CN112556495A - Automatic meter installing method for simple fire-controlled moving target of shoulder-shooting barrel type weapon - Google Patents

Automatic meter installing method for simple fire-controlled moving target of shoulder-shooting barrel type weapon Download PDF

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CN112556495A
CN112556495A CN202011399353.5A CN202011399353A CN112556495A CN 112556495 A CN112556495 A CN 112556495A CN 202011399353 A CN202011399353 A CN 202011399353A CN 112556495 A CN112556495 A CN 112556495A
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axis
aiming
angle
coordinate system
calculating
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黄鹏
李召
梁益铭
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Xian Institute of Modern Control Technology
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Xian Institute of Modern Control Technology
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F41—WEAPONS
    • F41G—WEAPON SIGHTS; AIMING
    • F41G3/00—Aiming or laying means

Abstract

The invention provides an automatic meter mounting method for a simple fire control moving target of a shoulder-fire barrel type weapon based on a strapdown inertial navigation moving base alignment principle. The method can greatly simplify the operation flow when the shoulder shooting type weapon strikes the moving target, and improve striking efficiency and aiming precision.

Description

Automatic meter installing method for simple fire-controlled moving target of shoulder-shooting barrel type weapon
Technical Field
The invention belongs to the technical field of direct-aiming weapon systems, and particularly relates to an automatic meter mounting method for a simple fire control moving target of a shoulder-shooting barrel type weapon based on a strapdown inertial navigation base alignment principle.
Background
The shoulder-shooting barrel type weapon comprises a portable antitank rocket, a recoil-free gun, an individual rocket and the like, and is mainly provided with ungulate breaking ammunitions, hard attacking ammunitions, multipurpose ammunitions and other unguided ammunitions, when striking moving targets such as infantry combat vehicles, self-propelled artillery, armored vehicles and the like, a shooter is required to use a simple fire control or aiming device to measure the target distance, judge the moving direction, predict the target moving rule and then calculate the distance advance according to the ammunition flight time. The traditional weapon aims at a moving target mainly by using a simple fire control and optical aiming device, and has high requirement on the operation of a firing hand, complex operation process and low hitting precision.
Disclosure of Invention
Technical problem to be solved
The invention provides an automatic meter loading method for a simple fire-control moving target of a shoulder-fired cylinder type weapon, which aims to solve the technical problems of low hit precision of a hitting moving target, complex operation process and great influence of shooter factors of a shoulder-fired direct-aiming weapon system.
(II) technical scheme
In order to solve the technical problem, the invention provides an automatic meter mounting method for a simple fire control moving target of a shoulder-shooting barrel type weapon, which is used for mounting an inertia measurement unit in simple fire control and comprises the following steps:
s1, starting the IMU, and collecting accelerometer and gyroscope data of the IMU
S2, calculating the inclination angle of the aiming device according to the data of the accelerometer and the gyroscope
Firstly, defining a coordinate system
Ground coordinate system Axyz: fixedly connected with the ground, and the origin A is at a transmitting point; the Ax axis is in the horizontal plane, is parallel to the projection of the simple fire-control aiming longitudinal axis at the starting moment of aiming tracking in the horizontal plane, and is positive forwards; the Ay axis is vertical to the horizontal plane and is positive upwards; the Az axis, the Ax axis and the Ay axis form a right-hand system, which is abbreviated as an A system, and the A system is taken as an inertial coordinate system;
line of sight coordinate system Oxcyczc: fixedly connected with the simple fire control, and the origin O is at the center of the simple fire control aiming axis; oz is a gas phasecThe axis coincides with the horizontal axis of the aiming "+" division; oycThe axis coincides with the vertical axis of the "+" division; oxcAxis is line of sight, forward is positive, and OycAxis and OzcThe axis forms the right-handed system, abbreviated as "c system";
