A two-axis accelerometer parameter calibration method for an inclination sensor

Abstract

The application discloses a two-axis accelerometer parameter calibration method for an inclination sensor, and steps are as follows: a plurality of to-be-calibrated accelerometers are fixed on a same rotating plate; a rotating platform is tilted by less than 45 degrees near a horizontal plane for multiple times to record batch sampling; a calibrated accelerometer is arranged to generate an initial reference standard value; for any two accelerometers, a difference between an inner product of an attitude vector and the reference standard value is taken as an objective function to calculate calibration values of required offset values offset and scale factors scale; a plurality of accelerometers in the batch of to-be-calibrated accelerometers are brought into the respective calibrated offset values offset and scale factors scale, a new reference standard value generated by the plurality of accelerometers is obtained by means of cumulative summation, and a reference standard value with smaller noise variance is obtained; and the calibration values of the offset values offset and the scale factors scale of all the accelerometers in the batch are iteratively output. The application guarantees calibration precision while reducing cost.

Description

TECHNICAL FIELD

[0001] The present application relates to calibrating two-axis MEMS accelerometer intrinsic parameters by rotating in the gravity field, and belongs to the field of MEMS accelerometer calibration method. BACKGROUND

[0002] For the gravity tilt sensor using MEMS accelerometer, in order to achieve higher measurement accuracy, the parameters of the accelerometer need to be calibrated before use due to the manufacturing process of the sensor itself and other problems. In the model equation of the accelerometer, the offset value offset and the scale factor scale are the main parameters affecting the accuracy. There are two main methods for accelerometer calibration: gravity rotation calibration method and centrifuge calibration method.

[0003] The gravity rotation calibration method refers to rotating the accelerometer in the naturally fixed earth gravity field at multiple angles, measuring the gravity with constant direction and size of 1g, collecting multiple sets of sensor measurement data, and using a specific numerical calculation method to obtain the required calibration parameters.

[0004] The centrifuge calibration method refers to using a precision centrifuge to rotate along multiple axes of the accelerometer, and generating multiple acceleration values greater than 1g by controlling the rotation speed, obtaining multiple sets of sensor measurement data corresponding to the set acceleration values of the precision centrifuge, and calculating the required calibration parameters. For example, the centrifugal acceleration field tumbling calibration method of a linear accelerometer disclosed in CN106443072A.

[0005] For the gravity rotation calibration method, there are mainly two specific implementation methods, ellipsoid fitting method and multi-attitude rotation fitting method, and the difference between the two is the different assumptions and target functions.

[0006] The ellipsoid fitting method requires a three-axis acceleration sensor to output a three-dimensional vector. The earth's gravity will produce corresponding acceleration components on the XYZ three axes of the accelerometer, and the three components of this vector represent the measurement values of each axis component. The ellipsoid fitting method needs to rotate the accelerometer at many different angles for sampling, and the vertices of these three-dimensional vectors will form an ellipsoid. Through least squares fitting, the equation of the ellipsoid can be obtained. For an ideal accelerometer, since the earth's gravity remains fixed, the obtained ellipsoid should be a sphere, and for an actual accelerometer, the center of the ellipsoid offset corresponds to the sensor offset value parameter offset, and the three axes of the ellipsoid correspond to the scale factors scale of the XYZ three axes of the sensor.

[0007] The multi-attitude rotation fitting method also requires the accelerometer to rotate at multiple angles. To calibrate the offset values ​​and scale factor (a total of six unknowns) across the X, Y, and Z axes, at least six different rotations are necessary. For the multi-attitude rotation fitting method, rotation within a 1g Earth gravitational field assumes that the magnitude of the three-dimensional vector output by an ideal accelerometer should be 1. Rotating at more than six different angles allows for the formulation of at least six equations concerning the offset and scale factors, forming a system of linear equations. Solving this system of linear equations yields the required calibration parameters.

[0008] Existing methods have certain limitations.

[0009] Centrifuge calibration is expensive due to the need for a precision centrifuge. Furthermore, precise alignment of the accelerometer on the centrifuge's working surface, ensuring its center coincides with the centrifuge's rotation center, is time-consuming, labor-intensive, and prone to introducing errors. Additionally, for tilt sensors used to detect only 1g of Earth's gravity, with acceleration components along the X, Y, and Z axes less than 1g, using a precision centrifuge to calibrate the range greater than 1g is largely meaningless. Therefore, using an expensive precision centrifuge is not an ideal choice for tilt sensor parameter calibration.

