CN114964224A - Micro inertial navigation system error autonomous inhibition method - Google Patents
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Abstract
The invention provides an error autonomous inhibition method of a micro inertial navigation system, which comprises the following steps: acquiring a rolling angle of the projectile body in real time; constructing a least square state variable; constructing a least square observation variable; obtaining a least square measurement equation according to the least square state variable and the least square observation variable, and performing least square estimation according to the least square measurement equation to obtain a rolling angle estimation value aligned with the initial moment; constructing a Kalman filtering state equation; constructing a Kalman filtering observation equation; and performing Kalman filtering according to a Kalman filtering state equation and a Kalman filtering observation equation to obtain a gyro scale factor error estimation value and a corrected gyro scale factor, thereby realizing the autonomous suppression of the error of the micro inertial navigation system. The invention can solve the technical problem that the performance of the micro inertial navigation system is reduced because the gyro scale factor is greatly changed due to the launching impact of the cannonball with high magnitude and long duration in the micro inertial navigation system for the guided cannonball in the prior art.
Description
Technical Field
The invention relates to the technical field of micro-inertial navigation systems for guided projectiles rotating at a high speed, in particular to an error autonomous suppression method for a micro-inertial navigation system.
Background
The high-overload micro inertial navigation system has the characteristics of small volume, light weight, strong autonomy, good concealment and the like, has the outstanding characteristic of resisting high-overload severe mechanical environment, and has wide application prospect in the application fields of manufacturing guided projectiles, electromagnetic guide rail projectiles, ultra-long distance guided projectiles and the like.
The guided projectile can simultaneously have high-speed rotation motion in the flight process, namely, the guided projectile rotates around the longitudinal axis of the projectile body while advancing, and certain stability can be obtained through a gyro effect generated by high-speed rotation. The rotating speed of an outlet of a guided projectile is usually dozens of revolutions per second, even if the rotation is reduced, the rotating speed of a projectile body is usually more than ten revolutions per second at the electrifying moment of a micro inertial navigation system, the maximum angular speed measuring range of the micro inertial navigation system is about thousands of degrees per second, and due to the fact that the projectile body rotates at a high speed in the flying process, the scale factor error of a rotating shaft can generate the vital influence on the precision of the micro inertial navigation system.
The micro inertial navigation system for the guided cannonball is generally electrified in the air after being launched to finish initial alignment and combined navigation, the quantity is as high as 10000g in the launching process of the cannonball, and the launching impact with the duration of about 10ms can cause the gyro scale factor to generate large change, so that the performance of the micro inertial navigation system is reduced.
Disclosure of Invention
The invention provides an autonomous error inhibition method for a micro inertial navigation system, which can solve the technical problem that in the prior art, a micro inertial navigation system for a guided projectile has high gyro scale factor variation caused by projectile launching impact with high magnitude and long duration, so that the performance of the micro inertial navigation system is reduced.
According to an aspect of the invention, an autonomous error suppression method for a micro inertial navigation system is provided, and the method comprises the following steps:
acquiring a rolling angle of the projectile body in real time by using a micro inertial navigation system;
constructing a least square state variable according to the rolling angle aligned with the initial moment;
constructing a least square observation variable according to the rolling angle at the current moment;
obtaining a least square measurement equation according to the least square state variable and the least square observation variable, and performing least square estimation according to the least square measurement equation to obtain a rolling angle estimation value aligned to the initial moment;
constructing a Kalman filtering state equation by taking the rolling angle error, the gyro scale factor error and the gyro zero position as Kalman filtering state variables;
constructing a Kalman filtering observation equation by taking the difference value of the rolling angle estimation values aligned with the initial moment, which is obtained by least square estimation at adjacent filtering moments, as a Kalman filtering observation variable;
and performing Kalman filtering according to a Kalman filtering state equation and a Kalman filtering observation equation to obtain a gyro scale factor error estimation value and a corrected gyro scale factor, thereby realizing the autonomous suppression of the error of the micro inertial navigation system.
