CN108759867A - Extraneous aided inertial navigation system moving alignment Observability Analysis method - Google Patents

Extraneous aided inertial navigation system moving alignment Observability Analysis method Download PDF

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CN108759867A
CN108759867A CN201810558155.5A CN201810558155A CN108759867A CN 108759867 A CN108759867 A CN 108759867A CN 201810558155 A CN201810558155 A CN 201810558155A CN 108759867 A CN108759867 A CN 108759867A
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vector
inertial navigation
coordinate
analysis
ornamental
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黄帅
汪宗洋
邹波
高畅
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Chang Guang Satellite Technology Co Ltd
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Chang Guang Satellite Technology Co Ltd
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G01C25/005Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • GPHYSICS
    • G01MEASURING; TESTING
    • G01CMEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/18Stabilised platforms, e.g. by gyroscope

Abstract

Extraneous aided inertial navigation system moving alignment Observability Analysis method is related to field of navigation technology, solve the problems, such as that existing analysis method process is cumbersome, workload increases with system dimension, modeling process introduces error and without fully disclosing principle, this method includes:One, inertial navigation system initial alignment on moving base model is established;Two, according to inertial navigation system initial alignment on moving base model, b is analyzedaAnd bgObservability;Three, according to two and one, analysisOrnamental;Four, according to three analysis fix error angle ornamentals;According to baThe analysis of ornamental, three and one analyze vnOrnamental;Five, according to bg, three, vnL is analyzed in the analysis of ornamental and onebOrnamental.Analytic process of the present invention is intuitive, succinct, and conclusion is more accurate, clear.And comprehensively, profoundly disclose system state estimation with carrier contacting between motor-driven, provide theoretical direction for the planning of carrier movement track and the design of filter, for inertial navigation system high-precision be aligned lay a good foundation.

Description

Extraneous aided inertial navigation system moving alignment Observability Analysis method
Technical field
The present invention relates to field of navigation technology, and in particular to extraneous aided inertial navigation system moving alignment ornamental point Analysis method.
Background technology
Initial alignment is the critical stage that inertial navigation system can normally resolve operation, refers to and enters working condition in system Primary condition necessary to navigation is established before, and the precision of alignment directly affects the performance of inertial navigation system.
For completing the carrier of inertial navigation system navigational parameter initialization, the side being initially aligned under the conditions of moving base Formula is usually Transfer Alignment or is aligned using the auxiliary of external information, to overcome the various interference shadows generated by movement environment It rings, while the inertial sensor of low precision can also be modified.Regardless of which kind of mode, alignment procedures are all high-precision It spends under the auxiliary of navigation information, using the difference of the two navigational parameter or metrical information as observed quantity, the mistake to inertial navigation system The navigational parameters such as quasi- angle, velocity error, site error error and inertial device error are estimated and are corrected, and are improved to reach The purpose of navigation accuracy.Being directed at flow is:Inertial navigation system carries out strap-down navigation solution according to the original measurement data of sensor It calculates, extraneous assisting navigation equipment provides high-precision navigational parameter information, the result and navigational parameter information that strap-down navigation resolves The two is merged by Kalman filter, and the quantity of state of system is estimated and corrected, correct alignment parameter is exported.
Ornamental describe system state variables can estimated capacity, considerable system is the convergent premise item of Kalman filter Part directly determines the effect being initially aligned.However, under the conditions of moving base, strap-down inertial system is non-linear, time-varying, Although theoretically can judge its ornamental by checking Grammian ranks of matrix, calculation amount is larger, and can only pass through number The method of value analysis studies its property, is not easy to use in Practical Project.
Document《Observability Analysis of Piece-Wise Constant Systems-Part I: Theory》And《Observability Analysis of Piece-Wise Constant Systems-Part II: Application to Inertial Navigation In-flight Alignment》PWCS (the Piece-Wise of proposition Constant System) it is theoretical, the nonlinear model of original system is replaced with modified linearized model, it can by solving system The property seen rank of matrix or singular value judge the ornamental of system, this is also the most commonly used method of current engineering field.
Although this method greatlies simplify the Observability Analysis of nonlinear time-varying Alignment model, but process is still cumbersome, And conclusion might not entirely accurate, there is problems simultaneously:1. workload can be with the increasing of system dimension or segments Add and increases;2. system model need to be approximate twice with subsection constant by linearizing, certain error can be introduced compared to master mould; 3. without contacting between abundant exposing system ornamental and carrier movement state and inherent mechanism.
