CN105242070A - Accelerometer unit calibration method without vector standard - Google Patents

Abstract

The invention belongs to a gyro calibration method, and specifically relates to an accelerometer unit calibration method without the need for any external datum. According to the technical scheme of the invention, the zero bias, scale factor and scale factor high-order term of an accelerometer unit error model are separated optimally through a least square method and an iteration method based on the principle that the sum of thee orthogonal axis acceleration vectors is always one acceleration gravity, and the only thing needed in calibration is to use a simple turning mechanism to arbitrarily turn an accelerometer unit to multiple positions. The problem that accelerometer unit calibration depends on the vector datum is solved, the calibration method has a very wide range of application, and the calibration precision is improved to the level of seconds of arc.

Description

A kind of accelerometer combination scaling method of scalar potential standard

Technical field

The invention belongs to Gyro Calibration method, be specifically related to a kind of accelerometer without the need to any extraneous benchmark combination scaling method.

Background technology

The published demarcation for combining for accelerometer in the scaling method of accelerometer combination at present all gives certain solution, these scaling methods all having some limitations property simultaneously, and main Problems existing is as follows:

1) scaling method is based on some vector benchmark

This kind of scaling method is that degree of will speed up meter is placed on diverse location successively, acceleration measurement meter output signal over these locations, it is compared with the corresponding projection of acceleration of gravity vector on accelerometer sensitive axle, calculates each parameter of accelerometer according to comparative result.The acceleration benchmark compared with accelerometer output valve is obtained by all kinds of calibration facility usually, such as turntable, dividing head, surface level etc.Leave this kind of calibration facility and then cannot obtain vector benchmark, thus accelerometer combination demarcation cannot be realized.

2) stated accuracy is limited to calibration facility

This kind of scaling method is based on various calibration facility, and its stated accuracy is directly by the impact of calibration facility precision.Calibration facility ubiquity, along with the phenomenon of time drift, needs regularly to correct, and especially high-precision turntable cost is high, safeguards loaded down with trivial details.Dependence for high-precision calibrating equipment seriously constrains the high-precision calibrating of accelerometer combination.

To sum up, known prior art must rely on extrinsic vectors benchmark to the demarcation that accelerometer combines, and departs from extrinsic vectors benchmark and then cannot demarcate.Therefore, a kind of combination of the accelerometer without the need to any extraneous benchmark of development scaling method is needed badly.

Summary of the invention

The technical problem to be solved in the present invention is to provide a kind of accelerometer without the need to any extrinsic vectors benchmark combination scaling method, thus solves without problem of calibrating during any extrinsic vectors benchmark, requires to have higher stated accuracy simultaneously.

In order to realize this purpose, the technical scheme that the present invention takes is:

An accelerometer combination scaling method for scalar potential standard, specifically comprises the following steps:

(1) the accelerometer combined error model applied is determined:

$\left\{\begin{array}{c}{A}_x={\mathrm{\Δ}}_{0x}+a_x+{\mathrm{\Δ}}_{1x}{a}_x+...+{\mathrm{\Δ}}_{\mathrm{ex}}{a}_x^e\\ A_y={\mathrm{\Δ}}_{0y}+a_y+{\mathrm{\Δ}}_{1y}{a}_y+...+{\mathrm{\Δ}}_{\mathrm{ey}}{a}_y^e\\ A_z={\mathrm{\Δ}}_{0z}+a_z+{\mathrm{\Δ}}_{1z}{a}_z+...+{\mathrm{\Δ}}_{\mathrm{ez}}{a}_z^e\end{array}\right....\left(1\right)$

In formula:

A _i, the acceleration that i=x, y, z---accelerometer exports respectively on x, y, z axle;

A _i, i=x, y, z---the true acceleration on the responsive x, y, z axle of accelerometer difference;

Δ _fi, i=x, y, z, the j rank error of f=0 ~ e, e>=2---accelerometer i constant multiplier;

The acceleration that accelerometer exports is by following formulae discovery:

$\left\{\begin{array}{c}{A}_x=(M_x/K_{1x})-K_{0x}\\ A_y=(M_y/K_{1y})-K_{0y}\\ A_z=(M_z/K_{1z})-K_{0z}\end{array}\right....\left(2\right)$

In formula:

M _i, the original output of i=x, y, z---accelerometer respectively on x, y, z axle;

K _i, the constant multiplier of i=x, y, z---accelerometer respectively on x, y, z axle;

During the accelerometer specific implementation of three orthogonal installations, due to the difference between ideal mounting position, obtain following equation:

