CN105242070B - A kind of accelerometer combination scaling method of scalar potential standard - Google Patents
A kind of accelerometer combination scaling method of scalar potential standard Download PDFInfo
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Abstract
The invention belongs to Gyro Calibration methods, and in particular to a kind of accelerometer without any extraneous benchmark combines scaling method.In technical solution of the present invention, using acceleration on 3 orthogonal axis and be always 1 acceleration of gravity principle, pass through least square method and alternative manner, zero bias in accelerometer combined error model, constant multiplier, constant multiplier high-order term are realized into optimal separation, the arbitrary overturning for carrying out multiple positions to accelerometer combination using simple switching mechanism is only needed in calibration.The accelerometer combination calibration of dependence when not only solving to(for) vector benchmark, the applicability of scaling method is very extensive, and improves stated accuracy to rad grade.
Description
Technical field
The invention belongs to Gyro Calibration methods, and in particular to a kind of accelerometer combination calibration without any extraneous benchmark
Method.
Background technology
The calibration of accelerometer combination is all provided in the scaling method for accelerometer combination published at present
Certain solution, while these scaling methods all having some limitations property, the problem of being primarily present, are as follows：
1) scaling method is based on some vector benchmark
This kind of scaling method is that accelerometer is placed sequentially on different location, measures accelerometer over these locations
Output signal, it is compared with projection of the corresponding acceleration of gravity vector on accelerometer sensitive axis, according to than
Each parameter of accelerometer is calculated in relatively result.Acceleration benchmark compared with accelerometer output valve is usually by each
Class calibration facility obtains, such as turntable, dividing head, horizontal plane etc..It leaves this kind of calibration facility and is then unable to get vector benchmark,
To cannot achieve accelerometer combination calibration.
2) stated accuracy is limited to calibration facility
This kind of scaling method is based on various calibration facilities, and stated accuracy is directly influenced by calibration facility precision.Calibration
The phenomenon that equipment generally existing is with time drift needs periodically to be corrected, and especially high-precision turntable cost is high, dimension
It protects cumbersome.The high-precision calibrating of accelerometer combination is seriously constrained for the dependence of high-precision calibrating equipment.
To sum up, it is known that the prior art must rely on extrinsic vectors benchmark to the calibration that accelerometer combines, and be detached from external arrow
Amount benchmark can not then be demarcated.Therefore, there is an urgent need for develop a kind of accelerometer combination scaling method without any extraneous benchmark.
Invention content
The technical problem to be solved in the present invention is to provide a kind of accelerometers without any extrinsic vectors benchmark to combine mark
Determine method, problem of calibrating when to solve without any extrinsic vectors benchmark, while requiring higher stated accuracy.
In order to realize the purpose, the technical solution adopted by the present invention is that：
A kind of accelerometer combination scaling method of scalar potential standard, specifically includes following steps：
(1) the accelerometer combined error model of application is determined：
In formula：
Ai, i=x, y, z --- accelerometer are respectively in the acceleration of x, y, z on-axis output；
ai, i=x, y, z --- the true acceleration on the sensitive x, y, z axis of accelerometer difference；
Δfi, i=x, y, z, f=0~e, the j rank errors of e >=2 --- accelerometer i constant multipliers；
The acceleration of accelerometer output is calculated by following formula：
In formula：
Mi, the original output on x, y, z axis respectively of i=x, y, z --- accelerometer；
Ki, i=x, y, z --- the accelerometer constant multiplier on x, y, z axis respectively；
When the accelerometer specific implementation of three orthogonal installations, due to the difference between ideal mounting position, obtain as
Lower equation：
In formula：Bi, i=x, y, z indicate that the accelerometer after installation error corrects is defeated on x, y, z axis respectively
