CN102654515B - Calibration algorithm for z sensitive shaft of three-shaft acceleration transducer - Google Patents

Abstract

The invention relates to a calibration method for a z sensitive shaft of a three-shaft acceleration transducer, which comprises the following steps of: setting the zero points of three sensitive shafts x, y and z of the three-shaft acceleration transducer as bx, by and bz, and setting sensitive degrees of the three sensitive shafts as sx, sy and sz, wherein the unit of the sensitive degree is the gravitational acceleration, and the zero point and the sensitive degree of the sensitive shaft z is bz and sz. Because the accuracy degrees of bz and sz are poor, bz and sz are regarded as unknown numbers. The formula is set as a*z<2>+b*z+c=g(x,y) (1). The calibration method also comprises the following steps of: adopting a fixed sampling frequency to sample three groups of initial data (namely x1, y1, z1, x2, y2, z2, x2, x3, y3 and z3) of the three-shaft acceleration transducer under different static conditions, substituting three groups of initial data into the formula (1) to obtain parameters a, b and c, and then calculating the actual zero point bz and the actual sensitive degree sz of the sensitive shaft Z of the three-shaft acceleration transducer.

Description

The calibration steps of the z sensitive axes of 3-axis acceleration sensor

Technical field

The present invention relates to a kind of calibration algorithm of z sensitive axes of 3-axis acceleration sensor.

Background technology

The popularity rate of current 3-axis acceleration sensor in consumer electronics is more and more higher, and thereupon its competition is also more and more fierce.Thus, the cost pressure of 3-axis acceleration sensor is increasing.And then the 3-axis acceleration sensor that also just result in some low costs more and more occurs.

In some low cost 3-axis acceleration sensors, acceleration sensitive axle performance parameter (zero point and sensitivity) on x-axis and y-axis direction generally can be guaranteed, but z sensitive axes is due to singularity such as techniques, its performance can be more far short of what is expected than x sensitive axes and y sensitive axes.That is, there is very large error and instability in zero point of its z sensitive axes and sensitivity.This can bring very large error to use, sometimes even cannot meet actual user demand.

Therefore, when using this type of acceleration transducer, due to the z sensitive axes that it is poor, bring a lot of errors and uncertainty can to follow-up calculating and process.

Summary of the invention

Technical matters to be solved by this invention is, the z sensitive axes poor-performing of existing low cost 3-axis acceleration sensor, exists the defect such as influence error and instability.The present invention aims to provide a kind of z sensitive axes calibration algorithm of 3-axis acceleration sensor, its can be larger to 3-axis acceleration sensor error in use z sensitive axes calibrate, obtain its real zero point and sensitivity, thus when not increasing processing step and cost, improve the performance of 3-axis acceleration sensor.

In order to solve the problems of the technologies described above, technical scheme proposed by the invention is:

The calibration algorithm of the z sensitive axes of 3-axis acceleration sensor, it includes following steps:

The x of setting 3-axis acceleration sensor, y, z tri-zero point of sensitive axes be followed successively by bx, by, bz, sensitivity is followed successively by sx, sy, sz, its unit is an acceleration of gravity, wherein z-axis zero point bz and sensitivity sz due to its poor accuracy, be regarded as unknown number at this;

Setting formula:

a*z ²+b*z+c＝g(x,y) (1)

Wherein:

$a=\frac{1}{{\mathrm{sz}}^2}$

$b=\frac{-2*\mathrm{bz}}{{\mathrm{sz}}^2}---\left(2\right)$

$c=\frac{{\mathrm{bz}}^2}{{\mathrm{sz}}^2}$

With 3 group raw data: the xs of fixed sampling frequency sampling 3-axis acceleration sensor under different attitude stationary state ₁, y ₁, z ₁, x ₂, y ₂, z ₂, x ₃, y ₃, z ₃; Then can be obtained by formula (1):

$\left[\begin{array}{ccc}{z}_1^2& z_1& 1\\ z_2^2& z_2& 1\\ z_3^2& z_3& 1\end{array}\right]\left[\begin{array}{c}a\\ b\\ c\end{array}\right]=\left[\begin{array}{c}g(x_1,y_1)\\ g(x_2,y_2)\\ g(x_3,y_3)\end{array}\right]---\left(3\right)$

Calculate the value of parameter a, b, c according to formula (3), then can calculate 3-axis acceleration sensor z sensitive axes bz at real zero point and sensitivity sz by formula (2).

