MEMS sensor high-bandwidth disturbance control method based on truncation distribution

Abstract

The invention discloses an MEMS sensor high-bandwidth disturbance control method based on truncated distribution, and the method comprises the following steps: initializing a weight coefficient, and calculating a minimum variance fusion corresponding weight coefficient through a noise variance and a disturbance variance; selecting a sliding window length, performing expectation estimation on the initial fusion data, calculating an estimation error in each window length, and selecting a sliding window with a small estimation error as a final estimation expectation; according to the judgment conditions of the disturbance environment and the normal environment, truncation fusion intervals are calculated respectively; setting a judgment criterion, and when an estimation error is smaller than a set confidence coefficient, selecting an initialization weight coefficient; when the initialization fusion is located in the clustering interval, selecting initialization weight coefficient fusion; and when the initial fusion is located outside the clustering interval, reconstructing a weight coefficient based on a difference value of expectation and initial fusion, and carrying out fusion. According to the method for controlling the high-bandwidth disturbance of the MEMS sensor based on the truncated distribution, the precision maintaining capability of the MEMS sensor in a severe environment is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of micro-electromechanical systems, and in particular to a high-bandwidth disturbance control method for a MEMS sensor based on truncated distribution. Background Art

[0002] MEMS sensors, due to their numerous advantages such as light weight, compact size, mass production, and low cost, hold broad application prospects in fields such as industrial robotics, autonomous driving, and intelligent manufacturing. However, the harsh environments of weaponry and heavy machinery, such as the high overloads generated during operation, can severely reduce the accuracy of MEMS sensors, limiting their application in high-end applications. MEMS sensor arrays can effectively address these issues, but mainstream methods such as state estimation reduce gyroscope bandwidth, limiting their application in dynamic scenarios. Therefore, improving the environmental adaptability of MEMS sensors within bandwidth constraints to maintain accuracy in harsh environments is crucial.

[0003] Weighted fusion is an effective method for improving the accuracy of MEMS sensors while maintaining bandwidth. In existing technologies, the average weighted fusion method is used to fuse multiple MEMS sensor measurements, improving the accuracy of MEMS gyroscopes. The minimum variance fusion method is used to fuse MEMS gyroscopes, minimizing the fusion variance of the MEMS sensors and effectively improving their accuracy. A conflict-consistent measurement fusion method performs variable weight fusion based on conflict metrics on low-cost MEMS sensor groups and high-vibration MEMS sensor groups, followed by minimum variance fusion of the two fused data, effectively improving the accuracy of MEMS sensors under vibration. A desired clustering interval variable weight fusion method breaks through the accuracy limit of traditional constant weight fusion methods.

[0004] The above method can effectively improve the accuracy of MEMS sensors in harsh environments. However, it cannot maintain accuracy in harsh environments where gyro precision attenuation is severe. A major reason is that the accuracy of constant weight coefficient fusion is a multivariate linear function of the weight coefficient (weight coefficient normalization limit), which inevitably has a minimum value, resulting in an accuracy limit. This accuracy limit is also limited by the number of sensors, typically 1 / 2 times the number of sensors. This means that the anti-interference performance of MEMS sensors conflicts with the advantages of low cost and small size. Another major reason is that although the expected cluster interval variable weight fusion method has exceeded the accuracy limit, its cluster interval is a function of the maximum difference in measurement. While cluster fusion can improve accuracy, it has not been theoretically proven that its improvement can achieve accuracy maintenance.

[0005] Therefore, in order to solve the above problems, the present invention proposes a high-bandwidth disturbance control method for MEMS sensors based on truncated distribution. This method first proves that the variance of the Gaussian truncated distribution can be equivalent to a Gaussian distribution with a smaller variance; further, by initializing the minimum variance of the weight coefficient and estimating the expectation of the fused signal, a Gaussian truncation interval is designed with the expectation as the center. By fusing the signals that do not belong to the interval into the interval, the Gaussian disturbance is truncation, and in theory, the accuracy is maintained through variance equivalence. Summary of the Invention

[0006] The purpose of the present invention is to provide a high-bandwidth disturbance control method for a MEMS sensor based on truncated distribution, so as to further improve the accuracy maintenance capability of the MEMS sensor in harsh environments.

