CN108088464B - Deflection estimation method for correcting installation error of closed loop - Google Patents

Deflection estimation method for correcting installation error of closed loop Download PDF

Info

Publication number
CN108088464B
CN108088464B CN201611031747.9A CN201611031747A CN108088464B CN 108088464 B CN108088464 B CN 108088464B CN 201611031747 A CN201611031747 A CN 201611031747A CN 108088464 B CN108088464 B CN 108088464B
Authority
CN
China
Prior art keywords
angle
error
deflection
inertial
matrix
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.)
Active
Application number
CN201611031747.9A
Other languages
Chinese (zh)
Other versions
CN108088464A (en
Inventor
郭元江
李海军
孙伟
徐海刚
李群
刘冲
原润
裴玉锋
钟润伍
韩雪
刘璐
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing Automation Control Equipment Institute BACEI
Original Assignee
Beijing Automation Control Equipment Institute BACEI
Priority date (The priority date 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 date listed.)
Filing date
Publication date
Application filed by Beijing Automation Control Equipment Institute BACEI filed Critical Beijing Automation Control Equipment Institute BACEI
Priority to CN201611031747.9A priority Critical patent/CN108088464B/en
Publication of CN108088464A publication Critical patent/CN108088464A/en
Application granted granted Critical
Publication of CN108088464B publication Critical patent/CN108088464B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

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 starting-up 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

Landscapes

  • Engineering & Computer Science (AREA)
  • Radar, Positioning & Navigation (AREA)
  • Remote Sensing (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Automation & Control Theory (AREA)
  • Manufacturing & Machinery (AREA)
  • Other Investigation Or Analysis Of Materials By Electrical Means (AREA)
  • Navigation (AREA)

Abstract

The invention belongs to the technical field of inertial measurement, and particularly relates to a deflection estimation method for correcting installation errors in a closed loop. The method comprises nine steps, wherein the first step is to define a coordinate system, the second step is to carry out navigation operation based on an inertial system, the third step is to establish a flexural error model, the fourth step is to establish a system error equation, the fifth step is to establish a measurement equation, the sixth step is to calculate a measurement value, the seventh step is to calculate by utilizing a Kalman filtering equation, the eighth step is to carry out closed-loop correction on an installation error angle and a flexural deformation angle, and the ninth step is to repeat the closed-loop correction on the flexural deformation angle. Compared with the traditional method, the method can greatly improve the measurement precision and the estimation speed, enhance the attitude information measurement precision of different parts of the carrier platform and improve the use efficiency of related equipment.