Preferably, the kalman filter equation of state is constructed by:
wherein ,
in the formula ,
is a Kalman filtering state variable, F is a continuous state equation state transition matrix,
is a systematic random noise vector, δ γ is the roll angle error, δ k x For X-axis gyro scale factor error, ε bx Is the zero position of the X-axis gyroscope,
the angular rate of the rotation axis to which the X-axis gyro is sensitive.
Preferably, the kalman filter observation equation is constructed by the following formula:
in the formula ,
in order to observe the variables by the Kalman filtering,
in order to be a kalman filter observation matrix,
in order to observe the noise, it is,
a roll angle estimation value aligned with the initial time and obtained by least square estimation at the current filtering time,
and obtaining the rolling angle estimation value aligned with the initial moment by least square estimation at the last filtering moment.
Preferably, the obtaining of the roll angle of the projectile in real time by using the micro inertial navigation system comprises:
acquiring angular rate information under a navigation coordinate system output by a micro inertial navigation system;
acquiring angular rate information under a carrier coordinate system according to the angular rate information under the navigation coordinate system;
and acquiring the rolling angle of the projectile according to the angular rate information in the carrier coordinate system.
Preferably, the angular rate information in the carrier coordinate system is obtained by the following formula:
wherein ,
the roll angle of the projectile is obtained by:
wherein ,
in the formula ,
is the X-axis gyro angular rate of a carrier coordinate system,
for the Y-axis gyro angular rate of the carrier coordinate system,
for the Z-axis gyro angular rate of the carrier coordinate system,
in order to be able to roll the angular rate,
in order to be the angular rate of the heading,
to pitch angle rate, c 1 For a transformation matrix rotating about the X-axis, c 3 Roller with gamma bodies for a transformation matrix rotating about the Z axisThe dynamic angle theta is the pitch angle of the projectile body,
is the heading angle of the projectile.
Preferably, the least squares state variables are constructed by:
X＝[cos(γ 0 ) sin(γ 0 )] T ；
constructing a least squares observation variable by:
Z＝[sin(γ) cos(γ)] T ；
wherein X is a least squares state variable, γ 0 And Z is a least square observation variable aiming at the rolling angle of the initial moment, and gamma is the rolling angle of the current moment.
Preferably, obtaining a least square measurement equation according to the least square state variable and the least square observation variable, and performing least square estimation according to the least square measurement equation to obtain the roll angle estimation value aligned to the initial time includes:
acquiring a least square observation matrix according to the least square state variable and the least square observation variable;
obtaining a least square measurement equation according to the least square state variable, the least square observation variable and the least square observation matrix;
obtaining a least square measurement equation set according to a least square measurement equation, wherein the least square measurement equation set comprises r least square measurement equations, and r is the measurement times in the alignment period;
and obtaining an estimated value of the least square state variable according to the least square measurement equation set, thereby obtaining a rolling angle estimated value aligned with the initial moment by least square estimation.
Preferably, the least squares observation matrix is obtained by:
obtaining a least squares measurement equation by:
Z＝HX+V；
obtaining a least squares measurement equation set by:
wherein H is the least squares observation matrix, t is time, V is the measurement noise, Z 1 、Z 2 、......、Z r The least squares observation variables of the first, second, and r-th measurements, H 1 、H 2 、......、H r A least squares observation matrix, V, of the first, second, and r-th measurements, respectively 1 、V 2 、......、V r The measurement noise of the first, second, and r-th measurements, respectively.
Preferably, the estimated value of the least squares state variable is obtained by:
obtaining a rolling angle estimated value of the alignment initial moment by the following formula:
in the formula ,
is an estimate of the least-squares state variable,
to align the roll angle estimate at the initial instant,
the first element of the estimate of the least squares state variable,
the second element of the estimate of the least squares state variable.
According to a further aspect of the invention, there is provided a computer apparatus comprising a memory, a processor and a computer program stored on the memory and executable on the processor, the processor implementing any of the methods described above when executing the computer program.