[0010] For the gravity rotation calibration method, taking the ellipsoid fitting method as an example, it is necessary to collect rotation results at various angles. In order to make the sampling points form a complete ellipsoid, the rotation platform needs to be flipped and rotated at large angles. This requires the accelerometer connection harness on the rotation platform to be specially arranged to avoid twisting interference, or to use wireless data transmission.

[0011] Secondly, both existing ellipsoidal fitting and multi-attitude rotational fitting methods require the accelerometer to output a three-dimensional vector, meaning the accelerometer needs to have three axes: X, Y, and Z. However, for tilt sensor applications, a lower-cost accelerometer with only X and Y axes can be used to measure the direction of gravity. Therefore, existing ellipsoidal fitting and multi-attitude rotational fitting methods are ineffective for accelerometers with only X and Y axes.

[0012] Even for accelerometers with XYZ axes, when the XY axes are approximately parallel to the horizontal plane, the Z-axis is approximately vertical, and the component of gravity on the Z-axis is close to saturation. The component of gravity on the Z-axis has a sinusoidal relationship with the tilt angle. When the Z-axis is approximately 90 degrees vertical, the Z-axis output value is not sensitive and is easily affected by noise. In this case, substituting the Z-axis value into the gravity rotation calibration calculation using ellipsoidal fitting and multi-attitude rotation fitting methods will affect the accuracy of the results. Summary of the Invention

[0013] To overcome the shortcomings of existing technologies, the present invention aims to provide a method for calibrating two-axis accelerometer parameters for tilt sensors. To reduce implementation costs, the present invention does not employ a high-precision rotating platform; to calibrate accelerometers with only X and Y axes, the present invention extends the two-dimensional output into a three-dimensional attitude vector; to achieve unrestricted accelerometer mounting positions, the present invention uses the inner product of attitude vectors with rotational invariance as a reference standard value; to improve measurement accuracy, the present invention employs an improved small-angle tilt rotation method, and utilizes the averaging property of the reference standard value in the present invention to achieve batch processing while simultaneously improving measurement accuracy.

[0014] A method for calibrating the parameters of a two-axis accelerometer used in a tilt sensor, comprising the following steps:

[0015] Step 1: A batch of accelerometers to be calibrated are fixed on the same rotating plate, with the X and Y axes of the accelerometers parallel to the rotating plate;

[0016] Step 2: The rotating platform is tilted at less than 45 degrees multiple times near the horizontal plane, and the outputs of all accelerometers are sampled and recorded in batches;

[0017] Step 3: Among the batch of accelerometers to be calibrated, set one calibrated accelerometer to generate the initial reference standard value;

[0018] Step 4: For any two accelerometers, use the difference between the inner product of the attitude vectors and the reference standard value as the objective function, and use stochastic gradient descent to perform parameter regression to calculate the required offset value and the calibration value of the scale factor.

[0019] Step 5: The multiple accelerometers in the batch to be calibrated are fed with their respective calibrated offset values ​​and scale factors. The generated new reference standard values ​​are summed to obtain reference standard values ​​with smaller noise variance, which are then applied to the parameter regression of the accelerometers.

[0020] Step 6: Iterate through Step 4 and Step 5 above to output the offset value and scale factor calibration value of all accelerometers in this batch.

[0021] The rotating platform includes a rotating plate, electric push rods, and a fixed base. The lower part of the electric push rod is connected to the base via a hinge, and the upper part is connected to the rotating plate via a ball joint. The tilting of the rotating plate is achieved by controlling the length of the three electric push rods.

[0022] The accelerometer to be calibrated is an XY two-axis MEMS accelerometer with two mutually perpendicular sensing axes and a measurement range from -1g to +1g. The parameters to be calibrated are the offset value and the scale factor.

[0023] The beneficial effects of this invention are:

[0024] For gravity tilt sensors using MEMS accelerometers, this invention reduces the manpower and material costs of parameter calibration in several aspects, and reduces measurement errors while ensuring calibration accuracy in an economical and efficient manner.

