CN100559123C - The gyrostatic difference measurement method of a kind of MEMS - Google Patents

Abstract

The gyrostatic difference measurement method of a kind of MEMS, select two approaching MEMS gyroscopes of environment sensitive characteristic similarity and form the gyroscope differential pair, make two the gyrostatic angular velocity sensitive axes of MEMS directions opposite by installation, and it is all parallel with same tested rotation axis, responsive same extraneous input angular velocity, by test, rating test, determine two gyrostatic major parameters and the environmental coefficient ratio between the two, when practical application, according to input angular velocity real-time resolving formula, calculate high-precision input angular velocity value.The present invention selects the gyroscope of same type, identical processing technology for use, utilized the similarity of same kind MEMS gyroscope to the environmental factor response characteristic, difference install to suppress the characteristic of output drift, by gyro is improved the gyrostatic measuring accuracy of MEMS to the processing of output data.The present invention is applicable to the gyrostatic application of various MEMS, and it is low to be particularly useful for requirement MEMS gyroscope cost, the occasion that system's output accuracy is high.

Description

The gyrostatic difference measurement method of a kind of MEMS

Technical field

The invention belongs to the Navigation, Guidance and Control technical field, particularly the application technology of MEMS gyrotron is applicable to various low costs, microminiature MEMS gyrotron.

Background technology

In many fields of science and technology, gyroscope plays an important role.Gyroscope is a kind of sensor of measured angular speed, its synoptic diagram as depicted in figs. 1 and 2, wherein Fig. 1 represents gyrostatic schematic perspective view, Fig. 2 represents gyrostatic floor map, the positive dirction of the angular velocity that it is responsive is determined according to the right-handed helix principle.Gyroscope can directly be measured the extraneous input angular velocity ω that acts on its sensitive axes OA _i, also can measure angle θ or the angular acceleration β that its sensitive axes turns over indirectly by computings such as integration or differential.

The concrete grammar of present measurement space bar axis angular rate, all be to make gyroscope sensitive axes OA parallel with tested rotation axis AX direction, and gyroscope and tested rotation axis be fixed together, as shown in Figure 3, when tested rotation axis rotates with angular velocity omega, rotational angular velocity ω will encourage gyroscope sensitive axes OA, makes gyroscope output represent the analog quantity of input angular velocity ω.It is exactly the core component Inertial Measurement Unit of forming inertial navigation system that a gyrostatic typical case uses.Inertial Measurement Unit is a kind of very important equipment in the Navigation, Guidance and Control system.It is made up of three gyroscopes and three accelerometers, and according to the requirement of inertial navigation principle, three gyrostatic sensitive axes are orthogonal in twos and parallel with three corresponding carrier coordinate axis respectively in the space, measures the input angular velocity of three carrier coordinate axis.Do not rely on external information during Inertial Measurement Unit work, also not to extraneous emittance, be difficult for being interfered, this distinct advantages makes it become carrier, a kind of widely used main air navigation aid of carrier in especially space flight, aviation and the navigation field.

Along with science and technology development, from engineering viewpoint, littler device, littler structural unit even littler subsystem have shown special advantages in many aspects, can satisfy the requirement of a lot of special occasions and function.So in recent years, along with the development of micro-fabrication technique and MEMS technology, MEMS gyroscope of new generation develops rapidly, their volumes are very little, very light in weight, cost are very low, have the many unrivaled advantages of traditional gyroscope.The micro-miniature inertial measuring unit of forming by the MEMS gyroscope, satisfied with space flight, aviation and navigation is the very urgent and outstanding demand of large quantities of miniaturization carriers of occurring in the field of representative, for example miniaturization aeroplane span is one meter of less than often, that have even have only as the palm big, its volume inside and the load that can bear are very limited, and this just requires their very little, the very light in weight of Inertial Measurement Unit volume.

Though the MEMS gyroscope has many unrivaled advantages, the traditional application process according to the moment gyroscope instrument still has very big shortcoming.