IMU coordinate system Oxmymzm: fixedly connected with the simple fire control, and the origin O is at the center of the IMU; ideally, OxmAxis, OymAxis, OzmAxes are respectively parallel to OxcAxis, OycAxis, OzcAxial, and uniform direction, abbreviated as "m is "; due to installation errors, the m and c have non-parallel errors;
temporary platform coordinate system
Figure BDA0002811751160000029
The origin O is at the center of the simple fire control aiming axis; c is coincident with the start time of aiming tracking; ideally, the temporary platform coordinate system is stabilized in inertial space, abbreviated as "
Figure BDA0002811751160000021
System "; due to the measurement error and the calculation error,
Figure BDA0002811751160000022
the direction of each axis has an error compared with the ideal case;
the letter is provided with a "" symbol above to represent the measured value, and the "" symbol above to represent the calculated value; the upper corner marks of the vector and the letters of the vector components sequentially represent a coordinate system of vector projection and a sequence number of a time node from left to right, and the lower corner marks sequentially represent a reference coordinate system, a motion coordinate system and a projection coordinate axis from left to right; the transformation matrix is represented by a letter C, the upper corner mark of the transformation matrix represents a destination coordinate system of coordinate transformation, and the lower corner mark of the transformation matrix sequentially represents a starting coordinate system of coordinate transformation and a sequence number of a time node from left to right;
calculating the inclined angle of the aiming device according to the formula (1)
Figure BDA0002811751160000023
Figure BDA0002811751160000024
Wherein the content of the first and second substances,
Figure BDA0002811751160000025
is an average proportional vector (acceleration of gravity)
Figure BDA0002811751160000026
The modulus of the component in the z-direction,
Figure BDA0002811751160000027
is composed of
Figure BDA0002811751160000028
A modulus in the y-direction component;
s3, detecting whether a tracking signal is received or not, and if the tracking signal is detected, carrying out the next step; otherwise, whether the tracking signal is received is always inquired
S4, defining initial value of conversion matrix
Figure BDA0002811751160000031
At t0Time is established according to c series
Figure BDA0002811751160000032
Is, t0Of time of day
Figure BDA0002811751160000033
Is coincident with c; c is relative to
Figure BDA0002811751160000034
For strapdown matrices of systems
Figure BDA0002811751160000035
Is shown at t0At the moment of time of
Figure BDA0002811751160000036
Is an identity matrix;
s5, collecting accelerometer data, and extracting specific force vector
Figure BDA0002811751160000037
Collecting gyroscope data, extracting angular velocity vector
Figure BDA0002811751160000038
At tkTime of day, IMU accelerometerExtracting specific force vectors
Figure BDA0002811751160000039
Gyroscope extraction angular velocity vector
Figure BDA00028117511600000310
S6 strapdown matrix
Figure BDA00028117511600000311
Quaternion real-time correction
Using quaternion to calculate the time of day
Figure BDA00028117511600000312
Let c be relative to
Figure BDA00028117511600000313
Is a rotational quaternion of
Figure BDA00028117511600000314
Wherein ic、jc、kcC is a unit vector on three coordinate axes, and the real-time correction of Q is carried out through a formula (2):
Figure BDA00028117511600000315
according to
Figure BDA00028117511600000316
Giving an initial value q0＝1、q1＝0、q2＝0、q3＝0；
Solving equation (2) to obtain tkQuaternion of time is obtained by calculation
Figure BDA00028117511600000317
Figure BDA00028117511600000318
S7, performing acceleration specific force coordinate conversion
Figure BDA00028117511600000319
If the aiming tracking is not finished, returning to S5, otherwise, entering the next step
S8, calculating the average specific force vector
Note t0Of time of day
Figure BDA00028117511600000320
At the finish time t of aiming trackingnAll will be
Figure BDA00028117511600000321
(k is 0,1,2.. times.n) is arithmetically averaged according to formula (4) at
Figure BDA00028117511600000322
Obtaining the average specific force vector in the system
Figure BDA00028117511600000323
Figure BDA0002811751160000041
