CN102680004B - Scale factor error calibration and compensation method of flexible gyroscope position and orientation system (POS) - Google Patents

Abstract

The invention relates to a scale factor error calibration and compensation method of a flexible gyroscope POS. According to the use environment characteristics of the POS, an inertial measurement unit (IMU) needs to precisely measure a small input angular velocity. The scale factor error calibration and compensation method is characterized in that a linear regression equation of the scale factor of an IMU angular velocity channel is constructed according to the positive and negative values of the input angular velocity in a small angular velocity range; and the scale factor and other error coefficient are updated synchronously according to the change of the input angular velocity during error compensation, thereby improving the error compensation accuracy. The method provided by the invention can accurately eliminate the scale factor error of the angular velocity channel to realize the accurate measurement of small angular velocity information by the IMU, thereby improving the orientation measurement accuracy of the POS.

Description

The scale factor error of a kind of flexible gyroscope position and attitude measuring system POS is demarcated and compensation method

Technical field

The present invention relates to a kind of flexible gyroscope position and attitude measuring system (Position and Orientation System, POS) scale factor error is demarcated and compensation method, can be used for the scale factor error in fine compensation flexible gyroscope POS angular velocity passage, belong to the direct geographical field of measuring technique of airborne remote sensing.

Background technology

POS is inertia/combinations of satellites measuring system of a kind of accurate measuring position, speed and attitude, and it and airborne remote sensing load are closely connected, for load data processing provides high-precision motion compensation information.

Flexible gyroscope, due to many-sided advantages such as volume, weight, precision, technology maturity and reliabilities, is suitable for building the POS system of miniaturization, is applied to small-sized airborne remote sensing.POS based on flexible gyroscope is mainly by flexible gyroscope Inertial Measurement Unit (Inertial Measurement Unit, IMU), POS computer system (POS Computer System, PCS), Global Positioning System (GPS) (Global Position System, GPS) receiver and the poster processing soft composition.Wherein flexible gyroscope IMU is mainly made up of flexure gyroscope assembly, quartz flexible accelerometer and interlock circuit.IMU is the core component of POS, and its precision has directly determined the measuring accuracy of system, therefore must determine the every error coefficient of IMU by rating test, and compensate in the time of data processing.

Great many of experiments shows, every error coefficient of flexible gyroscope IMU is not changeless, especially the constant multiplier of angular velocity passage, the outside mechanics environmental change causing along with air maneuver etc., can there is significant change thereupon, the scale factor error that generation be can not ignore, directly affects the attitude measurement accuracy of POS.POS compared to obvious difference of traditional integrated navigation system is, remote sensing load conventionally and IMU rigidity be connected, be then jointly arranged in inertially stabilized platform, platform is fixed on cabin base plate.In the time of remote sensing operation, aircraft enters mapping region and does rectilinear flight campaign, inertially stabilized platform isolates out the more violent body vibration of low frequency during this keep the attitude level of load, and POS is used for, those still interfere with the slight movement information of remote sensing load after measuring table vibration isolation.Thereby, if realize the requirement of POS high-acruracy survey movable information, should pay close attention to gyro in IMU the real-time high-precision of angular velocity information within the scope of little angular speed is measured, therefore must demarcate and compensation IMU scale factor error.Conventional IMU scaling method is multiposition mixed calibration method, the method is considered as normal value by the constant multiplier of angular velocity passage and demarcates, the calibration coefficient that uses the method to obtain, can cause the system angle data noise after compensation to increase, reduce POS attitude measurement accuracy, affected POS measurement performance.

Application number 200510086791.5, denomination of invention " a kind of Inertial Measurement Unit mixed calibration method of eliminating gyroscope constant value drift impact " discloses the static multiposition and the dynamic mixed calibration method that carry out imu error, but the method is directly considered as the Changing Pattern of constant multiplier a quafric curve, do not carry out corresponding linear fit analysis according to the concrete property of flexible gyroscope, this can cause the inaccurate of constant multiplier change curve matching and introduce extra error of fitting again.

The institutes such as the Wang Aihua of " navigation with control " periodical publication in 2009 paper " gyroscope linearity segmented compensation method research in quick-connecting inertia measurement system " of writing, pay close attention to gyro scale factor error segmented compensation method, change whole IMU speed measurement scope is divided into multiple approximately linear sections according to constant multiplier, and each linearity range carries out once fitting and calculates constant multiplier.The method does not realize the constant multiplier in little speed range " hyperbolic curve " Changing Pattern to flexible gyroscope and carries out careful analysis, still has larger quantization error, causes flexible gyroscope scale factor error compensation effect limited.

Summary of the invention

Technology of the present invention is dealt with problems and is: the deficiency that overcomes existing flexible gyroscope imu error demarcation and compensation method, proposing a kind of scale factor error according to error variation demarcates and compensation method, realize Accurate Calibration and the compensation of angular velocity passage scale factor error, improve the attitude measurement accuracy of POS.

Technical solution of the present invention is: the scale factor error of a kind of flexible gyroscope position and attitude measuring system POS is demarcated and compensation method, and its feature is to comprise the following steps:

(1) leveling turntable, is installed on reference field by IMU or fixes by machine frame and turntable, sets up benchmark transitive relation.Make POS in isoperibol, after the preheating that powered on, start data acquisition.

(2) carry out position measurement.Make successively the i axle (i=X, Y, Z) of IMU refer to sky, refer to ground perpendicular to local level as test axle by adjusting turntable.Under 6 test modes, determine the data acquisition plan of position measurement.

(3) X-axis is referred to respectively to sky, refers to ground as test axle, obtain corresponding position measurement data.

(4) Y-axis is referred to respectively to sky, refers to ground as test axle, obtain corresponding position measurement data.

(5) Z axis is referred to respectively to sky, refers to ground as test axle, obtain corresponding position measurement data.

(6) carry out rate test.The X-axis of IMU is referred to sky, and turntable, with one group of definite angular speed test shelves positive and negative rotating a circle respectively, obtains corresponding rate test data.

(7) Y-axis of IMU is referred to sky, turntable, with one group of definite angular speed test shelves positive and negative rotating a circle respectively, obtains corresponding rate test data.

