阅读说明：本技术 一种三轴加速度计标定方法 (Calibration method of triaxial accelerometer ) 是由 张征方 赵旭峰 蒋杰 李科 喻励志 吴业庆 卢学云 肖健 于 2019-08-27 设计创作，主要内容包括：本发明涉及一种三轴加速度计标定方法,包括固有误差离线标定方法和安装误差在线标定方法。其中,固有误差标定方法是通过将加速度计的三轴分别置于1g场和-1g场,通过求解加速度计的零偏和刻度因子从而获得加速度计经过固有误差标定后的输出；安装误差标定方法是基于阻尼最小二乘法,可以实现对加速度计的在线校准,方便快捷,同时能够避免传统高斯牛顿法发散的缺点；此外,在阻尼最小二乘法的基础上,本发明还提出了阻尼因子自适应的调节方法,使得算法收敛速度更快。(The invention relates to a calibration method of a triaxial accelerometer, which comprises an inherent error offline calibration method and an installation error online calibration method. The inherent error calibration method comprises the steps of respectively placing three axes of an accelerometer in a 1g field and a-1 g field, and solving zero offset and scale factors of the accelerometer to obtain output of the accelerometer after inherent error calibration; the mounting error calibration method is based on a damped least square method, can realize the online calibration of the accelerometer, is convenient and quick, and can avoid the disadvantage of divergence of the traditional Gauss-Newton method; in addition, on the basis of the damping least square method, the invention also provides a damping factor self-adaptive adjusting method, so that the algorithm convergence speed is higher.)

1. A three-axis accelerometer calibration method is characterized by comprising the following steps:

s1: mounting the accelerometer in a measured carrier;

s2: establishing a three-dimensional coordinate system oxyz based on the accelerometer;

s3: establishing a three-dimensional coordinate system ox ' y ' z ' based on the detected carrier;

s4: rotating the accelerometer coordinate system oxyz to the carrier coordinate system ox ' y ' z ', and setting the anticlockwise rotation angles of the x, y and z axes of the accelerometers as alpha, beta and gamma respectively; the angles alpha, beta and gamma are installation deflection angles of the accelerometer;

s5: let C be the transformation matrix from the accelerometer coordinate system oxyz to the carrier coordinate system ox ' y ' z ',

s6: solving the installation declination angles alpha, beta and gamma by using a damping least square method;

s7: calculating a conversion matrix C according to the obtained installation deflection angles alpha, beta and gamma;

s8: according to formula A_v＝CA_sObtaining the output of the accelerometer under a carrier coordinate system ox ' y ' z ', wherein A_sAnd outputting the accelerometer after the calibration of the inherent error.

2. The calibration method according to claim 1, wherein the solving process of the declination angles α, β, γ further comprises:

s61: establishing a function model of the accelerometer installation error

Wherein c is_ij(i ═ 1,2,3, j ═ 1,2,3) are elements in the transfer matrix C; a. the_vx、A_vy、A_vzAcceleration of the accelerometer x, y and z axes in a carrier coordinate system ox ' y ' z ' respectively;

s62: setting U (x) to U (alpha, beta, gamma), and establishing a mathematical model of a damped least squares method as

S63: solving the minimum point x of the function rho (x) by using a damped least squares method^*And outputting the values of alpha, beta and gamma at the moment; wherein

3. The calibration method according to claim 2, wherein the step S63 further comprises:

s631: setting initial values of alpha, beta and gamma as alpha₀、β₀、γ₀The damping factor mu is initially mu₀The scaling factor v is initially v₀The iteration number is k, and the iteration termination condition is an iteration error | ρ (x)_k+1)-ρ(x_k)|＜ε；

S632: carrying out equation solution by using a damping least square method;

s633: calculating an iteration error;

s634: judging whether the iteration error meets the iteration termination condition, if so, exiting the iteration, and outputting the values of alpha, beta and gamma at the moment; if not, the process returns to step S632.

4. The calibration method according to claim 3, wherein the damping factor μ is updated in an adaptive iterative manner, and the steps are as follows:

(1) assuming a is small enough, a second order approximation is made to ρ (x + a):

whereinA Jacobian matrix of U;

(2) definition of

(3) If η > 0, thenv_k+1＝v₀(ii) a Otherwise

μ_k+1＝μ_k*v_k，v_k+1＝2*v_k。

5. The calibration method according to claim 3, wherein the damping factor μ is updated by using intelligent algorithms such as fuzzy inference, neural network, etc.

