A method for modeling output errors of inertial microsystems

Abstract

The present invention proposes an inertial microsystem output error modeling method. The method is based on the correlation characteristics between the output error and output stability of the MEMS inertial instrument, establishes a polynomial model of the output error with respect to the output stability, adopts the least square method to identify the parameters of the model, and adopts the model significance analysis method to optimize the model. When the significance of the model and the significance of the model parameters both meet the theoretical value requirements, the output error model of the inertial microsystem is obtained. Different from the previous zero-bias modeling method based on factors such as temperature, the present invention enriches the methods and means of system error modeling, has a strong engineering practical value, can be used for output error modeling and compensation of MEMS gyroscopes and MEMS accelerometers, and can significantly improve the accuracy of the inertial microsystem.

Description

Technical Field

[0001] The invention relates to an inertial microsystem output error modeling method, and belongs to the field of inertial microsystem performance improvement. Background Art

[0002] Inertial microsystems mainly include two types of MEMS inertial instruments: MEMS gyroscopes and MEMS accelerometers. With the development of miniaturization and low-cost application requirements for various weapon platforms, MEMS inertial instruments are the core components for realizing the navigation and guidance of various guided munitions and drones. At present, micro inertial navigation systems have become a bottleneck in the development of various types of micro-aircraft. Error compensation of inertial microsystems is an important means to improve their accuracy. Therefore, many MEMS technology-leading research institutions have shifted their research focus to the research of MEMS inertial device error modeling and error compensation methods to improve the performance and application scope of MEMS inertial systems.

[0003] The static output error of an inertial microsystem refers to the additional amount of deviation from the true value contained in the output value when the system is in a stationary state. After each power-on startup of the inertial microsystem, there is a certain difference in the output error. This error is called zero bias in the zero input state and bias in the non-zero input state. The difference in output error at each power-on startup is usually characterized by a repeatability index. The output stability of an inertial instrument refers to the amount of change in the output within a specified time under the same test conditions, usually characterized by the standard deviation of the output. The output error and output stability of an inertial instrument will show a strong correlation when affected by the same factors. Therefore, a relationship model between output error and output stability can be established to achieve compensation for output error.

[0004] After the conventional error modeling and compensation method, the static output error of the inertial microsystem still has a certain residual error. For example, after the temperature modeling error compensation is usually adopted, the system still has errors caused by non-temperature factors. In order to further improve the measurement accuracy of the system, it is necessary to consider the errors caused by factors other than temperature. Summary of the invention

[0005] The technical problem solved by the present invention is to overcome the deficiencies of the prior art, provide an output error modeling method for an inertial microsystem, establish a relationship model between the output error and the output stability, and realize the compensation of the output error.

[0006] The technical solution of the present invention:

[0007] An inertial microsystem output error modeling method comprises the following steps:

[0008] (1) Carry out correlation analysis between static output error and output stability when the inertial microsystem is powered on, and calculate the correlation coefficient;

[0009] (2) When the correlation coefficient is greater than or equal to the threshold, a polynomial initial model of the static output error of the inertial microsystem with respect to output stability is established;

[0010] (3) Using the least squares method and sample data, the parameters of the established model are identified;

[0011] (4) Performing a significance analysis on the established model. If the significance analysis value is greater than the theoretical value, the currently established model and model parameters are credible, and the process goes to step (6). Otherwise, the process goes to step (5).

[0012] (5) Adjust the currently established model and repeat steps (3) and (4) to perform model parameter identification and significance analysis on the adjusted model until the model and its parameters are credible;

[0013] (6) Use sample data to analyze the effectiveness of the model. If it is effective, use the constructed model; if it is not effective, consider using other methods to build a model.