(8) Z axis of IMU is referred to sky, turntable, with one group of definite angular speed test shelves positive and negative rotating a circle respectively, obtains corresponding rate test data.

(9) speed data for the treatment of step (6) to (8), calculates respectively positive constant multiplier and negative constant multiplier that each angular speed is corresponding.According to " hyperbolic curve " relation of constant multiplier and input angle speed, set up both equations of linear regression, and calculate regression coefficient.

(10) set up the SYSTEM ERROR MODEL equation for error compensation.

(11), by raw data substitution " hyperbolic curve " equation, corresponding accurate constant multiplier comes out one after another.

(12) the position measurement data that treatment step (3) to (4) obtains, obtain the constant error in step (10) equation.

(13) utilize the constant multiplier result of calculation of step (9) and (11), obtain the alignment error in step (10) equation.

(14) utilize step (9), (12) and (13) calculation result, obtain relevant with acceleration in step (10) equation.

(15) according to step (10) error model, the Error model coefficients that utilizes step (11) to solve to (14), carries out accurate error compensation to raw data.

Principle of the present invention is: constant value drift, the constant multiplier equal error coefficient of flexible gyroscope IMU are not changeless, and especially angular velocity passage constant multiplier is affected obviously by external environment mechanics factor, changes along with the angular velocity varies of input IMU.This causes angular velocity can not complete error fine compensation, contains great scale factor error.The present invention proposes the flexible gyroscope POS scale factor error that a kind of position-based speed demarcates and demarcates and compensation method, by angular velocity passage constant multiplier by the positive and negative two class error coefficients that are divided into of input angular velocity.In the time of error calibration, when the each measurement axle of IMU is carried out to the speed experiment of the positive and negative rotation of many groups, due to flexible gyroscope self, be " hyperbolic curve " relation of rule at little angular speed scope interior angle speed channels constant multiplier and input angular velocity.The present invention utilizes this discovery to set up constant multiplier and the accurate regression equation of input angular velocity.In the time of error compensation, by the original value substitution regression equation of impulse form, obtain by iteration repeatedly the accurate constant multiplier that input angular velocity to be compensated is corresponding, upgrade on this basis all the other error coefficients simultaneously, thereby realize the high-accuracy compensation of imu error, improve POS angular velocity measurement precision.

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

(1) the present invention has improved the scale factor error scaling method of flexible IMU, refinement the demarcation to constant multiplier under little input angular velocity, set up the equation of linear regression of constant multiplier and input angular velocity according to flexible gyroscope " hyperbolic curve " rule of finding.

(2) the present invention has improved the scale factor error compensation method of IMU.Utilize raw data, iterate and obtain accurate constant multiplier by the regression equation of setting up, and then, the error compensation precision of IMU improved on this basis.

Brief description of the drawings

Fig. 1 is flexible gyroscope POS composition frame chart;

Fig. 2 is that the scale factor error that the present invention proposes is demarcated and compensation method process flow diagram;

Fig. 3 utilizes the method for the invention and conventional method to carry out respectively the POS course angle relative error comparison diagram after error compensation.

Embodiment

Fig. 1 is the POS composition based on flexible gyroscope, is mainly made up of flexible gyroscope IMU, PCS, GPS receiver and the poster processing soft.IMU is made up of flexible gyroscope, quartz flexible accelerometer, is used for measured angular speed and acceleration, is the core component of POS, and its precision has directly determined the precision that POS measures.The raw data of Inertial Measurement Unit output is carried out error compensation by PCS, and then calculate position, speed and attitude information.When calibration experiment, the IMU of POS is fixed in turntable framework by machine frame, and the remainders such as PCS can be fixed on outside turntable.

The present invention includes calibration experiment and data processing two parts based on turntable.IMU sensitivity to angular velocity positive and negatively determined by the right-hand rule.

Calibration experiment equipment of the present invention can be three shaft position rate tables, can be also that single shaft position rate table coordinates hexahedron machine frame.Calibration experiment preliminary work also comprises: under an indoor standard atmospheric pressure environment, and relative humidity 20% ~ 80%, 15 DEG C ~ 30 DEG C of temperature and ± 2 DEG C of maintenances are relatively stable; Turntable is arranged on independently on cement ground, with at least 1 meter of dark gully that is separated by, ground around; The electromagnetic environment index in laboratory should meet the requirement of dependence test specification.If select single axle table, for each benchmark transfer surface of hexahedron machine frame and the mounting plane of turntable, its processing verticality, flatness and roughness etc. all should meet the requirement of relevant processing test specification; Hexahedron machine frame should be able to make IMU be fixed on turntable installed surface, ensures the accurate transfer between IMU benchmark and turntable installed surface benchmark simultaneously.

As shown in Figure 2, concrete grammar of the present invention is as follows:

Step 1: start calibration experiment, the installation table top of leveling three-axle table or single axle table, the IMU bottom surface of POS is anchored on to frock transition frame, machine frame is installed on turntable table top, ensure that tri-of IMU measure axle and three-axle table shaft parallel, or by the reference field foundation of machine frame and the mechanical transfer relation of single axle table.POS is placed in isoperibol for a long time, makes to realize equalized temperature inside and outside IMU.The upper electric preheating of POS, reaches and starts to gather IMU output data after preheating time;

Step 2: first carry out calibration experiment IMU position measurement, collection position data.Make the i axle (i=X, Y, Z) of IMU refer to sky or refer to ground perpendicular to local level as test axle by adjusting turntable framework or machine frame, as a location status, total X refers to day, X refers to that ground, Y refer to day, Y refers to that ground, Z refer to day, Z refer to etc. 6 location statuss.This patent is established from each location status and is gathered 4 groups of position datas, first start to gather IMU output data 130 seconds from any reference position, then turntable arrives next position along a direction rotation 90 degree, IMU is image data again, the like, obtain 4 groups of position datas along a whole circumferencial direction.Due to 6 test modes being set, under each test mode, carry out 4 groups of position experiments, so have 24 groups of position datas.Position measurement layout is as following table.