By applying the technical scheme of the invention, the rolling angle of the projectile body is obtained in real time by using the micro inertial navigation system, the rolling angle estimation value of the alignment initial moment is estimated by using the least square, and then the difference value of the rolling angle estimation values of the alignment initial moment obtained by using the least square estimation of adjacent filtering moments is used as a Kalman filtering observation variable by using a Kalman filtering method to obtain the gyro scale factor error estimation value and the corrected gyro scale factor, so that the autonomous suppression of the error of the micro inertial navigation system is realized, and the navigation precision of the micro inertial navigation system is improved. The method is convenient for engineering realization, does not depend on external auxiliary information, can be widely applied to the field of guided projectiles rotating at high speed, and has very important significance on the micro-inertial navigation system for guided ammunition.
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The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort.
FIG. 1 is a flow chart illustrating an autonomous error suppression method for a micro inertial navigation system according to an embodiment of the present invention;
FIG. 2 illustrates a graph of results of gyro scale factor estimation provided in accordance with an embodiment of the present invention.
Detailed Description
It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict. 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. The following description of at least one exemplary embodiment is merely illustrative in nature and is in no way intended to limit the invention, its application, or uses. 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.
It is noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of exemplary embodiments according to the present application. As used herein, the singular forms "a", "an", and "the" are intended to include the plural forms as well, and it should be understood that when the terms "comprises" and/or "comprising" are used in this specification, they specify the presence of stated features, steps, operations, devices, components, and/or combinations thereof, unless the context clearly indicates otherwise.
The relative arrangement of the components and steps, the numerical expressions and numerical values set forth in these embodiments do not limit the scope of the present invention unless specifically stated otherwise. Meanwhile, it should be understood that the sizes of the respective portions shown in the drawings are not drawn in an actual proportional relationship for the convenience of description. Techniques, methods, and apparatus known to those of ordinary skill in the relevant art may not be discussed in detail but are intended to be part of the specification where appropriate. In all examples shown and discussed herein, any particular value should be construed as merely illustrative, and not limiting. Thus, other examples of the exemplary embodiments may have different values. It should be noted that: like reference numbers and letters refer to like items in the following figures, and thus, once an item is defined in one figure, further discussion thereof is not required in subsequent figures.
As shown in fig. 1, the present invention provides an autonomous error suppression method for a micro inertial navigation system, where the method includes:
s10, acquiring the roll angle of the projectile in real time by using a micro inertial navigation system;
s20, constructing a least square state variable according to the rolling angle aligned with the initial moment;
s30, constructing a least square observation variable according to the rolling angle at the current moment;
s40, obtaining a least square measurement equation according to the least square state variable and the least square observation variable, and performing least square estimation according to the least square measurement equation to obtain a rolling angle estimation value aligned with the initial moment;
s50, constructing a Kalman filtering state equation by taking the rolling angle error, the gyro scale factor error and the gyro zero position as Kalman filtering state variables;
s60, constructing a Kalman filtering observation equation by taking the difference value of the roll angle estimation values aligned with the initial moment and obtained by least square estimation of adjacent filtering moments as a Kalman filtering observation variable;
and S70, performing Kalman filtering according to a Kalman filtering state equation and a Kalman filtering observation equation to obtain a gyro scale factor error estimation value and a corrected gyro scale factor, thereby realizing the autonomous suppression of the micro inertial navigation system error.
The method comprises the steps of firstly utilizing a micro inertial navigation system to obtain a roll angle of a projectile body in real time, then estimating a roll angle estimation value of an alignment initial moment through least square, and then utilizing a Kalman filtering method to obtain a gyro scale factor error estimation value and a corrected gyro scale factor by taking a difference value of the roll angle estimation values of the alignment initial moments obtained through least square estimation of adjacent filtering moments as Kalman filtering observation variables so as to realize autonomous suppression of errors of the micro inertial navigation system and improve navigation precision of the micro inertial navigation system. The method is convenient for engineering realization, does not depend on external auxiliary information, can be widely applied to the field of guided projectiles rotating at high speed, and has very important significance on a micro inertial navigation system for guided ammunition.