[0014] Furthermore, step (1) specifically includes:

[0015] (1.1) Let the static output error of the inertial microsystem when it is powered on for the i-th time be y i , output stability is i=1,2,...,N;

[0016] Where, N represents the number of power-on times. Each time the power is on, a set of real-time output errors can be obtained. The real-time output error refers to the value obtained by subtracting the ideal output value from the real-time output value of the inertial instrument. M represents the number of real-time output errors in each set. j represents the jth real-time output of the inertial microsystem when it is powered on for the i-th time, I λ represents the ideal output value when the power is turned on for the i-th time, and i represents the i-th power-on;

[0017] (1.2) Correlation coefficient between static output error and output stability ρ XY Calculated as follows:

[0018]

[0019] where X = [x1, x2, ..., x N ],Y=[y1,y2,…,y N ], COV(X,Y) represents the covariance of variables X and Y, Var(X) and Var(Y) represent the variance of variables X and Y respectively.

[0020] Furthermore, step (2) specifically includes:

[0021] (2.1) The threshold value is not less than 0.7.

[0022] (2.2) The initial polynomial model of the static output error of the inertial microsystem with respect to output stability is a first-order model where X = [x1, x2, …, x N ], K1 represents the first model parameter of the model, K0 represents the 0th model parameter of the model, is the jth static output error estimate.

[0023] Furthermore, in step (3), when the parameters of the established model are identified,

[0024] Furthermore, step (4) specifically includes:

[0025] (4.1) Perform significance analysis on the model:

[0026] Calculate the ratio of the inertial microsystem error to the random error to obtain the F statistic, which is calculated as follows:

[0027]

[0028] Among them, μ represents the regression sum of squares of the static output error estimate, and the calculation formula is: Q represents the sum of squares of static output errors, calculated as: k represents the number of parameters of the model, and n is the number of parameters in [y1,y2,…,y N ] is the number of samples selected, y j is the jth static output error among n sample data, is the jth static output error estimate calculated using the established inertial microsystem output error model, for Take the mean;

[0029] If the calculated F value is greater than the theoretical value The model is credible; the theoretical value of F Obtained by querying the F distribution table;

[0030] (4.2) Perform significance analysis on model parameters:

[0031] The method for significance analysis of the rth model parameter is:

[0032] Calculate the t distribution value of the rth model parameter, the calculation formula is K r is the rth model parameter of the model, σ r is the standard deviation of the rth model parameter;

[0033] Assume that the significance level is a, and look up the t distribution table to get the t(nk-1) distribution value. If the calculated t distribution value is greater than the distribution value found in the t distribution table, then the model parameters are considered to be reasonable at the significance level a.

[0034] Furthermore, step (5) specifically includes:

[0035] If the currently established model is an R-order model, it is adjusted to an R+1-order model. The R-order model is in the form of where X = [x1, x2, …, x N ], K1, K2...K R represents the 1st, 2nd,...Rth model parameters, K0 represents the 0th model parameter, which is a constant term.

[0036] Furthermore, step (6) specifically includes:

[0037] Use sample data to verify the validity of the model. Substitute new sample data into the established model. The new sample data is a set of sample data selected to be different from the modeling samples. Use the established model to obtain the static output error estimate. The static output error Y is deducted from the error estimate Y' to obtain the residual value after error compensation. The ratio of the two norms of Y-Y' and Y is calculated. If p<1, it means that the model is reasonable and effective; if p≥1, it means that the model is invalid and it is necessary to consider applying other modeling methods for error modeling and compensation.

[0038] Compared with the prior art, the present invention has the following advantages:

[0039] (1) Aiming at the problem of poor output error repeatability of MEMS inertial instruments after each power-on, the present invention proposes a new error modeling method. For the first time, the output stability of the system is taken as a system characteristic index characterized by the influence of a complex factor. The independent variable of the error model is selected to establish a relationship model between the output error and the output stability. The model is optimized by using a model significance analysis method. The model is not limited to the errors caused by single influencing factors such as temperature and force. The constructed model has higher accuracy and can achieve effective compensation of the output error.

[0040] (2) The present invention selects output stability as the independent variable of the error model to model the output error of the inertial microsystem. This is different from the previous zero-bias modeling method based on factors such as temperature and force. It reduces the test environment requirements for modeling, enriches the methods and means of system output error modeling, and has strong engineering practical value.

