Method for optimizing the measurement of the tilt angle of a mems sensor based on a specific spatial angle

Abstract

The application relates to the field of micro electro mechanical systems, and discloses a specific spatial angle-based MEMS sensor inclination measurement optimization method, which comprises the following steps: S1, fixing at least three single-axis or double-axis MEMS accelerometers on a same rigid substrate in a specific spatial angle which is non-coplanar and non-orthogonal, to form a sensor array, wherein the specific spatial angle is that the sensitive axes of the sensors are directed to the vertex direction of a same regular polyhedron; in the application, at least three single-axis or double-axis MEMS accelerometers are selected and fixed on the same rigid substrate in a non-coplanar and non-orthogonal manner, the sensitive axes of the sensors are directed to the vertex direction of a same regular polyhedron, when a sensor deviates in measurement due to anisotropy error, the measurement data of other sensors can be compensated through geometric symmetry, and the installation positions and the sensitive axis directions of the sensors can be accurately calculated according to the geometric characteristics of the regular polyhedron.

Description

Technical Field

[0001] This invention relates to the field of microelectromechanical systems (MEMS), and more particularly to an optimization method for measuring the tilt angle of MEMS sensors based on a specific spatial angle. Background Technology

[0002] MEMS accelerometers, due to their advantages of small size, low cost, and low power consumption, have been widely used in tilt measurement systems. The core principle of tilt measurement is to calculate the tilt angle of the target object by sensing the projection of the gravity vector onto the sensor's sensitive axis. However, existing MEMS sensors inevitably suffer from anisotropic errors during manufacturing due to limitations in process precision (such as sensitive axis misalignment and residual packaging stress) and the influence of factors such as temperature changes and vibrations in the operating environment. This means that the measurement accuracy of the sensor varies in different spatial directions. This error is a systematic error and is difficult to completely eliminate through simple calibration methods.

[0003] Traditional tilt measurement solutions typically employ a single MEMS sensor or multiple sensors arranged orthogonally. A single sensor cannot compensate for systematic errors using multi-source data, limiting measurement accuracy. While orthogonal sensor arrays are structurally simple, their insufficient geometric symmetry prevents the systematic errors of individual sensors from canceling each other out. This leads to the amplification of errors during data fusion, consequently affecting the accuracy of tilt measurements. In scenarios requiring high measurement accuracy, such as industrial control and high-precision navigation for drones, the anisotropy error of traditional solutions is typically above ±0.1°, failing to meet practical application requirements.

[0004] Therefore, there is an urgent need for an optimized method that can effectively suppress anisotropic errors and improve the accuracy of tilt angle measurement. Summary of the Invention

[0005] To address the shortcomings of existing technologies, this invention provides an optimization method for MEMS sensor tilt angle measurement based on a specific spatial angle, thus solving the above problems.

[0006] To achieve the above objectives, the present invention provides the following technical solution: an optimization method for MEMS sensor tilt angle measurement based on a specific spatial angle, comprising the following steps:

[0007] S1. At least three single-axis or dual-axis MEMS accelerometers are fixed on the same rigid substrate at specific spatial angles that are not coplanar and not orthogonal, forming a sensor array. The specific spatial angles are the directions in which the sensitive axes of each sensor point to different vertices of the same regular polyhedron.

[0008] S2. Place the sensor array in a sealed environment to ensure that the systematic errors of each sensor have a uniform trend of change.

[0009] S3. Establish a three-dimensional rectangular coordinate system with the center of the substrate as the origin, construct a geometric configuration matrix according to the geometric configuration of the sensor array, and convert the measurement data of each MEMS accelerometer into a system of linear equations about the gravity vector G.

[0010] S4. Solve the linear equations using the least squares method to obtain the optimal estimate of the gravity vector G, and then calculate the tilt angle of the target object.

[0011] Preferably, the regular polyhedron is a regular tetrahedron, and the sensor array includes three MEMS accelerometers, with the sensitive axes of each sensor pointing towards the vertices of the regular tetrahedron.

[0012] Preferably, the rigid substrate is made of aluminum alloy, and the MEMS accelerometer is fixed by laser positioning technology, and the spatial angle deviation of the sensing axes of each sensor after fixing does not exceed ±0.1°.

[0013] Preferably, the temperature fluctuation range of the sealed environment is controlled within ±0.5℃, and the humidity does not exceed 60%RH.

[0014] Preferably, the least squares method solves for the estimated value of the gravity vector by minimizing the L2 norm of the error vector. The specific calculation method is as follows:

[0015] ,

[0016] in, For matrix The transpose of the matrix, For geometric configuration matrix, This represents the measurement data vector for each sensor. This is the matrix transpose operation. For the current moment, for The optimal estimate of the gravity vector G obtained at time t is calculated.

