A High-Bandwidth Perturbation Control Method for MEMS Sensors Based on Truncated Distribution

Abstract

This invention discloses a high-bandwidth perturbation control method for MEMS sensors based on truncated distribution, comprising the following steps: initializing weight coefficients by calculating the minimum variance fusion weight coefficients using noise variance and perturbation variance; selecting a sliding window length, performing expectation estimation on the initial fused data, calculating the estimation error within each window length, and selecting the smallest estimation error as the final expectation; calculating truncated fusion intervals based on the judgment conditions for perturbation environment and normal environment; setting judgment criteria: when the estimation error is less than the set confidence level, initializing weight coefficients is selected; when the initial fusion is within a clustering interval, initializing weight coefficient fusion is selected; when it is outside the clustering interval, reconstructing weight coefficients based on the difference between the expectation and the initial fusion for fusion. This invention employs the above-mentioned high-bandwidth perturbation control method for MEMS sensors based on truncated distribution, improving the accuracy maintenance capability of MEMS sensors in harsh environments.

Description

Technical Field

[0001] This invention relates to the field of microelectromechanical systems (MEMS) technology, and in particular to a high-bandwidth perturbation control method for MEMS sensors based on truncated distribution. Background Technology

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

[0003] Weighted fusion methods are an effective way to improve the accuracy of MEMS sensors while maintaining bandwidth. In existing technologies, average weighted fusion is used to fuse measurements from multiple MEMS sensors, improving the accuracy of MEMS gyroscopes; minimum variance fusion is used to fuse MEMS gyroscopes, minimizing the fusion variance of 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-resistant MEMS sensor groups respectively, followed by minimum variance fusion of the two fused data, effectively improving the accuracy of MEMS sensors under vibration; and a variable-weight fusion method for expected clustering intervals breaks through the accuracy limit of traditional constant-weight fusion methods.

[0004] The methods described above can effectively improve the accuracy of MEMS sensors in harsh environments. However, they cannot maintain accuracy even when gyroscope accuracy decays significantly in such environments. One major reason is that the accuracy of constant-weight coefficient fusion is a multivariate linear function of the weight coefficients (with weight coefficient normalization constraints). This function inevitably has a minimum value leading to an accuracy limit, which is constrained by the number of sensors, typically being a power of 1 / 2 of the number of sensors. This implies a conflict between the anti-interference performance of MEMS sensors and their low-cost, small-size advantages. Another major reason is that while the expected cluster interval variable-weight fusion method breaks through the accuracy limit, its cluster interval is a function of the maximum difference in measurements. While cluster fusion can improve accuracy, it has not been theoretically proven that this improvement can maintain accuracy.

[0005] Therefore, to solve the above problems, this invention proposes a high-bandwidth perturbation 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 small variance. Furthermore, by initializing the weight coefficients with minimum variance and estimating the expectation of the fused signal, a Gaussian truncated interval is designed with this expectation as the center. By fusing signals that do not belong to the interval into the interval, the Gaussian perturbation is truncated. Theoretically, the accuracy is maintained through variance equivalence. Summary of the Invention

[0006] The purpose of this invention is to provide a high-bandwidth perturbation control method for MEMS sensors based on truncated distribution, which further improves the accuracy maintenance capability of MEMS sensors in harsh environments.

[0007] To achieve the above objectives, this invention provides a high-bandwidth perturbation control method for MEMS sensors based on truncated distribution, comprising the following steps:

[0008] Step S1: Prove that the variance of the Gaussian truncated distribution is equivalent to that of the Gaussian distribution with a smaller variance;

[0009] Step S2: Use the discrete-time system state equation to describe the MEMS sensor signal, and construct a state model describing the real motion of the target and a MEMS sensor measurement model with noise.

[0010] Step S3: Initialize the weight coefficients and calculate the weight coefficients corresponding to the minimum variance fusion by using the noise variance and the disturbance variance.

[0011] Step S4: Select the sliding window length, perform expected estimation on the initial fused data, calculate the estimation error within each window length, and select the one with the smaller estimation error as the final expected estimate;

[0012] Step S5: Calculate the truncated fusion intervals based on the judgment conditions of the disturbed environment and the normal environment; 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;

[0013] Step S6: Set judgment criteria. When the estimation error is less than the set confidence level, select to initialize the weight coefficients. When the initial fusion is within the clustering interval, select to initialize the weight coefficients for fusion. When it is outside the clustering interval, reconstruct the weight coefficients for fusion based on the difference between the expected and the initial fusion.