One utilizes the input angular velocity of single MEMS gyroscope survey bar axle, just is difficult to the very big input angular velocity measuring error of avoiding its principle of work, manufacturing process and application mode to bring for the MEMS gyroscope.The gyrostatic measuring error of MEMS is broadly divided into two parts, and a part is an ascertainment error, and a part is uncertain error.Wherein, ascertainment error can utilize disposal routes such as gyroscope test, demarcation, modeling and compensation to reduce its influence, but the influence of uncertain error is difficult to be eliminated.The gyrostatic core sensitive element of MEMS with and treatment circuit partly be easy to be subjected to the influence of complicated surrounding environment, for example temperature, electromagnetism, vibrations even radiation, gravity anomaly, humidity, air pressure etc. all may influence the characteristic of gyroscope sensitive element and treatment circuit, thus the output accuracy that influence is measured.These influence the environmental factor of gyroscope characteristic, mostly be not easy accurately to quantize and research, and the error that these factors cause can be coupled mutually and stack, make total error lack regularity and show stronger randomness, even strict these environmental factors of disposal methods such as gyroscope test, demarcation, modeling and compensation of utilizing standard are also obvious inadequately to the raising of gyroscope precision.

Its two because at present the MEMS application process is subjected to Effect of Environmental too big, want further to improve inertia device and accuracy of navigation systems, have only the gyrostatic processing technology of MEMS is proposed higher requirement, and improve processing technology, the cycle is long, difficulty is big, and the complicacy height has a big risk.

In a word, utilize the method for the rotational angular velocity of single MEMS gyroscope survey bar axle at present, measuring accuracy can be subjected to having a strong impact on of complex environment factor on every side, and wants to reduce this influence, and difficulty is very big, and cost is very high.

Summary of the invention

The objective of the invention is: overcome the existing deficiency of utilizing a single MEMS gyroscope survey rotational angular velocity method, a kind of two MEMS gyroscope difference measurements methods of utilizing are provided, measure the method for same rotational angular velocity, raising measuring accuracy.

Technical solution of the present invention is: the gyrostatic difference measurement method of a kind of MEMS, select two approaching MEMS gyroscopes of environment sensitive characteristic similarity and form the gyroscope differential pair, make two the gyrostatic angular velocity sensitive axes of MEMS directions opposite by installation, and it is all parallel with same tested rotation axis, responsive same extraneous input angular velocity, by test, rating test, determine two gyrostatic major parameters and the environmental coefficient ratio between the two, when practical application, according to input angular velocity real-time resolving formula, calculate high-precision input angular velocity value.

The determination step of described sensitivity characteristic similarity is as follows:

(1) gyroscope to be measured is divided into two batches, a collection of forward is installed, and another batch oppositely installed, and carries out the speed experiment simultaneously, supposes that the gyroscope number that forward is installed is u, and oppositely the gyroscope number of installing is v, by time sequence t acquisition test data y (t);

(2) respectively with n rank polynomial expression y (t)=a ₀+ a ₁T+a ₂t ²+ a ₃t ³+ ... + a _N-1t ^N-1+ a _nt ⁿEach tested gyrostatic experimental data of match draws each gyrostatic each rank coefficient a ₀, a ₁, a ₂..., a _N-1, a _n

(3) with each forward gyroscope and each reverse gyroscope all one by one correspondence to form u * v gyroscope altogether right;

(4) with the gyrostatic fitting coefficient correspondences at different levels of the forward of gyroscope centering divided by reverse gyrostatic fitting coefficients at different levels, draw n fitting coefficient ratio data, obtain the variance of this n fitting coefficient ratio data then, all u * v gyroscope to all carrying out aforesaid operations, is obtained u * v variance yields altogether;

(5) in u * v variance, the gyroscope that variance yields is more little is right, and its similarity is approaching more.

Principle of the present invention is: the gyrostatic differential applications method of a kind of MEMS, and select two approaching MEMS gyroscopes of environment sensitive characteristic similarity and form the gyroscope differential pair, as shown in Figure 4, make two the gyrostatic angular velocity sensitive axes of MEMS OA by installation ₁And OA ₂Direction is opposite, and all parallel with same tested rotation axis AX, responsive same extraneous input angular velocity ω.In Fig. 4, claim that sensitive axes and extraneous input angular velocity gyroscope in the same way are the forward gyroscope, claim that the reverse gyroscope of sensitive axes and extraneous input angular velocity is the negative sense gyroscope.Forming two MEMS gyroscopes of gyroscope differential pair, generally is select in a collection of MEMS gyroscope.Use one, make under fabrication process condition of the same race with a collection of MEMS gyroscope, its environment sensitive characteristic is more similar.Then, utilize the gyroscope test experiments to test accurately, demarcate, mutually relatively, pick out the approaching gyroscope of environment sensitive characteristic similarity and form the gyroscope differential pair with a collection of MEMS gyroscope.So just satisfied the requirement of differential applications method.

