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

Abstract

The invention relates to an accelerometer error calibration and compensation method based on a rotary mechanism, which comprises the following steps that: an accelerator is arranged on the rotary mechanism according to a certain requirements; the relationship between the dynamic continuous output of the accelerator and the rotating angle of the rotary mechanism is obtained through the rotation of the rotary mechanism; and a least square method is used for estimating and obtaining the bias, the scale factor, the non-linear error coefficient of the scale factor, the cross-coupling error coefficient and the like of the accelerator. The method uses the rotary mechanism to estimate all error coefficients of the accelerator, and is characterized by accuracy, high efficiency, easy operation, high universality and the like. After the method estimates the error coefficients and carries out corresponding error compensation, the output precision of the accelerator can be greatly improved. The method is also applicable to the calibration of a gyroscope, and can greatly improve the precision in measuring the speed of a top.

Description

A kind of accelerometer error calibration and compensation method based on rotating mechanism

Technical field

The present invention relates to a kind of accelerometer error calibration and compensation method, can be applicable to the error calibration and the compensation of other inertia devices such as gyroscope, belong to inertia device test, inertial navigation field.

Technical background

Characteristics such as inertial navigation system has entirely independently, highly concealed type, high bandwidth, continuous output have strategic importance on national defence, be one of most important equipment in the fields such as Aeronautics and Astronautics, navigation.

The performance of inertia device (gyro and accelerometer) is the main factor that influences the inertial navigation system precision, 80% of inertial navigation system error is caused by the device error, therefore, the precision of raising inertia device is a research contents main in the inertial technology evolution.The precision that improves inertia device often has two approach: (1) principle of work or the processing technology of improving device performance of improving device by changing inertia device; (2) means of testing by the advanced person carries out error modeling and demarcation to device, and the method by error compensation improves device performance.Generally speaking, the processing technology of the described improvement inertia device of approach (1) often needs to pay bigger cost, and device cost also will improve greatly.The described advanced person's of approach (2) method of testing often needs advanced testing apparatus to be the basis, and generally speaking, the testing apparatus of inertia device is often relatively more expensive, and test process is loaded down with trivial details, needs to drop into a large amount of experimental periods.

Summary of the invention

Technology of the present invention is dealt with problems and is: overcome the deficiencies in the prior art, a kind of accelerometer error calibration and compensation method based on small-sized rotating mechanism is provided, this method can accurately calibrate accelerometer zero partially, the nonlinearity erron coefficient of scale-up factor, scale-up factor, cross-couplings error coefficient etc., have advantages such as accurate, efficient, easy to operate, high universalizable.

Technical solution of the present invention is: a kind of accelerometer error calibration and compensation method based on rotating mechanism, and implementation step is as follows:

The first step is made rotating mechanism, and described rotating mechanism is made up of torque motor, grating, turning axle, accelerometer signal acquisition system, grating angle measurement signal acquiring system, accelerometer mounting platform and electric machine control system; The rotor and the turning axle of torque motor are connected; Grating is installed on the turning axle, and rotates with the rotation of turning axle; Accelerometer is installed on the accelerometer mounting platform, and the accelerometer mounting platform is positioned at the turning axle top and is connected with turning axle, and rotates with the rotation of turning axle; The rotation of electric machine control system control moment motor, the accelerometer signal acquisition system is used for the output signal of real-time sampling accelerometer, and grating angular signal acquisition system is used for gathering in real time the corner output signal of grating;

Second step, set up the general output model of accelerometer, wherein output error comprise zero partially, scale-up factor error, scale-up factor nonlinearity erron and cross-couplings error;

The 3rd step was installed on two accelerometers on the accelerometer mounting platform of rotating mechanism as requested, and its installation requirement is: the turning axle of two accelerometer sensitive axles and rotating mechanism is orthogonal in twos, and turning axle and surface level keeping parallelism;

In the 4th step, the mounting means according to described accelerometer of the 3rd step obtains the relational expression between accelerometer input and the rotation angle, and with the general output model of this relational expression substitution accelerometer, can obtain the output model of accelerometer with respect to rotation angle;

The 5th step, the rotation of electric machine control system control moment motor, the accelerometer signal acquisition system is gathered the output information of two accelerometers in real time, and grating angular signal acquisition system is gathered the corner output information of grating in real time;

The 6th step, according to the output model of the 4th accelerometer that obtain of step with respect to rotation angle, with of the input of real-time grating corner information of gathering of the 5th step as parameter estimation model, the sampled value of two accelerometers is as the output of parameter estimation model, utilizes least square method to estimate to obtain fractional error item coefficient in the accelerometer output model;

In the 7th step, around separately sensitive axes half-twist in described mounting plane of the 3rd step, the 5th step of repeating step and the 6th goes on foot, and can obtain remainder error item coefficient in the accelerometer output model with two accelerometers;

The 8th step, estimate according to the 6th step and the 7th step the error term coefficient of the accelerometer output model obtain accelerometer to be carried out error compensation, and the compensation precision of testing model.