[0041] (3) The inertial microsystem error modeling method proposed in this invention is a beneficial supplement to the conventional modeling method. Aiming at the error residual existing in the system, the proposed modeling method is used to further perform error modeling and compensation, which can effectively improve the accuracy level of the system. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 Flowchart for modeling the output errors of inertial microsystems;

[0043] Figure 2 Validation plot of the output error model. DETAILED DESCRIPTION

[0044] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments:

[0045] The present invention provides a modeling method for error compensation of an inertial microsystem, thereby improving the accuracy level of the inertial microsystem.

[0046] Figure 1 A flow chart for modeling the output error of an inertial microsystem is provided, including the following steps:

[0047] (1) Carry out the correlation analysis between the static output error and output stability of the inertial microsystem when it is powered on, and calculate the correlation coefficient.

[0048] The specific process includes:

[0049] (1.1) Let the static output error of the inertial microsystem when it is powered on for the i-th time be y i , output stability is i=1,2,...,N;

[0050] Where, N represents the number of power-on times. Each time the power is on, a set of real-time output errors can be obtained. The real-time output error refers to the value obtained by subtracting the ideal output value from the real-time output value of the inertial instrument. M represents the number of real-time output errors in each set. j represents the jth real-time output of the inertial microsystem when it is powered on for the i-th time, I λ is the ideal output value when the power is turned on for the i-th time, i represents the i-th power-on;

[0051] (1.2) Correlation coefficient between static output error and output stability ρ XY Calculated as follows:

[0052]

[0053] where X = [x1, x2, …, x N ],Y=[y1,y2,…,y N], COV(X,Y) represents the covariance of variables X and Y, Var(X) and Var(Y) represent the variance of variables X and Y respectively.

[0054] (2) When the correlation coefficient is greater than or equal to the threshold, a polynomial initial model of the static output error of the inertial microsystem with respect to output stability is established.

[0055] The specific process includes:

[0056] (2.1) The threshold value is not less than 0.7.

[0057] (2.2) The initial polynomial model of the static output error of the inertial microsystem with respect to output stability is a first-order model where X = [x1, x2, …, x N ], K1 represents the first model parameter of the model, K0 represents the 0th model parameter of the model, is the jth static output error estimate.

[0058] (3) Using the least squares method and sample data, the parameters of the established model are identified.

[0059] (4) Perform a significance analysis on the established model. If the significance analysis value is greater than the theoretical value, the currently established model and model parameters are credible and proceed to step (6). Otherwise, proceed to step (5).

[0060] (4.1) Perform significance analysis on the model:

[0061] Calculate the ratio of the inertial microsystem error to the random error to obtain the F statistic, which is calculated as follows:

[0062]

[0063] Among them, μ represents the regression sum of squares of the static output error estimate, and the calculation formula is: Q represents the sum of squares of static output errors, calculated as: k represents the number of parameters of the model, and n is the number of parameters in [y1,y2,...,y N ] is the number of samples selected, y j is the jth static output error among n sample data, is the jth static output error estimate calculated using the established inertial microsystem output error model, for Take the mean;

[0064] If the calculated F value is greater than the theoretical value The model is credible; the theoretical value of F Obtained by querying the F distribution table;

[0065] (4.2) Perform significance analysis on model parameters:

[0066] The method for significance analysis of the rth model parameter is:

[0067] Calculate the t distribution value of the rth model parameter, the calculation formula is K r is the rth model parameter of the model, σ r is the standard deviation of the rth model parameter.

[0068] Assume that the significance level is a, and look up the t distribution table to get the t(nk-1) distribution value. If the calculated t distribution value is greater than the distribution value found in the table, it is considered that the model parameters are reasonable at the significance level a.