Temperature is a topmost error source in the environmental impact factor in the MEMS gyroscope.Experiment finds that variation of temperature can make the gyrostatic output voltage of MEMS change a lot.This mainly is because the gyrostatic sensitive element of MEMS is to be made by micro fabrication, volume is very little, thickness only has several microns, the several only millimeters of length and width, what temperature variation must cause expands with heat and contract with cold, the gyrostatic sensitive element of MEMS is deformed, and change its internal stress distribution, thereby change the gyrostatic dynamics of MEMS; In addition, variation of temperature also can seriously influence the characteristic of signal processing circuit, makes the variations such as electron component characteristic occurrence temperature drift of its internal integrated circuit, thereby influences the gyrostatic electrology characteristic of MEMS.General, when temperature raise, the gyrostatic output voltage of MEMS also increased, and in certain temperature range, voltage can be approximately linear relationship with variation of temperature.Certain structure that also has indivedual MEMS gyroscopes in little process, to form, make it when temperature raises, output voltage then needs to select the same MEMS gyroscope that output voltage reduces along with the temperature rising to match with it along with reduction to them, forms the gyroscope differential pair.The impact analysis of other error sources is similar.

According to gyrostatic principle of work and test philosophy, can draw the relational expression between MEMS gyroscope output voltage U and the input angular velocity ω, with output voltage U and n the ascertainment error item W that can test, demarcate and compensate _i, n=2～7 are placed on the left side of equation, and with the input angular velocity ω of the unknown be difficult to the right that the uncertain error term testing, demarcate, compensate and noise item are placed on equation, then equation form is as follows:

$U-\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{K}_{\mathrm{wi}}\·W_i=K\·\mathrm{\ω}+K_d\·D+N---\left(1\right)$

In the formula:

U---certain test is gyrostatic output voltage values constantly

W _i---test is i ascertainment error item constantly, i=1 ..., n, n=2～7

K _Wi---the coefficient of i ascertainment error item, i=1 ..., n, n=2～7

The number of n---the determinacy error term that can test, demarcate and compensate

ω---test input angular velocity constantly

K---this gyrostatic constant multiplier

D---test is the summation of the uncertain error term amount of influence constantly

K _d---uncertain total error coefficient, i.e. environmental coefficient

N---the measurement noise during test

Each parameter value of formula (1) the equation left side all can obtain by experimental techniques such as demarcation, and wherein, U is gyrostatic output voltage, can directly be drawn by D/A converting circuit; W _iCan be drawn by corresponding sensor measurement, for example, the acceleration in the relevant item with acceleration can be determined by the output of acceleration; K _WiCan and demarcate according to the testing standard test.The gyro constant multiplier K on formula (1) equation the right can and demarcate according to the testing standard test; The unknown quantity of ω for need accurately asking for; D is the summation of the uncertain error term amount of influence, does not still have effective means at present with its precise quantification, be to be difficult to hold, be difficult to amount by existing means test, demarcation, modeling, compensation, and also be the object that the present invention is directed to; Because D is difficult to quantize, make K _dAlso be difficult to quantize, only can determine K in the measuring process _dThe value of D can't be determined D or K separately _dValue; N is approximately white noise for measuring noise, and its mathematical expectation is approximately zero, and after a large amount of measured values in a period of time are average, the influence of N can eliminate substantially.

According to the right-handed helix principle, as shown in Figure 4, when when tested rotation axis AX has an input angular velocity ω, the gyrostatic sensitive axes OA of forward then ₁The input angular velocity of experiencing is+ω, and the gyrostatic sensitive axes OA of negative sense ₂The input angular velocity of experiencing is-ω.In order to distinguish two gyrostatic parameters, give forward gyroscope parameter mark subscript 1, give negative sense gyroscope parameter mark subscript 2.Then drawing the gyrostatic input/output relation of forward according to formula (1) satisfies:

$U_1-\underset{i=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="n\; K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{K}_{}{}_{1\mathrm{wi}}\&CenterDot;W_{1i}={\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_1\&CenterDot;\mathrm{\&omega;}+K_{1d}\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">D</figure-callout>}}_1+N_1---\left(2\right)$

The gyrostatic input/output relation of negative sense satisfies:

$U_2-\underset{i=1}{\overset{\mathrm{<figure-callout\; id="2"\; label="n\; K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{K}_{}{}_{2\mathrm{wi}}\&CenterDot;W_{2i}={\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_2\&CenterDot;(-\mathrm{\&omega;})+K_{2d}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">D</figure-callout>}}_2+N_2---\left(3\right)$