Go out；αxz、αxy、αyz、αyx、αzy、αzxIndicate installation error coefficient, it is specific as follows：
αxzIndicate z-axis on accelerometer sensitive to x-axis direction on acceleration；
αyzIndicate z-axis on accelerometer sensitive to y-axis direction on acceleration；
αxyIndicate y-axis on accelerometer sensitive to x-axis direction on acceleration；
αzyIndicate y-axis on accelerometer sensitive to z-axis direction on acceleration；
αyxIndicate x-axis on accelerometer sensitive to y-axis direction on acceleration；
αzxIndicate x-axis on accelerometer sensitive to z-axis direction on acceleration；
Formula (4) is calculated；
(2) position is overturn
Accelerometer is combined using turnover device and is overturn in space, on each position to accelerometer into
Row data acquire；
Error coefficient to be solved includes (e+1) a accelerometer constant multiplier on three axis of x, y, z in formula (4)
Order error coefficient, with αyz、αzy、αzxThis 3 installation error coefficients, a total of a error coefficient to be solved of 3* (e+2), are turned over
Positional number N >=the 3* (e+2) turned；
Restriction in switching process：Feelings of a certain axis both perpendicular to horizontal plane cannot occur in any two upturned position
Condition；
After having overturn N number of position, the initial data [M of N group x, y, z accelerometers output is obtainedxj Myj Mzj], j=1,
2...N；
(3) data preliminary treatment
One group of constant multiplier is preset, [K is set as1x0 K1y0 K1z0], subscript 0 indicates initial value；
All accelerometer zeros are initially set as 0, K0x0=K0y0=K0z0=0, subscript 0 indicates initial value；
N group accelerometers output initial data is calculated according to formula (2), obtains N groups [Axj0 Ayj0 Azj0], j=
1、2...N；
Approximate processing, all order error coefficients for setting constant multiplier are 0, are obtained according to formula (1)：
aij0=Aij0, i=x, y, z, j=1,2...N ... ... ... ... ... ... ... (5)
If installation error coefficient is 0, obtained according to formula (3)：
Bij0=Aij0, i=x, y, z, j=1,2...N ... ... ... ... ... ... ... (6)
By aij0And Bij0Formula (4) is substituted into, then obtains a N-dimensional equation group for including 3* (e+2) a unknown number；By most
The estimated value of one group of a unknown number of 3* (e+2) is calculated in small square law, is set as：
Constant multiplier that then first step is calculated, zero-bit, installation error coefficient are：
K1i1=K1i0·(1+Δ1i1), i=x, y, z ... ... ... ... ... ... ... (8)
K0i1=K0i0+Δ0i1, i=x, y, z ... ... ... ... ... ... ... ... (9)
(4) data iterative processing
H >=2, the constant multiplier being calculated according to (h-1) step and zero-bit, to the initial data of accelerometer output
[Mxj Myj Mzj], j=1,2...N calculate [A when h walks iteration using formula (2)xjh Ayjh Azjh], j=1,2...N,
Have：
Approximate processing, all order error coefficients for setting constant multiplier are 0, are obtained according to formula (1)：
aijh=Aijh, i=x, y, z, j=1,2...N (12)
Had according to formula (4)：
The result of calculation of formula (12) and formula (13) is substituted into formula (4), it includes 3* (e+2) a unknown number to obtain one
N-dimensional equation group；
The unknown number estimated value of the h times iteration is calculated by least square method, is set as：
Subscript h indicates h step Numericals (14)
It is as follows to calculate the accelerometer constant multiplier obtained after the h times iteration, zero-bit, installation error coefficient：
K1ih=Ki1(h-1)·(1+Δ1ih), i=x, y, z ... ... ... ... ... ... (15)
K0ih=K0i(h-1)+Δ0i(h-1), i=x, y, z ... ... ... ... ... ... (16)
A threshold value is set, the difference of (h-1) step iteration result and the h result for walking iteration is judged, when difference is less than
When this threshold value, iteration terminates, and obtains final calculation result；Otherwise step (4) is repeated, until (h-1) step iteration result and h steps change
When the difference of the result in generation is less than threshold value, iteration terminates.
Further, a kind of accelerometer of scalar potential standard as described above combines scaling method, in step (2), turns over
Rotary device is turntable.
Further, a kind of accelerometer of scalar potential standard as described above combines scaling method, e=4.
Further, a kind of accelerometer of scalar potential standard as described above combines scaling method, in step (4), threshold
Value judgment method is：
K1ih—K1ih-1≤ 5ppm, i=x, y, z；
K0ih—K0ih-1≤2×10-6G, i=x, y, z, g are acceleration of gravity；
αyzh—αyzh-1≤ 3 rads；
αzyh—αzyh-1≤ 3 rads；
αzxh—αzxh-1≤ 3 rads.