[0025] 1. The XY-axis parameters of the accelerometer were calibrated using only a simple rotating platform tilted at a small angle near the horizontal plane. Since Z-axis data was not used, the problem of Z-axis insensitivity and high noise at this position was avoided, and the invention can be applied to the calibration of XY-axis accelerometers that lack a Z-axis.

[0026] 2. Rotary platforms do not require precise control of rotation angles; they only need to be stable and vibration-free. This not only reduces equipment costs but also allows for the use of various mechanical structures due to the small angle of inclination only near the horizontal plane. Connecting harnesses can also be easily arranged, avoiding problems such as wiring harness twisting and interference encountered in large-angle rotations, as seen in ellipsoidal fitting methods.

[0027] 3. The accelerometer installation process on the rotating platform does not require deliberate alignment adjustments, and there is no need to consider assembly errors between the accelerometer housing and the internal measurement axis of the chip, saving time and effort. Since the inner product of attitude vectors is used as the objective function, the inner product of the attitude vectors of any two accelerometers is the same in the same rotation, independent of the initial installation attitude of the accelerometer.

[0028] 4. This invention is applicable to batch accelerometer calibration. Batch calibration not only reduces the calibration cost of a single accelerometer, but also allows sensors in the same batch to help each other during calibration. By summing the results, the noise variance can be reduced, thus achieving higher precision parameter calibration. Attached Figure Description

[0029] Figure 1 This is a schematic diagram of the device used in this invention.

[0030] Figure 2 This is a flowchart of one step of the present invention.

[0031] The diagram shows: 1-accelerometer module, 2-rotating plate, 3-electric push rod, 4-fixed base. Detailed Implementation

[0032] To provide a detailed explanation of the invention, the following sections define some concepts and elaborate on the invention itself.

[0033] 1. Attitude vector of the accelerometer

[0034] For a two-axis MEMS accelerometer (XY axis), which includes two mutually perpendicular measurement axes X and Y, two electrical signals are output to represent the acceleration components along these axes. This invention performs parameter calibration by rotating the accelerometer in a natural gravitational field. The angles between the horizontal plane and the X and Y axes of the accelerometer are denoted as a and b, respectively. The projected acceleration components of Earth's gravity along the X and Y axes are denoted as Ax and Ay, respectively. The relationship between the output electrical signals Vx and Vy and the acceleration components Ax and Ay is as follows:

[0035]

[0036] Where offset is the offset value that needs to be calibrated, and scale is the scaling factor that needs to be calibrated.

[0037] Since the natural gravitational field is fixed at 1g, the direction of Earth's gravity can be represented as a three-dimensional vector with a magnitude of 1 in the right-handed rectangular coordinate system formed by the X and Y axes of the accelerometer:

[0038]

[0039] In this invention, this vector is referred to as the attitude vector of the accelerometer, which can represent the attitude direction of the accelerometer after the rotation. This invention uses this method to represent the two outputs of the XY axis accelerometer as a direction vector in a three-dimensional XYZ space.

[0040] 2. Small angle tilt

[0041] Small-angle tilt means that during the gravity rotation calibration process, the tilt angle of the rotating platform relative to the horizontal plane does not exceed 45 degrees.

[0042] Analysis of the sine function sin(a) reveals that the derivative of the sin function is at its maximum when angle a is near 0 degrees, meaning even a small change in angle a can cause a change in sin(a). When angle a is near 90 degrees, the derivative of the sin function approaches 0, and sin(a) remains approximately constant as angle a changes. Therefore, when multiple accelerometers are fixed to the same rotating plate and mounted on a conventional rotating platform for multi-attitude rotation sampling, this invention, to ensure data sensitivity along the X and Y axes, only performs multiple small-angle tilting rotations near the horizontal plane, batch sampling and recording the outputs of all accelerometers.

[0043] 3. Reference standard value of accelerometer

[0044] The reference standard value refers to the inner product of the attitude vectors of an accelerometer at two rotational positions. This reference standard value should be equal for accelerometers in the same batch. Based on this, this invention uses batch stochastic gradient descent to perform parameter regression to obtain the required calibration parameters.

[0045] To illustrate the data calculation method of this invention, two accelerometers are selected from this batch and designated as Accelerometer 1 and Accelerometer 2, respectively. After the i-th rotation, the attitude vector of Accelerometer 1 is denoted as Ai, and the attitude vector of Accelerometer 2 is denoted as Bi. Since this invention fixes multiple accelerometers on the same rotating plate, for the same rotation from position i to position j, Accelerometer 1 and Accelerometer 2 will have the same rotation angle. That is, the angle between the two attitude vectors Ai and Aj of Accelerometer 1 will be equal to the angle between the two attitude vectors Bi and Bj of Accelerometer 2.