Description

Deflection estimation method for correcting installation error of closed loop
Technical Field
The invention belongs to the technical field of inertial measurement, and particularly relates to a deflection estimation method for correcting installation errors in a closed loop.
Background
The dynamic deflection deformation of the carrier platform can influence the use of the sub inertial navigation equipment on main reference information, and influence the measurement accuracy of equipment installed on the carrier platforms such as ships, aircraft wings and ground vehicles, so that the deflection deformation characteristic of the carrier platform must be effectively measured and compensated. The deflection deformation is mainly due to the influence of external stress such as temperature change, external impact, air flow, self load and the like and the surrounding environment, the structure of the carrier platform can be subjected to dynamic deformation in different degrees, and the deflection deformation can be divided into static deflection and dynamic deflection.
The static deflection deformation is a deformation phenomenon caused by expansion and contraction with heat, contraction with cold, structural stress release and the like of the carrier platform in the moving process, is mainly influenced by factors such as load, temperature, sunlight and the like, has long change period and is relatively stable, and the quasi-static deflection deformation can be considered as a constant value in a short transfer alignment time. Titterton et al in uk have shown that changes in load on ships and structural ageing cause deformation of the ship, which can produce angular changes of about 1 ° in the course of a day under the action of sunlight.
The dynamic deflection changes constantly as a function of external conditions, such as motion of the carrier, impact, etc., i.e., the dynamic deflection is a function of time. The static deformation can be approximately regarded as a fixed installation error between the main inertial navigation system and the sub inertial navigation system, while the dynamic deflection deformation is a physical quantity which is superposed on the static deflection and changes along with time, and the specific forming reason of the dynamic deflection deformation is different according to the type of the carrier platform.
In an offshore platform, the dynamic deflection deformation of a ship is a phenomenon that the ship body is not a rigid body and generates deformation and structural vibration under the action of external force, external moment and wave impact. The high-frequency deflection deformation is mainly deformation of missile launcher and hull structures caused by sea wave impact and ship maneuvering and shaking. According to the obtained deformation data measured during navigation under the six-level sea condition, the method comprises the following steps: the deformation of the installation position of the inertial navigation system around the longitudinal rocking shaft is 0.05-0.08 degrees at the position of +/-7 m along the direction of the transverse shaft and +/-1.5 m along the direction of the longitudinal shaft, and the deformation around the transverse rocking shaft is 0.17-0.2 degrees; the deformation at the installation position of the radar antenna pedestal is 0.38 degrees, and the deformation at the installation positions of the front cannon and the rear cannon is 0.23 degrees.
On an airplane platform, the flexural deformation refers to the phenomenon that the wing is not a rigid body and is deformed and structurally vibrated under the action of external force, external moment, aerodynamic load and turbulence. The deflection deformation of the carrier in flight is mainly divided into two types, one is static deflection deformation, and the other is high-frequency deflection deformation. The static deflection deformation is a low-frequency wing deformation phenomenon caused by the change of the load of the airplane due to the mechanical operation or weapon release of the airplane; the high-frequency deflection deformation is mainly the structural vibration of the airplane at 5-10 Hz caused by turbulent flow.
Currently, the common deflection measurement methods are classified into two types, one is optical measurement, and the other is achieved by high-precision inertial measurement. The high-precision inertial measurement is mainly realized by Kalman filtering and by using the attitude difference of inertial measurement distributed at different positions. And the current method can not realize on-line deflection error compensation.
Therefore, the difference of attitude measurement information of different positions of the naval vessel is considered to be utilized, an error equation of attitude difference is established, the error equation comprises inertial navigation gyro drift, fixed installation error, a flexural deformation model and the like, the estimation of installation error and flexural deformation is realized through a Kalman filtering technology, and the measurement of high-precision attitude of different positions is realized.
Disclosure of Invention
According to the problems, the invention provides a deflection estimation method for correcting installation errors in a closed loop mode.
In order to realize the purpose, the invention adopts the technical scheme that:
a deflection estimation method for correcting installation errors in a closed loop mode comprises nine steps, wherein a first step is to define a coordinate system, a second step is to perform navigation operation based on an inertial system, a third step is to establish a deflection error model, a fourth step is to establish a system error equation, a fifth step is to establish a measurement equation, a sixth step is to calculate a measurement value, a seventh step is to calculate by using a Kalman filter equation, an eighth step is to perform closed loop correction of an installation error angle and a deflection deformation angle, and a ninth step is to perform repeated closed loop correction of the deflection deformation angle, the coordinate system is defined, and an auxiliary coordinate system needs to be introduced into an attitude matching calculation method:
inertial frame i1：t0B, performing inertial solidification on a moment sub-inertial navigation calculation carrier system b;
inertial frame i2：t0The m series inertia of the moment main inertia load system is solidified;
terrestrial coordinate system e: the x axis is along the direction of the earth axis, the y axis is along the intersection line of the equatorial plane and the Greenwich meridian plane, and the z axis, the x axis and the y axis form a right-hand coordinate system in the equatorial plane;
earth inertial coordinate system i: t is t0And (4) obtaining a time terrestrial coordinate system e through inertial solidification.
The second step is based on navigation operation of an inertial system, and a quaternion is set:
Q1＝[q0 q1 q2 q3]Tand an initial value Q1(0)＝[1 0 0 0]T。
The analytic formula of quaternion update is as follows:
Figure BDA0001158579540000031
wherein:
i is a 4 multiplied by 4 order identity matrix;
Figure BDA0001158579540000032
Figure BDA0001158579540000033
Figure BDA0001158579540000034
calculating the angular incremental component of the projectile body relative to the inertial system for the moments k to k +1, i.e.
The angular increment sensed by the gyro is transformed to the angular increment after the computational ballistic system, obtained by:
Figure BDA0001158579540000041
wherein T isnIn order to solve the cycle for the navigation,
Figure BDA0001158579540000042
is the angular velocity of the gyroscope in the x, y and z directions,
Figure BDA0001158579540000043
the updating calculation formula of the attitude matrix is as follows:
Figure BDA0001158579540000044
the deflection estimation method for correcting installation errors in a closed loop mode comprises the third step of establishing a deflection error model and setting a deflection deformation model of a carrier platform
Figure BDA0001158579540000045
Namely, the dynamic deformation angle of the child inertial navigation relative to the parent inertial navigation is as follows:
Figure BDA0001158579540000046
wherein theta isx，θy，θzThe dynamic deformation angle of the child inertial navigation relative to the parent inertial navigation in the x, y and z directions is shown.
Assuming a deflection deformation angular velocity variable of
Figure BDA0001158579540000047
μx，μy，μzFor flexural deformation angular velocities in the x, y, z directions, and assuming that the deformation processes of the three axes are independent of each other, then
Figure BDA0001158579540000048
The second order Markov equation of motion for the flexural deformation can be derived as
Figure BDA0001158579540000049
In the formula, betai＝2.146/τi，τiThe relative time constant representing the deformation of the carrier platform i (i ═ x, y, z); w is ax、wyAnd wzRepresenting a white noise sequence which is driving information of deflection angles, whose variances are Qrx、QryAnd QrzAnd Q isri＝4β2 iσ2 i；
In summary, the state equation of the carrier stage deflection deformation is:
Figure BDA0001158579540000051
the method for estimating the deflection of the closed-loop corrected installation error comprises the fourth step of establishing a system error equation, and selecting 16 error state variables as
X＝[Φ Φa ξ ω ε tA]T
Wherein:
Φ＝[φx φy φz]three axis attitude error angles for the inertial system X, Y, Z;
Φa＝[φax φay φaz]three axis misalignment angles for carrier system X, Y, Z;
ξ＝[θx θy θz]Tthree axis misalignment angular deflections for carrier system X, Y, Z;
ω＝[μx μy μz]Tangular velocities for three axis misalignment angular deflection deformation of carrier system X, Y, Z;
ε＝[εx εy εz]x, Y, Z three-axis gyro drift;
tA: a reference attitude delay time.
Written in the form of a state equation as follows
Figure BDA0001158579540000052
Figure BDA0001158579540000053
Figure BDA0001158579540000054
Wherein
Figure BDA0001158579540000061
T represents transposition; and B is a system noise vector. Wherein,
Figure BDA0001158579540000062
may be obtained by inertial system based navigation solutions.
The deflection estimation method for correcting the installation error of the closed loop comprises the fifth step of establishing a measurement equation which is as follows
Figure BDA0001158579540000063
Wherein,
Figure BDA0001158579540000064
outputting a triaxial angular rate for the gyroscope; the calculation of A and B requires the use of a matrix
Figure BDA0001158579540000065
Obtained by the following formula:
Figure BDA0001158579540000066
wherein t is0The specific calculation method of each matrix represents the initial filtering time is as follows:
Figure BDA0001158579540000067
wherein, γ0、ψ0And theta0Respectively is a rolling angle, a course angle and a pitch angle of the reference inertial navigation system at the initial moment,
Figure BDA0001158579540000068
wherein L is0And λ0Respectively, longitude and latitude of the initial time reference inertial navigation system.
Figure BDA0001158579540000069
Is a unit array, namely:
Figure BDA00011585795400000610
Figure BDA00011585795400000611
for a change matrix from an earth system to an inertial system, the calculation method comprises the following steps:
Figure BDA00011585795400000612
wherein, ω isieIs the earth rotation angular rate and t is time.
Figure BDA0001158579540000071
Wherein λ and L are longitude and latitude of the reference inertial navigation system, respectively.
Figure BDA0001158579540000072
Wherein gamma, psi and theta are respectively a roll angle, a course angle and a pitch angle of the reference inertial navigation system.
Order to
Figure BDA0001158579540000073
Then
Figure BDA0001158579540000074
A method for estimating the deflection of a closed loop correcting installation error, the sixth step is to calculate a measurement value,
Figure BDA0001158579540000075
a deflection estimation method for correcting installation errors in a closed loop, wherein the seventh step is calculated by using a Kalman filtering equation,
after the error model is established, a Kalman filtering method is selected as a parameter identification method, and the formula is as follows:
state one-step prediction
Figure BDA0001158579540000076
State estimation
Figure BDA0001158579540000077
Filter gain matrix
Figure BDA0001158579540000078
One-step prediction error variance matrix
Figure BDA0001158579540000081
Estimation error variance matrix
Pk＝[I-KkHk]Pk,k-1
Wherein,
Figure BDA0001158579540000082
in order to predict the value of the one-step state,
Figure BDA0001158579540000083
estimate the matrix for the state, phik,k-1For a state one-step transition matrix, HkFor measuring the matrix, ZkMeasurement of quantitative value, KkFor filtering the gain matrix, RkFor observing noise arrays, Pk,k-1For one-step prediction of error variance matrix, PkTo estimate the error variance matrix, Γk,k-1For system noise driven arrays, Qk-1Is a system noise matrix.
A deflection estimation method for correcting installation errors in a closed loop mode comprises the following steps of correcting an installation error angle and a deflection deformation angle in the closed loop mode in eight steps:
let gamma bem＝XA(3)，ψm＝XA(4)，θm＝XA(5) Then the installation error angle matrix
Figure BDA0001158579540000084
Is composed of
Figure BDA0001158579540000085
Let gamma bem＝XA(6)，ψm＝XA(7)，θm＝XA(8) Then deflection deformation matrix
Figure BDA0001158579540000086
Is composed of
Figure BDA0001158579540000087
By
Figure BDA0001158579540000088
Calculate new
Figure BDA0001158579540000089
Computing
Figure BDA00011585795400000810
To replace the original
Figure BDA00011585795400000811
A deflection estimation method for correcting installation errors in a closed loop mode is characterized in that the step nine is repeated for correcting a deflection deformation angle in a closed loop mode, the error angle and the deflection deformation angle are corrected in the step one to eight, but the error angle and the deflection deformation angle are not converged and cannot reach the required precision, so that the error angle and the deflection deformation angle need to be repeatedly corrected, the step one to eight are repeated until the estimation results of the error angle and the deflection deformation angle are converged, and the method is finished.
The invention has the beneficial effects that:
according to the method, the attitude information of a plurality of sets of inertial navigation systems is utilized, the estimation of the inertial navigation gyro drift, the fixed mounting error, the flexural deformation model and other error information can be realized through the Kalman filtering technology, the fixed mounting error and the flexural deformation are corrected in a closed loop mode, the measurement precision and the estimation speed can be greatly improved compared with the traditional method, the attitude information measurement precision of different parts of a carrier platform can be enhanced, and the use efficiency of related equipment is improved.
Detailed Description
The specific embodiment of the invention is as follows:
the method provided by the invention comprises nine steps, wherein the first step is to define a coordinate system, the second step is to perform navigation operation based on an inertial system, the third step is to establish a flexural error model, the fourth step is to establish a system error equation, the fifth step is to establish a measurement equation, the sixth step is to calculate a measurement value, the seventh step is to calculate by using a Kalman filtering equation, the eighth step is to perform closed-loop correction on an installation error angle and a flexural deformation angle, and the ninth step is to repeat the closed-loop correction on the flexural deformation angle.
Step one, defining a coordinate system
In the pose matching calculation method, an auxiliary coordinate system needs to be introduced:
(1) inertial frame i1：t0B, performing inertial solidification on a moment sub-inertial navigation calculation carrier system b;
(2) inertial frame i2：t0The m series inertia of the moment main inertia load system is solidified;
(3) terrestrial coordinate system e: the x axis is along the direction of the earth axis, the y axis is along the intersection line of the equatorial plane and the Greenwich meridian plane, and the z axis, the x axis and the y axis form a right-hand coordinate system in the equatorial plane;
(4) earth inertial coordinate system i: t is t0And (4) obtaining a time terrestrial coordinate system e through inertial solidification.
Step two, navigation operation based on inertia system
Setting quaternion:
Q1＝[q0 q1 q2 q3]Tand an initial value Q1(0)＝[1 0 0 0]T。
The analytic formula of quaternion update is as follows:
Figure BDA0001158579540000091
wherein:
i is a 4 multiplied by 4 order identity matrix;
Figure BDA0001158579540000101
Figure BDA0001158579540000102
Figure BDA0001158579540000103
calculating the angular incremental component of the projectile body relative to the inertial system for the moments k to k +1, i.e.
The angular increment sensed by the gyro is transformed to the angular increment after the computational ballistic system, obtained by:
Figure BDA0001158579540000104
wherein T isnIn order to solve the cycle for the navigation,
Figure BDA0001158579540000105
is the angular velocity of the gyroscope in the x, y and z directions,
Figure BDA0001158579540000106
the updating calculation formula of the attitude matrix is as follows:
Figure BDA0001158579540000107
step three, establishing a flexural error model
The establishment of the carrier platform flexural deformation model involves the professional knowledge in the aspects of complex elastic mechanics and the like, and the flexure cannot be simply ignored or the flexural deformation is taken as a constant condition. Causing deformation of the carrier platform
Figure BDA0001158579540000108
The reasons for (1) mainly include the effects of various factors such as impact, which is consistent with the condition of white noise excitation; in addition, carrier platform deflections, both inertial and restoring moments, can be considered as typical mass-spring systems. The second order Markov process modeling can adapt to the common flexural deformation and can ensure the considerable precision, therefore, the second order Markov process is adopted to build a mathematical model for the flexural deformation of the carrier platform.