[0014] Preferably, in step S1, it is proven that the variance of the Gaussian truncated distribution is equivalent to a Gaussian distribution with a smaller variance. The specific process is as follows:

[0015] Step S11, the weighted fusion expression for random variables, is as follows:

[0016] (1);

[0017] in, Indicates the first One random variable; It is a fusion of random variables; These are weighting coefficients;

[0018] The variance of the fused random variables is calculated as follows:

[0019] (2);

[0020] in, Represents a fused random variable The variance; and Represents the sample space; and Let the first and second variables be the sample spaces of the merged random variable and the random variable before fusion, respectively. k One sample; It is the number of samples in the sample space; yes Expectations; Each sample The weighting coefficients, and in the minimum variance fusion Define two set intervals and , Indicates the length of a half-interval;

[0021] Step S12, Existence make If true, then:

[0022] (3);

[0023] in, Indicates the reconstructed weight coefficients;

[0024] Furthermore, it can be deduced that:

[0025] (4);

[0026] in, ;

[0027] Step S13, for random variables Its cutoff distribution variance is shown below:

[0028] (5);

[0029] in, , ; This represents the standard deviation without truncation. It is a standard Gaussian distribution;

[0030] Then by solving The cutoff distribution interval for maintaining accuracy is obtained as follows:

[0031] (6);

[0032] in, It is the target variance.

[0033] Preferably, in step S2, the MEMS sensor signal is described using the discrete-time system state equation, and a state model describing the actual motion of the target and a noisy MEMS sensor measurement model are constructed, as shown below:

[0034] (7);

[0035] in, This represents the measurement of the i-th gyroscope; This represents the corresponding sensitivity coefficient; Represents the true angular velocity; This represents the measurement noise, and its variance is... ; This represents the disturbance error, and its variance is... .

[0036] Preferably, in step S3, the weighting coefficients are initialized, and the weighting coefficients corresponding to the minimum variance fusion are calculated using the noise variance and the disturbance variance, as shown below:

[0037] (8);

[0038] in, This represents the minimum variance.

[0039] Preferably, in step S4, the sliding window length is selected, the expected value of the initial fused data is estimated, and the estimation error within each window length is calculated. The one with the smaller estimation error is selected as the final expected value. The specific process is as follows:

[0040] (9);

[0041] in, and These are expected estimated parameters; This represents the expected parameter merging matrix; This represents the minimum variance fused data; Indicates expected estimate , representing the estimated expected set; Represents the set of sampling time intervals within the sliding window; Indicates the first Each sampling time and has Indicates the length of the sliding window; Indicates the sampling time interval;

[0042] (10);

[0043] (11);

[0044] in, It is an empirical coefficient; This indicates the expected estimation error within the sliding window; It represents the standard deviation.

[0045] Preferably, in step S5, the truncated fusion interval is calculated based on the judgment conditions of the disturbed environment and the normal environment; wherein, the static interval is calculated based on the absolute value of the residual, as shown below:

[0046] (12);

[0047] Among them, the conditions are ;

[0048] The disturbance interval is calculated based on the variance of the normal environment, as shown below:

[0049] (13);

[0050] Among them, the conditions are ;

[0051] in, and It is a proportional parameter. It is the interval length;

[0052] Then calculate the upper bound of the interval. and the lower world As shown below:

[0053] (14);

[0054] in, This represents the expected estimate.

[0055] Preferably, in step S6, the following judgment criteria are set: when the estimation error is less than the set confidence level, the initial weight coefficients are selected; when the initial fusion is within the cluster interval, the initial weight coefficients are selected for fusion; when it is outside the cluster interval, the weight coefficients are reconstructed based on the difference between the expected and initial fusion values ​​for fusion, as shown below:

[0056] , or (15);

[0057] (16);

[0058] in, It is the final fusion output;

[0059] The interval is defined as: ;

[0060] in, ;

[0061] Define the estimation error: ;in, This represents the expected estimation error; Indicates fusion noise; Indicates fusion perturbation;

[0062] Therefore, the weighting coefficients are as follows:

[0063] (17);

[0064] (18);

[0065] in, Indicates the reconstructed weight coefficients; Indicates the minimum variance fusion coefficient; This represents the weight adjustment value.

