阅读说明：本技术 一种基于重力场的加速度计标度因数非线性度测试方法 (Gravity field-based accelerometer scale factor nonlinearity testing method ) 是由 芶志平 王文 罗华 于 2020-05-25 设计创作，主要内容包括：本发明涉及属于惯性传感技术领域,涉及一种基于重力场的加速度计标度因数非线性度测试方法；所述方法包括安装好加速度计后,旋转分度头或者多轴转台,将敏感轴分别以不同角度向左和向右倾斜,采集不同角度下加速度计的输出值；求平均值从而计算出在不同角度下加速度计的输出值；建立加速度计输入值与输出值关系的线性模型,将每个输入的加速度值和对应输出的加速度值通过线性回归法进行数据处理；找出最佳直线,采用最小二乘法求出加速度计的标度因数；计算出每个输入加速度的非线性度,选择最大的非线性度作为加速度计标度因数的非线性度。本发明将重力加速度作为加速度计的输入值,能够使得输入的加速度精度高,并消除了加速度计的安装误差。(The invention relates to the technical field of inertial sensing, and relates to an accelerometer scale factor nonlinearity testing method based on a gravity field; after the accelerometer is installed, rotating a dividing head or a multi-axis turntable, respectively inclining a sensitive axis to the left and the right at different angles, and collecting output values of the accelerometer at different angles; averaging to calculate output values of the accelerometer under different angles; establishing a linear model of the relation between the input value and the output value of the accelerometer, and carrying out data processing on each input acceleration value and the corresponding output acceleration value through a linear regression method; finding out the optimal straight line, and solving the scale factor of the accelerometer by adopting a least square method; calculating the nonlinearity of each input acceleration, and selecting the maximum nonlinearity as the nonlinearity of the accelerometer scale factor. The invention takes the gravity acceleration as the input value of the accelerometer, can ensure high precision of the input acceleration and eliminates the installation error of the accelerometer.)

1. A gravity field-based accelerometer scale factor nonlinearity testing method is characterized by comprising the following steps:

fixedly mounting an accelerometer to be tested on a dividing head or a multi-axis turntable, keeping the dividing head or the multi-axis turntable in a zero input state, and adjusting an X axis of the accelerometer, namely a sensitive axis, so that the positive direction of the sensitive axis is opposite to the gravity direction;

rotating the dividing head or the multi-axis turntable to enable included angles between the sensitive axis of the accelerometer and the initial position of the accelerometer to be different angles in sequence; respectively inclining the sensitive shaft to the left and the right, and collecting output values of the accelerometer when the sensitive shaft is inclined to the left and the right at different angles; averaging output values of the accelerometer when the accelerometer tilts leftwards and rightwards at a certain angle, thereby calculating the output values of the accelerometer at different angles;

based on the calculated output values of the accelerometer under different angles, a linear model of the relation between the input value and the output value of the accelerometer is established, and each input acceleration value and the corresponding output acceleration value are subjected to data processing through a linear regression method; finding out the optimal straight line, and solving the scale factor of the accelerometer by adopting a least square method;

and respectively calculating the deviation value of each output value of the accelerometer and the optimal straight line and the maximum output value of the accelerometer, thereby calculating the nonlinearity of each input acceleration, and selecting the maximum nonlinearity as the nonlinearity of the accelerometer scale factor.

2. The method of claim 1, wherein the tilt axis of sensitivity is left and right, and the collecting the output values of the accelerometer when the accelerometer is tilted left and right at different angles comprises:

when leaning to the left:

V_θ1＝K₁·g·cosθ+K₀+G_y·k_yx·G_z·k_zx；

G_y＝g·sinθ；

G_z＝0；

when tilting to the right:

V_θ2＝K₁·g·cosθ+K₀+G_y·k_yx·G_z·k_zx；

G_y＝g·sin(90+θ)；

G_z＝0；

wherein, V_θ1For the output value of the accelerometer tilting to the left theta, K₁Is the scale factor of the accelerometer; g represents the gravitational acceleration; θ represents the angle at which the accelerometer is tilted to the left and right; k₀Zero position of acceleration; g_yRepresenting an accelerometer Y-axis gravitational acceleration component; g_zRepresents the Z-axis gravitational acceleration component; k is a radical of_yxAn accelerometer cross-coupling coefficient representing the Y axis and the X axis; k is a radical of_zxAccelerometer cross-coupling coefficients representing the Z-axis and the X-axis; v_θ2Is the output value of the accelerometer tilting to the right by theta.

3. The method according to claim 1, wherein the values of the angle θ for tilting the accelerometer to the left and right are 0 °, 30 °, 45 °, 60 °, 90 °, 120 °, 135 °, 150 ° and 180 ° in sequence.

