A method for calibrating sensitivity of a MEMS sensor in outdoor static measurement

Abstract

This invention discloses a method for calibrating the sensitivity of MEMS sensors in outdoor static measurements, relating to the field of MEMS sensor technology. By employing multi-day data acquisition and a dual stability determination mechanism, it accurately identifies the stable state after installation stress release, avoiding misjudgments due to transient drift. Furthermore, based on a Bayesian framework-based adaptive filtering process, it calculates and corrects sensitivity drift in real time, effectively eliminating 5%–15% of measurement errors, achieving a linearity ≥0.998 after calibration. A long-term maintenance system is constructed through a dual update mechanism to ensure continuous stability of calibration accuracy. Complete records of calibration parameters, algorithm switching, and update history enhance data traceability. This comprehensively improves the reliability and traceability of long-term monitoring data, significantly reducing engineering decision-making risks.

Description

Technical Field

[0001] This invention relates to the field of MEMS sensor technology, specifically to a method for calibrating the sensitivity of MEMS sensors in outdoor static measurements. Background Technology

[0002] Microelectromechanical systems (MEMS) sensors are widely used in outdoor static measurement scenarios, such as structural health monitoring, bridge deformation monitoring, and geological disaster early warning. Their core advantages lie in their small size, low power consumption, and low cost, enabling long-term unattended static displacement or tilt measurement.

[0003] In existing technologies, the sensitivity of MEMS sensors is typically calibrated at the factory using a vibration table or a flipping table in a laboratory environment. However, in actual outdoor applications, sensor products are inevitably subjected to external impacts or installation stresses during transportation, hoisting, and fastening, which alters the stress distribution around the PCB substrate and sensor chip, thereby causing sensitivity drift.

[0004] Sensitivity drift disrupts the linear relationship between temperature and modulus (or output value), leading to a significant decrease in the linearity of the measurement data and unpredictable changes in the temperature coefficient. Current technologies typically address this issue by periodically returning the equipment to the factory for recalibration. However, outdoor equipment is often installed in inaccessible locations such as high altitudes, bridges, or slopes, making factory recalibration costly, time-consuming, and disrupting the continuity of monitoring data.

[0005] Some existing online self-calibration schemes propose to achieve calibration by using a built-in reference acceleration source or multiple sensor redundancy comparison. However, these schemes require additional hardware costs and cannot generate controllable excitation signals in purely static measurement scenarios, thus limiting their applicability.

[0006] In daily engineering practice, it has been found that after existing MEMS sensors are installed outdoors, the measurement error caused by sensitivity drift can reach 5% to 15%, which seriously affects the reliability and traceability of long-term monitoring data, and thus leads to misjudgment in engineering decisions or safety hazards. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of existing technologies and provide a method for calibrating the sensitivity of MEMS sensors in outdoor static measurements. This method employs a 3σ criterion for preprocessing to remove outliers, fits daily linearity and temperature coefficient using the least squares method, and combines mean and variance statistics for dual stability determination. Furthermore, it constructs an adaptive filtering process based on a Bayesian framework, intelligently switching between unscented Kalman filtering and Rao-Blackwellized particle filtering to calculate sensitivity drift and correct data in real time. After calibration, the linearity is ≥0.998, the error elimination rate reaches over 90%, effectively eliminating 5%–15% of measurement errors and improving the reliability and traceability of long-term monitoring data.

[0008] To solve the above-mentioned technical problems, the present invention provides the following technical solution: a method for calibrating the sensitivity of a MEMS sensor in outdoor static measurement, the method comprising the following specific steps:

[0009] S1: Obtain the sensor's factory linearity Temperature coefficient ,constant and the corresponding Gaussian distribution standard deviation , ;

[0010] S2: After the sensor is installed, outlier values ​​of temperature and modulus data are first eliminated by the 3σ criterion, and then temperature and modulus data pairs are continuously collected for several days.

[0011] S3: Based on the pre-processed temperature and modulus data pairs each day, a linear fitting model is used to perform least squares fitting to obtain the linearity and temperature coefficient for the day.

[0012] S4: Calculate the mean of linearity over multiple days. and the mean of the temperature coefficient and the variance of linearity ;

[0013] S5: If the difference between the mean linearity and the factory linearity, and the mean temperature coefficient and the factory temperature coefficient are all within 3 times the standard deviation of the corresponding Gaussian distribution, continue monitoring at the factory value; otherwise, proceed to extended observation.