Rotating mechanism rotates by the following characteristics of motion in above-mentioned the 5th step: rotation angle speed is ω, and positive and negative complete cycle rotation in 0-360 ° of scope, promptly move to 360 ° from 0 ° with rotation angle speed ω, and then move to 0 ° from 360 ° with the rotation angle speed of-ω, so both guaranteed that there was complete frequency component input in system, and made estimation of error accurate, also can avoid using simultaneously conducting slip ring, it is low to have reduced cost, has improved reliability.

The present invention's advantage compared with prior art is:

(1) traditional accelerometer error calibration need be by many group experiments, simultaneously also need be by equipment such as hydro-extractor, position table, the designed accelerometer scaling method of the present invention only needs just can calibrate all error coefficients by 2 groups of experiments, simplified the calibration process of error coefficient greatly, by the relation between degree of will speed up meter output and the input acceleration be converted to and rotation angle between relation, improved the estimated accuracy of error coefficient, and calibration process need be by other expensive utility appliance.This scaling method also is applicable to the demarcation of gyro error coefficient simultaneously, has certain versatility.

(2) rotating mechanism of the present invention has small-sized, advantage cheaply, therefore the present invention, therefore adopt this rotating mechanism, excite every error of inertia device by the rotation of mechanism, only need carry out the corresponding algorithm for estimating of 2 groups of experiments and combination and just can estimate the complete error coefficient of device, after error compensation, can improve the performance of device greatly.Characteristics such as the inventive method tool is accurate, efficient, easy to operate, equipment simple, low cost.

(3) rotating mechanism of the present invention is according to certain rotation regulation, it is rotation angle speed ω positive and negative complete cycle rotation in 0-360 ° of scope, so both guaranteed that there was complete frequency component input in system, make estimation of error accurate, simultaneously also can avoid using conducting slip ring, it is low further to have reduced cost, has improved reliability.

Description of drawings

Fig. 1 is the realization flow figure of the inventive method;

Fig. 2 is the rotating mechanism structural representation among the present invention;

Fig. 3 is the accelerometer measures system coordinate graph of a relation between being in the embodiment of the invention with carrier;

Fig. 4 is the curve of output of x accelerometer in rotary course in the embodiment of the invention;

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

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

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

Embodiment

Calibration process with the Switzerland MS8002 of colibrys company acceleration is that example is set forth specific implementation process of the present invention below.

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

1, preparation rotating mechanism.Fig. 2 is used for the rotating mechanism synoptic diagram that accelerometer is demarcated.

Rotating mechanism is by torque motor 5, turning axle 4, grating 3, accelerometer mounting platform 6, electric machine control system 7, accelerometer signal acquisition system 8, grating angular signal acquisition system 9 is formed, accelerometer 1 and accelerometer 2 are installed on the platform 6, accelerometer mounting platform 6, grating 3 is connected with turning axle 4 and rotates with the rotation of turning axle 4, turning axle 4 is connected with the rotor of torque motor 5, electric machine control system 7 can rotate according to certain rules by control moment motor 5, accelerometer signal acquisition system 8 can the real-time sampling accelerometer output valve, the corner output information that grating angular signal acquisition system 9 can the real-time sampling grating.

The torque motor of rotating mechanism adopts PWM control, electric machine control system is made up of DSP and power amplifier, DSP is by calculating the PWM ripple of the certain dutycycle of back output, and power amplifier carries out the rotation of power amplification rear drive motor to the PWM ripple, thereby realizes that motor moves according to design rule.Grating adopts the round grating of Britain renishow company, form by grating chi and read head, when the grating chi rotates with motor shaft, the pulse of read head output orthogonal, grating angular signal acquisition system is realized by the QEP modular circuit of DSP, this modular circuit obtains the umber of pulse corresponding with corner to the quadrature pulse decoding.The accelerometer signal acquisition system is realized that by the ADS1258 chip this AD conversion chip can be realized the high-speed sampling of accelerometer output simulating signal and the conversion output digital signal corresponding with simulating signal.