Status number	Location status	Position 1	Position 2	Position 3	Position 4
						1	X refers to sky	N 1	N 2	N 3	N 4
2	X refers to ground	N 5	N 6	N 7	N 8
						3	Y refers to sky	N 9	N 10	N 11	N 12
4	Y refers to ground	N 13	N 14	N 15	N 16
						5	Z refers to sky	N 17	N 18	N 19	N 20
6	Z refers to ground	N 21	N 22	N 23	N 24

Step 3: adjust IMU and make X-axis refer to sky as test axle perpendicular to local level, arrange according to step 2 test, start to gather IMU output data from any reference position, half-twist arrives next position, carry out successively placement data acquisition, be total to obtain 4 groups of position data N ₁, N ₂, N ₃, N ₄; Adjust IMU and make X-axis refer to ground, carry out successively placement data acquisition, be total to obtain 4 groups of position data N ₅, N ₆, N ₇, N ₈, complete the position measurement to X-axis;

Step 4: using the Y-axis of IMU as test axle, the experimental implementation of repeating step 3, Y-axis refers to that sky obtains 4 groups of data N ₉, N ₁₀, N ₁₁, N ₁₂y-axis refers to obtain 4 groups of data N ₁₃, N ₁₄, N ₁₅, N ₁₆, complete the position measurement to Y-axis;

Step 5: using the Z axis of IMU as test axle, the experimental implementation of repeating step 3, Z axis refers to that sky obtains 4 groups of data N ₁₇, N ₁₈, N ₁₉, N ₂₀, Z axis refers to obtain 4 groups of data N ₂₁, N ₂₂, N ₂₃, N ₂₄, complete the position measurement to Z axis;

Step 6: carry out calibration experiment rate test, acquisition rate data.The X-axis of IMU is referred to sky, this patent from small to large ord, choose the seven groups of angular speeds such as 0.1 °/s, 1 °/s, 3 °/s, 5 °/s, 10 °/s, 15 °/s, 20 °/s that are not more than 20 °/s as test shelves, turntable is rotated in the forward respectively one week according to the angular speed of choosing along circumference, gather IMU output, obtain seven groups of corresponding data then with one group of identical angular speed along circumference respectively negative sense rotate a circle, gather IMU output, obtain seven groups of corresponding data complete the rate test to X-axis;

Step 7: the Y-axis of IMU is referred to sky, and the experimental implementation of repeating step 6, obtains seven groups of data that IMU gathers in the time that circumference is rotated in the forward with seven groups of data that gather in the time that circumference negative sense rotates complete the rate test to Y-axis;

Step 8: the Z axis of IMU is referred to sky, and the experimental implementation of repeating step 6, obtains seven groups of data that IMU gathers in the time that circumference is rotated in the forward with seven groups of data that gather in the time that circumference negative sense rotates complete the rate test to Z axis;

Step 9: treatment step 6 is to the speed experimental data of step 8.The 1st group of angular velocity of POS input (0.1 °/s) time, the i(i=X of IMU, Y, Z) axis scale factor component be can be written as:

$\left\{\begin{array}{c}{K}_{X+}^1\left(i\right)=\frac{R_{X+}^1\left(i\right)}{360\×3600},K_{X-}^1\left(i\right)=\frac{R_{X-}^1\left(i\right)}{360\×3600}\\ K_{Y+}^1\left(i\right)=\frac{R_{Y+}^1\left(i\right)}{360\×3600},K_{Y-}^1\left(i\right)=\frac{R_{Y-}^1\left(i\right)}{360\×3600}\\ K_{Z+}^1\left(i\right)=\frac{R_{Z+}^1\left(i\right)}{360\×3600},K_{Z-}^1\left(i\right)=\frac{R_{Z-}^1\left(i\right)}{360\×3600}\end{array}\right.$

Wherein, represent respectively test axle I(I=X, Y, Z) the positive and negative constant multiplier component of i axle when the 1st group of angular velocity of input, represent respectively the raw data of IMU i axle output in the time that I axle rotates with the 1st group of angular speed forward, negative sense.

And then, obtain positive constant multiplier corresponding to i axle under the 1st group of input rate with negative constant multiplier can be written as:

$\left\{\begin{array}{c}{k}_{\mathrm{\ωi}+}^1=\sqrt{{\left(K_{X+}^1\left(i\right)\right)}^2+{\left(K_{Y+}^1\left(i\right)\right)}^2+{\left(K_{Z+}^1\left(i\right)\right)}^2}\\ K_{\mathrm{\ωi}-}^1=\sqrt{{\left(K_{X-}^1\left(i\right)\right)}^2+{\left(K_{Y-}^1\left(i\right)\right)}^2+{\left(K_{Z-}^1\left(i\right)\right)}^2}\end{array}\right.$

Same, calculate successively i axle at 1 °/s, 3 °/s, 5 °/s, 10 °/s, 15 °/s, the positive constant multiplier under 20 °/other six groups of speed shelves such as s with negative constant multiplier

The situation of the corresponding ω > 0 of positive constant multiplier, order $K={\left(\begin{array}{ccccccc}{K}_{\mathrm{\ωi}+}^1& K_{\mathrm{\ωi}+}^2& K_{\mathrm{\ωi}+}^3& K_{\mathrm{\ωi}+}^4& K_{\mathrm{\ωi}+}^5& K_{\mathrm{\ωi}+}^6& K_{\mathrm{\ωi}+}^7\end{array}\right)}^T,$ B＝(β _i1+ β _i0+) ^T ， $W={\left(\begin{array}{ccccccc}\frac{1}{0.1}& \frac{1}{1}& \frac{1}{3}& \frac{1}{5}& \frac{1}{10}& \frac{1}{15}& \frac{1}{20}\\ 1& 1& 1& 1& 1& 1& 1\end{array}\right)}^T,$ , by K=WB, obtain B=(W ^tw) ^-1w ^tk, obtains β _i0+, β _i1+.