S9, calculating the initial height angle and direction angle of the aiming line
Will be provided with
Figure BDA0002811751160000042
As a result of the recognition of the gravitational acceleration g at the point of emission, then
Figure BDA0002811751160000043
The decomposition in the A system is the decomposition of the gravity acceleration in the A system;
will be provided with
Figure BDA0002811751160000044
Expressed as:
Figure BDA0002811751160000045
Figure BDA0002811751160000046
is a mold of
Figure BDA0002811751160000047
Then
Figure BDA0002811751160000048
The decomposition in system A is:
Figure BDA0002811751160000049
Figure BDA00028117511600000410
is at a high or low angle with respect to the A system
Figure BDA00028117511600000411
And an angle of inclination
Figure BDA00028117511600000412
Angle of direction
Figure BDA00028117511600000413
According to the coordinate transformation relation,
Figure BDA00028117511600000414
transformation matrix of system and A system
Figure BDA00028117511600000415
Comprises the following steps:
Figure BDA00028117511600000416
will be provided with
Figure BDA00028117511600000417
Transposing to obtain A is
Figure BDA00028117511600000418
Transformation matrix of system
Figure BDA00028117511600000419
Figure BDA00028117511600000420
Then
Figure BDA00028117511600000421
And
Figure BDA00028117511600000422
the expression between is:
Figure BDA00028117511600000423
the expansion form is as follows:
Figure BDA0002811751160000051
the sub-items are listed as follows:
Figure BDA0002811751160000052
obtaining:
Figure BDA0002811751160000053
calculating the initial elevation angle and the direction angle of the line of sight according to the formula (13):
Figure BDA0002811751160000054
s10, calculating a transformation matrix
Figure BDA0002811751160000055
Substituting the calculation result of the formula (12) into the formula (7) to obtain a conversion matrix
Figure BDA0002811751160000056
According to equation (14), using
Figure BDA0002811751160000057
And tnOf time of day
Figure BDA0002811751160000058
C-system to A-system conversion matrix for calculating aiming tracking end time
Figure BDA0002811751160000059
Figure BDA00028117511600000510
Figure BDA00028117511600000511
The expression of (a) is:
Figure BDA00028117511600000512
wherein, thetan、ψn、γnIs tracking end tnTime c is the attitude angle relative to system A, called θnFor high and low angles of the line of sight,. psinIs the boresight direction angle;
s11, calculating the elevation angle and the direction angle of the aiming line at the end time
And (3) calculating the elevation angle and the direction angle of the sight line at the end moment according to the formula (15):
Figure BDA0002811751160000061
the numbers in parentheses indicate
Figure BDA0002811751160000062
The row and column positions of the middle element; according to
Figure BDA0002811751160000063
Calculating each time node tkThe elevation angle and the direction angle of the aiming line;
s12, calculating the rotation angular speed of the aiming line and outputting the result
(1) Tracking start t0At the moment, the initial angular position of the line of sight in the ground coordinate system is determined by
Figure BDA0002811751160000064
It is determined that,
Figure BDA0002811751160000065
initial high-low angle of aiming line in ground coordinate system
Figure BDA0002811751160000066
Calculated according to equation (13), the initial azimuth angle ψc0＝0；
(2) End of tracking tnAt the moment, the angular position of the line of sight in the ground coordinate system is determined by
Figure BDA0002811751160000067
Determining, calculating the elevation angle of the aiming line in the ground coordinate system according to the formula (16)
Figure BDA00028117511600000611
And the direction angle psicn(ii) a Calculating the rotation angular velocity of the aiming line according to the formula (17), including high and low angular velocities
Figure BDA0002811751160000068
Direction angular velocity
Figure BDA0002811751160000069
Figure BDA00028117511600000610
(III) advantageous effects
The invention provides an automatic meter mounting method for a simple fire control moving target of a shoulder-fire barrel type weapon based on a strapdown inertial navigation moving base alignment principle. The method can greatly simplify the operation flow when the shoulder shooting type weapon strikes the moving target, and improve striking efficiency and aiming precision. The method obtains good application effect in the development of a certain shoulder-carried anti-tank weapon system project, and has wide military application prospect.