6. A calibration method according to claim 1, wherein the accelerometer is calibrated for intrinsic errorsOutput A_sObtained by the following calibration steps:

(1) selecting a horizontal object surface as a carrier surface of the accelerometer;

(2) selecting three axes of the accelerometer as sensitive axes, and respectively placing the x axis, the y axis and the z axis of the sensitive axes in a 1g field and a-1 g field for a duration not less than 1 minute;

(3) filtering the static data output by the accelerometer, and taking the average value of the filtered data;

(4) according to the formulaCalculating the zero offset O and the scale factor S of the three axes of the accelerometer respectively when tau is x, y and z, wherein A is_oτAnd A_-oτRespectively placing the sensitive shaft in a 1g field and a-1 g field, and filtering output data of the accelerometer to obtain average values;

(5) according to formula A_s＝SA_o+ O calculation to obtain the output A of the accelerometer after the calibration of the inherent error_sWherein A is_oAnd outputting the accelerometer before the intrinsic error calibration.

Technical Field

The invention relates to the field of sensor calibration, in particular to a calibration method of a triaxial accelerometer.

Background

At present, error calibration of an accelerometer is mainly performed off-line calibration based on a high-precision calibration platform, the method has high precision requirement on the calibration platform, and common users and laboratories are rarely equipped with such expensive test equipment. In addition, the calibration method in the prior art mainly aims at the inherent error of the accelerometer, and in practical use, besides the inherent error, the installation error of the accelerometer can also bring great influence on the measurement result.

Disclosure of Invention

In order to solve the technical problems, the invention provides a triaxial accelerometer calibration method capable of performing off-line calibration of inherent errors and on-line calibration of installation errors.

The technical scheme adopted by the invention for solving the technical problems is as follows:

a three-axis accelerometer calibration method comprises the following steps:

s1: mounting the accelerometer in a measured carrier;

s2: establishing a three-dimensional coordinate system oxyz based on the accelerometer;

s3: establishing a three-dimensional coordinate system ox ' y ' z ' based on the detected carrier;

s4: rotating the accelerometer coordinate system oxyz to the carrier coordinate system ox ' y ' z ', and setting the anticlockwise rotation angles of the x axis, the y axis and the z axis of the accelerometer to be alpha, beta and gamma respectively; the angles alpha, beta and gamma are installation deflection angles of the accelerometer;

s5: the transformation matrix of the accelerometer coordinate system oxyz to the carrier coordinate system ox ' y ' z ' is C,

s6: solving the installation declination angles alpha, beta and gamma by using a damping least square method;

s7: calculating a conversion matrix C according to the obtained installation deflection angles alpha, beta and gamma; for the convenience of solution, the trigonometric function in the transformation matrix C is subjected to approximate equivalent transformation by taylor expansion, high-order terms are ignored, and the expansion is as follows:

s8: according to formula A_v＝CA_sObtaining the output of the accelerometer under a carrier coordinate system ox ' y ' z ', wherein A_sAnd outputting the accelerometer after the calibration of the inherent error.

Preferably, the solving process of the declination angles α, β, γ further includes:

s61: establishing a function model of the accelerometer installation error

Wherein c is_ij(i ═ 1,2,3, j ═ 1,2,3) are elements in the transfer matrix C; a. the_vx、A_vy、A_vzAcceleration of the accelerometer x, y and z axes in a carrier coordinate system ox ' y ' z ' respectively;

s62: setting U (x) to U (alpha, beta, gamma), and establishing a mathematical model of a damped least squares method as

S63: solving the minimum point x of the function rho (x) by using a damped least squares method^*And outputting the values of alpha, beta and gamma at the moment; wherein

Preferably, the step S63 further includes:

s631: setting initial values of alpha, beta and gamma as alpha₀、β₀、γ₀The damping factor mu is initially mu₀The scaling factor v is initially v₀Number of iterationsThe number is k, and the iteration termination condition is the iteration error | ρ (x)_k+1)-ρ(x_k)|＜ε；

S632: carrying out equation solution by using a damping least square method;

s633: calculating an iteration error;

s634: judging whether the iteration error meets the iteration termination condition, if so, exiting the iteration, and outputting the values of alpha, beta and gamma at the moment; if not, the process returns to step S632.

Preferably, the damping factor μ is updated in an adaptive iterative manner, and the steps are as follows:

(1) assuming a is small enough, a second order approximation is made to ρ (x + a):

whereinA Jacobian matrix of U;

(2) definition of

(3) If η > 0, thenv_k+1＝v₀(ii) a Otherwise

μ_k+1＝μ_k*v_k，v_k+1＝2*v_k。

As another optional mode of the present invention, the damping factor μ is updated by using an intelligent algorithm such as fuzzy inference, neural network, etc.