The situation of the corresponding ω < 0 of negative constant multiplier, order $K^{\&prime;}={\left(\begin{array}{ccccccc}{K}_{\mathrm{\&omega;i}-}^1& K_{\mathrm{\&omega;i}-}^2& K_{\mathrm{\&omega;i}-}^3& K_{\mathrm{\&omega;i}-}^4& K_{\mathrm{\&omega;i}-}^5& K_{\mathrm{\&omega;i}-}^6& K_{\mathrm{\&omega;i}-}^7\end{array}\right)}^T,$ B'＝(β _i1- β _i0-) ^T ， $W^{\&prime;}={\left(\begin{array}{ccccccc}-\frac{1}{0.1}& -\frac{1}{1}& -\frac{1}{3}& -\frac{1}{5}& -\frac{1}{10}& -\frac{1}{15}& -\frac{1}{20}\\ 1& 1& 1& 1& 1& 1& 1\end{array}\right)}^T,$ , by K'=W'B', obtain B'=(W' ^tw') ^-1w' ^tk', obtains β _i0-, β _i1-.

So, can set up " hyperbolic curve " equation of i axis scale factor and input angular velocity:

Wherein, ω is input angular velocity, β _i0+, β _i1+and β _i0-, β _i1-for corresponding regression equation coefficient, K _i+and K _i-the positive and negative constant multiplier value of i axle matching while being respectively ω > 0 and ω < 0.

Step 10: the POS angular velocity channel error model of setting up error compensation is:

Wherein, N _{ω i+}, N _{ω i-}be i(i=X, Y, Z) positive and negative umber of pulse that axle is exported within the unit interval, unit is (pulse)/s, K _i+, K _i-the positive and negative constant multiplier of measuring axle i corresponding angles speed, unit be (pulse)/", D _{ω i+}, D _{ω i-}be to measure the positive and negative normal value deviation of axle, unit is °/h, D _iX+, D _iY+, D _iZ+, D _iX-, D _iY-, D _iZ-be respectively relevant of the positive and negative and acceleration of three axles, unit is °/h/g, ω _x, ω _y, ω _zbe the projection components of input angular velocity ω at IMU tri-axles, unit is °/h, A _x, A _y, A _zbe the projection components of input acceleration at three axles, unit is gravity acceleration g, and cos (i, X), cos (i, Y), cos (i, Z) measure the alignment error of axle in system.

Step 11: IMU is exported to " hyperbolic curve " equation that raw data substitution step 9 is set up, go out accurate constant multiplier by iterative computation.Concrete steps are:

Step a: the nominal technical indicator according to POS with gyro, set constant multiplier representative value 0.5(pulse)/", as iteration constant multiplier initial value.By the pulse sum N measuring in i axis angular rate passage 1 second divided by obtain an initial magnitude of angular velocity:

$\widetilde{\mathrm{\&omega;}}=\frac{N}{\tilde{K}}---\left(1\right)$

Step b: according to positive and negative, select the equation of linear regression set up in step 9 step 9, obtain new

Step c: step b is obtained substitution equation (1), calculating makes new advances again will again substitution equation (2), calculating makes new advances so constantly carry out iteration, until the front constant multiplier value of substitution equation (2) differs and is less than setting threshold with the constant multiplier calculating, choose the per mille of nominal constant multiplier value as threshold value, be 0.0005.Now can think that the constant multiplier obtaining is very accurate, the constant multiplier obtaining, for error compensation afterwards, is designated as to K _{ω i+}or K _{ω i-}.

Step 12: the accurate constant multiplier K that utilizes step 11 to obtain _{ω i+}or K _{ω i-}24 groups of position measurement data N that obtain with step 3 to step 5 ₁, N ₂... N ₂₄, the normal value deviation in calculation procedure 10 error model equations.

Ask for the average of the each axle output of IMU data under each location status,

$\left\{\begin{array}{c}{\hat{N}}_1\left(i\right)=\frac{(N_1\left(i\right)+\&CenterDot;\&CenterDot;\&CenterDot;+N_4\left(i\right))}{4},{\hat{N}}_2\left(i\right)=\frac{(N_5\left(i\right)+\&CenterDot;\&CenterDot;\&CenterDot;+N_8\left(i\right))}{4}\\ {\hat{N}}_3\left(i\right)=\frac{(N_9\left(i\right)+\&CenterDot;\&CenterDot;\&CenterDot;+N_{12}\left(i\right))}{4},{\hat{N}}_4\left(i\right)=\frac{(N_{13}\left(i\right)+\&CenterDot;\&CenterDot;\&CenterDot;+N_{16}\left(i\right))}{4}\\ {\hat{N}}_5\left(i\right)=\frac{(N_{17}\left(i\right)+\&CenterDot;\&CenterDot;\&CenterDot;+N_{20}\left(i\right))}{4},{\hat{N}}_6\left(i\right)=\frac{(N_{21}\left(i\right)+\&CenterDot;\&CenterDot;\&CenterDot;+N_{24}\left(i\right))}{4}\end{array}\right.$

Wherein, represent the i axle output umber of pulse mean value of IMU under 6 groups of location statuss, N _k(i) (k=1,2 ..., 24) represent the i axle output umber of pulse of IMU in every group of test data.

The normal value deviation of i axle is:

Step 13: utilize the calculation result of step 9 and step 11 constant multiplier, the alignment error in calculation procedure 10 error model equations:

$\left\{\begin{array}{c}\cos (i,X)=\frac{K_{X+}^1\left(i\right)}{K_{\mathrm{\&omega;i}+}^1}\\ \cos (i,Y)=\frac{K_{Y+}^1\left(i\right)}{K_{\mathrm{\&omega;i}+}^1}\\ \cos (i,Z)=\frac{K_{Z+}^1\left(i\right)}{K_{\mathrm{\&omega;i}+}^1}\end{array}\right.$

Wherein, be respectively step 6 in step 8 rate test around X, Y, the i(i=X of Z axis rotating acquisition, Y, Z) constant multiplier component corresponding to axle output data.

Step 14: the model coefficient calculation result that utilizes step 9, step 12 and step 13 to obtain, the item relevant to acceleration in calculation procedure 10 error model equations:

Wherein, Lat represents the on-site geographic latitude of calibration experiment.

