CN109724626A - A kind of model compensation method for polar region Transfer Alignment Dynamic flexural lever arm effect - Google Patents
A kind of model compensation method for polar region Transfer Alignment Dynamic flexural lever arm effect Download PDFInfo
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Abstract
The invention belongs to the transfer alignment technique fields of inertial navigation system, and in particular to a kind of model compensation method for polar region Transfer Alignment Dynamic flexural lever arm effect.Comprehensively consider influence of the deflection deformation angle caused by carrier deformation to static fixed lever arm, combine grid navigation error equation, it has been specifically designed a kind of model of Transfer Alignment lever arm effect under polar region grid coordinate system, and using the matching way of " speed+posture " rapid alignment, it is resolved using Kalman filtering, the posture misalignment and speed error value for estimating sub- inertial navigation system compensate sub- inertial navigation, complete Transfer Alignment.The method of the present invention efficiently solves the coupling influence of deflection deformation and lever arm effect under polar region environment, improves the Transfer Alignment precision and applicability of polar region.
Description
Technical field
The invention belongs to the transfer alignment technique fields of inertial navigation system, and in particular to one kind is for polar region Transfer Alignment dynamic
Bend the model compensation method of lever arm effect.
Background technique
The one kind of transfer alignment technique as Initial Alignment Technique, suitable for the dynamic of carrier-borne aircraft or Ship-launched Weapon INS
Pedestal is initially aligned.Under normal conditions, main inertial navigation system is installed in the swing center of large ship, and carries the attached of sub- inertial navigation
Belong to aircraft or marine surface or any position are then stopped or be suspended in workboat.Since the installation of sub- inertial navigation is far from ship
Swing center, cause between main and sub inertial navigation there are a certain distance, this distance referred to as lever arm.When carrier system is relative to used
Property system is there are when angular movement, and the presence of lever arm causes the accelerometer sensitive of main and sub inertial navigation to different ratio force informations, to solve
Different movement velocitys is calculated, this phenomenon is known as lever arm effect.Also, in severe polar region marine environment, high wind, billow
With frequently occurring for undercurrent, bulky large ship can be made inevitably to deform, so that Transfer Alignment is estimated
The misalignment of meter is unstable.Compensation for polar region lever arm effect, the calculating penalty method being typically employed under grid tie, i.e., in structure
To lever arm velocity compensation when making speed observed quantity.The mathematical model of traditional lever arm is mutually only in lever arm effect and deflection deformation
It is derived under vertical, non-interfering hypothesis, but during actual transfer, the long range between main and sub inertial navigation makes lever arm
Length is very big, so that there are certain coupling between lever arm effect and deflection deformation, lever arm length is also considered as constant value by approximation and becomes
At time-varying vector.For this problem, the lever arm during polar region Transfer Alignment is divided into fixed lever arm and dynamic lever arm two
Point, the length of fixed lever arm is considered as fixed value, and the length of dynamic lever arm is then to establish under polar region grid tie based on bending deformation
The model of shape angle θ carries out error compensation, thus solves to deform the dynamic change for leading to lever arm length because of hull deflection, to improve
The accuracy of polar region Transfer Alignment.
Zhou Qi et al. is in " the polar region flight grid inertial navigation algorithm original for being published in periodical " Northwestern Polytechnical University's journal "
Reason " in a text, a kind of polar region flight grid inertial navigation algorithm is proposed, polar navigation can be effectively solved in polar region without available
Direction reference line problem, but without solving polar region alignment issues.Wu Feng et al. is being published in periodical " Chinese inertial technology
Report " " air weapon Transfer alignment algorithm " text in, propose it is a kind of based on grid navigation mechanization polar region transmitting pair
Quasi- algorithm can complete the Air launching of air weapon faster.In its airborne transfer alignment method in polar region proposed, although
Lever arm speed is compensated in desin speed observed quantity, but all lever arm is imitated without embodying in state equation and observational equation
The compensation of error is answered, while also not accounting for the deflection deformation angle θ's and lever arm length formed due to carrier flexural deformations
Coupling, does not also compensate deflection deformation error.In conclusion existing Transfer Alignment can not be effectively to dynamic
State scratches toggle-lever arm and carries out calculating compensation.
