CN112363195B - Rotary missile air rapid coarse alignment method based on kinematic equation - Google Patents
Rotary missile air rapid coarse alignment method based on kinematic equation Download PDFInfo
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- 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
- G01S19/42—Determining position
- G01S19/48—Determining position by combining or switching between position solutions derived from the satellite radio beacon positioning system and position solutions derived from a further system
- G01S19/49—Determining position by combining or switching between position solutions derived from the satellite radio beacon positioning system and position solutions derived from a further system whereby the further system is an inertial position system, e.g. loosely-coupled
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- 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
- G01C21/165—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 combined with non-inertial navigation instruments
Abstract
The invention provides a kinematic equation-based rotary missile rapid coarse alignment method, which comprises the following steps of: load for acquiring alignment time given by Beidou satellite navigation systemBody position, velocity; further acquiring carrier pitch angle and course angle information at the alignment moment through the speed information; obtaining the rotation angular rate of the navigation coordinate system relative to the inertial coordinate system at the time of alignment through position information
Obtaining a rolling angle alignment preliminary algorithm at the alignment moment through a kinematic equation; the pitch angle and course angle information of the alignment moment obtained by the previous steps and
acquiring a compensation term M; compensating M into a rolling angle alignment preliminary algorithm to obtain a more accurate rolling angle alignment result, so that initial position, speed and attitude information required by the aerial alignment of the spinning projectile is realized; compared with other roll angle alignment algorithms, the alignment algorithm compensates the influence of earth rotation on alignment, is simple and high in alignment speed, and lays an important foundation for a subsequent combined navigation part.
Description
Technical Field
The invention relates to the field of high-dynamic initial alignment and integrated navigation of a spinning projectile, in particular to a kinematic equation-based rapid aerial coarse alignment method for the spinning projectile.
Background
Accurate combat is a key pursuit of modern war. With the rapid development of the electronic information technology in the 21 st century, guidance and informatization requirements are put forward for low-cost conventional ammunition at home and abroad so as to ensure the effectiveness and accuracy of firepower coverage in modern war. For the cannonball, the spinning body can simplify the composition of a control system and reduce the influence of structural asymmetry, so that the performance of the cannonball is improved.
The high-speed autorotation brings numerous advantages and brings special problems for researching guided weapons of a rotating system. The first is high overload (not less than 10000g) at the moment of transmission, and the requirement of high overload resistance is put on IMU components. Meanwhile, due to high spin, the range of the gyroscope is also highly required. Furthermore, the carrier spins induce complex cone motion, which poses a serious challenge to the measurement of attitude, especially roll angle, further affecting the reliability and accuracy of navigation and guidance.
Inertial navigation, as a system capable of independently completing a navigation task without any external connection, first needs to give an initial posture, i.e., perform initial alignment. Typical initial alignment algorithms are generally longer and only suitable for alignment in the case of a stationary base or a constant velocity base. The projectile has fast ejection speed after being launched, short flight time in the air, high spin, high overload and other difficulties, so that the BDS (Beidou satellite navigation System) is required to assist in completing air alignment. The BDS can give the speed and position information of the cannonball in the flying process and further calculate the pitch angle and the course angle information. So that a parameter of the roll angle remains in the initial state to be calculated.
Disclosure of Invention
In order to solve the problems, the invention discloses a new roll angle alignment algorithm for compensating the earth rotation influence by further derivation based on the kinematics equation of rigid body rotation around the mass center and on the basis of the existing roll angle on-line rough alignment algorithm, and the alignment precision of the roll angle is further improved.
The invention aims to overcome the defects of the prior art and provides a rotary missile rapid coarse alignment method based on a kinematic equation. On one hand, the method gives the position and speed information of the spinning projectile through the BDS, and calculates the course angle and pitch angle information of the spinning projectile according to the speed information; on the other hand, a roll angle alignment equation is deduced through a kinematic equation, and a more accurate roll angle alignment equation for compensating the influence of the earth rotation is deduced by further combining an earth model.
