CN100585602C - Inertial measuring system error model demonstration test method - Google Patents

Abstract

This invention relates to a test method for error model verification of an inertial measurement system, which sets up a multifunction software platform to simulate and argue the airliner load test plan directly including: designing specific flying trails based on the error model of an inertial sensor, in which, an aircraft flies along the designed flying trail and collects inertial sensor data of specific flight path points and transmits them to a master navigation computer, then the collected data are compared with the data output by a measurement primary standard device to get the measurement error of the sensor to compute and get the error parameters in the inertial navigation error model with an airborne inertial navigation space multi-position online demarcating method to understand the inertial navigation performance and is convenient for the compensation in navigation computation.

Description

Inertial measuring system error model demonstration test method

Technical field

The present invention is a kind of flexible strapdown inertial navitation system (SINS) error model checking test method under the seating plane airborne circumstance, belongs to the civil aviation technical field.

Background technology

Inertial measuring unit is the important navigator on the seating plane, and this equipment can cause the error of Civil Aviation System navigator fix owing to many reasons of aspects such as principle, self design, manufacturing process, installation, algorithm.How the error model parameters that is installed in the inertial measuring unit on the passenger plane is analyzed, is verified that with the validity of the modeling of check inertial measuring system error, compensation, the navigation performance for improving seating plane is extremely important.

Generally speaking, before inertial navigation system was not installed in passenger plane, the examination of airborne performance test was what to be undertaken by ground experiment and Computer Simulation; And after inertial navigation system is installed on the passenger plane, just more limited to excitation and the analysis thereof of its error model under airborne current intelligence.Therefore be necessary very much to study to carry out the performance evaluation of inertial navigation system under airborne condition how targetedly, research is at the aircraft trace of the airborne performance evaluation of inertial navigation system and the method for designing of dynamic perfromance, make the error term of inertia measurement device obtain optimal excitation and estimation, thereby the error to inertial navigation system compensates, and improves the precision and the performance of civil aviaton's inertial navigation system.

Summary of the invention

Technical matters: the purpose of this invention is to provide a kind of inertial measuring system error model demonstration test method, this method can be verified inertial measuring system error under airborne situation.

Technical scheme: the method for designing that the invention provides multianalysis aircraft carrier track, Trajectory Design can be so that the different error terms of inertia measurement device obtain the method for optimal excitation, simultaneously by distributing the inertia measurement device installation site rationally, make the various measuring error of bringing because of installation obtain excitation, finish the integration test of the system-level navigation performance of inertia measurement error model under the complicated high dynamic condition under the aircraft carrier situation, for the verification experimental verification of inertial navigation system error model provides foundation.This method fundamentally improves the navigator fix ability, also will provide support for inertial measuring system error parameter identification and real-Time Compensation, thereby significantly improve the navigation accuracy of airline carriers of passengers, for civil aviaton's flight safety provides safeguard.In order to reach above-mentioned goal of the invention, the present invention includes the following step and structure:

The concrete steps of inertial measuring system error model demonstration test method of the present invention are: at first design specific flight path according to the error model of inertial sensor; Aircraft is transported to leading boat computing machine along the flight of designed flight path and the inertial sensor data of gathering specific track points; Again the data of collection and the data of measuring basis equipment output are compared, obtain the measuring error of inertial sensor; Calculate error parameter in the ins error model by the aerial multiposition online calibration method of airborne ins, to understand the inertial navigation performance and to make things convenient for compensation in the navigation calculation.