[0066] Therefore, this invention employs the aforementioned high-bandwidth perturbation control method for MEMS sensors based on truncated distribution. First, the initial weighting coefficients are set to minimum variance weighting coefficients, and the fusion expectation under multiple sliding windows is estimated using ordinary least squares. Second, the expectation errors of multiple estimates are compared, and a suitable expectation is selected. Finally, the standard deviation of the multiple gyroscopes is used to distinguish between disturbances and normal environments, and the truncation interval is calculated. When the initial fusion result is within the interval and the expectation error is large, the weighting coefficients remain unchanged. When the fusion result is outside the interval, the weighting coefficients are recalculated based on the difference between the expectation value and the initial fusion result. This method achieves a precision degradation greater than [a certain value]. The accuracy maintenance over time further improves the accuracy maintenance capability of MEMS sensors.

[0067] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0068] Figure 1 This is a flowchart of a high-bandwidth perturbation control method for MEMS sensors based on truncated distribution, according to the present invention.

[0069] Figure 2 This is a technical roadmap for a high-bandwidth perturbation control method for MEMS sensors based on truncated distribution, as described in this invention.

[0070] Figure 3 This is a test result diagram from an embodiment of the present invention. Detailed Implementation

[0071] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0072] like Figure 1 As shown, the present invention provides a high-bandwidth perturbation control method for MEMS sensors based on truncated distribution, comprising the following steps:

[0073] Step S1: Prove that the variance of the Gaussian truncated distribution is equivalent to that of the Gaussian distribution with a smaller variance;

[0074] Step S2: Use the discrete-time system state equation to describe the MEMS sensor signal, and construct a state model describing the real motion of the target and a MEMS sensor measurement model with noise.

[0075] Step S3: Initialize the weight coefficients and calculate the weight coefficients corresponding to the minimum variance fusion by using the noise variance and the disturbance variance.

[0076] Step S4: Select the sliding window length, perform expected estimation on the initial fused data, calculate the estimation error within each window length, and select the one with the smaller estimation error as the final expected estimate;

[0077] Step S5: Calculate the truncated fusion intervals based on the judgment conditions of the disturbed environment and the normal environment; 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;

[0078] Step S6: Set judgment criteria. When the estimation error is less than the set confidence level, select to initialize the weight coefficients. When the initial fusion is within the clustering interval, select to initialize the weight coefficients for fusion. When it is outside the clustering interval, reconstruct the weight coefficients for fusion based on the difference between the expected and the initial fusion.

[0079] Example

[0080] like Figure 2 As shown, the present invention provides a high-bandwidth perturbation control method for MEMS sensors based on truncated distribution, the specific process of which is as follows:

[0081] Step S1: Prove that the variance of the Gaussian truncated distribution is equivalent to that of the Gaussian distribution with a smaller variance.

[0082] Step S11, the weighted fusion expression for random variables, is as follows:

[0083] (1);

[0084] in, Indicates the first One random variable; It is a fusion of random variables; It is the weighting coefficient.

[0085] The variance of the fused random variables is calculated as follows:

[0086] (2);

[0087] in, Represents a fused random variable The variance; and Represents the sample space; and Let the first and second variables be the sample spaces of the merged random variable and the random variable before fusion, respectively. k One sample; It is the number of samples in the sample space; yes Expectations; Each sample The weighting coefficients, and in the minimum variance fusion Define two set intervals and , The length of a half-interval is represented by an arbitrary number greater than 0.

[0088] Step S12, Existence make If true, then:

[0089] (3);

[0090] in, This represents the reconstructed weighting coefficient, calculated based on a certain statistic.

[0091] Furthermore, it can be deduced that:

[0092] (4);

[0093] in, .

[0094] Step S13, for random variables Its cutoff distribution variance is shown below:

[0095] (5);

[0096] in, , ; This represents the standard deviation without truncation. It is a standard Gaussian distribution.

[0097] Then by solving The cutoff distribution interval for maintaining accuracy is obtained as follows:

[0098] (6);

[0099] in, It is the target variance.