[0069] (5) Adjust the currently established model and repeat steps (3) and (4) to perform model parameter identification and significance analysis on the adjusted model until the model and its parameters are credible;

[0070] If the currently established model is an R-order model, it is adjusted to an R+1-order model. The R-order model is in the form of where X = [x1, x2, …, x N ], K1, K2...K R represents the 1st, 2nd,...Rth model parameters, K0 represents the 0th model parameter, which is a constant term.

[0071] (6) Use sample data to analyze the effectiveness of the model. If it is effective, use the constructed model; if it is not effective, consider using other methods to build a model.

[0072] Use sample data to verify the validity of the model. Substitute new sample data into the established model. The new sample data is a set of sample data selected to be different from the modeling samples. Use the established model to obtain the static output error estimate. The static output error Y is deducted from the error estimate Y' to obtain the residual value after error compensation. The ratio of the two norms of Y-Y' and Y is calculated. If p<1, it means that the model is reasonable and effective; if p≥1, it means that the model is invalid and it is necessary to consider applying other modeling methods for error modeling and compensation.

[0073] Example:

[0074] (1) The output error of the MEMS gyroscope is obtained by sampling data 6 minutes after the stable output, a total of 194 times, 72,000 data each time. The output error is obtained by calculating the mean of the output and deducting the input value, and the output stability is obtained by calculating the standard deviation of the output. The correlation analysis between the static output error and output stability of the inertial microsystem MEMS gyroscope is carried out, and the correlation coefficient is calculated to be 0.865;

[0075] (2) Taking the threshold as 0.7 and the correlation coefficient as 0.865, which is greater than the threshold, the output error and output stability are modeled;

[0076] (3) Establish a polynomial initial model of the inertial instrument output error with respect to output stability. The initial model selects a first-order polynomial K1 is the coefficient of the first-order term of the model, and K0 is the constant term of the model;

[0077] (4) The least square method was used to identify the model parameters using 114 modeling sample data. The calculated model parameters were K1 = 36.6164, K0 = -178.1707;

[0078] (5) The rationality of the model and its parameters is determined through model significance analysis and model parameter significance analysis. The F distribution value of the model is calculated to be 296.94, and the significance level is 0.05. The theoretical reference value is (2,114) is 3.07, and the F value is greater than the theoretical value The model is credible. After calculating the significant t distribution values ​​of the model parameters K1 and K0, they are 24.3697 and 29.9571 respectively. Taking the significance level of 0.05, the t distribution table shows that the t(114-2-1) distribution value is 1.66. The t distribution value is greater than the distribution value found in the table. The model parameters are reasonable at the significance level of 0.05.

[0079] (6) Select a new set of sample data that is different from the modeling sample and conduct model validity analysis. Figure 2 As shown in the figure, 80 new sample data are used to verify the validity of the model. Substituting the sample data into the polynomial, the p value is calculated to be 0.2515, indicating that the model is reasonable and effective.

[0080] The present invention proposes an inertial microsystem output error modeling method. The method is based on the correlation characteristics between the output error and output stability of the MEMS inertial instrument, establishes a polynomial model of the output error with respect to the output stability, adopts the least square method to identify the parameters of the model, and adopts the model significance analysis method to optimize the model. When the significance of the model and the significance of the model parameters both meet the theoretical value requirements, the output error model of the inertial microsystem is obtained. Different from the previous zero-bias modeling method based on factors such as temperature, the present invention enriches the methods and means of system error modeling, has a strong engineering practical value, can be used for output error modeling and compensation of MEMS gyroscopes and MEMS accelerometers, and can significantly improve the accuracy of the inertial microsystem.