Drawings
FIG. 1 is a flowchart of an automatic table installing method for a moving object according to an embodiment 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 an automatic meter installation method for a shoulder-fire barrel type weapon simple fire control moving target based on a strapdown inertial navigation base alignment principle, the method installs a set of Inertial Measurement Unit (IMU) in simple fire control, and the flow is shown in fig. 1, and the method specifically comprises the following steps:
s1, starting the IMU, and collecting accelerometer and gyroscope data of the IMU
S2, calculating the inclination angle of the aiming device according to the data of the accelerometer and the gyroscope
Firstly, defining a coordinate system
Ground coordinate system Axyz: fixedly connected with the ground, and the origin A is at a transmitting point; the Ax axis is in the horizontal plane, is parallel to the projection of the simple fire-control aiming longitudinal axis at the starting moment of aiming tracking in the horizontal plane, and is positive forwards; the Ay axis is vertical to the horizontal plane and is positive upwards; the Az axis forms a right-handed system, abbreviated as "system A", with the Ax and Ay axes. The flight time of the shoulder shooting barrel type weapon ammunition is short, the distance is short, the influence of the rotation angular velocity of the earth on the striking precision can be ignored, and the A system can be used as an inertial coordinate system. Calculating local gravity acceleration, establishing a ground coordinate system, determining an inclination angle of the simple fire control relative to a horizontal plane, outputting the inclination angle to a display assembly of the simple fire control, displaying the inclination angle in an eyepiece, and prompting a shooter to keep the fire control in a horizontal state;
line of sight coordinate system Oxcyczc: fixedly connected with the simple fire control, and the origin O is at the center of the simple fire control aiming axis; oz is a gas phasecThe axis coincides with the horizontal axis of the aiming "+" division; oycThe axis coincides with the vertical axis of the "+" division; oxcAxis is line of sight, forward is positive, and OycAxis and OzcThe axis forms the right hand system, abbreviated as "c system".
IMU coordinate system Oxmymzm: fixedly connected with the simple fire control, and the origin O is at the center of the IMU. Ideally, OxmAxis, OymAxis, OzmAxes are respectively parallel to OxcAxis, OycAxis, OzcThe axes and directions are coincident and are abbreviated as "m-system". Due to the installation error, m and c have non-parallel error.
Temporary platform coordinate system
Figure BDA0002811751160000071
The origin O is at the center of the simple fire control aiming axis; the coordinate system of the line of sight (c-system) coincides with the start time of the aiming tracking. Ideally, the temporary platform coordinate system is stabilized in inertial space, abbreviated as "
Figure BDA0002811751160000081
Is a series of. Due to the influence of factors such as measurement errors and calculation errors,
Figure BDA0002811751160000082
the direction of each axis and its ideal conditionThere may be an error in the comparison.
The letter has a "" symbol above it to indicate that the letter represents the measured value and a "" symbol above it to indicate that the letter represents the calculated value. The upper corner marks of the letters of the vectors and the vector components sequentially represent a coordinate system of vector projection and a sequence number of a time node from left to right, and the lower corner marks sequentially represent a reference coordinate system, a motion coordinate system and a projection coordinate axis from left to right. Such as
Figure BDA0002811751160000083
Represents: at the kth time node, c is the angular velocity projection relative to A in c is OycMeasurement of on-axis components. The transformation matrix is denoted by the letter C, the upper corner mark of which represents the destination coordinate system of the coordinate transformation, and the lower corner mark of which represents the departure coordinate system of the coordinate transformation and the serial number of the time node in turn from left to right. Such as
Figure BDA0002811751160000084
Represents: from c to k at the time node
Figure BDA0002811751160000085
A transformation matrix of the system. The vector sum matrix may have one or more, or none, of its superscripts, whichever is more, in the order described above.
Calculating the inclined angle of the aiming device according to the formula (1)
Figure BDA0002811751160000086
Figure BDA0002811751160000087
Wherein the content of the first and second substances,
Figure BDA0002811751160000088
is an average proportional vector (acceleration of gravity)
Figure BDA0002811751160000089
The modulus of the component in the z-direction,
Figure BDA00028117511600000810
is composed of
Figure BDA00028117511600000811
The modulus of the component in the y-direction.