Deflection of carrier platform
Figure BDA0001158579540000109
Namely, the dynamic deformation angle of the child inertial navigation relative to the parent inertial navigation is as follows:
Figure BDA0001158579540000111
wherein theta isx，θy，θzThe dynamic deformation angle of the child inertial navigation relative to the parent inertial navigation in the x, y and z directions is shown.
Assuming a deflection deformation angular velocity variable of
Figure BDA0001158579540000112
μx，μy，μzFor flexural deformation angular velocities in the x, y, z directions, and assuming that the deformation processes of the three axes are independent of each other, then
Figure BDA0001158579540000113
The second order Markov equation of motion for the flexural deformation can be derived as
Figure BDA0001158579540000114
In the formula, betai＝2.146/τi，τiThe relative time constant representing the deformation of the carrier platform i (i ═ x, y, z); w is ax、wyAnd wzRepresenting a white noise sequence which is driving information of deflection angles, whose variances are Qrx、QryAnd QrzAnd Q isri＝4β2 iσ2 i。
In summary, the state equation of the carrier stage deflection deformation is:
Figure BDA0001158579540000115
step four, establishing a system error equation
According to the error characteristics of the inertial navigation system, selecting 16 error state variables as
X＝[Φ Φa ξ ω ε tA]T
Wherein:
Φ＝[φx φy φz]three axis attitude error angles for the inertial system X, Y, Z;
Φa＝[φax φay φaz]three axis misalignment angles for carrier system X, Y, Z;
ξ＝[θx θy θz]Tthree axis misalignment angular deflections for carrier system X, Y, Z;
ω＝[μx μy μz]Tangular velocities for three axis misalignment angular deflection deformation of carrier system X, Y, Z;
ε＝[εx εy εz]x, Y, Z three-axis gyro drift;
tA: a reference attitude delay time.
Written in the form of a state equation as follows
Figure BDA0001158579540000121
Figure BDA0001158579540000122
Figure BDA0001158579540000123
Wherein
Figure BDA0001158579540000124
T represents transposition; and B is a system noise vector. Wherein,
Figure BDA0001158579540000125
may be obtained by inertial system based navigation solutions.
Step five, establishing a measurement equation
The measurement equation is as follows
Figure BDA0001158579540000126
Wherein,
Figure BDA0001158579540000127
outputting a triaxial angular rate for the gyroscope; the calculation of A and B requires the use of a matrix
Figure BDA0001158579540000128
Obtained by the following formula:
Figure BDA0001158579540000129
wherein t is0The specific calculation method of each matrix represents the initial filtering time is as follows:
Figure BDA0001158579540000131
wherein, γ0、ψ0And theta0Respectively is a rolling angle, a course angle and a pitch angle of the reference inertial navigation system at the initial moment,
Figure BDA0001158579540000132
wherein L is0And λ0Respectively, longitude and latitude of the initial time reference inertial navigation system.
Figure BDA0001158579540000133
Is a unit array, namely:
Figure BDA0001158579540000134
Figure BDA0001158579540000139
for a change matrix from an earth system to an inertial system, the calculation method comprises the following steps:
Figure BDA0001158579540000135
wherein, ω isieIs the earth rotation angular rate and t is time.
Figure BDA0001158579540000136
Wherein λ and L are longitude and latitude of the reference inertial navigation system, respectively.
Figure BDA0001158579540000137
Wherein gamma, psi and theta are respectively a roll angle, a course angle and a pitch angle of the reference inertial navigation system.
Order to
Figure BDA0001158579540000138
Then
Figure BDA0001158579540000141
Step six, calculating a measured value
Figure BDA0001158579540000142
Step seven, calculating by using a Kalman filtering equation
After the error model is established, a Kalman filtering method is selected as a parameter identification method, a Kalman filtering equation adopts a form in a document Kalman filtering and integrated navigation principle (first edition, edited by Qin Yongyuan and the like), and a specific formula is as follows:
state one-step prediction
Figure BDA0001158579540000143
State estimation
Figure BDA0001158579540000144
Filter gain matrix
Figure BDA0001158579540000145
One-step prediction error variance matrix
Figure BDA0001158579540000146
Estimation error variance matrix
Pk＝[I-KkHk]Pk,k-1
Wherein,
Figure BDA0001158579540000147
in order to predict the value of the one-step state,
Figure BDA0001158579540000148
estimate the matrix for the state, phik,k-1For a state one-step transition matrix, HkFor measuring the matrix, ZkMeasurement of quantitative value, KkFor filtering the gain matrix, RkFor observing noise arrays, Pk,k-1For one-step prediction of error variance matrix, PkTo estimate the error variance matrix, Γk,k-1For system noise driven arrays, Qk-1Is a system noise matrix.
Step eight, closed-loop correction of installation error angle and deflection deformation angle
The correction method comprises the following steps:
let gamma bem＝XA(3)，ψm＝XA(4)，θm＝XA(5) Then the installation error angle matrix
Figure BDA0001158579540000151
Is composed of
Figure BDA0001158579540000152
Let gamma bem＝XA(6)，ψm＝XA(7)，θm＝XA(8) Then deflection deformation matrix
Figure BDA0001158579540000153
Is composed of
Figure BDA0001158579540000154
By
Figure BDA0001158579540000155
Calculate new
Figure BDA0001158579540000156
Computing
Figure BDA0001158579540000157
To replace the original
Figure BDA0001158579540000158
Nine steps, repeated deflection deformation angle closed loop correction
Since the error angle and the deflection deformation angle are corrected in the above steps one to eight, but the error angle and the deflection deformation angle are not converged and cannot reach the required precision, the error angle and the deflection deformation angle need to be repeatedly corrected, so the above steps one to eight are repeated until the estimation results of the error angle and the deflection deformation angle are converged, and the method is ended.

