CN114966115A - Acceleration calibration method based on missile-borne inertia/starlight combined navigation - Google Patents

Acceleration calibration method based on missile-borne inertia/starlight combined navigation Download PDF

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CN114966115A
CN114966115A CN202210611092.1A CN202210611092A CN114966115A CN 114966115 A CN114966115 A CN 114966115A CN 202210611092 A CN202210611092 A CN 202210611092A CN 114966115 A CN114966115 A CN 114966115A
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attitude
navigation
star
matrix
accelerometer
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CN114966115B (en
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杨艳强
田一卓
李天琦
张春熹
宋凝芳
田龙杰
李皓阳
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Beihang University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01P—MEASURING LINEAR OR ANGULAR SPEED, ACCELERATION, DECELERATION, OR SHOCK; INDICATING PRESENCE, ABSENCE, OR DIRECTION, OF MOVEMENT
    • G01P21/00—Testing or calibrating of apparatus or devices covered by the preceding groups
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
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Abstract

The invention discloses an acceleration calibration method based on missile-borne inertia/starlight combined navigation, which comprises the following steps of: acquiring an initial attitude of a carrier before transmission; establishing a posture updating model based on inertial navigation; measuring the star observation, and recording fixed star coordinates observed by the star sensor and coordinate data of a geocentric equatorial coordinate system stored in a missile-borne navigation star library to obtain star observation data; constructing a comprehensive observation model according to the attitude updating model and the star observation measurement data; calculating the current attitude error according to the comprehensive observation model; calculating an initial attitude error provided by an accelerometer in the current attitude error through a Kalman filtering algorithm; and calculating a horizontal addition table error according to the initial attitude error, and correcting the accelerometer.

Description

Acceleration calibration method based on missile-borne inertia/starlight combined navigation
Technical Field
The invention relates to the technical field of integrated navigation, in particular to an acceleration calibration method based on missile-borne inertia/starlight integrated navigation.
Background
The starlight/inertia combined navigation is a typical combined navigation mode, combines starlight navigation and inertia navigation, makes good use of advantages and avoids disadvantages, complements advantages, corrects an inertial navigation system by using high-precision attitude information provided by a star sensor, compensates drift of an inertial device, has the advantages of high precision, full autonomy, light weight, small size, no outward radiation of energy, no external interference and the like, and shows extremely strong vitality and wide application prospect.
Generally, in inertial navigation, a gyroscope tracks to obtain rotation information of a carrier relative to an inertial coordinate system, an accelerometer provides initial attitude required in the tracking process, the rotation information is used for determining the orientation of the accelerometer at each moment, and then the acceleration can be decomposed into the inertial coordinate system to obtain information such as speed, position and the like of the carrier through integration. In missile-borne inertial/starlight combined navigation applications, initial attitude information is typically obtained by external light aiming. Therefore, when the high-precision attitude information provided by the star sensor corrects the inertial navigation system and compensates the drift of the inertial device, the horizontal accelerometer cannot be calibrated, and the performance of the accelerometer is prevented from being improved.
Therefore, how to provide an acceleration calibration method based on missile-borne inertia/starlight combined navigation is a problem that needs to be solved urgently by those skilled in the art.
Disclosure of Invention
In view of this, the invention provides an acceleration calibration method based on missile-borne inertia/starlight combined navigation, which can calibrate a horizontal accelerometer, thereby improving the performance of the accelerometer.
In order to achieve the purpose, the invention adopts the following technical scheme:
an acceleration calibration method based on missile-borne inertia/starlight combined navigation comprises the following steps:
acquiring an initial attitude matrix before carrier emission;
performing inertial navigation based on the initial attitude matrix and a preset attitude updating model to obtain a navigation attitude matrix;
carrying out star observation measurement on the navigation attitude matrix to obtain a star observation attitude matrix;
correcting the navigation attitude matrix through the star viewing attitude matrix to obtain a corrected attitude matrix;
calculating an attitude error according to the corrected attitude matrix; calculating an initial attitude error provided by an accelerometer in the attitude errors by adopting a Kalman filtering algorithm; and calculating a horizontal addition table error according to the initial attitude error, and calibrating the accelerometer.
Further, an initial attitude matrix before carrier emission is obtained, including,
acquiring output data of a gyroscope and an accelerometer in a navigation self-alignment process;
and performing double-vector attitude determination according to the mean value of the gyroscope and accelerometer data to obtain an initial attitude matrix.