Invention content
Existing analysis method process is cumbersome, workload increases with system dimension, modeling process introduces error in order to solve and The problem of without fully disclosing principle, the present invention provide extraneous aided inertial navigation system moving alignment Observability Analysis side Method.
The present invention is that technical scheme applied to solve the technical problem is as follows:
Extraneous aided inertial navigation system moving alignment Observability Analysis method, includes the following steps:
Step 1: establishing inertial navigation system initial alignment on moving base model
In formula, rnIndicate position vector of the inertial navigation system under navigational coordinate system, vnIndicate inertial navigation system in navigational coordinate system Under velocity vector,Indicate coordinate conversion matrix of the inertial navigation system by carrier coordinate system to navigational coordinate system,Table Show coordinate conversion matrix of the inertial navigation system by navigational coordinate system to carrier coordinate system,To be indicated under navigational coordinate system Rotational-angular velocity of the earth vector,Navigational coordinate system to be indicated under navigational coordinate system turns relative to earth axes Dynamic angular velocity vector,For the rotational angular velocity arrow of the carrier coordinate system Relative Navigation coordinate system indicated under carrier coordinate system Amount, gnFor the local gravitational acceleration vector indicated under navigational coordinate system, fbFor the ratio force vector of accelerometer measures, ωbFor Rotational angular velocity vector of the carrier that gyroscope measures relative to inertial coodinate system, symbol × expression vector product operation,Table It is shown as vectorAntisymmetric matrix;baFor accelerometer bias vector, bgFor gyroscopic drift vector,For extraneous assisting navigation Position vector of the carrier of equipment output under navigational coordinate system,It is sat in navigation for the carrier of extraneous assisting navigation equipment output Velocity vector under mark system, lbFor lever arm vector;
Step 2: according to inertial navigation system initial alignment on moving base model, accelerometer bias vector b is analyzedaIt is considerable Property and analysis gyroscopic drift vector bgOrnamental;
Step 3: according to step 2 and inertial navigation system initial alignment on moving base model, analytic inertial navigation system by Coordinate conversion matrix of the carrier coordinate system to navigational coordinate systemOrnamental;
Step 4: according to step 3, fix error angle ornamental is analyzed;According to accelerometer bias vector baOrnamental Analysis, step 3 and inertial navigation system initial alignment on moving base model, speed of the analysis inertial navigation system under navigational coordinate system Vector vnOrnamental;
Step 5: according to gyroscopic drift vector bg, inertial navigation system by carrier coordinate system to navigational coordinate system coordinate Transition matrixVelocity vector v of the inertial navigation system under navigational coordinate systemnThe analysis of ornamental and inertial navigation system move base Seat initial alignment model, analysis lever arm vector lbOrnamental.
The beneficial effects of the invention are as follows:
1, the present invention proposes non-linear Observability Analysis method from basic definition, solves existing for conventional method The problems such as model error is inevitable, calculation amount is larger, physical significance is indefinite, analytic process is intuitive, succinct, and conclusion is more Accurately, clearly.
2, disclose comprehensively, profoundly system state estimation with carrier contacting between motor-driven, be carrier movement track Planning and the design of filter provide theoretical direction, while being also that inertial navigation system high-precision alignment is laid a good foundation.
Description of the drawings
Fig. 1 is the f of the extraneous aided inertial navigation system moving alignment Observability Analysis method of the present inventionbVariation it is bent Line chart.
Fig. 2 is the ω of the extraneous aided inertial navigation system moving alignment Observability Analysis method of the present inventionbVariation Curve graph.
Fig. 3 is the accelerometer zero of the extraneous aided inertial navigation system moving alignment Observability Analysis method of the present invention Inclined vector baEstimation curve.
Fig. 4 is the gyroscopic drift arrow of the extraneous aided inertial navigation system moving alignment Observability Analysis method of the present invention Measure bgEstimation curve.
Fig. 5 is the fix error angle of the extraneous aided inertial navigation system moving alignment Observability Analysis method of the present invention ψaEstimation curve.
Fig. 6 is the lever arm vector l of the extraneous aided inertial navigation system moving alignment Observability Analysis method of the present inventionb Estimation curve.
