VI-GMM Based Gyroscope Temperature Drift Error Compensation Method

Abstract

The present invention discloses a gyroscope temperature drift error compensation method based on VI-GMM, which relates to the technical field of gyroscope detection and includes the following steps: Step S1, collect data on temperature and the output angular velocity of the three axes of the gyroscope; Step S2, preprocess the collected data; Step S3, establish a three-dimensional joint Gaussian mixture model for the gyroscope temperature drift error based on the gyroscope three-axis coupling characteristics; Step S4, derive the parameters in the model through the variational inference algorithm (VI), including the weights of each Gaussian distribution π k 、 model expectation µ k , covariance matrix Σ k ; Step S5, use the temperature drift error model in Step S3 to calculate the temperature drift error generated when the gyroscope is actually used, and then subtract the corresponding temperature drift error from the output of the gyroscope to obtain the compensated output data. The error compensation method of the present invention can effectively correct the gyroscope temperature drift error and provide a more accurate error compensation method.

Description

Technical Field

[0001] The present invention relates to the technical field of gyroscope detection, and particularly to a method for compensating gyroscope temperature drift error 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 the fields of navigation, aviation, aerospace, electronic products, robotics, etc. The sensitive structure and signal processing circuit of gyroscopes are very sensitive to temperature changes. Environmental temperature changes and internal heat generation will cause zero drift and scale factor changes in gyroscopes, thus affecting the measurement accuracy.

[0003] In order to improve the measurement accuracy and stability of gyroscopes, it is necessary to compensate for the temperature drift of gyroscopes. However, traditional compensation methods usually adopt 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 performance and accuracy of temperature drift, it is necessary to develop a method that can estimate and compensate for 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 average value method is used to perform linear fitting on temperature and zero angular velocity to establish an error model (Reference: Institute of Software, Chinese Academy of Sciences. A method for compensating gyroscope temperature drift: CN 201110104532.6 [P]. 2012-11-28.), or the Kalman filter is used to establish a zero-bias temperature nth-order error model (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:

[0005] First, using the average value to perform linear fitting on errors cannot adapt to complex data distributions. When the data distribution is complex and there are multiple modes, the average value method may not be able to accurately capture the true characteristics of the data. Moreover, the fitted straight line cannot directly quantify the uncertain relationship between data points and the model.

[0006] Second, the Kalman filter is more suitable for linear or approximately linear systems, and has limited effect on non-linear error modeling and cannot directly handle multi-modal errors. Moreover, its performance depends to a large extent on the accuracy of the initial parameters, and the selection of the initial state estimate and noise covariance has a greater impact on the filtering effect. In addition, in the scenario of multi-sensor data fusion, the Kalman filter usually requires complex joint modeling and state estimation of the error models of each sensor, and the process is relatively cumbersome. Summary of the Invention

[0007] To solve the above technical problems, the present invention provides a method for compensating the temperature drift error of a gyroscope based on VI-GMM, which can effectively correct the temperature drift error of the gyroscope and provide a more accurate error compensation method.

[0008] To solve the above technical problems, the technical solution proposed by the present invention is as follows:

[0009] A method for compensating the temperature drift error of a gyroscope based on VI-GMM includes the following steps:

[0010] Step S1: Collect data on temperature and the output angular velocity of the three axes of the gyroscope within the operating temperature range of the triaxial gyroscope sensor.

[0011] Step S2: Preprocess the collected data.

[0012] Step S3: Establish a three-dimensional joint Gaussian mixture model for the temperature drift error of the gyroscope based on the triaxial coupling characteristics of the gyroscope.

[0013] The temperature drift error model is:

[0014] ;

[0015] Where: ω is the measured value of the angular velocity of the gyroscope; represents the probability density function of the k th Gaussian sub-model with respect to the measured value of the angular velocity ω , K is the number of single Gaussian models included in the Gaussian mixture model of the temperature drift error, K is a hyperparameter; is the weight of the k th Gaussian distribution, satisfying 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;

[0016] Step S4. Derive the parameters in the model through the variational inference algorithm, including the weights of each Gaussian distribution π k 、 Model expectation µ k , covariance matrix Σ k ;

[0017] Step S5. Use the temperature drift error model in Step S3 to calculate the temperature drift error generated by the gyroscope during actual use, and then subtract the corresponding temperature drift error from the output of the gyroscope to obtain the compensated output data.

