CN102680004A - 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

Constant multiplier error calibration and the compensation method of a kind of flexible gyroscope position and attitude measuring system POS

Technical field

The present invention relates to a kind of flexible gyroscope position and attitude measuring system (Position and Orientation System; POS) constant multiplier error calibration and compensation method; Can be used for the constant multiplier error in the 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 the inertia/combinations of satellites measuring system of a kind of accurate measuring position, speed and attitude, and it and airborne remote sensing load closely are connected, and handling for load data provides high-precision motion compensation information.

Flexible gyroscope is suitable for making up the POS system of miniaturization owing to many-sided advantages such as volume, weight, precision, technology maturity and reliabilities, is applied to small-sized airborne remote sensing.Based on the POS of flexible gyroscope 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) form by receiver and the poster processing soft.Wherein flexible gyroscope IMU mainly is 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 confirm IMU each item error coefficient through rating test, and when data processing, compensate.

A large amount of experiments show; Each item error coefficient of flexible gyroscope IMU is not changeless; Especially the constant multiplier of angular velocity passage, significant change can take place in the outside mechanics environmental change along with air maneuver etc. causes thereupon; The constant multiplier error that generation can not ignore directly influences the attitude measurement accuracy of POS.POS compared to tangible difference of traditional integrated navigation system is, remote sensing load usually and the IMU rigidity be connected, be installed in jointly then on the inertially stabilized platform, platform is fixed in the cabin base plate.When the remote sensing operation; Aircraft gets into the mapping zone and does the rectilinear flight campaign; Inertially stabilized platform isolates out and keeps the attitude level of load with the more violent body vibration of low frequency during this, and those still interfere with the slight movement information of remote sensing load and POS is used for after the measuring table vibration isolation.Thereby, if realize the requirement of POS high-acruracy survey movable information, should pay close attention among the IMU gyro real-time high-precision of angular velocity information in the little angular speed scope is measured, therefore must demarcate and compensation IMU constant multiplier error.IMU scaling method commonly used is a multiposition mixed calibration method; This method is regarded as normal value with the constant multiplier of angular velocity passage and demarcates; The calibration coefficient that uses this method to obtain; System angle data noise after can causing compensating increases, and has reduced the POS attitude measurement accuracy, has influenced the POS measurement performance.

Application number 200510086791.5; Denomination of invention " a kind of Inertial Measurement Unit mixed calibration method of eliminating the gyroscope constant value drift influence " discloses the static multiposition and dynamic mixed calibration method that carries out imu error; But this method directly is regarded as a quafric curve with the Changing Pattern of constant multiplier; The concrete property according to flexible gyroscope does not carry out the corresponding linear Fitting Analysis again, and this can cause the inaccurate of constant multiplier change curve match and introduce extra error of fitting.

The institutes such as Wang Aihua of " navigation with control " periodical publication in 2009 paper " gyroscope linearity segmented compensation method research in the quick-connecting inertia measurement system " of writing; Paid close attention to gyro constant multiplier error segmented compensation method; Change according to constant multiplier entire I MU speed measurement scope is divided into a plurality of approximately linear sections, and each linearity range carries out once fitting and calculates constant multiplier.This method does not have to realize constant multiplier " hyperbolic curve " Changing Pattern of flexible gyroscope in little speed range carried out careful analysis, still has bigger quantization error, causes flexible gyroscope constant multiplier 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; According to the error Changing Pattern a kind of constant multiplier error calibration and compensation method are proposed; Realize the accurate demarcation and the compensation of angular velocity passage constant multiplier error, improve the attitude measurement accuracy of POS.

Technical solution of the present invention is: constant multiplier error calibration and the compensation method of a kind of flexible gyroscope position and attitude measuring system POS, its characteristics are to comprise the following steps:

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

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

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

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

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

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

(7) the Y axle with IMU refers to the sky, and turntable obtains corresponding rate test data with one group of positive and negative respectively rotating a circle of angular speed test shelves of confirming.

(8) the Z axle with IMU refers to the sky, and turntable obtains corresponding rate test data with one group of positive and negative respectively rotating a circle of angular speed test shelves of confirming.

(9) speed data of treatment step (6) to (8) calculates each angular speed corresponding positive constant multiplier and negative constant multiplier respectively.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 that is used for error compensation.

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

(12) the position measurement data that obtain of treatment step (3) to (4) are obtained 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) to resolve the result, obtain relevant with acceleration in step (10) equation.