Because forward gyroscope and negative sense gyroscope are very near at space length, and volume own is very little, be fixed together again and experience the angular velocity of importing on the same tested rotation axis, so, have adequate reasons to be similar to and think that two residing external environments of gyroscope are identical, be i.e. uncertain error total amount D in the formula (2) ₁With the uncertain error total amount D in the formula (3) ₂Identical, be assumed to be D, then:

D ₁＝D ₂＝D (4)

Get by formula (2):

$K_{1d}\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">D</figure-callout>}}_1=U_1-\underset{i=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="n\; K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{K}_{}{}_{1\mathrm{wi}}\&CenterDot;W_{1i}-{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_1\&CenterDot;\mathrm{\&omega;}-N_1---\left(5\right)$

Get by formula (3):

$K_{2d}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">D</figure-callout>}}_2=U_2-\underset{i=1}{\overset{\mathrm{<figure-callout\; id="2"\; label="n\; K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{K}_{}{}_{2\mathrm{wi}}\&CenterDot;W_{2i}+{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_2\&CenterDot;\mathrm{\&omega;}-N_2---\left(6\right)$

Under certain known input angular velocity ω, to get interior m data of a period of time and do on average, m=8～30 are to remove the influence of noise N, U _1j, U _2jRepresent j voltage sample value of positive and negative gyroscope respectively, N _1j, N _2jRepresent j contained noise of sampled data of positive and negative gyroscope respectively, j=1...m, m=8～30.Get by formula (5) and formula (6):

${\stackrel{\&OverBar;}{K}}_{1d}=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{K}_{1d}\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">D</figure-callout>}}_1=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}(U_1-\underset{i=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="n\; K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{K}_{}{}_{1\mathrm{wi}}\&CenterDot;W_{1i}-{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_1\&CenterDot;\mathrm{\&omega;}-N_1)---\left(7\right)$

${\stackrel{\&OverBar;}{K}}_{2d}=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{K}_{2d}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">D</figure-callout>}}_2=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}(U_2-\underset{i=1}{\overset{\mathrm{<figure-callout\; id="2"\; label="n\; K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{K}_{}{}_{2\mathrm{wi}}\&CenterDot;W_{2i}-{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_2\&CenterDot;\mathrm{\&omega;}-N_2)---\left(8\right)$

Can obtain by the environmental coefficient definition:

K _1d≈K _1d K _2d≈K _2d (9)

Environmental coefficient ratio is:

$K_{\mathrm{bd}}=\frac{K_{1d}}{K_{2d}}\&ap;\frac{{\stackrel{\&OverBar;}{K}}_{1d}}{{\stackrel{\&OverBar;}{K}}_{2d}}---\left(10\right)$

Consider that formula (4) then has:

$K_{\mathrm{bd}}=\frac{K_{1d}}{K_{2d}}\&ap;\frac{{\stackrel{\&OverBar;}{K}}_{1d}}{{\stackrel{\&OverBar;}{K}}_{2d}}=\frac{\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{K}_{1d}\&CenterDot;D}{\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{K}_{2d}\&CenterDot;D}=\frac{\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{K}_{1d}\&CenterDot;{\mathrm{<figure-callout\; id="1"\; label="D"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">D</figure-callout>}}_1}{\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{K}_{2d}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">D</figure-callout>}}_2}$

$=\frac{\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}(U_{1j}-\underset{i=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="n\; K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{K}_{}{}_{1\mathrm{wi}}\&CenterDot;W_{1i}-{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_1\&CenterDot;\mathrm{\&omega;}-N_{1j})}{\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}(U_{2j}-\underset{i=1}{\overset{\mathrm{<figure-callout\; id="2"\; label="n\; K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{K}_{}{}_{2\mathrm{wi}}\&CenterDot;W_{2i}+{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_2\&CenterDot;\mathrm{\&omega;}-N_{2j})}---\left(11\right)$

$=\frac{\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}(U_{1j}-\underset{i=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="n\; K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{K}_{}{}_{1\mathrm{wi}}\&CenterDot;W_{1i}-{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_1\&CenterDot;\mathrm{\&omega;})-\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{N}_{1j}}{\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}(U_{2j}-\underset{i=1}{\overset{\mathrm{<figure-callout\; id="2"\; label="n\; K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{K}_{}{}_{2\mathrm{wi}}\&CenterDot;W_{2i}+{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_2\&CenterDot;\mathrm{\&omega;})-\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{N}_{2j}}$