4. The gravity field-based accelerometer scale factor nonlinearity test method according to claim 1, wherein said linear model of accelerometer input value to output value relationship comprises:

V_i＝K₁G_i+K₀+σ

wherein, V_iRepresenting the ith output value of the accelerometer; k₁Is the scale factor of the accelerometer; g_iThe ith input acceleration of the accelerometer; k₀Is the zero position of the accelerometer; σ is the fitting error.

5. The method according to claim 1, wherein the finding the scale factor of the accelerometer by a least square method comprises:

wherein n is the number of input accelerations; g_iThe ith input acceleration of the accelerometer; v_iThe output value is the ith accelerometer output value.

6. The gravity field based accelerometer scale factor nonlinearity test method according to claim 1, wherein said nonlinearity of each input acceleration comprises:

where ρ is_iA non-linearity indicative of an ith input acceleration of the accelerometer; Δ V_iFor each deviation of the output value from the optimum curve, Δ V_i＝V_i-K₁G_i；V_iRepresenting the ith accelerometer output value; g_iThe ith input acceleration of the accelerometer; v_maxIs the maximum output value, V, of the accelerometer_max＝K₁G_max；K₁Is the scale factor of the accelerometer; g_maxIs the maximum input acceleration of the accelerometer.

Technical Field

The invention belongs to the technical field of inertial sensing, and particularly relates to a gravity field-based accelerometer scale factor nonlinearity testing method.

Background

The accelerometer is a sensor for measuring linear acceleration, and the higher the sensitivity is, the better the sensitivity is, because the more sensitive the change of the acceleration occurring to the surrounding environment is, the more easily the change of the acceleration is, naturally, the change of the output voltage is correspondingly larger, so the measurement is easier and more convenient, and the measured data is more accurate. The non-linearity of the scale factor, which is an important indicator of the accuracy of the accelerometer measurements, is usually represented by the slope of a particular line that can be fit using least squares based input/output data obtained by varying the input periodically over the input range. In inertial navigation systems, relevant scale factors include gyroscope scale factors, accelerometer scale factors, torquer scale factors, sensor scale factors, command rate scale factors, and temperature scale factors, among others.

The non-linearity of the accelerometer scale factor is typically tested using a centrifuge test. But limited by the accuracy of the centrifuge, the non-linearity test is less accurate for scale factors within 1g (one acceleration of gravity).

Disclosure of Invention

Based on the problems in the prior art, the gravity acceleration is used as the input of the accelerometer, and the input of the accelerometer can be accurately calculated within the range of 1 g.

The technical scheme adopted by the invention for solving the technical problems comprises the following steps:

a gravity field-based accelerometer scale factor nonlinearity test method, the method comprising:

fixedly mounting an accelerometer to be tested on a dividing head or a multi-axis turntable, keeping the dividing head or the multi-axis turntable in a zero input state, and adjusting an X axis of the accelerometer, namely a sensitive axis, so that the positive direction of the sensitive axis is opposite to the gravity direction;

rotating the dividing head or the multi-axis turntable to enable included angles between the sensitive axis of the accelerometer and the initial position of the accelerometer to be different angles in sequence; respectively inclining the sensitive shaft to the left and the right, and collecting output values of the accelerometer when the sensitive shaft is inclined to the left and the right at different angles; averaging output values of the accelerometer when the accelerometer tilts leftwards and rightwards at a certain angle, thereby calculating the output values of the accelerometer at different angles;

based on the calculated output values of the accelerometer under different angles, a linear model of the relation between the input value and the output value of the accelerometer is established, and each input acceleration value and the corresponding output acceleration value are subjected to data processing through a linear regression method; finding out the optimal straight line, and solving the scale factor of the accelerometer by adopting a least square method;

and respectively calculating the deviation value of each output value of the accelerometer and the optimal straight line and the maximum output value of the accelerometer, thereby calculating the nonlinearity of each input acceleration, and selecting the maximum nonlinearity as the nonlinearity of the accelerometer scale factor.

The invention has the beneficial effects that:

1. the gravity acceleration is used as the input value of the accelerometer, the input acceleration precision is higher than that of the centrifuge, and the test precision of the accelerometer can be improved;

2. the invention adopts the same angle of left and right deflection and adopts a mean value solving mode, thereby eliminating the influence of the installation error of the accelerometer on the test precision.

Drawings

FIG. 1 is a flow chart of a gravity field-based method for testing the non-linearity of the scale factor of an accelerometer according to the present invention;

FIG. 2 is a state diagram of the initial position of the accelerometer of the present invention;

FIG. 3 is a state diagram of the accelerometer in a left tilted position according to the present invention;

FIG. 4 is a diagram of the position of the accelerometer tilting to the right in the present invention.