S3, detecting whether a tracking signal is received or not, and if the tracking signal is detected, carrying out the next step; otherwise, whether the tracking signal is received is always inquired
S4, defining initial value of conversion matrix
Figure BDA00028117511600000812
At t0Time is established according to c series
Figure BDA00028117511600000813
Is, i.e. t0Of time of day
Figure BDA00028117511600000814
Is overlapped with c. c is relative to
Figure BDA00028117511600000815
For strapdown matrices of systems
Figure BDA00028117511600000816
Is shown at t0At the moment of time of
Figure BDA00028117511600000817
According to
Figure BDA00028117511600000818
The definition of the series of the compound is,
Figure BDA00028117511600000819
is an identity matrix.
S5, collecting accelerometer data, and extracting specific force vector
Figure BDA00028117511600000820
Collecting gyroscope dataExtracting angular velocity vector
Figure BDA00028117511600000821
Since the system A can be used as the inertial coordinate system, and the system m is fixedly connected with the system c, then at tkMoment, accelerometer extraction specific force vector in IMU
Figure BDA0002811751160000091
Gyroscope extraction angular velocity vector
Figure BDA0002811751160000092
S6 strapdown matrix
Figure BDA0002811751160000093
Quaternion real-time correction
With the proceeding of the aiming tracking process, the simple fire control posture is continuously changed, the aiming line coordinate system (c system) is continuously rotated,
Figure BDA0002811751160000094
with consequent change, the time of each moment is calculated using quaternion
Figure BDA0002811751160000095
Let c be relative to
Figure BDA0002811751160000096
Is a rotational quaternion of
Figure BDA0002811751160000097
Figure BDA0002811751160000098
Wherein ic、jc、kcC is unit vector on three coordinate axes, and the real-time correction of Q is realized by the formula (2):
Figure BDA0002811751160000099
according to
Figure BDA00028117511600000910
Giving an initial value q0＝1、q1＝0、q2＝0、q3＝0；
Solving equation (2) to obtain tkQuaternion of time is obtained by calculation
Figure BDA00028117511600000911
Figure BDA00028117511600000912
S7, performing acceleration specific force coordinate conversion
Figure BDA00028117511600000913
If the aiming tracking is not finished, returning to S5, otherwise, entering the next step
S8, calculating average specific force vector (gravity acceleration)
Noting time t0
Figure BDA00028117511600000914
At the finish time t of aiming trackingnAll will be
Figure BDA00028117511600000915
(k is 0,1,2.. times.n) is arithmetically averaged according to formula (4) at
Figure BDA00028117511600000916
Obtaining the average specific force vector in the system
Figure BDA00028117511600000917
Figure BDA00028117511600000918
S9, calculating the initial height angle and direction angle of the aiming line
Due to the fact that the shooter after training can control the body to shake in the aiming and tracking process, the target motion is stably tracked, and the own disturbance acceleration degree of the shooter is small. Thus, can be
Figure BDA0002811751160000101
As a result of the recognition of the gravitational acceleration g at the point of emission, then
Figure BDA0002811751160000102
The decomposition in the system A is the decomposition of the gravitational acceleration in the system A.