Summary of the invention
The purpose of the present invention is to provide one kind can effective compensation naval vessel deformation angle is bent under polar region environment to transmitting
The method for being directed at lever arm effects.
The object of the present invention is achieved like this:
A kind of model compensation method for polar region Transfer Alignment Dynamic flexural lever arm effect, comprising the following steps:
(1) sub- inertial navigation system starting, preheating, sub- inertial navigation system are completed primary using the navigational parameter that main inertial navigation system is sent
Bookbinding, the navigational parameter includes speed, attitude matrix and location information；
(2) the dynamic lever arm model between main and sub inertial navigation system is constructed, lever arm rate equation is carried out again under grid tie
It derives, Dynamic flexural lever arm velocity compensation is carried out to the velocity information that collected main inertial navigation system exports under grid tie；
(3) sub- inertial navigation system carries out inertial reference calculation, mends by the sub- inertial navigation system of synchronous acquisition and through Dynamic flexural lever arm speed
The speed and posture information that main inertial navigation system after repaying exports under grid tie, and obtain speed and attitude error accordingly to constitute
Observed quantity；
(4) on polar region naval vessel there are in the case where deflection deformation, according to the navigation mechanization under grid tie, in conjunction with grid
Navigation error equation establishes the system state equation and observational equation under grid tie using the matching way of " speed+posture "；
(5) using the observed quantity of state equation, observational equation and construction under the grid coordinate system of design, Kalman is carried out
Filtering resolves, and estimates the posture misalignment of sub- inertial navigation system, the state estimation value of speed, completes Transfer Alignment.
Lever arm model r involved in step (2)m, expression formula are as follows:
rm=r0+L2θ
In formula: rmIt is the Dynamic flexural lever arm under main inertial navigation carrier coordinate system m system；r0It is static fixed lever arm, L2It is dynamic
Toggle-lever arm penalty coefficient is scratched, θ is deflection deformation angle；
Related Dynamic flexural lever arm speedIts expression formula are as follows:
In formula:It is that sub- inertial navigation calculates attitude matrix,It is rotation of the main inertial navigation relative to inertial space under grid tie
Corner rate.
Observed quantity Z involved in step (3), expression formula are as follows:
Z=[δ VGφm G]T
In formula: δ VGIt is the speed error value under grid tie；φm GIt is the measurement posture misalignment under grid tie.
State variable involved in step (4) is
Related system state equation are as follows:
In formula,It is acceleration constant value drift,It is gyro drift, φa GIt is installation error angle,It is to accelerate
Measurement is spent,It is earth rate under grid tie,Be under grid tie grid tie relative to the rotation of geographic coordinate system
Angular speed,It is measurement turning rate of the sub- inertial navigation carrier system downloading system with respect to grid tie；
Related observational equation are as follows:
Z=HX+v
In formula, Z is observed quantity, and v is observation noise, and H is observing matrix, are as follows:
The beneficial effects of the present invention are:
The method of the present invention comprehensively considers the lever arm effect and deflection deformation angle θ of Transfer Alignment in the case where deflection deformation
Between relationship, establish the mathematical model of Dynamic flexural lever arm and calculating compensation carried out to observed quantity, in conjunction with grid navigation mechanics
Layout can effectively improve the alignment precision of naval vessel Transfer Alignment under polar region deflection deformation environment.