Specific implementation mode
To better understand the objects, features and advantages of the present invention, below in conjunction with the accompanying drawings and specific real Mode is applied the present invention is further described in detail.
Many details are elaborated in the following description to facilitate a thorough understanding of the present invention, still, the present invention may be used also To be implemented different from other modes described here using other, therefore, protection scope of the present invention is not by described below Specific embodiment limitation.
Before introducing technical scheme of the present invention, first to be related to coordinate system situations such as illustrate, it is as follows:
The extraneous assisting navigation equipment receiver coordinate system of definition is a systems;Inertial navigation system abbreviation inertial navigation system, inertial navigation system System coordinate system is denoted as b systems, and inertial navigation system is mounted on carrier, ignores the deformation that carrier may occur, that is, think inertial navigation system with The installation relation of carrier will not change, that is, carrier coordinate system;With local geographic coordinate system, (north-day-east coordinate system is N-U-E coordinate systems) it is used as navigational coordinate system, it is denoted as n systems;Definition inertial coodinate system is i systems, and definition earth axes are e systems.This In text extraneous assisting navigation equipment can be used GNSS or other can to provide position and speed of the carrier under navigational coordinate system contour The equipment of precision external information navigational parameter.Respectively rn、lbvnFirst derivative,ForSecond dervative, according to this known to herein all first derivatives and second dervative expression way.
Extraneous aided inertial navigation system moving alignment Observability Analysis method, including following step:
Step 1: establishing inertial navigation system initial alignment on moving base model, model includes formula (1)~formula (6), tool Body is as follows:
Consider that inertial device error, inertia device include accelerometer and gyroscope, it is contemplated that accelerometer error with Gyro error establishes following department pattern
In formula, rnIndicate position vector of the inertial navigation system under navigational coordinate system, vnIndicate inertial navigation system in navigational coordinate system Under velocity vector, vn=[vN vU vE]T, (vN、νU、νERespectively represent vnNorth orientation, day to east component value);It indicates Inertial navigation system is by the coordinate conversion matrix namely inertial navigation system of carrier coordinate system to navigational coordinate system in navigation coordinate It is the attitude matrix of output;Indicate coordinate conversion matrix of the inertial navigation system by navigational coordinate system to carrier coordinate system; For the rotational-angular velocity of the earth vector indicated under navigational coordinate system,ωieForMould;The rotational angular velocity vector for being the navigational coordinate system that is indicated under navigational coordinate system relative to earth axes,Wherein L, h and R respectively represent latitude, elevation and earth radius,To be sat in carrier The rotational angular velocity vector of the lower carrier coordinate system Relative Navigation coordinate system indicated of mark system;gnIt is indicated under navigational coordinate system Local gravitational acceleration vector;fbFor the ratio force vector of accelerometer measures;ωbFor gyroscope measure carrier relative to inertia The rotational angular velocity vector of coordinate system;Symbol × expression vector product operation,It is expressed as vectorAntisymmetric matrix;ba For accelerometer bias vector, i.e. accelerometer error vector;bgFor gyroscopic drift vector, i.e. gyro error, baAnd bgRegard For arbitrary constant, i.e., to baAnd bgDerivation is equal to 0 respectively
Consider installation site difference caused by being influenced by lever arm, the high-precision assisting navigation that extraneous assisting navigation equipment provides There are following relationships between the position of information and carrier inertial navigation output, speed
In formula,For position vector of the carrier under navigational coordinate system of extraneous assisting navigation equipment output,For the external world Velocity vector of the carrier of assisting navigation equipment output under navigational coordinate system, lbFor lever arm vector, (inertial navigation system is auxiliary with the external world Help installation site of the navigation equipment on carrier different, lever arm vector is used to describe the relative position of two systems).
rn、vngn、fb、ωb、ba、bgAnd lbIt is vector
Ignore the deformation that carrier may occur, that is, thinks that the installation relation of inertial navigation system and carrier will not change, it can Lever arm vector is considered as constant, i.e., to lever arm vector lbDerivation is equal to 0
Above equation constitutes inertial navigation system initial alignment on moving base model, and system state amount includes rn、vnAnd inertial device error (baAnd bg) and lb
Step 2: the inertial navigation system initial alignment on moving base model obtained according to step 1, analyzes accelerometer zero Inclined vector baOrnamental and analysis gyroscopic drift vector bgOrnamental.