$\left|\begin{array}{c}{B}_x\\ B_y\\ B_z\end{array}\right|=\left|\begin{array}{ccc}1& 0& 0\\ {\mathrm{\α}}_{\mathrm{yz}}& 1& 0\\ {\mathrm{\α}}_{\mathrm{zy}}& {\mathrm{\α}}_{\mathrm{zx}}& 1\end{array}\right|\×\left|\begin{array}{c}{A}_x\\ A_y\\ A_z\end{array}\right|---\left(3\right)$

In formula: B _i, i=x, y, z represent the output of accelerometer respectively on x, y, z axle after alignment error corrects; α _xz, α _xy, α _yz, α _yx, α _zy, α _zxrepresent alignment error coefficient, specific as follows:

α _xzrepresent accelerometer sensitive in z-axis to x-axis direction on acceleration;

α _yzrepresent accelerometer sensitive in z-axis to y-axis direction on acceleration;

α _xyrepresent accelerometer sensitive in y-axis to x-axis direction on acceleration;

α _zyrepresent accelerometer sensitive in y-axis to z-axis direction on acceleration;

α _yxrepresent accelerometer sensitive in x-axis to y-axis direction on acceleration;

α _zxrepresent accelerometer sensitive in x-axis to z-axis direction on acceleration;

Calculate formula (4);

$\begin{array}{c}\underset{f=0}{\overset{e}{\mathrm{\Σ}}}{\mathrm{\Δ}}_{\mathrm{fx}}{a}_x^{f+1}+\underset{f=0}{\overset{e}{\mathrm{\Σ}}}{\mathrm{\Δ}}_{\mathrm{fy}}{a}_y^{f+1}+\underset{f=0}{\overset{e}{\mathrm{\Σ}}}{\mathrm{\Δ}}_{\mathrm{fz}}{a}_z^{f+1}-a_x{a}_y{\mathrm{\α}}_{\mathrm{yz}}+a_y{a}_z{\mathrm{\α}}_{\mathrm{zy}}\\ +a_z{a}_x{\mathrm{\α}}_{\mathrm{zx}}=\frac{B{x}^2+B{y}^2+B{z}^2-1}{2}\end{array}---\left(4\right)$

(2) position upset

Use turning device degree of will speed up meter to be combined in space to overturn, data acquisition is carried out to accelerometer in each position;

In formula (4), error coefficient to be solved comprises the order error coefficient of (e+1) the individual accelerometer constant multiplier on x, y, z three axles, with α _yz, α _zy, α _zxthese 3 alignment error coefficients, the always total individual error coefficient to be solved of 3* (e+2), the positional number N>=3* (e+2) of upset;

Restriction in switching process: any two upturned positions can not occur a certain axle simultaneously perpendicular to the situation of surface level;

After having overturn N number of position, obtain the raw data [M that N group x, y, z accelerometer exports _xjm _yjm _zj], j=1,2...N;

(3) data rough handling

Preset one group of constant multiplier, be set to [K _1x0k _1y0k _1z0], subscript 0 represents initial value;

Initially set all accelerometer zero as 0, K _0x0=K _0y0=K _0z0=0, subscript 0 represents initial value;

Export raw data according to formula (2) to N group accelerometer to calculate, obtain N group [A _xj0a _yj0a _zj0], j=1,2...N;

Approximate processing, all order error coefficients of setting constant multiplier are 0, obtain according to formula (1):

a _ij0＝A _ij0，i＝x、y、z，j＝1、2...N……………………………………(5)

If alignment error coefficient is 0, obtain according to formula (3):

B _ij0＝A _ij0，i＝x、y、z，j＝1、2...N……………………………………(6)

By a _ij0and B _ij0substitute into formula (4), then obtain a N comprising 3* (e+2) individual unknown number and tie up system of equations; Calculated the estimated value of one group of individual unknown number of 3* (e+2) by least square method, be set to:

$\begin{array}{c}[{\mathrm{\Δ}}_{0x1},{\mathrm{\Δ}}_{1x1}...{\mathrm{\Δ}}_{\mathrm{ex}1},{\mathrm{\Δ}}_{0y1},{\mathrm{\Δ}}_{1y1}...{\mathrm{\Δ}}_{\mathrm{ey}1},\\ {\mathrm{\Δ}}_{0z1},{\mathrm{\Δ}}_{1z1}...{\mathrm{\Δ}}_{\mathrm{ez}1},{\mathrm{\α}}_{\mathrm{yz}1},{\mathrm{\α}}_{\mathrm{zy}1},{\mathrm{\α}}_{\mathrm{zx}1}]\end{array}$ Subscript 1 represents first step numerical value; (7)