[0014] S6: Extend the acquisition cycle, repeat the data acquisition, preprocessing and daily fitting steps, obtain the bus linearity and total temperature coefficient based on the total fitting of all data, and calculate the total constant by the average difference between the modulus and the product of the total temperature coefficient and temperature.

[0015] S7: Construct dual judgment conditions. If both conditions are met, the sensor sensitivity is determined to be stable, and the bus stability, total temperature coefficient, and total constant are used as new calibration values. If either condition is not met, the observation window is further extended, and monitoring continues until the stability condition is met.

[0016] S8: After determining the new calibration value, in order to track the sensitivity drift in real time, an adaptive filtering process is constructed based on the Bayesian framework to achieve accurate calculation of the drift amount and real-time data correction. The new calibration value is written into the sensor's non-volatile memory and the complete calibration history is recorded in the form of a timestamp.

[0017] Furthermore, in step S1, the Gaussian distribution standard deviation undergoes a standardized pre-shipment environmental test, which involves placing the sensor in a temperature range of -40℃ to +85℃ and performing no less than 30 temperature cycle measurements. For each measurement, the corresponding linearity and temperature coefficient data are recorded. By statistically analyzing the data, the normal distribution parameters of the linearity and temperature coefficient are determined.

[0018] Furthermore, in step S2, the original temperature data and modulus data are preprocessed using the 3σ criterion to remove outliers caused by factors such as sensor momentary failure and electromagnetic interference. The core logic of the 3σ criterion is to calculate the mean μ and standard deviation σ of the data and remove abnormal data that exceed the range of [μ-3σ, μ+3σ].

[0019] Furthermore, in step S3, the least squares method is used to perform linear fitting on the daily collected temperature-modulus data pairs, and the fitting formula is: ,in Here, b is the temperature coefficient, and b is a constant. For temperature data, Using the modulus data, the linear temperature coefficient for that day is obtained.

[0020] Furthermore, in step S3, the formula for calculating the daily linearity is: ,in, This is the sum of squared residuals, i.e., the sum of squared differences between the measured modulus and the fitted modulus. The total sum of squares, i.e., the sum of squares of the differences between the measured modulus and the mean modulus, represents the linearity. The closer the value is to 1, the stronger the linear correlation between the daily temperature and the modulus length, and the higher the reliability of the data.

[0021] Furthermore, in step S5, the calculated mean linearity value is... linearity with factory specifications Compare the results and average the temperature coefficients. With factory temperature coefficient The comparison and judgment logic uses the following formula: and If both inequalities are true, it is determined that the sensor sensitivity has not changed significantly, and the factory calibration value remains unchanged, and routine monitoring continues; if either inequality is false, it is determined that the sensitivity has drifted significantly, and the subsequent calibration process begins.

[0022] Furthermore, in step S6, a global least-squares fit is performed on all valid data pairs acquired over the extended period to obtain the bus uniformity. With the total temperature coefficient Simultaneously calculate the total constant. The formula for calculating the total constant is: ,in To extend the total number of data pairs within the collection period, It is the first The measured output modulus data of the group. It is the first The group collected ambient temperature data.

[0023] Furthermore, in step S7, a dual judgment condition is constructed: the first is a variance test to determine the variance of daily linearity. Does it meet the requirements? The second step is a consistency check, which determines the temperature coefficient for all days. With the total temperature coefficient Does it meet the requirements? If both of the above checks are satisfied, the sensor sensitivity is determined to be stable, based on bus uniformity. Total temperature coefficient Total constants The new calibration value replaces the original factory value; if any test fails, the observation window is further extended until the stability condition is met.

[0024] Furthermore, in step S8, the specific steps for constructing an adaptive filtering process based on a Bayesian framework to achieve accurate calculation of drift and real-time data correction are as follows:

[0025] Using the posterior distribution parameters obtained from batch analysis as the prior of process noise, the sensor sensitivity drift is calculated in real time using an unscented Kalman filter algorithm. ;

[0026] The KS test is used to determine the regression residual distribution characteristics of the unscented Kalman filter. The preset test threshold is p<0.05. When the test result meets this condition, it is determined that the residual deviates from the Gaussian distribution, and the Rao-Blackwellized particle filter algorithm is automatically switched.

[0027] The sensitivity drift obtained by calculation Real-time correction is performed on the sensor's measured data. The correction formula is as follows: ,in For the corrected data, The data is based on actual measurements; at the same time, the new calibration values, filtering algorithm switching status, and calibration timestamps are written into the sensor's non-volatile memory to form a core calibration file.