Will be provided with
Figure BDA0002811751160000103
Expressed as:
Figure BDA0002811751160000104
Figure BDA0002811751160000105
is a mold of
Figure BDA0002811751160000106
Then
Figure BDA0002811751160000107
The decomposition in system A is:
Figure BDA0002811751160000108
according to the A series and
Figure BDA0002811751160000109
definition of system, origin at emission point, x-axis pointing to t0The target at the moment, where the Ax axis is directed towards the target parallel to the horizontal plane,
Figure BDA00028117511600001010
the axis points directly at the target. Therefore, the temperature of the molten metal is controlled,
Figure BDA00028117511600001011
is at a high or low angle with respect to the A system
Figure BDA00028117511600001012
(caused by target elevation angle) and inclination angle
Figure BDA00028117511600001013
(caused by horizontal deviation of fire control) angle of direction
Figure BDA00028117511600001014
According to the coordinate transformation relation,
Figure BDA00028117511600001015
transformation matrix of system and A system
Figure BDA00028117511600001016
Comprises the following steps:
Figure BDA00028117511600001017
will be provided with
Figure BDA00028117511600001018
Transposing to obtain A is
Figure BDA00028117511600001019
Transformation matrix of system
Figure BDA00028117511600001020
Figure BDA00028117511600001021
Then
Figure BDA00028117511600001022
And
Figure BDA00028117511600001023
the expression between is:
Figure BDA00028117511600001024
the expansion form is as follows:
Figure BDA0002811751160000111
the sub-items are listed as follows:
Figure BDA0002811751160000112
it is possible to obtain:
Figure BDA0002811751160000113
therefore, the initial elevation angle and the direction angle of the line of sight are calculated as in equation (13):
Figure BDA0002811751160000114
s10, calculating a transformation matrix
Figure BDA0002811751160000115
Substituting the calculation result of the formula (12) into the formula (7) to obtain a conversion matrix
Figure BDA0002811751160000116
According to equation (14), using
Figure BDA0002811751160000117
And tnOf time of day
Figure BDA0002811751160000118
C-system to A-system conversion matrix for calculating aiming tracking end time
Figure BDA0002811751160000119
Figure BDA00028117511600001110
Figure BDA00028117511600001111
The expression of (a) is:
Figure BDA00028117511600001112
wherein, thetan、ψn、γnIs tracking end tnTime c is the attitude angle relative to system A, called θnFor high and low angles of the line of sight,. psinFor line-of-sight direction angle, for gammanAnd is not of concern.
S11, calculating the elevation angle and the direction angle of the aiming line at the end time
From equation (15), one can solve:
Figure BDA0002811751160000121
the numbers in parentheses indicate
Figure BDA0002811751160000122
The row and column positions of the middle element. In the same way, can also be based on
Figure BDA0002811751160000123
Calculating each time node tkThe elevation angle and the azimuth angle of the line of sight.
S12, after the main task of the aiming tracking process is finished, calculating the rotation angular speed of the aiming line and outputting the result
(1) Tracking start t0At the moment, the initial angular position of the line of sight in the ground coordinate system is determined by
Figure BDA0002811751160000124
Is determined to be obvious
Figure BDA0002811751160000125
Thus, the initial elevation angle of the line of sight in the ground coordinate system
Figure BDA0002811751160000126
Calculated according to equation (13), the initial azimuth angle ψc0＝0；
(2) End of tracking tnAt the moment, the angular position of the line of sight in the ground coordinate system is determined by
Figure BDA0002811751160000127
Determining the elevation angle of the aiming line in the ground coordinate system
Figure BDA00028117511600001211
And the direction angle psicnCalculated by equation (16).
Therefore, the rotation angular velocity of the aiming line, high and low angular velocities can be calculated
Figure BDA0002811751160000128
Direction angular velocity
Figure BDA0002811751160000129
The calculation formula of (2) is as follows:
Figure BDA00028117511600001210
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 (1)

1. A method for automatically installing a watch on a simple fire control moving target of a shoulder-shooting barrel type weapon is characterized in that an inertia measurement unit is installed in the simple fire control, and comprises the following steps:
s1, starting the IMU, and collecting accelerometer and gyroscope data of the IMU
S2, calculating the inclination angle of the aiming device according to the data of the accelerometer and the gyroscope
Firstly, defining a coordinate system