The error model of inertial sensor is as follows:

Gyro error:

$\mathrm{\&Delta;}{\mathrm{\&omega;}}_x={\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="C2007100193470012H2.png,C2007100193470013H1.png"\; state="\{\{state\}\}">k</figure-callout>}}_0+k_1{\mathrm{\&omega;}}_x+k_2{f}_x+k_3{f}_y+k_4{f}_z+k_5{f}_x{f}_z+k_6\stackrel{\&CenterDot;}{{\mathrm{\&omega;}}_y}+k_7{\mathrm{\&omega;}}_x{\mathrm{\&omega;}}_z+k_8{\mathrm{\&omega;}}_y{\mathrm{\&omega;}}_z$

${\mathrm{\&Delta;\&omega;}}_y={\mathrm{<figure-callout\; id="0"\; label="I"\; filenames="C2007100193470012H2.png,C2007100193470013H1.png"\; state="\{\{state\}\}">I</figure-callout>}}_0+I_1{\mathrm{\&omega;}}_y+l_2{f}_x+l_3{f}_y+l_4{f}_z+l_5{f}_y{f}_z+l_6{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_x+l_7{\mathrm{\&omega;}}_y{\mathrm{\&omega;}}_z+l_8{\mathrm{\&omega;}}_x{\mathrm{\&omega;}}_z$

${\mathrm{\&omega;}}_z{\mathrm{<figure-callout\; id="0"\; label="h"\; filenames="C2007100193470012H2.png,C2007100193470013H1.png"\; state="\{\{state\}\}">h</figure-callout>}}_0+h_1{\mathrm{\&omega;}}_z{h}_2{f}_x+f_3{f}_y+h_4{f}_z+h_5{f}_x{f}_z+h_6\stackrel{\&CenterDot;}{{\mathrm{\&omega;}}_z}+h_7{\mathrm{\&omega;}}_x{\mathrm{\&omega;}}_z+h_8{\mathrm{\&omega;}}_x{\mathrm{\&omega;}}_y$

Accelerometer error

Δf _x＝k′ ₀+k′ ₁f _x+k′ ₂f _y+k′ ₃f _z

Δf _y＝l′ ₀+l′ ₁f _x+l′ ₂f _y+l′ ₃f _z

Δf _z＝h′ ₀+h′ ₁f _x+h′ ₂f _y+h′ ₃f _z

In the leading boat computing machine, the data of collection and the data of measuring basis equipment are compared, the method that obtains the measuring error of inertial sensor is; Before correlation data, the output of measuring basis need be converted to body is angular velocity signal and acceleration signal, with it as ideal value; Control methods is exactly the gyroscope of tested inertial navigation system to be exported deduct ideal value, promptly obtains gyrostatic angular velocity output error.

The aerial multiposition online calibration method of airborne ins is as follows;

1., can obtain the sensor measurement error in conjunction with n group measurement data) for the X-axis gyro:

$\mathrm{\&Delta;m}=\left[\begin{array}{ccccccccc}1& {\mathrm{\&omega;}}_x^1& f_x^1& f_y^1& f_z^1& f_x^1{f}_z^1& \stackrel{\&CenterDot;}{{\mathrm{\&omega;}}_z^1}& {\mathrm{\&omega;}}_x^1{\mathrm{\&omega;}}_z^1& {\mathrm{\&omega;}}_y^1{\mathrm{\&omega;}}_z^1\\ & & & & & ...& & & \\ 1& {\mathrm{\&omega;}}_x^n& f_x^n& f_y^n& f_z^n& f_x^n{f}_z^n& \stackrel{\&CenterDot;}{{\mathrm{\&omega;}}_z^n}& {\mathrm{\&omega;}}_x^n{\mathrm{\&omega;}}_x^n& {\mathrm{\&omega;}}_y^n{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="0"\; label="n\; z\; k"\; filenames="C2007100193470012H2.png,C2007100193470013H1.png"\; state="\{\{state\}\}">n</figure-callout>}}^z& \\ \end{array},\right]\left[\begin{array}{c}{k}_{}\end{array}\right]\left[\begin{array}{c}{}_0\\ .\\ .\\ .\\ k_8\end{array}\right]=\mathrm{MX}$

In the formula:

Be the error amount vector of each time measurement, subscript is represented the n time measurement, asks difference to obtain by airborne IMU output and reference data; M is an observing matrix, and the subscript of its element is represented the n time measurement, because the ideal value of angular speed and acceleration can not obtain, the output of therefore same employing reference data is calculated; X is a state vector to be calibrated, and its component is every error coefficient of inertial sensor;

2.) try to achieve inertial sensor error parameter: X=(M ' M) by least-squares estimation ^-1M ' Δ m.

