CN113418535A - Rotary inertial navigation system multi-position alignment method based on two-dimensional inner lever arm estimation - Google Patents

Rotary inertial navigation system multi-position alignment method based on two-dimensional inner lever arm estimation Download PDF

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CN113418535A
CN113418535A CN202110657601.XA CN202110657601A CN113418535A CN 113418535 A CN113418535 A CN 113418535A CN 202110657601 A CN202110657601 A CN 202110657601A CN 113418535 A CN113418535 A CN 113418535A
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Prior art keywords
lever arm
inner lever
measurement
formula
error
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付强文
沈晴晴
魏栋
李四海
严恭敏
清华
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Northwestern Polytechnical University
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Northwestern Polytechnical University
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    • 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
    • G01C21/183—Compensation of inertial measurements, e.g. for temperature effects

Abstract

The invention discloses a multi-position alignment method of a rotary inertial navigation system based on two-dimensional inner lever arm estimation, which defines the sensitive center of an inertial measurement unit in the measurement center of one horizontal accelerometer, reduces the error of the inner lever arm generating influence to 2 dimensions, and synchronously carries out online estimation through a fine alignment Kalman filter, thereby reducing the algorithm complexity and improving the estimation precision of the inner lever arm on the basis of ensuring the alignment precision and rapidity.