Detailed Description

In order to make the objects, technical solutions and advantages of the present invention more clearly and completely apparent, the technical solutions in the embodiments of the present invention are described below with reference to the accompanying drawings, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments.

As shown in fig. 1, the present invention provides a gravity field-based accelerometer scale factor nonlinearity testing method, including:

fixedly mounting an accelerometer to be tested on a dividing head or a multi-axis turntable, keeping the dividing head or the multi-axis turntable in a zero input state, and adjusting an X axis of the accelerometer, namely a sensitive axis, so that the positive direction of the sensitive axis is opposite to the gravity direction;

rotating the dividing head or the multi-axis turntable to enable included angles between the sensitive axis of the accelerometer and the initial position of the accelerometer to be different angles in sequence; respectively inclining the sensitive shaft to the left and the right, and collecting output values of the accelerometer when the sensitive shaft is inclined to the left and the right at different angles; averaging output values of the accelerometer when the accelerometer tilts leftwards and rightwards at a certain angle, thereby calculating the output values of the accelerometer at different angles;

based on the calculated output values of the accelerometer under different angles, a linear model of the relation between the input value and the output value of the accelerometer is established, and each input acceleration value and the corresponding output acceleration value are subjected to data processing through a linear regression method; finding out the optimal straight line, and solving the scale factor of the accelerometer by adopting a least square method;

and respectively calculating the deviation value of each output value of the accelerometer and the optimal straight line and the maximum output value of the accelerometer, thereby calculating the nonlinearity of each input acceleration, and selecting the maximum nonlinearity as the nonlinearity of the accelerometer scale factor.

In one embodiment, the accelerometer to be measured is preferably fixedly mounted in the rotary carrier, and then the rotary carrier is mounted on the index head or the multi-axis turntable, so that the sensitive axis of the accelerometer is perpendicular to the table surface of the index head or the multi-axis turntable.

The dividing head or the multi-axis turntable is kept in a zero input state, and the X axis of the accelerometer, namely the sensitive axis, is adjusted, so that the positive direction of the sensitive axis is opposite to the gravity direction; as shown in fig. 2, the X, Y, Z three axes are mutually orthogonal two by two, and the X axis is the sensitive axis of the accelerometer; in this embodiment, the gravity direction is downward, the positive direction of the sensitive axis is vertical upward, the positive direction of the Y axis is horizontal rightward, and the positive direction of the Z axis is vertical inward.

In one embodiment, the included angles between the sensitive axis of the accelerometer and the initial position of the accelerometer are sequentially presented as different angles by rotating the dividing head or the multi-axis turntable; wherein the initial position is the positive direction of the X axis in fig. 2.

Specifically, the sensing axis is tilted to the left and the right respectively according to the included angles, and as shown in fig. 3 and 4, the acceleration values when the sensing axis is tilted to the left by a certain angle θ and when the sensing axis is tilted to the right by a certain angle θ are respectively collected;

when leaning to the left:

V_θ1＝K₁·g·cosθ+K₀+G_y·k_yx·G_z·k_zx；

G_y＝g·sinθ；

G_z＝0；

when tilting to the right:

V_θ2＝K₁·g·cosθ+K₀+G_y·k_yx·G_z·k_zx；

G_y＝g·sin(90+θ)＝-g·sin(θ)；

G_z＝0；

wherein, V_θ1For the output value of the accelerometer tilting to the left theta, K₁Is the scale factor of the accelerometer; g represents the gravitational acceleration; θ represents the angle at which the accelerometer is tilted to the left and right; k₀Zero position of acceleration; g_yRepresenting an accelerometer Y-axis gravitational acceleration component; g_zRepresents the Z-axis gravitational acceleration component; k is a radical of_yxAn accelerometer cross-coupling coefficient representing the Y axis and the X axis; k is a radical of_zxAccelerometer cross-coupling coefficients representing the Z-axis and the X-axis; v_θ2Is the output value of the accelerometer tilting to the right by theta.

Theta is a variable value and can be 0 DEG, 30 DEG, 45 DEG, 60 DEG, 90 DEG, 120 DEG, 135 DEG, 150 DEG and 180 DEG in sequence; the value of the inclination angle set in this embodiment is a preferred value of the present invention, but the present invention is not limited to the above optimal value, and may be set to another set of angles between 0 ° and 180 °.

In the process, the output values of the accelerometer are averaged when the accelerometer inclines leftwards and rightwards at a certain angle, so that the output values of the accelerometer at different angles are calculated;

V_i＝(V_θ1+V_θ2)/2

＝(K₁·g·cosθ+K₀+g·sinθ·k_yx+K₁·g·cosθ+K₀-g·sinθ·k_yx)/2

＝K₁·g·cosθ+K₀

by adopting the mode, the test error caused by the installation of the accelerometer in the test process can be eliminated.