(people is directly or people passes through control system) control vector is for linear motion, and posture does not change.
Accelerometer bias vector baObservability Analysis:
When carrier is moved in a straight line relative to ground, and posture does not change, i.e.,Then willSubstituting into formula (6) has
Speed of the carrier of i.e. extraneous assisting navigation equipment output under navigational coordinate system is with inertial navigation system in navigation coordinate Speed under system is equal, in formula (6)It is not influenced by lever arm.
To the derivation of above formula both ends, can further obtain:
It solves:
In formula, fbIt is obtained by accelerometer measures,WithPosition that can be by the output of extraneous assisting navigation equipment and speed It spends information and calculates acquisition (i.e.With), and gnIn place Set vector it is known after, you can carry out calculating acquisition (as caused by lever arm position using rope meter Li Yana (Somigliana) model Error is smaller, can be neglected, it is believed that the acceleration of gravity vector that extraneous assisting navigation equipment is provided is to navigate to sit The lower local gravitational acceleration vector g indicated of mark systemn).Therefore above formula equal sign right end removesOutside, items are known.
Therefore, it enables
That is ba=fb- f, enabling carrier specific force f=a-g=0, (f is the specific force of carrier, and a is the absolute acceleration of carrier, and g attaches most importance to Power acceleration), b can be uniquely determineda, ba=fb, therefore accelerometer bias vector is considerable.
Carrier specific force is 0, you can it is considerable to meet accelerometer bias vector;However in earth 1g gravitational fields in concrete application Under environment, carrier specific force is difficult to meet for 0, if maintaining initial attitude constant, enables carrier stationary or does linear uniform motion, can be same Sample is met the requirements.
Gyroscopic drift vector bgObservability Analysis:
It is known in the state that carrier is moved in a straight line relative to ground and posture does not change, (Substitute into formula (6)).Had according to the formula (4) of inertial navigation system initial alignment on moving base model
According to the formula (2) of inertial navigation system initial alignment on moving base model, formula (6) andIt can obtain
It arranges
In formula, fbAnd gnIt can get (fbAnd gnAcquisition pattern is shown in accelerometer zero Inclined vector baObservability Analysis,Exported by extraneous assisting navigation equipment), therefore its corresponding derivative is also known quantity.
If there are two unequal moment t1、t2, meetWithIt is linear uncorrelated, then it can determine the fortune Attitude matrix under dynamic state
It again will be knownWithIt substitutes into simultaneouslyIn, you can determine bg, i.e. gyro drift It is considerable to move vector.
MakeWithIt is linear it is uncorrelated there are two methods, one:If carrier is for linear motion, the change of specific force Change the direction that will advance always along carrier, cannot be satisfied linear incoherent requirement.Therefore, it in the end of straight-line travelling, carries The movement locus of body must change, and different moments f is realized by the side acceleration of turning momentbDerivative's It is linear uncorrelated.Two:Making carrier, progress rise and fall or lateral translation etc. are motor-driven while becoming acceleration linear motion and ensure Posture does not change, then carrier is in motor-driven front and back fbDerivativeIt is linear incoherent.Preferably method two, one Motor-driven can only be met within the very short periodIt is linear uncorrelated, it is difficult to reach satisfied estimation effect, two Preferable simulation result can be obtained.
Step 3: according to step 2 (accelerometer bias vector baWith analysis gyroscopic drift vector bgAnalysis) and step One obtained inertial navigation system initial alignment on moving base model, analytic inertial navigation system is by carrier coordinate system to navigation coordinate The coordinate conversion matrix of systemOrnamental.
Carrier moves in a straight line relative to ground and in the state that posture does not change, and obtainsIt willGeneration Enter formula (6) to obtain
It willFormula (2) and derivation are substituted into, is had
Wherein,Item meets
In formula, φn(t0, t) be navigational coordinate system relative to inertial space from t0To the posture transfer matrix (t of t moment0For Initial time, t are the time), φb(t0, t) be carrier coordinate system relative to inertial space from t0Posture to t moment shifts square Battle array (can be equal to subsequent by the gyroscope measurement data after the navigation information of extraneous assisting navigation equipment offer and compensation Gyroscope measurement obtains ωb, it is to cut gyroscopic drift vector b after compensationgCut error) it is calculated, it is known quantity.Wherein T indicates transposition.