Step 15: according to the error model in step 10, utilize the projection components A of input acceleration at three axles _x, A _y, A _zthe Error model coefficients obtaining with step 11 to step 14 is often worth deviation, alignment error and item relevant to acceleration, and the pulse value of tri-angular velocity passages outputs of IMU is compensated, and when note ω > 0, corresponding output pulse is N _x+, N _y+, N _z+, when ω < 0, be N _x-, N _y-, N _z-,

Make alignment error matrix be:

$M=\left(\begin{array}{ccc}\cos (X,X)& \cos (X,Y)& \cos (X,Z)\\ \cos (Y,X)& \cos (Y,Y)& \cos (Y,Z)\\ \cos (Z,X)& \cos (Z,Y)& \cos (Z,Z)\end{array}\right)$

Wherein, cos (i, j) is the alignment error of i axle and j between centers, i=X, Y, Z, j=X, Y, Z;

The error coefficient that order does not comprise constant multiplier is related to that battle array is:

$P=\left(\begin{array}{c}\frac{N_{X+}}{K_{\mathrm{\&omega;X}+}}-D_{\mathrm{\&omega;X}+}-D_{\mathrm{XX}+}{A}_X-D_{\mathrm{XY}+}{A}_Y-D_{\mathrm{XZ}+}{A}_Z\\ \frac{N_{Y+}}{K_{\mathrm{\&omega;Y}+}}-D_{\mathrm{\&omega;Y}+}-D_{\mathrm{YX}+}{A}_X-D_{\mathrm{YY}+}{A}_Y-D_{\mathrm{YZ}+}{A}_Z\\ \frac{N_{Z+}}{K_{\mathrm{\&omega;Z}+}}-D_{\mathrm{\&omega;Z}+}-D_{\mathrm{ZX}+}{A}_X-D_{\mathrm{ZY}+}{A}_Y-D_{\mathrm{ZZ}+}{A}_Z\end{array}\right),$ In the time of ω > 0

Or

$P=\left(\begin{array}{c}\frac{N_{X-}}{K_{\mathrm{\&omega;X}-}}-D_{\mathrm{\&omega;X}-}-D_{\mathrm{XX}-}{A}_X-D_{\mathrm{XY}-}{A}_Y-D_{\mathrm{XZ}-}{A}_Z\\ \frac{N_{Y-}}{K_{\mathrm{\&omega;Y}-}}-D_{\mathrm{\&omega;Y}-}-D_{\mathrm{YX}-}{A}_X-D_{\mathrm{YY}-}{A}_Y-D_{\mathrm{YZ}-}{A}_Z\\ \frac{N_{Z-}}{K_{\mathrm{\&omega;Z}-}}-D_{\mathrm{\&omega;Z}-}-D_{\mathrm{ZX}-}{A}_X-D_{\mathrm{ZY}-}{A}_Y-D_{\mathrm{ZZ}-}{A}_Z\end{array}\right),$ In the time of ω < 0

Wherein, D _{ω i+}, D _{ω i-}for normal value deviation, D _ij+, D _ij-for relevant with acceleration.

Angular velocity matrix representation is:

Ω＝M ^-1P

Wherein, Ω=(ω _x, ω _y, ω _z) ^tbe three and measure the vector that axis angular rate forms.

Calculate Ω, obtained the accurate measured value of three axis angular rates of error compensation.

Embodiment

First flexible gyroscope POS is carried out to position speed calibration experiment, select 24 static position tests and 1 °/s, 3 °/s, 5 °/s, 10 °/s, 20 °/five groups of rate tests such as s.Carry out linear regression fit by " hyperbolic curve " equation form, the coefficient that obtains constant multiplier regression equation is as shown in table 1.

Table 1 constant multiplier regression equation coefficient

Coefficient	β 0+	β 1+	Β 0-	β 1-
					X-axis	1.970e-003	4.857e-001	2.017e-003	4.856e-001
Y-axis	6.254e-004	4.914e-001	5.967e-004	4.913e-001
					Z axis	1.177e-003	4.925e-001	1.158e-003	4.925e-001

Then carry out the precision of rate compensation experimental verification calibration coefficient.Make the constant rate of speed rotation of turntable with 8 °/s, utilize the method for the conventional method that is constant depending on constant multiplier and this patent to compensate respectively POS output raw data, the residual error statistics after compensation is as shown in table 2.

Residual error statistics after table 2 error compensation

Can find out, utilize after the compensation of this patent method, the residual error of POS measurement data has obvious minimizing.

Finally utilize vehicle-mounted experiment, from system level, scale factor error compensation effect is tested.Using the optical fibre gyro POS of 0.02 °/h of precision as attitude reference system, itself and flexible gyroscope POS rigidity are connected on same rebound, utilize respectively the experimental data of the method compensation flexible gyroscope POS of conventional scale factor error compensation method and the present invention's proposition.Two cover POS are due to fixed installation deviation, and measuring axle can not be completely parallel, therefore using POS attitude relative error as accuracy test index.With optical fibre gyro, POS is output as benchmark, and contrast flexible gyroscope POS course angle relative error changes, and Fig. 3 is the error change curve under both methods.Table 3 has been listed course relative error statistics.

Table 3 course relative error statistics

Relative error standard deviation	Conventional method	Put forward the methods of the present invention
			Course angle	0.109694	0.087097

Can find out, utilize error compensating method of the present invention, POS course angle error to standard deviation can reduce 20%.

Claims (4)

1. the scale factor error of flexible gyroscope position and attitude measuring system POS is demarcated and a compensation method, it is characterized in that comprising the following steps:

Step 1: the installation table top of leveling three-axle table or single axle table, the IMU part of POS is anchored on to machine frame, machine frame is installed on turntable table top, tri-of X, Y, Z ensureing IMU measure axle and three-axle table shaft parallel, or by the reference field foundation of machine frame and the mechanical transfer relation of single axle table, and make POS in isoperibol, after upper electric preheating, start to gather IMU output data;

Step 2: carry out calibration experiment IMU position measurement, make the i axle (i=X, Y, Z) of IMU refer to sky or refer to ground perpendicular to local level as test axle respectively by adjusting turntable framework or machine frame, as a location status, have that X refers to day, X refers to that ground, Y refer to day, Y refers to that ground, Z refer to day, Z refer to totally 6 location statuss, if gather a group position data, wherein a>=4 from each location status; First start to gather IMU output data from any reference position, then turntable is along a direction rotation iMU image data again after degree, the like, meet together and obtain a group position data along a whole circumferencial direction, therefore calibration experiment can obtain altogether 6a group position measurement data;