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

$A_x={\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HSA00000159437100042.png"\; state="\{\{state\}\}">k</figure-callout>}}_0+k_1{a}_x+k_2{a}_x^2+k_3{a}_x^3+k_4{a}_y+k_5{a}_z+k_6{a}_x{a}_y+k_7{a}_x{a}_z---\left(1\right)$

In the following formula (1), a _x, a _y, a _zRepresent x respectively, y, the input acceleration of three directions of z, k ₀Be accelerometer bias, k ₁Be scale-up factor, k ₂Be the quadratic nonlinearity error coefficient of scale-up factor, k ₃Be the cubic non-linearity error coefficient of scale-up factor, k ₄For with a _yRelevant cross-couplings error coefficient, k ₅For with a _zRelevant cross-couplings error coefficient, k ₆For with a _xAnd a _yThe cross-couplings error coefficient that product is relevant, k ₇For with a _xAnd a _zThe cross-couplings error coefficient that product is relevant.

In like manner, can obtain the accelerometer of z direction and the general output model of y directional acceleration meter.

3, two accelerometers (x and z accelerometer) are installed on the rotating mechanism, wherein x accelerometer sensitive axle, z accelerometer sensitive axle, rotating mechanism turning axle are orthogonal in twos, and turning axle and surface level keeping parallelism, as shown in Figure 2, this rotating mechanism need be installed in the cabinet and measure use.In the rotary course, the relation between x, z accelerometer measures coordinate system and the cabinet housing coordinate system as shown in Figure 3, o-x wherein _by _bz _bExpression cabinet housing coordinate system, o-x _my _mz _mExpression accelerometer measures coordinate system.The input acceleration of postulated mechanism tank shell coordinate system

a _Bx, a _By, a _BzThe input acceleration of machine representation tank shell coordinate system is at the component of x, y, z three directions respectively, and the input acceleration expression formula that just can draw accelerometer measures system in rotary course in conjunction with Fig. 3 is:

$\left\{\begin{array}{c}{a}_x=\cos (\mathrm{\&theta;}+{\mathrm{\&theta;}}_0)a_{\mathrm{bx}}+({\mathrm{\&delta;}}_z\cos (\mathrm{\&theta;}+{\mathrm{\&theta;}}_0)+{\mathrm{\&delta;}}_x\sin (\mathrm{\&theta;}+{\mathrm{\&theta;}}_0))a_{\mathrm{by}}-\sin (\mathrm{\&theta;}+{\mathrm{\&theta;}}_0)a_{\mathrm{bz}}\\ a_z=\sin (\mathrm{\&theta;}+{\mathrm{\&theta;}}_0)a_{\mathrm{bx}}+({\mathrm{\&delta;}}_z\sin (\mathrm{\&theta;}+{\mathrm{\&theta;}}_0)-{\mathrm{\&delta;}}_x\cos (\mathrm{\&theta;}+{\mathrm{\&theta;}}_0))a_{\mathrm{by}}+\cos (\mathrm{\&theta;}+{\mathrm{\&theta;}}_0)a_{\mathrm{bz}}\end{array}\right.---\left(2\right)$

A wherein _x, a _zBe x, the input acceleration of z directional acceleration meter Department of Survey, δ _zBe the drift angle of rotating mechanism with respect to cabinet housing coordinate system Z axle, δ _xBe the drift angle of rotating mechanism with respect to cabinet housing coordinate system X-axis, θ is the rotation angle of rotating mechanism, θ ₀Starting phase angle for rotating mechanism.Rotating mechanism is installed on the surface level, obtains [a _Bx, a _By, a _Bz] '=[0,0 ,-g] ', g is local acceleration of gravity, substitution following formula (2) can get:

$\left\{\begin{array}{c}{a}_x=g\sin (\mathrm{\&theta;}+{\mathrm{\&theta;}}_0)\\ a_y=0\\ a_z=-g\cos (\mathrm{\&theta;}+{\mathrm{\&theta;}}_0)\end{array}\right.---\left(3\right)$

4, the output model of the accelerometer that the input information substitution formula (1) of the accelerometer of following formula (3) expression is represented obtains accelerometer and is shown below with respect to the output model of rotation angle:

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

Wherein:

$a=k_0+\frac{1}{2}{g}^2{k}_2,b=g{k}_1+\frac{3}{4}{g}^3{k}_3,c=-g{k}_5$ $d=-\frac{1}{2}{g}^2{\mathrm{<figure-callout\; id="7"\; label="k"\; filenames="HSA00000159437100021.png"\; state="\{\{state\}\}">k</figure-callout>}}_7,e=-\frac{1}{2}{g}^2{k}_2,f=-\frac{1}{4}{g}^3{k}_3$ θ '=θ+θ ₀, a, b, c, d, e, f are intermediate variable.