[0007] To achieve the above object, the present invention provides a high-bandwidth disturbance control method for a MEMS sensor based on truncated distribution, comprising the following steps: Step S1, proving that the variance of the Gaussian truncated distribution is equivalent to a Gaussian distribution with a smaller variance; Step S2: Use the discrete-time system state equation to describe the MEMS sensor signal, and construct a state model that describes the actual motion of the target and a MEMS sensor measurement model with noise; Step S3: Initialize the weight coefficient and calculate the minimum variance fusion corresponding weight coefficient through the noise variance and the disturbance variance; Step S4: Select a sliding window length, perform expected estimation on the initial fusion data, calculate the estimation error within each window length, and select the one with the smallest estimation error as the final estimated expectation; Step S5: Calculate the truncated fusion intervals based on the judgment conditions of the disturbed environment and the normal environment respectively; wherein the static interval is calculated based on the absolute value of the residual, and the disturbed interval is calculated based on the variance of the normal environment; Step S6, set the judgment criteria. When the estimation error is less than the set confidence level, select the initialization weight coefficient; when the initialization fusion is within the clustering interval, select the initialization weight coefficient fusion; when it is outside the clustering interval, reconstruct the weight coefficient based on the difference between the expected and initial fusion for fusion.

[0008] Preferably, in step S1, it is proved that the variance of the Gaussian truncated distribution is equivalent to a Gaussian distribution with a smaller variance, and the specific process is as follows: Step S11, random variable weighted fusion expression, as shown below: (1); in, Indicates the random variables; is the fused random variable; is the weight coefficient; Compute the variance of the fused random variable as follows: (2); in, represents the fused random variable variance; and represents the sample space; and denote the first random variable in the sample space of the fused random variable and the random variable before fusion. k samples; is the number of samples in the sample space; yes expectations; Each sample The weight coefficient of , and in the minimum variance fusion ; Define two set intervals and , Indicates the half interval length; Step S12: Existence make If established, then: (3); in, represents the reconstruction weight coefficient; Furthermore, it can be deduced that: (4); in, ; Step S13: For random variables , and its truncated distribution variance is as follows: (5); in, , ; is the standard deviation when not truncated; is a standard Gaussian distribution; Then by solving , the precision-maintained truncated distribution interval is obtained as follows: (6); in, is the target variance.

[0009] Preferably, in step S2, the discrete-time system state equation is used to describe the MEMS sensor signal, and a state model describing the actual motion of the target and a MEMS sensor measurement model with noise are constructed as follows: (7); in, represents the measurement of the i-th gyroscope; Indicates the corresponding sensitivity coefficient; represents the true angular velocity; represents the measurement noise, and its variance is ; represents the disturbance error, and its variance is .

[0010] Preferably, in step S3, the weight coefficient is initialized, and the weight coefficient corresponding to the minimum variance fusion is calculated by using the noise variance and the disturbance variance, as shown below: (8); in, represents the minimum variance.

[0011] Preferably, in step S4, a sliding window length is selected, an expected estimate is performed on the initial fusion data, and the estimation error within each window length is calculated, and the one with the smallest estimation error is selected as the final estimated expectation. The specific process is as follows: (9); in, and is the expected estimated parameter; represents the expected estimated parameter merging matrix; represents the minimum variance fusion data; Represents the expected estimate , represents the estimated expectation set; represents the set of sampling time intervals within the sliding window; Indicates the sampling moments and have represents the sliding window length; Indicates the sampling time interval; (10); (11); in, is the empirical coefficient; represents the expected estimation error within the sliding window; Represents standard deviation.

[0012] Preferably, in step S5, the truncated fusion interval is calculated respectively according to the judgment conditions of the disturbance environment and the normal environment; wherein the static interval is calculated based on the absolute value of the residual, as shown below: (12); Among them, the conditions are ; The perturbation interval is calculated based on the variance of the normal environment as follows: (13); Among them, the conditions are ; in, and is the scale parameter, is the interval length; Then calculate the upper bound of the interval and the Nether , as shown below: (14); in, Represents the expected estimate.

[0013] Preferably, in step S6, a judgment criterion is set: when the estimation error is less than the set confidence level, the initialization weight coefficient is selected; when the initialization fusion is within the cluster interval, the initialization weight coefficient fusion is selected; when it is outside the cluster interval, the weight coefficient is reconstructed based on the difference between the expected and initial fusion for fusion, as shown below: , or (15); (16); in, is the final fusion output; The interval is defined as: ; in, ; Define the estimation error: ;in, represents the expected estimation error; represents fusion noise; represents fusion disturbance; Therefore, the weight coefficients are as follows: (17); (18); in, represents the reconstruction weight coefficient; represents the minimum variance fusion coefficient; Indicates the weight correction value.