It willAfter substituting into formula (7), further arranging can obtain
In formula, removeOutside, items are all known.Note
Therefore, if there are fb(0)(t3) and fb(0)(t4) and t3≠t4, make the f at the two momentb(0)It is (t) linear uncorrelated, ThenIt can be now uniquely determined, and then any timeAll be it is known, i.e., inertial navigation system by carrier coordinate system to The coordinate conversion matrix of navigational coordinate systemIt is considerable.
Carrier, which is made to become, accelerates linear motion, can meet fb(0)(t) linear uncorrelated.It can be seen that carrier machine at this time Dynamic scheme is contained inIt is linear it is uncorrelated in, there is no need to again it is additional carry out it is specific motor-driven.
About φn(t0,t)、φb(t0, t) calculation specifications:
If current time is tk, then
φb(t0, t) and=φb(t0,tk)=φb(tk-1,tk)…φb(t1,t2b(t0,t1)
Wherein, matrix φb(tk-1,tk) can be by inertial navigation system coordinate system b from tk-1Moment is to tkThe rotating vector σ tables at moment It is shown as:
In formula, [σ ×] is the antisymmetric matrix of σ, and rotating vector σ can be calculated by rotating vector differential equation, i.e.,
WhereinThe rotational angular velocity vector for being the carrier that is indicated under carrier coordinate system relative to inertial coodinate system,
φn(t0, t) calculation and φb(t0, t) and similar, be:
φn(t0, t) and=φn(t0,tk)=φ n (tk-1,tk)…φn(t1,t2n(t0,t1)
Wherein, matrix φn(tk-1,tk) can be by navigational coordinate system n from tk-1Moment is to tkThe rotating vector ξ at moment is expressed as:
In formula, [ξ ×] is the antisymmetric matrix of ξ, and rotating vector ξ can be calculated by rotating vector differential equation, i.e.,
Wherein, It is the navigational coordinate system that is indicated under navigational coordinate system relative to inertial coodinate system Rotational angular velocity vector.
Above-mentioned t0、t1、t2、tk-1、tkIt is common art-recognized meanings, indicates a certain moment, so φb(t0, tk)、φb(tk-1, tk)、φb(t1, t2) and φb(t0, t1) meaning correspond to φb(t0, t) meaning i.e. it is found that φn(t0, tk)、φn(tk-1, tk)、 φn(t1, t2) and φn(t0, t1) meaning correspond to φn(t0, t) understand.
Step 4: according to step 3 (The analysis of ornamental), analysis fix error angle ψaOrnamental;According in step 2 Accelerometer bias vector baThe analysis of ornamental, step 3 (The analysis of ornamental) and the obtained inertial navigation system of step 1 System initial alignment on moving base model, velocity vector v of the analysis inertial navigation system under navigational coordinate systemnOrnamental.
Fix error angle ψaObservability Analysis:
Other than inertial device error and lever arm, installation error is equally to lead to extraneous auxiliary information (extraneous assisting navigation Equipment output information) with inertial navigation system export inconsistent one of factor.Define ψaFor the fix error angle of inertial navigation system, i.e.,
Wherein it isFor installation error matrix, I is unit matrix, [ψa×] it is ψaAntisymmetric matrix;
ThereforeAfter known, installation error matrixIt is as known.It can then solve
It is inertial navigation system by the transformation matrix of coordinates of receiver coordinate system to navigational coordinate system,By extraneous auxiliary Navigation equipment is helped to provide.
Thus ψ can be uniquely determineda, i.e. fix error angle ψaIt is considerable.
Fix error angle ψaIt is based onIt is considerable, it is additionally carried out again without carrier specific motor-driven.
vnOrnamental:
Carrier moves in a straight line relative to ground and in the state that posture does not change, (simultaneous formula (2) and formula (6)) have
It can solve
Then any time vnIt all can determine, vnIt is considerable.
vnIt is based onIt is considerable, it is additionally carried out again without carrier specific motor-driven.
Step 5: according to gyroscopic drift vector bg, inertial navigation system by carrier coordinate system to navigational coordinate system coordinate Transition matrixWith velocity vector v of the inertial navigation system under navigational coordinate systemnThe analysis of ornamental and step 1 (inertial navigation system System initial alignment on moving base model), analysis lever arm vector lbOrnamental.