According to an embodiment of the present invention, in S10 of the present invention, the obtaining the roll angle of the projectile in real time by using the micro inertial navigation system includes:
s11, acquiring angular rate information under a navigation coordinate system output by the micro inertial navigation system;
s12, acquiring angular rate information under a carrier coordinate system according to the angular rate information under the navigation coordinate system;
and S13, acquiring the roll angle of the projectile according to the angular rate information in the carrier coordinate system.
Specifically, in S12 of the present invention, angular rate information in the carrier coordinate system is obtained by the following equation:
wherein ,
c is to 1 、c 3 Substituting the above formula and expanding, can obtain:
according to the above formula, can obtain
Order to
Then according to the above equation:
the rolling angle of the projectile can be calculated according to the formula as follows:
in the formula ,
is the X-axis gyro angular rate of a carrier coordinate system,
for the Y-axis gyro angular rate of the carrier coordinate system,
for the Z-axis gyro angular rate of the carrier coordinate system,
to be the roll angle rate, the angular velocity of the roll,
is the angular rate of the heading, and,
to the pitch angle rate, c 1 For a transformation matrix rotating about the X-axis, c 3 Is a conversion matrix rotating around the Z axis, gamma is the rolling angle of the projectile body, theta is the pitch angle of the projectile body,
is the heading angle of the projectile.
In the invention, as can be seen from the analysis, the measurement errors of the gyro angular rates of the Y axis and the Z axis have great influence on the calculation result of the rolling angle, the calculation is directly carried out by using the method, and the calculation result is singular due to the influence of factors such as gyro measurement noise and the like, so that the rolling angle is estimated by using the least square algorithm to improve the estimation precision and reliability of the rolling angle.
According to an embodiment of the present invention, in S20 of the present invention, the least squares state variables are constructed by:
X＝[cos(γ 0 ) sin(γ 0 )] T ；
in S30 of the present invention, a least squares observation variable is constructed by the following formula:
Z＝[sin(γ) cos(γ)] T ；
wherein X is a least squares state variable, γ 0 And Z is a least square observation variable aiming at the rolling angle of the initial moment, and gamma is the rolling angle of the current moment.
According to an embodiment of the present invention, in S40 of the present invention, obtaining a least square measurement equation according to the least square state variable and the least square observation variable, and performing least square estimation according to the least square measurement equation, and obtaining the roll angle estimation value aligned to the initial time includes:
s41, acquiring a least square observation matrix according to the least square state variable and the least square observation variable;
s42, obtaining a least square measurement equation according to the least square state variable, the least square observation variable and the least square observation matrix;
s43, obtaining a least square measurement equation set according to the least square measurement equation, wherein the least square measurement equation set comprises r least square measurement equations, and r is the measurement times in the alignment period;
and S44, obtaining an estimated value of the least square state variable according to the least square measurement equation set, thereby obtaining a rolling angle estimated value of the alignment initial moment obtained by least square estimation.
Specifically, in S41 of the present invention, a least squares observation matrix is obtained by:
in S42 of the present invention, a least squares measurement equation is obtained by:
Z＝HX+V；
in S43 of the present invention, the least squares measurement equation set is obtained by:
wherein H is the least squares observation matrix, t is time, V is the measurement noise, Z 1 、Z 2 、......、Z r The least squares observation variables of the first, second, and r-th measurements, H 1 、H 2 、......、H r A least squares observation matrix, V, of the first, second, and r-th measurements, respectively 1 、V 2 、......、V r The measurement noise of the first, second, and r-th measurements, respectively.
Further, in S44 of the present invention, the estimated value of the least squares state variable is obtained by:
obtaining a rolling angle estimated value of the alignment initial moment by the following formula:
in the formula ,
is an estimate of the least-squares state variable,
to align the roll angle estimate at the initial instant,
the first element of the estimate of the least squares state variable,
the second element of the estimate of the least squares state variable.