(15) according to step (10) error model, the error model coefficient that utilizes step (11) to (14) to find the solution carries out accurate error compensation to raw data.

Principle of the present invention is: the constant value drift of flexible gyroscope IMU, constant multiplier equal error coefficient are not changeless, and especially angular velocity passage constant multiplier is influenced obviously by the external environment mechanics factor, change along with the angular velocity varies of input IMU.This causes angular velocity can not accomplish the error fine compensation, contains great constant multiplier error.The present invention proposes flexible gyroscope POS constant multiplier error calibration and the compensation method that a kind of position-based speed is demarcated, and angular velocity passage constant multiplier is divided into two types of error coefficients by input angular velocity is positive and negative.When error calibration, when each measurement axis of IMU was carried out the speed experiment of the positive and negative rotation of many groups, because flexible gyroscope self, angular velocity passage constant multiplier and input angular velocity were " hyperbolic curve " relation of rule in little angular speed scope.The present invention utilizes this discovery to set up constant multiplier and the accurate regression equation of input angular velocity.When error compensation; With the original value substitution regression equation of impulse form, obtain the corresponding accurate constant multiplier of input angular velocity to be compensated through iteration repeatedly, upgrade all the other error coefficients simultaneously on this basis; Thereby realize the high-accuracy compensation of imu error, improve POS angular velocity measurement precision.

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

(1) the present invention has improved the constant multiplier error calibrating method of flexible IMU, refinement to the demarcation of constant multiplier under the 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 constant multiplier error compensating method of IMU.Utilize raw data, iterating through the regression equation of setting up obtains accurate constant multiplier, and then, improved the error compensation precision of IMU on this basis.

Description of drawings

Fig. 1 is a flexible gyroscope POS composition frame chart;

Constant multiplier error calibration and compensation method process flow diagram that Fig. 2 proposes for the present invention;

Fig. 3 is the POS course angle relative error comparison diagram that utilizes after the method for the invention and conventional method are carried out error compensation respectively.

Embodiment

Fig. 1 is the POS composition based on flexible gyroscope, mainly is 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.PCS carries out error compensation with the raw data of Inertial Measurement Unit output, and then calculates position, speed and attitude information.During calibration experiment, the IMU of POS is fixed in the turntable framework through machine frame, and remainders such as PCS can be fixed in outside the turntable.

The present invention includes calibration experiment and data processing two parts based on turntable.The angular velocity that the IMU sensitivity arrives is positive and negative to be confirmed by the right-hand rule.

Calibration experiment equipment of the present invention can be three shaft position rate tables, also can be that single shaft position rate table cooperates the hexahedron machine frame.Calibration experiment preliminary work also comprises: under an indoor standard atmospheric pressure environment, and relative humidity 20% ~ 80%, 15 ℃ ~ 30 ℃ of temperature and ± 2 ℃ of maintenances are relatively stable; Turntable is installed in independently on the cement ground, with at least 1 meter dark gully that is separated by, ground on every side; Breadboard electromagnetic environment index should meet the requirement of dependence test standard.If select single axle table for use, then for each the 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; The hexahedron machine frame should be able to make IMU be fixed in the turntable installed surface, guarantees the accurate transfer between IMU benchmark and turntable installed surface benchmark simultaneously.

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

Step 1: beginning calibration experiment; The installation table top of leveling three-axle table or single axle table; The IMU bottom surface of POS is anchored on the frock transition frame; Machine frame is installed on the turntable table top, guarantees three measurement axis of IMU and three-axle table shaft parallel, or through the reference field foundation of machine frame and the mechanical transfer relation of single axle table.POS places isoperibol for a long time, makes the inside and outside realization of IMU temperature balance.The last electric preheating of POS begins to gather the IMU output data after reaching preheating time;

Step 2: at first carry out calibration experiment IMU position measurement, collects position data.Make the i axle (i=X, Y, Z) of IMU refer to the sky or refer to ground perpendicular to local level as the test axle through adjustment turntable framework or machine frame; As a location status, total X refers to that sky, X refer to that ground, Y refer to that sky, Y refer to that ground, Z refer to that sky, Z refer to 6 location statuss such as ground.This patent is established from each location status and is gathered 4 groups of position datas; Then at first began to gather the IMU output data 130 seconds from any reference position; Turntable revolves to turn 90 degrees along a direction and arrives next position then; IMU is image data once more, and the like, obtain 4 groups of position datas along a full circle Zhou Fangxiang.Owing to 6 test modes are set, carry out 4 groups of position experiments under each test mode, so have 24 groups of position datas.Position measurement layout such as following table.