Consider that N measures noise, be approximately white noise, its mathematical expectation is approximately zero, then has:

$\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{N}_{1j}=\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}{N}_{2j}=0---\left(12\right)$

Then have:

$K_{\mathrm{bd}}=\frac{\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}(U_{1j}-\underset{i=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="n\; K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{K}_{}{}_{1\mathrm{wi}}\&CenterDot;W_{1i}-{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_1\&CenterDot;\mathrm{\&omega;})}{\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}(U_{2j}-\underset{i=1}{\overset{\mathrm{<figure-callout\; id="2"\; label="n\; K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{K}_{}{}_{2\mathrm{wi}}\&CenterDot;W_{2i}+{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_2\&CenterDot;\mathrm{\&omega;})}---\left(13\right)$

In the known testing experiment of input angular velocity ω, each parameter of equation (13) the right all can be determined, so utilize said method can measure environmental coefficient ratio $K_{\mathrm{bd}}=\frac{K_{1d}}{K_{2d}}$ Size.

When the gyroscope real work was used, input angular velocity ω was in the variation that does not stop, and the topmost task of system is exactly the accurate as far as possible input angular velocity ω of determining, is got by formula (10):

K _1d＝K _bd·K _2d (14)

So K is multiply by at formula (3) two ends simultaneously _Bd, then:

$K_{\mathrm{bd}}\&CenterDot;U_2-\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{K}_{\mathrm{bd}}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_{2\mathrm{wi}}\&CenterDot;W_{2i}=K_{\mathrm{bd}}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_2\&CenterDot;(-\mathrm{\&omega;})+K_{\mathrm{bd}}\&CenterDot;K_{2d}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">D</figure-callout>}}_2+K_{\mathrm{bd}}\&CenterDot;N_2---\left(15\right)$

Deducting formula (15) with formula (2) gets:

$(U_1-\underset{i=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="n\; K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{K}_{}{}_{1\mathrm{wi}}\&CenterDot;W_{1i})-(K_{\mathrm{bd}}\&CenterDot;U_2-\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{K}_{\mathrm{bd}}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_{2\mathrm{wi}}\&CenterDot;W_{2i})---\left(16\right)$

$=({\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_1+K_{\mathrm{bd}}\&CenterDot;K_2)\&CenterDot;\mathrm{\&omega;}+(K_{1d}\&CenterDot;D_1-K_{\mathrm{bd}}\&CenterDot;K_{2d}\&CenterDot;D_2)+(N_1-K_{\mathrm{bd}}\&CenterDot;N_2)$

Consider the relation of formula (4), then following formula turns to:

$(U_1-\underset{i=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="n\; K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{K}_{}{}_{1\mathrm{wi}}\&CenterDot;W_{1i})-(K_{\mathrm{bd}}\&CenterDot;U_2-\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{K}_{\mathrm{bd}}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_{2\mathrm{wi}}\&CenterDot;W_{2i})---\left(17\right)$

$=({\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_1+K_{\mathrm{bd}}\&CenterDot;K_2)\&CenterDot;\mathrm{\&omega;}+(K_{1d}-K_{\mathrm{bd}}\&CenterDot;K_{2d})\&CenterDot;D+(N_1-K_{\mathrm{bd}}\&CenterDot;N_2)$

Consider the relation of formula (14) again, then the coefficient of D equals 0 in the following formula, and following formula turns to:

$(U_1-\underset{i=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="n\; K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{K}_{}{}_{1\mathrm{wi}}\&CenterDot;W_{1i})-(K_{\mathrm{bd}}\&CenterDot;U_2-\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{K}_{\mathrm{bd}}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_{2\mathrm{wi}}\&CenterDot;W_{2i})=({\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_1+K_{\mathrm{bd}}\&CenterDot;K_2)\&CenterDot;\mathrm{\&omega;}+(N_1-K_{\mathrm{bd}}\&CenterDot;N_2)---\left(18\right)$

Can be drawn when the gyroscope real work is used by formula (18), the real-time resolving formula of input angular velocity ω is:

$\mathrm{\&omega;}=\frac{(U_1-\underset{i=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="n\; K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{K}_{}{}_{1\mathrm{wi}}\&CenterDot;W_{1i})-(K_{\mathrm{bd}}\&CenterDot;U_2-\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{K}_{\mathrm{bd}}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_{2\mathrm{wi}}\&CenterDot;W_{2i})-(N_1-K_{\mathrm{bd}}\&CenterDot;N_2)}{({\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_1+K_{\mathrm{bd}}\&CenterDot;K_2)}---\left(19\right)$