[0018] As a further improvement of the above technical solution:

[0019] Preferably, in the said Step S3 represents the probability density function of the k -th Gaussian sub-model with respect to the angular velocity measurement value ω :

[0020] ;

[0021] wherein ω is the angular velocity measurement value, which is a column vector with a dimension of 3 and contains the three angular velocity data of the gyroscope x, y, z axis:

[0022] ;

[0023] wherein ω x represents the angular velocity measurement value in the direction of the x axis of the gyroscope, ω y represents the angular velocity measurement value in the direction of the y axis of the gyroscope, ω z represents the angular velocity measurement value in the direction of the z axis of the gyroscope.

[0024] Preferably, in the said Step S4, the variational inference algorithm derives the parameters in the model, including the following steps:

[0025] S4-1. Initialization: Use the K-means clustering algorithm to cluster the samples, and use the cluster center of the final cluster as µ k0 , use the covariance matrix of the final cluster as Σ k0 , and take the proportion of the final cluster samples in the total number of samples as π k0 ;

[0026] S4-2, Introduce latent variables: Introduce latent variables z i , denoted as ω i belonging to the exponential variable of the k th distribution: P(z i =k）= π k ;

[0027] Among them, z i ∈ { 1，2，...，K}; The temperature drift error model is rewritten as:

[0028] ;

[0029] S4-3, Define variational distribution: Let the variational posterior distribution q(θ) be in a factorized form:

[0030] ;

[0031] Among them, represents the variational distribution of the mixing weights, represents the variational distribution of the means, represents the variational distribution of the covariance;

[0032] S4-4, Optimize variational parameters: Optimize the variational distribution parameters by maximizing the evidence lower bound;

[0033] S4-5, Confirm the optimal solution: Repeat step S4-4 until the change in the variational distribution parameters Ф is less than the threshold to obtain the final variational distribution parameters;

[0034] S4-6, Calculate the final model parameters: Calculate the final parameters of the Gaussian mixture model according to the final variational distribution parameters optimized by variational inference.

[0035] Preferably, when the K-means clustering algorithm clusters the samples, the steps of initializing the data are:

[0036] S4-1-1, Determine the value of K': Determine the number of clusters K' to be created. The number of clusters is numerically equal to the number K of single Gaussian models in the Gaussian mixture model, i.e., K' = K;

[0037] S4-1-2, Initialize the cluster centers: Randomly select K' data points as the initial centers of the clusters , where the superscript (0) represents the initial iteration state and the subscript j represents the jth cluster, j ∈ {1, 2,..., K'};

[0038] S4-1-3, Assign data points: For each data point, calculate its distance to each cluster center and assign it to the cluster with the minimum distance; that is, calculate each angular velocity measurement ω i from each cluster center for the Euclidean distance, where t represents the number of iterations, and assign it to the cluster with the minimum Euclidean distance as follows:

[0039] S4-1-4, Update cluster centers: Update the center of each cluster, that is, take the average value of all data in the cluster as the new cluster center:

[0040] S4-1-5, Convergence judgment: Repeat S4-1-3 and S4-1-4 until the cluster centers no longer change, then consider the algorithm to converge. At this time, the clusters are the final clusters, and take the cluster centers of the final clusters as the initialization parameters ; that is ;

[0041] S4-1-6, Calculate the covariance matrix of the final clusters , and take the covariance matrix of the final clusters as Σ k0 in the initial parameters;

[0042] S4-1-7, Calculate the mixing weights: Calculate the proportion of the samples in the final clusters to the total samples as the initial mixing weights π k0 ;

[0043] Since θ k0 ={π k0 ，µ k0 ,Σ k0 ,k = 1, 2, …, K’}, θ 0 =( θ 1 , θ 2 ,... θ k’ ) T , and after calculation, obtain the initial parameter θ0 of θ to complete the data initialization.

