CN108759867A  Extraneous aided inertial navigation system moving alignment Observability Analysis method  Google Patents
Extraneous aided inertial navigation system moving alignment Observability Analysis method Download PDFInfo
 Publication number
 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
 Authority
 CN
 China
 Prior art keywords
 vector
 inertial navigation
 coordinate
 analysis
 ornamental
 Prior art date
 Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
 Pending
Links
 238000004458 analytical method Methods 0.000 title claims abstract description 64
 239000000969 carrier Substances 0.000 claims abstract description 80
 238000000034 method Methods 0.000 claims abstract description 16
 239000011159 matrix material Substances 0.000 claims description 38
 238000006243 chemical reaction Methods 0.000 claims description 12
 230000001133 acceleration Effects 0.000 claims description 9
 238000009434 installation Methods 0.000 claims description 8
 238000009795 derivation Methods 0.000 claims description 6
 238000005259 measurement Methods 0.000 claims description 6
 230000001131 transforming Effects 0.000 claims description 2
 238000005516 engineering process Methods 0.000 abstract description 3
 238000004364 calculation method Methods 0.000 description 4
 230000000694 effects Effects 0.000 description 3
 238000005096 rolling process Methods 0.000 description 2
 238000007796 conventional method Methods 0.000 description 1
 230000000875 corresponding Effects 0.000 description 1
 230000005484 gravity Effects 0.000 description 1
 239000002965 rope Substances 0.000 description 1
 238000004088 simulation Methods 0.000 description 1
 230000017105 transposition Effects 0.000 description 1
Classifications

 G—PHYSICS
 G01—MEASURING; TESTING
 G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
 G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
 G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or startingup of inertial devices

 G—PHYSICS
 G01—MEASURING; TESTING
 G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
 G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00  G01C19/00
 G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00  G01C19/00 by using measurements of speed or acceleration
 G01C21/12—Navigation; 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
 G01C21/16—Navigation; 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