Beneficial effect: method of the present invention has following advantage: the scaling method that airborne inertia system is provided; Adopt flare maneuver and IMU mounting means to change the output that encourages error, thereby improve the precision of calibrating parameters.Beneficial effect of the present invention is described as follows:

The design flight path comprises each excitation action, as shown in Figure 4.In the flight path, the desirable output of IMU is referring to Fig. 5, Fig. 6.Pull-up speed 7.5deg/s, climb 5m/s, turning roll angle 30deg, rate of turn 1.5deg/s, the speed-7.5deg/s that bows, the flat rate of deceleration-2.5m/s, underriding luffing angle-45deg of flying.The navigation calculation correlation curve is seen Fig. 7, Fig. 8.

In flight path, get the measurement point in the following process, carry out the desirable demarcation computing of demarcating computing and error being arranged with reference to inertial navigation respectively.Desirable to demarcate computing be in order to verify the feasibility of calibration principle, and with reference to inertial navigation the situation of error being arranged is exactly the rating test of simulating actual conditions.And utilize calibration result to carry out navigation calculation.The result shows, utilizes this method can demarcate out every error parameter of IMU, has improved navigation accuracy.

Description of drawings

Fig. 1 is flight track figure.

Fig. 2 is that body is a gyro output synoptic diagram in the design flight path.

Fig. 3 is that body is an accelerometer output synoptic diagram in the design flight path.

Fig. 4 is the latitude error curve.

Fig. 5 is the longitude error curve.

Embodiment

At first design specific flight path according to the error model of inertial sensor; Aircraft is transported to leading boat computing machine along the flight of designed flight path and the inertial sensor data of gathering specific track points; Again the data of collection and the data of measuring basis equipment output are compared, obtain the measuring error of inertial sensor; Calculate error parameter in the ins error model by the aerial multiposition online calibration method of airborne ins, to understand the inertial navigation performance and to make things convenient for compensation in the navigation calculation.

1) gathers the IMU signal

Utilize the sensor sensing carrier movement characteristic in the six degree of freedom inertial measurement cluster (being called for short IMU): IMU to pass through the responsive motion carrier of gyro along its axial angular velocity signal, by accelerometer measures along carrier shaft to the linear acceleration signal, and signal passed to navigational computer.

Here needing to estimate gyrostatic error model parameters, therefore provide reference model, is x with body _by _bz _bMiddle x _bThe axle gyroscope is output as example, comprises dynamically and the x of static error _bAxle gyro output error is:

$\mathrm{\&Delta;}{\mathrm{\&omega;}}_x={\mathrm{<figure-callout\; id="0"\; label="k"\; filenames="C2007100193470012H2.png,C2007100193470013H1.png"\; state="\{\{state\}\}">k</figure-callout>}}_0+k_1{\mathrm{\&omega;}}_x+k_2{f}_x+k_3{f}_y+k_4{f}_z+k_5{f}_x{f}_z+k_6\stackrel{\&CenterDot;}{{\mathrm{\&omega;}}_y}+k_7{\mathrm{\&omega;}}_x{\mathrm{\&omega;}}_z+k_8{\mathrm{\&omega;}}_y{\mathrm{\&omega;}}_z$

2) method of estimation

Aerial online error calibration algorithm is based on static demarcating method.In the static demarcating, twin shaft or three-axle table are used as the angle benchmark, IMU shows different angles with respect to the local earth's axis (or gravity direction), at the measured value of each location records gyro and accelerometer module, writes calibration equation by the error model row that provide and solves unknown error coefficient.In general, if estimate X the error coefficient of IMU, then at least need be fixed at X/3 the enterprising rower in position.For off-line calibration, this conditionally complete can satisfy; And for airflight, the aircraft carrier then needs to finish a plurality of actions, just can offer the needed position data of rating test.