In each parameter on formula (19) the right, N ₁And N ₂For measuring noise, generally be approximately Gaussian distribution, in the real-time navigation process, have ripe filtering method to can be used to suppress its influence, order:

$N_c=-\frac{N_1-K_{\mathrm{bd}}\&CenterDot;N_2}{{\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_1+K_{\mathrm{bd}}\&CenterDot;K_2}---\left(20\right)$

N then _cIt also is the measurement noise of Gaussian distribution.Like this, the real-time resolving formula (19) of input angular velocity ω turns to:

$\mathrm{\&omega;}=\frac{(U_1-\underset{i=1}{\overset{\mathrm{<figure-callout\; id="1"\; label="n\; K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">n</figure-callout>}}{\mathrm{\&Sigma;}}}{K}_{}{}_{1\mathrm{wi}}\&CenterDot;W_{1i})-(K_{\mathrm{bd}}\&CenterDot;U_2-\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{K}_{\mathrm{bd}}\&CenterDot;{\mathrm{<figure-callout\; id="2"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_{2\mathrm{wi}}\&CenterDot;W_{2i})}{({\mathrm{<figure-callout\; id="1"\; label="K"\; filenames="C20071017633800141.png,C20071017633800151.png"\; state="\{\{state\}\}">K</figure-callout>}}_1+K_{\mathrm{bd}}\&CenterDot;K_2)}+N_c---\left(21\right)$

In the real-time resolving formula (21), U ₁And U ₂Be respectively forward and the gyrostatic real-time output voltage values of reverse two MEMS, K _BdCan utilize formula (13) to obtain according to test data, other remaining parameters all can be utilized traditional standard method of test test, demarcate before navigation.Can in navigation procedure, obtain the value of input angular velocity ω in real time so utilize formula (21).Do not contain the expression test parameter D of the uncertain error term amount of influence constantly in the formula (21), so the input angular velocity ω that utilizes above method to ask in real time is not subjected to Effect of Environmental.

The present invention's advantage compared with prior art is: the present invention utilizes two input angular velocities on the same tested rotation axis of MEMS gyroscope survey, has the advantage of following two aspects:

(1) the gyro view differential applications method of the present invention's employing, angular velocity when making the navigational system practical application is asked in the formula, the amount of influence that does not contain uncertain environmental error factor, thereby can avoid most of environmental factor, for example the measuring error that causes of factors such as temperature, electromagnetism, vibrations even radiation, gravity anomaly, humidity, air pressure can improve measuring accuracy greatly.

(2) in the gyro view differential applications method that the present invention adopts, it is high more to form two right gyrostatic similaritys of difference gyro, navigation accuracy after the composition navigational system just can improve more greatly, this method of just very big the passing through of present difficulty being improved MEMS gyroscope processing technology improves the problem of inertia device and navigational system precision, transforms the problem that the method that improves two gyroscope similaritys for little the passing through of difficulty improves inertia device and navigational system precision.Reduce the difficulty and the cost of dealing with problems, improved accuracy of navigation systems.

Description of drawings

Fig. 1 is a MEMS gyroscope 3 D stereo synoptic diagram;

Fig. 2 is a MEMS gyroscope two dimensional surface synoptic diagram;

Fig. 3 is the synoptic diagram that utilizes the tested rotation axis of single MEMS gyroscope survey;

Fig. 4 be the miniature MEMS gyroscope of the vertical datum clamp face of sensitive axes to measured angular speed synoptic diagram, among the figure: 1, forward gyroscope, 2, reverse gyroscope;

Fig. 5 be the miniature MEMS gyroscope of the parallel datum clamp face of sensitive axes to measured angular speed synoptic diagram, among the figure: 1, forward gyroscope, 2, reverse gyroscope;

Fig. 6 be the CRS03 miniature MEMS gyroscope of the vertical datum clamp face of sensitive axes to measured angular speed synoptic diagram, wherein Fig. 6 a is a front view, Fig. 6 b is a left view, Fig. 6 c is a vertical view, Fig. 6 d is left vertical view, among the figure: 1, forward gyroscope, 2, reverse gyroscope;

Fig. 7 be the LCG50 miniature MEMS gyroscope of the parallel datum clamp face of sensitive axes to measured angular speed synoptic diagram, wherein Fig. 7 a is a front view, Fig. 7 b is a left view, Fig. 7 c is a vertical view, Fig. 7 d is left vertical view, among the figure: 1, forward gyroscope, 2, reverse gyroscope.