[0017] Preferably, the method further includes step S5: filtering the obtained gravity vector, wherein the filtering process adopts the Kalman filtering algorithm to further reduce the influence of random errors.

[0018] Preferably, the Kalman filter algorithm includes the following steps:

[0019] S51. Define the state vector: using the three components of the gravity vector. As a state variable, construct a state vector. ,in These are the components of the gravity vector along the x, y, and z axes in a three-dimensional rectangular coordinate system;

[0020] S52. Establish the core equation:

[0021] Equations of state: ,in, For the current moment, The previous time before the current time k, This is process noise;

[0022] Observation equation: ,in, This is the gravity vector estimate obtained by the least squares method, which is also the measured value of the observed vector at time k. To observe noise;

[0023] S53. Set key parameters: The process noise covariance matrix Q is set to a fixed value. The observation noise covariance matrix R takes a fixed value. Initial state covariance matrix Pick ;

[0024] S54. Simplify iterative updates:

[0025] Calculate the Kalman gain: ;in, This represents the state covariance matrix at time k. To observe the noise covariance matrix;

[0026] Update state estimates: ;in, Represents the gravity vector at time t. The estimated value at the previous moment, This represents the measured value of the observation vector at time k. Indicates the Kalman gain coefficient;

[0027] Update the covariance matrix: ;in, Represented as the process noise covariance matrix;

[0028] S55. Termination condition: After 5 to 10 iterations, directly output the filtered gravity vector for subsequent tilt angle calculation.

[0029] Preferably, the tilt angle calculation includes pitch angle and roll angle, which are calculated using the components of the gravity vector G in a three-dimensional Cartesian coordinate system. The pitch angle is calculated as follows: Roll angle ,in These are the components of the gravity vector G along the x, y, and z axes, respectively.

[0030] Preferably, the measurement range of the MEMS accelerometer is -2g to +2g or -10g to +10g, and the resolution is not less than 0.001g.

[0031] Preferably, the sensor array includes four MEMS accelerometers, and the mounting positions of each sensor on the substrate are symmetrical about the center of the substrate.

[0032] This invention provides an optimized method for MEMS sensor tilt angle measurement based on a specific spatial angle. Compared with existing technologies, it has the following advantages:

[0033] In this invention, at least three single-axis or dual-axis MEMS accelerometers are selected and fixed on the same rigid substrate in a non-coplanar and non-orthogonal manner. The sensitive axes of each sensor point to the vertex direction of the same regular polyhedron. When a sensor causes a measurement deviation due to anisotropic error, the measurement data of other sensors can be compensated by geometric symmetry. For example, if a sensor has a positive deviation in a certain direction, a sensor in another direction may produce a negative deviation. The two cancel each other out during the data fusion process, thereby effectively suppressing systematic errors. Based on the geometric characteristics of the regular polyhedron, the installation position and sensitive axis direction of each sensor can be accurately calculated.

[0034] 2. In this invention, during the data processing stage, a unified measurement model is established to transform the measurement data from each sensor into a system of linear equations concerning the gravity vector. The optimal estimation value of the gravity vector is then obtained using optimal estimation algorithms such as the least squares method. In this process, the design of the geometric configuration matrix directly determines the amplification or suppression effect of the error. The symmetrical layout of the regular polyhedron gives the geometric configuration matrix a good condition number, effectively suppressing the error vector and enhancing the true signal during the solution process. After obtaining the optimal estimation value of the gravity vector, a Kalman filter algorithm is further used to reduce the influence of random errors. The Kalman filter further optimizes the measurement results by iteratively updating the state estimate and covariance matrix, ensuring high accuracy and stability of the tilt angle measurement. Multiple measurements are performed within the range of 0° to 90°. The anisotropy error of the method in this invention is only ±0.025°, which is 83.6% lower than the ±0.153° of the traditional orthogonal three-sensor scheme. Attached Figure Description

[0035] Figure 1 This is a flowchart of the MEMS sensor tilt angle measurement optimization method based on a specific spatial angle proposed in this invention.