Further, the gyroscope and the accelerometer output data in the navigation self-alignment process, which comprises:
the direction of the x axis:
Figure BDA0003672008990000021
y-axis direction:
Figure BDA0003672008990000022
the z-axis direction:
Figure BDA0003672008990000023
wherein ,
Figure BDA0003672008990000024
and
Figure BDA0003672008990000025
representing the three-axis output values of the gyro and accelerometer, respectively, i.e. the angular velocity and acceleration of the carrier system relative to the inertial system.
Further, the dual-vector attitude determination calculation formula is as follows:
Figure BDA0003672008990000026
wherein ,
Figure BDA0003672008990000027
Figure BDA0003672008990000028
Figure BDA0003672008990000029
Figure BDA00036720089900000210
and
Figure BDA00036720089900000211
expressed as earth gravity vector estimation value and earth rotation vector estimation value, T 0 Indicating a self-alignment start time; t is a unit of 1 Indicating the moment when the self-alignment ends.
Further, the posture updating model is as follows:
Figure BDA0003672008990000031
Figure BDA0003672008990000032
wherein ,
Figure BDA0003672008990000033
representing a true attitude matrix at a kth time;
Figure BDA0003672008990000034
to represent
Figure BDA0003672008990000035
A derivative of (a);
Figure BDA0003672008990000036
the measured values provided for the gyro at time k,
Figure BDA0003672008990000037
is the attitude matrix at time (k-1),
Figure BDA0003672008990000038
is the projection of the rotational angular velocity of the earth system relative to the inertial system in the navigation system at the moment (k-1),
Figure BDA0003672008990000039
and (k-1) projecting the rotational angular velocity of the navigation system relative to the earth system in the navigation system at the moment.
Further, the observing the star measurement on the navigation attitude matrix to obtain an observing star attitude matrix includes:
recording fixed star coordinates observed by the star sensor and coordinate data of a geocentric equatorial coordinate system stored in a missile-borne navigation satellite library:
Figure BDA00036720089900000310
calculating matrix performance indexes by adopting a least square method according to the star observation data to obtain an optimal attitude matrix
Figure BDA00036720089900000311
Figure BDA00036720089900000312
wherein ,J* Represents a performance index, λ i Is a weighting coefficient;
and calculating a star viewing attitude matrix through matrix transmission.
Further, the calculation model for calculating the attitude error is as follows:
Figure BDA00036720089900000313
ε b ＝[ε x ε y ε z ] T ，
Figure BDA00036720089900000314
wherein Z (t) is an attitude error;
Figure BDA00036720089900000315
a navigation attitude matrix during the star observation measurement;
Figure BDA00036720089900000316
and
Figure BDA00036720089900000317
three-axis attitude error expressed as a star viewing time; epsilon x 、ε y and εz Gyro drift, expressed as three axes when looking at the star measurement;
Figure BDA00036720089900000318
and
Figure BDA00036720089900000319
expressed as the three-axis initial attitude error.
Further, the calculating an initial attitude error provided by an accelerometer in the attitude error by using a kalman filtering algorithm includes:
constructing a combined system state equation:
Z(t)＝XH
wherein ,
Figure BDA00036720089900000320
Figure BDA0003672008990000041
m navigation attitude matrixes obtained according to starlight observation
Figure BDA0003672008990000042
And combining the system states Z (t) to calculate an initial attitude error matrix
Figure BDA0003672008990000043
Figure BDA0003672008990000044
Further, the calculation formula of the calculation level plus the table error is as follows:
Figure BDA0003672008990000045
wherein ,▽N Represents the equivalent northbound measurement error of the accelerometer + E Representing the equivalent east measurement error of the accelerometer and g representing the earth gravitational acceleration.
The invention has the beneficial effects that:
according to the technical scheme, compared with the prior art, the invention discloses an acceleration calibration method based on missile-borne inertia/starlight combined navigation, the initial attitude is confirmed through the accelerometer self-alignment process, the initial attitude error is calculated by combining with star observation measurement, and the calibration of the accelerometer in the horizontal direction is realized.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the provided drawings without creative efforts.