(1) formula can be obtained the sensor measurement error in conjunction with n group measurement data:

$\mathrm{\&Delta;m}=\left[\begin{array}{ccccccccc}1& {\mathrm{\&omega;}}_x^1& f_x^1& f_y^1& f_z^1& f_x^1{f}_z^1& \stackrel{\&CenterDot;}{{\mathrm{\&omega;}}_z^1}& {\mathrm{\&omega;}}_x^1{\mathrm{\&omega;}}_z^1& {\mathrm{\&omega;}}_y^1{\mathrm{\&omega;}}_z^1\\ & & & & & ...& & & \\ 1& {\mathrm{\&omega;}}_x^n& f_x^n& f_y^n& f_z^n& f_x^n{f}_z^n& \stackrel{\&CenterDot;}{{\mathrm{\&omega;}}_z^n}& {\mathrm{\&omega;}}_x^n{\mathrm{\&omega;}}_x^n& {\mathrm{\&omega;}}_y^n{\mathrm{\&omega;}}_{\mathrm{<figure-callout\; id="0"\; label="n\; z\; k"\; filenames="C2007100193470012H2.png,C2007100193470013H1.png"\; state="\{\{state\}\}">n</figure-callout>}}^z& \\ \end{array},\right]\left[\begin{array}{c}{k}_{}\end{array}\right]\left[\begin{array}{c}{}_0\\ .\\ .\\ .\\ k_8\end{array}\right]=\mathrm{MX}---\left(2\right)$

In the formula: $\mathrm{\&Delta;m}={\left[\begin{array}{ccc}[{\mathrm{\&Delta;\&omega;}}_x^1& ...& {\mathrm{\&Delta;\&omega;}}_x^n]\end{array}\right]}^T$ Be the error amount vector of each time measurement, subscript is represented the n time measurement.Ask difference to obtain by airborne IMU output and reference data; M is an observing matrix, and the subscript of its element is represented the n time measurement, because the ideal value of angular speed and acceleration can not obtain, the output of therefore same employing reference data is calculated; X is a state vector to be calibrated, and its component is every error coefficient of inertial sensor.

So, after gathering n position data, just can be in the hope of the inertial sensor error parameter:

X＝(M′M) ^-1M′Δm (3)

In this course, comprise two important steps:

● the high precision reference data, referring to 3)

● the acquisition of position data must make that each error is all effectively encouraged, referring to 4)

3) high precision reference data

The selection of high precision frame of reference has multiple, can utilize more high-precision inertial navigation system, also can select outer survey schemes such as GPS receiver, laser measurement, radar.For airborne flight, can utilize generally speaking and assemble on the flight test vehicle that more the precise navigation system is as measuring basis, this benchmark utilizes the known more high precision inertia device of error characteristics, makes up the reference measurement platform.The present invention selects for use inertial navigation system that precision is higher than an order of magnitude of system under test (SUT) as high precision reference, and the output of high-precision angular speed and acceleration just can be provided.

4) flight track design

In order to demarcate out gyrostatic error parameter, must adopt the suitable IMU navigation data of collection to export and carry out computational analysis.And, each error can both effectively be encouraged in order to demarcate out all error parameters.So-called excitation is meant: by certain mode of motion, this error can effectively be amplified.The difference of flight path brings different influences can for tested inertial navigation system.Therefore influence and the excitation that needs the exploratory flight track that the inertial navigation system error model is brought.