The technical scheme of the invention comprises the following steps:
s1, definition of coordinate system: inertial frame OX i Y i Z i And the navigation coordinate system is a northeast geographic coordinate system OX n Y n Z n The coordinate system of the projectile is OX b Y b Z b Wherein Y is b The shaft being a spinning shaft of a spinning projectile, X b The axis being a horizontal axis, Z b The axis is the zenith axis and the trajectory coordinate system is OX 2 Y 2 Z 2 Wherein Y is 2 The axis is a ballistic pointing axis;
s2, acquiring data information required by the rapid coarse alignment: the method comprises the steps of obtaining Beidou satellite Navigation information and obtaining INS (inertial Navigation System) data;
s2.1, obtaining the navigation information of the Beidou satellite: the method comprises the steps of setting the speed and the position of a spinning projectile and setting TBDS as sampling time for outputting a Beidou satellite navigation result;
s2.2, acquiring INS data: the system comprises a right-direction gyroscope, a forward-direction gyroscope and angular rates output by a natural-direction gyroscope, wherein the pitch angle rate of a right-direction gyroscope sensitive elastomer, the roll angle rate of the forward-direction gyroscope sensitive elastomer and the course angular rate of the natural-direction gyroscope sensitive elastomer are set, and TINS is set as sampling time for INS data output;
s3, calculating and obtaining a ballistic heading angle psi corresponding to the time according to the speed information of the spinning projectile obtained at each sampling time in the Beidou satellite navigation result 2 And ballistic pitch angle θ a Calculating a heading angle psi and a pitch angle theta of the projectile body according to the heading angle and the pitch angle of the projectile path;
s4, according to the position and speed information of the spinning projectile obtained at each sampling time in the Beidou satellite navigation result and the curvature radius information of the earth, calculating the angular rate of the navigation coordinate system at the position relative to the inertial coordinate system
S5, deriving an uncompensated roll angle alignment formula according to a kinematic equation of rigid body rotating around a fixed point;
s6, obtaining the heading angle psi and the pitch angle theta of the projectile body obtained in S3 and the heading angle theta obtained in S4
For calculating a compensation term M, compensating the M term into the formula obtained in S5, and countingCalculating to obtain a projectile rolling angle gamma;
and S7, taking the roll angle gamma of the projectile obtained in the S6, the heading angle psi and the pitch angle theta of the projectile obtained in the S3 and the speed and position information in the Beidou satellite navigation result at the moment as a rotating projectile air rapid coarse alignment result, and providing initial values for subsequent rotating projectile air fine alignment and combined navigation.
Further, the missile path heading angle Ψ in the step S3 2 And ballistic pitch angle θ a The method for calculating the heading angle psi and the pitch angle theta of the projectile body comprises the following specific steps:
wherein the heading angle is defined with positive north as a reference and north is negative east. v. of e ,v n ,v u The Beidou satellite navigation system respectively represents an east-direction speed, a north-direction speed and a sky-direction speed in the Beidou satellite navigation result.
According to the theory of external ballistic theory, the following relationship exists between the projectile coordinate system and the trajectory coordinate system:
ψ≈ψ 2 +δ 1 ；θ≈θ a +δ 2
(3)
wherein; delta 1 Angle of attack, delta, in the horizontal direction 2 Is the angle of attack in the vertical direction;
in the rising portion of the spinning projectile flight, the angle of attack induced by the initial disturbance will decay rapidly to a small amount in a short time, and therefore can be approximated as follows:
ψ≈ψ 2 ；θ≈θ a
(4)
further, the calculation in the step S4
The method comprises the following specific steps:
wherein v is e ,v n ,v u Respectively representing the east speed, the north speed and the sky speed in the Beidou satellite navigation result; omega ie Represents the rotation angular rate of the earth and is a constant value; l is latitude information; RM, RN are the radius of curvature of the earth.
Further, the specific steps in step S5 are:
from the theory of external ballistics, the kinematic equation of the projectile body rotating around the center of mass is as follows:
in the formula
Respectively representing the pitch angle rate, the roll angle rate and the course angle rate of the rotating projectile,
respectively representing the three-axis sensitive angular rates of the projectile coordinate system relative to the navigation coordinate system;
it can be deduced that:
meanwhile, according to the characteristics of the guided projectile in the projectile trajectory in the flight ascending period, the method comprises the following steps:
if the roll angle zone is defined by a range of [ -180 °,180 ° ], a unique solution for roll angle can be obtained by combining (7) and (8), as shown in Table 1.
