CN101852818B - Accelerometer error calibration and compensation method based on rotary mechanism - Google Patents

Abstract

An accelerometer error calibration and compensation method based on a rotating mechanism refers to installing the accelerometer on the rotating mechanism according to certain requirements, and obtaining the relationship between the dynamic continuous output of the accelerometer and the rotation angle of the rotating mechanism through the rotation of the rotating mechanism , and use the least squares method to estimate the zero bias of the accelerometer, the proportional coefficient, the nonlinear error coefficient of the proportional coefficient, the cross-coupling error coefficient, etc. The invention uses the rotating mechanism to estimate all the error coefficients of the accelerometer, and has the characteristics of accuracy, high efficiency, easy operation, high versatility and the like. After the error coefficient is estimated by this method and the corresponding error compensation is performed, the output accuracy of the accelerometer can be greatly improved. This method is also applicable to the calibration of the gyroscope, which can greatly improve the speed measurement accuracy of the gyroscope.

Description

A Method of Accelerometer Error Calibration and Compensation Based on Rotating Mechanism

technical field

The invention relates to an accelerometer error calibration and compensation method, which can be applied to the error calibration and compensation of other inertial devices such as gyroscopes, and belongs to the fields of inertial device testing and inertial navigation.

technical background

The inertial navigation system has the characteristics of full autonomy, high concealment, high bandwidth, and continuous output. It has strategic significance in national defense and is one of the most important equipment in the fields of aviation, aerospace, and navigation.

The performance of inertial devices (gyroscopes and accelerometers) is the most important factor affecting the accuracy of inertial navigation systems. 80% of inertial navigation system errors are caused by device errors. Therefore, improving the accuracy of inertial devices is the most important factor in the development of inertial technology. research content. There are often two ways to improve the accuracy of inertial devices: (1) improve the performance of the device by changing the working principle of the inertial device or improving the processing technology of the device; (2) perform error modeling and calibration on the device through advanced testing methods, Improve device performance by means of error compensation. In general, the improvement of the processing technology of the inertial device mentioned in the route (1) often requires a relatively large price, and the cost of the device will also be greatly increased. The advanced test method described in approach (2) often requires advanced test equipment as the basis. Generally, the test equipment for inertial devices is often expensive, and the test process is cumbersome, requiring a lot of experimental time.

Contents of the invention

The technical problem of the present invention is: to overcome the deficiencies of the prior art, and to provide a method for calibrating and compensating the accelerometer error based on a small rotating mechanism. Linear error coefficient, cross-coupling error coefficient, etc., have the advantages of accuracy, high efficiency, easy operation, and high versatility.

The technical solution of the present invention is: an accelerometer error calibration and compensation method based on a rotating mechanism, and its realization steps are as follows:

The first step is to make a rotating mechanism. The rotating mechanism is composed of a torque motor, a grating, a rotating shaft, an accelerometer signal acquisition system, a grating angle measurement signal acquisition system, an accelerometer mounting platform and a motor control system; the rotor of the torque motor is connected to the The rotating shaft is fixed; the grating is installed on the rotating shaft and rotates with the rotation of the rotating shaft; the accelerometer is installed on the accelerometer mounting platform, and the accelerometer mounting platform is located on the top of the rotating shaft and is fixedly connected with the rotating shaft, and rotates with the rotating shaft The motor control system controls the rotation of the torque motor, the accelerometer signal acquisition system is used to sample the output signal of the accelerometer in real time, and the grating rotation angle signal acquisition system is used to collect the rotation angle output signal of the grating in real time;

The second step is to establish a general output model of the accelerometer, in which the output error includes zero bias, proportional coefficient error, proportional coefficient non-linear error and cross-coupling error;

The third step is to install the two accelerometers on the accelerometer installation platform of the rotating mechanism according to the requirements. The installation requirements are: the sensitive axes of the two accelerometers and the rotating axis of the rotating mechanism are perpendicular to each other, and the rotating axes are kept parallel to the horizontal plane ;