Detailed description of the invention
Fig. 1 is the basic procedure of the model compensation method proposed by the present invention for polar region Transfer Alignment Dynamic flexural lever arm
Block diagram；
Fig. 2 is the schematic diagram of polar region Transfer Alignment Dynamic flexural lever arm model compensation proposed by the present invention；
Fig. 3 is the transfer alignment method in polar region and traditional polar region biography after Dynamic flexural lever arm model compensation proposed by the present invention
Pass the φ of alignment methodsaxEstimation error curve comparison diagram；
Fig. 4 is the transfer alignment method in polar region and traditional polar region biography after Dynamic flexural lever arm model compensation proposed by the present invention
Pass the φ of alignment methodsayEstimation error curve comparison diagram；
Fig. 5 is the transfer alignment method in polar region and traditional polar region biography after Dynamic flexural lever arm model compensation proposed by the present invention
Pass the φ of alignment methodsazEstimation error curve comparison diagram.
Specific embodiment
The present invention is described in further detail below in conjunction with the accompanying drawings.
The invention proposes a kind of Dynamic flexural lever arm model compensation methods of polar region Transfer Alignment, as shown in Fig. 1, should
The key step of method is as follows:
1. completing the starting of sub- inertial navigation system, preheating preparation, sub- inertial navigation system is joined using the navigation that main inertial navigation system is sent
Primary bookbinding is counted up into, the navigational parameter includes speed, attitude matrix and location information；
2. the Dynamic flexural lever arm model between main and sub inertial navigation system is constructed, as shown in Fig. 2, to lever arm under grid tie
Rate equation is derived again, carries out Dynamic flexural to the velocity information that collected main inertial navigation system exports under grid tie
Lever arm velocity compensation；
Related Dynamic flexural lever arm model rm, expression formula are as follows:
rm=r0+L2θ
In formula: rmIt is the Dynamic flexural lever arm under main inertial navigation carrier coordinate system；r0=[x0y0z0]TIt is the length of fixed lever arm
Degree, θ=[θxθyθz]TIt is deflection deformation angle, L2It is Dynamic flexural lever arm penalty coefficient, can be obtained by following relationships:
As shown in Fig. 2, line segment oa is component of the fixed lever arm in x-axis, value x0, line segment oc is that fixed lever arm exists
Component in y-axis, value y0, camber line line segmentIt is lever arm of the oa after deflection deformation, camber line line segmentIt is oc by scratching
Bent deformed lever arm has in the case where deflection deformation angle is the hypothesis of low-angle:
Ab=oa*tan θz=x0θz
Cd=oc*tan θz=y0θz
In formula, x0θzAnd y0θzIt is the exhausted of z-axis deflection deformation angle lever arm length variation caused in y-axis and x-axis respectively
It is similar to value, z0θyWith-x0θyIt is the exhausted of y-axis deflection deformation angle lever arm length variation caused in x-axis and z-axis respectively
To value ,-y0θxAnd z0θxIt is the absolute value of x-axis deflection deformation angle lever arm length variation caused in z-axis and y-axis respectively.By
This, it can be deduced that Dynamic flexural lever arm is as follows:
To Dynamic flexural lever arm rmDerivation can obtain:
Second order Markov Process Modeling is carried out to deflection deformation angle θ:
In formula, τ=[τx τy τz]TFor the mean square error at deflection deformation angle, β=[βx βy βz]TFor constant value, η=[ηx ηy
ηz]TFor white noise, Qη=[Qηx Qηy Qηz]TFor its noise intensity, and meet η~Ν (0, Qη), Qη, the relationship between τ and β beEach τiAnd βiRelationship be βi=2.146/ τi；
It is rightDerivation simultaneously combines above formula, can obtain:
Related Dynamic flexural lever arm speedIts expression formula are as follows:
The second order ignored in formula is a small amount ofWithDynamic flexural lever arm speedIt can table
It is shown as:
In formula,It is that sub- inertial navigation system calculates attitude matrix,It is the turning rate of main inertial navigation system under grid tie；
3. sub- inertial navigation system carries out inertial reference calculation, by the sub- inertial navigation system of synchronous acquisition and through Dynamic flexural lever arm velocity compensation
The speed and posture information that main inertial navigation system afterwards exports under grid tie, and obtain speed and attitude error accordingly come the amount of composition
Measurement；
