CN111504256A - Roll angle real-time estimation method based on least square method - Google Patents

Roll angle real-time estimation method based on least square method Download PDF

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Publication number
CN111504256A
CN111504256A CN202010358933.3A CN202010358933A CN111504256A CN 111504256 A CN111504256 A CN 111504256A CN 202010358933 A CN202010358933 A CN 202010358933A CN 111504256 A CN111504256 A CN 111504256A
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roll angle
angle
estimation
roll
axis
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杨哲
李传军
解禹
周续源
郝彦君
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Beijing Institute of Technology BIT
China North Industries Corp
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China North Industries Corp
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C1/00—Measuring angles
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
    • G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
    • G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO

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Abstract

The invention relates to a roll angle real-time estimation method based on a least square method, and belongs to the field of inertial navigation. The invention aims to solve the problems that a blind area exists in time magnetic measurement during roll angle measurement, the platform type inertial navigation has larger volume and higher cost, an MEMS gyroscope in the roll direction has high precision, small time-measuring range and low time-measuring precision when the range is large, an error accumulation exists in a strapdown inertial navigation system and the like, and the Z-shaped form is obtained according to a trajectory equation2×1＝H2×2·X2×1A matrix equation of (c); estimating the pitch angle, the pitch angle speed and the yaw angle speed of the projectile body at n sampling moments according to the satellite navigation data, and obtaining the shape of Z by combining the data of a double-shaft gyroscope2n+1＝H2n×2·X2×1A matrix equation of (c); further obtaining X containing roll angle information2×1Least squares estimation of (d); according to X2×1And determining the roll angle according to the least square estimation and the roll angle value range. Obtained by the methodThe roll angle precision is high, the error accumulation of a strapdown inertial navigation system is effectively avoided, and the problems of insufficient range and low precision of the MEMS gyroscope are solved.