In the fourth step, according to the installation method of the accelerometer described in the third step, the relational expression between the input of the accelerometer and the rotation angle is obtained, and the relational expression is substituted into the general output model of the accelerometer, and the relative rotation angle of the accelerometer can be obtained Angular output model;

In the fifth step, the motor control system controls the rotation of the torque motor, the accelerometer signal acquisition system collects the output information of the two accelerometers in real time, and the grating rotation angle signal acquisition system collects the grating rotation angle output information in real time;

In the sixth step, according to the output model of the accelerometer relative to the rotation angle obtained in the fourth step, the grating rotation angle information collected in real time in the fifth step is used as the input of the parameter estimation model, and the sampling values of the two accelerometers are used as the output of the parameter estimation model , using the least squares method to estimate part of the error term coefficients in the accelerometer output model;

The seventh step is to rotate the two accelerometers around their respective sensitive axes by 90° in the installation plane described in the third step, and repeat the fifth and sixth steps to obtain the remaining error term coefficient in the accelerometer output model ;

In the eighth step, according to the error term coefficient of the accelerometer output model estimated in the sixth and seventh steps, error compensation is performed on the accelerometer, and the compensation accuracy of the model is checked.

In the fifth step above, the rotating mechanism rotates according to the following motion law: the rotation angular rate is ω, and it rotates positively and negatively within the range of 0-360°, that is, it moves from 0° to 360° at the rotation angular rate ω, and then It moves from 360° to 0° at the rotational angular rate of -ω, which not only ensures that the system has a complete frequency component input, but also makes the error estimation accurate, and also avoids the use of conductive slip rings, which reduces the cost and improves reliability.

The advantage of the present invention compared with prior art is:

(1) The traditional accelerometer error calibration requires multiple sets of experiments, and also requires the use of centrifuges, position tables and other equipment. The accelerometer calibration method designed in the present invention only needs to pass 2 sets of experiments to calibrate all the error coefficients , which greatly simplifies the calibration process of the error coefficient. By converting the relationship between the output of the accelerometer and the input acceleration into the relationship with the rotation angle, the estimation accuracy of the error coefficient is improved, and the calibration process does not require other expensive assistance. equipment. The calibration method is also applicable to the calibration of the error coefficient of the gyroscope, and has certain versatility.

(2) the rotary mechanism of the present invention has the advantages of small size and low cost, so the present invention adopts this rotary mechanism to excite various errors of the inertial device through the rotation of the mechanism, and only needs to carry out 2 groups of experiments and combine corresponding estimates The algorithm can estimate the complete error coefficient of the device, and the performance of the device can be greatly improved after error compensation. The method of the invention has the characteristics of accuracy, high efficiency, easy operation, simple equipment, low cost and the like.

(3) The rotating mechanism of the present invention follows a certain rotation law, that is, the rotation angular rate ω rotates positively and negatively within the range of 0-360°, so as to ensure that the system has a complete frequency component input, so that the error estimation is accurate, and at the same time The use of conductive slip rings can be avoided, further reducing costs and improving reliability.

Description of drawings

Fig. 1 is the realization flowchart of the inventive method;

Fig. 2 is a structural schematic diagram of a rotating mechanism in the present invention;

Fig. 3 is a coordinate relationship diagram between the accelerometer measurement system and the carrier system in the embodiment of the present invention;

Fig. 4 is the output curve of x accelerometer in the rotation process in the embodiment of the present invention;

Fig. 5 is the accelerometer error curve without nonlinear error compensation in the embodiment of the present invention;

Fig. 6 is the accelerometer output model parameter estimation curve in the embodiment of the present invention;

Fig. 7 is the error curve of the accelerometer after error calibration and compensation in the embodiment of the present invention.

Detailed ways

The specific implementation process of the present invention is described below by taking the calibration process of the MS8002 acceleration of the Swiss colibrys company as an example.