According to an embodiment of the invention, in S50 of the invention, the kalman filtering state equation is constructed by:
wherein ,
in the formula ,
is a Kalman filtering state variable, F is a continuous state equation state transition matrix,
is a systematic random noise vector, δ γ is the roll angle error, δ k x Is the X-axis gyro scale factor error, ε bx Is the zero position of the X-axis gyroscope,
the angular rate of the rotation axis to which the X-axis gyro is sensitive.
In S60 of the present invention, according to an embodiment of the present invention, the kalman filtering observation equation is constructed by the following formula:
in the formula ,
in order to observe the variables by the Kalman filtering,
in order to be a kalman filter observation matrix,
in order to observe the noise, it is,
the roll angle estimation value aligned with the initial moment is obtained by least square estimation at the current filtering moment,
and obtaining a rolling angle estimation value aligned with the initial moment by least square estimation at the previous filtering moment.
The invention also provides a computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements any of the above methods when executing the computer program.
Taking flight test data of a certain model as an example, the method of the invention is used for estimating the gyro scale factor error, and the obtained Kalman filtering estimation result is shown in FIG. 2.
As can be seen from fig. 2, the gyro scale factor error can be quickly estimated, and the gyro scale factor is corrected by using the result obtained by estimation, so that the measurement accuracy of the micro inertial navigation system can be greatly improved.
In summary, the invention provides an autonomous error suppression method for a micro inertial navigation system, which includes obtaining a roll angle of a projectile in real time by using the micro inertial navigation system, estimating a roll angle estimation value at an initial alignment time by using least squares, and then obtaining a gyro scale factor error estimation value and a corrected gyro scale factor by using a kalman filtering method and using a difference value of the roll angle estimation values at the initial alignment time, which are obtained by least square estimation at adjacent filtering times, as a kalman filtering observation variable, thereby realizing autonomous error suppression for the micro inertial navigation system and improving navigation accuracy of the micro inertial navigation system. The method is convenient for engineering realization, does not depend on external auxiliary information, can be widely applied to the field of guided projectiles rotating at high speed, and has very important significance on the micro-inertial navigation system for guided ammunition.
Spatially relative terms, such as "above … …," "above … …," "above … …," "above," and the like, may be used herein for ease of description to describe one device or feature's spatial relationship to another device or feature as illustrated in the figures. It will be understood that the spatially relative terms are intended to encompass different orientations of the device in use or operation in addition to the orientation depicted in the figures. For example, if a device in the figures is turned over, devices described as "above" or "on" other devices or configurations would then be oriented "below" or "under" the other devices or configurations. Thus, the exemplary term "above … …" can include both an orientation of "above … …" and "below … …". The device may be otherwise variously oriented (rotated 90 degrees or at other orientations) and the spatially relative descriptors used herein interpreted accordingly.
It should be noted that the terms "first", "second", and the like are used to define the components, and are only used for convenience of distinguishing the corresponding components, and the terms have no special meanings unless otherwise stated, and therefore, the scope of the present invention should not be construed as being limited.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (10)
1. An autonomous error suppression method for a micro inertial navigation system, the method comprising:
acquiring a rolling angle of the projectile body in real time by using a micro inertial navigation system;
constructing a least square state variable according to the rolling angle aligned with the initial moment;
constructing a least square observation variable according to the rolling angle at the current moment;
obtaining a least square measurement equation according to the least square state variable and the least square observation variable, and performing least square estimation according to the least square measurement equation to obtain a rolling angle estimation value aligned with the initial moment;
constructing a Kalman filtering state equation by taking the rolling angle error, the gyro scale factor error and the gyro zero position as Kalman filtering state variables;
constructing a Kalman filtering observation equation by taking a difference value of rolling angle estimation values aligned with the initial moment, which is obtained by least square estimation at adjacent filtering moments, as a Kalman filtering observation variable;
and performing Kalman filtering according to a Kalman filtering state equation and a Kalman filtering observation equation to obtain a gyro scale factor error estimation value and a corrected gyro scale factor, thereby realizing the autonomous suppression of the error of the micro inertial navigation system.