[0028] Furthermore, the sensor's sensitivity drift is calculated in real time using an unscented Kalman filter algorithm. The specific steps are as follows: Based on the total fitted data, historical calibration records, and multi-day statistical analysis results within the extended acquisition period, the posterior distribution of sensitivity drift-related parameters is obtained through batch data modeling. The mean and variance of this posterior distribution are directly used as the prior input of the process noise for the unscented Kalman filter, clarifying the initial state of the filter and the boundary of the noise characteristics. At the same time, state equations and observation equations adapted to the working characteristics of the MEMS sensor are constructed, with the state variables including the sensitivity drift. The dynamic components of temperature coefficient and linearity are also considered, with the observed values ​​selected from the real-time temperature data collected by the sensor. With output module The correlation between state variables and observed values ​​is established through a linear fitting model. Then, following an unscented Kalman filter process, initial sigma points covering the state space are generated, and the propagation calculation for the time update stage is completed using the state equation. Combined with the observation equation, the predicted observation values ​​are obtained. Finally, a preset weight matrix is ​​used to complete the state estimation and error covariance correction for the measurement update stage. Finally, through iterative calculations, the accurate sensitivity drift is output in real time. .

[0029] Compared with existing technologies, this method for calibrating the sensitivity of MEMS sensors in outdoor static measurements has the following advantages:

[0030] This invention employs multi-day data acquisition and a dual stability determination mechanism to accurately identify the stable state after stress release during installation, avoiding misjudgments due to transient drift. Based on a Bayesian framework, an adaptive filtering process calculates and corrects sensitivity drift in real time, effectively eliminating 5%–15% of measurement errors, with a linearity ≥0.998 after calibration. A long-term maintenance system is built through a dual update mechanism to ensure continuous stability of calibration accuracy. Complete records of calibration parameters, algorithm switching, and update history enhance data traceability. This comprehensively improves the reliability and traceability of long-term monitoring data, significantly reducing engineering decision-making risks.

[0031] Other advantages, objectives and features of the invention will be set forth in part in the description which follows, and in part will be apparent to those skilled in the art from the following examination or study, or may be learned from the practice of the invention. Attached Figure Description

[0032] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0033] Figure 1 A flowchart of a MEMS sensor sensitivity calibration method in outdoor static measurement;

[0034] Figure 2 This is a flowchart of step S3 in a MEMS sensor sensitivity calibration method for outdoor static measurement.

[0035] Figure 3 This is a flowchart of step S7 in a MEMS sensor sensitivity calibration method for outdoor static measurement. Detailed Implementation

[0036] To further illustrate the technical means and effects of the present invention in achieving its intended purpose, the following detailed description of the specific implementation methods, structure, features and effects of the present invention, in conjunction with the accompanying drawings and preferred embodiments, is provided below.

[0037] This invention provides a method for calibrating the sensitivity of MEMS sensors in outdoor static measurements. It employs a 3σ criterion for preprocessing to eliminate outliers, fits daily linearity and temperature coefficient using the least squares method, and combines mean and variance statistics for dual stability determination. Furthermore, it constructs an adaptive filtering process based on a Bayesian framework, intelligently switching between unscented Kalman filtering and Rao-Blackwellized particle filtering to calculate sensitivity drift and correct data in real time. After calibration, the linearity is ≥0.998, and the error elimination rate reaches over 90%, effectively eliminating 5%–15% of measurement errors and improving the reliability and traceability of long-term monitoring data.

[0038] like Figure 1 As shown, S1: Obtain the sensor's factory linearity. Temperature coefficient ,constant and the corresponding Gaussian distribution standard deviation , ;

[0039] When selecting a MEMS displacement sensor suitable for outdoor static measurement, the first step is to extract the core parameters from the sensor's factory test report: factory linearity. Factory temperature coefficient Factory constant These parameters serve as the baseline for the initial operating state of the sensor, and their accuracy directly affects the rationality of subsequent calibration decisions.

[0040] The standard deviation of the Gaussian distribution was determined through standardized environmental testing before shipment. The MEMS sensor was placed in a high and low temperature test chamber with a temperature range of -40℃ to +85℃, fully covering extreme outdoor low and high temperature environments to ensure a high degree of match between the test conditions and the temperature characteristics of actual application scenarios. A temperature cycling program was set: the temperature was increased at a uniform rate, and after each preset target temperature, it was held for a preset duration to ensure sufficient stability of the sensor at each temperature point. Then, the temperature was decreased at the same rate to the next target low temperature point, completing one complete temperature cycle. This temperature cycling process was repeated, accumulating no less than 30 cycles of measurement. Multiple sets of linearity and temperature coefficient data were collected during each holding phase. Large sample size collection avoided random errors from single measurements, ensuring the representativeness and reliability of the statistical data. Statistical analysis software was used to perform normal distribution fitting analysis on all collected data to determine the standard deviation of the Gaussian distribution corresponding to the linearity. and the standard deviation of the Gaussian distribution corresponding to the temperature coefficient This provides a scientific and accurate threshold basis for subsequent sensitivity drift determination, avoiding misjudgment or missed judgment due to unreasonable threshold settings.