Description

Rotary inertial navigation system multi-position alignment method based on two-dimensional inner lever arm estimation
Technical Field
The invention belongs to the technical field of inertial navigation, and particularly relates to a multi-position alignment method of a rotary inertial navigation system.
Background
The rotary inertial navigation system can inhibit the influence of the zero offset error of the sensor through continuous rotation around an azimuth axis or multi-position rotation and stop, and can improve the self-alignment precision under the condition of certain device precision. Limited by the size and installation conditions of the sensor, the measurement centers of the three-axis accelerometers in the Inertial Measurement Unit (IMU) cannot coincide to one point, so that an inner rod-arm error is formed, and the initial alignment accuracy of the rotary inertial navigation system is seriously influenced if the error is not compensated.
The document "initial alignment of a rotary strapdown inertial navigation system based on size effect on-line compensation, war of military science, 2020, Vol41(10), p 2016-2022" discloses a method for estimating the inner lever arm in real time during continuous rotational alignment. According to the method, the IMU sensitive center is defined in the rotation center of the indexing mechanism, so that a 4-dimensional inner rod arm model is established and online estimation is carried out, the influence of the error of the inner rod arm is effectively compensated, and the rotation alignment precision is improved. The method disclosed by the document is suitable for continuous rotation alignment, but the 4-dimensional inner lever arm cannot be independently observed when the method is applied to multi-position alignment, the algorithm redundancy and complexity are high, and the lever arm separation precision is reduced.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention provides a multi-position alignment method of a rotary inertial navigation system based on two-dimensional inner lever arm estimation, which defines the sensitive center of an inertial measurement unit in the measurement center of one horizontal accelerometer, reduces the error of the inner lever arm generating influence to 2 dimensions, and synchronously carries out online estimation through a fine alignment Kalman filter, thereby reducing the algorithm complexity and improving the estimation precision of the inner lever arm on the basis of ensuring the alignment precision and rapidity.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps:
step 1: defining an IMU coordinate system b, fixedly connecting with the inertial measurement unit and pointing to the right front upper direction; defining a navigation coordinate system n pointing to the northeast direction of the local geographic position; defining IMU sensitivity center at AxAnd (3) a two-dimensional inner lever arm specific force model is established after the second-order small quantity is ignored in the measurement center of the axis accelerometer:
Figure BDA0003113900810000011
in the formula
Figure BDA0003113900810000012
Specific force measurement error, r, caused by the inner lever armYIs a two-dimensional inner rod arm vector, W is an angular rate matrix
Figure BDA0003113900810000021
Figure BDA0003113900810000022
In the formula of omegazIs zbThe angular rate of the axis gyro is,
Figure BDA0003113900810000023
and
Figure BDA0003113900810000024
respectively represent AyInner lever arm r of axial accelerometerYAt xbAxis and ybA component of the axis;
step 2: establishing error state vectors of multi-position fine alignment:
Figure BDA0003113900810000025
and simplifying error equations
Figure BDA0003113900810000026
Wherein X is a 14-dimensional error state; phi is anAnd δ vnObtaining n-series platform misalignment angle and speed error for navigation calculation; epsilonbAnd
Figure BDA0003113900810000027
the gyroscope drift and the accelerometer zero offset are in a b system;
Figure BDA0003113900810000028
is an attitude transformation matrix from b to n;
Figure BDA0003113900810000029
and gnThe rotation angular rate and the gravity acceleration vector of the earth under n series;
and step 3: establishing a state equation of the multi-position alignment filter:
Figure BDA00031139008100000210
and the measurement equation:
Z＝δvn＝[03×3 I3×3 03×3 03×3 03×2]X+wv (7)
in the formula
Figure BDA00031139008100000211
And
Figure BDA00031139008100000212
for gyroscopic and accelerometer noise, Z is the velocity measurement, wvMeasuring noise for the velocity;
and 4, step 4: in the multi-position alignment process, the filter time is updated according to the formula (6) in the whole process, and the filter measurement is updated according to the formula (7) only when the indexing mechanism stops.
The invention has the following beneficial effects:
according to the method, the sensitive center of the inertial measurement unit is defined in the measurement center of the horizontal accelerometer, so that the error of the inner rod arm is reduced to 2 dimensions, the algorithm complexity of a filter can be reduced on the basis of ensuring the alignment precision, and the estimation precision of the inner rod arm is improved; and the filtering updating is carried out in the stop time period of the indexing mechanism, so that the initial alignment environment is improved, and the convergence speed is accelerated.
Drawings
Fig. 1 is a schematic view of an inner lever arm according to the present invention.
Fig. 2 is a multi-position alignment rotation strategy provided by an embodiment of the present invention.
FIG. 3 is the difference between the alignment results of the method of the present invention and the background method.
Fig. 4 shows the results of the four-dimensional inner lever arm estimation obtained by the background method.
FIG. 5 is a two-dimensional inner boom arm estimation obtained by the method of the present invention.
Detailed Description
The invention is further illustrated with reference to the following figures and examples.
A multi-position alignment method of a rotary inertial navigation system based on two-dimensional inner lever arm estimation comprises the following steps:
step 1: defining an IMU coordinate system b, fixedly connecting with the inertial measurement unit and pointing to the right front upper direction; defining a navigation coordinate system n pointing to the northeast direction of the local geographic position; referring to FIG. 1, the IMU sensitivity center is defined at AxMeasurement center of axial accelerometer due to IMU only around z during multi-position alignmentbThe shaft stops rotating, a two-dimensional inner lever arm specific force model is built after a second-order small quantity is ignored:
Figure BDA0003113900810000031
in the formula
Figure BDA0003113900810000032
Specific force measurement error, r, caused by the inner lever armYIs a two-dimensional inner rod arm vector, W is an angular rate matrix
Figure BDA0003113900810000033
Figure BDA0003113900810000034
In the formula of omegazIs zbThe angular rate of the axis gyro is,
Figure BDA0003113900810000035
and
Figure BDA0003113900810000036
respectively represent AyInner lever arm r of axial accelerometerYAt xbAxis and ybA component of the axis;
step 2: establishing an error state and an error equation;
after a two-dimensional inner lever arm is added, an error state vector of multi-position fine alignment is established:
Figure BDA0003113900810000037
and simplifying error equations
Figure BDA0003113900810000041
Wherein X is a 14-dimensional error state; phi is anAnd δ vnObtaining n-series platform misalignment angle and speed error for navigation calculation; epsilonbAnd
Figure BDA0003113900810000042
the gyroscope drift and the accelerometer zero offset are in a b system;
Figure BDA0003113900810000043
is an attitude transformation matrix from b to n;
Figure BDA0003113900810000044
and gnThe rotation angular rate and the gravity acceleration vector of the earth under n series;
and step 3: establishing a state equation of the multi-position alignment filter:
Figure BDA0003113900810000045
and the measurement equation:
Z＝δvn＝[03×3 I3×3 03×3 03×3 03×2]X+wv (7)
in the formula
Figure BDA0003113900810000046
And
Figure BDA0003113900810000047
for gyroscopic and accelerometer noise, Z is the velocity measurement, wvMeasuring noise for the velocity;
and 4, step 4: in the multi-position alignment process, the filter time is updated according to the formula (6) in the whole process, and the filter measurement is updated according to the formula (7) only when the indexing mechanism stops.
The specific embodiment is as follows:
in this embodiment, a three-axis rotational inertial navigation system is adopted, in which the fiber-optic gyroscope drift is 0.002 °/h, and the random walk coefficient is
Figure BDA0003113900810000048
The accelerometer accuracy is 20 μ g. The inertial navigation system was mounted in a fixed position in a laboratory environment and 8 multi-position alignment tests were performed.
FIG. 2 is a graph of the angular rotation rate and angle of the azimuth frame during multi-position alignment, showing an azimuth frame angular rotation rate of 20/s, a total alignment time of 110s, and a dwell of 30s at each of the 0, 180, and 0 angular positions.
FIG. 3 is a graph of the difference between the alignment results obtained by the method of the present invention and the background method, showing a pitch angle difference δ θ within 0.0035 ", a roll angle difference δ γ within 0.003", and a heading angle difference δ ψ within 1 ".
FIG. 4 is an estimate of the 4-dimensional inner lever arm obtained from the background method, showing repeatability on the order of 1mm (1 σ) for the 8 alignment trial lever arm estimates.
FIG. 5 is an estimated curve of a 2-dimensional inner lever arm obtained by the method of the present invention, showing that the repeatability of the 8 alignment test lever arm estimation is on the order of 0.1mm (1 σ).
The effect of the embodiment shows that the method can obtain the alignment precision equivalent to that of the background method, the maximum angle difference value of the 8-time alignment result is not more than 1', and the method reduces the dimension of the inner rod arm from 4 dimensions of the background method to 2 dimensions, thereby reducing the complexity of the filter algorithm and reducing the calculated amount. On the other hand, the redundancy of the inner rod arm definition in the multi-position alignment of the background method is eliminated, the estimation precision of the inner rod arm is improved, and the repeatability of the inner rod arm estimation for 8 times is improved from 1mm (1 sigma) to 0.1mm (1 sigma).