TABLE 1 Rolling angle value range decision table
The determination of the roll angle interval is given as follows:
when tan gamma is more than or equal to 0:
if it is
From (8), sin gamma is less than or equal to 0, cos gamma is less than 0, the gamma is in the range of [ -180 DEG, -90 DEG ], and the conversion formula is γ | -180 DEG;
if it is
From (8), gamma is-90 degrees;
if it is
From (8), sin gamma is more than or equal to 0, cos gamma is more than 0, the interval of gamma is [0 degree, 90 degrees ], and the conversion formula is gamma' |;
when tan gamma is less than or equal to 0:
if it is
From (8), sin gamma is less than or equal to 0, cos gamma is greater than 0, and the gamma is in the range of (-90 DEG, 0 DEG)]The conversion formula is- | gamma |;
if it is
From (8), sin gamma is less than or equal to 0, cos gamma is greater than 0, and gamma is 90 degrees;
if it is
From (8), sin gamma is less than or equal to 0, cos gamma is greater than 0, then gamma is in the interval of (90 deg., 180 deg. °)]The conversion formula is 180 ° - | γ |.
Further, the specific steps in step S6 are:
from the inertial navigation theory:
wherein
Is the output value of the strap-down gyroscope,
as determined in step S4, equation (9) is developed by component and substituted into equation (7), so that the equation for compensating the effect of the earth rotation can be obtained:
in the formula:
after the roll angle is finally calculated, the judgment of the roll angle value range is consistent with that in the table 1.
The invention has the advantages that:
1. the invention realizes the rotary missile air alignment by the assistance of BDS (Beidou satellite navigation system) signals, and overcomes the limitations that the traditional initial alignment algorithm consumes long time and the carrier can not carry out high dynamic maneuvering;
2. according to the method, the rapid alignment equation of the rolling angle is derived through the rigid body kinematic equation, the rapidity of the algorithm is greatly improved compared with the complex initial alignment of the movable base, the real-time rapid alignment of the rolling angle can be realized, and the estimation and filtering of a navigation error model are not depended;
3. according to the method, under the condition that the kinematic equation does not consider the limitation of the earth rotation influence, a new rolling angle rapid alignment equation is obtained through further derivation, and the accuracy of rolling angle alignment is further improved;
4. the method does not use the information of an accelerometer in the IMU, is favorable for reducing the calculation amount, and simultaneously avoids the influence on the initial alignment under the complicated weightless environment in the air.
Drawings
FIG. 1 is a flow chart of the rotary missile air alignment according to the invention;
FIG. 2 is a diagram of the rotational relationship between the navigational coordinate system and the projectile coordinate system used in the present invention;
FIG. 3 is a diagram of the rotational relationship of a projectile coordinate system and a ballistic coordinate system as used in the present invention;
FIG. 4 is a graph of pitch angle and course angle errors calculated by the method of the present invention;
FIG. 5 is a roll angle solution calculated by the method of the present invention;
FIG. 6 is a roll angle error map calculated by the method of the present invention;
FIG. 7 is a roll angle error map for the uncorrected roll angle alignment method referred to in the present invention;
FIGS. 8-10 are rolling angle alignment error diagrams for the method of the present invention at heading angles of-45, 0, and 45, respectively;
Detailed Description
The present invention will be further illustrated with reference to the accompanying drawings and specific embodiments, which are to be understood as merely illustrative of the invention and not as limiting the scope of the invention. It should be noted that the terms "front," "back," "left," "right," "upper" and "lower" used in the following description refer to directions in the drawings, and the terms "inner" and "outer" refer to directions toward and away from, respectively, the geometric center of a particular component.
For the purpose of promoting an understanding of the invention, reference will now be made in detail to the present invention as illustrated in the accompanying drawings:
with reference to fig. 1, the method for fast rough alignment in rotating missile based on kinematic equation includes the following steps:
s1, definition of coordinate system: inertial frame OX i Y i Z i The navigation coordinate system is a northeast geographic coordinate system OX n Y n Z n The coordinate system of the projectile is OX b Y b Z b Wherein Y is b The axis being a spinning axis of rotation, X b The axis being a horizontal axis, Z b The axis is the zenith axis and the trajectory coordinate system is OX 2 Y 2 Z 2 Wherein Y is 2 The axis is a ballistic pointing axis;
FIG. 2 shows a rotation relationship diagram of a navigation coordinate system and a projectile coordinate system, and FIG. 3 shows a rotation relationship diagram of a navigation coordinate system and a ballistic coordinate system;
s2, acquiring data information required by the rapid coarse alignment: obtaining Beidou satellite navigation information and INS data;
s2.1, obtaining the navigation information of the Beidou satellite: the method comprises the steps of setting the speed and the position of a spinning projectile and setting TBDS as sampling time for outputting a Beidou satellite navigation result;
s2.2, obtaining INS data: the system comprises a right-direction gyroscope, a forward-direction gyroscope and angular rates output by a natural-direction gyroscope, wherein the pitch angle rate of a right-direction gyroscope sensitive elastomer, the roll angle rate of the forward-direction gyroscope sensitive elastomer and the course angular rate of the natural-direction gyroscope sensitive elastomer are set, and TINS is set as sampling time for INS data output;
s3 component v of velocity measurement value output by BDS receiver in navigation coordinate system e ,v n ,v u And calculating the trajectory inclination angle and trajectory deflection angle of the rotating projectile trajectory at the moment, as shown in the following formula:
wherein the heading angle is defined with positive north as a reference and north is negative east. v. of e ,v n ,v u The compass navigation device represents the east speed, the north speed and the sky speed in the compass navigation result respectively.