Fig. 1 is the flow chart of accelerometer error calibration method that the present invention refers, and its specific implementation process is as follows:

1. Prepare the rotating mechanism. Figure 2 is a schematic diagram of the rotation mechanism used for accelerometer calibration.

The rotating mechanism is composed of a torque motor 5, a rotating shaft 4, a grating 3, an accelerometer installation platform 6, a motor control system 7, an accelerometer signal acquisition system 8, and a grating rotation angle signal acquisition system 9. The accelerometer 1 and the accelerometer 2 are installed on the platform 6, the accelerometer installation platform 6, the grating 3 are fixedly connected with the rotating shaft 4 and rotate with the rotation of the rotating shaft 4, the rotating shaft 4 is fixedly connected with the rotor of the torque motor 5, and the motor control system 7 can control the torque motor 5 according to a certain The accelerometer signal acquisition system 8 can sample the output value of the accelerometer in real time, and the grating rotation angle signal acquisition system 9 can sample the rotation angle output information of the grating in real time.

The torque motor of the rotating mechanism is controlled by PWM. The motor control system is composed of DSP and power amplifier circuit. After calculation, the DSP outputs a PWM wave with a certain duty ratio. Exercise regularly. The grating adopts the circular grating of the British Renishow company, which is composed of the grating ruler and the reading head. When the grating ruler rotates with the motor shaft, the reading head outputs orthogonal pulses. The grating rotation angle signal acquisition system is realized by the QEP module circuit of DSP. Orthogonal pulse decoding to obtain the number of pulses corresponding to the rotation angle. Accelerometer signal acquisition system is realized by ADS1258 chip, which can realize high-speed sampling of accelerometer output analog signal and convert and output digital signal corresponding to analog signal.

2. Taking the accelerometer in the x direction as an example, its general output model is expressed as:

${\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="k"\; filenames="HSA00000159437100042.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="2"\; label="x"\; filenames="HSA00000159437100021.png,HSA00000159437100042.png"\; state="\{\{state\}\}">x</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 3</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="3"\; label="x"\; filenames="HSA00000159437100021.png,HSA00000159437100042.png"\; state="\{\{state\}\}">x</figure-callout></span>}}^{\mathrm{<span\; class="notranslate">\; 3</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 4</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 5</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 6</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 7</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>$

In the above formula (1), a _x , a _y , a _z represent the input acceleration in the three directions of x, y, and z respectively, k ₀ is the zero bias of the accelerometer, k ₁ is the proportional coefficient, and k ₂ is the two of the proportional coefficient The second nonlinear error coefficient, k ₃ is the cubic nonlinear error coefficient of the proportional coefficient, k ₄ is the cross-coupling error coefficient related to a _y , k ₅ is the cross-coupling error coefficient related to a _z , k ₆ is the cross-coupling error coefficient related to a _x and the cross-coupling error coefficient related to the product of a _y , k ₇ is the cross-coupling error coefficient related to the product of a _x and a _z .

Similarly, a general output model of the z-direction accelerometer and the y-direction accelerometer can be obtained.

a_bx、a_by、a_bz分别代表机箱壳体坐标系的输入加速度在x、y、z三方向的分量，结合图3便可以得出在旋转过程中加速度计测量系的输入加速度表达式为：3. Install two accelerometers (x and z accelerometers) on the rotating mechanism, where the sensitive axis of the x accelerometer, the sensitive axis of the z accelerometer, and the rotating axis of the rotating mechanism are perpendicular to each other, and the rotating axis is kept parallel to the horizontal plane. As shown in Figure 2, the rotating mechanism needs to be installed in a case for measurement. During the rotation process, the relationship between the x, z accelerometer measurement coordinate system and the chassis shell coordinate system is shown in Figure 3, where ox _b y _b z _b represents the chassis shell coordinate system, and ox _m y _m z _m represents the acceleration Measuring coordinate system. Assuming the input acceleration of the chassis shell coordinate system

a _bx , a _by , a _bz respectively represent the components of the input acceleration in the x, y, and z directions of the chassis shell coordinate system. Combining with Figure 3, it can be obtained that the input acceleration expression of the accelerometer measurement system during the rotation process is :