Status number	Location status	Position 1	Position 2	Position 3	Position 4
						1	X refers to the 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 the 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 the sky	?N 17	?N 18	?N 19	?N 20
6	Z refers to ground	?N 21	?N 22	?N 23	?N 24

Step 3: adjustment IMU makes the X axle refer to the sky as the test axle perpendicular to local level; Arrange according to step 2 test, begin to gather the IMU output data from any reference position, half-twist arrives next position; Carry out placement data acquisition successively, altogether 4 groups of position data N ₁, N ₂, N ₃, N ₄Adjustment IMU makes the X axle refer to ground, carries out placement data acquisition successively, common 4 groups of position data N ₅, N ₆, N ₇, N ₈, accomplish position measurement to the X axle;

Step 4: with the Y axle of IMU as the test axle, the experimental implementation of repeating step 3, the Y axle refers to that the sky obtains 4 groups of data N ₉, N ₁₀, N ₁₁, N ₁₂The Y axle obtains 4 groups of data N with referring to ₁₃, N ₁₄, N ₁₅, N ₁₆, accomplish position measurement to the Y axle;

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

Step 6: carry out the calibration experiment rate test, the acquisition rate data.The X axle of IMU is referred to the sky; This patent is pressed order from small to large; Choose seven groups of angular speeds such as 0.1 °/s being not more than 20 °/s, 1 °/s, 3 °/s, 5 °/s, 10 °/s, 15 °/s, 20 °/s as the test shelves; Turntable is rotated in the forward a week according to the angular speed of choosing respectively along circumference; Gather IMU output; Obtain corresponding seven groups of data then with one group of identical angular speed along circumference respectively negative sense rotate a circle; Gather IMU output, obtain corresponding seven groups of data

and accomplish rate test the X axle;

Step 7: the Y axle of IMU is referred to the sky; The experimental implementation of repeating step 6 obtains seven groups of data

that IMU gathers when circumference is rotated in the forward and seven groups of data

of when the circumference negative sense rotates, gathering accomplished the rate test to the Y axle;

Step 8: the Z axle of IMU is referred to the sky; The experimental implementation of repeating step 6 obtains seven groups of data

that IMU gathers when circumference is rotated in the forward and seven groups of data

of when the circumference negative sense rotates, gathering accomplished the rate test to the Z axle;

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

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

Wherein,

representes (I=X to test axle I respectively; Y; The positive and negative constant multiplier component of i axle when Z) importing the 1st group of angular velocity,

represent that respectively IMU is around the raw data of I axle with the 1st group of angular speed forward, i axle output when negative sense rotates.

And then obtaining the i axle is corresponding under the 1st group of input rate positive constant multiplier

and 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 the i axle successively at 1 °/s; 3 °/s; 5 °/s; 10 °/s, 15 °/s, positive constant multiplier

under 20 °/other six groups of speed shelves such as s and negative constant multiplier

The situation of the corresponding ω of positive constant multiplier＞0, order $K={\left(\begin{array}{ccccccc}{K}_{\mathrm{\ω\; i}+}^1& K_{\mathrm{\ω\; i}+}^2& K_{\mathrm{\ω\; i}+}^3& K_{\mathrm{\ω\; i}+}^4& K_{\mathrm{\ω\; i}+}^5& K_{\mathrm{\ω\; i}+}^6& K_{\mathrm{\ω\; i}+}^7\end{array}\right)}^T,$ B=(β _I1+ β _I0+) ^T, $W={\left(\begin{array}{ccccccc}\frac{1}{0.1}& \frac{1}{1}& \frac{1}{3}& \frac{1}{5}& \frac{1}{10}& \frac{1}{15}& \frac{1}{20}\\ 1& 1& 1& 1& 1& 1& 1\end{array}\right)}^T,$ Then, get B=(W by K=WB ^TW) ^-1W ^TK obtains β _I0+, β _I1+