Claims (6)

1. A deflection estimation method for correcting installation errors in a closed loop mode comprises nine steps, wherein a first step is to define a coordinate system, a second step is to perform navigation operation based on an inertial system, a third step is to establish a deflection error model, a fourth step is to establish a system error equation, a fifth step is to establish a measurement equation, a sixth step is to calculate a measurement value, a seventh step is to calculate by using a Kalman filtering equation, an eighth step is to perform closed loop correction of an installation error angle and a deflection deformation angle, and a ninth step is to perform repeated closed loop correction of the deflection deformation angle, and the method is characterized in that: the step defines a coordinate system, and in the attitude matching calculation method, an auxiliary coordinate system needs to be introduced: inertial frame i1：t0B, performing inertial solidification on a moment sub-inertial navigation calculation carrier system b; inertial frame i2：t0The m series inertia of the moment main inertia load system is solidified; terrestrial coordinate system e: the x axis is along the direction of the earth axis, the y axis is along the intersection line of the equatorial plane and the Greenwich meridian plane, and the z axis, the x axis and the y axis form a right-hand coordinate system in the equatorial plane; earth inertial coordinate system i: t is t0The e system of the earth coordinate system is obtained by inertial solidification at any moment;
secondly, navigation operation based on an inertial system;
setting quaternion:
Q1＝[q0 q1 q2 q3]Tand an initial value Q1(0)＝[1 0 0 0]T；
The analytic formula of quaternion update is as follows:
Figure FDA0002998592560000011
wherein:
i is a 4 multiplied by 4 order identity matrix;
Figure FDA0002998592560000012
Figure FDA0002998592560000013
calculating the angular increment component of the elastic system relative to the inertia system for the time k to k +1, namely converting the angular increment sensed by the gyro into the angular increment after the elastic system is calculated, and obtaining the following formula:
Figure FDA0002998592560000021
wherein T isnIn order to solve the cycle for the navigation,
Figure FDA0002998592560000022
is the angular velocity of the gyroscope in the x, y and z directions,
Figure FDA0002998592560000023
the updating calculation formula of the attitude matrix is as follows:
Figure FDA0002998592560000024
thirdly, establishing a flexural error model;
deflection of carrier platform
Figure FDA0002998592560000025
Namely, the dynamic deformation angle of the child inertial navigation relative to the parent inertial navigation is as follows:
Figure FDA0002998592560000026
wherein theta isx，θy，θzThe dynamic deformation angle of the child inertial navigation relative to the parent inertial navigation in the x, y and z directions is obtained;
assuming a deflection deformation angular velocity variable of
Figure FDA0002998592560000027
μx，μy，μzIs the angle of deflection in the x, y, z directionsSpeed, provided that the deformation processes of the three axes are independent of each other, then
Figure FDA0002998592560000028
The second order Markov equation of motion for the flexural deformation can be derived as
Figure FDA0002998592560000029
In the formula, betai＝2.146/τi，τiThe relative time constant representing the deformation of the carrier platform i, i ═ x, y, z; w is ax、wyAnd wzRepresenting a white noise sequence which is driving information of deflection angles, whose variances are Qrx、QryAnd QrzAnd Q isri＝4β2 iσ2 i；
In summary, the state equation of the carrier stage deflection deformation is:
Figure FDA0002998592560000031
establishing a system error equation;
according to the error characteristics of the inertial navigation system, selecting 16 error state variables as
X＝[Φ Φa ξ ω ε tA]T
Wherein:
Φ＝[φx φy φz]three axis attitude error angles for the inertial system X, Y, Z;
Φa＝[φax φay φaz]three axis misalignment angles for carrier system X, Y, Z;
ξ＝[θx θy θz]Tis a vector system X, Y, Z IIIDeflection deformation of an installation error angle of each shaft;
ω＝[μx μy μz]Tangular velocities for three axis misalignment angular deflection deformation of carrier system X, Y, Z;
ε＝[εx εy εz]x, Y, Z three-axis gyro drift;
tA: a reference attitude delay time;
written in the form of a state equation:
Figure FDA0002998592560000032
Figure FDA0002998592560000033
Figure FDA0002998592560000034
wherein
Figure FDA0002998592560000035
T represents transposition; b is a system noise vector; wherein,
Figure FDA0002998592560000036