Desirable gyro is output as:

${\mathrm{\&omega;}}_{\mathrm{ib}}^b={\mathrm{\&omega;}}_{\mathrm{nb}}^b+{\mathrm{\&omega;}}_{\mathrm{ie}}^b+{\mathrm{\&omega;}}_{\mathrm{en}}^b$

In the formula: ${\mathrm{\&omega;}}_{\mathrm{ib}}^b=({\mathrm{\&omega;}}_x,{\mathrm{\&omega;}}_y,{\mathrm{\&omega;}}_z)$ Be the gyrostatic desirable output of strapdown; ω _Nb ^bThe angular velocity of the relative geographic coordinate system of expression carrier coordinate system is at the axial component of carrier coordinate system; ω _Ie ^bBe the component of rotational-angular velocity of the earth on carrier coordinate system; ω _En ^bFor the component that the angular velocity of relative earth system of Department of Geography is fastened at carrier, be the relative angle speed that causes in earth non-plane motion owing to carrier.

In order to encourage ω _Ib ^b, need be to ω _Nb ^b, ω _Ie ^b, ω _En ^bEncourage.Through many dynamic flight paths are carried out simulation analysis, think at dynamic ω in-flight _Nb ^bBe to influence ω _Ib ^bMain factor, ω _Ie ^bMagnitude be generally less than 0.005deg/s, ω _En ^bMagnitude be generally less than 0.01deg/s.

Desirable accelerometer is output as:

$f_{\mathrm{ib}}^b=\stackrel{\&CenterDot;}{V^b}+(2{\mathrm{\&omega;}}_{\mathrm{ie}}^b+{\mathrm{\&omega;}}_{\mathrm{en}}^b)\&times;V^b+g^b)$

In the formula: $f_{\mathrm{ib}}^b=(f_x,f_y,f_z)$ Ideal output for the strapdown accelerometer.V ^b,

Movement velocity and acceleration for the relative geographic coordinate system of carrier.g ^bBe the projection of acceleration of gravity on carrier coordinate system.

Same, through many dynamic flight paths are carried out simulation analysis, think dynamically in-flight

And g ^bBe to influence f _Ib ^bMain factor, (2 ω _Ie ^b+ ω _En ^b) * V ^bMagnitude be generally less than 0.1m/s/s.

Therefore in order to encourage the every error of inertia device, need indirect to ω _Nb ^b,

+ g ^bEncourage.

Directly related with bearer rate, ω _Nb ^b, g ^bAs follows with the relation of attitude angle:

$\left[\begin{array}{c}{\mathrm{\&omega;}}_{\mathrm{nbx}}^b\\ {\mathrm{\&omega;}}_{\mathrm{nby}}^b\\ {\mathrm{\&omega;}}_{\mathrm{nbz}}^b\end{array}\right]=\left[\begin{array}{ccc}\cos \mathrm{\&gamma;}& 0& \sin \mathrm{\&gamma;}\cos \mathrm{\&theta;}\\ 0& 1& -\sin \mathrm{\&theta;}\\ \sin \mathrm{\&gamma;}& 0& -\cos \mathrm{\&theta;}\cos \mathrm{\&gamma;}\end{array}\right]\left[\begin{array}{c}\stackrel{\&CenterDot;}{\mathrm{\&theta;}}\\ \stackrel{\&CenterDot;}{\mathrm{\&gamma;}}\\ \stackrel{\&CenterDot;}{\mathrm{\&psi;}}\end{array}\right]$