By the formula (6) of inertial navigation system initial alignment on moving base model, have
In formula,It is the velocity error under n coordinate systems,For the velocity error under b coordinate systems, i.e. δ vbFor the velocity error under b coordinate systems.
Except lbOuter items are knownNotice matrixOrder be 2, if therefore there are moment t5 ≠t6, meetWithIt is linear uncorrelated, then have
Due to
That is coefficient matrix full rank, lbThere is unique solution.Therefore, carrier moves along a curved path, and there are expire at the time of two differences FootIt is linear uncorrelated, then it is considerable can to meet lever arm vector.
Carrier moves along a curved path, if in traveling process there are in 3 kinds of pitching, yaw or rolling attitude motions whole or appoint Two kinds of meaning, you can meet different momentsLinear incoherent requirement, makes lever arm vector lbIt is considerable.
To sum up, for the Observability Analysis problem in inertial navigation system initial alignment on moving base, just like drawing a conclusion:
Conclusion 1:Carrier is for linear motion, and posture does not change, i.e.,And carrier specific force is 0, then Accelerometer bias vector is considerable;
Conclusion 2:Carrier is for linear motion, and posture does not change, i.e.,And there are two moment t1 ≠t2, meetWithLinear uncorrelated, then gyroscopic drift vector is considerable;
Conclusion 3:Carrier is for linear motion, and posture does not change, i.e.,And there are two moment t3 ≠t4, meet fb(0)(t3) and fb(0)(t4) linear uncorrelated, then inertial navigation system is by carrier coordinate system to navigational coordinate system Coordinate conversion matrixVelocity vector v of the inertial navigation system under navigational coordinate systemnWith fix error angle ψaIt is considerable;
Conclusion 4:Carrier moves along a curved path, and posture changes, and there are two moment t5≠t6, meetWithIt is linear uncorrelated, then lever arm vector lbIt is considerable.
By the analysis to every conclusion, and the inclusion relation between its required carrier maneuvering condition is considered, if needing to meet Each state variable of system is considerable, can the motor-driven scheme of design vector it is as follows:
Motorized segment 1:Carrier stationary is motionless;
Motorized segment 2:Carrier does change and accelerates linear motion;
Motorized segment 3:Carrier is carried out at the same time rolling movement and pitching movement.
The example for naming a concrete application proves above-mentioned analysis method:
Setting inertial navigation system accelerometer bias vector is ba=[0.01 0.01 0.01]T(m/s2), gyroscopic drift Vector is bg=[0.005 0.005 0.005]T(°/s), fix error angle ψa=[1 3 2]T(°), lever arm vector are lb= [1 4 2]T(m)。
Fig. 1 is fbChange curve, i.e., accelerometer measurement output.Fig. 2 is ωbChange curve, i.e. gyroscope Measurement output.Fig. 3 is accelerometer bias vector baEstimation curve.Fig. 4 is gyroscopic drift vector bgEstimation curve.Fig. 5 is peace Fill error angle ψaEstimation curve.Fig. 6 is lever arm vector lbEstimation curve.Changed by comparison vehicle motion state and each quantity of state Estimated result curve can verify the correctness of the put forward theoretical analysis method of the present invention, can instruct inertia system moving alignment The planning of carrier movement track and the design of respective filter in the process.