Description

Roll angle real-time estimation method based on least square method
Technical Field
The invention belongs to the field of inertial navigation, and particularly relates to a method for estimating a roll angle of an aerial rotating carrier in real time based on a least square method.
Background
The requirement of modern war on the hitting precision of weapon system is higher and higher, and how to improve the hitting precision of the power-on guided ammunition after launching becomes a research hotspot. The strapdown inertial navigation system is an autonomous navigation system, can completely and autonomously provide continuous and complete navigation information, has strong external interference resistance and good short-term stability, basically does not influence the navigation precision by carrier mobility, has higher relative navigation precision, but has the problem that the navigation parameter error is accumulated along with time. The accurate guided munition using GNSS/SINS combined navigation not only has the advantages of high GNSS accuracy and strong SINS anti-jamming capability, but also can avoid the problems that the satellite signal is easy to interfere or lose and the trajectory can not be detected continuously when the GNSS is used alone to detect the trajectory, and the error accumulation exists when the SINS is used alone to detect the trajectory, so that the accurate guided munition is more and more applied to guided munitions.
The GNSS/SINS combined navigation system applied to guided munitions such as guided munitions is generally required to bear severe conditions such as high overload and high rotating speed in the launching process of a conventional platform, and both the SINS and the GNSS cannot work normally in the launching process. Thus, the SINS requires aerial alignment in a pitch stabilized or low speed rotating flight after the carrier enters the controlled segment. Through two stages of rough alignment and fine alignment, more accurate attitude information and inertial error information can be obtained, so that the ballistic parameters can be accurately calculated according to the alignment parameters in the ballistic correction process of the projectile, and the ballistic correction task can be reliably completed. However, when the SINS is aligned in the air, because the moment of guiding the projectile to be launched is subjected to great overload impact in the bore, the SINS cannot be electrified during launching, the initial alignment is not carried out before launching, the SINS normally works after the projectile is delivered out of the muzzle, and the projectile is in a rolling state in the bore, so that the rolling angle of the projectile after the projectile is delivered out of the muzzle is unknown, and the difficulty is brought to the air alignment of the SINS.
At present, in the aspect of research on initial roll angle, geomagnetic navigation and platform type inertial navigation are more applied. However, the geomagnetic measurement has a blind area and needs other navigation methods for assistance; the platform type inertial navigation has larger volume and higher cost, and is not suitable for being applied to low-cost guided munitions. In addition, the MEMS gyroscope in the rolling direction has the problems of high accuracy, small time-measuring range, and large measuring range, and low accuracy.
Disclosure of Invention
Technical problem to be solved
The invention aims to solve the technical problems that a rolling angle real-time estimation method based on a least square method is provided to overcome the problems that a blind area exists in magnetic measurement during the rolling angle measurement, a platform type inertial navigation device is large in size and high in cost, an MEMS gyroscope in a rolling direction is high in precision, small in time-measuring range and low in time-measuring precision, and a strapdown inertial navigation system has error accumulation.
(II) technical scheme
In order to solve the technical problem, the invention provides a roll angle real-time estimation method based on a least square method, which is characterized by comprising the following steps of:
step one, obtaining the shape as Z according to a ballistic equation2×1＝H2×2·X2×1A matrix equation of (c); the matrix equation is
Figure BDA0002474404920000031
Wherein the content of the first and second substances,
Figure BDA0002474404920000032
is the output of the y-axis and z-axis of the two-axis gyroscope,
Figure BDA0002474404920000033
And
Figure BDA0002474404920000034
the pitch angle, pitch angle speed and yaw angle speed of the projectile body are respectively, and gamma is the rolling angle of the projectile body;
estimating the pitch angle theta and the pitch angle speed of the projectile body at n sampling moments according to the satellite navigation data
Figure BDA0002474404920000035
And yaw rate
Figure BDA0002474404920000036
Combining the data of the dual-axis gyroscope to obtain the shape of Z2n×1＝H2n×2·X2×1A matrix equation of (c);
step three, obtaining X containing roll angle information according to the matrix equation of the step two2×1Least squares estimation of (d);
step four, according to X2×1And determining the roll angle gamma by the least square estimation and the roll angle range.
Further, the first step specifically includes:
from the ballistic equation, a system of equations can be obtained:
Figure BDA0002474404920000037
arranging into a matrix form to obtain:
Figure BDA0002474404920000038
wherein the content of the first and second substances,
Figure BDA0002474404920000039
for the outputs of the y-axis and z-axis of the two-axis gyroscope,
Figure BDA00024744049200000312
Figure BDA00024744049200000310
and
Figure BDA00024744049200000311
the pitch angle, pitch angle speed and yaw angle speed of the projectile body are respectively, and r is the roll angle of the projectile body.
Further, Z is2n×1Z for n sampling instants2×1Are combined in sequence to form H2n×2H for n sampling instants2×2Are combined in sequence.
Further, the third step specifically includes:
to make it possible to
Figure BDA0002474404920000041
Can obtain X2×1The least squares estimate of (d) is:
Figure BDA0002474404920000042
wherein Z is Z in the second step2n×1H is H in the second step2n×2，
Figure BDA0002474404920000043
Is X2×1Is estimated by least squares.
Further, the roll angle γ is calculated by the formula:
Figure BDA0002474404920000044
wherein X (1) and X (2) are X2×1Least squares estimation of
Figure BDA0002474404920000045
The first term and the second term of (1).