Constant multiplier, zero-bit, alignment error coefficient that then the first step calculates are:

K _1i1＝K _1i0·(1+Δ _1i1),i＝x、y、z……………………………………(8)

K _0i1＝K _0i0+Δ _0i1,i＝x、y、z…………………………………………(9)

$\left\{\begin{array}{c}{\mathrm{\α}}_{\mathrm{yz}1}={\mathrm{\Δ}}_{\mathrm{yz}1}+{\mathrm{\α}}_{\mathrm{yz}0}\\ {\mathrm{\α}}_{\mathrm{zy}1}={\mathrm{\Δ}}_{\mathrm{zy}1}+{\mathrm{\α}}_{\mathrm{zy}0}\\ {\mathrm{\α}}_{\mathrm{zx}1}={\mathrm{\Δ}}_{\mathrm{zx}1}+{\mathrm{\α}}_{\mathrm{zx}0}\end{array}\right....\left(10\right)$

(4) data iterative processing

H>=2, the constant multiplier calculated according to (h-1) step and zero-bit, to the raw data [M that accelerometer exports _xjm _yjm _zj], j=1,2...N, application of formula (2) calculates [A during h step iteration _xjha _yjha _zjh], j=1,2...N, have:

$A_{\mathrm{ijh}}=\frac{M_{\mathrm{ij}}}{K_{1i(h-1)}}-K_{0i(h-1)}---\left(11\right)$

Approximate processing, all order error coefficients of setting constant multiplier are 0, obtain according to formula (1):

a _ijh＝A _ijh，i＝x、y、z，j＝1、2...N(12)

Have according to formula (4):

$\left|\begin{array}{c}{B}_{\mathrm{xh}}\\ B_{\mathrm{yh}}\\ B_{\mathrm{zh}}\end{array}\right|=\left|\begin{array}{ccc}1& 0& 0\\ {\mathrm{\α}}_{\mathrm{yz}(h-1)}& 1& 0\\ {\mathrm{\α}}_{\mathrm{zy}(h-1)}& {\mathrm{\α}}_{\mathrm{zx}(h-1)}& 1\end{array}\right|\×\left|\begin{array}{c}{A}_{x(h-1)}\\ A_{y(h-1)}\\ A_{z(h-1)}\end{array}\right|---\left(13\right)$

The result of calculation of formula (12) and formula (13) is substituted into formula (4), obtains a N comprising 3* (e+2) individual unknown number and tie up system of equations;

Calculated the unknown number estimated value of the h time iteration by least square method, be set to:

subscript h represents h step Numerical (14)

The accelerometer constant multiplier obtained after calculating the h time iteration, zero-bit, alignment error coefficient are as follows:

K _1ih＝K _i1(h-1)·(1+Δ _1ih)，i＝x、y、z………………………………(15)

K _0ih＝K _0i(h-1)+Δ _0i(h-1),i＝x、y、z………………………………(16)

$\left\{\begin{array}{c}{\mathrm{\α}}_{\mathrm{yzh}}={\mathrm{\Δ}}_{\mathrm{yzh}}+{\mathrm{\α}}_{\mathrm{yz}(h-1)}\\ {\mathrm{\α}}_{\mathrm{zyh}}={\mathrm{\Δ}}_{\mathrm{zyh}}+{\mathrm{\α}}_{\mathrm{zy}(h-1)}\\ {\mathrm{\α}}_{\mathrm{zxh}}={\mathrm{\Δ}}_{\mathrm{zxh}}+{\mathrm{\α}}_{\mathrm{zx}(h-1)}\end{array}\right.---\left(17\right)$

Set a threshold value, the difference (h-1) step iteration result and h being walked to the result of iteration judges, when difference is less than this threshold value, iteration terminates, and obtains final calculation result; Otherwise repeat step (4), until when the difference of the result of (h-1) step iteration result and h step iteration is less than threshold value, iteration terminates.

Further, the accelerometer combination scaling method of a kind of scalar potential standard as above, in step (2), turning device is turntable.

Further, the accelerometer combination scaling method of a kind of scalar potential standard as above, e=4.

Further, the accelerometer combination scaling method of a kind of scalar potential standard as above, in step (4), thresholding method is:

K _1ih—K _1ih-1≤5ppm，i＝x、y、z；

K _0ih-K _0ih-1≤ 2 × 10 ^-6g, i=x, y, z, g is acceleration of gravity;

α _yzh-α _yzh-1≤ 3 rads;

α _zyh-α _zyh-1≤ 3 rads;

α _zxh-α _zxh-1≤ 3 rads.