Preferably, the output A of the accelerometer after calibration of inherent error_sObtained by the following calibration steps:

(1) selecting a horizontal object surface as a carrier surface of the accelerometer;

(2) selecting three axes of the accelerometer as sensitive axes, and respectively placing the x axis, the y axis and the z axis of the sensitive axes in a 1g field and a-1 g field for a duration not less than 1 minute;

(3) filtering the static data output by the accelerometer, and taking the average value of the filtered data;

(4) according to the formulaTau is x, y and z are respectively used for calculating the zero offset O of the three axes of the accelerometer_x O_y O_z]^TAnd scale factorWherein A is_oτAnd A_-oτRespectively placing the sensitive shaft in a 1g field and a-1 g field, and filtering output data of the accelerometer to obtain average values;

(5) according to formula A_s＝SA_o+ O calculation to obtain the output A of the accelerometer after the calibration of the inherent error_sWherein A is_oAnd outputting the accelerometer before the intrinsic error calibration.

The invention has the following beneficial effects:

(1) the method has the advantages that the on-line calibration of the installation error of the accelerometer based on the damping least square method is provided, the on-line calibration of the accelerometer can be realized conveniently and quickly, and meanwhile, the defect of divergence of the traditional Gauss-Newton method is avoided;

(2) on the basis of a damping least square method, a damping factor self-adaptive adjusting method is provided, so that the algorithm convergence speed is higher;

(3) the simple calibration method of the intrinsic error of the accelerometer is provided, and the calibration cost is reduced.

Drawings

The foregoing summary, as well as the following detailed description of the invention, will be better understood when read in conjunction with the appended drawings. It is to be noted that the appended drawings are intended as examples of the claimed invention. In the drawings, like reference characters designate the same or similar elements.

FIG. 1 is a flow chart of calibration of intrinsic error of an accelerometer according to an embodiment of the present invention;

FIG. 2 is a flowchart illustrating an accelerometer mounting error calibration process according to an embodiment of the present invention;

fig. 3 is a flowchart of calculating a damped least squares method in an accelerometer mounting error calibration process according to an embodiment of the present invention.

Detailed Description

For a better understanding of the present invention, reference is made to the following detailed description taken in conjunction with the accompanying drawings and examples.

In order to calibrate the installation error of the accelerometer on line, the inherent error of the accelerometer needs to be calibrated.

The specific principle of the inherent error calibration is as follows:

the intrinsic error model of the accelerometer is: a. the_s＝SA_o+ O. In the formula, A_s＝[A_sx A_sy A_sz]^TOutputs for the x, y, z axes after accelerometer calibration; a. the_o＝[A_ox A_oy A_oz]^TCalibrating the outputs of the x, y and z axes before the accelerometer is calibrated; o ═ O_x O_y O_z]^TZero offset for the x, y, z axes of the accelerometer;scale factors for the x, y, z axes of the accelerometer.

Therefore, the inherent error of the accelerometer can be calibrated by solving the zero offset O and the scale factor S of the accelerometer.

The off-line calibration method for intrinsic errors of the triaxial accelerometer in the embodiment of the invention is shown in FIG. 1 and comprises the following steps:

(1) detecting a relatively horizontal object surface by using a level gauge as a carrier surface of the accelerometer;

(2) selecting three axes of an accelerometer as sensitive axes, and respectively placing the x axis, the y axis and the z axis of the sensitive axes in a 1g field and a-1 g field for a duration not less than 1 minute;

(3) filtering the static data output by the accelerometer, and taking the average value of the filtered data;

(4) respectively calculating a zero offset O and a scale factor S of three axes of the accelerometer;

(5) intrinsic error model A from accelerometer_s＝SA_o+ O, calculating to obtain the output A of the accelerometer after the calibration of the inherent error_s。

Wherein, the process of calculating the zero offset O and the scale factor S in the step (4) further comprises:

taking the x-axis of the accelerometer as an example, placing the x-axis in a 1g field and a-1 g field respectively hasIn the formula A_oxAnd A_-oxThe filtered mean values of accelerometer output data with the x-axis placed in the 1g field and the-1 g field, respectively. Therefore, the x-axis zero offset and scale factor can be found as:similarly, the y-axis and the z-axis are respectively placed in the 1g field and the-1 g field, and the corresponding zero offset and scale factor can be obtained.

Obtaining the output A of the accelerometer by the above-mentioned inherent error off-line calibration method_sAnd then, the installation error of the accelerometer can be calibrated on line.

The specific principle of the online calibration of the installation error is as follows:

assuming that the coordinate system of the accelerometer is oxyz, the coordinate system of the carrier is ox 'y' z ', the coordinate system oxyz is rotated to ox' y 'z', and assuming that the counterclockwise rotation angles of the x, y and z axes are respectively alpha, beta and gamma, and the counterclockwise rotation angles of the alpha, beta and gamma, namely the installation deflection angles of the accelerometer, are defined to be positive around the counterclockwise rotation angles of the coordinate axes. According to the rotation sequence of x → y → z, the conversion matrix of the accelerometer coordinate system oxyz to the carrier coordinate system ox ' y ' z ' is

Carrier coordinate system ox 'y'The triaxial acceleration in z' can be expressed as: a. the_v＝CA_s

For the convenience of solving, the trigonometric function in the transformation matrix C is subjected to approximate equivalent transformation by using Taylor expansion, high-order terms are ignored, and the expansion is as follows:

therefore, the three angles alpha, beta and gamma in the conversion matrix C are obtained, the mounting error of the accelerometer is calibrated, and the influence of the mounting error on the measurement result is overcome.