[0046] This invention constructs an objective function based on the condition that the rotation angles of two accelerometers are the same in the same rotation, and uses batch stochastic gradient descent to perform parameter regression to obtain the required calibration parameters. Since attitude vectors Ai and Aj are both vectors with a magnitude of 1, the cosine of the angle between them is equal to the dot product of the two vectors. Therefore, the same rotation angle can be equivalently represented as the same dot product of the attitude vectors, satisfying the following relationship:

[0047] The objective function can then be written as: The optimization parameters are the offset and scale parameters to be calibrated, contained in the attitude vector A. The dot product of the attitude vectors of one accelerometer is used as a reference standard, and the difference between the dot product of the attitude vectors of the other accelerometer and the reference standard should be minimized. To minimize the objective function E, the batch stochastic gradient method is used to solve for the offset and scale parameters, which are then used as the calibration results.

[0048] 4. Batch calibration

[0049] Batch calibration refers to the requirement in this invention that multiple accelerometers be fixed on the same rotating platform, and that batch calibration is used to reduce noise variance and improve calibration accuracy.

[0050] This invention requires batch calibration of sensors because sensors within the same batch assist each other during calibration. Unlike other gravity-based rotation calibration methods, it does not rely on a special rotating platform to control the rotation attitude each time. Instead, it uses the interrelationships between multiple accelerometers across multiple rotations as a condition for calculation. To reduce costs, this invention can use a common rotating platform, which does not output the angle and direction of each rotation. Therefore, during initialization, one calibrated accelerometer from this batch is used to generate a reference standard value. Other accelerometers use this value as input into the objective function for parameter regression. Once the parameters of a portion of the accelerometers are roughly calibrated, their calibrated outputs are also used as reference standard values ​​in the parameter regression of other accelerometers. The cumulative average of the reference standard values ​​output by multiple sensors has a smaller noise variance than a single reference standard value. Through multiple iterations of the above process, the parameter calibration of the entire batch of accelerometers is achieved. According to the law of large numbers in probability theory, the average of the reference standard values ​​output by multiple sensors will converge to the expected value with probability. Furthermore, since a calibrated sensor is added during initialization, the average of the accumulated reference standard values ​​will be unbiased. Simultaneously, because the noise models of the same batch of accelerometers are independent and identically distributed, the reference value after averaging will have a smaller noise variance, resulting in more accurate calibration parameters compared to using a single reference standard value. This invention utilizes only a common rotating platform to perform high-precision parameter calibration for mass-produced tilt sensor accelerometers.

[0051] In combination with the above-mentioned improved methods, the objective of this invention is achieved through the following technical solution:

[0052] The operation process is roughly divided into two parts. First, the raw data output from the multi-attitude rotation of a batch of accelerometers is sampled and saved. Then, the data is iterated and calculated multiple times to finally obtain the calibration parameter results.

[0053] Step 1: Accelerometer Installation. This invention utilizes the fact that two accelerometers rotate at the same angle during the same rotation; therefore, multiple accelerometers need to be fixed to the same rotating plate. Since the reference standard used is a rotational invariant, the X and Y axes of the accelerometers only need to be approximately parallel to the rotating plate during installation. They can then be installed on a standard rotating platform for multi-pose rotation sampling.

[0054] Step two involves a small-angle tilt to batch sample and record the outputs of all accelerometers. To ensure the sensitivity of the XY-axis data, the accelerometers are installed with their XY axes roughly parallel to the horizontal plane. The rotating platform is tilted at small angles multiple times near the horizontal plane, resulting in sensitive data that is less susceptible to noise.

[0055] Step 3: Calculate the initial reference standard value. During initialization, a calibrated initial accelerometer needs to be set among this batch of accelerometers to generate the initial reference standard value. Since this invention optimizes calibration parameters by comparing pairs of accelerometers, setting this accelerometer can provide initial parameter calibration for other sensors and ensure that the calibration values ​​do not deviate during subsequent iterative calibration processes. Based on the original data sampling records in Step 2, calculate the reference standard values ​​generated by the initial accelerometer under pairs of different rotational attitudes.