[0044] Preferably, in the said S4-3, q(π k ) is the variational distribution of the mixing weights, and is set as the Dirichlet distribution:

[0045] ;

[0046] where is the mixing weight, satisfying and , is the parameter of the Dirichlet distribution, ;

[0047] q(μ k ) is the variational distribution of the mean, assumed to be a normal distribution:

[0048] ;

[0049] where is the mean of the k-th Gaussian distribution (i.e., the model expectation), is the mean parameter of the normal distribution, is the covariance matrix parameter of the normal distribution;

[0050] q(Σ k ) is the variational distribution of the covariance, assumed to be an inverse Wishart distribution:

[0051] ;

[0052] is the covariance matrix of the k-th Gaussian distribution, is the degree of freedom of the inverse Wishart distribution, , is the scale matrix parameter of the inverse Wishart distribution, is a positive definite matrix.

[0053] Preferably, in the S4-4, the specific optimization of the variational distribution parameters is as follows:

[0054] S4-4-1, calculating the expectation of the latent variable: According to the current variational distribution parameters, calculate the posterior probability z i of the latent variable ;

[0055] S4-4-2, updating the mixing weight parameter :

[0056] ;

[0057] where, is the Dirichlet prior parameter, assuming , indicating that the initial assumption for the mixing weight is a uniform distribution;

[0058] S4-4-3, updating the mean parameters and :

[0059] ;

[0060] ;

[0061] Among them, and are the prior parameters of the mean. Let be the sample mean, ， indicating a weak initial assumption about the mean parameter; I is the identity matrix;

[0062] S4-4-4, update the covariance parameters and :

[0063] ;

[0064] ;

[0065] Among them, and are the inverse Wishart prior parameters. Let , d be the dimension of the angular velocity measurement data, which is taken as 3 here; , I is the identity matrix; indicating a weak initial assumption about the covariance matrix.

[0066] The VI-GMM-based gyroscope temperature drift error compensation method provided by the present invention has the following advantages compared with the prior art:

[0067] (1) The VI-GMM-based gyroscope temperature drift error compensation method of the present invention can flexibly adapt to the multi-modal distribution characteristics of data. Even if there are multiple different temperature drift patterns in the data, GMM can better model it. The VI-GMM-based gyroscope temperature drift error compensation method of the present invention assigns probabilities belonging to each Gaussian component to each data point, provides a clear clustering explanation, and can quantify the uncertainty of data points under different temperature drift patterns.

[0068] (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 captures the non-linear characteristics in the gyroscope temperature drift error, and provides a more accurate error model; in addition, in the multi-sensor data fusion scenario, it can flexibly use GMM to fuse the error distributions of different sensors, and comprehensively consider the error characteristics of each sensor by adjusting the weights and parameters of the mixture components. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1It is the flowchart of the error compensation method of the present invention.

[0070] Figure 2 It is the flowchart for establishing the error model parameters of the present invention. Detailed implementation manners

[0071] The following details the specific implementation manners of the present invention. It should be understood that the specific implementation manners described herein are only for explaining and illustrating the present invention, and are not used to limit the present invention.

[0072] When the three-axis gyroscope is completely stationary, the speeds on the three axes are theoretically zero. However, in reality, 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 gyroscope temperature drift error compensation method based on VI-GMM of the present invention compensates for the temperature drift of the gyroscope, thereby minimizing the temperature drift error of the gyroscope.

[0073] As Figure 1 shown, the gyroscope temperature drift error compensation method based on VI-GMM of the present invention includes the following steps:

[0074] Step S1, within the operating temperature range of the three-axis gyroscope sensor, collect the data of temperature and the output angular velocities of the three axes of the gyroscope.

[0075] Construct a curve of the gyroscope zero point varying with temperature. In the state where the gyroscope is stably stationary and only the temperature changes, collect the temperature data and the angular velocity data in the three-axis directions, and multiple measurements are required to collect the data.

[0076] Step S2, preprocess the collected data.

[0077] First, convert the units of the data. The unit of temperature is degrees Celsius (°C), and the unit of angular velocity data is degrees per second (° / s) or radians per second (rad / s); then remove the outliers, with the assistance of the standard deviation, identify and remove the data values with obvious anomalies; if there are missing values in the data, use the interpolation method to fill in the missing values to ensure the integrity of the data; finally, use the Kalman filter to remove the noise and uncertainty of the data.