Beneficial effect of the present invention is, utilize acceleration on 3 orthogonal axles and be always the principle of 1 acceleration of gravity, by least square method and alternative manner, in degree of will speed up meter combined error model zero inclined, the optimum separation of constant multiplier, constant multiplier high-order term realization, only needs in demarcation to use simple and easy switching mechanism to carry out the arbitrary overturn of multiple position to accelerometer combination.Use this scaling method to carry out accelerometer combination to demarcate, not only solve the dependence of accelerometer combination timing signal for vector benchmark, the applicability of scaling method widely, and improves stated accuracy to rad level.In actual application, the accelerometer combination scaling method applying scalar potential standard of the present invention can use simple machine overturn product and realize very high stated accuracy and demarcate repeatability, through verifying its calibration result and using high precision turntable calibration result suitable.

Embodiment

Below in conjunction with specific embodiment, technical solution of the present invention is described in detail.

An accelerometer combination scaling method for scalar potential standard, specifically comprises the following steps:

(1) the accelerometer combined error model applied is determined:

$\left\{\begin{array}{c}{A}_x={\mathrm{\Δ}}_{0x}+a_x+{\mathrm{\Δ}}_{1x}{a}_x+...+{\mathrm{\Δ}}_{\mathrm{ex}}{a}_x^e\\ A_y={\mathrm{\Δ}}_{0y}+a_y+{\mathrm{\Δ}}_{1y}{a}_y+...+{\mathrm{\Δ}}_{\mathrm{ey}}{a}_y^e\\ A_z={\mathrm{\Δ}}_{0z}+a_z+{\mathrm{\Δ}}_{1z}{a}_z+...+{\mathrm{\Δ}}_{\mathrm{ez}}{a}_z^e\end{array}\right....\left(1\right)$

In formula:

A _i, the acceleration that i=x, y, z---accelerometer exports respectively on x, y, z axle;

A _i, i=x, y, z---the true acceleration on the responsive x, y, z axle of accelerometer difference;

Δ _fi, i=x, y, z, the j rank error of f=0 ~ e, e>=2---accelerometer i constant multiplier;

In this specific embodiment, e=4.

The acceleration that accelerometer exports is by following formulae discovery:

$\left\{\begin{array}{c}{A}_x=(M_x/K_{1x})-K_{0x}\\ A_y=(M_y/K_{1y})-K_{0y}\\ A_z=(M_z/K_{1z})-K_{0z}\end{array}\right....\left(2\right)$

In formula:

M _i, the original output of i=x, y, z---accelerometer respectively on x, y, z axle;

K _i, the constant multiplier of i=x, y, z---accelerometer respectively on x, y, z axle;

During the accelerometer specific implementation of three orthogonal installations, due to the difference between ideal mounting position, obtain following equation:

$\left|\begin{array}{c}{B}_x\\ B_y\\ B_z\end{array}\right|=\left|\begin{array}{ccc}1& 0& 0\\ {\mathrm{\α}}_{\mathrm{yz}}& 1& 0\\ {\mathrm{\α}}_{\mathrm{zy}}& {\mathrm{\α}}_{\mathrm{zx}}& 1\end{array}\right|\×\left|\begin{array}{c}{A}_x\\ A_y\\ A_z\end{array}\right|---\left(3\right)$

In formula: B _i, i=x, y, z represent the output of accelerometer respectively on x, y, z axle after alignment error corrects; α _xz, α _xy, α _yz, α _yx, α _zy, α _zxrepresent alignment error coefficient, specific as follows:

α _xzrepresent accelerometer sensitive in z-axis to x-axis direction on acceleration;

α _yzrepresent accelerometer sensitive in z-axis to y-axis direction on acceleration;

α _xyrepresent accelerometer sensitive in y-axis to x-axis direction on acceleration;

α _zyrepresent accelerometer sensitive in y-axis to z-axis direction on acceleration;

α _yxrepresent accelerometer sensitive in x-axis to y-axis direction on acceleration;

α _zxrepresent accelerometer sensitive in x-axis to z-axis direction on acceleration;

Calculate formula (4);

$\begin{array}{c}\underset{f=0}{\overset{e}{\mathrm{\Σ}}}{\mathrm{\Δ}}_{\mathrm{fx}}{a}_x^{f+1}+\underset{f=0}{\overset{e}{\mathrm{\Σ}}}{\mathrm{\Δ}}_{\mathrm{fy}}{a}_y^{f+1}+\underset{f=0}{\overset{e}{\mathrm{\Σ}}}{\mathrm{\Δ}}_{\mathrm{fz}}{a}_z^{f+1}-a_x{a}_y{\mathrm{\α}}_{\mathrm{yz}}+a_y{a}_z{\mathrm{\α}}_{\mathrm{zy}}\\ +a_z{a}_x{\mathrm{\α}}_{\mathrm{zx}}=\frac{B{x}^2+B{y}^2+B{z}^2-1}{2}\end{array}---\left(4\right)$

(2) position upset

Use turning device degree of will speed up meter to be combined in space to overturn, data acquisition is carried out to accelerometer in each position; In this specific embodiment, turning device is turntable.