Step 3: adjust IMU and make its X-axis refer to sky, start to gather IMU output data according to step 2 from any reference position, rotation θ degree, arrives next position, again carries out placement data acquisition, is total to obtain a group position data N ₁, N ₂..., N _a, X-axis is referred to ground, obtain a group data N _a+1, N _a+2..., N _2a, complete X-axis position measurement;

Step 4: using the Y-axis of IMU as test axle, the experimental implementation of repeating step 3, refers to sky by Y-axis, obtains a group data N _2a+1, N _2a+2..., N _3a, Y-axis is referred to ground, obtain a group data N _3a+1, N _3a+2..., N _4a, complete Y-axis position measurement;

Step 5: using the Z axis of IMU as test axle, the experimental implementation of repeating step 3, refers to sky by Z axis, obtains a group data N _4a+1, N _4a+2..., N _5a, Z axis is referred to ground, obtain a group data N _5a+1, N _5a+2..., N _6a, complete Z axis position measurement;

Step 6: carry out calibration experiment IMU rate test, the X-axis of IMU is referred to sky, according to from small to large sequentially, choose d the angular speed ω that is not more than 20 °/s ¹, ω ²... ω ^das test shelves, wherein d>=5, turntable is rotated in the forward one week along circumference respectively according to the angular speed of choosing, and gathers IMU output, obtains d group data then IMU rotates a circle along circumference negative sense respectively with identical angular speed, gathers IMU output, obtains corresponding d group data complete X-axis rate test;

Step 7: the Y-axis of IMU is referred to sky, and repeating step 6, obtains the d group data that IMU gathers in the time that circumference is rotated in the forward with the d group data that gather in the time that circumference negative sense rotates complete Y-axis rate test;

Step 8: the Z axis of IMU is referred to sky, and repeating step 6, obtains the d group data that IMU gathers in the time that circumference is rotated in the forward with the d group data that gather in the time that circumference negative sense rotates complete Z axis rate test;

Step 9: the speed data that utilizes step 6 to step 8 to gather resolves constant multiplier, to the 1st group of angular velocity omega of POS input ¹time, i (i=X, Y, Z) the axis scale factor component of IMU can be written as:

$\left\{\begin{array}{c}{K}_{X+}^1\left(i\right)=\frac{R_{X+}^1\left(i\right)}{360\&times;3600},K_{X-}^1\left(i\right)=\frac{R_{X-}^1\left(i\right)}{360\&times;3600}\\ K_{Y+}^1\left(i\right)=\frac{R_{Y+}^1\left(i\right)}{360\&times;3600},K_{Y-}^1\left(i\right)=\frac{R_{Y-}^1\left(i\right)}{360\&times;3600}\\ K_{Z+}^1\left(i\right)=\frac{R_{Z+}^1\left(i\right)}{360\&times;3600},K_{Z-}^1\left(i\right)=\frac{R_{Z-}^1\left(i\right)}{360\&times;3600}\end{array}\right.$

Wherein, the positive and negative constant multiplier component of i axle while representing respectively the 1st group of angular velocity of test axle I (I=X, Y, Z) input, represent respectively the raw data of IMU i axle output in the time that I axle rotates with the 1st group of angular speed forward, negative sense;

And then, obtain positive constant multiplier corresponding to i axle under the 1st group of input rate with negative constant multiplier can be written as:

$\left\{\begin{array}{c}{K}_{\mathrm{\&omega;i}+}^1=\sqrt{{\left(K_{X+}^1\left(i\right)\right)}^2+{\left(K_{Y+}^1\left(i\right)\right)}^2+{\left(K_{Z+}^1\left(i\right)\right)}^2}\\ K_{\mathrm{\&omega;i}-}^1=\sqrt{{\left(K_{X-}^1\left(i\right)\right)}^2+{\left(K_{Y-}^1\left(i\right)\right)}^2+{\left(K_{Z-}^1\left(i\right)\right)}^2}\end{array}\right.$

Same, calculate successively i axle at ω ², ω ³... ω ^ddeng the positive constant multiplier under all the other (d-1) group speed shelves $K_{\mathrm{\&omega;i}+}^2,\&CenterDot;\&CenterDot;\&CenterDot;,K_{\mathrm{\&omega;i}+}^d$ With negative constant multiplier $K_{\mathrm{\&omega;i}-}^2,\&CenterDot;\&CenterDot;\&CenterDot;,K_{\mathrm{\&omega;i}-}^d,$

So, can set up " hyperbolic curve " equation of i axis scale factor and input angular velocity:

Wherein, ω is input angular velocity, β _i0+, β _i1+and β _i0-, β _i1-for corresponding regression equation coefficient, K _i+and K _i-the positive and negative constant multiplier value of i axle matching while being respectively ω > 0 and ω < 0;

Step 10: the POS angular velocity channel error model of setting up error compensation is:

wherein, N _{ω i+}, N _{ω i-}be the positive and negative umber of pulse that i (i=X, Y, Z) axle is exported within the unit interval, unit is (pulse)/s, K _i+, K _i-the positive and negative constant multiplier of measuring axle i corresponding angles speed, unit be (pulse)/", D _{ω i+}, D _{ω i-}be to measure the positive and negative normal value deviation of axle, unit is °/h, D _iX+, D _iY+, D _iZ+, D _iX-, D _iY-, D _iZ-be respectively relevant of the positive and negative and acceleration of three axles, unit is °/h/g, ω _x, ω _y, ω _zbe the projection components of input angular velocity ω at IMU tri-axles, unit is °/h, A _x, A _y, A _zbe the projection components of input acceleration at three axles, unit is gravity acceleration g, and cos (i, X), cos (i, Y), cos (i, Z) measure the alignment error of axle in system;

Step 11: " hyperbolic curve " equation that IMU raw data substitution step 9 is set up, goes out accurate constant multiplier K by iterative computation _{ω i+}or K _{ω i-};