Ground coordinate system Axyz: fixedly connected with the ground, and the origin A is at a transmitting point; the Ax axis is in the horizontal plane, is parallel to the projection of the simple fire-control aiming longitudinal axis at the starting moment of aiming tracking in the horizontal plane, and is positive forwards; the Ay axis is vertical to the horizontal plane and is positive upwards; the Az axis, the Ax axis and the Ay axis form a right-hand system, which is abbreviated as an A system, and the A system is taken as an inertial coordinate system;
line of sight coordinate system Oxcyczc: fixedly connected with the simple fire control, and the origin O is at the center of the simple fire control aiming axis; oz is a gas phasecThe axis coincides with the horizontal axis of the aiming "+" division; oycThe axis coincides with the vertical axis of the "+" division; oxcAxis is line of sight, forward is positive, and OycAxis and OzcThe axis forms the right-handed system, abbreviated as "c system";
IMU coordinate system Oxmymzm: fixedly connected with the simple fire control, and the origin O is at the center of the IMU; ideally, OxmAxis, OymAxis, OzmAxes are respectively parallel to OxcAxis, OycAxis, OzcAxes, and consistent directions, abbreviated as "m is"; due to installation errors, the m and c have non-parallel errors;
temporary platform coordinate system
Figure FDA0002811751150000011
The origin O is at the center of the simple fire control aiming axis; c is coincident with the start time of aiming tracking; ideally, the temporary platform coordinate system is stabilized in inertial space, abbreviated as
Figure FDA0002811751150000012
Due to the measurement error and the calculation error,
Figure FDA0002811751150000013
the direction of each axis has an error compared with the ideal case;
the letter is provided with a-' symbol to indicate that the letter represents the measured value and the letter is provided with a
Figure FDA0002811751150000014
The symbol indicates that the letter represents the calculated value; the upper corner marks of the vector and the letters of the vector components sequentially represent a coordinate system of vector projection and a sequence number of a time node from left to right, and the lower corner marks sequentially represent a reference coordinate system, a motion coordinate system and a projection coordinate axis from left to right; the transformation matrix is represented by a letter C, the upper corner mark of the transformation matrix represents a destination coordinate system of coordinate transformation, and the lower corner mark of the transformation matrix sequentially represents a starting coordinate system of coordinate transformation and a sequence number of a time node from left to right;
calculating the inclined angle of the aiming device according to the formula (1)
Figure FDA0002811751150000021
Figure FDA0002811751150000022
Wherein the content of the first and second substances,
Figure FDA0002811751150000023
is an average proportional vector (acceleration of gravity)
Figure FDA0002811751150000024
The modulus of the component in the z-direction,
Figure FDA0002811751150000025
is composed of
Figure FDA0002811751150000026
A modulus in the y-direction component;
s3, detecting whether a tracking signal is received or not, and if the tracking signal is detected, carrying out the next step; otherwise, whether the tracking signal is received is always inquired
S4, defining initial value of conversion matrix
Figure FDA0002811751150000027
At t0Time is established according to c series
Figure FDA0002811751150000028
Is, t0Of time of day
Figure FDA0002811751150000029
Is coincident with c; c is relative to
Figure FDA00028117511500000210
For strapdown matrices of systems
Figure FDA00028117511500000211
Is shown at t0At the moment of time of
Figure FDA00028117511500000212
Figure FDA00028117511500000213
Is an identity matrix;
s5, collecting accelerometer data, and extracting specific force vector
Figure FDA00028117511500000214
Collecting gyroscope data, extracting angular velocity vector
Figure FDA00028117511500000215
At tkMoment, accelerometer extraction specific force vector in IMU
Figure FDA00028117511500000216
Gyroscope extraction angular velocity vector
Figure FDA00028117511500000217
S6 strapdown matrix
Figure FDA00028117511500000218
Quaternion real-time correction
Using quaternion to calculate the time of day
Figure FDA00028117511500000219
Let c be relative to
Figure FDA00028117511500000220
Is a rotational quaternion of
Figure FDA00028117511500000221
Wherein ic、jc、kcC is a unit vector on three coordinate axes, and the real-time correction of Q is carried out through a formula (2):
Figure FDA00028117511500000222
according to
Figure FDA00028117511500000223
Giving an initial value q0＝1、q1＝0、q2＝0、q3＝0；