5, the corner information θ that utilizes real-time sampling to obtain _iAs input, the sampled value A of accelerometer _XiAs output, and utilize the method for least square fitting to estimate to obtain in the accelerometer output model and a _x, a _zRelevant error coefficient item, wherein method of estimation is:

$\left[\begin{array}{c}a\\ b\\ c\\ d\\ e\\ f\end{array}\right]={\left[\begin{array}{cccccc}1& \sin {\mathrm{\&theta;}}_1^{\&prime;}& \cos {\mathrm{\&theta;}}_1^{\&prime;}& \sin {\mathrm{\&theta;}}_1^{\&prime;}& \cos {\mathrm{\&theta;}}_1^{\&prime;}& \sin {\mathrm{\&theta;}}_1^{\&prime;}\\ 1& \sin {\mathrm{\&theta;}}_2^{\&prime;}& \cos {\mathrm{\&theta;}}_2^{\&prime;}& \sin {\mathrm{\&theta;}}_2^{\&prime;}& \cos {\mathrm{\&theta;}}_2^{\&prime;}& \sin {\mathrm{\&theta;}}_2^{\&prime;}\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ .& .& .& .& .& .\\ 1& \sin {\mathrm{\&theta;}}_i^{\&prime;}& \cos {\mathrm{\&theta;}}_i^{\&prime;}& \sin {\mathrm{\&theta;}}_i^{\&prime;}& \cos {\mathrm{\&theta;}}_i^{\&prime;}& \sin {\mathrm{\&theta;}}_i^{\&prime;}\end{array}\right]}^{-}\&times;\left[\begin{array}{c}{A}_{x1}\\ A_{x2}\\ .\\ .\\ .\\ A_{\mathrm{xi}}\end{array}\right]---\left(5\right)$

In the following formula (5), A _XiBe the real-time output valve of accelerometer, θ ' _i=(θ _i+ θ ₀) be the real-time output valve of grating, wherein θ ₀Can estimate in advance to obtain, its method of estimation be seen step 6.Obtain a, b, c, d, e after the f value, can obtain the model parameter k of accelerometer ₀, k ₁, k ₂, k ₃, k ₅, k ₇As 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 θ that mentions of step 5 ₀Method of estimation as follows:

K in the output model of the accelerometer that following formula (1) is represented ₂-k ₇Be in a small amount, ignore in a small amount after, the output of x accelerometer can be reduced to:

A _x＝k ₀+k ₁a _x

＝k ₀+k ₁gsin(θ+θ ₀) (7)

＝k ₀+k ₁gcosθ ₀sinθ+k ₁gsinθ ₀cosθ

Control rotating mechanism rotation makes θ=0 ° respectively, and 45 °, 90 °

$\left\{\begin{array}{c}{A}_x^0={\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HSA00000159437100042.png"\; state="\{\{state\}\}">k</figure-callout>}}_0+k_{1}g\sin {\mathrm{\&theta;}}_0\\ A_x^{45}={\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HSA00000159437100042.png"\; state="\{\{state\}\}">k</figure-callout>}}_0+\sqrt{2}/2\\ A_x^{90}={\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="HSA00000159437100042.png"\; state="\{\{state\}\}">k</figure-callout>}}_0+k_{1}g\cos {\mathrm{\&theta;}}_0\end{array}(k_{1}g\sin {\mathrm{\&theta;}}_0+k_{1}g\cos {\mathrm{\&theta;}}_0)---\left(8\right)\right.$

In the following formula (8),

The rotation angle that is respectively rotating mechanism is 0 °, 45 °, and the output valve of x accelerometer in the time of 90 °.The above system of equations of simultaneous (8) just can solve θ ₀

7, with two accelerometers around sensitive axes half-twist in the mounting plane of step 3 appointment separately, repeating step 3-6 can obtain in the accelerometer error model and a _yRelevant error coefficient item k ₄And k ₆

8, estimate the accelerometer output model parameter k that obtains according to step 5 and step 7 ₀, k ₁, k ₂, k ₃, k ₄, k ₅, k ₆, k ₇, can carry out error compensation to accelerometer.