obtained by inertial system based navigation solution.
2. A closed-loop, installation error corrected, deflection estimation method as set forth in claim 1, wherein: step five, establishing a measurement equation;
the measurement equation is as follows:
Figure FDA0002998592560000041
wherein,
Figure FDA0002998592560000042
outputting a triaxial angular rate for the gyroscope; the calculation of A and B requires the use of a matrix
Figure FDA0002998592560000043
Obtained by the following formula:
Figure FDA0002998592560000044
wherein t is0The specific calculation method of each matrix represents the initial filtering time is as follows:
Figure FDA0002998592560000045
wherein, γ0、ψ0And theta0Respectively is a rolling angle, a course angle and a pitch angle of the reference inertial navigation system at the initial moment,
Figure FDA0002998592560000046
wherein L is0And λ0Respectively representing the longitude and the latitude of the initial time reference inertial navigation system;
Figure FDA0002998592560000047
is a unit array, namely:
Figure FDA0002998592560000048
Figure FDA0002998592560000049
for a matrix of changes from the earth system to the inertial systemThe calculation method comprises the following steps:
Figure FDA00029985925600000410
wherein, ω isieThe rotation angular rate of the earth, and t is time;
Figure FDA0002998592560000051
wherein, λ and L are respectively longitude and latitude of the reference inertial navigation system;
Figure FDA0002998592560000052
wherein gamma, psi and theta are respectively a rolling angle, a course angle and a pitch angle of the reference inertial navigation system;
order to
Figure FDA0002998592560000053
Then
Figure FDA0002998592560000054
3. A closed-loop, installation error corrected, deflection estimation method as set forth in claim 2, wherein: sixthly, calculating a measurement value
Figure FDA0002998592560000055
4. A closed-loop, installation error corrected, deflection estimation method as set forth in claim 1, wherein: seventhly, calculating by using a Kalman filtering equation;
after the error model is established, a Kalman filtering method is selected as a parameter identification method, and the specific formula is as follows:
state one-step prediction
Figure FDA0002998592560000056
State estimation
Figure FDA0002998592560000057
Filter gain matrix
Figure FDA0002998592560000061
One-step prediction error variance matrix
Figure FDA0002998592560000062
Estimation error variance matrix
Pk＝[I-KkHk]Pk,k-1
Wherein,
Figure FDA0002998592560000063
in order to predict the value of the one-step state,
Figure FDA0002998592560000064
estimate the matrix for the state, phik,k-1For a state one-step transition matrix, HkFor measuring the matrix, ZkMeasurement of quantitative value, KkFor filtering the gain matrix, RkFor observing noise arrays, Pk,k-1For one-step prediction of error variance matrix, PkTo estimate the error variance matrix, Γk,k-1For system noise driven arrays, Qk-1Is a system noise matrix.
5. A closed-loop, installation error corrected, deflection estimation method as set forth in claim 2, wherein: step eight, correcting the installation error angle and the deflection deformation angle in a closed loop manner;
the correction method comprises the following steps:
let gamma bem＝X(3)，ψm＝X(4)，θmX (5), then the error angle matrix is installed
Figure FDA0002998592560000065
Is composed of
Figure FDA0002998592560000066
Let gamma bem＝X(6)，ψm＝X(7)，θmX (8), then flexural deformation matrix
Figure FDA0002998592560000067
Is composed of
Figure FDA0002998592560000068
By
Figure FDA0002998592560000069
Calculate new
Figure FDA00029985925600000610
Computing
Figure FDA00029985925600000611
To replace the original
Figure FDA00029985925600000612
6. A closed-loop, installation error corrected, deflection estimation method as set forth in claim 1, wherein: the step nine is repeated for the deflection deformation angle closed loop correction, and since the error angle and the deflection deformation angle are corrected in the steps one to eight, but the error angle and the deflection deformation angle are not converged and cannot reach the required precision, the error angle and the deflection deformation angle are required to be repeatedly corrected, and the steps one to eight are repeated until the estimation results of the error angle and the deflection deformation angle are converged.
CN201611031747.9A 2016-11-22 2016-11-22 Deflection estimation method for correcting installation error of closed loop Active CN108088464B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201611031747.9A CN108088464B (en) 2016-11-22 2016-11-22 Deflection estimation method for correcting installation error of closed loop