[0100] Step S2: Use the discrete-time system state equation to describe the MEMS sensor signal, and construct a state model describing the actual motion of the target and a noisy MEMS sensor measurement model, as shown below:

[0101] (7);

[0102] in, This represents the measurement of the i-th gyroscope; This represents the corresponding sensitivity coefficient; Represents the true angular velocity; This represents the measurement noise, and its variance is... ; This represents the disturbance error, and its variance is... .

[0103] Step S3: Initialize the weighting coefficients. Calculate the minimum variance fusion weighting coefficients using the noise variance and disturbance variance, as shown below:

[0104] (8);

[0105] in, This represents the minimum variance.

[0106] Step S4: Select the sliding window length, perform expected estimation on the initial fused data, calculate the estimation error within each window length, and select the one with the smaller estimation error as the final expected estimate.

[0107] (9);

[0108] in, and These are expected estimated parameters; This represents the expected parameter merging matrix; This represents the minimum variance fused data; Indicates expected estimate , representing the estimated expected set; Represents the set of sampling time intervals within the sliding window; Indicates the first Each sampling time and has Indicates the length of the sliding window; Indicates the sampling time interval.

[0109] (10);

[0110] (11);

[0111] in, It is an empirical coefficient; This indicates the expected estimation error within the sliding window; It represents the standard deviation.

[0112] Step S5: Calculate the truncated fusion intervals based on the judgment conditions for disturbed and normal environments. The static interval calculation is based on the absolute value of the residuals, as shown below:

[0113] (12);

[0114] Among them, the conditions are .

[0115] The disturbance interval is calculated based on the variance of the normal environment, as shown below:

[0116] (13);

[0117] Among them, the conditions are .

[0118] in, and It is a proportional parameter. It is the interval length.

[0119] Then calculate the upper bound of the interval. and the lower world As shown below:

[0120] (14);

[0121] in, This represents the expected estimate.

[0122] Step S6: Set judgment criteria: When the estimation error is less than the set confidence level, select to initialize the weight coefficient; when the initial fusion is within the cluster interval, select to initialize the weight coefficient fusion; when it is outside the cluster interval, reconstruct the weight coefficient based on the difference between the expected and the initial fusion and perform fusion.

[0123] , or (15);

[0124] (16);

[0125] in, It is the final fusion output;

[0126] The interval is defined as: ;

[0127] in, .

[0128] Define the estimation error: ;in, This represents the expected estimation error; Indicates fusion noise; This indicates a fusion disturbance.

[0129] Therefore, the weighting coefficients are as follows:

[0130] (17);

[0131] (18);

[0132] in, Indicates the reconstructed weight coefficients; Indicates the minimum variance fusion coefficient; This represents the weight adjustment value.

[0133] To evaluate the method proposed in this invention, it was tested and compared with average fusion algorithm, conflict consensus algorithm, wavelet covariance fusion and minimum variance weighted fusion, such as... Figure 2 As shown, the method proposed in this invention further improves the accuracy of MEMS sensors, demonstrating that the method proposed in this invention can break through the minimum variance limit and further improve the accuracy of MEMS sensors.

[0134] Therefore, this invention employs the aforementioned high-bandwidth perturbation control method for MEMS sensors based on truncated distribution. First, the initial weighting coefficients are set to minimum variance weighting coefficients, and the fusion expectation under multiple sliding windows is estimated using ordinary least squares. Second, the expectation errors of multiple estimates are compared, and a suitable expectation is selected. Finally, the standard deviation of the multiple gyroscopes is used to distinguish between disturbances and normal environments, and the truncation interval is calculated. When the initial fusion result is within the interval and the expectation error is large, the weighting coefficients remain unchanged. When the fusion result is outside the interval, the weighting coefficients are recalculated based on the difference between the expectation value and the initial fusion result. This method achieves a precision degradation greater than [a certain value]. The accuracy maintenance over time further improves the accuracy maintenance capability of MEMS sensors.