According to the theory of external ballistic theory, the following relationship exists between the projectile coordinate system and the trajectory coordinate system:
ψ≈ψ 2 +δ 1 ；θ≈θ a +δ 2
(3)
in the rising part of the spinning projectile flight, the angle of attack induced by the initial disturbance will decay rapidly to a small amount in a short time, and can therefore be approximated as follows:
ψ≈ψ 2 ；θ≈θ a
(4)
because TBDS is generally larger than TINS, to make the solution frequency of the alignment algorithm reach the frequency of the inertial navigation system, curve fitting needs to be performed on the velocity data between BDS output points, and a least square fitting method is generally adopted.
S4, calculating the rotation angular rate of the navigation coordinate system compared with the inertial coordinate system, as shown in the following formula:
wherein v is e ,v n ,v u Respectively representing the east speed, the north speed and the sky speed in the Beidou satellite navigation result; omega ie Represents the rotation angular rate of the earth and is a constant value; l is latitude information in the position; r M ，R N The radius of curvature of the earth.
Similarly, because the TBDS is generally larger than the TINS, in order to make the resolving frequency of the alignment algorithm reach the frequency of the inertial navigation system, curve fitting needs to be performed on the position data between the BDS output points, and a least square fitting method is generally adopted.
S5, according to the theory of external ballistics, the kinematic equation of the projectile body rotating around the center of mass is as follows:
in the formula
Respectively representing the pitch angle rate, the roll angle rate and the course angle rate of the rotating projectile,
respectively representing the three-axis sensitive angular rates of the projectile coordinate system relative to the navigation coordinate system;
the following two equations can be solved from equation (6):
(7) it can be deduced that:
for a well-designed projectile, the angular velocity of the heading after launch is small and negligible, so (8) can be simplified as follows:
meanwhile, according to the characteristics of the guided projectile in the projectile trajectory in the flight ascending period, the method comprises the following steps:
if the roll angle region is defined in the range of [ -180 °,180 ° ], a unique solution for roll angle can be obtained by combining (9) and (10), as shown in table 1.
TABLE 1 Rolling angle value range decision table
S6, based on the inertial navigation theory:
wherein
Is the output value of the strap-down gyroscope,
as determined in step S4, equation (9) is expanded by components:
wherein:
further, it is possible to obtain:
substituting (13) and (14) into (9) can obtain a formula after compensating the influence of the earth rotation:
in the formula:
equation (15) is the roll angle fast calculation equation after correction.
Since the roll angle is defined as [ -180 °,180 ° ], equation (15) is specifically calculated:
if it is not
Then
If it is not
Then
After the roll angle is finally calculated, the judgment of the roll angle value range is consistent with that in the table 1.
Examples
In this embodiment, a certain time is required for acquiring the BDS signal after the spin bomb is fired. After the recapture of the BDS signals is realized and the navigation result can be stably output, the aerial alignment can be carried out in real time.