Fig. 1 is a schematic diagram of an acceleration calibration method based on missile-borne inertia/starlight combined navigation provided by the invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Firstly, explaining labels in parameters in the invention, wherein i in a corner mark in the parameters represents an inertial coordinate system, e in the corner mark represents a terrestrial coordinate system, and n in the corner mark represents a navigation coordinate system;
secondly, the embodiment of the invention discloses an acceleration calibration method based on missile-borne inertia/starlight combined navigation, which comprises the following steps:
s1: acquiring an initial attitude matrix before carrier emission, comprising the following steps:
s11: acquiring gyroscope and accelerometer data in a navigation self-alignment process:
confirming a gyro output model and an accelerometer output model through accelerometer self-alignment;
the gyro output model is expressed as
Figure BDA0003672008990000051
Wherein epsilon is the drift of the gyroscope, omega is the true value of the rotation vector of the earth,
Figure BDA0003672008990000052
representing an earth rotation vector estimate;
the accelerometer output model is represented as
Figure BDA0003672008990000053
Wherein ^ is zero offset of the accelerometer, f is the true value of the gravity vector,
Figure BDA0003672008990000054
is a gravity vector estimation value;
the navigation starts to carry out self-alignment work, and the output data of the gyro and the accelerometer are recorded:
the direction of the x axis:
Figure BDA0003672008990000055
y-axis direction:
Figure BDA0003672008990000056
the z-axis direction:
Figure BDA0003672008990000057
wherein ,
Figure BDA0003672008990000058
and
Figure BDA0003672008990000059
the three-axis output values of the gyroscope and the accelerometer are respectively represented, namely the angular velocity and the acceleration of the carrier system relative to the inertial system;
S13：T 0 -T 1 self-aligning within time, and calculating the gravity vector estimation value under a b coordinate system according to the output data of the gyro output model and the accelerometer output model
Figure BDA00036720089900000510
And earth rotation vector estimation value w & i b e ：
Figure BDA00036720089900000511
wherein ,
Figure BDA00036720089900000512
S14：T 1 and (3) finishing the time self-alignment, calculating the average value of output data of the gyroscope and the accelerometer in the time period, and performing double-vector attitude determination according to the gravity vector and the earth rotation vector to obtain an initial attitude matrix:
Figure BDA0003672008990000061
wherein ,
Figure BDA0003672008990000062
and
Figure BDA0003672008990000063
respectively representing a gravity vector estimation value and a terrestrial rotation vector estimation value under an n coordinate system;
s2: based on inertial navigation, establishing a posture updating model after carrier emission to obtain a navigation posture matrix at each moment
Figure BDA0003672008990000064
The method comprises the following steps:
s21: the attitude updating model of the inertial navigation from the (k-1) moment to the k moment is as follows:
Figure BDA0003672008990000065
Figure BDA0003672008990000066
wherein ,
Figure BDA0003672008990000067
representing the measurement attitude at the kth time in a carrier coordinate systemA matrix;
Figure BDA0003672008990000068
representing a measurement attitude matrix at the kth moment under a carrier coordinate system;
Figure BDA0003672008990000069
the measured value provided by the gyroscope at the k moment under the carrier coordinate system,
Figure BDA00036720089900000610
is an attitude matrix measured at the time of (k-1) under a carrier coordinate system,
Figure BDA00036720089900000611
is the projection of the rotational angular velocity of the earth system relative to the inertial system in the navigation system at the moment (k-1),
Figure BDA00036720089900000612
and (k-1) projecting the rotational angular velocity of the navigation system relative to the earth system in the navigation system at the moment.
S3: measuring the star observation, and acquiring fixed star coordinates observed by a star sensor and coordinate data of a geocentric equatorial coordinate system stored in a missile-borne navigation star library to obtain a star observation attitude matrix;
s31: recording fixed star coordinates observed by the star sensor and coordinate data of a geocentric equatorial coordinate system stored in a missile-borne navigation satellite library,
Figure BDA00036720089900000613
i＝1,2,3,...n(n≥2)
s32: according to the star observation data, the matrix performance index is calculated by adopting a least square method to obtain an optimal attitude matrix
Figure BDA00036720089900000614
Figure BDA00036720089900000615
wherein ,J* Represents a performance index, λ i Is a weighting coefficient;
s33: calculating starlight observation attitude matrix
Figure BDA00036720089900000616
Since the celestial coordinate system (r system) the navigation system (n system) is a known coordinate system, i.e. the system
Figure BDA00036720089900000617
The method comprises the steps of (1) knowing; then the equation is transferred through the matrix
Figure BDA00036720089900000618
S34: observing the attitude matrix according to the starlight
Figure BDA0003672008990000071
To navigation attitude matrix
Figure BDA0003672008990000072
Correcting to obtain a corrected attitude matrix
Figure BDA0003672008990000073
In an assisted inertial system, the output signal of the inertial navigation system is compared with independent measurements of the same quantity from an external source, and a correction to the inertial navigation system is then deduced from the difference between these measurements.