The situation of the corresponding ω of negative constant multiplier＜0, order $K^{\′}={\left(\begin{array}{ccccccc}{K}_{\mathrm{\ω\; i}-}^1& K_{\mathrm{\ω\; i}-}^2& K_{\mathrm{\ω\; i}-}^3& K_{\mathrm{\ω\; i}-}^4& K_{\mathrm{\ω\; i}-}^5& K_{\mathrm{\ω\; i}-}^6& K_{\mathrm{\ω\; i}-}^7\end{array}\right)}^T,$ B'=(β _I1-β _I0-) ^T, $W^{\′}={\left(\begin{array}{ccccccc}-\frac{1}{0.1}& -\frac{1}{1}& -\frac{1}{3}& -\frac{1}{5}& -\frac{1}{10}& -\frac{1}{15}& -\frac{1}{20}\\ 1& 1& 1& 1& 1& 1& 1\end{array}\right)}^T,$ Then, get B'=(W' by K'=W'B' ^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 an input angular velocity, β _I0+, β _I1+And β _I0-, β _I1-Be the regression equation coefficient of correspondence, K _I+And K _I-Be respectively the positive and negative constant multiplier value of ω＞0 and ω＜0 o'clock i axle match.

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) the positive and negative umber of pulse in the unit interval, exported of axle, unit is (pulse)/s, K _I+, K _I-Be the positive and negative constant multiplier of measurement axis i corresponding angles speed, unit be (pulse)/", D _{ω i+}, D _{ω i-}Be the positive and negative normal value deviation of measurement axis, unit is °/h D _IX+, D _IY+, D _IZ+, D _IX-, D _IY-, D _IZ-Be respectively relevant of three positive and negative and acceleration, unit is °/h/g ω _x, ω _y, ω _zBe the projection components of input angular velocity ω three of IMU, unit is °/h A _x, A _y, A _zBe input acceleration three projection components, unit is a gravity acceleration g, cos (i, X), cos (i, Y), (i Z) is the alignment error of measurement axis in system to cos.

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

Step a: according to the nominal technical indicator of POS with gyro; Set a constant multiplier representative value 0.5 (pulse)/", as the initial value of iteration with constant multiplier

.The pulse sum N that measures in the i axis angular rate passage 1 second is obtained an initial magnitude of angular velocity divided by

:

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

Step b: positive and negative according to

; Select the equation of linear regression of foundation in step 9 step 9, obtain new

Step c:

substitution equality (1) that step b is obtained;

that calculating makes new advances is more again with

substitution equality (2);

that calculating makes new advances so constantly carries out iteration; Till the preceding constant multiplier value of substitution equality (2) differs less than setting threshold with the constant multiplier that calculates; The per mille of choosing nominal constant multiplier value is 0.0005 as threshold value.Can think that the constant multiplier that obtains is very accurate this moment, and the error compensation after the constant multiplier that obtains is used for is designated as 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 the calculation procedure 10 error model equations.

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

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

Wherein,

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

Then the normal value deviation of i axle is:

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

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

Wherein,

is respectively in the rate test of step 6 to step 8 around X; Y; The i that the rotation of Z axle is gathered (i=X, Y, Z) the corresponding constant multiplier component of axle output data.

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

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

Step 15:, utilize input acceleration at three projection components A according to the error model in the step 10 _X, A _Y, A _ZOften be worth deviation, alignment error and relevant item with acceleration with the error model coefficient that step 11 to step 14 obtains, the pulse value that three angular velocity passages of IMU are exported compensates, and o'clock corresponding output pulse of note ω＞0 is N _X+, N _Y+, N _Z+, ω＜0 o'clock is N _X-, N _Y-, N _Z-,

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

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

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

Or

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

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

Then the angular velocity matrix representation is:

Ω＝M ^-1P

Wherein, Ω=(ω _X, ω _Y, ω _Z) ^TIt is the vector that three measurement axis angular velocity constitute.

Calculate Ω, promptly obtain accomplishing the accurate measured value of three axis angular rates of error compensation.

Embodiment

At first flexible gyroscope POS is carried out 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 the 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-
					The X axle	1.970e-003	4.857e-001	2.017e-003	4.856e-001
The Y axle	6.254e-004	4.914e-001	5.967e-004	4.913e-001
					The Z axle	1.177e-003	4.925e-001	1.158e-003	4.925e-001

Carry out the precision of rate compensation experimental verification calibration coefficient then.Make turntable with the rotation of the constant rate of speed of 8 °/s, utilize sighting target degree factor to export raw data for the method for the conventional method of constant and this patent compensates POS respectively, the residual error statistics after the compensation is as shown in table 2.