[0056] Step four, calibration parameter calculation. For two different rotational attitudes, the transition from the first attitude to the second attitude can be considered as one rotation. For any two accelerometers, their rotation angles should be the same in the same rotation. Using the difference between the dot product of the attitude vectors and the reference standard value as the objective function, stochastic gradient descent is used to perform parameter regression to calculate the required offset and scale calibration values.

[0057] Step 5, Batch Calibration. After a portion of the accelerometer parameters have been roughly calibrated, the calibrated outputs of these accelerometers are used to calculate more reference standard values. The reference standard values ​​generated by multiple accelerometers are summed to obtain a reference standard value with smaller noise variance, which is then applied to the accelerometer parameter regression.

[0058] Step six: Through multiple iterations of steps four and five above, output the calibration parameters for all accelerometers in this batch.

[0059] The present invention will be further described below with reference to the accompanying drawings and embodiments. Example

[0060] The implementation process of this invention is divided into two main parts: first, data sampling is performed on a batch of accelerometer modules under multiple tilt attitudes on a rotating mechanical device, and the data is stored and recorded; second, the parameter calibration method proposed in this invention is used to calculate the calibration values ​​of offset and scale factor of each accelerometer.

[0061] In an embodiment of the present invention, a rotating device driven by three electric push rods is used, such as... Figure 1 As shown, the device includes a rotating plate 2, electric actuators 3, and a fixed base 4. The lower part of the electric actuator 3 is connected to the base 4 via a hinge, and the upper part is connected to the rotating plate 2 via a ball joint. By controlling the lengths of the three electric actuators 3, the rotating plate 2 can be tilted at different angles and in different directions. In this embodiment, this device achieves the small-angle tilt required by the present invention, but this is only one preferred solution. For those skilled in the art, several simple deductions or substitutions can be made.

[0062] The accelerometer module used in this embodiment is an XY thermocouple-type MEMS accelerometer with two mutually perpendicular sensing axes. Its measurement range is from -1g to +1g, and it outputs a digital signal representing acceleration. The theoretical output digital signal value is 512000 at 0g, 768000 at +1g, and 256000 at -1g. Both the X and Y axes have an offset value and a scale factor that require calibration. The nominal value of the offset is 512000, and the nominal value of the scale factor is 256000. The acceleration is equal to the digital signal value minus the offset value, divided by the scale factor.

[0063] Multiple accelerometer modules need to be such Figure 1 As shown, all accelerometer modules are fixedly mounted on a rotating plate. The X and Y axes of the accelerometers need to be approximately parallel to the rotating plate, but strict alignment is not required. The relative positions of the individual accelerometer modules are also not limited. By controlling the extension and retraction of the electric push rod, all accelerometer modules can be tilted together. In this embodiment, the rotating plate is controlled to tilt in 10 different directions at angles of 10 degrees, 20 degrees, 30 degrees, and 40 degrees, requiring a total of 40 different tilting postures for gravity rotation calibration.

[0064] Examples of the parameter calibration method of the present invention Figure 2 The process is shown in the diagram:

[0065] Step 1: Accelerometer Installation. In this example, 13 accelerometers are fixed on the same rotating plate, with their XY axes roughly parallel to the plate. They are then mounted on a standard rotating platform for multi-pose rotation sampling.

[0066] Step two, small-angle tilt. To ensure the sensitivity of the XY axis data, the rotating platform is tilted at small angles multiple times only near the horizontal plane, requiring a total of 40 different tilt positions, and the outputs of all accelerometers are sampled and recorded in batches.

[0067] Step 3: Calculate the initial reference standard values. During initialization, a calibrated initial accelerometer needs to be selected from this batch of accelerometers to generate the initial reference standard values. For two different attitudes, the transition from one attitude to the next can be considered as one rotation. Step 2 collected 40 attitudes, which can be equivalent to 40*39 / 2 rotations. Based on the sampling records from Step 2, the inner product of the attitude vectors of the initial accelerometer under these 780 rotations is calculated, thus forming 780 initial reference standard values.