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; bx</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; by</span>}}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; bz</span>}}\\ {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; bx</span>}}<span\; class="notranslate">\; +</span><span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span>{\mathrm{<span\; class="notranslate">\; \&delta;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; by</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; bz</span>}}\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span>$

Where a _x , a _z are the input accelerations of the accelerometer measurement system in the x and z directions, δ _z is the deflection angle of the rotating mechanism relative to the Z-axis of the chassis shell coordinate system, and δ _x is the rotation mechanism relative to the chassis shell coordinate system X The deflection angle of the shaft, θ is the rotation angle of the rotary mechanism, and θ ₀ is the initial phase angle of the rotary mechanism. Install the rotating mechanism on the horizontal plane, get [a _bx , a _by , a _bz ]'=[0, 0, -g]', g is the local acceleration of gravity, substituting the above formula (2) to get:

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; sin</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\\ {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 0</span>}\\ {\mathrm{<span\; class="notranslate">\; a</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; cos</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; \&theta;</span>}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span>\end{array}\right.<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

4. Substitute the input information of the accelerometer represented by the above formula (3) into the output model of the accelerometer represented by formula (1), and obtain the output model of the accelerometer relative to the rotation angle as shown in the following formula:

A _x ＝a+bsinθ'+ccosθ'+dsin2θ'+ecos2θ'+fsin3θ'(4)

in:

$a={\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HSA00000159437100042.png"\; state="\{\{state\}\}">k</figure-callout>}}_0+\frac{1}{2}{g}^2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000159437100021.png,HSA00000159437100042.png"\; state="\{\{state\}\}">k</figure-callout>}}_2,b=\mathrm{<figure-callout\; id="1"\; label="g\; k"\; filenames="HSA00000159437100021.png,HSA00000159437100031.png"\; state="\{\{state\}\}">g</figure-callout>}{k}_{}{}_1+\frac{3}{4}{g}^3{\mathrm{<figure-callout\; id="3"\; label="k"\; filenames="HSA00000159437100021.png,HSA00000159437100042.png"\; state="\{\{state\}\}">k</figure-callout>}}_3,c=-g{k}_5$ $d=-\frac{1}{2}{g}^2{\mathrm{<figure-callout\; id="7"\; label="k"\; filenames="HSA00000159437100021.png"\; state="\{\{state\}\}">k</figure-callout>}}_7,e=-\frac{1}{2}{g}^2{\mathrm{<figure-callout\; id="2"\; label="k"\; filenames="HSA00000159437100021.png,HSA00000159437100042.png"\; state="\{\{state\}\}">k</figure-callout>}}_2,f=-\frac{1}{4}{g}^3{\mathrm{<figure-callout\; id="3"\; label="k"\; filenames="HSA00000159437100021.png,HSA00000159437100042.png"\; state="\{\{state\}\}">k</figure-callout>}}_3$ θ'=θ+θ ₀ , a, b, c, d, e, f are intermediate variables.

5. Use the rotation angle information θ _i obtained by real-time sampling as input, and the sampling value A _xi of the accelerometer as the output, and use the method of least square fitting to estimate the error coefficient related to a _x and a _z in the accelerometer output model item, where the estimation method is:

