimension 3, containing the gyroscope x, y, z Three angular velocity data of the axis: ; in, ω x Indicates gyroscope x Axis angular velocity measurement value, ω y Indicates gyroscope y Axis angular velocity measurement value, ω z Indicates gyroscope z Axis direction angular velocity measurement value.

3. The VI-GMM-based gyroscope temperature drift error compensation method according to claim 2, characterized in that: In step S4, the variational inference algorithm deduces the parameters in the model, including the following steps: S4-1, Initialization: Use K-means clustering algorithm to cluster samples, and use the cluster center of the final cluster as µ k0 , the covariance matrix of the final cluster is taken as Σ k0 , and take the proportion of the final cluster samples to the total number of samples as π k0 ； S4-2, Introducing Hidden Variables: Introducing Hidden Variables z i ,express ω i Belong to k An exponential variable of a distribution: P(z i =k）=π k； in, z i ∈ { 1，2，...，K }; The temperature drift error model is rewritten as: ； S4-3, define variational distribution: let variational posterior distribution In factorized form: ； in, Represents the variational distribution of the mixture weights ， represents the variational distribution of the mean, represents the variational distribution of covariance; S4-4, Optimize variational parameters: Optimize variational distribution parameters by maximizing the evidence lower bound; S4-5, confirm the optimal solution: repeat step S4-4 until the variational distribution parameter Ф The change in is less than the threshold, and the final variational distribution parameters are obtained; S4-6, calculate the final model parameters: According to the final variational distribution parameters obtained by variational inference optimization, calculate the final parameters of the Gaussian mixture model 。 4. The VI-GMM-based gyroscope temperature drift error compensation method according to claim 3, characterized in that: When the K-means clustering algorithm clusters samples, the steps of initializing data are: S4-1-1, determine the K' value: determine the number of clusters K' to be created, the number of clusters is numerically equal to the number of single Gaussian models K in the Gaussian mixture model, that is, K'=K; S4-1-2, Initialize cluster center: Randomly select K' data points as the initial center of the cluster , where the superscript (0) represents the initial iteration state, the subscript j represents the jth cluster, j∈{1,2,…,K′}; S4-1-3, assign data points: For each data point, calculate its distance to the center of each cluster and assign it to the cluster with the smallest distance; that is, calculate each angular velocity measurement value ω i With each cluster center The Euclidean distance of t Indicates the number of iterations and is assigned to the cluster with the smallest Euclidean distance middle: S4-1-4, Update cluster center: Update the center of each cluster, that is, use the average value of all data in the cluster as the new cluster center: S4-1-5, convergence judgment: repeat S4-1-3 and S4-1-4 until the cluster center no longer changes, the algorithm is considered to have converged, the cluster at this time is the final cluster, take the cluster center of the final cluster As initialization parameter ,Right now ; S4-1-6, calculate the covariance matrix of the final cluster , using the covariance matrix of the final cluster as the initial parameter Σ k0 ; S4-1-7, calculate the mixing weight: calculate the proportion of samples in the final cluster to the total samples as the initial mixing weight π k0 ; because θ k0 ={π k0 ，µ k0 ,Σ k0 , k=1, 2, …, K'}, θ 0 =( θ 1 , θ 2 ,... θ k’ ) T , after calculation, the initial parameter θ0 of θ is obtained, and the data initialization is completed.

5. The VI-GMM-based gyroscope temperature drift error compensation method according to claim 3, characterized in that: In S4-3, is the variational distribution of the mixed weight, set to Dirichlet distribution: ； in is a mixing weight that satisfies and , are the parameters of the Dirichlet distribution, ; is the variational distribution of the mean, assuming it is a normal distribution: ； in, is the mean of the kth Gaussian distribution (i.e., model expectation), is the mean parameter of the normal distribution, are the covariance matrix parameters of the normal distribution; is the variational distribution of the covariance, set to the inverse Wishart distribution: ； is the covariance matrix of the kth Gaussian distribution, is the degrees of freedom of the inverse Wishart distribution, , is the scale matrix parameter of the inverse Wishart distribution, is a positive definite matrix.

6. The VI-GMM-based gyroscope temperature drift error compensation method according to claim 3, characterized in that: In S4-4, the optimization of variational distribution parameters is specifically as follows: S4-4-1, Calculate the expectation of hidden variables: Calculate the hidden variables according to the current variational distribution parameters z i The posterior probability ; S4-4-2, update the mixed weight parameters : ； in, is the Dirichlet prior parameter, let , indicating that the initial assumption for the mixing weights is uniform distribution; S4-4-3, Update mean parameters and : ； ； in, and is the prior parameter of the mean, let is the sample mean, ， This indicates that the initial assumption about the mean parameter is weak; I is the identity matrix; S4-4-4, Update covariance parameters and : ； ； in, and is the inverse Wishart prior parameter, let , d is the angular velocity measurement data dimension, which is 3 here; , I is the identity matrix; and indicates that the initial assumption on the covariance matrix is ​​weak.

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