$g^b=C_n^b{g}^n$

$C_n^b=\left[\begin{array}{ccc}\cos \mathrm{\&gamma;}\cos \mathrm{\&psi;}+\sin \mathrm{\&gamma;}\sin \mathrm{\&theta;}\sin \mathrm{\&psi;}& -\cos \mathrm{\&gamma;}\sin \mathrm{\&psi;}+\sin \mathrm{\&gamma;}\sin \mathrm{\&theta;}\sin \mathrm{\&psi;}& -\sin \mathrm{\&gamma;}\cos \mathrm{\&theta;}\\ \cos \mathrm{\&theta;}\sin \mathrm{\&psi;}& \cos \mathrm{\&theta;}\cos \mathrm{\&psi;}& \sin \mathrm{\&theta;}\\ \sin \mathrm{\&gamma;}\cos \mathrm{\&psi;}-\cos \mathrm{\&gamma;}\sin \mathrm{\&theta;}\sin \mathrm{\&psi;}& -\sin \mathrm{\&gamma;}\sin \mathrm{\&psi;}-\cos \mathrm{\&gamma;}\sin \mathrm{\&theta;}\cos \mathrm{\&psi;}& \cos \mathrm{\&gamma;}\cos \mathrm{\&theta;}\end{array}\right]$

Roll γ, pitching θ and course ψ represent from the n of Department of Geography to carrier to be a kind of rotation of b.So just together with the flare maneuver ocular connection of the output of strapdown IMU and carrier.In conjunction with the output of IMU and the relation of resolving of attitude of flight vehicle, can obtain the relation of error excitation and aircraft action.(supposing that the aircraft initial attitude is γ=0, θ=0, ψ=90 degree).

(1) ω _xExcitation: produce bigger ω _xExcitation requires aircraft should have bigger pitching and yaw rate, the appropriate tilt angle and the less angle of pitch.Based on this requirement, aircraft spirals for 45 ° can satisfy this requirement, be that the pitch angle is 45 °, continuously change the course with certain yaw rate, because aircraft is to descend or rise from putting down to fly to transfer to, starting stage has certain rate of pitch, and the somersault in motor-driven in addition is motor-driven also can satisfy this requirement.The starting stage of aircraft pitch motion is because the change of the angle of pitch needs rate of pitch, so also can be to ω _xProduce excitation, but this moment, pitch acceleration is generally little.Put down and change course when flying, can be to ω _xProduce excitation.

(2) f _xExcitation: want in X-direction, produce bigger pumping signal, the simplest motor-driven be exactly that aircraft is made level and breakked away, strengthen the side acceleration of aircraft; The decline of spiraling of the other one bigger gradient also encourages it.

(3) f ^yExcitation: produce f ^yEncourage fairly simplely, airplane nose down motion just can produce bigger excitation.

(4) f _zExcitation: aircraft is flat to fly can both guarantee that with inverted flight g acts on the z axle fully, makes g _z ^bMaximum, rising to also of aircraft can produce bigger normal acceleration.

(5) f _xf _zExcitation: make f _xf _zPumping signal bigger, produce big f simultaneously _xAnd f _zBecause these two amounts are mutually perpendicular, general maneuver is difficult to satisfy simultaneously this requirement, must be that two kinds of motions are crosslinked, just might accomplish, specific practice is at first to be the certain angle of aircraft lift-over, is that the aircraft band oppositely breaks away then, promptly is that aircraft is done rectilinear flight under the attitude that tilts.So just can obtain bigger f _xf _zExcitation.

(6)

Excitation: produce the excitation of roll angle acceleration, can achieve the goal as long as change the pitch angle of aircraft.Snakelike motor-driven (turning of S type) can continuously change the value of angular acceleration.

(7) ω _xω _zExcitation: with f _xf _zSimilar, as to produce two orthogonal amounts excitation, relatively difficulty.Because need aircraft to move around the xz axle simultaneously.Diagonal bar bucket with certain pitch angle can satisfy this requirement substantially.

(8) ω _yω _zExcitation: the generation of this excitation, have than other analogue complexity many, because this process aircraft that is the athleticism in the yz plane of aircraft obtains to encourage should rotate around the z axle, rotate around the y axle again, have only helical motion can satisfy this requirement.

(9)

Excitation: this is the aircraft pitch angular acceleration, as long as change the pitch attitude of aircraft, just can encourage

(10) Excitation: flatting turn of aircraft, be commonly considered as the crab angle acceleration of aircraft.Change the course of aircraft, just have the crab angle acceleration, and then produce

(11) ω _xω _yExcitation: this is the angular motion of the machine longitudinal axis and transverse axis of being diversion.Just can produce this pumping signal by putting down to fly to change to spiral to descend or rise.