S4: calculating the current attitude error according to the attitude updating model and the star observation measurement data, and the method comprises the following steps:
establishing an error calculation model:
Figure BDA0003672008990000074
ε b ＝[ε x ε y ε z ] T ，
Figure BDA0003672008990000075
wherein ；εx 、ε y and εz Denoted as gyro drift;
Figure BDA0003672008990000076
and
Figure BDA0003672008990000077
expressed as the three-axis initial attitude error.
The method comprises the following specific steps:
calculating an initial attitude error provided by an accelerometer in the current attitude error by adopting a Kalman filtering algorithm;
the method comprises the following specific steps:
s41: constructing a combined system state equation,
Z(t)＝XH；X＝(H T H) -1 H T Z(t)；
wherein ,
Figure BDA0003672008990000078
Figure BDA0003672008990000079
s42: m correction state matrixes obtained according to starlight observation
Figure BDA00036720089900000710
And combining the system states Z (t), establishing an error measurement equation and calculating an initial attitude error matrix
Figure BDA00036720089900000711
Figure BDA00036720089900000712
wherein ,t1 -t m Measuring time for m satellites in view in the navigation process,
Figure BDA00036720089900000713
measuring a navigation attitude matrix at the moment for the m satellites;
s5: calculating a horizontal addition table error according to the initial attitude error:
Figure BDA0003672008990000081
wherein ,▽N Represents the equivalent northbound measurement error of the accelerometer + E Representing the equivalent east measurement error of the accelerometer, g representing the earth gravitational acceleration;
using the horizontal meter adding error to horizontally calibrate the accelerometer;
assuming an initial attitude matrix
Figure BDA0003672008990000082
And its true value
Figure BDA0003672008990000083
There is a small amount of mathematical plateau misalignment angle phi in between, then:
Figure BDA0003672008990000084
where I is the identity matrix.
Typically, the measurement error of the gyroscope with respect to the rotation of the earth is greater than the measurement error of the accelerometer with respect to the gravity of the earth, i.e. the measurement error is greater
Figure BDA0003672008990000085
When there is
Figure BDA0003672008990000086
wherein ,
Figure BDA0003672008990000087
the equivalent east measurement error of the gyroscope is shown, and L represents the latitude of the carrier.
It can be seen that the alignment accuracy of the horizontal misalignment angle depends on the equivalent horizontal measurement error of the accelerometer, while the alignment accuracy of the azimuth misalignment angle depends mainly on the equivalent east measurement error of the gyroscope, and the alignment of the horizontal attitude can be performed by using the accelerometer.
In the present specification, the embodiments are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other. The device disclosed by the embodiment corresponds to the method disclosed by the embodiment, so that the description is simple, and the relevant points can be referred to the method part for description.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (9)

1. An acceleration calibration method based on missile-borne inertia/starlight combined navigation is characterized by comprising the following steps:
acquiring an initial attitude matrix before carrier emission;
performing inertial navigation based on the initial attitude matrix and a preset attitude updating model to obtain a navigation attitude matrix;
observing star measurement is carried out on the navigation attitude matrix to obtain an observation star attitude matrix;
correcting the navigation attitude matrix through the star viewing attitude matrix to obtain a corrected attitude matrix;
calculating an attitude error according to the corrected attitude matrix; calculating an initial attitude error provided by an accelerometer in the attitude errors by adopting a Kalman filtering algorithm; and calculating a horizontal addition table error according to the initial attitude error, and calibrating the accelerometer.
2. The method for calibrating the acceleration based on the missile-borne inertia/starlight combined navigation as claimed in claim 1, wherein the method for calibrating the acceleration comprises the steps of obtaining an initial attitude matrix before the carrier is launched,
acquiring output data of a gyroscope and an accelerometer in a navigation self-alignment process;
and carrying out double-vector attitude determination according to the mean value of the gyroscope and accelerometer data to obtain an initial attitude matrix.