Wherein, fig. 2 and fig. 3 show the coordinate system transformation relationship diagram used in the present invention, and the definitions and positive-negative relationships of the variables in all algorithms of the present invention are based on the coordinate transformation. FIG. 2 illustrates the navigation coordinate system used herein as the northeast sky coordinate system, the projectile coordinate system as the upper right-front coordinate system, and the y-axis as the axis of rotation. Fig. 3 illustrates the relationship between the pitch angle and heading angle of a projectile and the pitch angle and heading angle of a trajectory. FIG. 4 shows the pitch angle and heading angle errors of the spinning projectile resolved when the BDS receiving speed error is set to [1m/s,1m/s,1m/s ]. It can be seen that the pitch angle error is less than 2.5 x 10-5rad and the course angle error is less than 10-3 rad. Fig. 5 is a rolling angle calculation result diagram of the method of the present invention when the IMU error is set to be 20deg/h of gyroscope zero offset, 1000ug/h of accelerometer zero offset, 5deg/sqrt (h) of angle random walk, 10ug/sqrt (hz) of velocity random walk, and the BDS position error is set to be [5m,5m,5m ], and it can be seen from fig. 6 that the error of the rolling angle alignment method of the present invention is less than 1 ° (where the error is mutated to an error from-180 ° to 180 °, such as an ideal 179 °, and when the alignment result is-179 °, the actual error is 2 ° instead of 358 °). While FIG. 7 shows a roll angle alignment error map without accounting for the effects of Earth rotation, a comparison of FIG. 6 shows that the roll angle alignment results will drift by more than 1 if the effects of Earth rotation are not compensated for. Therefore, the method has higher roll angle alignment precision. FIGS. 8-10 show the roll angle alignment errors for a spinning projectile at heading angles of-45, 0, and 45, respectively.
All the information needed for the initial alignment is thus available: initial position information (error 5m), initial velocity information (error 1m/s), initial attitude information (pitch angle error 0.015 degree, roll angle error 1 degree, course angle error 0.5 degree)
The examples are preferred embodiments of the invention but the invention is not limited to the embodiments described above and any obvious modifications can be made by a person skilled in the art without departing from the essence of the invention.
The technical means disclosed in the invention scheme are not limited to the technical means disclosed in the above embodiments, but also include the technical scheme formed by any combination of the above technical features.
Claims (5)
1. A rotary missile air rapid coarse alignment method based on a kinematic equation is characterized by comprising the following steps:
s1, definition of coordinate system: inertial frame OX i Y i Z i The navigation coordinate system is a northeast geographic coordinate system OX n Y n Z n The coordinate system of the projectile is OX b Y b Z b Wherein Y is b The shaft being a spinning shaft of a spinning projectile, X b The axis being a horizontal axis, Z b The axis is the zenith axis and the trajectory coordinate system is OX 2 Y 2 Z 2 Wherein Y is 2 The axis is a ballistic pointing axis;
s2, acquiring data information required by the rapid coarse alignment: the method comprises the steps of obtaining Beidou satellite Navigation information and obtaining INS (inertial Navigation System) data;
s2.1, obtaining the navigation information of the Beidou satellite: the method comprises the steps of setting the speed and the position of a spinning projectile and setting TBDS as sampling time for outputting a Beidou satellite navigation result;
s2.2, obtaining INS data: the system comprises a right-direction gyroscope, a forward-direction gyroscope and angular rates output by a natural-direction gyroscope, wherein the pitch angle rate of a right-direction gyroscope sensitive elastomer, the roll angle rate of the forward-direction gyroscope sensitive elastomer and the course angular rate of the natural-direction gyroscope sensitive elastomer are set, and TINS is set as sampling time for INS data output;
s3, calculating and obtaining a ballistic heading angle psi corresponding to the time according to the speed information of the spinning projectile obtained at each sampling time in the Beidou satellite navigation result 2 And ballistic pitch angle θ a Calculating a heading angle psi and a pitch angle theta of the projectile body according to the trajectory heading angle and the pitch angle;
s4, according to the position and speed information of the spinning projectile obtained at each sampling time in the Beidou satellite navigation result and the curvature radius information of the earth, calculating the angular rate of the navigation coordinate system at the position relative to the inertial coordinate system
S5, deriving an uncompensated roll angle alignment formula according to a kinematic equation of rigid body rotating around a fixed point;
s6, obtaining the heading angle psi and the pitch angle theta of the projectile body obtained in S3 and the heading angle theta obtained in S4
The compensation term M is calculated and compensated into the formula obtained in S5, and the projectile rolling angle gamma is calculated;
and S7, taking the roll angle gamma of the projectile obtained in the S6, the heading angle psi and the pitch angle theta of the projectile obtained in the S3 and the speed and position information in the Beidou satellite navigation result at the moment as a rotating projectile air rapid coarse alignment result, and providing initial values for subsequent rotating projectile air fine alignment and combined navigation.