[0078] After the data is preprocessed, stable data of the gyroscope zero point output value with respect to temperature is obtained, forming a variation curve.

[0079] Step S3, use the Gaussian mixture model (GMM) to construct a temperature drift error model.

[0080] The temperature drift modeling formula is:

[0081] ;

[0082] Among them, ω is the angular velocity measurement value of the gyroscope; K is the number of single Gaussian models included in the Gaussian mixture model for temperature drift error, K which is a hyperparameter; is the weight of the k th Gaussian distribution, satisfying and 0；µ k 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 ={π k ，µ 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.

[0083] represents the probability density function of the k th Gaussian sub-model with respect to the angular velocity measurement value ω :

[0084] ;

[0085] Among them, ω is the angular velocity measurement value, which is a column vector with a dimension of 3 and contains three angular velocity data of the x, y, z axis of the gyroscope:

[0086] ;

[0087] Among them, ω x represents the angular velocity measurement value in the x axis direction of the gyroscope, ω y represents the angular velocity measurement value in the y axis direction of the gyroscope, ω z represents the angular velocity measurement value in the z axis direction of the gyroscope.

[0088] Step S4: Derive the parameters in the model through the variational inference algorithm, including the weights of each Gaussian distribution 、 Model expectation , covariance matrix .

[0089] After the modeling in step S3 is completed, in order to obtain the accurate parameters of the temperature drift error model simply and quickly, the present invention uses the variational inference algorithm to calculate the parameters, and the calculation process is as Figure 2 .

[0090] S4-1: Initialization: Use the K-means clustering algorithm to cluster the samples, and use the cluster centers of the final clusters as µ k0 , and use the covariance matrix of the final clusters as Σ k0 , and take the proportion of the final cluster samples in the total number of samples as π k0 .

[0091] Furthermore, the steps for initializing the data of the K-means clustering algorithm are as follows:

[0092] S4-1-1: Determine the value of K': Determine the number of clusters K' to be created. The number of clusters is numerically equal to the number K of single Gaussian models in the Gaussian mixture model, that is, K' = K.

[0093] S4-1-2: Initialize the cluster centers: Randomly select K' data points as the initial centers of the clusters , where the superscript (0) represents the initial iteration state, and the subscript j represents the jth cluster, j ∈ {1, 2,..., K'}.

[0094] S4-1-3: Assign data points: For each data point, calculate its distance from each cluster center and assign it to the cluster with the minimum distance. That is, calculate the Euclidean distance between each angular velocity measurement value ω i and each cluster center , where t represents the number of iterations, and assign it to the cluster with the minimum Euclidean distance :

[0095] ;

[0096] Among them, represents the Euclidean distance, is the center of the t th iteration of the k th cluster.

[0097] S4-1-4: Update the cluster centers: Update the centers of each cluster, that is, take the average value of all the data in the cluster as the new cluster center:

[0098] ;

[0099] Among them, represents the number of data points in

[0100] S4-1-5, Convergence judgment: Repeat S4-1-3 and S4-1-4 until the cluster centers no longer change or when, it is considered that the algorithm converges, where ε is a very small positive number and is valued according to the actual situation. The clusters at this time are the final clusters, and the cluster centers of the final clusters are used as the initialization parameters , that is ;

[0101] S4-1-6, Calculate the covariance matrix of the final clusters :

[0102] ;

[0103] Take the covariance matrix of the final clusters as in the initial parameters Σ k0 : .

[0104] S4-1-7, Calculate the mixing weights: Calculate the proportion of the samples in the final clusters to the total samples as the initial mixing weights π k0 :

[0105] ; Among them, N is the total number of samples

[0106] Since θ k0 ={π k0 ，µ k0 ,Σ k0 ,k = 1, 2, …, K’}, θ 0 =( θ 1 , θ 2 ,... θ k’ ) T , the initial parameter θ0 of θ can be obtained through the above steps to complete data initialization

[0107] S4-2, Introduce latent variables

[0108] Since each angular velocity measurement value ω iIt is uncertain which Gaussian distribution it belongs to. Therefore, when using the variational inference algorithm to calculate the model parameters, latent variables need to be introduced z i , used to represent ω i the indicator variable belonging to the k th distribution:

[0109] P(z i =k）=π k ； Among them, z i ∈ { 1，2，...，K}.