Further, the roll angle γ has a value range as follows:
Figure BDA0002474404920000046
(III) advantageous effects
The invention provides a rolling angle real-time estimation method based on a least square method, which obtains a shape like Z according to a trajectory equation2×1＝H2×2·X2×1A matrix equation of (c); estimating the pitch angle theta and the pitch angle speed of the projectile body at n sampling moments according to satellite navigation data
Figure BDA0002474404920000047
Yaw rate
Figure BDA0002474404920000048
Combining the two-axis gyroscope data to obtain the shape z2n×1＝H2n×2·X2×1A matrix equation of (c); obtaining X containing roll angle information according to the matrix equation of the second step2×1Least squares estimation of (d); according to X2×1And determining the roll angle gamma by the least square estimation and the roll angle range. The roll angle obtained by the method provided by the invention has high precision and meets the requirement of further precise alignment; in addition, the method adopts satellite navigation data to assist in roll angle estimation, and estimates the roll angle in real time by a least square method, so that the error accumulation problem of a strapdown inertial navigation system is effectively avoided, and the accuracy of the roll angle estimation result is higher; in addition, the invention adopts the y-axis and z-axis outputs of the dual-axis gyroscope to estimate the roll angle, thereby effectively solving the problems of high precision, small time-measuring range and low precision of the MEMS gyroscope on the x axis of the roll direction due to the over-high rotating speed of the projectile body.
Drawings
FIG. 1 is a rolling angle estimation result obtained by simulation analysis in Matlab according to the rolling angle real-time on-line estimation method based on the least square method of the present invention;
FIG. 2 shows the rolling angle estimation error obtained by simulation analysis in Matlab according to the present invention;
FIG. 3 is a rolling angle real-time online estimation method based on the least square method, which performs semi-physical simulation on a turntable to obtain a rolling angle estimation result;
FIG. 4 shows the estimated roll angle error obtained from the semi-physical simulation of the present invention.
Detailed Description
In order to make the objects, contents, and advantages of the present invention clearer, the following detailed description of the embodiments of the present invention will be made in conjunction with the accompanying drawings and examples.
The embodiment provides a roll angle real-time online estimation method based on a least square method, which comprises the following steps:
step one, obtaining the shape as Z according to a ballistic equation2×1＝H2×2·X2×1A matrix equation of (c);
from the ballistic equation, a system of equations can be obtained:
Figure BDA0002474404920000051
arranging into a matrix form to obtain:
Figure BDA0002474404920000052
wherein the content of the first and second substances,
Figure BDA0002474404920000053
is the output of the y-axis and z-axis of the two-axis gyroscope,
Figure BDA0002474404920000054
And
Figure BDA0002474404920000055
the pitch angle, pitch angle velocity and yaw angle velocity of the projectile body are respectively, and gamma is the roll angle of the projectile body.
Estimating the pitch angles of the projectiles at n sampling moments according to the satellite navigation data
Figure BDA0002474404920000069
Pitch angular velocity
Figure BDA0002474404920000061
And yaw rate
Figure BDA0002474404920000062
Combining the data of the dual-axis gyroscope to obtain the shape of Z2n×1＝H2n×2·X2×1And (4) matrix equation. Wherein, the sampling interval can be self-defined according to actual requirements, Z2n×1Z for n sampling instants2×1Are combined in sequence to form H2n×2H for n sampling instants2×2Are combined in sequence.
Step three, obtaining X containing roll angle information according to the matrix equation of the step two2×1Least squares estimation of (d);
to make it possible to
Figure BDA0002474404920000063
Can obtain X2×1The least squares estimate of (d) is:
Figure BDA0002474404920000064
wherein Z is Z obtained in the second step2n×1H is H obtained in the second step2n×2，
Figure BDA0002474404920000065
Is X2×1Is estimated by least squares.
Step four, according to X2×1And determining the roll angle gamma by the least square estimation and the roll angle range.
The roll angle γ is calculated as:
Figure BDA0002474404920000066
wherein X (1) and X (2) are X2×1Least squares estimation of
Figure BDA0002474404920000067
The first term and the second term of (1).
The roll angle γ is given by the following formula:
Figure BDA0002474404920000068
the real-time online rolling angle estimation method based on the least square method is subjected to simulation analysis in Matlab to obtain the rolling angle estimation result shown in FIG. 1 and the rolling angle estimation error shown in FIG. 2. It can be seen from fig. 2 that the roll angle error estimated based on the least square method is stable in the whole flight time of the projectile, the error fluctuates up and down within a range of +/-4 degrees, and the fluctuation range is smaller and smaller, so that the requirement of inertial navigation fine alignment on the roll angle estimation accuracy is met.
According to the rolling angle real-time online estimation method based on the least square method, provided by the invention, a semi-physical simulation experiment is carried out on the rolling angle real-time online estimation method. The experiment uses the biax revolving stage, is fixed in the revolving stage center with MIMU, lets the revolving stage rotate with fixed rotational speed simultaneously, does the pitch motion with the pitch angle rate that changes. The result of the roll angle estimation shown in fig. 3 and the roll angle estimation error shown in fig. 4 are obtained. As can be seen from the rolling angle error of FIG. 4, when the rotating speed of the turntable is 3r/s, the error range is within the range of +/-4 degrees, and the experimental result shows that the estimation method can maintain better performance under the condition of high rotating speed.
The above description is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, several modifications and variations can be made without departing from the technical principle of the present invention, and these modifications and variations should also be regarded as the protection scope of the present invention.