The beneficial effects of the present invention are using acceleration on 3 orthogonal axis and be always 1 acceleration of gravity
Principle, by least square method and alternative manner, by zero bias, constant multiplier, the scale in accelerometer combined error model
Factor high-order term realizes optimal separation, only needs to carry out multiple positions to accelerometer combination using simple switching mechanism in calibration
Arbitrary overturning.Accelerometer combination calibration is carried out using this scaling method, not only solves accelerometer combination calibration
When dependence for vector benchmark, the applicability of scaling method is very extensive, and improves stated accuracy to rad grade.In reality
In the application process of border, simple machine overturning production can be used using the accelerometer combination scaling method of scalar potential standard of the present invention
Product and realize very high stated accuracy and calibration repeatability, demarcated with using high precision turntable by verifying its calibration result
As a result quite.
Specific implementation mode
Technical solution of the present invention is described in detail with reference to specific embodiment.
A kind of accelerometer combination scaling method of scalar potential standard, specifically includes following steps：
(1) the accelerometer combined error model of application is determined：
In formula：
Ai, i=x, y, z --- accelerometer are respectively in the acceleration of x, y, z on-axis output；
ai, i=x, y, z --- the true acceleration on the sensitive x, y, z axis of accelerometer difference；
Δfi, i=x, y, z, f=0~e, the j rank errors of e >=2 --- accelerometer i constant multipliers；
In this embodiment, e=4.
The acceleration of accelerometer output is calculated by following formula：
In formula：
Mi, the original output on x, y, z axis respectively of i=x, y, z --- accelerometer；
Ki, i=x, y, z --- the accelerometer constant multiplier on x, y, z axis respectively；
When the accelerometer specific implementation of three orthogonal installations, due to the difference between ideal mounting position, obtain as
Lower equation：
In formula：Bi, i=x, y, z indicate that the accelerometer after installation error corrects is defeated on x, y, z axis respectively
Go out；αxz、αxy、αyz、αyx、αzy、αzxIndicate installation error coefficient, it is specific as follows：
αxzIndicate z-axis on accelerometer sensitive to x-axis direction on acceleration；
αyzIndicate z-axis on accelerometer sensitive to y-axis direction on acceleration；
αxyIndicate y-axis on accelerometer sensitive to x-axis direction on acceleration；
αzyIndicate y-axis on accelerometer sensitive to z-axis direction on acceleration；
αyxIndicate x-axis on accelerometer sensitive to y-axis direction on acceleration；
αzxIndicate x-axis on accelerometer sensitive to z-axis direction on acceleration；
Formula (4) is calculated；
(2) position is overturn
Accelerometer is combined using turnover device and is overturn in space, on each position to accelerometer into
Row data acquire；In this embodiment, turnover device is turntable.
Error coefficient to be solved includes (e+1) a accelerometer constant multiplier on three axis of x, y, z in formula (4)
Order error coefficient, with αyz、αzy、αzxThis 3 installation error coefficients, a total of a error coefficient to be solved of 3* (e+2), are turned over
Positional number N >=the 3* (e+2) turned；
Restriction in switching process：Feelings of a certain axis both perpendicular to horizontal plane cannot occur in any two upturned position
Condition；
After having overturn N number of position, the initial data [M of N group x, y, z accelerometers output is obtainedxj Myj Mzj], j=1,
2...N；
(3) data preliminary treatment
One group of constant multiplier is preset, [K is set as1x0 K1y0 K1z0], subscript 0 indicates initial value；
All accelerometer zeros are initially set as 0, K0x0=K0y0=K0z0=0, subscript 0 indicates initial value；
N group accelerometers output initial data is calculated according to formula (2), obtains N groups [Axj0 Ayj0 Azj0], j=
1、2...N；
Approximate processing, all order error coefficients for setting constant multiplier are 0, are obtained according to formula (1)：
aij0=Aij0, i=x, y, z, j=1,2...N ... ... ... ... ... ... ... (5)