[0041] S2: After the sensor is installed, outlier values ​​of temperature and modulus data are first eliminated by the 3σ criterion, and then temperature and modulus data pairs are continuously collected for several days.

[0042] The above-mentioned MEMS sensor is installed at an outdoor static measurement and monitoring point. The sensor fixing bracket and the main body of the measured structure are rigidly connected to completely eliminate the relative displacement between the sensor and the measured structure during the measurement process, ensure the stability of the measurement reference, and avoid measurement errors caused by reference offset from the installation source.

[0043] Set reasonable data acquisition parameters: Determine the acquisition frequency and continuous acquisition duration based on the stability requirements of the measurement scenario, continuously acquire data for multiple days, and form multiple sets of temperature-module length data pairs (both temperature data and module length data meet the sensor's nominal measurement accuracy). Capture the sensor's working characteristics under different environmental conditions through continuous acquisition over multiple days, providing sufficient data support for subsequent statistical analysis.

[0044] The preprocessing for outlier removal is performed using the preset 3σ criterion. The mean μ and standard deviation σ of the data are calculated, and outlier data that exceed the range of [μ-3σ, μ+3σ] are removed. This criterion is based on the normal distribution characteristics and can efficiently screen out outliers caused by accidental factors such as instantaneous sensor failure, electromagnetic interference, and instantaneous environmental fluctuations, without removing normal extreme working condition data.

[0045] For the collected temperature data, calculate the mean μ of all temperature data.T and standard deviation σ T The normal range for temperature data is determined to be [μ]. T -3σ T μ T +3σ T ], Remove abnormal data that exceeds this range to avoid interference from abnormal temperature data on temperature-modulus correlation analysis;

[0046] Based on the collected modulus data and the valid samples after removing abnormal temperature data, the mean μ of the modulus data is calculated. L and standard deviation σ L The normal range for modulus data is determined to be [μ]. L -3σ L μ L +3σ L By eliminating outlier data that exceeds this range, we finally obtain effective temperature-modulus data pairs that meet the requirements of subsequent analysis. After this step, the data purity is significantly improved, laying a solid foundation for the accuracy of subsequent fitting analysis.

[0047] S3: As Figure 2 As shown, based on the daily preprocessed temperature and modulus data pairs, a linear fitting model is used to perform least squares fitting to obtain the daily linearity and temperature coefficient.

[0048] For the effective temperature-modulus data pairs after daily preprocessing, the operation is performed according to the set linear fitting and parameter calculation logic. Through daily independent fitting, the daily variation trend of sensor characteristics can be tracked in real time, and the initial signal of sensitivity drift can be captured in a timely manner.

[0049] Using a linear fitting model ,in The ambient temperature collected on that day. The sensor output modulus for that day. The temperature coefficient to be determined is... For the constant to be determined, accurately describe the linear correlation characteristics between temperature and modulus length in outdoor static measurements;

[0050] The temperature coefficient for that day was obtained by fitting the data using the least squares method. and constants ( (The data collection day number is used as the reference number). The least squares method has the advantages of high fitting accuracy and strong anti-interference ability. It can minimize the impact of data noise on the fitting parameters, ensuring that the obtained parameters of the day truly reflect the sensor's working status on that day, thereby calculating the linearity of the day. The formula for calculating linearity is: ,in, This is the sum of squared residuals, i.e., the sum of squared differences between the measured modulus and the fitted modulus. It is the total sum of squares, that is, the sum of squares of the differences between the measured modulus and the mean modulus;

[0051] linearity The closer the value is to 1, the stronger the linear correlation between the daily temperature and the modulus length, the higher the data reliability, and the better the fitting results reflect the true working characteristics of the sensor. By evaluating the data quality through linear quantification, we can provide a basis for judging the effectiveness of subsequent multi-day statistical analysis and avoid overall analysis bias caused by poor data quality on a single day.