Residual error statistics after table 2 error compensation

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

Utilize vehicle-mounted experiment at last, constant multiplier error compensation effect is tested from system level.With the optical fibre gyro POS of 0.02 °/h of precision as attitude reference system; Itself and flexible gyroscope POS rigidity are connected on the same rebound, and the method for utilizing conventional constant multiplier error compensating method and the present invention to propose respectively compensates the experimental data of flexible gyroscope POS.Two the cover POS since the fixed installation deviation, measurement axis can not be parallel fully, thus with POS attitude relative error as the accuracy test index.POS is output as benchmark with optical fibre gyro, 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

The relative error standard deviation	Conventional method	The present invention proposes method
			Course angle	0.109694	0.087097

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

Claims (4)

1. constant multiplier error calibration and the compensation method of a flexible gyroscope position and attitude measuring system POS 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 of POS partly is anchored on machine frame; Machine frame is installed on the turntable table top, guarantees three measurement axis of X, Y, Z and the three-axle table shaft parallel of IMU, or through the reference field foundation of machine frame and the mechanical transfer relation of single axle table; And POS is in the isoperibol, begin to gather the IMU output data behind the last electric preheating;

Step 2: carry out calibration experiment IMU position measurement; Make the i axle (i=X, Y, Z) of IMU refer to the sky or refer to ground perpendicular to local level as the test axle respectively through adjustment 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 refers to ground totally 6 location statuss, establish from each location status and gather a group position data, wherein a>=4; At first begin to gather the IMU output data from any reference position; Turntable is spent back IMU image data once more along a direction rotation

then; And the like; The full circle Zhou Fangxiang in edge meets together and obtains a group position data, so calibration experiment can obtain 6a group position measurement data altogether;

Step 3: adjustment IMU makes its X axle refer to the sky, begins to gather the IMU output data according to step 2 from any reference position, and rotation θ degree arrives next position, carries out placement data acquisition once more, is total to such an extent that a organizes position data N ₁, N ₂..., N _a, the X axle is referred to ground, obtain a group data N _A+1, N _A+2..., N _2a, accomplish the test of X shaft position;

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

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

Step 6: carry out calibration experiment IMU rate test, the X axle of IMU is referred to the sky,, choose d the angular speed ω that is not more than 20 °/s according to order from small to large ¹, ω ²... ω ^dAs test shelves, d>=5 wherein, turntable is rotated in the forward a week along circumference respectively according to the angular speed of choosing, and gathers IMU output, obtains d group data

IMU rotates a circle along the circumference negative sense respectively with identical angular speed then, gathers IMU output, obtains corresponding d group data Accomplish the rate test of X axle;

Step 7: the Y axle of IMU is referred to the sky; Repeating step 6, d group data

the completion Y axle rate test that obtains the d group data that IMU gathers and when the circumference negative sense rotate, gather when circumference is rotated in the forward;

Step 8: the Z axle of IMU is referred to the sky; Repeating step 6, d group data

the completion Z axle rate test that obtains the d group data

that IMU gathers and when the circumference negative sense rotate, gather when circumference is rotated in the forward;

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

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

Wherein,

representes (I=X to test axle I respectively; Y; The positive and negative constant multiplier component of i axle when Z) importing the 1st group of angular velocity,

represent that respectively IMU is around the raw data of I axle with the 1st group of angular speed forward, i axle output when negative sense rotates;

And then obtaining the i axle is corresponding under the 1st group of input rate positive constant multiplier and 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 the i axle successively at ω ², ω ³... ω ^dWait the positive constant multiplier under all the other (d-1) group speed shelves

With negative constant multiplier

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

Wherein, ω is an input angular velocity, β _I0+, β _I1+And β _I0-, β _I1-Be the regression equation coefficient of correspondence, K _I+And K _I-Be respectively the positive and negative constant multiplier value of ω＞0 and ω＜0 o'clock i axle match;

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

Wherein, N _{ω 1+}, N _{ω i-}Be i (i=X, Y, Z) the positive and negative umber of pulse in the unit interval, exported of axle, unit is (pulse)/s, K _I+, K _I-Be the positive and negative constant multiplier of measurement axis i corresponding angles speed, unit be (pulse)/", D _{ω i+}, D _{ω i-}Be the positive and negative normal value deviation of measurement axis, unit is °/h D _IX+, D _IY+, D _IZ+, D _IX-, D _IY-, D _IZ-Be respectively relevant of three positive and negative and acceleration, unit is °/h/g ω _x, ω _y, ω _zBe the projection components of input angular velocity ω three of IMU, unit is °/h A _x, A _y, A _zBe input acceleration three projection components, unit is a gravity acceleration g, cos (i, X), cos (i, Y), (i Z) is the alignment error of measurement axis in system to cos;

Step 11: " hyperbolic curve " equation with IMU raw data substitution step 9 is set up goes out accurate constant multiplier K through 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-}, reach the position experimental data that step 3 to step 5 obtains, the normal value deviation in solution procedure 10 equations,

Handle each output data of IMU under each location status, ask for average:

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

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

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

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

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

Wherein,

is respectively in the rate test of step 6 to step 8 around X; Y, i (i=X, Y that the rotation of Z axle is gathered; Z) the corresponding constant multiplier component of axle output data

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

Wherein, Lat representes the geographic latitude that calibration experiment is local;

Step 15: according to the error model in the step 10, the error model coefficient that utilizes step 11 to step 14 to resolve carries out error compensation to the POS raw data, obtains high-precision POS angular velocity measurement information.