Related measurement Z, expression formula are as follows:
Z=[δ VGφm G]T
In formula, δ VGIt is the speed error value under grid tie, φm GIt is the measurement posture misalignment under grid tie；
4. on polar region naval vessel there are in the case where deflection deformation, according to the navigation mechanization under grid tie, in conjunction with grid
Navigation error equation establishes the system state equation and measurement equation under grid tie using the matching way of " speed+posture "；
Related state variable are as follows:
Related system state equation are as follows:
In formula, s ' is to calculate carrier coordinate system for sub- inertial navigation, and m system is carrier coordinate system where main inertial navigation, and s system is sub- inertial navigation
Place carrier coordinate system, e system are ECEF coordinate system, and g system is northeast day geographic coordinate system, and G system is grid coordinate system, i system
For geocentric inertial coordinate system,It is s ' is posture misalignment between m system, φa=[φax φay
φaz]TIt is the installation error angle between s system and m system, due to including deflection deformation angle in actual physics misalignment, is needed in modeling
By deflection deformation angle θ include that m is lain in the misalignment between s system, and posture misalignmentWith installation error angle φa?
It is regarded as low-angle, thereforeWithIt can simplify are as follows:
In the ideal situation, the posture differential equation of the main inertial navigation system under grid tie is respectively as follows:
In formula,For the attitude matrix of ideally main inertial navigation system,Rotation angle speed for m system relative to G system
Spend the projection under m system；
In actual transfer alignment, since the alignment time is shorter, it can be considered that main inertial navigation system is error-free, but
It is sub- inertial navigation system is the practical posture differential equation there are error, under grid tie are as follows:
In formula,For the practical attitude matrix of sub- inertial navigation system,It is sub- inertial navigation relative to grid tie angular velocity of rotation
Actual measured value, caused by the error by sub- inertial navigation system, can indicate are as follows:
In formula,For the angular speed of sub- inertial navigation gyroscope reality output, can be unfolded are as follows:
In formula,Projection of the angular velocity of rotation under s system for m system relative to G system.
In conjunction with above formula,It can rewrite are as follows:
In formula,WithRespectivelyWithMeasurement error, mainly influenced by location error, since son is used
Influence of the misalignment of guiding systems to location error is very slow, during time shorter Transfer Alignment, can ignoreWithHaveTherefore, above formula can be rewritten are as follows:
Measurement misalignment φ under low-angle hypothesis, after initial timemIt can indicate are as follows:
To φm× derivation can obtain:
Ignore that second order in formula is a small amount of, and according to triple rules of vector, can arrange are as follows:
For actual physics misalignment φa, because during time shorter Transfer Alignment, main and sub inertial navigation system it
Between relative attitude be kept essentially constant, can be regarded as constant value, therefore the improvement attitude error side of grid tie Transfer Alignment
Journey are as follows:
Velocity differentials equation of the main inertial navigation system under grid tie is as follows:
In formula,For the grid tie speed of ideally main inertial navigation system,Add for ideally main inertial navigation system
The specific force of speedometer output,For the attitude matrix of main inertial navigation system ideally,For ideally main inertial navigation
Projection of the weight component that system sensitive arrives under grid tie.
Since main inertial navigation system is considered as error-free, and there are errors for sub- inertial navigation system, therefore sub- inertial navigation system is in lattice
The actual speed differential equation under net system are as follows:
In formula,WithFor the practical attitude matrix and grid tie speed of sub- inertial navigation system,It is real for sub- inertial navigation system
The weight component that border measures,For the specific force of sub- inertial navigation system accelerometer reality output, indicate are as follows:
In formula,It is projection of the specific force in m system of the main inertial navigation system of son,It is the specific force of main inertial navigation system in m system
Projection,It is projection of the lever arm acceleration in m system.