Comprehensive, as long as analyze selection, just can determine the flight track that can encourage whole objects at the object of needs excitation.The design flight path comprises excitation action: climb, straight and level flight, turning, acceleration pull-up, quicken to climb, decelerating flight, turning, underriding, turning.As shown in Figure 1.In the flight path, the desirable output of IMU is referring to Fig. 2, Fig. 3, and adding table is accelerometer, and g is an acceleration of gravity.7.5 degree/seconds of pull-up speed, climb 5 meter per seconds, turning roll angle 30 degree the speed of bowing-7.5 degree/second put down flying rate of deceleration-2.5 meter per second 1.5 degree/seconds of rate of turn, and underriding luffing angle-45 is spent.

Effect analysis:

Order is being got flight path measurement point (each stage is got 10 measurement points) with the next stage: climb, straight and level flight, turning, acceleration pull-up, quicken to climb, decelerating flight, turning, underriding, turning.

The IMU model is carried out integral calibrating, and table 1 is depicted as calibration result.

Table 1IMU calibration result

In order further to understand the effect of demarcating.The gained error parameter is used for navigation calculation, compensates later navigation error curve and see Fig. 4, shown in Figure 5.Can see that compensation back system accuracy obviously improves.Proved the validity of design proposal.

Claims (4)

1. an inertial measuring system error model demonstration test method is characterized in that the concrete steps of this method are: the flight path of at first designing formulation according to the error model of inertial sensor; With aircraft along the flight of designed flight path and gather the inertial sensor data of formulating track points and be transported to leading boat computing machine; Again the data of collection and the data of measuring basis equipment output are compared, obtain the measuring error of inertial sensor; Calculate the error parameter in the error model of inertial sensor by the aerial multiposition online calibration method of airborne ins, to understand the inertial navigation performance and to make things convenient for compensation in the navigation calculation.

2. inertial measuring system error model demonstration test method according to claim 1 is characterized in that the error model of inertial sensor is as follows:

Gyro error:

$\mathrm{\&Delta;}{\mathrm{\&omega;}}_x=k_0+k_1{\mathrm{\&omega;}}_x+k_2{f}_x+k_3{f}_y+k_4{f}_z+k_5{f}_x{f}_z+k_6{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_y+k_7{\mathrm{\&omega;}}_x{\mathrm{\&omega;}}_z+k_8{\mathrm{\&omega;}}_y{\mathrm{\&omega;}}_z$

$\mathrm{\&Delta;}{\mathrm{\&omega;}}_y=l_0+l_1{\mathrm{\&omega;}}_y+l_2{f}_x+l_3{f}_y+l_4{f}_z+l_5{f}_y{f}_z+l_6{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_x+l_7{\mathrm{\&omega;}}_y{\mathrm{\&omega;}}_z+l_8{\mathrm{\&omega;}}_x{\mathrm{\&omega;}}_z$

$\mathrm{\&Delta;}{\mathrm{\&omega;}}_z=h_0+h_1{\mathrm{\&omega;}}_z+h_2{f}_x+h_3{f}_y+h_4{f}_z+h_5{f}_x{f}_z+h_6{\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_z+h_7{\mathrm{\&omega;}}_x{\mathrm{\&omega;}}_z+h_8{\mathrm{\&omega;}}_x{\mathrm{\&omega;}}_y$

Accelerometer error:

Δf _x＝k′ ₀+k′ ₁f _x+k′ ₂f _y+k′ ₃f _z

Δf _y＝l′ ₀+l′ ₁f _x+l′ ₂f _y+l′ ₃f _z

Δf _z＝h′ ₀+h′ ₁f _x+h′ ₂f _y+h′ ₃f _z

In the formula: k _iThe expression body is the gyrostatic error parameter of X-axis, and subscript is represented the sequence number of error parameter; l _iThe expression body is the gyrostatic error parameter of Y-axis, and subscript is represented the sequence number of error parameter; h _iThe expression body is the gyrostatic error parameter of Z axle, and subscript is represented the sequence number of error parameter; ω _x, ω _y, ω _zRepresent that respectively body is the desirable angle speed output of X, Y, Z axle;

Represent that respectively body is the desirable angle acceleration output of X, Y, Z axle; f _x, f _y, f _zRepresent that respectively body is the desirable acceleration output of X, Y, Z axle; K ' _iExpression X-axis accelerometer error parameter, subscript is represented the differentiation with the gyro error parameter, subscript is represented the sequence number of error parameter; L ' _iExpression Y-axis accelerometer error parameter, subscript is represented the differentiation with the gyro error parameter, subscript is represented the sequence number of error parameter; H ' _iExpression Z axis accelerometer error parameter, subscript is represented the differentiation with the gyro error coefficient, subscript is represented the sequence number of error parameter.

3. inertial measuring system error model demonstration test method according to claim 1, it is characterized in that in the leading boat computing machine, the data of collection and the data of measuring basis equipment are compared, the method that obtains the measuring error of inertial sensor is: before correlation data, need convert measuring basis equipment output to body is angular velocity signal and acceleration signal, with it as ideal value; The gyroscope output of inertial measurement system is deducted the angular velocity ideal value, promptly obtain gyrostatic angular velocity output error.

4. inertial measuring system error model demonstration test method according to claim 1 is characterized in that the aerial multiposition online calibration method of airborne ins is as follows:

1., can obtain the sensor measurement error in conjunction with n group measurement data) for the X-axis gyro:

$\mathrm{\&Delta;m}=\left[\begin{array}{ccccccccc}1& {\mathrm{\&omega;}}_x^1& f_x^1& f_y^1& f_z^1& f_x^1{f}_z^1& {\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_z^1& {\mathrm{\&omega;}}_x^1{\mathrm{\&omega;}}_z^1& {\mathrm{\&omega;}}_y^1{\mathrm{\&omega;}}_z^1\\ & & & & & \&CenterDot;\&CenterDot;\&CenterDot;& & & \\ 1& {\mathrm{\&omega;}}_x^n& f_x^n& f_y^n& f_z^n& {f_x^{n}f}_z^n& {\stackrel{\&CenterDot;}{\mathrm{\&omega;}}}_z^n& {\mathrm{\&omega;}}_x^n{\mathrm{\&omega;}}_z^n& {\mathrm{\&omega;}}_y^n{\mathrm{\&omega;}}_z^n\end{array}\right]\left[\begin{array}{c}{k}_0\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ k_8\end{array}\right]=\mathrm{MX}$

In the formula: $\mathrm{\&Delta;m}={\left[\begin{array}{ccc}\mathrm{\&Delta;}{\mathrm{\&omega;}}_x^1& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{\&Delta;\&omega;}}_x^n\end{array}\right]}^T$ Be the error amount vector of each time measurement, Δ is expressed as error amount, and subscript is represented the n time measurement, asks difference to obtain by airborne inertial measurement cluster IMU output and reference data; M is an observing matrix, and the subscript of its element is represented the n time measurement, adopts reference data to calculate; X is a state vector to be calibrated, and its component is every error parameter of inertial sensor; ω _x, ω _y, ω _zRepresent that respectively body is the desirable angle speed output of X, Y, Z axle;

Represent that respectively body is the desirable angle acceleration output of X, Y, Z axle; f _x, f _y, f _zRepresent that respectively body is the desirable acceleration output of X, Y, Z axle;

2.) try to achieve inertial sensor error parameter: X=(M ' M) by least-squares estimation ^-1M ' Δ m, the transposition of M ' representing matrix M.

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