2. The method for rotary missile aerial fast coarse alignment based on the kinematic equation as claimed in claim 1, wherein the missile path heading angle Ψ in the step S3 2 And ballistic pitch angle θ a The method for calculating the heading angle psi and the pitch angle theta of the projectile body comprises the following specific steps:
wherein the heading angle is defined by taking the positive north as a reference and the north is negative with the east offset; v. of e ,v n ,v u Respectively representing the east speed, the north speed and the sky speed in the Beidou satellite navigation result;
according to the theory of outer ballistics, the projectile coordinate system and the trajectory coordinate system have the following relations:
ψ≈ψ 2 +δ 1 ；θ≈θ a +δ 2 (3)
wherein; delta 1 Angle of attack, delta, in the horizontal direction 2 Is the angle of attack in the vertical direction;
in the rising part of the spinning projectile flight, the angle of attack induced by the initial disturbance rapidly decays to a small amount in a short time, and can therefore be approximated as follows:
ψ≈ψ 2 ；θ≈θ a (4)。
3. the method for rotary missile-borne fast rough alignment based on the kinematic equation according to claim 1, wherein the calculation in the step S4 is carried out
The method comprises the following specific steps:
wherein v is e ,v n ,v u Respectively representing the east speed, the north speed and the sky speed in the Beidou satellite navigation result; omega ie Represents the rotation angular rate of the earth and is a constant value; l is latitude information; r M ，R N The radius of curvature of the earth.
4. The method for rotary missile-borne fast coarse alignment based on the kinematic equation according to claim 1, wherein the specific steps in the step S5 are as follows:
from the theory of external ballistics, the kinematic equation of the projectile body rotating around the center of mass is as follows:
in the formula
Respectively representing the pitch angle rate, the roll angle rate and the course angle rate of the rotating projectile,
respectively representing the three-axis sensitive angular rates of the projectile coordinate system relative to the navigation coordinate system;
it can be deduced that:
meanwhile, according to the characteristics of the guided projectile in the projectile trajectory in the flight ascending period, the method comprises the following steps:
if the definition domain of the roll angle region is [ -180 degrees, 180 degrees ], a unique roll angle solution can be obtained by combining (7) and (8);
the determination of the roll angle interval is given as follows:
when tan gamma is more than or equal to 0:
if it is
From (8), sin gamma is less than or equal to 0, cos gamma is less than 0, the range of gamma is [ -180 DEG, -90 DEG ], and the conversion formula is | gamma | -180 DEG;
if it is
From (8), gamma is-90 degrees;
if it is
From (8), sin gamma is more than or equal to 0, cos gamma is more than 0, the interval where gamma is located is [0 degrees and 90 degrees ], and the conversion formula is | gamma |;
when tan gamma is less than or equal to 0:
if it is
From (8), sin gamma is less than or equal to 0, cos gamma is greater than 0, and the interval of gamma is (-90 DEG, 0 DEG)]The conversion formula is- | gamma |;
if it is
From (8), sin gamma is less than or equal to 0, cos gamma is more than 0, and gamma is 90 degrees;
if it is
From (8), sin gamma is less than or equal to 0, cos gamma is greater than 0, and the interval of gamma is (90 degrees, 1 degree)80°]The conversion formula is 180 ° - | γ |.
5. The method for rotary missile-borne fast coarse alignment based on the kinematic equation according to claim 1, wherein the specific steps in the step S6 are as follows:
by the theory of inertial navigation:
wherein
Is the output value of the strap-down gyroscope,
as determined in step S4, equation (9) is developed by component and substituted into equation (7), so that the equation for compensating the effect of the earth rotation can be obtained:
in the formula:
and finally, after the rolling angle is calculated, the judgment of the rolling angle value range is consistent with the rolling angle interval judgment method given above.
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| US6883747B2 (en) * | 2003-03-28 | 2005-04-26 | Northrop Grumman Corporation | Projectile guidance with accelerometers and a GPS receiver |
| CN101256080B (en) * | 2008-04-09 | 2010-06-23 | 南京航空航天大学 | Midair aligning method for satellite/inertia combined navigation system |
| CN103728647B (en) * | 2013-12-20 | 2016-02-03 | 西安电子工程研究所 | A kind of body roll angle measurement method based on satellite carrier signal modulation |
| CN105115508B (en) * | 2015-08-27 | 2017-12-22 | 北京航天控制仪器研究所 | Alignment methods in rotation guided cartridge Quick air based on rear data |
| CN105180728B (en) * | 2015-08-27 | 2017-01-11 | 北京航天控制仪器研究所 | Front data based rapid air alignment method of rotary guided projectiles |
| CN107478110B (en) * | 2017-07-28 | 2019-12-20 | 北京航天控制仪器研究所 | Rotating elastic attitude angle calculation method based on state observer |
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