2. constant multiplier error calibration and the compensation method of a kind of flexible gyroscope position and attitude measuring system POS according to claim 1 is characterized in that: the concrete method for solving of the regression equation coefficient of said step 9 is:

(Z) axle calculates it respectively successively at rate test shelves ω for i=X, Y to i among the POS ¹, ω ²... ω ^dUnder positive constant multiplier With negative constant multiplier

Calculate the regression equation coefficient then:

The situation of the corresponding ω of positive constant multiplier＞0, order $K={\left(\begin{array}{cccc}{K}_{\mathrm{\ω\; i}+}^1& K_{\mathrm{\ω\; i}+}^2& \·\·\·& K_{\mathrm{\ω\; i}+}^d\end{array}\right)}^T,$ B=(β _I1+β _I0+) ^T, $W{=\left(\begin{array}{cccc}\frac{1}{{\mathrm{\ω}}^1}& \frac{1}{{\mathrm{\ω}}^2}& \·\·\·& \frac{1}{{\mathrm{\ω}}^d}\\ 1& 1& \·\·\·& 1\end{array}\right)}^T,$ Then, get B=(W by K=WB ^TW) ^-1W ^TK obtains β _I0+, β _I1+

The situation of the corresponding ω of negative constant multiplier＜0, order $K^{\′}={\left(\begin{array}{cccc}{K}_{\mathrm{\ω\; i}-}^1& K_{\mathrm{\ω\; i}-}^2& \·\·\·& K_{\mathrm{\ω\; i}-}^d\end{array}\right)}^T,$ B'=(β _I1-β _I0-) ^T, $W^{\′}{=\left(\begin{array}{cccc}-\frac{1}{{\mathrm{\ω}}^1}& -\frac{1}{{\mathrm{\ω}}^2}& \·\·\·& -\frac{1}{{\mathrm{\ω}}^d}\\ 1& 1& \·\·\·& 1\end{array}\right)}^T,$ Then, get B'=(W' by K'=W'B' ^TW') ^-1W' ^TK' obtains β _I0-, β _I1-

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

Step a: set the nominal constant multiplier of POS institute use gyro, as the initial value of iteration with constant multiplier

.The i-axis angular velocity per unit time measured by dividing the total number N of the channel impulse

to get an initial angular velocity value

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

Step b: positive and negative according to

; The equation of linear regression of selecting step 9 to set up is obtained new

Step c: step b is obtained

Substitution equality (1), calculating makes new advances

Again with its substitution equality (2), calculate new again

So constantly carry out iteration; Till the preceding constant multiplier value of substitution equality (2) differs less than setting threshold with the constant multiplier that calculates; The per mille of choosing nominal constant multiplier value is as threshold value; Can think that the constant multiplier that obtains is very accurate this moment, and the error compensation after the constant multiplier that obtains is used for is designated as K _{ω i+}Or K _{ω i-}

4. constant multiplier error calibration and the compensation method of a kind of flexible gyroscope position and attitude measuring system POS according to claim 1, it is characterized in that: the error compensating method in the said step 15 is:

Utilize input acceleration at three projection components A _X, A _Y, A _ZOften be worth deviation, alignment error and relevant item with acceleration with the error model coefficient that step 11 to step 14 obtains, the pulse value that three angular velocity passages of IMU are exported compensates, and o'clock corresponding output pulse of note ω＞0 is N _X+, N _Y+, N _Z+, ω＜0 o'clock is N _X-, N _Y-, N _Z-,

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

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

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

Or

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

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

The angular velocity matrix that then obtains after the compensation is:

Ω＝M ^-1P

Wherein, Ω=(ω _X, ω _Y, ω _Z) ^TBe the vector that three measurement axis angular velocity constitute, calculate Ω, promptly obtain accomplishing the accurate measured value of three axis angular rates of error compensation.

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