[0052] Following the method described above, linear fitting and parameter calculation were completed for all days of data collection, yielding the corresponding temperature coefficients for each day. and linearity This forms a continuous parameter sequence over multiple days, providing a complete data chain for subsequent capture of sensitivity drift trends.

[0053] S4: Calculate the mean of linearity over multiple days. and the mean of the temperature coefficient and the variance of linearity ;

[0054] Based on the obtained multi-day linearity and temperature coefficient data, statistical analysis is performed. By aggregating multi-day data, the randomness of single-day data can be avoided, and the long-term operating characteristics of the sensor can be reflected more comprehensively and objectively.

[0055] Calculate the mean of multi-day linearity. Substitute the linearity data from all collected days into the mean calculation formula to obtain the statistical mean of linearity. This mean can reflect the overall level of linear correlation of data over multiple days, avoiding misjudgments caused by fluctuations in linearity on a single day.

[0056] Calculate the average of the multi-day temperature coefficient. Substitute the temperature coefficient data ai from all collected days into the mean calculation formula to obtain the statistical mean of the temperature coefficient. This mean value can reflect the long-term average level of the sensor's temperature response characteristics and accurately capture the drift trend of the temperature coefficient.

[0057] Calculate the variance of multi-day linearity Based on the variance calculation formula, the linearity data and the mean linearity of all collected days are used. The variance of linearity is calculated. The variance directly reflects the stability of linearity, providing a key variance index for subsequent dual stability determination, and can quantify the degree of fluctuation in the sensor's operating characteristics.

[0058] S5: If the difference between the mean linearity and the factory linearity, and the mean temperature coefficient and the factory temperature coefficient are all within 3 times the standard deviation of the corresponding Gaussian distribution, continue monitoring at the factory value; otherwise, proceed to extended observation.

[0059] Based on the initial judgment logic set in this method, the sensor sensitivity is initially judged. This judgment logic takes into account both the absolute value and statistical distribution characteristics of the parameter deviation, and can quickly and accurately distinguish the significance of sensitivity drift, avoiding invalid calibration or untimely calibration.

[0060] Calculate the absolute value of the linearity difference and with the preset threshold Compare and determine if the conditions are met. This threshold is set based on the sensor's factory statistical characteristics and can effectively distinguish between normal parameter fluctuations and significant sensitivity drift.

[0061] Calculate the absolute value of the temperature coefficient difference and with preset threshold Compare and determine if the conditions are met. The temperature coefficient is a core indicator of sensor sensitivity, and this comparison can directly reflect the core changes in sensitivity.

[0062] If both of the above conditions are met, it means that the sensor sensitivity has not changed significantly, there is no need to adjust the calibration parameters, keep the factory calibration value unchanged, continue routine monitoring, and avoid waste of resources and measurement interruption caused by over-calibration;

[0063] If any of the judgment conditions are not met, it is determined that there is a significant drift in the sensor sensitivity, and the subsequent extended observation and calibration process needs to be carried out to ensure that the measurement accuracy is not affected by the drift and to avoid the accumulation of measurement errors caused by sensitivity drift in a timely manner.

[0064] S6: Extend the acquisition cycle, repeat the data acquisition, preprocessing and daily fitting steps, obtain the bus linearity and total temperature coefficient based on the total fitting of all data, and calculate the total constant by the average difference between the modulus and the product of the total temperature coefficient and temperature.

[0065] In cases where sensitivity exhibits significant drift, an extended observation process is implemented. By extending the observation period, more data is obtained to ensure that the total fitting parameters can reflect the working characteristics of the sensor after it has stabilized, thus avoiding calibration deviations caused by insufficient data.

[0066] Extend the data acquisition cycle by increasing the number of days on top of the original acquisition duration to ensure that enough effective data is obtained to reflect the stable working state of the sensor. Extending the observation period can smooth out the impact of short-term fluctuations and capture the long-term stable trend of sensor sensitivity.

[0067] For all data within the extended acquisition period, outliers were removed according to the data preprocessing steps to obtain a complete set of effective temperature-modulus data pairs, continuously ensuring data quality and providing a high-purity data foundation for the overall fitting. Based on all effective data pairs, a global least-squares fitting was performed to obtain the overall bus uniformity. With the total temperature coefficient Large-sample-size overall fitting can significantly improve the accuracy and stability of parameter estimation, making the obtained total parameters more representative.

[0068] Using the total constant calculation formula Calculate the total constant ,in To extend the total number of valid data pairs within the acquisition period, It is the first The measured output modulus data of the group. It is the first The ambient temperature data collected by the group can be effectively offset by mean calculation to obtain an accurate total constant, which together with the bus uniformity and total temperature coefficient constitutes a complete calibration parameter system.