 G—PHYSICS
 G01—MEASURING; TESTING
 G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
 G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00  G01C19/00
 G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00  G01C19/00 by using measurements of speed or acceleration
 G01C21/12—Navigation; 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
 G01C21/16—Navigation; 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
 G01C21/18—Stabilised 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 analyzed_{a}And b_{g}Observability；Three, according to two and one, analysisOrnamental；Four, according to three analysis fix error angle ornamentals；According to b_{a}The analysis of ornamental, three and one analyze v^{n}Ornamental；Five, according to b_{g}, three, v^{n}L is analyzed in the analysis of ornamental and one^{b}Ornamental.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 motordriven, provide theoretical direction for the planning of carrier movement track and the design of filter, for inertial navigation system highprecision be aligned lay a good foundation.
Description
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 highprecision
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 strapdown navigation solution according to the original measurement data of sensor
It calculates, extraneous assisting navigation equipment provides highprecision navigational parameter information, the result and navigational parameter information that strapdown 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, strapdown inertial system is nonlinear, timevarying,
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 PieceWise Constant SystemsPart I:
Theory》And《Observability Analysis of PieceWise Constant SystemsPart II:
Application to Inertial Navigation Inflight Alignment》PWCS (the PieceWise 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 timevarying 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, r^{n}Indicate position vector of the inertial navigation system under navigational coordinate system, v^{n}Indicate 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
Rotationalangular 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, g^{n}For the local gravitational acceleration vector indicated under navigational coordinate system, f^{b}For the ratio force vector of accelerometer measures, ω^{b}For
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；b_{a}For accelerometer bias vector, b_{g}For 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, l^{b}For lever arm vector；
Step 2: according to inertial navigation system initial alignment on moving base model, accelerometer bias vector b is analyzed_{a}It is considerable
Property and analysis gyroscopic drift vector b_{g}Ornamental；
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 b_{a}Ornamental
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 v^{n}Ornamental；
Step 5: according to gyroscopic drift vector b_{g}, inertial navigation system by carrier coordinate system to navigational coordinate system coordinate
Transition matrixVelocity vector v of the inertial navigation system under navigational coordinate system^{n}The analysis of ornamental and inertial navigation system move base
Seat initial alignment model, analysis lever arm vector l^{b}Ornamental.
The beneficial effects of the invention are as follows：
1, the present invention proposes nonlinear 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 motordriven, be carrier movement track
Planning and the design of filter provide theoretical direction, while being also that inertial navigation system highprecision 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 invention^{b}Variation 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 invention^{b}Variation
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 b_{a}Estimation 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 b_{g}Estimation curve.
Fig. 5 is the fix error angle of the extraneous aided inertial navigation system moving alignment Observability Analysis method of the present invention
ψ_{a}Estimation curve.
Fig. 6 is the lever arm vector l of the extraneous aided inertial navigation system moving alignment Observability Analysis method of the present invention^{b}
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, (northdayeast coordinate system is
NUE 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 r^{n}、l^{b}、v^{n}、First 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, r^{n}Indicate position vector of the inertial navigation system under navigational coordinate system, v^{n}Indicate inertial navigation system in navigational coordinate system
Under velocity vector, v^{n}=[v_{N} v_{U} v_{E}]^{T}, (v_{N}、ν_{U}、ν_{E}Respectively represent v^{n}North 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 rotationalangular velocity of the earth vector indicated under navigational coordinate system,ω_{ie}ForMould；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；g^{n}It is indicated under navigational coordinate system
Local gravitational acceleration vector；f^{b}For the ratio force vector of accelerometer measures；ω^{b}For 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；b_{a}
For accelerometer bias vector, i.e. accelerometer error vector；b_{g}For gyroscopic drift vector, i.e. gyro error, b_{a}And b_{g}Regard
For arbitrary constant, i.e., to b_{a}And b_{g}Derivation is equal to 0 respectively
Consider installation site difference caused by being influenced by lever arm, the highprecision 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, l^{b}For 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).
r^{n}、v^{n}、g^{n}、f^{b}、ω^{b}、b_{a}、b_{g}、And l^{b}It 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 l^{b}Derivation is equal to 0
Above equation constitutes inertial navigation system initial alignment on moving base model, and system state amount includes r^{n}、v^{n}、And inertial device error (b_{a}And b_{g}) and l^{b}。
Step 2: the inertial navigation system initial alignment on moving base model obtained according to step 1, analyzes accelerometer zero
Inclined vector b_{a}Ornamental and analysis gyroscopic drift vector b_{g}Ornamental.
(people is directly or people passes through control system) control vector is for linear motion, and posture does not change.
Accelerometer bias vector b_{a}Observability 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, f^{b}It 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 g^{n}In 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 system^{n}).Therefore above formula equal sign right end removesOutside, items are known.
Therefore, it enables
That is b_{a}=f^{b} f, enabling carrier specific force f=ag=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 determined_{a}, b_{a}=f^{b}, 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 b_{g}Observability 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, f^{b}、And g^{n}It can get (f^{b}、And g^{n}Acquisition pattern is shown in accelerometer zero
Inclined vector b_{a}Observability Analysis,Exported by extraneous assisting navigation equipment), therefore its corresponding derivative is also known quantity.
If there are two unequal moment t_{1}、t_{2}, 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 b_{g}, 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 straightline travelling, carries
The movement locus of body must change, and different moments f is realized by the side acceleration of turning moment^{b}Derivative's