[0036] Figure 2 This is a schematic diagram of the spatial layout of the sensor array in an embodiment of the present invention;

[0037] Figure 3This is a comparison chart of the combined tilt angle standard deviation between the method of this invention and the traditional method. Detailed Implementation

[0038] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0039] Please see Figures 1-3 The present invention provides two technical solutions, specifically including the following embodiments:

[0040] Example 1:

[0041] An optimization method for MEMS sensor tilt angle measurement based on a specific spatial angle includes the following steps:

[0042] S1. At least three single-axis or dual-axis MEMS accelerometers are fixed on the same rigid substrate at specific spatial angles that are non-coplanar and non-orthogonal, forming a sensor array. The specific spatial angles are such that the sensitive axes of each sensor point to different vertices of the same regular polyhedron, which is a regular tetrahedron. The sensor array includes three MEMS accelerometers, and the sensitive axes of each sensor point to the vertices of the regular tetrahedron. The rigid substrate is made of aluminum alloy. The MEMS accelerometers are fixed by laser positioning technology. The spatial angle deviation of the sensitive axes of each sensor after fixing does not exceed ±0.1°. The measurement range of the MEMS accelerometer is -2g to +2g or -10g to +10g, and the resolution is not less than 0.001g. The sensor array includes four MEMS accelerometers, and the mounting positions of each sensor on the substrate are symmetrical about the center of the substrate.

[0043] S2. Place the sensor array in a sealed environment to ensure that the systematic errors of each sensor have a uniform trend. The temperature fluctuation range of the sealed environment is controlled within ±0.5℃, and the humidity does not exceed 60%RH.

[0044] S3. Establish a three-dimensional rectangular coordinate system with the center of the substrate as the origin. Construct a geometric configuration matrix based on the geometric configuration of the sensor array and convert the measurement data of each MEMS accelerometer into a system of linear equations about the gravity vector G.

[0045] S4. Solve the linear equations using the least squares method to obtain the optimal estimate of the gravity vector G, and then calculate the tilt angle of the target object. The least squares method solves for the estimate of the gravity vector by minimizing the L2 norm of the error vector. The specific calculation method is as follows:

[0046] ,

[0047] in, For matrix The transpose of the matrix, For geometric configuration matrix, This represents the measurement data vector for each sensor. This is the matrix transpose operation. For the current moment, for The optimal estimate of the gravity vector G obtained at time t is calculated.

[0048] The process also includes step S5: filtering the obtained gravity vector using the Kalman filter algorithm to further reduce the impact of random errors. The Kalman filter algorithm includes the following steps:

[0049] S51. Define the state vector: using the three components of the gravity vector. As a state variable, construct a state vector. ,in These are the components of the gravity vector along the x, y, and z axes in a three-dimensional rectangular coordinate system;

[0050] S52. Establish the core equation:

[0051] Equations of state: ,in, For the current moment, The previous time before the current time k, This is process noise;

[0052] Observation equation: ,in, This is the gravity vector estimate obtained by the least squares method, which is also the measured value of the observed vector at time k. To observe noise;

[0053] S53. Set key parameters: The process noise covariance matrix Q is set to a fixed value. The observation noise covariance matrix R takes a fixed value. Initial state covariance matrix Pick ;

[0054] S54. Simplify iterative updates:

[0055] Calculate the Kalman gain: ;in, This represents the state covariance matrix at time k. To observe the noise covariance matrix;

[0056] Update state estimates: ;in, Represents the gravity vector at time t. The estimated value at the previous moment, This represents the measured value of the observation vector at time k. Indicates the Kalman gain coefficient;

[0057] Update the covariance matrix: ;in, Represented as the process noise covariance matrix;

[0058] S55. Termination Condition: After 5-10 iterations, directly output the filtered gravity vector for subsequent tilt angle calculation. The tilt angle calculation includes pitch and roll angles, which are calculated using the components of the gravity vector G in a three-dimensional Cartesian coordinate system. The pitch angle is calculated as follows: Roll angle ,in These are the components of the gravity vector G along the x, y, and z axes, respectively.

[0059] Example 2:

[0060] Based on Example 1, in order to verify the optimization results of MEMS sensor tilt angle measurement;

[0061] S1. At least three single-axis or dual-axis MEMS accelerometers are fixed at specific spatial angles that are non-coplanar and non-orthogonal on a 50mm×50mm×5mm aluminum alloy substrate to form a sensor array. The specific spatial angle is the direction in which the sensitive axis of each sensor points to different vertices of the same regular polyhedron. The regular polyhedron is a regular tetrahedron. The sensor array includes three MEMS accelerometers, and the sensitive axis of each sensor points to different vertices of the regular tetrahedron. The rigid substrate is made of aluminum alloy. The MEMS accelerometers are fixed by laser positioning technology. The spatial angle deviation of the sensitive axis of each sensor after fixing does not exceed ±0.1°. The measurement range of the MEMS accelerometer is -2g to +2g or -10g to +10g, and the resolution is not less than 0.001g. Four dual-axis MEMS accelerometers are selected, with a measurement range of ±2g, a resolution of 0.0001g, and a zero-bias stability better than ±0.5mg. The mounting position of each sensor on the substrate is symmetrical about the center of the substrate.