Embodiment

The MEMS gyroscope is an example with silicon MEMS gyroscopes CRS03 among first embodiment of the present invention.

At first, get a collection of silicon MEMS gyroscopes CRS03, present embodiment is got 20, according to gyroscope testing standard commonly used, carries out test experiments.Test, calibrate each important parameter of MEMS gyroscope, comprise each ascertainment error item and their coefficient, zero inclined to one side, zero stable partially, the zero parameters such as the repeatability of renaturation, constant multiplier, constant multiplier degree of asymmetry, constant multiplier, maximum input angular velocity, threshold value, resolution, random walk coefficient, input shaft misalignment, frequency span that lay particular stress on are arranged usually.

Secondly, CRS03 is equally divided into two groups with this batch MEMS gyroscope, 10 every group.Utilize the single shaft rate table to carry out the turntable test.Anchor clamps upwards are fixed in the one group of parallel turntable axis of rotation of the gyrostatic sensitive axes of MEMS direction on the turntable by experiment, the parallel turntable axis of rotation of another group gyrostatic sensitive axes of MEMS is directed downwards is fixed on the turntable.In the input angle speed range, choose a plurality of input angle speed, according to sample frequency test of setting and storage gyroscope output data.

Once more, form the gyroscope differential pair according to immediate two the MEMS gyroscopes of the data decimation environment sensitive characteristic similarity of handling.The determination step of described sensitivity characteristic similarity is as follows:

(1) 20 gyroscopes to be measured are divided into two batches, 10 forwards are installed, and oppositely install for 10, carry out the speed experiment simultaneously, by time sequence t acquisition test data y (t);

(2) respectively with 4 rank polynomial expression y (t)=a ₀+ a ₁T+a ₂t ²+ a ₃t ³+ a ₄t ⁴Each tested gyrostatic experimental data of match draws each gyrostatic each rank coefficient a ₀, a ₁, a ₂, a ₃, a ₄

(3) with 10 forward gyroscopes and 10 reverse gyroscopes all one by one correspondence to form 10 * 10=100 gyroscope altogether right;

(4) with the gyrostatic fitting coefficient correspondences at different levels of the forward of gyroscope centering divided by reverse gyrostatic fitting coefficients at different levels, draw 5 fitting coefficient ratio data, obtain the variance of these 5 fitting coefficient ratio data then, all 100 gyroscopes to all carrying out aforesaid operations, are obtained 100 variance yields altogether;

In (5) 100 variances, the gyroscope that variance yields is more little is right, and its similarity is approaching more.

At last, with the little silicon MEMS gyroscopes of the CRS03 that selects to being installed on the carrier of need measuring, its differential principle synoptic diagram as shown in Figure 4, concrete scheme of installation as shown in Figure 6, make two the gyrostatic angular velocity sensitive axes of MEMS directions opposite by installation, and all parallel with tested rotation axis, responsive same extraneous input angular velocity, application of formula (21) can real-time resolving go out high-precision input angular velocity value in system.

The MEMS gyroscope is an example with the quartzy MEMS gyroscope LCG50 that BEI company produces among second embodiment of the present invention.

At this moment, gyrostatic test experiments, scaling method, data acquisition, data processing, right the choosing of gyroscope, all identical with embodiment one.Different is, the angular velocity sensitive axes direction of CRS03 is perpendicular to the gyroscope datum clamp face, and the angular velocity sensitive axes direction of LCG50 is parallel to the gyroscope datum clamp face.

So LCG50MEMS gyroscope that will select is when being installed on the carrier that needs to measure, the differential principle synoptic diagram of mounting means as shown in Figure 5, concrete scheme of installation is as shown in Figure 7.Make two the gyrostatic angular velocity sensitive axes of MEMS directions opposite by installation, and all parallel with tested rotation axis, responsive same extraneous input angular velocity, application of formula (21) real-time resolving in system goes out high-precision input angular velocity value.

Claims (4)

1, the gyrostatic difference measurement method of a kind of MEMS is characterized in that comprising the following steps:

(1) selects two approaching MEMS gyroscopes of environment sensitive characteristic similarity and form the gyroscope differential pair;

(2) make two the gyrostatic angular velocity sensitive axes of MEMS directions opposite by installation, and all parallel with same tested rotation axis, responsive same extraneous input angular velocity;

(3) by test, rating test, determine two gyrostatic characterisitic parameters and the environmental coefficient ratio between the two, when practical application,, calculate high-precision input angular velocity value according to input angular velocity real-time resolving formula.