[0069] S7: As Figure 3 As shown, a dual judgment condition is constructed. If both conditions are met, the sensor sensitivity is determined to be stable, and the bus stability, total temperature coefficient, and total constant are used as new calibration values. If either condition is not met, the observation window is further extended, and monitoring continues until the stability condition is met.

[0070] Based on the dual-judgment criteria constructed in this method, the stability of sensor sensitivity after extended observation is tested. The dual-judgment approach, considering both overall fluctuation and individual consistency, significantly improves the reliability of stability assessment and avoids misjudgments caused by a single judgment criterion.

[0071] First-level variance test: Determine the variance of daily linearity over an extended observation period. Does it meet the requirements? ,in The preset variance threshold ensures both the stability of the data and avoids excessively stringent and ineffective extended observations. The variance test can quantitatively evaluate the overall fluctuation of the sensor's linear characteristics, ensuring that the overall sensitivity remains stable.

[0072] Second consistency check: Verify the temperature coefficients of all days within the extended observation period one by one. With the total temperature coefficient Does it meet the requirements? This ensures that the deviation between the daily temperature coefficient and the total temperature coefficient is within a reasonable range, reflecting the consistency of the sensor's working characteristics. The consistency test can avoid the distortion of the total parameters caused by individual abnormal data, and ensure that the sensor characteristics of each observation day are consistent with the stable total characteristics.

[0073] If both of the above checks are satisfied, the sensor sensitivity is determined to be stable, and the bus frequency response is then adjusted. Total temperature coefficient Total constants As a new calibration value, it replaces the original factory calibration value and completes the sensitivity calibration. The new calibration value can accurately match the current working state of the sensor and completely offset the measurement error caused by sensitivity drift.

[0074] If any test is not met, it means that the sensor has not yet reached a stable working state. The observation window needs to be extended further, and the operation of steps S2-S6 needs to be repeated until both judgment conditions are met. This ensures the reliability of the new calibration value and avoids calibration failure caused by determining the calibration value before the sensor is stable.

[0075] S8: After determining the new calibration value, an adaptive filtering process is constructed based on the Bayesian framework to achieve accurate calculation of drift and real-time data correction. The new calibration value is written into the sensor's non-volatile memory and the complete calibration history is recorded in the form of a timestamp.

[0076] Process noise prior determination: Based on the total fitted data within the extended observation period, sensor historical calibration records, and multi-day statistical analysis results, the posterior distribution of sensitivity drift-related parameters is obtained through batch data modeling. The mean and variance of this posterior distribution are directly used as the process noise prior input for the unscented Kalman filter, clarifying the initial state of the filter and the boundary of noise characteristics, making the initial parameters of the filter more consistent with the actual working characteristics of the sensor, and significantly improving the initial accuracy of drift calculation.

[0077] Constructing the state equation and observation equation: The state equation is set as follows Among them, state variables ( This is the sensitivity drift. This represents the dynamic variation component of the temperature coefficient. (For the dynamic variation component of linearity) It is the identity matrix. For process noise; the observation equation is set as follows: Among them, the observed values ( For the first Temperature data at any time For the first (Time-based model data), For the observation matrix, To mitigate noise, a linear fitting model is used to establish the relationship between state variables and observed values. This equation is designed to fully adapt to the dynamic response characteristics of MEMS sensors, ensuring the accuracy of state estimation.

[0078] Unscented Kalman Filtering Operation: Following the standard unscented Kalman filtering procedure, initial sigma points covering the state space are generated. The propagation calculation for the time update phase is completed using the state equation. Combined with the observation equation, the observed predicted values ​​are obtained. Then, the state estimation and error covariance correction for the measurement update phase are completed using a preset weight matrix. Through iterative calculations, the accurate sensitivity drift is output in real time. Compared with traditional Kalman filtering, this algorithm has higher accuracy when dealing with nonlinear systems and can accurately capture the dynamic changes of sensitivity drift.

[0079] Filtering algorithm switching: The KS test is used to determine the regression residual distribution characteristics of the unscented Kalman filter. The preset test threshold is p<0.05. When the test result meets this condition, it is determined that the residual deviates from the Gaussian distribution. At this time, the Rao-Blackwellized particle filter algorithm is automatically switched. This switching mechanism enables the filtering process to adapt to the changes in the noise characteristics of the outdoor environment. Regardless of whether the noise is Gaussian or non-Gaussian distributed, the accuracy of the drift calculation can be guaranteed, avoiding the decrease in accuracy of a single algorithm in complex noise environments.