Based on the calculated output values of the accelerometer under different angles, a linear model of the relation between the input value and the output value of the accelerometer is established, and the linear model is expressed as follows:

V_i＝K₁G_i+K₀+σ

wherein, V_iRepresenting the ith output value of the accelerometer; k₁Is the scale factor of the accelerometer; g_iThe ith input acceleration of the accelerometer; k₀Is the zero position of the accelerometer; σ is the fitting error.

Processing data of each input acceleration value and the corresponding output acceleration value by a linear regression method; finding out the best straight line, and calculating the scale factor K of the accelerometer by least square method₁：

Wherein n represents the number of input accelerations; g_iThe ith input acceleration of the accelerometer; v_iThe output value is the ith accelerometer output value.

Calculating the deviation of each output value from the optimal curve and the maximum output value of the accelerometer according to the following formula:

ΔV_i＝V_i-K₁G_i；

V_max＝K₁G_max；

wherein, is Δ V_iFor each output value and optimum curveDeviation; g_iThe ith input acceleration of the accelerometer; g_maxMaximum input acceleration of accelerometer, G in the invention_max＝g。

Based on the above equation, the non-linearity of each input acceleration of the accelerometer is calculated, and is expressed as:

the invention takes the maximum nonlinearity as the nonlinearity of the accelerometer scale factor, and the maximum nonlinearity is expressed as rho-max (rho)_i)。

The test procedure of the present invention is given below, including:

installing an accelerometer to be tested in a rotating carrier, and then installing the rotating carrier on a dividing head or a multi-axis turntable to enable a rolling axis of a gyroscope to be vertical to the table top of the turntable; adjusting the X axis of the accelerometer, namely the sensitive axis, so that the positive direction of the sensitive axis is opposite to the gravity direction;

rotating the dividing head or the multi-axis turntable to enable included angles between the sensitive axis of the accelerometer and the initial position of the accelerometer to be different angles in sequence; respectively inclining the sensitive shaft to the left and the right, and collecting output values of the accelerometer when the sensitive shaft is inclined to the left and the right at different angles; averaging output values of the accelerometer when the accelerometer tilts leftwards and rightwards at a certain angle, thereby calculating the output values of the accelerometer at different angles;

based on the calculated output values of the accelerometer under different angles, a linear model of the relation between the input value and the output value of the accelerometer is established, and each input acceleration value and the corresponding output acceleration value are subjected to data processing through a linear regression method; finding out the optimal straight line, and solving the scale factor of the accelerometer by adopting a least square method;

and respectively calculating the deviation value of each output value of the accelerometer and the optimal straight line and the maximum output value of the accelerometer, thereby calculating the nonlinearity of each input acceleration, and selecting the maximum nonlinearity as the nonlinearity of the accelerometer scale factor.

For the calculated output values of the accelerometer under different angles, the non-linearity of the final accelerometer scale factor is obtained through a device.

Specifically, the present application provides an embodiment of an apparatus for testing non-linearity of accelerometer scale factor based on a gravitational field, where the apparatus specifically includes the following components: a processor (processor), a memory (memory), a communication Interface (Communications Interface), and a bus; the processor, the memory and the communication interface complete mutual communication through the bus; the communication interface is used for realizing information transmission between related devices; the electronic device may be a desktop computer, a tablet computer, a mobile terminal, and the like, but the embodiment is not limited thereto. In this embodiment, the electronic device may refer to an embodiment for implementing the testing method of the present invention, and the contents thereof are incorporated herein, and repeated descriptions are omitted.

The processor is used for calculating output values of the accelerometer under different calculated angles, establishing a linear model of the relation between the input values and the output values of the accelerometer, and carrying out data processing on each input acceleration value and the corresponding output acceleration value through a linear regression method; finding out the optimal straight line, and solving the scale factor of the accelerometer by adopting a least square method; and respectively calculating the deviation value of each output value of the accelerometer and the optimal straight line and the maximum output value of the accelerometer, thereby calculating the nonlinearity of each input acceleration, and selecting the maximum nonlinearity as the nonlinearity of the accelerometer scale factor.

The memory is used for storing the acceleration value of each input and the corresponding acceleration value of the output and the nonlinearity of the final accelerometer scale factor.

Those skilled in the art will appreciate that all or part of the steps in the methods of the above embodiments may be implemented by associated hardware instructed by a program, which may be stored in a computer-readable storage medium, and the storage medium may include: ROM, RAM, magnetic or optical disks, and the like.

The above-mentioned embodiments, which further illustrate the objects, technical solutions and advantages of the present invention, should be understood that the above-mentioned embodiments are only preferred embodiments of the present invention, and should not be construed as limiting the present invention, and any modifications, equivalents, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.