Claims (8)

1. extraneous aided inertial navigation system moving alignment Observability Analysis method, which is characterized in that include the following steps:
Step 1: establishing inertial navigation system initial alignment on moving base model
In formula, rnIndicate position vector of the inertial navigation system under navigational coordinate system, vnIndicate inertial navigation system under navigational coordinate system Velocity vector,Indicate coordinate conversion matrix of the inertial navigation system by carrier coordinate system to navigational coordinate system,Indicate inertia Navigation system by navigational coordinate system to carrier coordinate system coordinate conversion matrix,For the earth indicated under navigational coordinate system Spin velocity vector,Angle of rotation speed for the navigational coordinate system that is indicated under navigational coordinate system relative to earth axes Vector is spent,For the rotational angular velocity vector of the carrier coordinate system Relative Navigation coordinate system indicated under carrier coordinate system, gnFor The local gravitational acceleration vector indicated under navigational coordinate system, fbFor the ratio force vector of accelerometer measures, ωbFor gyroscope Rotational angular velocity vector of the carrier of measurement relative to inertial coodinate system, symbol × expression vector product operation,Be expressed as to AmountAntisymmetric matrix;baFor accelerometer bias vector, bgFor gyroscopic drift vector,It is defeated for extraneous assisting navigation equipment Position vector of the carrier gone out under navigational coordinate system,For extraneous assisting navigation equipment output carrier under navigational coordinate system Velocity vector, lbFor lever arm vector;
Step 2: according to inertial navigation system initial alignment on moving base model, accelerometer bias vector b is analyzedaOrnamental and point Analyse gyroscopic drift vector bgOrnamental;
Step 3: according to step 2 and inertial navigation system initial alignment on moving base model, analytic inertial navigation system is by carrier Coordinate conversion matrix of the coordinate system to navigational coordinate systemOrnamental;
Step 4: according to step 3, fix error angle ornamental is analyzed;According to accelerometer bias vector baThe analysis of ornamental, Step 3 and inertial navigation system initial alignment on moving base model, velocity vector v of the analysis inertial navigation system under navigational coordinate systemn Ornamental;
Step 5: according to gyroscopic drift vector bg, inertial navigation system by carrier coordinate system to navigational coordinate system coordinate convert square Battle arrayVelocity vector v of the inertial navigation system under navigational coordinate systemnThe analysis of ornamental and inertial navigation system moving base are initially right Quasi-mode type, analysis lever arm vector lbOrnamental.
2. external world's aided inertial navigation system moving alignment Observability Analysis method as described in claim 1, feature exist In in the step 1
3. external world's aided inertial navigation system moving alignment Observability Analysis method as described in claim 1, feature exist In the analysis accelerometer bias vector baThe detailed process of ornamental is:
Control vector is for linear motion and posture does not change, and obtains It willFormula (6) is substituted into obtain It arrives
Simultaneous formula (2), obtains
It enablesObtain ba=fb, accelerometer bias vector baIt is considerable.
4. external world's aided inertial navigation system moving alignment Observability Analysis method as described in claim 1, feature exist In the analysis gyroscopic drift vector bgThe detailed process of ornamental is:
Control vector is for linear motion and posture does not change, and obtains
Formula (4) is substituted into obtain Formula (6) is substituted into obtainSimultaneousWith formula (2) and derivation, obtainAnd it solves
It willWithIt substitutes intoB is calculatedg, gyroscopic drift vector bgIt is considerable.
5. external world's aided inertial navigation system moving alignment Observability Analysis method as described in claim 1, feature exist In the detailed process of the step 3 is:
Control vector is for linear motion and posture does not change, and obtainsIt willFormula (6) is substituted into obtain
It willFormula (2) and derivation are substituted into, is obtainedWhereinφ in formulan(t0, t) be navigational coordinate system relative to inertial space from t0To t moment Posture transfer matrix, φb(t0, t) be carrier coordinate system relative to inertial space from t0To the posture transfer matrix of t moment;
It solvesObtain coordinate conversion matrix of the inertial navigation system by carrier coordinate system to navigational coordinate systemIt is considerable.
6. external world's aided inertial navigation system moving alignment Observability Analysis method as described in claim 1, feature exist In the detailed process of the analysis fix error angle ornamental is:
SimultaneousWithAnd obtained according to step 3Solve ψa, fix error angle can It sees;For installation error matrix, I is unit matrix, ψaFor the fix error angle of inertial navigation system, [ψa×] it is ψaAntisymmetry square Battle array,It is inertial navigation system by the transformation matrix of coordinates of receiver coordinate system to navigational coordinate system.
7. external world's aided inertial navigation system moving alignment Observability Analysis method as described in claim 1, feature exist In velocity vector v of the analysis inertial navigation system under navigational coordinate systemnThe detailed process of ornamental is:Simultaneous formula (2) and Formula (6) solves vn, obtain velocity vector v of the inertial navigation system under navigational coordinate systemnIt is considerable.
8. external world's aided inertial navigation system moving alignment Observability Analysis method as described in claim 1, feature exist In the analysis lever arm vector lbThe detailed process of ornamental is:Control vector moves along a curved path, and l is solved according to formula (6)b, Obtain lever arm vector lbIt is considerable.
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