Since Transfer Alignment filtering is actually to execute in sub- inertial navigation system, it is therefore desirable to by the defeated of main inertial navigation system
It is transformed into the form of sub- inertial navigation system out, therefore the velocity differentials equation of main inertial navigation system is transformed into the form of sub- inertial navigation system are as follows:
In formula, a small amount of φ of second orderm×(φa+ θ) × andNegligible, the above-mentioned main inertial navigation with the product of small misalignment
The velocity differentials equation of system may be expressed as:
Definition:
In formula, δ vGIt is sub- inertial navigation system output speed and the main inertial navigation system speed by the compensation of Dynamic flexural lever arm
Difference, i.e., the velocity error of sub- inertial navigation system；
Known by step 2, lever arm speed under grid tie are as follows:
Velocity error equation by fast transfer alignment under the compensated grid tie of Dynamic flexural lever arm can indicate are as follows:
Related observational equation are as follows:
Z=HX+v
In formula, Z is observed quantity, and v is observation noise, and H is observing matrix, as follows:
5. carrying out Kalman using the measurement of state equation, measurement equation and construction under the grid coordinate system of design
Filtering resolves, and estimates the posture misalignment of sub- inertial navigation system, the state estimation value of speed, completes Transfer Alignment.
In order to verify reasonability of the invention, feasibility, using Matlab program to the polar region Transfer Alignment dynamic of design
Toggle-lever arm model compensation method is scratched to be emulated.In order to realize that analysis is compared, the method for the present invention is defined as grid tie improvement side
Case will not be known as existing method to the method for Dynamic flexural lever arm compensation；
The setting of Matlab simulated conditions:
1) relevant parameter of posture be respectively as follows: amplitude/period of pitch angle, roll angle and yaw angle be respectively 2 °/3s,
3 °/5s and 6 °/7s, initial phase and course angle are respectively 0 ° and 45 °；
2) state is selected as uniformly accelrated rectilinear motion state: Its oscillating motion posture is set to the sine of following form
Function:
3) relevant parameter of sub- inertia device measurement error are as follows: gyroscope constant value drift is 0.01 °/h, and random drift is
0.001 °/h, acceleration constant value drift is 1 × 10-4g0, random drift is 1 × 10-5g0；
4) relevant parameter of Transfer Alignment is respectively as follows: three axis actual physics misalignment φax、φayAnd φazTrue value difference
It is set to 0.3 °, 0.5 ° and 0.8 °；Three axis fix lever arm r0Length be each set to 2m, 10m and 5m；Three shaft flexings become
The second order Markov Parameters at shape angle are each set to ax=2, ay=1, az=3, bx=1, by=1 and bz=2, motivate white noise
Sound σ2Noise intensity be set to 0.001rad2/s2；Three axis σ2Value be 0.00025rad respectively2/s2、0.0005rad2/s2
And 0.00167rad2/s2, while for the robustness of safeguards system, three axis σ2Value should be set to be higher than the above calculated value；
5) the alignment time is 25s, step-length 0.1s.
6) Initial state estimation covariance matrix P0, systematic procedure noise covariance battle array Q and observation noise covariance battle array R difference
It is set to:
R=diag { (0.01m/s)2,(0.01m/s)2,(0.01°)2,(0.01°)2,(0.01°)2}
7) simulation result
In the case of emulation experiment it can be seen from Fig. 3~Fig. 5, improved method can be completed within 20 seconds to practical object
The estimation of reason misalignment, and φ in existing methodaEvaluated error be then constantly in divergent state, that is, be unable to complete to practical object
Manage the estimation of misalignment.
The methodical evaluated error of co-occurrence is compared, and the evaluated error of improved method is lower, while under different motion state
Also more stable.Also, compared to longitudinal with lateral misalignment angle error, it would be highly desirable to which solution is that the Large azimuth angle of existing method misses
Difference.This is because the essence of existing method is still classical Transfer Alignment, it is unable to complete under uniformly accelrated rectilinear motion and orientation is lost
Quasi- angle is effectively estimated.