[0062] S2. The sensor array is placed in a sealed environment using a tetrahedral layout with an edge length of 50mm. Four sensors are installed at the four corners of the substrate to ensure that the systematic errors of each sensor have a uniform trend. The temperature fluctuation range of the sealed environment is controlled within ±0.5℃, and the humidity does not exceed 60%RH. The sensor array and temperature compensation module are encapsulated together in a stainless steel shell. The sensor array is connected to the data acquisition module via an I2C interface. The acquisition frequency is set to 100Hz, and 100 sets of data are collected in each batch for subsequent fusion calculations. Outlier removal (using the 3σ criterion) and mean filtering (window size of 5) are performed on the collected data to remove the influence of random noise and sudden interference.

[0063] S3. Establish a three-dimensional rectangular coordinate system with the center of the substrate as the origin. Construct a geometric configuration matrix based on the geometric configuration of the sensor array. Convert the measurement data of each MEMS accelerometer into a linear equation system about the gravity vector G. Construct a 4-row, 3-column geometric configuration matrix based on the direction cosines of the four sensors. Each element in the matrix corresponds to the direction cosine value of the sensitive axis of each sensor.

[0064] S4. Solve the linear equations using the least squares method to obtain the optimal estimate of the gravity vector G, and then calculate the tilt angle of the target object. The least squares method solves for the estimate of the gravity vector by minimizing the L2 norm of the error vector. The specific calculation method is as follows:

[0065] ,

[0066] in, For matrix The transpose of the matrix, For geometric configuration matrix, This represents the measurement data vector for each sensor. This is the matrix transpose operation. For the current moment, for The optimal estimate of the gravity vector G obtained at time t is calculated.

[0067] The process also includes step S5: filtering the obtained gravity vector using the Kalman filter algorithm to further reduce the impact of random errors. The Kalman filter algorithm includes the following steps:

[0068] S51. Define the state vector: using the three components of the gravity vector. As a state variable, construct a state vector. ,in These are the components of the gravity vector along the x, y, and z axes in a three-dimensional rectangular coordinate system;

[0069] S52. Establish the core equation:

[0070] Equations of state: ,in, For the current moment, The previous time before the current time k, This is process noise;

[0071] Observation equation: ,in, This is the gravity vector estimate obtained by the least squares method, which is also the measured value of the observed vector at time k. To observe noise;

[0072] S53. Set key parameters: The process noise covariance matrix Q is set to a fixed value. The observation noise covariance matrix R takes a fixed value. Initial state covariance matrix Pick ;

[0073] S54. Simplify iterative updates:

[0074] Calculate the Kalman gain: ;in, This represents the state covariance matrix at time k. To observe the noise covariance matrix;

[0075] Update state estimates: ;in, Represents the gravity vector at time t. The estimated value at the previous moment, This represents the measured value of the observation vector at time k. Indicates the Kalman gain coefficient;

[0076] Update the covariance matrix: ;in, Represented as the process noise covariance matrix;

[0077] S55. Termination Condition: After 5-10 iterations, directly output the filtered gravity vector for subsequent tilt angle calculation. The tilt angle calculation includes pitch and roll angles, which are calculated using the components of the gravity vector G in a three-dimensional Cartesian coordinate system. The pitch angle is calculated as follows: Roll angle ,in These are the components of the gravity vector G along the x, y, and z axes, respectively. The calculation results are rounded to three decimal places.

[0078] The method of this invention was compared with the traditional orthogonal three-sensor scheme in a laboratory with a temperature of 25°C and a humidity of 50% RH. The target object was a high-precision turntable (accuracy ±0.001°). Ten measurement angles were selected in the range of 0° to 90°, and each angle was measured 50 times. The anisotropy error and measurement standard deviation were statistically analyzed.

[0079] The following is a table of test results:

[0080]

[0081] As can be seen from the table above, arrays offer improvements over single-axis or traditional orthogonal methods.

[0082] Experimental results show that the method in this embodiment is significantly better than the traditional orthogonal three-sensor scheme in terms of measurement standard deviation and long-term stability. This indicates that the present invention, through sensor array layout at a specific spatial angle and optimized data fusion algorithm, can effectively suppress anisotropic errors of MEMS sensors, significantly improve the accuracy and stability of tilt angle measurement, and fully meet the needs of high-precision application scenarios.