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201611031747.9A CN108088464B (en) 2016-11-22 2016-11-22 Deflection estimation method for correcting installation error of closed loop

Publications (2)

Publication Number Publication Date
CN108088464A CN108088464A (en) 2018-05-29
CN108088464B true CN108088464B (en) 2021-07-13

Family

ID=62169638

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201611031747.9A Active CN108088464B (en) 2016-11-22 2016-11-22 Deflection estimation method for correcting installation error of closed loop

Country Status (1)

Country Link
CN (1) CN108088464B (en)

Families Citing this family (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111623770B (en) * 2020-04-28 2022-06-03 北京航天控制仪器研究所 Method for improving inertial guidance precision based on speed error open-loop correction

Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH0989585A (en) * 1995-09-22 1997-04-04 Tokimec Inc Inertial navigation system
CN104567930A (en) * 2014-12-30 2015-04-29 南京理工大学 Transfer alignment method capable of estimating and compensating wing deflection deformation
CN104977001A (en) * 2014-04-02 2015-10-14 北京自动化控制设备研究所 Relative navigation method applied to individual indoor navigation system

Patent Citations (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPH0989585A (en) * 1995-09-22 1997-04-04 Tokimec Inc Inertial navigation system
CN104977001A (en) * 2014-04-02 2015-10-14 北京自动化控制设备研究所 Relative navigation method applied to individual indoor navigation system
CN104567930A (en) * 2014-12-30 2015-04-29 南京理工大学 Transfer alignment method capable of estimating and compensating wing deflection deformation

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
"舰载武器SINS速度+姿态匹配传递对准建模与仿真";申亮亮 等;《鱼雷技术》;20081031;第16卷(第5期);正文第22-27页 *

Also Published As

Publication number Publication date
CN108088464A (en) 2018-05-29

Similar Documents

Publication Publication Date Title
CN104764467B (en) Re-entry space vehicle inertial sensor errors online adaptive scaling method
CN104567930A (en) Transfer alignment method capable of estimating and compensating wing deflection deformation
CN109724624B (en) Airborne self-adaptive transfer alignment method suitable for wing deflection deformation
CN109683628B (en) Spacecraft relative position control method based on finite time distributed speed observer
CN108613674A (en) A kind of attitude error suppressing method based on adaptive differential Evolutionary BP neural network
CN109211230B (en) Method for estimating shell attitude and accelerometer constant error based on Newton iteration method
Xiong et al. Dynamic calibration method for SINS lever-arm effect for HCVs
CN107063300B (en) Inversion-based disturbance estimation method in underwater navigation system dynamic model
CN109211231A (en) A kind of shell Attitude estimation method based on Newton iteration method
CN107356246A (en) Hull miniature deformation measuring method based on inertial measurement cluster
CN108088464B (en) Deflection estimation method for correcting installation error of closed loop
CN105300407B (en) A kind of marine dynamic starting method for single axis modulation laser gyro inertial navigation system
CN111220182B (en) Rocket transfer alignment method and system
CN109211232A (en) A kind of shell Attitude estimation method based on least squares filtering
CN117452961A (en) Aircraft guidance control integrated control method based on backstepping-high-order sliding mode
He et al. A model-free hull deformation measurement method based on attitude quaternion matching
CN114061575B (en) Missile attitude angle precise alignment method and system under condition of large misalignment angle
CN109737960A (en) Deformation of hull measurement method based on velocity plus angular rate matching
CN114923483A (en) DVL/SINS integrated navigation method based on state transformation Kalman filtering
Xiong et al. Online calibration research on the lever arm effect for the hypersonic vehicle
CN113806950A (en) Strapdown inertial navigation system simulation method based on submersible vehicle space motion model
Jarrell et al. Aircraft attitude, position, and velocity determination using sensor fusion
Viswanathan et al. Mechatronics architecture of smartphone-based spacecraft adcs using vscmg actuators
CN102508819A (en) Angular-speed-based quaternion Legendre approximate output method during extreme flying of aircraft
Cho et al. A two-stage initial alignment technique for underwater vehicles dropped from a mother ship

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
GR01 Patent grant
GR01 Patent grant