Claims (1)

1. A rotational inertial navigation system multi-position alignment method based on two-dimensional inner lever arm estimation is characterized by comprising the following steps:
step 1: defining an IMU coordinate system b, fixedly connecting with the inertial measurement unit and pointing to the right front upper direction; defining a navigation coordinate system n pointing to the northeast direction of the local geographic position; defining IMU sensitivity center at AxAnd (3) a two-dimensional inner lever arm specific force model is established after the second-order small quantity is ignored in the measurement center of the axis accelerometer:
Figure FDA0003113900800000011
in the formula
Figure FDA0003113900800000012
Specific force measurement error, r, caused by the inner lever armYIs a two-dimensional inner rod arm vector, W is an angular rate matrix
Figure FDA0003113900800000013
Figure FDA0003113900800000014
In the formula of omegazIs zbThe angular rate of the axis gyro is,
Figure FDA0003113900800000015
and
Figure FDA0003113900800000016
respectively represent AyInner lever arm r of axial accelerometerYAt xbAxis and ybA component of the axis;
step 2: establishing error state vectors of multi-position fine alignment:
Figure FDA00031139008000000111
and simplifying error equations
Figure FDA0003113900800000017
Wherein X is a 14-dimensional error state; phi is anAnd δ vnObtaining n-series platform misalignment angle and speed error for navigation calculation; epsilonbAnd
Figure FDA00031139008000000112
the gyroscope drift and the accelerometer zero offset are in a b system;
Figure FDA0003113900800000018
is an attitude transformation matrix from b to n;
Figure FDA0003113900800000019
and gnThe rotation angular rate and the gravity acceleration vector of the earth under n series;
and step 3: establishing a state equation of the multi-position alignment filter:
Figure FDA00031139008000000110
and the measurement equation:
Z＝δvn＝[03×3 I3×3 03×3 03×3 03×2]X+wv (7)
in the formula
Figure FDA0003113900800000021
And
Figure FDA0003113900800000022
for gyroscopic and accelerometer noise, Z is the velocity measurement, wvMeasuring noise for the velocity;
and 4, step 4: in the multi-position alignment process, the filter time is updated according to the formula (6) in the whole process, and the filter measurement is updated according to the formula (7) only when the indexing mechanism stops.
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Citations (7)

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* Cited by examiner, † Cited by third party
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GB9224847D0 (en) * 1992-11-27 1993-01-13 Gec Ferranti Defence Syst Minimised compensation for accelerometer offsets
CN103363989A (en) * 2012-04-09 2013-10-23 北京自动化控制设备研究所 Estimation and error compensation method for inner lever arm of strapdown inertial navigation system
CN104019828A (en) * 2014-05-12 2014-09-03 南京航空航天大学 On-line calibration method for lever arm effect error of inertial navigation system in high dynamic environment
CN106052715A (en) * 2016-05-23 2016-10-26 西北工业大学 Backtracking type self-aligning method of single-axial rotation strapdown inertial navigation system
CN106482746A (en) * 2016-11-25 2017-03-08 北京航空航天大学 In a kind of accelerometer for hybrid inertial navigation system, lever arm is demarcated and compensation method
CN110940357A (en) * 2019-12-20 2020-03-31 湖北航天技术研究院总体设计所 Inner rod arm calibration method for self-alignment of rotary inertial navigation single shaft
CN112595350A (en) * 2020-12-31 2021-04-02 福建星海通信科技有限公司 Automatic calibration method and terminal for inertial navigation system

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QIANGWEN FU ET.AL: "Automatic Estimation of Dynamic Lever Arms for a Position and Orientation System", 《SENSORS》, vol. 18, no. 12, 31 December 2018 (2018-12-31), pages 1 - 19 *
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