[0110] Then the joint probability in the temperature drift error model can be written as:

[0111] ;

[0112] The temperature drift error model is rewritten as:

[0113] .

[0114] S4-3, define the variational distribution.

[0115] Assume that the variational posterior distribution is in a factorized form (mean field approximation):

[0116] ;

[0117] Among them, represents the variational distribution of the mixing weights, represents the variational distribution of the means, represents the variational distribution of the covariances.

[0118] is the variational distribution of the mixing weights and is assumed to be a Dirichlet distribution:

[0119] ;

[0120] Among them are the mixing weights, satisfying and . are the parameters of the Dirichlet distribution, .

[0121] The probability density function of

[0122] is:

[0123] where is the multivariate beta function:

[0124] ;

[0125] where Γ represents the Gamma function.

[0126] is the variational distribution of the mean, assumed to be a normal distribution:

[0127] ;

[0128] where is the mean of the k-th Gaussian distribution (i.e., the model expectation), is the mean parameter of the normal distribution, is the covariance matrix parameter of the normal distribution.

[0129] The probability density function of

[0130] ;

[0131] where, d is the data dimension, d = 3.

[0132] where the mean of the k-th Gaussian distribution, is the mean parameter of the normal distribution, is the covariance matrix parameter of the normal distribution.

[0133] q(Σ k ) is the variational distribution of the covariance, assumed to be an inverse Wishart distribution:

[0134] ;

[0135] is the covariance matrix of the k-th 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.

[0136] q(Σ k )'s probability density function is:

[0137] ;

[0138] where is the multivariate Gamma function:

[0139] 。

[0140] S4-4. Optimize variational parameters.

[0141] Optimize the variational distribution parameters by maximizing the evidence lower bound (ELBO) as follows:

[0142] S4-4-1. Calculate the expectation of the latent variable: Calculate the posterior probability of the latent variable z i according to the current variational distribution parameters:

[0143] ;

[0144] where is the angular velocity measurement ω i is the posterior probability (i.e., responsibility) belonging to the k-th distribution, , ; 。

[0145] S4-4-2. Update the mixture weight parameter :

[0146] ;

[0147] where is the Dirichlet prior parameter. Let , and the value of

[0148] S4-4-3. Update the mean parameters and :

[0149] ;

[0150] 。

[0151] where and are the prior parameters of the mean. Let be the sample mean, ， and and the value of I is the identity matrix.

[0152] S4-4-4. Update the covariance parameters and :

[0153] ;

[0154] 。

[0155] Among them, and are the inverse Wishart prior parameters. Let , d be the dimension of the angular velocity measurement data, which is taken as 3 here; , I is the identity matrix. and The values of indicate a weak initial assumption about the covariance matrix.

[0156] S4-5, confirm the optimal solution.

[0157] Repeat step S4-4 until the change in the variational distribution parameter Ф is less than the threshold, that is, When, the final variational distribution parameters , , , and are obtained.

[0158] Among them is the variational distribution parameter at the t-th iteration, represents the Euclidean distance of the parameter vector, takes 10 -5 。

[0159] S4-6, calculate the final model parameters: According to the final variational distribution parameters , , , and optimized by variational inference, calculate the final parameters θ k ={ ， ,Σ k ，k=1， 2，…，K}。

[0160] Furthermore, the steps for calculating the final model parameters are as follows:

[0161] 4-6-1, calculate the mixing weights :

[0162] ;

[0163] 4-6-2, calculate the mean :

[0164] ;

[0165] 4 - 6 - 3, calculate the covariance :

[0166] ;

[0167] wherein, d is the dimension of the angular velocity measurement data, taking d=3 .

[0168] Step S5, use the temperature drift error model in Step S3 to calculate the temperature drift error generated by the gyroscope during actual use, and then subtract the corresponding temperature drift error from the output of the gyroscope to obtain the compensated output data.

[0169] The above embodiments are only preferred embodiments of the present invention and do not impose any form of limitation on the present invention. Although the present invention has been disclosed above with preferred embodiments, it is not intended to limit the present invention. Therefore, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from 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 the 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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