If installation error coefficient is 0, obtained according to formula (3)：
Bij0=Aij0, i=x, y, z, j=1,2...N ... ... ... ... ... ... ... (6)
By aij0And Bij0Formula (4) is substituted into, then obtains a N-dimensional equation group for including 3* (e+2) a unknown number；By most
The estimated value of one group of a unknown number of 3* (e+2) is calculated in small square law, is set as：
Constant multiplier that then first step is calculated, zero-bit, installation error coefficient are：
K1i1=K1i0·(1+Δ1i1), i=x, y, z ... ... ... ... ... ... ... (8)
K0i1=K0i0+Δ0i1, i=x, y, z ... ... ... ... ... ... ... ... (9)
(4) data iterative processing
H >=2, the constant multiplier being calculated according to (h-1) step and zero-bit, to the initial data of accelerometer output
[Mxj Myj Mzj], j=1,2...N calculate [A when h walks iteration using formula (2)xjh Ayjh Azjh], j=1,2...N,
Have：
Approximate processing, all order error coefficients for setting constant multiplier are 0, are obtained according to formula (1)：
aijh=Aijh, i=x, y, z, j=1,2...N (12)
Had according to formula (4)：
The result of calculation of formula (12) and formula (13) is substituted into formula (4), it includes 3* (e+2) a unknown number to obtain one
N-dimensional equation group；
The unknown number estimated value of the h times iteration is calculated by least square method, is set as：
Subscript h indicates h step Numericals (14)
It is as follows to calculate the accelerometer constant multiplier obtained after the h times iteration, zero-bit, installation error coefficient：
K1ih=Ki1(h-1)·(1+Δ1ih), i=x, y, z ... ... ... ... ... ... (15)
K0ih=K0i(h-1)+Δ0i(h-1), i=x, y, z ... ... ... ... ... ... (16)
Set a threshold value：
K1ih—K1ih-1≤ 5ppm, i=x, y, z；
K0ih—K0ih-1≤2×10-6G, i=x, y, z, g are acceleration of gravity；
αyzh—αyzh-1≤ 3 rads；
αzyh—αzyh-1≤ 3 rads；
αzxh—αzxh-1≤ 3 rads.
The difference of (h-1) step iteration result and the h result for walking iteration is judged, when difference is less than this threshold value, iteration
Terminate, obtains final calculation result；Otherwise step (4) is repeated, until the difference of (h-1) step iteration result and the result of h step iteration
When less than threshold value, iteration terminates.
Claims (4)
1. a kind of accelerometer of scalar potential standard combines scaling method, which is characterized in that specifically include following steps：
(1) the accelerometer combined error model of application is determined：
In formula：
Ai, i=x, y, z --- accelerometer are respectively in the acceleration of x, y, z on-axis output；
ai, i=x, y, z --- the true acceleration on the sensitive x, y, z axis of accelerometer difference；
Δfi, i=x, y, z, f=0~e, the j rank errors of e >=2 --- accelerometer i constant multipliers；
The acceleration of accelerometer output is calculated by following formula：
In formula：
Mi, the original output on x, y, z axis respectively of i=x, y, z --- accelerometer；
Ki, i=x, y, z --- the accelerometer constant multiplier on x, y, z axis respectively；
When the accelerometer specific implementation of three orthogonal installations, due to the difference between ideal mounting position, obtain such as lower section
Journey：
In formula：Bi, i=x, y, z indicate the accelerometer output on x, y, z axis respectively after installation error corrects；αxz、
αxy、αyz、αyx、αzy、αzxIndicate installation error coefficient, it is specific as follows：
αxzIndicate z-axis on accelerometer sensitive to x-axis direction on acceleration；
αyzIndicate z-axis on accelerometer sensitive to y-axis direction on acceleration；
αxyIndicate y-axis on accelerometer sensitive to x-axis direction on acceleration；
αzyIndicate y-axis on accelerometer sensitive to z-axis direction on acceleration；
αyxIndicate x-axis on accelerometer sensitive to y-axis direction on acceleration；
αzxIndicate x-axis on accelerometer sensitive to z-axis direction on acceleration；
Formula (4) is calculated；
(2) position is overturn
Accelerometer is combined using turnover device and is overturn in space, to accelerometer into line number on each position
According to acquisition；
Error coefficient to be solved includes the order of (e+1) a accelerometer constant multiplier on three axis of x, y, z in formula (4)
Error coefficient, with αyz、αzy、αzxThis 3 installation error coefficients, a total of a error coefficient to be solved of 3* (e+2), overturning