[0014] Therefore, the present invention adopts the above-mentioned high-bandwidth disturbance control method for MEMS sensors based on truncated distribution. First, the initial weight coefficient is set to the minimum variance weight coefficient, and the fusion expectation under multiple sliding windows is estimated using ordinary least squares; secondly, the expected errors of multiple estimates are compared and the appropriate expectation is selected; finally, the interference and normal environment are distinguished according to the standard deviation of multiple gyroscopes, and the truncation interval is calculated; when the initial fusion result is within the interval and the expected error is large, the weight coefficient remains unchanged. When the fusion result is outside the interval, the weight coefficient is recalculated according to the difference between the expected value and the initial fusion result. The above method achieves an accuracy deterioration greater than The accuracy maintenance of the MEMS sensor is further improved.

[0015] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a flow chart of a high-bandwidth disturbance control method for a MEMS sensor based on truncated distribution according to the present invention; Figure 2 This is a technical roadmap for a high-bandwidth disturbance control method for MEMS sensors based on truncated distribution in the present invention; Figure 3 2 is a diagram of test results in an embodiment of the present invention. DETAILED DESCRIPTION

[0017] The technical solution of the present invention is further described below with reference to the accompanying drawings and embodiments.

[0018] like Figure 1 As shown, the present invention provides a high-bandwidth disturbance control method for a MEMS sensor based on truncated distribution, comprising the following steps: Step S1, proving that the variance of the Gaussian truncated distribution is equivalent to a Gaussian distribution with a smaller variance; Step S2: Use the discrete-time system state equation to describe the MEMS sensor signal, and construct a state model that describes the actual motion of the target and a MEMS sensor measurement model with noise; Step S3: Initialize the weight coefficient and calculate the minimum variance fusion corresponding weight coefficient through the noise variance and the disturbance variance; Step S4: Select a sliding window length, perform expected estimation on the initial fusion data, calculate the estimation error within each window length, and select the one with the smallest estimation error as the final estimated expectation; Step S5: Calculate the truncated fusion intervals based on the judgment conditions of the disturbed environment and the normal environment respectively; wherein the static interval is calculated based on the absolute value of the residual, and the disturbed interval is calculated based on the variance of the normal environment; Step S6, set the judgment criteria. When the estimation error is less than the set confidence level, select the initialization weight coefficient; when the initialization fusion is within the clustering interval, select the initialization weight coefficient fusion; when it is outside the clustering interval, reconstruct the weight coefficient based on the difference between the expected and initial fusion for fusion.

[0019] Example like Figure 2 As shown, the present invention provides a high-bandwidth disturbance control method for MEMS sensors based on truncated distribution, and the specific process is as follows: Step S1: Prove that the variance of the truncated Gaussian distribution is equivalent to a Gaussian distribution with a smaller variance.

[0020] Step S11, random variable weighted fusion expression, as shown below: (1); in, Indicates the random variables; is the fused random variable; is the weight coefficient.

[0021] Compute the variance of the fused random variable as follows: (2); in, represents the fused random variable variance; and represents the sample space; and denote the first random variable in the sample space of the fused random variable and the random variable before fusion. k samples; is the number of samples in the sample space; yes expectations; Each sample The weight coefficient of , and in the minimum variance fusion ; Define two set intervals and , Represents the length of the half interval, which is an arbitrary number greater than 0.

[0022] Step S12: Existence make If established, then: (3); in, Represents the reconstruction weight coefficient, which is calculated based on a certain statistic.

[0023] Furthermore, it can be deduced that: (4); in, .

[0024] Step S13: For random variables , and its truncated distribution variance is as follows: (5); in, , ; is the standard deviation when not truncated; is a standard Gaussian distribution.

[0025] Then by solving , the precision-maintained truncated distribution interval is obtained as follows: (6); in, is the target variance.

[0026] Step S2: Use the discrete-time system state equation to describe the MEMS sensor signal, and construct a state model that describes the actual motion of the target and a MEMS sensor measurement model with noise, as shown below: (7); in, represents the measurement of the i-th gyroscope; Indicates the corresponding sensitivity coefficient; represents the true angular velocity; represents the measurement noise, and its variance is ; represents the disturbance error, and its variance is .