Further, in different embodiments, wherein three axle raw data x, y, z meet following formula:

${\left(\frac{x-\mathrm{bx}}{\mathrm{sx}}\right)}^2+{\left(\frac{y-\mathrm{by}}{\mathrm{sy}}\right)}^2+{\left(\frac{z-\mathrm{bz}}{\mathrm{sz}}\right)}^2=1---(1-1)$

Further, in different embodiments, wherein following formula is set by formula (1-1):

$g(x,y)=1-{\left(\frac{x-\mathrm{bx}}{\mathrm{sx}}\right)}^2+{\left(\frac{y-\mathrm{by}}{\mathrm{sy}}\right)}^2---(1-2)$

Formula (1-2) is substituted into formula (1-1) can obtain:

${\left(\frac{z-\mathrm{bz}}{\mathrm{sz}}\right)}^2=g(x,y)---(1-3)$

And formula (1) is namely converted by formula (1-3).

Further, in different embodiments, wherein formula (3) can change into further:

$\left[\begin{array}{c}a\\ b\\ c\end{array}\right]={\left[\begin{array}{ccc}{z}_1^2& z_1& 1\\ z_2^2& z_2& 1\\ z_3^2& z_3& 1\end{array}\right]}^{-1}\left[\begin{array}{c}g(x_1,y_1)\\ g(x_2,y_2)\\ g(x_3,y_3)\end{array}\right]---(3-1)$

Calculate the value of parameter a, b, c according to formula (3-1), then can calculate 3-axis acceleration sensor z sensitive axes bz at real zero point and sensitivity sz by formula (2).

Compared with prior art, the invention has the beneficial effects as follows: the calibration algorithm that use the present invention relates to can very easily in the use procedure of 3-axis acceleration sensor, and the z sensitive axes larger to its error is calibrated, and obtains real zero point and sensitivity.Thus, the performance of 3-axis acceleration sensor is improved when not increasing processing step and cost.

Embodiment

An embodiment of the invention provide the calibration algorithm that a kind of acceleration transducer to having poor z sensitive axes carries out z sensitive axes zero point and sensitivity, and it includes following steps:

According to the databook of 3-axis acceleration sensor, can x be obtained, y, z tri-zero point of sensitive axes be followed successively by bx, by, bz, sensitivity is followed successively by sx, sy, sz, and its unit is an acceleration of gravity.Wherein zero point of z-axis and sensitivity are due to its poor accuracy, and be regarded as unknown number at this, the object of this algorithm is exactly the actual value calculating this Two Variables.Because it is subject to the effect of acceleration of gravity under 3-axis acceleration sensor static position, therefore, its three axle raw data x, y, z meet following formula:

${\left(\frac{x-\mathrm{bx}}{\mathrm{sx}}\right)}^2+{\left(\frac{y-\mathrm{by}}{\mathrm{sy}}\right)}^2+{\left(\frac{z-\mathrm{bz}}{\mathrm{sz}}\right)}^2=1---(1-1)$

3-axis acceleration sensor three axle raw data x, the unit of y, z is an acceleration of gravity.If:

$g(x,y)=1-{\left(\frac{x-\mathrm{bx}}{\mathrm{sx}}\right)}^2+{\left(\frac{y-\mathrm{by}}{\mathrm{sy}}\right)}^2---(1-2)$

Formula (1-2) can be obtained on behalf of formula (1-1):

${\left(\frac{z-\mathrm{bz}}{\mathrm{sz}}\right)}^2=g(x,y)---(1-3)$

Formula (1-3) is converted to following form:

a*z ²+b*z+c＝g(x,y) (1)

Wherein:

$a=\frac{1}{{\mathrm{sz}}^2}$

$b=\frac{-2*\mathrm{bz}}{{\mathrm{sz}}^2}---\left(2\right)$

$c=\frac{{\mathrm{bz}}^2}{{\mathrm{sz}}^2}$

With 3 group raw data: the xs of fixed sampling frequency sampling 3-axis acceleration sensor under different attitude stationary state ₁, y ₁, z ₁, x ₂, y ₂, z ₂, x ₃, y ₃, z ₃; Then can be obtained by formula (2):

$\left[\begin{array}{ccc}{z}_1^2& z_1& 1\\ z_2^2& z_2& 1\\ z_3^2& z_3& 1\end{array}\right]\left[\begin{array}{c}a\\ b\\ c\end{array}\right]=\left[\begin{array}{c}g(x_1,y_1)\\ g(x_2,y_2)\\ g(x_3,y_3)\end{array}\right]---\left(3\right)$

Formula (3) can change into further:

$\left[\begin{array}{c}a\\ b\\ c\end{array}\right]={\left[\begin{array}{ccc}{z}_1^2& z_1& 1\\ z_2^2& z_2& 1\\ z_3^2& z_3& 1\end{array}\right]}^{-1}\left[\begin{array}{c}g(x_1,y_1)\\ g(x_2,y_2)\\ g(x_3,y_3)\end{array}\right]---(3-1)$

Calculate the value of parameter a, b, c according to formula (3-1), then can calculate 3-axis acceleration sensor z sensitive axes bz at real zero point and sensitivity sz by formula (2).