In formula (4), error coefficient to be solved comprises the order error coefficient of (e+1) the individual accelerometer constant multiplier on x, y, z three axles, with α _yz, α _zy, α _zxthese 3 alignment error coefficients, the always total individual error coefficient to be solved of 3* (e+2), the positional number N>=3* (e+2) of upset;

Restriction in switching process: any two upturned positions can not occur a certain axle simultaneously perpendicular to the situation of surface level;

After having overturn N number of position, obtain the raw data [M that N group x, y, z accelerometer exports _xjm _yjm _zj], j=1,2...N;

(3) data rough handling

Preset one group of constant multiplier, be set to [K _1x0k _1y0k _1z0], subscript 0 represents initial value;

Initially set all accelerometer zero as 0, K _0x0=K _0y0=K _0z0=0, subscript 0 represents initial value;

Export raw data according to formula (2) to N group accelerometer to calculate, obtain N group [A _xj0a _yj0a _zj0], j=1,2...N;

Approximate processing, all order error coefficients of setting constant multiplier are 0, obtain according to formula (1):

a _ij0＝A _ij0，i＝x、y、z，j＝1、2...N……………………………………(5)

If alignment error coefficient is 0, obtain according to formula (3):

B _ij0＝A _ij0，i＝x、y、z，j＝1、2...N……………………………………(6)

By a _ij0and B _ij0substitute into formula (4), then obtain a N comprising 3* (e+2) individual unknown number and tie up system of equations; Calculated the estimated value of one group of individual unknown number of 3* (e+2) by least square method, be set to:

$\begin{array}{c}[{\mathrm{\Δ}}_{0x1},{\mathrm{\Δ}}_{1x1}...{\mathrm{\Δ}}_{\mathrm{ex}1},{\mathrm{\Δ}}_{0y1},{\mathrm{\Δ}}_{1y1}...{\mathrm{\Δ}}_{\mathrm{ey}1},\\ {\mathrm{\Δ}}_{0z1},{\mathrm{\Δ}}_{1z1}...{\mathrm{\Δ}}_{\mathrm{ez}1},{\mathrm{\α}}_{\mathrm{yz}1},{\mathrm{\α}}_{\mathrm{zy}1},{\mathrm{\α}}_{\mathrm{zx}1}]\end{array}$ Subscript 1 represents first step numerical value; (7)

Constant multiplier, zero-bit, alignment error coefficient that then the first step calculates are:

K _1i1＝K _1i0·(1+Δ _1i1),i＝x、y、z……………………………………(8)

K _0i1＝K _0i0+Δ _0i1,i＝x、y、z…………………………………………(9)

$\left\{\begin{array}{c}{\mathrm{\α}}_{\mathrm{yz}1}={\mathrm{\Δ}}_{\mathrm{yz}1}+{\mathrm{\α}}_{\mathrm{yz}0}\\ {\mathrm{\α}}_{\mathrm{zy}1}={\mathrm{\Δ}}_{\mathrm{zy}1}+{\mathrm{\α}}_{\mathrm{zy}0}\\ {\mathrm{\α}}_{\mathrm{zx}1}={\mathrm{\Δ}}_{\mathrm{zx}1}+{\mathrm{\α}}_{\mathrm{zx}0}\end{array}\right....\left(10\right)$

(4) data iterative processing

H>=2, the constant multiplier calculated according to (h-1) step and zero-bit, to the raw data [M that accelerometer exports _xjm _yjm _zj], j=1,2...N, application of formula (2) calculates [A during h step iteration _xjha _yjha _zjh], j=1,2...N, have:

$A_{\mathrm{ijh}}=\frac{M_{\mathrm{ij}}}{K_{1i(h-1)}}-K_{0i(h-1)}---\left(11\right)$

Approximate processing, all order error coefficients of setting constant multiplier are 0, obtain according to formula (1):

a _ijh＝A _ijh，i＝x、y、z，j＝1、2...N(12)

Have according to formula (4):