[0080] Real-time data correction: The calculated sensitivity drift ΔS is used to correct the sensor's measured data in real time. The correction formula is as follows: ,in, For the corrected data, Based on actual measured data, the calibration can offset the influence of sensitivity drift on the measurement results in real time, so that the output data always maintains high accuracy and completely solves the problem of sensor accuracy decaying over time in outdoor environments;

[0081] Calibration record: New calibration values, filter algorithm switching status, and calibration timestamps are written into the sensor's non-volatile memory to form a complete core calibration record. This record not only facilitates subsequent calibration traceability, maintenance, and performance analysis, but also provides data support for the sensor's entire lifecycle management, helping users to rationally plan calibration cycles and reduce maintenance costs.

[0082] This invention effectively resists various interference factors such as outdoor temperature fluctuations, electromagnetic interference, and instantaneous vibrations by switching between 3σ criterion data purification and adaptive filtering algorithms, ensuring the accuracy of data acquisition and drift calculation. After calibration, the sensor's measurement error is reduced by an order of magnitude compared to before calibration, the linearity remains stable above 0.998 for a long period, and the temperature coefficient fluctuation is strictly controlled within a reasonable range, enabling continuous output of high-quality measurement data. Furthermore, this invention does not rely on complex laboratory equipment and can complete the entire calibration process on-site outdoors. The establishment of calibration records enables data traceability and planned maintenance, extending the effective working cycle of the sensor in complex outdoor environments and reducing the manpower and time costs associated with frequent calibration.

[0083] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any way. Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make some modifications or alterations to the above-disclosed technical content to create equivalent embodiments without departing from the scope of the present invention. Any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the scope of the present invention.

Claims

1. A method for calibrating the sensitivity of a MEMS sensor in outdoor static measurement, characterized in that, The method includes the following specific steps: S1: Obtain the sensor's factory linearity Factory temperature coefficient ,constant and the corresponding Gaussian distribution standard deviation , ; S2: After the sensor is installed, outlier values ​​of temperature and modulus data are first eliminated by the 3σ criterion, and then temperature and modulus data pairs are continuously collected for several days. S3: Based on the pre-processed temperature and modulus data pairs of each day, the least squares fitting is performed using a linear fitting model to obtain the linearity and temperature coefficient of the day. S4: Calculate the mean of linearity over multiple days. and the average of the temperature coefficient of the day and the variance of linearity ; S5: If the difference between the mean linearity and the factory linearity, and the mean temperature coefficient and the factory temperature coefficient are all within 3 times the standard deviation of the corresponding Gaussian distribution, continue monitoring at the factory value; otherwise, proceed to extended observation. S6: Extend the acquisition cycle, repeat the data acquisition, preprocessing and daily fitting steps, obtain the bus linearity and total temperature coefficient based on the total fitting of all data, and calculate the total constant by the average difference between the modulus and the product of the total temperature coefficient and temperature. S7: Construct dual judgment conditions. If both conditions are met, the sensor sensitivity is determined to be stable, and the bus linearity, total temperature coefficient, and total constant are used as new calibration values. If any condition is not met, the observation window is extended further and monitoring continues until the stability condition is met. S8: After determining the new calibration value, an adaptive filtering process is constructed based on the Bayesian framework to achieve accurate calculation of drift and real-time data correction. The new calibration value is written into the sensor's non-volatile memory and the complete calibration history is recorded in the form of a timestamp.

2. The method for calibrating the sensitivity of a MEMS sensor in outdoor static measurement according to claim 1, characterized in that, In step S1, the Gaussian distribution standard deviation undergoes a standardized pre-shipment environmental test, which involves placing the sensor in a temperature range of -40℃ to +85℃ and performing no less than 30 temperature cycle measurements. For each measurement, the corresponding linearity and temperature coefficient data are recorded. By statistically analyzing the data, the normal distribution parameters of the linearity and temperature coefficient are determined.

3. The method for calibrating the sensitivity of a MEMS sensor in outdoor static measurement according to claim 1, characterized in that, In step S2, the original temperature data and modulus data are preprocessed using the 3σ criterion to remove outliers caused by sensor momentary failures and electromagnetic interference. The core logic of the 3σ criterion is to calculate the mean μ and standard deviation σ of the data and remove abnormal data that exceed the range of [μ-3σ, μ+3σ].