Step 12: the accurate constant multiplier K that utilizes step 11 to obtain _{ω i+}or K _{ω i-}, and the position experimental data that obtains of step 3 to step 5, the normal value deviation in solution procedure 10 equations,

Process the each axle output of IMU data under each location status, ask for average:

$\left\{\begin{array}{c}{\hat{N}}_1\left(i\right)=\frac{(N_1\left(i\right)+\&CenterDot;\&CenterDot;\&CenterDot;+N_a\left(i\right))}{a},{\hat{N}}_2\left(i\right)=\frac{(N_{a+1}\left(i\right)+\&CenterDot;\&CenterDot;\&CenterDot;+N_{2a}\left(i\right))}{a}\\ {\hat{N}}_3\left(i\right)=\frac{(N_{2a+1}\left(i\right)+\&CenterDot;\&CenterDot;\&CenterDot;+N_{3a}\left(i\right))}{a},{\hat{N}}_4\left(i\right)=\frac{(N_{3a+1}\left(i\right)+\&CenterDot;\&CenterDot;\&CenterDot;+N_{4a}\left(i\right))}{a}\\ {\hat{N}}_5\left(i\right)=\frac{(N_{4a+1}\left(i\right)+\&CenterDot;\&CenterDot;\&CenterDot;+N_{5a}\left(i\right))}{a},{\hat{N}}_6\left(i\right)=\frac{(N_{5a+1}\left(i\right)+\&CenterDot;\&CenterDot;\&CenterDot;+N_{6a}\left(i\right))}{a}\end{array}\right.$

Wherein, represent respectively the i axle output pulse average of IMU under 6 location statuss, N _k(i) (k=1,2 ..., 6a) and represent respectively the i axle output umber of pulse of IMU in every group of position measurement data,

Utilize step 11 gained constant multiplier to calculate normal value deviation:

Step 13: utilize the calculation result of step 9 and step 11 constant multiplier, the alignment error in solution procedure 10 equations:

$\left\{\begin{array}{c}\cos (i,X)=\frac{K_{X+}^1\left(i\right)}{K_{\mathrm{\&omega;i}+}^1}\\ \cos (i,Y)=\frac{K_{Y+}^1\left(i\right)}{K_{\mathrm{\&omega;i}+}^1}\\ \cos (i,Z)=\frac{K_{Z+}^1\left(i\right)}{K_{\mathrm{\&omega;i}+}^1}\end{array}\right.$

Wherein, be respectively step 6 in step 8 rate test around X, Y, the constant multiplier component corresponding to i (i=X, Y, Z) axle output data of Z axis rotating acquisition,

Step 14: utilize the calculation result of step 9, step 12 and step 13, the item relevant to acceleration in solution procedure 10 equations:

$\left\{\begin{array}{c}{D}_{\mathrm{iX}+}=\frac{[{\hat{N}}_1\left(i\right)-{\hat{N}}_2\left(i\right)]}{2K_{\mathrm{\&omega;i}+}}-{\mathrm{\&omega;}}_{\mathrm{ie}}\sin \left(\mathrm{Lat}\right)\cos (i,X)\\ D_{\mathrm{iY}+}=\frac{[{\hat{N}}_3\left(i\right)-{\hat{N}}_4\left(i\right)]}{2K_{\mathrm{\&omega;i}+}}-{\mathrm{\&omega;}}_{\mathrm{ie}}\sin \left(\mathrm{Lat}\right)\cos (i,Y)\\ D_{\mathrm{iZ}+}=\frac{[{\hat{N}}_5\left(i\right)-{\hat{N}}_6\left(i\right)]}{2K_{\mathrm{\&omega;i}+}}-{\mathrm{\&omega;}}_{\mathrm{ie}}\sin \left(\mathrm{Lat}\right)\cos (i,Z)\end{array}\right.,$ In the time of ω > 0

$\left\{\begin{array}{c}{D}_{\mathrm{iX}-}=\frac{[{\hat{N}}_1\left(i\right)-{\hat{N}}_2\left(i\right)]}{2K_{\mathrm{\&omega;i}-}}-{\mathrm{\&omega;}}_{\mathrm{ie}}\sin \left(\mathrm{Lat}\right)\cos (i,X)\\ D_{\mathrm{iY}-}=\frac{[{\hat{N}}_3\left(i\right)-{\hat{N}}_4\left(i\right)]}{2K_{\mathrm{\&omega;i}-}}-{\mathrm{\&omega;}}_{\mathrm{ie}}\sin \left(\mathrm{Lat}\right)\cos (i,Y)\\ D_{\mathrm{iZ}-}=\frac{[{\hat{N}}_5\left(i\right)-{\hat{N}}_6\left(i\right)]}{2K_{\mathrm{\&omega;i}-}}-{\mathrm{\&omega;}}_{\mathrm{ie}}\sin \left(\mathrm{Lat}\right)\cos (i,Z)\end{array}\right.,$ In the time of ω < 0

Wherein, Lat represents the geographic latitude of calibration experiment locality;

Step 15: according to the error model in step 10, utilize the projection components A of input acceleration at three axles _x, A _y, A _zthe Error model coefficients obtaining with step 11 to step 14 is often worth deviation, alignment error and item relevant to acceleration, and the pulse value of tri-angular velocity passages outputs of IMU is compensated, and obtains high-precision POS angular velocity measurement information.