The calibration algorithm that the present invention relates to can easily in the use procedure of 3-axis acceleration sensor, and the z sensitive axes larger to its error is calibrated, and obtains real zero point and sensitivity.Thus, the performance of 3-axis acceleration sensor is improved when not increasing processing step and cost.

The foregoing is only better embodiment of the present invention; protection scope of the present invention is not limited with above-mentioned embodiment; in every case those of ordinary skill in the art modify or change according to the equivalence that disclosure of the present invention is done, and all should include in the protection domain recorded in claims.

Claims (4)

1. the calibration steps of the z sensitive axes of 3-axis acceleration sensor, is characterized in that: it includes following steps:

The zero point of x, y, z three sensitive axes of setting 3-axis acceleration sensor is followed successively by bx, by, bz, sensitivity is followed successively by sx, sy, sz, its unit is an acceleration of gravity, wherein z-axis zero point bz and sensitivity sz due to its poor accuracy, be regarded as unknown number at this;

Setting formula:

a*z ²+b*z+c＝g(x,y) (1)

Wherein:

$\begin{array}{c}a=\frac{1}{{\mathrm{sz}}^2}\\ b=\frac{-2*\mathrm{bz}}{{\mathrm{sz}}^2}\\ c=\frac{{\mathrm{bz}}^2}{{\mathrm{sz}}^2}\end{array}---\left(2\right)$

With 3 group raw data: the xs of fixed sampling frequency sampling 3-axis acceleration sensor under different attitude stationary state ₁, y ₁, z ₁, x ₂, y ₂, z ₂, x ₃, y ₃, z ₃; Then can be obtained by formula (1):

$\left[\begin{array}{ccc}{z}_1^2& z_1& 1\\ z_2^2& z_2& 1\\ z_3^2& z_3& 1\end{array}\right]\left[\begin{array}{c}a\\ b\\ c\end{array}\right]=\left[\begin{array}{c}g(x_1,y_1)\\ g(x_2,y_2)\\ g(x_3,y_3)\end{array}\right]---\left(3\right)$

Calculate the value of parameter a, b, c according to formula (3), then can calculate 3-axis acceleration sensor z sensitive axes bz at real zero point and sensitivity sz by formula (2).

2. the calibration steps of the z sensitive axes of 3-axis acceleration sensor as claimed in claim 1, it is characterized in that: wherein three axle raw data x, y, z meet following formula:

${\left(\frac{x-\mathrm{bx}}{\mathrm{sx}}\right)}^2+{\left(\frac{y-\mathrm{by}}{\mathrm{sy}}\right)}^2+{\left(\frac{z-\mathrm{bz}}{\mathrm{sz}}\right)}^2=1---(1-1).$

3. the calibration steps of the z sensitive axes of 3-axis acceleration sensor as claimed in claim 2, is characterized in that: wherein set following formula by formula (1-1):

$g(x,y)=1-{\left(\frac{x-\mathrm{bx}}{\mathrm{sx}}\right)}^2+{\left(\frac{y-\mathrm{by}}{\mathrm{sy}}\right)}^2---(1-2)$

Formula (1-2) is substituted into formula (1-1) can obtain:

${\left(\frac{z-\mathrm{bz}}{\mathrm{sz}}\right)}^2=g(x,y)---(1-3)$

And formula (1) is namely converted by formula (1-3).

4. the calibration steps of the z sensitive axes of 3-axis acceleration sensor as claimed in claim 1, is characterized in that: wherein formula (3) can change into further:

$\left[\begin{array}{c}a\\ b\\ c\end{array}\right]={\left[\begin{array}{ccc}{z}_1^2& z_1& 1\\ z_2^2& z_2& 1\\ z_3^2& z_3& 1\end{array}\right]}^{-1}\left[\begin{array}{c}g(x_1,y_1)\\ g(x_2,y_2)\\ g(x_3,y_3)\end{array}\right]---(3-1)$

Calculate the value of parameter a, b, c according to formula (3-1), then can calculate 3-axis acceleration sensor z sensitive axes bz at real zero point and sensitivity sz by formula (2).