Solving equation (2) to obtain tkQuaternion of time is obtained by calculation
Figure FDA00028117511500000224
Figure FDA00028117511500000225
S7, performing acceleration specific force coordinate conversion
Figure FDA0002811751150000031
If the aiming tracking is not finished, returning to S5, otherwise, entering the next step
S8, calculating the average specific force vector
Note t0Of time of day
Figure FDA0002811751150000032
At the finish time t of aiming trackingnAll will be
Figure FDA0002811751150000033
Figure FDA0002811751150000034
Making an arithmetic mean, according to equation (4), in
Figure FDA0002811751150000035
Obtaining the average specific force vector in the system
Figure FDA0002811751150000036
Figure FDA0002811751150000037
S9, calculating the initial height angle and direction angle of the aiming line
Will be provided with
Figure FDA0002811751150000038
As a result of the recognition of the gravitational acceleration g at the point of emission, then
Figure FDA0002811751150000039
The decomposition in the A system is the decomposition of the gravity acceleration in the A system;
will be provided with
Figure FDA00028117511500000310
Expressed as:
Figure FDA00028117511500000311
Figure FDA00028117511500000312
is a mold of
Figure FDA00028117511500000313
Then
Figure FDA00028117511500000314
The decomposition in system A is:
Figure FDA00028117511500000315
Figure FDA00028117511500000316
is at a high or low angle with respect to the A system
Figure FDA00028117511500000317
And an angle of inclination
Figure FDA00028117511500000318
Angle of direction
Figure FDA00028117511500000319
According to the coordinate transformation relation,
Figure FDA00028117511500000320
transformation matrix of system and A system
Figure FDA00028117511500000321
Comprises the following steps:
Figure FDA00028117511500000322
will be provided with
Figure FDA00028117511500000323
Transposing to obtain A is
Figure FDA00028117511500000324
Transformation matrix of system
Figure FDA00028117511500000325
Figure FDA0002811751150000041
Then
Figure FDA0002811751150000042
And
Figure FDA0002811751150000043
the expression between is:
Figure FDA0002811751150000044
the expansion form is as follows:
Figure FDA0002811751150000045
the sub-items are listed as follows:
Figure FDA0002811751150000046
obtaining:
Figure FDA0002811751150000047
calculating the initial elevation angle and the direction angle of the line of sight according to the formula (13):
Figure FDA0002811751150000048
s10, calculating a transformation matrix
Figure FDA0002811751150000049
Substituting the calculation result of the formula (12) into the formula (7) to obtain a conversion matrix
Figure FDA00028117511500000410
According to equation (14), using
Figure FDA00028117511500000411
And tnOf time of day
Figure FDA00028117511500000412
C-system to A-system conversion matrix for calculating aiming tracking end time
Figure FDA00028117511500000413
Figure FDA00028117511500000414
Figure FDA00028117511500000415
The expression of (a) is:
Figure FDA0002811751150000051
wherein, thetan、ψn、γnIs tracking end tnTime c is the attitude angle relative to system A, called θnFor high and low angles of the line of sight,. psinIs the boresight direction angle;
s11, calculating the elevation angle and the direction angle of the aiming line at the end time
And (3) calculating the elevation angle and the direction angle of the sight line at the end moment according to the formula (15):
Figure FDA0002811751150000052
the numbers in parentheses indicate
Figure FDA0002811751150000053
The row and column positions of the middle element; according to
Figure FDA0002811751150000054
Calculating each time node tkThe elevation angle and the direction angle of the aiming line;
s12, calculating the rotation angular speed of the aiming line and outputting the result
(1) Tracking start t0At the moment, the initial angular position of the line of sight in the ground coordinate system is determined by
Figure FDA0002811751150000055
It is determined that,
Figure FDA0002811751150000056
initial high-low angle of aiming line in ground coordinate system
Figure FDA0002811751150000057
Calculated according to equation (13), the initial azimuth angle ψc0＝0；
(2) End of tracking tnAt the moment, the angular position of the line of sight in the ground coordinate system is determined by
Figure FDA0002811751150000058
Determining, calculating the high and low angles theta of the aiming line on the ground coordinate system according to the formula (16)cnAnd the direction angle psicn(ii) a Calculating the rotation angular velocity of the aiming line according to the formula (17), including high and low angular velocities
Figure FDA0002811751150000059
Direction angular velocity
Figure FDA00028117511500000510
Figure FDA00028117511500000511
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