It is linear uncorrelated.Two：Making carrier, progress rise and fall or lateral translation etc. are motordriven while becoming acceleration linear motion and ensure
Posture does not change, then carrier is in motordriven front and back f^{b}DerivativeIt is linear incoherent.Preferably method two, one
Motordriven 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 b_{a}With analysis gyroscopic drift vector b_{g}Analysis) 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, φ_{n}(t_{0}, t) be navigational coordinate system relative to inertial space from t_{0}To the posture transfer matrix (t of t moment_{0}For
Initial time, t are the time), φ_{b}(t_{0}, t) be carrier coordinate system relative to inertial space from t_{0}Posture 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 ω^{b}, it is to cut gyroscopic drift vector b after compensation_{g}Cut 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 f^{b(0)}(t_{3}) and f^{b(0)}(t_{4}) and t_{3}≠t_{4}, make the f at the two moment^{b(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 f^{b(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 motordriven.
About φ_{n}(t_{0},t)、φ_{b}(t_{0}, t) calculation specifications：
If current time is t_{k}, then
φ_{b}(t_{0}, t) and=φ_{b}(t_{0},t_{k})=φ_{b}(t_{k1},t_{k})…φ_{b}(t_{1},t_{2})φ_{b}(t0,t_{1})
Wherein, matrix φ_{b}(t_{k1},t_{k}) can be by inertial navigation system coordinate system b from t_{k1}Moment is to t_{k}The 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,
φ_{n}(t_{0}, t) calculation and φ_{b}(t_{0}, t) and similar, be：
φ_{n}(t_{0}, t) and=φ_{n}(t_{0},t_{k})=φ n (t_{k1},t_{k})…φ_{n}(t1,t_{2})φ_{n}(t_{0},t_{1})
Wherein, matrix φ_{n}(t_{k1},t_{k}) can be by navigational coordinate system n from t_{k1}Moment is to t_{k}The 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.
Abovementioned t_{0}、t_{1}、t_{2}、t_{k1}、t_{k}It is common artrecognized meanings, indicates a certain moment, so φ_{b}(t_{0}, t_{k})、φ_{b}(t_{k1},
t_{k})、φ_{b}(t_{1}, t_{2}) and φ_{b}(t_{0}, t_{1}) meaning correspond to φ_{b}(t_{0}, t) meaning i.e. it is found that φ_{n}(t_{0}, t_{k})、φ_{n}(t_{k1}, t_{k})、
φ_{n}(t_{1}, t_{2}) and φ_{n}(t_{0}, t_{1}) meaning correspond to φ_{n}(t_{0}, t) understand.
Step 4: according to step 3 (The analysis of ornamental), analysis fix error angle ψ_{a}Ornamental；According in step 2
Accelerometer bias vector b_{a}The 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 system^{n}Ornamental.
Fix error angle ψ_{a}Observability 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 ψ_{a}For the fix error angle of inertial navigation system, i.e.,
Wherein it isFor installation error matrix, I is unit matrix, [ψ_{a}×] it is ψ_{a}Antisymmetric 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 determined_{a}, i.e. fix error angle ψ_{a}It is considerable.
Fix error angle ψ_{a}It is based onIt is considerable, it is additionally carried out again without carrier specific motordriven.
v^{n}Ornamental：
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 v^{n}It all can determine, v^{n}It is considerable.
v^{n}It is based onIt is considerable, it is additionally carried out again without carrier specific motordriven.
Step 5: according to gyroscopic drift vector b_{g}, 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 system^{n}The analysis of ornamental and step 1 (inertial navigation system
System initial alignment on moving base model), analysis lever arm vector l^{b}Ornamental.
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
v^{b}For the velocity error under b coordinate systems.
Except l^{b}Outer items are knownNotice matrixOrder be 2, if therefore there are moment t_{5}
≠t_{6}, meetWithIt is linear uncorrelated, then have
Due to
That is coefficient matrix full rank, l^{b}There 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 l^{b}It 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 t_{1}
≠t_{2}, 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 t_{3}
≠t_{4}, meet f^{b(0)}(t_{3}) and f^{b(0)}(t_{4}) 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 system^{n}With fix error angle ψ_{a}It is considerable；
Conclusion 4：Carrier moves along a curved path, and posture changes, and there are two moment t_{5}≠t_{6}, meetWithIt is linear uncorrelated, then lever arm vector l^{b}It 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 motordriven 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 abovementioned analysis method：
Setting inertial navigation system accelerometer bias vector is b_{a}=[0.01 0.01 0.01]^{T}(m/s^{2}), gyroscopic drift
Vector is b_{g}=[0.005 0.005 0.005]^{T}(°/s), fix error angle ψ_{a}=[1 3 2]^{T}(°), lever arm vector are l^{b}=
[1 4 2]^{T}(m)。
Fig. 1 is f^{b}Change curve, i.e., accelerometer measurement output.Fig. 2 is ω^{b}Change curve, i.e. gyroscope
Measurement output.Fig. 3 is accelerometer bias vector b_{a}Estimation curve.Fig. 4 is gyroscopic drift vector b_{g}Estimation curve.Fig. 5 is peace
Fill error angle ψ_{a}Estimation curve.Fig. 6 is lever arm vector l^{b}Estimation 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, r^{n}Indicate position vector of the inertial navigation system under navigational coordinate system, v^{n}Indicate 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, g^{n}For
The local gravitational acceleration vector indicated under navigational coordinate system, f^{b}For the ratio force vector of accelerometer measures, ω^{b}For 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；b_{a}For accelerometer bias vector, b_{g}For 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, l^{b}For lever arm vector；
Step 2: according to inertial navigation system initial alignment on moving base model, accelerometer bias vector b is analyzed_{a}Ornamental and point
Analyse gyroscopic drift vector b_{g}Ornamental；
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 b_{a}The 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 system^{n}
Ornamental；
Step 5: according to gyroscopic drift vector b_{g}, 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 system^{n}The analysis of ornamental and inertial navigation system moving base are initially right
Quasimode type, analysis lever arm vector l^{b}Ornamental.
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 b_{a}The 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 b_{a}=f^{b}, accelerometer bias vector b_{a}It 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 b_{g}The 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 calculated_{g}, gyroscopic drift vector b_{g}It 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 formula_{n}(t_{0}, t) be navigational coordinate system relative to inertial space from t_{0}To t moment
Posture transfer matrix, φ_{b}(t_{0}, t) be carrier coordinate system relative to inertial space from t_{0}To 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 ψ_{a}, fix error angle can
It sees；For installation error matrix, I is unit matrix, ψ_{a}For the fix error angle of inertial navigation system, [ψ_{a}×] it is ψ_{a}Antisymmetry 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 system^{n}The detailed process of ornamental is：Simultaneous formula (2) and
Formula (6) solves v^{n}, obtain velocity vector v of the inertial navigation system under navigational coordinate system^{n}It 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 l^{b}The 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 l^{b}It is considerable.
Priority Applications (1)
Application Number  Priority Date  Filing Date  Title 