2. The method of claim 1, wherein the kalman filter state equation is constructed by:
wherein ,
in the formula ,
is a Kalman filtering state variable, F is a continuous state equation state transition matrix,
is a systematic random noise vector, δ γ is the roll angle error, δ k x For X-axis gyro scale factor error, ε bx Is the zero position of the X-axis gyroscope,
the angular rate of the rotation axis to which the X-axis gyro is sensitive.
3. The method of claim 1, wherein the kalman filter observation equation is constructed by:
in the formula ,
in order to allow for the kalman filter to observe the variables,
in order to be a kalman filter observation matrix,
in order to observe the noise, it is,
the roll angle estimation value aligned with the initial moment is obtained by least square estimation at the current filtering moment,
and obtaining the rolling angle estimation value aligned with the initial moment by least square estimation at the last filtering moment.
4. The method of claim 1, wherein acquiring the roll angle of the projectile in real time using a micro inertial navigation system comprises:
acquiring angular rate information under a navigation coordinate system output by a micro inertial navigation system;
acquiring angular rate information under a carrier coordinate system according to the angular rate information under the navigation coordinate system;
and acquiring the rolling angle of the projectile according to the angular rate information in the carrier coordinate system.
5. The method of claim 4, wherein the angular rate information in the carrier coordinate system is obtained by:
wherein ,
the roll angle of the projectile is obtained by:
wherein ,
in the formula ,
is the X-axis gyro angular rate of a carrier coordinate system,
for the Y-axis gyro angular rate of the carrier coordinate system,
for the Z-axis gyro angular rate of the carrier coordinate system,
to be rolledThe angular rate of the light emitted by the light source,
in order to be the angular rate of the heading,
to pitch angle rate, c 1 For a transformation matrix rotating about the X-axis, c 3 Is a conversion matrix rotating around the Z axis, gamma is the rolling angle of the projectile body, theta is the pitch angle of the projectile body,
is the heading angle of the projectile.
6. The method of claim 1, wherein the least squares state variables are constructed by:
X＝[cos(γ 0 ) sin(γ 0 )] T ；
constructing a least squares observation variable by:
Z＝[sin(γ) cos(γ)] T ；
wherein X is a least squares state variable, γ 0 And Z is a least square observation variable aiming at the rolling angle of the initial moment, and gamma is the rolling angle of the current moment.
7. The method of claim 1, wherein obtaining a least squares measurement equation based on the least squares state variables and the least squares observation variables, and performing a least squares estimation based on the least squares measurement equation to obtain the roll angle estimate for the initial time comprises:
acquiring a least square observation matrix according to the least square state variable and the least square observation variable;
obtaining a least square measurement equation according to the least square state variable, the least square observation variable and the least square observation matrix;
obtaining a least square measurement equation set according to a least square measurement equation, wherein the least square measurement equation set comprises r least square measurement equations, and r is the measurement times in the alignment period;
and obtaining an estimated value of the least square state variable according to the least square measurement equation set, thereby obtaining a rolling angle estimated value aligned with the initial moment by least square estimation.
8. The method of claim 1 or 7, wherein the least squares observation matrix is obtained by:
obtaining a least squares measurement equation by:
Z＝HX+V；
obtaining a least squares measurement equation set by:
wherein H is the least squares observation matrix, t is time, V is the measurement noise, Z 1 、Z 2 、......、Z r The least squares observation variables of the first, second, and r-th measurements, H 1 、H 2 、......、H r A least squares observation matrix, V, of the first, second, and r-th measurements, respectively 1 、V 2 、......、V r The measurement noise of the first, second, and r-th measurements, respectively.
9. The method of claim 7 or 8, wherein the estimate of the least squares state variable is obtained by:
obtaining a rolling angle estimated value of the alignment initial moment by the following formula:
in the formula ,
is an estimate of the least-squares state variable,
to align the roll angle estimate at the initial instant,
the first element of the estimate of the least squares state variable,
the second element of the estimate of the least squares state variable.
10. A computer device comprising a memory, a processor and a computer program stored on the memory and executable on the processor, wherein the processor implements the method of any of claims 1 to 9 when executing the computer program.
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