$\left[\begin{array}{c}\mathrm{<span\; class="notranslate">\; a</span>}\\ \mathrm{<span\; class="notranslate">\; b</span>}\\ \mathrm{<span\; class="notranslate">\; c</span>}\\ \mathrm{<span\; class="notranslate">\; d</span>}\\ \mathrm{<span\; class="notranslate">\; e</span>}\\ \mathrm{<span\; class="notranslate">\; f</span>}\end{array}\right]<span\; class="notranslate">\; =</span>{\left[\begin{array}{cccccc}\mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}& \mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}& \mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; \&prime;</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; \&prime;</span>}& \mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; \&prime;</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; \&prime;</span>}& \mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 2</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\\ <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>& <span\; class="notranslate">\; .</span>\\ \mathrm{<span\; class="notranslate">\; 1</span>}& \mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}& \mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}& \mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}& \mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}^{<span\; class="notranslate">\; \&prime;</span>}\end{array}\right]}^{<span\; class="notranslate">\; -</span>}<span\; class="notranslate">\; \&times;</span>\left[\begin{array}{c}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}\\ {\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ <span\; class="notranslate">\; .</span>\\ {\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; xi</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 5</span>}<span\; class="notranslate">\; )</span>$

In the above formula (5), A _xi is the real-time output value of the accelerometer, θ′ _i = (θ _i + θ ₀ ) is the real-time output value of the grating, where θ ₀ can be estimated in advance, and the estimation method is shown in step 6. After obtaining the values of a, b, c, d, e, and f, the model parameters k ₀ , k ₁ , k ₂ , k ₃ , k ₅ , and k ₇ of the accelerometer can be obtained as follows:

k ₀ =a+e

k ₁ =(b+3f)/g

k ₂ =-2e/g ²

k ₃ =-4f/g ³ (6)

k ₅ =-c/g

k ₇ =-2d/g ²

6. The estimation method of θ ₀ mentioned in step 5 is as follows:

The k ₂ -k ₇ in the output model of the accelerometer represented by the above formula (1) are small quantities, after ignoring the small quantities, the output of the x accelerometer can be simplified as:

A _x =k ₀ +k ₁ a _x

＝k ₀ +k ₁ gsin(θ+θ ₀ ) (7)

＝k ₀ +k ₁ gcosθ ₀ sinθ+k ₁ gsinθ ₀ cosθ

Control the rotation of the rotating mechanism so that θ=0°, 45°, 90° respectively

$\left\{\begin{array}{c}{\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="k"\; filenames="HSA00000159437100042.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\\ {\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 45</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="k"\; filenames="HSA00000159437100042.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\sqrt{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; /</span>\mathrm{<span\; class="notranslate">\; 2</span>}\\ {\mathrm{<span\; class="notranslate">\; A</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 90</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; <figure-callout\; id="0"\; label="k"\; filenames="HSA00000159437100042.png"\; state="\{\{state\}\}">k</figure-callout></span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}\end{array}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; sin</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; k</span>}}_{\mathrm{<span\; class="notranslate">\; 1</span>}}\mathrm{<span\; class="notranslate">\; g</span>}\mathrm{<span\; class="notranslate">\; cos</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}_{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 8</span>}<span\; class="notranslate">\; )</span>\right.$

分别为旋转机构的旋转角为0°，45°，90°时x加速度计的输出值。联立以上方程组(8)，便可以解得θ₀。In the above formula (8),

are the output values of the x accelerometer when the rotation angle of the rotating mechanism is 0°, 45°, and 90° respectively. By combining the above equations (8), θ ₀ can be solved.

7. Rotate the two accelerometers 90° around their respective sensitive axes in the installation plane specified in step 3, and repeat steps 3-6 to obtain the error coefficient items k ₄ and k ₆ related to a _y in the accelerometer error model.

8. According to the accelerometer output model parameters k ₀ , k ₁ , k ₂ , k ₃ , k ₄ , k ₅ , k ₆ , and k ₇ estimated in steps 5 and 7, error compensation can be performed on the accelerometer.