When the carrier is still at a horizontal plane, the carrier coordinate system and the earth coordinate system are considered to be coincident, and the gravity acceleration values in the three axial directions are A_v＝[0 0 g]^TAnd at the moment, the three-axis acceleration value of the accelerometer is the component of the gravity acceleration on each axis of the accelerometer coordinate system.

The on-line calibration method for the installation error of the triaxial accelerometer in the embodiment of the invention is shown in FIG. 2 and comprises the following steps:

s1: mounting a triaxial accelerometer to be calibrated in a measured carrier;

s2: establishing a three-dimensional coordinate system oxyz based on the accelerometer;

s3: establishing a three-dimensional coordinate system ox ' y ' z ' based on the detected carrier;

s4: rotating the accelerometer coordinate system oxyz to the carrier coordinate system ox ' y ' z ', and setting the anticlockwise rotation angles of the x axis, the y axis and the z axis of the accelerometer to be alpha, beta and gamma respectively, namely setting the installation declination angle of the accelerometer;

s5: let the transformation matrix of the accelerometer coordinate system oxyz to the carrier coordinate system ox ' y ' z ' be C,

s6: solving the installation declination angles alpha, beta and gamma by using a damping least square method;

s7: calculating a conversion matrix C according to the obtained installation deflection angles alpha, beta and gamma; preferably, for the convenience of solution, the trigonometric function in the transformation matrix C is approximately transformed by taylor expansion, ignoring higher-order terms, as follows:

s8: according to formula A_v＝CA_sAnd obtaining the output of the accelerometer under the carrier coordinate system ox ' y ' z ', namely the output after the calibration of the installation error. Wherein A is_sThe output of the accelerometer described above is calibrated for intrinsic error.

Further, the solving process of the installation declination angles α, β, γ in the step S6 includes:

s61: function model for establishing accelerometer installation error

Wherein c is_ij(i ═ 1,2,3, j ═ 1,2,3) are elements in the transfer matrix C described above; a. the_vx、A_vy、A_vzAcceleration of an accelerometer x, y and z axis under a carrier coordinate system ox ' y ' z ' respectively;

s62: let U (x) be U (alpha, beta, gamma), and establish a mathematical model of damped least squares as

S63: minimum value point x of multivariate function rho (x) is solved by using damped least square method^*And outputting the values of alpha, beta and gamma at the moment; wherein

As shown in fig. 3, the step S63 further includes:

s631: setting of alpha, beta, gammaInitial value of alpha₀、β₀、γ₀The damping factor mu is initially mu₀The scaling factor v is initially v₀The iteration number is k, and the iteration termination condition is an iteration error | ρ (x)_k+1)-ρ(x_k)|＜ε；

S632: carrying out equation solution by using a damping least square method;

s633: calculating an iteration error;

s634: judging whether the iteration error meets the iteration termination condition, if so, exiting the iteration, and outputting the values of alpha, beta and gamma at the moment; if not, the process returns to step S632.

Further, in order to make the convergence rate of the algorithm faster, the damping factor μ is updated in a self-adaptive iteration manner, and the steps are as follows:

(1) assuming a is small enough, a second order approximation is made to ρ (x + a):

whereinA Jacobian matrix of U;

(2) definition of

(3) If η > 0, thenv_k+1＝v₀(ii) a Otherwise

μ_k+1＝μ_k*v_k，v_k+1＝2*v_k。

Optionally, the damping factor μmay also be updated by using intelligent algorithms such as fuzzy inference, neural network, and the like.

Further, in the present embodiment, the range of the mounting angle deviations α, β, γ is [ - σ σ σ ], and 0 ≦ σ ≦ 30 o.

The terms and expressions which have been employed herein are used as terms of description and not of limitation. The use of such terms and expressions is not intended to exclude any equivalents of the features shown and described (or portions thereof), and it is recognized that various modifications may be made within the scope of the claims. Other modifications, variations, and alternatives are also possible. Accordingly, the claims should be looked to in order to cover all such equivalents.

Also, it should be noted that although the present invention has been described with reference to the current specific embodiments, it should be understood by those skilled in the art that the above embodiments are merely illustrative of the present invention, and various equivalent changes or substitutions may be made without departing from the spirit of the present invention, and therefore, it is intended that all changes and modifications to the above embodiments be included within the scope of the claims of the present application.