2, the gyrostatic difference measurement method of a kind of MEMS according to claim 1, it is characterized in that: the determination step of described sensitivity characteristic similarity is as follows:

(1) gyroscope to be measured is divided into two batches, a collection of forward is installed, and another batch oppositely installed, and carries out the speed experiment simultaneously, supposes that the gyroscope number that forward is installed is u, and oppositely the gyroscope number of installing is v, by time sequence t acquisition test data y (t);

(2) respectively with n rank polynomial expression y (t)=a ₀+ a ₁T+a ₂t ²+ a ₃t ³+ ... + a _N-1t ^N-1+ a _nt ⁿEach tested gyrostatic experimental data of match draws each gyrostatic each rank coefficient a ₀, a ₁, a ₂..., a _N-1, a _n

(3) with each forward gyroscope and each reverse gyroscope all one by one correspondence to form u * v gyroscope altogether right;

(4) with the gyrostatic fitting coefficient correspondences at different levels of the forward of gyroscope centering divided by reverse gyrostatic fitting coefficients at different levels, draw n fitting coefficient ratio data, obtain the variance of this n fitting coefficient ratio data then, all u * v gyroscope to all carrying out aforesaid operations, is obtained u * v variance yields altogether;

(5) in u * v variance, the gyroscope that variance yields is more little is right, and its similarity is approaching more.

3, the gyrostatic difference measurement method of a kind of MEMS according to claim 1 is characterized in that: described environmental coefficient ratio K _BdComputing formula be:

$K_{\mathrm{bd}}=\frac{\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}(U_{1j}-\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{K}_{1\mathrm{wi}}\&CenterDot;W_{1i}-K_1\&CenterDot;\mathrm{\&omega;})}{\frac{1}{m}\underset{j=1}{\overset{m}{\mathrm{\&Sigma;}}}(U_{2j}-\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{K}_{2\mathrm{wi}}\&CenterDot;W_{2i}+K_2\&CenterDot;\mathrm{\&omega;})}$

Wherein, K _BdExpression environment coefficient ratio value; I represents the sequence number of ascertainment error, i=1 ... n, n=2～7, j represents to participate in the data number that data smoothing is handled at every turn, j=1 ... m, m=8～30.U _1jThe output voltage of j sampled point of expression forward gyroscope, U _2jThe output voltage of j sampled point of expression negative sense gyroscope, K _1wjThe determinacy error term coefficient of j sampled point of expression forward gyroscope, K _2wjThe determinacy error term coefficient of j sampled point of expression negative sense gyroscope, W _1iThe test of expression forward gyroscope is i ascertainment error item constantly, W _2iThe test of expression negative sense gyroscope is i ascertainment error item constantly, K ₁The gyrostatic constant multiplier of expression forward, K ₂The gyrostatic constant multiplier of expression negative sense, ω represent to test input angular velocity constantly.

4, the gyrostatic difference measurement method of a kind of MEMS according to claim 1 is characterized in that: described input angular velocity real-time resolving formula is:

$\mathrm{\&omega;}=\frac{(U_1-\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{K}_{1\mathrm{wi}}\&CenterDot;W_{1i})-(K_{\mathrm{bd}}\&CenterDot;U_2-\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{K}_{\mathrm{bd}}\&CenterDot;K_{2\mathrm{wi}}\&CenterDot;W_{2i})}{(K_1+K_{\mathrm{bd}}\&CenterDot;K_2)}+N_c$

Wherein, N _cBe white Gaussian noise, $N_c=-\frac{N_1-K_{\mathrm{bd}}\&CenterDot;N_2}{K_1+K_{\mathrm{bd}}\&CenterDot;K_2},$ N ₁Measurement noise during the test of expression forward gyroscope, N ₂Measurement noise during the test of expression negative sense gyroscope, K _BdExpression environment coefficient ratio value, K ₁The gyrostatic constant multiplier of expression forward, K ₂The gyrostatic constant multiplier of expression negative sense, K _1wiThe determinacy error term coefficient of i sampled point of expression forward gyroscope, K _2wiThe determinacy error term coefficient of i sampled point of expression negative sense gyroscope, W _1iThe test of expression forward gyroscope is i ascertainment error item constantly, W _2iThe test of expression negative sense gyroscope is i ascertainment error item constantly, U ₁The gyrostatic output voltage of expression forward, U ₂The gyrostatic output voltage of expression negative sense.

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