Positional number N >=3* (e+2)；
Restriction in switching process：The case where a certain axis is both perpendicular to horizontal plane cannot occur in any two upturned position；
After having overturn N number of position, the initial data [M of N group x, y, z accelerometers output is obtainedxj Myj Mzj], j=1,2...N；
(3) data preliminary treatment
One group of constant multiplier is preset, [K is set as1x0 K1y0 K1z0], subscript 0 indicates initial value；
All accelerometer zeros are initially set as 0, K0x0=K0y0=K0z0=0, subscript 0 indicates initial value；
N group accelerometers output initial data is calculated according to formula (2), obtains N groups [Axj0 Ayj0 Azj0], j=1,
2...N；
Approximate processing, all order error coefficients for setting constant multiplier are 0, are obtained according to formula (1)：
aij0=Aij0, i=x, y, z, j=1,2...N ... ... ... ... ... ... ... (5)
If installation error coefficient is 0, obtained according to formula (3)：
Bij0=Aij0, i=x, y, z, j=1,2...N ... ... ... ... ... ... ... (6)
By aij0And Bij0Formula (4) is substituted into, then obtains a N-dimensional equation group for including 3* (e+2) a unknown number；Pass through minimum two
The estimated value of one group of a unknown number of 3* (e+2) is calculated in multiplication, is set as：
Subscript 1 indicates the first step Numerical；(7)
Constant multiplier that then first step is calculated, zero-bit, installation error coefficient are：
K1i1=K1i0·(1+Δ1i1), i=x, y, z ... ... ... ... ... ... ... (8)
K0i1=K0i0+Δ0i1, i=x, y, z ... ... ... ... ... ... ... ... (9)
(4) data iterative processing
H >=2, the constant multiplier being calculated according to (h-1) step and zero-bit, to the initial data [M of accelerometer outputxj Myj
Mzj], j=1,2...N calculate [A when h walks iteration using formula (2)xjh Ayjh Azjh], j=1,2...N have：
Approximate processing, all order error coefficients for setting constant multiplier are 0, are obtained according to formula (1)：
aijh=Aijh, i=x, y, z, j=1,2...N (12)
Had according to formula (4)：
The result of calculation of formula (12) and formula (13) is substituted into formula (4), obtains a N for including 3* (e+2) a unknown number
Tie up equation group；
The unknown number estimated value of the h times iteration is calculated by least square method, is set as：
Subscript h indicates h step Numericals (14)
It is as follows to calculate the accelerometer constant multiplier obtained after the h times iteration, zero-bit, installation error coefficient：
Klih=Ki1(h-1)(1+Δ1ih), i=x, y, z ... ... ... ... ... ... (15)
K0ih=K0i(h-1)+Δ0i(h-1), i=x, y, z ... ... ... ... ... ... (16)
A threshold value is set, the difference of (h-1) step iteration result and the h result for walking iteration is judged, when difference is less than this threshold
When value, iteration terminates, and obtains final calculation result；Otherwise step (4) is repeated, until (h-1) step iteration result and h walk iteration
As a result when difference is less than threshold value, iteration terminates.
2. a kind of accelerometer of scalar potential standard as described in claim 1 combines scaling method, it is characterised in that：Step
(2) in, turnover device is turntable.
3. a kind of accelerometer of scalar potential standard as described in claim 1 combines scaling method, it is characterised in that：E=4.
4. a kind of accelerometer of scalar potential standard as described in claim 1 combines scaling method, it is characterised in that：Step
(4) in, thresholding method is：
K1ih—K1i(h-1)≤ 5ppm, i=x, y, z；
K0ih—K0i(h-1)≤2×10-6G, i=x, y, z, g are acceleration of gravity；
αyzh—αyz(h-1)≤ 3 rads；
αzyh—αzy(h-1)≤ 3 rads；
αzxh—αzx(h-1)≤ 3 rads.
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| CN108982918B (en) * | 2018-07-27 | 2020-07-14 | 北京航天控制仪器研究所 | Method for separating and calibrating combined error coefficients of accelerometer under condition of uncertain datum |
| CN110174122B (en) * | 2019-05-08 | 2021-03-12 | 苏州大学 | MEMS triaxial accelerometer calibration method based on maximum likelihood estimation algorithm |
| CN110988399A (en) * | 2019-11-28 | 2020-04-10 | 北京自动化控制设备研究所 | Accelerometer compensation method |
| CN110988400A (en) * | 2019-12-11 | 2020-04-10 | 北京自动化控制设备研究所 | MEMS accelerometer combination calibration method and calibration device |
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