$\left|\begin{array}{c}{B}_{\mathrm{xh}}\\ B_{\mathrm{yh}}\\ B_{\mathrm{zh}}\end{array}\right|=\left|\begin{array}{ccc}1& 0& 0\\ {\mathrm{\α}}_{\mathrm{yz}(h-1)}& 1& 0\\ {\mathrm{\α}}_{\mathrm{zy}(h-1)}& {\mathrm{\α}}_{\mathrm{zx}(h-1)}& 1\end{array}\right|\×\left|\begin{array}{c}{A}_{x(h-1)}\\ A_{y(h-1)}\\ A_{z(h-1)}\end{array}\right|---\left(13\right)$

The result of calculation of formula (12) and formula (13) is substituted into formula (4), obtains a N comprising 3* (e+2) individual unknown number and tie up system of equations;

Calculated the unknown number estimated value of the h time iteration by least square method, be set to:

subscript h represents h step Numerical (14)

The accelerometer constant multiplier obtained after calculating the h time iteration, zero-bit, alignment error coefficient are as follows:

K _1ih＝K _i1(h-1)·(1+Δ _1ih)，i＝x、y、z………………………………(15)

K _0ih＝K _0i(h-1)+Δ _0i(h-1),i＝x、y、z………………………………(16)

$\left\{\begin{array}{c}{\mathrm{\α}}_{\mathrm{yzh}}={\mathrm{\Δ}}_{\mathrm{yzh}}+{\mathrm{\α}}_{\mathrm{yz}(h-1)}\\ {\mathrm{\α}}_{\mathrm{zyh}}={\mathrm{\Δ}}_{\mathrm{zyh}}+{\mathrm{\α}}_{\mathrm{zy}(h-1)}\\ {\mathrm{\α}}_{\mathrm{zxh}}={\mathrm{\Δ}}_{\mathrm{zxh}}+{\mathrm{\α}}_{\mathrm{zx}(h-1)}\end{array}\right.---\left(17\right)$

Set a threshold value:

K _1ih—K _1ih-1≤5ppm，i＝x、y、z；

K _0ih-K _0ih-1≤ 2 × 10 ^-6g, i=x, y, z, g is acceleration of gravity;

α _yzh-α _yzh-1≤ 3 rads;

α _zyh-α _zyh-1≤ 3 rads;

α _zxh-α _zxh-1≤ 3 rads.

The difference (h-1) step iteration result and h being walked to the result of iteration judges, when difference is less than this threshold value, iteration terminates, and obtains final calculation result; Otherwise repeat step (4), until when the difference of the result of (h-1) step iteration result and h step iteration is less than threshold value, iteration terminates.

Claims (4)

1. an accelerometer combination scaling method for scalar potential standard, is characterized in that, specifically comprise the following steps:

(1) the accelerometer combined error model applied is determined:

$\left\{\begin{array}{c}{A}_x={\mathrm{\Δ}}_{0x}+a_x+{\mathrm{\Δ}}_{1x}{a}_x+...+{\mathrm{\Δ}}_{\mathrm{ex}}{a}_x^e\\ A_y={\mathrm{\Δ}}_{0y}+a_y+{\mathrm{\Δ}}_{1y}{a}_y+...+{\mathrm{\Δ}}_{\mathrm{ey}}{a}_y^e\\ A_z={\mathrm{\Δ}}_{0z}+a_z+{\mathrm{\Δ}}_{1z}{a}_z+...+{\mathrm{\Δ}}_{\mathrm{ez}}{a}_z^e\end{array}\right....\left(1\right)$

In formula:

A _i, the acceleration that i=x, y, z---accelerometer exports respectively on x, y, z axle;

A _i, i=x, y, z---the true acceleration on the responsive x, y, z axle of accelerometer difference;

Δ _fi, i=x, y, z, the j rank error of f=0 ~ e, e>=2---accelerometer i constant multiplier;

The acceleration that accelerometer exports is by following formulae discovery:

$\left\{\begin{array}{c}{A}_x=(M_x/K_{1x})-K_{0x}\\ A_y=(M_y/K_{1y})-K_{0y}\\ A_z=(M_z/K_{1z})-K_{0z}\end{array}\right....\left(2\right)$

In formula:

M _i, the original output of i=x, y, z---accelerometer respectively on x, y, z axle;

K _i, the constant multiplier of i=x, y, z---accelerometer respectively on x, y, z axle;

During the accelerometer specific implementation of three orthogonal installations, due to the difference between ideal mounting position, obtain following equation:

$\left|\begin{array}{c}{B}_x\\ B_y\\ B_z\end{array}\right|=\left|\begin{array}{ccc}1& 0& 0\\ {\mathrm{\α}}_{\mathrm{yz}}& 1& 0\\ {\mathrm{\α}}_{\mathrm{zy}}& {\mathrm{\α}}_{\mathrm{zx}}& 1\end{array}\right|\×\left|\begin{array}{c}{A}_x\\ A_y\\ A_z\end{array}\right|---\left(3\right)$

In formula: B _i, i=x, y, z represent the output of accelerometer respectively on x, y, z axle after alignment error corrects; α _xz, α _xy, α _yz, α _yx, α _zy, α _zxrepresent alignment error coefficient, specific as follows:

α _xzrepresent accelerometer sensitive in z-axis to x-axis direction on acceleration;

α _yzrepresent accelerometer sensitive in z-axis to y-axis direction on acceleration;

α _xyrepresent accelerometer sensitive in y-axis to x-axis direction on acceleration;

α _zyrepresent accelerometer sensitive in y-axis to z-axis direction on acceleration;

α _yxrepresent accelerometer sensitive in x-axis to y-axis direction on acceleration;

α _zxrepresent accelerometer sensitive in x-axis to z-axis direction on acceleration;

Calculate formula (4);

$\begin{array}{c}\underset{f=0}{\overset{e}{\mathrm{\Σ}}}{\mathrm{\Δ}}_{\mathrm{fx}}{a}_x^{f+1}+\underset{f=0}{\overset{e}{\mathrm{\Σ}}}{\mathrm{\Δ}}_{\mathrm{fy}}{a}_y^{f+1}+\underset{f=0}{\overset{e}{\mathrm{\Σ}}}{\mathrm{\Δ}}_{\mathrm{fz}}{a}_z^{f+1}-a_x{a}_y{\mathrm{\α}}_{\mathrm{yz}}+a_y{a}_z{\mathrm{\α}}_{\mathrm{zy}}\\ +a_z{a}_x{\mathrm{\α}}_{\mathrm{zx}}=\frac{B{x}^2+B{y}^2+B{z}^2-1}{2}\end{array}---\left(4\right)$

(2) position upset

Use turning device degree of will speed up meter to be combined in space to overturn, data acquisition is carried out to accelerometer in each position;

In formula (4), error coefficient to be solved comprises the order error coefficient of (e+1) the individual accelerometer constant multiplier on x, y, z three axles, with α _yz, α _zy, α _zxthese 3 alignment error coefficients, the always total individual error coefficient to be solved of 3* (e+2), the positional number N>=3* (e+2) of upset;

Restriction in switching process: any two upturned positions can not occur a certain axle simultaneously perpendicular to the situation of surface level;

After having overturn N number of position, obtain the raw data [M that N group x, y, z accelerometer exports _xjm _yjm _zj], j=1,2...N;

(3) data rough handling

Preset one group of constant multiplier, be set to [K _1x0k _1y0k _1z0], subscript 0 represents initial value;

Initially set all accelerometer zero as 0, K _0x0=K _0y0=K _0z0=0, subscript 0 represents initial value;

Export raw data according to formula (2) to N group accelerometer to calculate, obtain N group [A _xj0a _yj0a _zj0], j=1,2...N;

Approximate processing, all order error coefficients of setting constant multiplier are 0, obtain according to formula (1):

a _ij0＝A _ij0，i＝x、y、z，j＝1、2...N……………………………………(5)

If alignment error coefficient is 0, obtain according to formula (3):

B _ij0＝A _ij0，i＝x、y、z，j＝1、2...N……………………………………(6)

By a _ij0and B _ij0substitute into formula (4), then obtain a N comprising 3* (e+2) individual unknown number and tie up system of equations; Calculated the estimated value of one group of individual unknown number of 3* (e+2) by least square method, be set to:

$\begin{array}{c}[{\mathrm{\Δ}}_{0x1},{\mathrm{\Δ}}_{1x1}...{\mathrm{\Δ}}_{\mathrm{ex}1},{\mathrm{\Δ}}_{0y1},{\mathrm{\Δ}}_{1y1}...{\mathrm{\Δ}}_{\mathrm{ey}1},\\ {\mathrm{\Δ}}_{0z1},{\mathrm{\Δ}}_{1z1}...{\mathrm{\Δ}}_{\mathrm{ez}1},{\mathrm{\α}}_{\mathrm{yz}1},{\mathrm{\α}}_{\mathrm{zy}1},{\mathrm{\α}}_{\mathrm{zx}1}]\end{array}$ Subscript 1 represents first step numerical value; (7)

Constant multiplier, zero-bit, alignment error coefficient that then the first step calculates are:

K _1i1＝K _1i0·(1+Δ _1i1),i＝x、y、z……………………………………(8)

K _0i1＝K _0i0+Δ _0i1,i＝x、y、z…………………………………………(9)

$\left\{\begin{array}{c}{\mathrm{\α}}_{\mathrm{yz}1}={\mathrm{\Δ}}_{\mathrm{yz}1}+{\mathrm{\α}}_{\mathrm{yz}0}\\ {\mathrm{\α}}_{\mathrm{zy}1}={\mathrm{\Δ}}_{\mathrm{zy}1}+{\mathrm{\α}}_{\mathrm{zy}0}\\ {\mathrm{\α}}_{\mathrm{zx}1}={\mathrm{\Δ}}_{\mathrm{zx}1}+{\mathrm{\α}}_{\mathrm{zx}0}\end{array}\right....\left(10\right)$

(4) data iterative processing

H>=2, the constant multiplier calculated according to (h-1) step and zero-bit, to the raw data [M that accelerometer exports _xjm _yjm _zj], j=1,2...N, application of formula (2) calculates [A during h step iteration _xjha _yjha _zjh], j=1,2...N, have:

$A_{\mathrm{ijh}}=\frac{M_{\mathrm{ij}}}{K_{1i(h-1)}}-K_{0i(h-1)}---\left(11\right)$

Approximate processing, all order error coefficients of setting constant multiplier are 0, obtain according to formula (1):

a _ijh＝A _ijh，i＝x、y、z，j＝1、2...N(12)

Have according to formula (4):

$\left|\begin{array}{c}{B}_{\mathrm{xh}}\\ B_{\mathrm{yh}}\\ B_{\mathrm{zh}}\end{array}\right|=\left|\begin{array}{ccc}1& 0& 0\\ {\mathrm{\α}}_{\mathrm{yz}(h-1)}& 1& 0\\ {\mathrm{\α}}_{\mathrm{zy}(h-1)}& {\mathrm{\α}}_{\mathrm{zx}(h-1)}& 1\end{array}\right|\×\left|\begin{array}{c}{A}_{x(h-1)}\\ A_{y(h-1)}\\ A_{z(h-1)}\end{array}\right|---\left(13\right)$

The result of calculation of formula (12) and formula (13) is substituted into formula (4), obtains a N comprising 3* (e+2) individual unknown number and tie up system of equations;

Calculated the unknown number estimated value of the h time iteration by least square method, be set to:

subscript h represents h step Numerical (14)

The accelerometer constant multiplier obtained after calculating the h time iteration, zero-bit, alignment error coefficient are as follows:

K _1ih＝K _i1(h-1)·(1+Δ _1ih)，i＝x、y、z………………………………(15)

K _0ih＝K _0i(h-1)+Δ _0i(h-1),i＝x、y、z………………………………(16)

$\left\{\begin{array}{c}{\mathrm{\α}}_{\mathrm{yzh}}={\mathrm{\Δ}}_{\mathrm{yzh}}+{\mathrm{\α}}_{\mathrm{yz}(h-1)}\\ {\mathrm{\α}}_{\mathrm{zyh}}={\mathrm{\Δ}}_{\mathrm{zyh}}+{\mathrm{\α}}_{\mathrm{zy}(h-1)}\\ {\mathrm{\α}}_{\mathrm{zxh}}={\mathrm{\Δ}}_{\mathrm{zxh}}+{\mathrm{\α}}_{\mathrm{zx}(h-1)}\end{array}\right.---\left(17\right)$

Set a threshold value, the difference (h-1) step iteration result and h being walked to the result of iteration judges, when difference is less than this threshold value, iteration terminates, and obtains final calculation result; Otherwise repeat step (4), until when the difference of the result of (h-1) step iteration result and h step iteration is less than threshold value, iteration terminates.

2. the accelerometer combination scaling method of a kind of scalar potential standard as claimed in claim 1, it is characterized in that: in step (2), turning device is turntable.

3. the accelerometer combination scaling method of a kind of scalar potential standard as claimed in claim 1, is characterized in that: e=4.

4. the accelerometer combination scaling method of a kind of scalar potential standard as claimed in claim 1, is characterized in that: in step (4), thresholding method is:

K _1ih—K _1ih-1≤5ppm，i＝x、y、z；

K _0ih-K _0ih-1≤ 2 × 10 ^-6g, i=x, y, z, g is acceleration of gravity;

α _yzh-α _yzh-1≤ 3 rads;

α _zyh-α _zyh-1≤ 3 rads;

α _zxh-α _zxh-1≤ 3 rads.