[0027] Step S3: Initialize the weight coefficients and calculate the minimum variance fusion corresponding weight coefficients by using the noise variance and the disturbance variance, as shown below: (8); in, represents the minimum variance.

[0028] Step S4: Select a sliding window length, perform expected estimation on the initial fusion data, calculate the estimation error within each window length, and select the one with the smallest estimation error as the final estimated expectation.

[0029] (9); in, and is the expected estimated parameter; represents the expected estimated parameter merging matrix; represents the minimum variance fusion data; Represents the expected estimate , represents the estimated expectation set; represents the set of sampling time intervals within the sliding window; Indicates the sampling moments and have represents the sliding window length; Indicates the sampling time interval.

[0030] (10); (11); in, is the empirical coefficient; represents the expected estimation error within the sliding window; Represents standard deviation.

[0031] Step S5: Calculate the truncated fusion intervals based on the judgment conditions of the disturbance environment and the normal environment. The static interval calculation is based on the absolute value of the residual, as shown below: (12); Among them, the conditions are .

[0032] The perturbation interval is calculated based on the variance of the normal environment as follows: (13); Among them, the conditions are .

[0033] in, and is the scale parameter, is the interval length.

[0034] Then calculate the upper bound of the interval and the Nether , as shown below: (14); in, Represents the expected estimate.

[0035] Step S6, set the judgment criteria: when the estimation error is less than the set confidence level, select the initialization weight coefficient; when the initialization fusion is within the clustering interval, select the initialization weight coefficient fusion; when it is outside the clustering interval, reconstruct the weight coefficient based on the difference between the expected and initial fusion for fusion.

[0036] , or (15); (16); in, is the final fusion output; The interval is defined as: ; in, .

[0037] Define the estimation error: ;in, represents the expected estimation error; represents fusion noise; represents the fusion perturbation.

[0038] Therefore, the weight coefficients are as follows: (17); (18); in, represents the reconstruction weight coefficient; represents the minimum variance fusion coefficient; Indicates the weight correction value.

[0039] In order to evaluate the proposed method, it is tested and compared with the average fusion algorithm, conflict consensus algorithm, wavelet covariance fusion and minimum variance weighted fusion. Figure 2 As shown, the method proposed in the present invention further improves the accuracy of the MEMS sensor, indicating that the method proposed in the present invention can break through the minimum variance limit and further improve the accuracy of the MEMS sensor.

[0040] Therefore, the present invention adopts the above-mentioned high-bandwidth disturbance control method for MEMS sensors based on truncated distribution. First, the initial weight coefficient is set to the minimum variance weight coefficient, and the fusion expectation under multiple sliding windows is estimated using ordinary least squares; secondly, the expected errors of multiple estimates are compared and the appropriate expectation is selected; finally, the interference and normal environment are distinguished according to the standard deviation of multiple gyroscopes, and the truncation interval is calculated; when the initial fusion result is within the interval and the expected error is large, the weight coefficient remains unchanged. When the fusion result is outside the interval, the weight coefficient is recalculated according to the difference between the expected value and the initial fusion result. The above method achieves an accuracy deterioration greater than The accuracy maintenance of the MEMS sensor is further improved.

[0041] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A high-bandwidth disturbance control method for MEMS sensors based on truncated distribution, characterized in that: The following steps are involved: Step S1, proving that the variance of the Gaussian truncated distribution is equivalent to a Gaussian distribution with a smaller variance; Step S2: Use the discrete-time system state equation to describe the MEMS sensor signal, and construct a state model that describes the actual motion of the target and a MEMS sensor measurement model with noise; Step S3: Initialize the weight coefficient and calculate the minimum variance fusion corresponding weight coefficient through the noise variance and the disturbance variance; Step S4: Select a sliding window length, perform expected estimation on the initial fusion data, calculate the estimation error within each window length, and select the one with the smallest estimation error as the final estimated expectation; Step S5: Calculate the truncated fusion intervals based on the judgment conditions of the disturbed environment and the normal environment respectively; wherein the static interval is calculated based on the absolute value of the residual, and the disturbed interval is calculated based on the variance of the normal environment; Step S6, set the judgment criteria. When the estimation error is less than the set confidence level, select the initialization weight coefficient; when the initialization fusion is within the clustering interval, select the initialization weight coefficient fusion; when it is outside the clustering interval, reconstruct the weight coefficient based on the difference between the expected and initial fusion for fusion.