CN201810558155.5A CN108759867A (en)  20180601  20180601  Extraneous aided inertial navigation system moving alignment Observability Analysis method 
Applications Claiming Priority (1)
Application Number  Priority Date  Filing Date  Title 

CN201810558155.5A CN108759867A (en)  20180601  20180601  Extraneous aided inertial navigation system moving alignment Observability Analysis method 
Publications (1)
Publication Number  Publication Date 

CN108759867A true CN108759867A (en)  20181106 
Family
ID=64002111
Family Applications (1)
Application Number  Title  Priority Date  Filing Date 

CN201810558155.5A Pending CN108759867A (en)  20180601  20180601  Extraneous aided inertial navigation system moving alignment Observability Analysis method 
Country Status (1)
Country  Link 

CN (1)  CN108759867A (en) 
Cited By (2)
Publication number  Priority date  Publication date  Assignee  Title 

CN109596144A (en) *  20181210  20190409  苏州大学  Initial Alignment Method between GNSS location assists SINS to advance 
CN110030998A (en) *  20190423  20190719  北京航天自动控制研究所  A kind of flat matrix computational approach of moving base platform slop regulation, device and storage medium 
Citations (4)
Publication number  Priority date  Publication date  Assignee  Title 

CN101566477A (en) *  20090603  20091028  哈尔滨工程大学  Quick measurement method of initial attitude of ship local strapdown inertial navigation system 
CN101750066A (en) *  20091231  20100623  中国人民解放军国防科学技术大学  SINS dynamic base transfer alignment method based on satellite positioning 
CN103604442A (en) *  20131114  20140226  哈尔滨工程大学  Observability analysis method applied to online calibration of strapdown inertial navitation system 
CN103791918A (en) *  20140210  20140514  哈尔滨工程大学  Polar region moving base alignment method for naval vessel strapdown inertial navigation system 