And the simulation experiment result shows δ φax、δφayWith δ φazThe absolute value and root-mean-square error ten of average value tap
Closely, this explanation is in δ φaAfter convergence, convergence result is very steady.It is right in the Transfer Alignment application under polar region adverse circumstances
The alignment precision and speed of the compensated Transfer Alignment of Dynamic flexural lever arm will be substantially better than existing grid tie Transfer Alignment
Method, and compensated method can realize fast and accurately Transfer Alignment under polar region environment and effectively compensate for bending deformation
The mushing error that shape generates.
It should be understood that these examples are only for illustrating the present invention and are not intended to limit the scope of the present invention.In addition, it should also be understood that,
After reading the content taught by the present invention, those skilled in the art can make various modifications or changes to the present invention, these
Equivalent form is also fallen within the scope of the appended claims of the present application.
Claims (4)
1. a kind of model compensation method for polar region Transfer Alignment Dynamic flexural lever arm effect, which is characterized in that including following
Step:
(1) sub- inertial navigation system starting, preheating, sub- inertial navigation system complete primary dress using the navigational parameter that main inertial navigation system is sent
It orders, the navigational parameter includes speed, attitude matrix and location information；
(2) the dynamic lever arm model between main and sub inertial navigation system is constructed, lever arm rate equation is pushed away again under grid tie
It leads, Dynamic flexural lever arm velocity compensation is carried out to the velocity information that collected main inertial navigation system exports under grid tie；
(3) sub- inertial navigation system carries out inertial reference calculation, by the sub- inertial navigation system of synchronous acquisition and after Dynamic flexural lever arm velocity compensation
The speed that is exported under grid tie of main inertial navigation system and posture information, and obtain speed and attitude error accordingly to constitute observation
Amount；
(4) on polar region naval vessel there are in the case where deflection deformation, according to the navigation mechanization under grid tie, in conjunction with grid navigation
Error equation establishes the system state equation and observational equation under grid tie using the matching way of " speed+posture "；
(5) using the observed quantity of state equation, observational equation and construction under the grid coordinate system of design, Kalman filtering is carried out
It resolves, estimates the posture misalignment of sub- inertial navigation system, the state estimation value of speed, complete Transfer Alignment.
2. a kind of model compensation method for polar region Transfer Alignment Dynamic flexural lever arm effect according to claim 1,
It is characterized by: lever arm model r involved in step (2)m, expression formula are as follows:
rm=r0+L2θ
In formula: rmIt is the Dynamic flexural lever arm under main inertial navigation carrier coordinate system m system；r0It is static fixed lever arm, L2It is Dynamic flexural
Lever arm penalty coefficient, θ are deflection deformation angles；
Related Dynamic flexural lever arm speedIts expression formula are as follows:
In formula:It is that sub- inertial navigation calculates attitude matrix,It is rotation angle of the main inertial navigation relative to inertial space under grid tie
Rate.
3. a kind of model compensation method for polar region Transfer Alignment Dynamic flexural lever arm effect according to claim 1,
It is characterized by: observed quantity Z involved in step (3), expression formula are as follows:
Z=[δ VGφm G]T
In formula: δ VGIt is the speed error value under grid tie；φm GIt is the measurement posture misalignment under grid tie.
4. a kind of model compensation method for polar region Transfer Alignment Dynamic flexural lever arm effect according to claim 1,
It is characterized by: state variable involved in step (4) is
Related system state equation are as follows:
In formula,It is acceleration constant value drift,It is gyro drift, φa GIt is installation error angle,It is accelerometer
Measurement,It is earth rate under grid tie,It is that grid tie is fast with respect to the rotation angle of geographic coordinate system under grid tie
Rate,It is measurement turning rate of the sub- inertial navigation carrier system downloading system with respect to grid tie；
Related observational equation are as follows:
Z=HX+v
In formula, Z is observed quantity, and v is observation noise, and H is observing matrix, is
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