[0083] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. An optimization method for MEMS sensor tilt angle measurement based on a specific spatial angle, characterized in that: Includes the following steps: S1. At least three single-axis or dual-axis MEMS accelerometers are fixed on the same rigid substrate at specific spatial angles that are not coplanar and not orthogonal, forming a sensor array. The specific spatial angles are the directions in which the sensitive axes of each sensor point to different vertices of the same regular polyhedron. S2. Place the sensor array in a sealed environment to ensure that the systematic errors of each sensor have a uniform trend of change. S3. Establish a three-dimensional rectangular coordinate system with the center of the substrate as the origin, construct a geometric configuration matrix according to the geometric configuration of the sensor array, and convert the measurement data of each MEMS accelerometer into a system of linear equations about the gravity vector G. S4. Solve the linear equations using the least squares method to obtain the optimal estimate of the gravity vector G, and then calculate the tilt angle of the target object.

2. The MEMS sensor tilt angle measurement optimization method based on a specific spatial angle according to claim 1, characterized in that: The regular polyhedron is a regular tetrahedron, and the sensor array includes three MEMS accelerometers, with the sensitive axes of each sensor pointing towards the vertices of the regular tetrahedron.

3. The MEMS sensor tilt angle measurement optimization method based on a specific spatial angle according to claim 1, characterized in that: The rigid substrate is made of aluminum alloy, and the MEMS accelerometer is fixed by laser positioning technology. The spatial angle deviation of the sensing axes of each sensor after fixing does not exceed ±0.1°.

4. The MEMS sensor tilt angle measurement optimization method based on a specific spatial angle according to claim 1, characterized in that: The temperature fluctuation range of the sealed environment is controlled within ±0.5℃, and the humidity does not exceed 60%RH.

5. The MEMS sensor tilt angle measurement optimization method based on a specific spatial angle according to claim 1, characterized in that: The least squares method solves for the estimated value of the gravity vector by minimizing the L2 norm of the error vector. The specific calculation method is as follows: ， in, For matrix The transpose of the matrix, For geometric configuration matrix, This represents the measurement data vector for each sensor. This is the matrix transpose operation. For the current moment, for The optimal estimate of the gravity vector G obtained at time t is calculated.

6. The MEMS sensor tilt angle measurement optimization method based on a specific spatial angle according to claim 1, characterized in that: It also includes step S5: filtering the obtained gravity vector, wherein the filtering process adopts the Kalman filtering algorithm to further reduce the influence of random errors.

7. The MEMS sensor tilt angle measurement optimization method based on a specific spatial angle according to claim 6, characterized in that: The Kalman filter algorithm includes the following steps: S51. Define the state vector: using the three components of the gravity vector. As a state variable, construct a state vector. ,in These are the components of the gravity vector along the x, y, and z axes in a three-dimensional rectangular coordinate system; S52. Establish the core equation: Equations of state: ,in, For the current moment, The previous time before the current time k, This is process noise; Observation equation: ,in, This is the gravity vector estimate obtained by the least squares method, which is also the measured value of the observed vector at time k. To observe noise; S53. Set key parameters: The process noise covariance matrix Q is set to a fixed value. The observation noise covariance matrix R takes a fixed value. Initial state covariance matrix Pick ; S54. Simplify iterative updates: Calculate the Kalman gain: ;in, This represents the state covariance matrix at time k. To observe the noise covariance matrix; Update state estimates: ;in, Represents the gravity vector at time t. The estimated value at the previous moment, This represents the measured value of the observation vector at time k. Indicates the Kalman gain coefficient; Update the covariance matrix: ;in, Represented as the process noise covariance matrix; S55. Termination condition: After 5 to 10 iterations, directly output the filtered gravity vector for subsequent tilt angle calculation.

8. The MEMS sensor tilt angle measurement optimization method based on a specific spatial angle according to claim 7, characterized in that: The tilt angle calculation includes pitch angle and roll angle, which are obtained by calculating the components of the gravity vector G in a three-dimensional rectangular coordinate system. The pitch angle is calculated as follows: Roll angle ,in These are the components of the gravity vector G along the x, y, and z axes, respectively.

9. The MEMS sensor tilt angle measurement optimization method based on a specific spatial angle according to claim 1, characterized in that: The MEMS accelerometer has a measurement range of -2g to +2g or -10g to +10g, and a resolution of not less than 0.001g.

10. The MEMS sensor tilt angle measurement optimization method based on a specific spatial angle according to claim 1, characterized in that: The sensor array includes four MEMS accelerometers, and the mounting positions of each sensor on the substrate are symmetrical about the center of the substrate.

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