2. The method for controlling high-bandwidth disturbances of a MEMS sensor based on truncated distribution according to claim 1, characterized in that: In step S1, it is proved that the variance of the Gaussian truncated distribution is equivalent to a Gaussian distribution with a smaller variance. The specific process is as follows: Step S11, random variable weighted fusion expression, as shown below: （1）； in, Indicates the random variables; is the fused random variable; is the weight coefficient; Compute the variance of the fused random variable as follows: （2）； in, represents the fused random variable variance; and represents the sample space; and represent the kth sample in the sample space of the fused random variable and the random variable before fusion respectively; is the number of samples in the sample space; yes expectations; Each sample The weight coefficient of , and in the minimum variance fusion ; Define two set intervals and , Indicates the half interval length; Step S12: Existence make If established, then: （3）； in, represents the reconstruction weight coefficient; Furthermore, it can be deduced that: （4）； in, ; Step S13: For random variables , and its truncated distribution variance is as follows: （5）； in, , ; is the standard deviation when not truncated; is a standard Gaussian distribution; Then by solving , the precision-maintained truncated distribution interval is obtained as follows: （6）； in, is the target variance.

3. The method for controlling high-bandwidth disturbances of a MEMS sensor based on truncated distribution according to claim 1, characterized in that: In step S2, the discrete-time system state equation is used to describe the MEMS sensor signal, and a state model describing the actual motion of the target and a MEMS sensor measurement model with noise are constructed as follows: （7）； in, represents the measurement of the i-th gyroscope; Indicates the corresponding sensitivity coefficient; represents the true angular velocity; represents the measurement noise, and its variance is ; represents the disturbance error, and its variance is .

4. The method for controlling high-bandwidth disturbances of a MEMS sensor based on truncated distribution according to claim 1, wherein: In step S3, the weight coefficient is initialized, and the weight coefficient corresponding to the minimum variance fusion is calculated by the noise variance and the disturbance variance, as shown below: （8）； in, represents the minimum variance.

5. The method for controlling high-bandwidth disturbances of a MEMS sensor based on truncated distribution according to claim 1, characterized in that: In step S4, the sliding window length is selected, the expected estimation is performed on the initial fusion data, and the estimation error within each window length is calculated. The one with the smallest estimation error is selected as the final estimated expectation. The specific process is as follows: （9）； in, and is the expected estimated parameter; represents the expected estimated parameter merging matrix; represents the minimum variance fusion data; Represents the expected estimate , represents the estimated expectation set; represents the set of sampling time intervals within the sliding window; Indicates the sampling moments and have represents the sliding window length; Indicates the sampling time interval; （10）； （11）； in, is the empirical coefficient; represents the expected estimation error within the sliding window; Represents standard deviation.

6. The method for controlling high-bandwidth disturbances of a MEMS sensor based on truncated distribution according to claim 1, characterized in that: In step S5, the truncated fusion intervals are calculated based on the judgment conditions of the disturbance environment and the normal environment. The static interval calculation is based on the absolute value of the residual, as shown below: （12）； Among them, the conditions are ; The perturbation interval is calculated based on the variance of the normal environment as follows: （13）； Among them, the conditions are ; in, and is the scale parameter, is the interval length; Then calculate the upper bound of the interval and the Nether , as shown below: （14）； in, Represents the expected estimate.

7. The method for controlling high-bandwidth disturbances of a MEMS sensor based on truncated distribution according to claim 1, characterized in that: In step S6, the judgment criteria are set: when the estimation error is less than the set confidence level, the initialization weight coefficient is selected; when the initialization fusion is within the cluster interval, the initialization weight coefficient is selected for fusion; when it is outside the cluster interval, the weight coefficient is reconstructed based on the difference between the expected and initial fusion values ​​for fusion, as shown below: , or (15); （16）； in, is the final fusion output; The interval is defined as: ; in, ; Define the estimation error: ;in, represents the expected estimation error; represents fusion noise; represents fusion disturbance; Therefore, the weight coefficients are as follows: （17）； （18）； in, represents the reconstruction weight coefficient; represents the minimum variance fusion coefficient; Indicates the weight correction value.

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