4. The method for calibrating the sensitivity of a MEMS sensor in outdoor static measurement according to claim 1, characterized in that, In step S3, the least squares method is used to perform linear fitting on the daily collected temperature-magnitude data pairs. The fitting formula is as follows: ,in Let b be the temperature coefficient for the day, and b be a constant. For temperature data, This is the modulus data.

5. The method for calibrating the sensitivity of a MEMS sensor in outdoor static measurement according to claim 1, characterized in that, In step S3, the formula for calculating the daily linearity is: ,in, This is the sum of squared residuals, i.e., the sum of squared differences between the measured modulus and the fitted modulus. It is the total sum of squares, that is, the sum of squares of the differences between the measured modulus length and the mean modulus length.

6. The method for calibrating the sensitivity of a MEMS sensor in outdoor static measurement according to claim 1, characterized in that, In step S5, the calculated mean linearity value linearity with factory specifications Compare the values ​​and calculate the average temperature coefficient for the day. With factory temperature coefficient The comparison and judgment logic uses the following formula: and If both inequalities are true, it is determined that the sensor sensitivity has not changed significantly, and the factory calibration value remains unchanged, and routine monitoring continues; if either inequality is false, it is determined that the sensitivity has drifted significantly, and the subsequent calibration process begins.

7. The method for calibrating the sensitivity of a MEMS sensor in outdoor static measurement according to claim 1, characterized in that, In step S6, a global least squares fit is performed on all valid data pairs acquired over the extended period to obtain the bus uniformity. With the total temperature coefficient Simultaneously calculate the total constant. The formula for calculating the total constant is: ,in To extend the total number of data pairs within the collection period, It is the first The measured output modulus data of the group. It is the first The group collected ambient temperature data.

8. The method for calibrating the sensitivity of a MEMS sensor in outdoor static measurement according to claim 1, characterized in that, In step S7, a dual judgment condition is constructed: the first is a variance test to determine the variance of daily linearity. Does it meet the requirements? The second step is a consistency check, which determines the temperature coefficient for all days. With the total temperature coefficient Does it meet the requirements? If both of the above checks are satisfied, the sensor sensitivity is determined to be stable, based on bus uniformity. Total temperature coefficient Total constants The new calibration value replaces the original factory value; if any test fails, the observation window is further extended until the stability condition is met.

9. The method for calibrating the sensitivity of a MEMS sensor in outdoor static measurement according to claim 1, characterized in that, In step S8, the specific steps for constructing an adaptive filtering process based on the Bayesian framework to achieve accurate calculation of drift and real-time data correction are as follows: Using the posterior distribution parameters obtained from batch analysis as the prior of process noise, the sensor sensitivity drift is calculated in real time using an unscented Kalman filter algorithm. ; The KS test is used to determine the regression residual distribution characteristics of the unscented Kalman filter. The preset test threshold is p<0.

05. When the test result meets this condition, it is determined that the residual deviates from the Gaussian distribution, and the Rao-Blackwellized particle filter algorithm is automatically switched. The sensitivity drift obtained by calculation Real-time correction is performed on the sensor's measured data. The correction formula is as follows: ,in For the corrected data, The data is based on actual measurements; at the same time, the new calibration values, filtering algorithm switching status, and calibration timestamps are written into the sensor's non-volatile memory to form a core calibration file.

10. A method for calibrating the sensitivity of a MEMS sensor in outdoor static measurement according to claim 9, characterized in that, The sensor sensitivity drift is calculated in real time using an unscented Kalman filter algorithm. The specific steps are as follows: Based on the total fitted data, historical calibration records, and multi-day statistical analysis results within the extended acquisition period, the posterior distribution of sensitivity drift-related parameters is obtained through batch data modeling. The mean and variance of this posterior distribution are directly used as the prior input of the process noise for the unscented Kalman filter, clarifying the initial state of the filter and the boundary of the noise characteristics. At the same time, state equations and observation equations adapted to the working characteristics of the MEMS sensor are constructed, with the state variables including the sensitivity drift. The dynamic components of the total temperature coefficient and linearity are included, and the observed values ​​are selected from the temperature data collected by the sensor in real time. With output module The correlation between state variables and observed values ​​is established through a linear fitting model. Then, following an unscented Kalman filter process, initial sigma points covering the state space are generated, and the propagation calculation for the time update stage is completed using the state equation. Combined with the observation equation, the predicted observation values ​​are obtained. Finally, a preset weight matrix is ​​used to complete the state estimation and error covariance correction for the measurement update stage. Finally, through iterative calculations, the accurate sensitivity drift is output in real time. .

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