[0135] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions 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 perturbation control method for MEMS sensors based on truncated distribution, characterized in that, Includes the following steps: Step S1: Prove that the variance of the Gaussian cutoff distribution is equivalent to that of a Gaussian distribution with a smaller variance. The specific process is as follows: Step S11, the weighted fusion expression for random variables, is as follows: （1）； in, Indicates the first One random variable; It is a fusion of random variables; These are weighting coefficients; The variance of the fused random variables is calculated as follows: （2）； in, Representing a fused random variable The variance; and Represents the sample space; and Let represent the k-th sample in the sample space of the merged random variable and the random variable before fusion, respectively; It is the number of samples in the sample space; yes Expectations; Each sample The weighting coefficients, and in the minimum variance fusion Define two set intervals and , Indicates the length of a half-interval; Step S12, Existence make If true, then: （3）； in, Indicates the reconstructed weight coefficients; Furthermore, it can be deduced that: （4）； in, ; Step S13, for random variables Its cutoff distribution variance is shown below: （5）； in, , ; This represents the standard deviation without truncation. It is a standard Gaussian distribution; Then by solving The cutoff distribution interval for maintaining accuracy is obtained as follows: （6）； in, It is the target variance; Step S2: Use the discrete-time system state equation to describe the MEMS sensor signal, and construct a state model describing the actual motion of the target and a noisy MEMS sensor measurement model, as shown below: （7）； in, This represents the measurement of the i-th gyroscope; This represents the corresponding sensitivity coefficient; Represents the true angular velocity; This represents the measurement noise, and its variance is... ; This represents the disturbance error, and its variance is... ; Step S3: Initialize the weight coefficients and calculate the weight coefficients corresponding to the minimum variance fusion by using the noise variance and the disturbance variance. Step S4: Select the sliding window length, perform expected estimation on the initial fused data, calculate the estimation error within each window length, and select the one with the smaller estimation error as the final expected estimate; Step S5: Calculate the truncated fusion intervals based on the judgment conditions of the disturbed environment and the normal environment; 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 judgment criteria. When the estimation error is less than the set confidence level, select to initialize the weight coefficients. When the initial fusion is within the clustering interval, select to initialize the weight coefficients for fusion. When it is outside the clustering interval, reconstruct the weight coefficients for fusion based on the difference between the expected and the initial fusion.

2. The high-bandwidth perturbation control method for MEMS sensors based on truncated distribution according to claim 1, characterized in that, In step S3, the weighting coefficients are initialized, and the weighting coefficients corresponding to the minimum variance fusion are calculated using the noise variance and the disturbance variance, as shown below: （8）； in, This represents the minimum variance.

3. The high-bandwidth perturbation control method for MEMS sensors based on truncated distribution according to claim 1, characterized in that, In step S4, the sliding window length is selected, the expected value of the initial fused data is estimated, and the estimation error within each window length is calculated. The one with the smaller estimation error is selected as the final expected value. The specific process is as follows: （9）； in, and These are expected estimated parameters; This represents the expected parameter merging matrix; This represents the minimum variance fused data; Indicates expected estimate , representing the estimated expected set; Represents the set of sampling time intervals within the sliding window; Indicates the first Each sampling time and has Indicates the length of the sliding window; Indicates the sampling time interval; （10）； （11）； in, It is an empirical coefficient; This indicates the expected estimation error within the sliding window; It represents the standard deviation.

4. The high-bandwidth perturbation control method for MEMS sensors 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 for disturbed and normal environments, respectively; wherein, the static interval is calculated based on the absolute value of the residual, as shown below: （12）； Among them, the conditions are ; The disturbance interval is calculated based on the variance of the normal environment, as shown below: （13）； Among them, the conditions are ; in, and It is a proportional parameter. It is the interval length; Then calculate the upper bound of the interval. and the lower world As shown below: （14）； in, This represents the expected estimate.

5. The high-bandwidth perturbation control method for MEMS sensors based on truncated distribution according to claim 1, characterized in that, In step S6, the following judgment criteria are set: when the estimation error is less than the set confidence level, the initial weight coefficients are selected; when the initial fusion is within the cluster interval, the initial weight coefficient fusion is selected; when it is outside the cluster interval, the weight coefficients are reconstructed based on the difference between the expected and the initial fusion, as shown below: , or (15); （16）； in, It is the final fusion output; The interval is defined as: ; in, ; Define the estimation error: ;in, This represents the expected estimation error; Indicates fusion noise; Indicates fusion perturbation; Therefore, the weighting coefficients are as follows: （17）； （18）； in, Indicates the reconstructed weight coefficients; Indicates the minimum variance fusion coefficient; This represents the weight adjustment value.

Images