2. the scale factor error of a kind of flexible gyroscope position and attitude measuring system POS according to claim 1 is demarcated and compensation method, it is characterized in that: the concrete method for solving of the regression equation coefficient of described step 9 is:

To i in POS (i=X, Y, Z) axle, calculate respectively successively it at rate test shelves ω ¹, ω ²... ω ^dunder positive constant multiplier with negative constant multiplier then calculate regression equation coefficient:

The situation of the corresponding ω > 0 of positive constant multiplier, order $K={\left(\begin{array}{cccc}{K}_{\mathrm{\&omega;i}+}^1& K_{\mathrm{\&omega;i}+}^2& \&CenterDot;\&CenterDot;\&CenterDot;& K_{\mathrm{\&omega;i}+}^d\end{array}\right)}^T,$ Β＝(β _i1+ β _i0+) ^T， $W={\left(\begin{array}{cccc}\frac{1}{{\mathrm{\&omega;}}^1}& \frac{1}{{\mathrm{\&omega;}}^2}& \&CenterDot;\&CenterDot;\&CenterDot;& \frac{1}{{\mathrm{\&omega;}}^d}\\ 1& 1& \&CenterDot;\&CenterDot;\&CenterDot;& 1\end{array}\right)}^T,$ , by K=W Β, obtain Β=(W ^tw) ^-1w ^tk, obtains β _i0+, β _i1+;

The situation of the corresponding ω < 0 of negative constant multiplier, order $K^{\&prime;}={\left(\begin{array}{cccc}{K}_{\mathrm{\&omega;i}-}^1& K_{\mathrm{\&omega;i}-}^2& \&CenterDot;\&CenterDot;\&CenterDot;& K_{\mathrm{\&omega;i}-}^d\end{array}\right)}^T,$ Β′＝(β _i1- β _i0-) ^T， $W^{\&prime;}={\left(\begin{array}{cccc}-\frac{1}{{\mathrm{\&omega;}}^1}& -\frac{1}{{\mathrm{\&omega;}}^2}& \&CenterDot;\&CenterDot;\&CenterDot;& -\frac{1}{{\mathrm{\&omega;}}^d}\\ 1& 1& \&CenterDot;\&CenterDot;\&CenterDot;& 1\end{array}\right)}^T,$ , by K '=W ' Β ', obtain Β '=(W ^{' T}w ') ^-1w ^{' T}k ', obtains β _i0-, β _i1-.

3. the scale factor error of a kind of flexible gyroscope position and attitude measuring system POS according to claim 1 is demarcated and compensation method, it is characterized in that: the computing method of the constant multiplier in described step 11 are:

Step a: set the nominal constant multiplier of gyro that POS uses, as iteration constant multiplier initial value.By the angular velocity channel pulse sum N measuring in the i axle unit interval divided by obtain an initial magnitude of angular velocity

$\widetilde{\mathrm{\&omega;}}=\frac{N}{\tilde{K}}---\left(1\right)$

Step b: according to positive and negative, select the equation of linear regression set up of step 9, obtain new

Step c: step b is obtained substitution equation (1), calculating makes new advances again by its substitution equation (2), calculate new again so constantly carry out iteration, until the front constant multiplier value of substitution equation (2) differs and is less than setting threshold with the constant multiplier calculating, choose the per mille of nominal constant multiplier value as threshold value, now can think that the constant multiplier obtaining is very accurate, the constant multiplier obtaining, for error compensation afterwards, is designated as to K _{ω i+}or K _{ω i-}.

4. the scale factor error of a kind of flexible gyroscope position and attitude measuring system POS according to claim 1 is demarcated and compensation method, it is characterized in that: the error compensating method in described step 15 is:

Utilize the projection components A of input acceleration at three axles _x, A _y, A _zthe Error model coefficients obtaining with step 11 to step 14 is often worth deviation, alignment error and item relevant to acceleration, and the pulse value of tri-angular velocity passages outputs of IMU is compensated, and when note ω > 0, corresponding output pulse is N _x+, N _y+, N _z+, when ω < 0, be N _x-, N _y-, N _z-,

Make alignment error matrix be:

$M=\left(\begin{array}{ccc}\cos (X,X)& \cos (X,Y)& \cos (X,Z)\\ \cos (Y,X)& \cos (Y,Y)& \cos (Y,Z)\\ \cos (Z,X)& \cos (Z,Y)& \cos (Z,Z)\end{array}\right)$

Wherein, cos (i, j) is the alignment error of i axle and j between centers, i=X, Y, Z, j=X, Y, Z;

The error coefficient that order does not comprise constant multiplier is related to that battle array is:

$P=\left(\begin{array}{c}\frac{N_{X+}}{K_{\mathrm{\&omega;X}+}}-D_{\mathrm{\&omega;X}+}-D_{\mathrm{XX}+}{A}_X-D_{\mathrm{XY}+}{A}_Y-D_{\mathrm{XZ}+}{A}_Z\\ \frac{N_{Y+}}{K_{\mathrm{\&omega;Y}+}}-D_{\mathrm{\&omega;Y}+}-D_{\mathrm{YX}+}{A}_X-D_{\mathrm{YY}+}{A}_Y-D_{\mathrm{YZ}+}{A}_Z\\ \frac{N_{Z+}}{K_{\mathrm{\&omega;Z}+}}-D_{\mathrm{\&omega;Z}+}-D_{\mathrm{ZX}+}{A}_X-D_{\mathrm{ZY}+}{A}_Y-D_{\mathrm{ZZ}+}{A}_Z\end{array}\right),$ In the time of ω > 0

Or

$P=\left(\begin{array}{c}\frac{N_{X-}}{K_{\mathrm{\&omega;X}-}}-D_{\mathrm{\&omega;X}-}-D_{\mathrm{XX}-}{A}_X-D_{\mathrm{XY}-}{A}_Y-D_{\mathrm{XZ}-}{A}_Z\\ \frac{N_{Y-}}{K_{\mathrm{\&omega;Y}-}}-D_{\mathrm{\&omega;Y}-}-D_{\mathrm{YX}-}{A}_X-D_{\mathrm{YY}-}{A}_Y-D_{\mathrm{YZ}-}{A}_Z\\ \frac{N_{Z-}}{K_{\mathrm{\&omega;Z}-}}-D_{\mathrm{\&omega;Z}-}-D_{\mathrm{ZX}-}{A}_X-D_{\mathrm{ZY}-}{A}_Y-D_{\mathrm{ZZ}-}{A}_Z\end{array}\right),$ In the time of ω < 0

Wherein, D _{ω i+}, D _{ω i-}for normal value deviation, D _ij+, D _ij-for relevant with acceleration,

The angular velocity matrix obtaining after compensation is:

Ω＝M ^-1P

Wherein, Ω=(ω _x, ω _y, ω _z) ^tbe three and measure the vector that axis angular rate forms, calculate Ω, obtained the accurate measured value of three axis angular rates of error compensation.