Claims (6)

1. A roll angle real-time estimation method based on a least square method is characterized by comprising the following steps:
step one, obtaining the shape as Z according to a ballistic equation2×1＝H2×2·X2×1A matrix equation of (c); the matrix equation is
Figure FDA0002474404910000011
Wherein the content of the first and second substances,
Figure FDA0002474404910000018
is the output of the y-axis and z-axis of the two-axis gyroscope,
Figure FDA0002474404910000012
And
Figure FDA0002474404910000013
the pitch angle, pitch angle speed and yaw angle speed of the projectile body are respectively, and gamma is the rolling angle of the projectile body;
estimating the pitch angle theta and the elevation angle speed of the projectile body at n sampling moments according to the satellite navigation data
Figure FDA0002474404910000014
And yaw rate
Figure FDA0002474404910000015
Combining the data of the dual-axis gyroscope to obtain the shape of Z2n×1＝H2n×2·X2×1A matrix equation of (c);
step three, obtaining X containing roll angle information according to the matrix equation of the step two2×1Least squares estimation of (d);
step four, according to X2×1And determining the roll angle gamma by the least square estimation and the roll angle range.
2. The method for real-time estimation of roll angle based on least square method as claimed in claim 1, wherein said step one includes:
from the ballistic equation, a system of equations can be obtained:
Figure FDA0002474404910000016
arranging into a matrix form to obtain:
Figure FDA0002474404910000017
wherein the content of the first and second substances,
Figure FDA0002474404910000029
is the output of the y-axis and z-axis of the two-axis gyroscope,
Figure FDA0002474404910000021
And
Figure FDA0002474404910000022
the pitch angle, pitch angle velocity and yaw angle velocity of the projectile body are respectively, and gamma is the roll angle of the projectile body.
3. The method of claim 1 for real-time estimation of roll angle based on least squares, wherein Z is2n×1Z for n sampling instants2×1Are combined in sequence to form H2n×2H for n sampling instants2×2Are combined in sequence.
4. The method for estimating roll angle in real time based on least square method as claimed in any one of claims 1-3, wherein the third step specifically comprises:
to make it possible to
Figure FDA0002474404910000023
Can obtain X2×1The least squares estimate of (d) is:
Figure FDA0002474404910000024
wherein Z is Z in the second step2n×1H is H in the second step2n×2，
Figure FDA0002474404910000025
Is X2×1Is estimated by least squares.
5. The method for estimating the roll angle in real time based on the least square method as claimed in claim 4, wherein the roll angle γ is calculated by the formula:
Figure FDA0002474404910000026
wherein X (1) and X (2) are X2×1Least squares estimation of
Figure FDA0002474404910000027
The first term and the second term of (1).
6. The method as claimed in claim 5, wherein the roll angle γ is estimated in real time by the least square method as follows:
Figure FDA0002474404910000028
CN202010358933.3A 2020-04-29 2020-04-29 Roll angle real-time estimation method based on least square method Pending CN111504256A (en)

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