[0081] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

Claims

1. A method for modeling output errors of an inertial microsystem, characterized in that The steps include: (1) Carry out correlation analysis between static output error and output stability when the inertial microsystem is powered on, and calculate the correlation coefficient; including: (1.1) Let the static output error of the inertial microsystem when it is powered on for the i-th time be y i , output stability is x i , i=1,2,...,N; Where, N represents the number of power-on times, each time a set of real-time output errors can be obtained, M represents the number of each set of real-time output errors, and I j represents the jth real-time output of the inertial microsystem when it is powered on for the i-th time, I λ is the ideal output value when the power is turned on for the i-th time, i represents the i-th power-on; (1.2) Correlation coefficient between static output error and output stability ρ XY Calculated as follows: where X = [x1, x2, ..., x N ],Y=[y1,y2,...,y N ], COV(X,Y) represents the covariance of variables X and Y, Var(X) and Var(Y) represent the variance of variables X and Y respectively; (2) When the correlation coefficient is greater than or equal to the threshold, a polynomial initial model of the static output error of the inertial microsystem with respect to output stability is established; (3) Using the least squares method and sample data, the parameters of the established model are identified; (4) Perform a significance analysis on the established model. If the significance analysis value is greater than the theoretical value, the currently established model and model parameters are credible. Otherwise, proceed to step (5); (5) Adjust the currently established model and repeat steps (3) and (4) to perform parameter identification and significance analysis on the adjusted model until the model and its parameters are credible.

2. The inertial microsystem output error modeling method according to claim 1, characterized in that: The real-time output error in step (1.1) refers to the value obtained by subtracting the ideal output value from the real-time output value of the inertial instrument.

3. The inertial microsystem output error modeling method according to claim 1, characterized in that: The threshold in step (2) is set to a value not less than 0.

7.

4. The method for modeling output errors of an inertial microsystem according to claim 1, characterized in that: In the step (2), the polynomial initial model of the static output error of the inertial microsystem with respect to the output stability is a first-order model where X = [x1, x2, ..., x N ], K1 represents the first model parameter of the model, K0 represents the 0th model parameter of the model, is the estimated value of the static output error at the i-th power-on.

5. The inertial microsystem output error modeling method according to claim 4, characterized in that: In the step (3), when the parameters of the established model are identified, 6. The inertial microsystem output error modeling method according to claim 4, characterized in that: In step (4), the significance analysis is performed as follows: (4.1) Perform significance analysis on the model by: Calculate the ratio of the inertial microsystem error to the random error to obtain the F statistic, which is calculated as follows: Among them, μ represents the regression sum of squares of the static output error estimate, and the calculation formula is: Q represents the sum of squares of static output errors, calculated as: k represents the number of parameters of the model, and n is the number of parameters in [y1,y2,...,y N ] is the number of samples selected, y j is the jth static output error among n sample data, is the jth static output error estimate calculated using the established inertial microsystem output error model, for Take the mean; If the calculated F value is greater than the theoretical value The model is credible; the theoretical value of F Obtained by querying the F distribution table; (4.2) Perform significance analysis on model parameters: The method for significance analysis of the rth model parameter is: Calculate the t distribution value of the rth model parameter, the calculation formula is K r is the rth model parameter of the model, σ r is the standard deviation of the rth model parameter; Assume the significance level is a, look up the t distribution table to obtain the t(nk-1) distribution value. If the calculated t distribution value is greater than the distribution value found in the t distribution table, then the model parameters are considered reasonable at the significance level a.

7. The method for modeling output errors of an inertial microsystem according to claim 1, characterized in that: In step (5), if the currently established model is an R-order model, it is adjusted to an R+1-order model. The R-order model is in the form of Where X=[x1,x2,...,x N ], K1, K2...K R represents the 1st, 2nd,...Rth model parameters, K0 represents the 0th model parameter, which is a constant term.

8. The method for modeling output errors of an inertial microsystem according to claim 1, characterized in that: The validity of the model is analyzed using sample data. If it is valid, the constructed model is adopted. If it is not valid, other methods are used to build a model.

9. The method for modeling output errors of an inertial microsystem according to claim 8, characterized in that: The way to analyze the effectiveness of the model using sample data is as follows: Substitute new sample data into the constructed model, where the new sample data is different from the sample data used in parameter identification, and use the constructed model to obtain a static output error estimate. Static output error Y minus error estimate Get the residual value after error compensation and calculate The ratio of the two norms of Y If p<1, it means the model is reasonable and effective; if p≥1, it means the model is invalid.

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