As shown in Figure 4, to be output as amplitude to accelerometer be 1000mg to x in the rotating mechanism rotary course, and the cycle is the sinusoidal component of 5s;

As shown in Figure 5, if uncompensation nonlinearity erron and cross-couplings error are carried out linear fit to curve of output shown in Figure 4, the output error that then obtains accelerometer in the rotary course is 2 frequencys multiplication and the 3 frequency multiplication components of input signal, and maximum amplitude reaches 3mg;

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

As shown in Figure 7, after utilizing the present invention to estimate the output model parameter of accelerometer and carrying out error compensation, 2 frequencys multiplication and the 3 frequency multiplication components that no longer contain swing circle in the output signal of accelerometer illustrate that the model parameter of the present invention's estimation is accurate, and error compensation reaches better effects;

The content that is not described in detail in the instructions of the present invention belongs to this area professional and technical personnel's known prior art.

It should be noted last that: above embodiment is the unrestricted technical scheme of the present invention in order to explanation only, and all modifications that does not break away from the spirit and scope of the present invention or local the replacement all should be encompassed in the middle of the claim scope of the present invention.

Claims (2)

1. accelerometer error calibration and compensation method based on a rotating mechanism is characterized in that step is as follows:

The first step, make rotating mechanism, described rotating mechanism is made up of torque motor (5), grating (3), turning axle (4), accelerometer signal acquisition system (8), grating angular signal sampling system (9), accelerometer mounting platform (6) and electric machine control system (7); The rotor of torque motor (5) and turning axle (4) are connected; Grating (3) is installed on turning axle (4), and rotates with the rotation of turning axle (4); Accelerometer is installed on the accelerometer mounting platform (6), and accelerometer mounting platform (6) is positioned at turning axle (4) top and is connected with turning axle (4), and rotates with the rotation of turning axle (4); Electric machine control system (7) control moment motor (5) rotation, accelerometer signal acquisition system (8) is used for the output valve of real-time sampling accelerometer, and grating angular signal sampling system (9) is used for gathering in real time the corner output information of grating (3);

Second step, set up the general output model of accelerometer, wherein output error comprise zero partially, scale-up factor error, scale-up factor nonlinearity erron and cross-couplings error;

The 3rd step was installed on two accelerometers on the accelerometer mounting platform (6) of rotating mechanism as requested, and its installation requirement is: the turning axle of two accelerometer sensitive axles and rotating mechanism is orthogonal in twos, and turning axle and surface level keeping parallelism;

In the 4th step, the mounting means according to described accelerometer of the 3rd step obtains the relational expression between accelerometer input and the rotation angle, and with the general output model of this relational expression substitution accelerometer, can obtain the output model of accelerometer with respect to rotation angle;

The 5th step, electric machine control system (7) control moment motor (5) rotation, the output information that accelerometer signal acquisition system (8) is gathered two accelerometers in real time, grating angular signal acquisition system (9) is gathered the corner output information of grating (3) in real time;

The 6th step, according to the output model of the 4th accelerometer that obtain of step with respect to rotation angle, with the corner output information of the grating (3) of the 5th step real-time sampling as the input of parameter estimation model, the sampled value of two accelerometers is as the output of parameter estimation model, utilizes least square method can estimate to obtain fractional error coefficient entry in the accelerometer output model;

In the 7th step, around separately sensitive axes half-twist in mounting plane, the 5th step of repeating step and the 6th goes on foot, and can obtain remainder error coefficient entry in the accelerometer output model with two accelerometers;

The 8th step, estimate according to the 6th step and the 7th step the error coefficient item of the accelerometer output model obtain accelerometer to be carried out error compensation, and the compensation precision of testing model.

2. accelerometer error calibration and compensation method based on rotating mechanism according to claim 1, it is characterized in that: the 5th described torque motor of step (5) rotates by the following characteristics of motion: rotation angle speed ω, and positive and negative complete cycle rotation in 0-360 ° of scope, promptly move to 360 ° from 0 °, and then move to 0 ° from 360 ° with the rotation angle speed of-ω with rotation angle speed ω.

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