[0068] Step 4: Calibration Parameter Calculation. For any two accelerometers, their rotation angles should be the same in the same rotation. Since the reference standard value is rotationally invariant, the accelerometer can use the difference between its own attitude vector's inner product and the reference standard value as the objective function. Batch stochastic gradient descent is used for parameter regression, iteratively calculating the required offset and scale calibration values. The minimum squared error (MSE) of the objective function is used as the loss. In each cycle, 50 reference standard values ​​are selected from 780 to form a mini-batch. The Adam optimization algorithm with a step size of 5 is used, iterating for 1000 cycles, or stopping when the loss is less than the order of 10^-8, to obtain the calibration parameters offset and scale.

[0069] Step 5, Batch Calibration. After the parameters of a portion of the accelerometers have been roughly calibrated, the outputs of these calibrated accelerometers are used to calculate more reference standard values. The reference standard values ​​generated by multiple accelerometers are summed to obtain a reference standard value with a smaller noise variance. In this example, the standard deviation of the accelerometer sampling noise is 53, and the standard deviation of the reference standard value obtained from a single accelerometer is 0.0001862, while the standard deviation of the reference standard value obtained when 13 accelerometers are calibrated in batch is 0.0000583, the former being approximately 3.2 times the latter.

[0070] Step six: Apply the reference standard values ​​obtained in step five to the parameter regression in step four. By repeatedly iterating through steps four and five, output the calibration parameters for all accelerometers in this batch.

[0071] The embodiments described above are merely illustrative of several implementations of the present invention, and while the descriptions are specific and detailed, they should not be construed as limiting the scope of the invention. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of the present invention, and these modifications and improvements all fall within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the appended claims.

Claims

1. A method for calibrating the offset value and scale factor of a biaxial accelerometer used in a tilt sensor, characterized in that, The steps are as follows: Step 1: A batch of accelerometers to be calibrated are fixed on the same rotating plate. The X and Y axes of the accelerometers are parallel to the rotating plate. There are no limit requirements, and the rotating plate does not have any limit devices for accelerometer alignment. Step 2: The rotating platform is tilted at less than 45 degrees multiple times near the horizontal plane. The raw output data Vx and Vy of all accelerometers are sampled and recorded in batches. There is no requirement for the positioning accuracy of the tilt angle, and it is not necessary to obtain the angle value. Step 3: Among the batch of accelerometers to be calibrated, set one calibrated accelerometer to generate the initial reference standard value; Step 4: Select two accelerometers, A and B, and define attitude vectors A and B respectively. The formula for the attitude vector is: The length of this vector is constant at 1; where A x =(Vx-offset) x ) / Scale x Includes X-axis parameters to be calibrated, A y =(Vy-offset) y ) / scale y Includes Y-axis parameters to be calibrated; the attitude vector of accelerometer A is defined as A under two different tilt attitudes, i and j. i and A j The attitude vector of accelerometer B is B i and B j ; construct rotation invariant A through the inner product of attitude vectors i ·A j and B i ·B j The objective function is constructed using the difference between the inner product of the attitude vectors and the reference standard value, with the formula E = A. i ·A j -B i ·B j The objective function does not contain trigonometric function operations, which facilitates gradient calculation; stochastic gradient descent is used to perform parameter regression on the objective function to calculate the required offset values ​​of the X and Y axes and the calibration values ​​of the scale factor. Step 5: The multiple accelerometers in the batch to be calibrated are fed with their respective calibrated offset values ​​and scale factors. The generated new reference standard values ​​are summed to obtain reference standard values ​​with smaller noise variance, which are then applied to the parameter regression of the accelerometers. Step 6: Iterate through Step 4 and Step 5 above to output the offset value and scale factor calibration value of all accelerometers in this batch.

2. The biaxial accelerometer parameter calibration method according to claim 1, characterized in that, The rotating platform does not require precise control of the rotation angle; it only needs to ensure stability and no vibration. It includes a rotating plate, electric push rods, and a fixed base. The lower part of the electric push rod is connected to the base via a hinge, and the upper part is connected to the rotating plate via a ball joint. The tilting of the rotating plate is achieved by controlling the length of the three electric push rods.

3. The biaxial accelerometer parameter calibration method according to claim 1, characterized in that, The accelerometer to be calibrated is a two-axis MEMS accelerometer with only two mutually perpendicular measurement axes, X and Y, and does not use the Z axis; the measurement range is from -1g to +1g, and the parameters to be calibrated are the offset values ​​of the X measurement axis and the scale factor of the Y measurement axis.

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