As shown in Figure 4, the output of the x-direction accelerometer during the rotation of the rotating mechanism is a sinusoidal component with an amplitude of 1000mg and a period of 5s;

As shown in Figure 5, if the nonlinear error and cross-coupling error are not compensated, and the output curve shown in Figure 4 is linearly fitted, the output error of the accelerometer during the rotation process is twice the frequency and three times the input signal Frequency components, and the maximum amplitude reaches 3mg;

As shown in Figure 6, the accelerometer output model parameter estimation method mentioned in step 5 of the present invention can easily estimate the model parameters, wherein the convergence time of the parameter estimation algorithm is less than 100s;

As shown in Figure 7, after using the present invention to estimate the output model parameters of the accelerometer and performing error compensation, the output signal of the accelerometer no longer contains the 2 times frequency and 3 times frequency components of the rotation period, illustrating the model estimated by the present invention The parameters are accurate, and the error compensation achieves better results;

The contents not described in detail in the description of the present invention belong to the prior art known to those skilled in the art.

Finally, it should be noted that: the above implementation examples are only used to illustrate rather than limit the technical solutions of the present invention, and all modifications or partial replacements that do not depart from the spirit and scope of the present invention should be included in the claims of the present invention .

Claims (2)

1. A kind of accelerometer error calibration and compensation method based on rotating mechanism, it is characterized in that the steps are as follows: The first step is to make a rotating mechanism, and the rotating mechanism is composed of a torque motor (5), a grating (3), a rotating shaft (4), an accelerometer signal acquisition system (8), a grating rotation angle signal sampling system (9), an acceleration Meter installation platform (6) and motor control system (7); the rotor of the torque motor (5) is fixedly connected to the rotating shaft (4); the grating (3) is installed on the rotating shaft (4), and The rotation of the accelerometer is installed on the accelerometer mounting platform (6), and the accelerometer mounting platform (6) is located at the top of the rotating shaft (4) and is fixedly connected with the rotating shaft (4), and moves along with the rotating shaft (4) rotate and rotate; the motor control system (7) controls the rotation of the torque motor (5), the accelerometer signal acquisition system (8) is used for real-time sampling of the output value of the accelerometer, and the grating rotation angle signal sampling system (9) is used for real-time acquisition of the grating ( 3) The corner output information; The second step is to establish a general output model of the accelerometer, in which the output error includes zero bias, proportional coefficient error, proportional coefficient non-linear error and cross-coupling error; The third step is to install the two accelerometers on the accelerometer mounting platform (6) of the rotating mechanism according to the requirements. horizontal planes remain parallel; In the fourth step, according to the installation method of the accelerometer described in the third step, the relational expression between the input of the accelerometer and the rotation angle is obtained, and the relational expression is substituted into the general output model of the accelerometer, and the relative rotation angle of the accelerometer can be obtained Angular output model; In the fifth step, the motor control system (7) controls the rotation of the torque motor (5), the accelerometer signal acquisition system (8) collects the output information of the two accelerometers in real time, and the grating rotation angle signal acquisition system (9) collects the grating (3) in real time The corner output information; The sixth step, according to the output model of the accelerometer relative to the rotation angle obtained in the fourth step, the output information of the rotation angle of the grating (3) sampled in real time in the fifth step is used as the input of the parameter estimation model, and the sampling values of the two accelerometers are used as The output of the parameter estimation model can be estimated by using the least square method to obtain some error coefficient items in the accelerometer output model; In the seventh step, the two accelerometers are rotated 90° around their respective sensitive axes in the installation plane, and the fifth and sixth steps are repeated to obtain the remaining error coefficient item in the accelerometer output model; In the eighth step, according to the error coefficient item of the accelerometer output model estimated in the sixth and seventh steps, error compensation is performed on the accelerometer, and the compensation accuracy of the model is checked. 2. the accelerometer error calibration and compensation method based on rotating mechanism according to claim 1, is characterized in that: the torque motor (5) described in the 5th step rotates by following law of motion: rotation angular rate ω, and at In the range of 0-360°, the positive and negative full circle rotation, that is, to move from 0° to 360° at the rotational angular rate ω, and then to move from 360° to 0° at the rotational angular rate of -ω.

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