2018
 20180601 CN CN201810558155.5A patent/CN108759867A/en active Pending
Patent Citations (4)
Publication number  Priority date  Publication date  Assignee  Title 

CN101566477A (en) *  20090603  20091028  哈尔滨工程大学  Quick measurement method of initial attitude of ship local strapdown inertial navigation system 
CN101750066A (en) *  20091231  20100623  中国人民解放军国防科学技术大学  SINS dynamic base transfer alignment method based on satellite positioning 
CN103604442A (en) *  20131114  20140226  哈尔滨工程大学  Observability analysis method applied to online calibration of strapdown inertial navitation system 
CN103791918A (en) *  20140210  20140514  哈尔滨工程大学  Polar region moving base alignment method for naval vessel strapdown inertial navigation system 
NonPatent Citations (1)
Title 

黄帅等: "惯性导航系统动基座传递对准可观测性分析", 《北京航空航天大学学报》 * 
Cited By (2)
Publication number  Priority date  Publication date  Assignee  Title 

CN109596144A (en) *  20181210  20190409  苏州大学  Initial Alignment Method between GNSS location assists SINS to advance 
CN110030998A (en) *  20190423  20190719  北京航天自动控制研究所  A kind of flat matrix computational approach of moving base platform slop regulation, device and storage medium 
Similar Documents
Publication  Publication Date  Title 

CN104736963B (en)  mapping system and method  
Martin et al.  Design and implementation of a lowcost observerbased attitude and heading reference system  
Yi et al.  IMUbased localization and slip estimation for skidsteered mobile robots  
CN103424114B (en)  A kind of full combined method of vision guided navigation/inertial navigation  
Dissanayake et al.  The aiding of a lowcost strapdown inertial measurement unit using vehicle model constraints for land vehicle applications  
Ren et al.  A multiposition selfcalibration method for dualaxis rotational inertial navigation system  
US10550686B2 (en)  Tumble gyro surveyor  
CN100587641C (en)  A kind of attitude determination system that is applicable to the arbitrary motion mini system  
Kong  INS algorithm using quaternion model for low cost IMU  
Sheng et al.  MEMSbased lowcost strapdown AHRS research  
CN104655152B (en)  A kind of realtime Transfer Alignments of airborne distributed POS based on federated filter  
CN103090870B (en)  Spacecraft attitude measurement method based on MEMS (microelectromechanical systems) sensor  
CN101706281B (en)  Inertia/astronomy/satellite highprecision integrated navigation system and navigation method thereof  
Schopp et al.  Design, geometry evaluation, and calibration of a gyroscopefree inertial measurement unit  
Yoon et al.  Robust vehicle sideslip angle estimation through a disturbance rejection filter that integrates a magnetometer with GPS  
Bloesch et al.  State estimation for legged robotsconsistent fusion of leg kinematics and IMU  
CN104655131B (en)  Inertial navigation Initial Alignment Method based on ISTSSRCKF  
CN103743414B (en)  Initial Alignment Method between the traveling of vehiclemounted SINS assisted by a kind of speedometer  
CN101514900B (en)  Method for initial alignment of a singleaxis rotation strapdown inertial navigation system (SINS)  
US5331578A (en)  Procedure for measuring angles and trajectories by means of gyros and inertial systems  
CN101405570B (en)  Motion capture device and associated method  
CN102289306B (en)  Attitude sensing equipment and positioning method thereof as well as method and device for controlling mouse pointer  
CN103196445B (en)  Based on the carrier posture measuring method of the earth magnetism supplementary inertial of matching technique  
CN101726295B (en)  Unscented Kalman filterbased method for tracking inertial pose according to acceleration compensation  
CN101949703B (en)  Strapdown inertial/satellite combined navigation filtering method 
Legal Events
Date  Code  Title  Description 

PB01  Publication  
PB01  Publication  
SE01  Entry into force of request for substantive examination  
SE01  Entry into force of request for substantive examination  
WD01  Invention patent application deemed withdrawn after publication  
WD01  Invention patent application deemed withdrawn after publication 
Application publication date: 20181106 