3. The method for calibrating the acceleration based on the missile-borne inertia/starlight combined navigation as claimed in claim 2, wherein the gyroscope and the accelerometer output data in the navigation self-alignment process comprise:
the direction of the x axis:
Figure FDA0003672008980000011
y-axis direction:
Figure FDA0003672008980000012
the z-axis direction:
Figure FDA0003672008980000013
wherein ,
Figure FDA0003672008980000014
and
Figure FDA0003672008980000015
representing the three-axis output values of the gyro and accelerometer, respectively, i.e. the angular velocity and acceleration of the carrier system relative to the inertial system.
4. The acceleration calibration method based on missile-borne inertia/starlight combined navigation as claimed in claim 3, wherein the double-vector attitude determination calculation formula is as follows:
Figure FDA0003672008980000016
wherein ,
Figure FDA0003672008980000021
Figure FDA0003672008980000022
Figure FDA0003672008980000023
Figure FDA0003672008980000024
Figure FDA0003672008980000025
and
Figure FDA0003672008980000026
expressed as earth gravity vector estimation value and earth rotation vector estimation value, T 0 Indicating a self-alignment start time; t is 1 Indicating the moment when the self-alignment ends.
5. The acceleration calibration method based on missile-borne inertia/starlight combined navigation as claimed in claim 1, wherein the attitude update model is:
Figure FDA0003672008980000027
Figure FDA0003672008980000028
wherein ,
Figure FDA0003672008980000029
representing a true attitude matrix at a kth time;
Figure FDA00036720089800000210
to represent
Figure FDA00036720089800000211
A derivative of (a);
Figure FDA00036720089800000212
the measured values provided for the gyro at time k,
Figure FDA00036720089800000213
is the attitude matrix at time (k-1),
Figure FDA00036720089800000214
is the projection of the rotational angular velocity of the earth system relative to the inertial system in the navigation system at the moment (k-1),
Figure FDA00036720089800000215
and (k-1) projecting the rotational angular velocity of the navigation system relative to the earth system in the navigation system at the moment.
6. The method of claim 1, wherein the step of performing a star observation measurement on the navigation attitude matrix to obtain a star observation attitude matrix comprises:
recording fixed star coordinates observed by the star sensor and coordinate data of a geocentric equatorial coordinate system stored in a missile-borne navigation satellite library:
Figure FDA00036720089800000216
calculating matrix performance indexes by adopting a least square method according to the star observation data to obtain an optimal attitude matrix
Figure FDA00036720089800000217
Figure FDA00036720089800000218
wherein ,J* Represents a performance index, λ i Is a weighting coefficient;
and calculating a star viewing attitude matrix through matrix transmission.
7. The method for calibrating the acceleration based on the missile-borne inertia/combined navigation as claimed in claim 6, wherein the calculation model for calculating the attitude error is as follows:
Figure FDA00036720089800000219
ε b ＝[ε x ε y ε z ] T ，
Figure FDA0003672008980000031
wherein Z (t) is an attitude error;
Figure FDA0003672008980000032
a navigation attitude matrix during the star observation measurement;
Figure FDA0003672008980000033
and
Figure FDA0003672008980000034
three-axis attitude error expressed as a star viewing time; epsilon x 、ε y and εz Gyro drift, expressed as three axes when looking at the star measurement;
Figure FDA0003672008980000035
and
Figure FDA0003672008980000036
expressed as the three-axis initial attitude error.
8. The method for calibrating the acceleration based on the missile-borne inertia/integrated navigation system according to claim 1, wherein the calculating the initial attitude error provided by the accelerometer in the attitude errors by using the kalman filter algorithm includes:
constructing a combined system state equation:
Z(t)＝XH
wherein ,
Figure FDA0003672008980000037
Figure FDA0003672008980000038
m navigation attitude matrixes obtained according to starlight observation
Figure FDA0003672008980000039
And combining the system states Z (t) to calculate an initial attitude error matrix
Figure FDA00036720089800000310
Figure FDA00036720089800000311
9. The method for calibrating the acceleration based on the missile-borne inertia/combined navigation as claimed in claim 1, wherein the formula for calculating the horizontal plus table error is as follows:
Figure FDA00036720089800000312
wherein ,
Figure FDA00036720089800000313
representing the equivalent north measurement error of the accelerometer,
Figure FDA00036720089800000314
representing the equivalent east measurement error of the accelerometer and g representing the earth gravitational acceleration.
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