CN109373832B - Method for measuring initial parameters of rotating projectile muzzle based on magnetic rolling - Google Patents

Method for measuring initial parameters of rotating projectile muzzle based on magnetic rolling Download PDF

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CN109373832B
CN109373832B CN201811493274.3A CN201811493274A CN109373832B CN 109373832 B CN109373832 B CN 109373832B CN 201811493274 A CN201811493274 A CN 201811493274A CN 109373832 B CN109373832 B CN 109373832B
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projectile
muzzle
initial
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angle
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CN109373832A (en
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魏晓慧
龙达峰
曹建忠
黄近秋
孙俊丽
罗中良
徐瑜
周英隆
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Beijing Hengzhun Times Technology Co ltd
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Huizhou University
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    • F—MECHANICAL ENGINEERING; LIGHTING; HEATING; WEAPONS; BLASTING
    • F42—AMMUNITION; BLASTING
    • F42B—EXPLOSIVE CHARGES, e.g. FOR BLASTING, FIREWORKS, AMMUNITION
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Abstract

The invention discloses a method for measuring initial parameters of a rotating projectile muzzle based on magnetic rolling measurement, which comprises the following steps: (1) measuring scheme of initial parameters of a rotating projectile muzzle, (2) magnetic measurement roll rate and filtering estimation method thereof, (3) calculating method of initial velocity of the rotating projectile muzzle, (4)A method for calculating the initial attitude of the muzzle of the rotating projectile, (5) projectile three-dimensional attitude information obtained by calculating the initial attitude of the muzzle, (5)ψ 0，θ 0Andγ 0) Then, calculating each initial velocity component when the gun muzzle is ejected by rotation according to a velocity projection formula (υ 0,x，υ 0,yAndυ 0,z). The method provided by the invention realizes accurate measurement of the initial attitude parameter of the rotating projectile body, and has the advantages of simplicity, easiness in implementation, high performance ratio and the like.

Description

Method for measuring initial parameters of rotating projectile muzzle based on magnetic rolling
Technical Field
The invention relates to the technical field of measurement of initial parameters of a high-speed rotating projectile muzzle, in particular to a combined measurement method for the initial attitude and the speed of the rotating projectile muzzle based on a three-axis accelerometer and a single-axis magnetic sensor.
Background
The guided reformation of the spinning projectile is the development direction of a conventional weapon, and the real-time measurement of the flight attitude of the spinning projectile is the premise of realizing the navigation and control of the spinning projectile. However, due to the limitations of high autorotation, high overload and the like when the rotating projectile is launched, the used missile-borne attitude measurement system has the performance requirements of high overload resistance, small volume, low cost and the like. Particularly, due to the high-speed rotation characteristic of the spinning projectile, the range and the precision of the prior missile-borne gyroscope are difficult to meet the application requirements at the same time, so that the accurate acquisition of the initial attitude and the speed of the projectile navigation is influenced, and the initial attitude and the speed are preconditions for inertial navigation solution, so that the accurate acquisition of the initial attitude and the speed parameters of the spinning projectile is one of the difficulties in the guidance transformation.
Disclosure of Invention
The invention aims to provide a method for measuring the initial attitude and the speed of a rotating projectile, which is suitable for accurately measuring the initial attitude parameters of the rotating projectile body.
The invention is realized by adopting the following technical scheme:
a method for measuring initial parameters of a rotating projectile muzzle based on magnetic rolling comprises the following steps:
(1) scheme for measuring initial parameters of gun muzzle of rotating projectile
Projectile coordinate system (OX)bYbZb) The front part, the upper part and the right part are defined and accord with the right-hand relationship;
the three-axis accelerometer is completely installed in a missile body coordinate system in a strapdown mode, the directions of all sensitive axes of the accelerometer are consistent with the directions of all axes of the missile body coordinate system, and the X, Y and the Z-axis accelerometer are used for measuring output respectively
Figure BDA0001896205020000021
And
Figure BDA0001896205020000022
showing that each accelerometer is used to measure an acceleration component in the projectile;
single-shaft magnetic sensor and projectile rolling axis XbThe shaft is completely installed in a strapdown mode, the single-shaft magnetic sensor is used for measuring the roll angle rate information of the rotating bomb, and the measurement output of the single-shaft magnetic sensor is MxRepresents;
selecting a launch coordinate system as a spinning projectile navigation reference coordinate system (OX)nYnZn) Wherein
Figure BDA0001896205020000023
The yaw angle of the projectile body is theta, the pitch angle of the projectile body is theta, and gamma is the roll angle of the projectile body;
(2) magnetic survey roll rate and filtering estimation method thereof
2.1 method for acquiring rolling angle rate observed quantity of spinning projectile
According to the electromagnetic induction law, the output voltage of the single-shaft magnetic sensor installed on the elastic shaft in a strapdown mode meets the following equation:
Figure BDA0001896205020000024
in the above formula (1), phimIs the maximum magnetic flux in the bore of the gun, N is the number of turns of the coil, psimIs a flux linkage, omegaxIs the angular rate of projectile self-rotation;
magnetic measurement output M mounted on rolling shaft by utilizing strapdownxEstimating projectile roll rate ωm,x；
2.2 elastomer roll angular rate filter
Measuring output M with a magnetic sensorxEstimated projectile roll rate omegam,xThere is always some error, and the measurement error equation is expressed as:
ωm,x＝ωi,x+nx(2)
in the above formula (2), ω ism,xEstimating the resulting roll rate, ω, for measurementi,xFor ideal roll angular rate, nxTo measure noise;
selecting roll angle rate omega by filterxAs the state variable X ═ ω of the systemxThe equation of state is expressed as:
X(k)＝X(k-1)+w(k-1)(3)
in the above formula (3), w(k-1)Assuming zero mean Gaussian white noise, satisfy E [ w (t)]＝0， E[w(t),wT(τ)]＝Q(t)(t-τ)；
Selecting a magnetic rolling angle rate omega obtained by reverse-push calculation according to the formula (1)m,xObserved variable z (t) ═ ω as a filter systemm,xThe observation equation is expressed as:
z(t)＝X(t)+v(t) (4)
in the above formula, v (t) is the measurement noise of the system, and v (t) is assumed to be GaussianWhite noise, and satisfies E [ v (t)]＝0，E[v(t),vT(τ)]＝R(t)(t-τ)；
Therefore, the filter jointly constructs a system filtering equation set by the state equation (3) and the observation equation (4), and adopts a filter based on a discrete kalman filtering algorithm to perform optimal estimation on the roll rate, wherein the filtering algorithm comprises the following two processes of time updating and measurement updating:
2.2.1, time update process:
Figure BDA0001896205020000031
2.2.2, measurement updating process:
Figure BDA0001896205020000032
in the above formula, K(k)Representing the filter gain; hkIs a measured value; rkTo measure noise; qk-1Is the system noise; p(k,k-1)Estimating a variance for the system at a previous time; p(k)The system variance at the current moment; i is a unit array; p(k-1)Estimating a variance for the system;
Figure BDA0001896205020000049
is a measuring array; k is the sampling instant.
Therefore, the projectile roll angular rate omega is finally completed through a discrete kalman filtering algorithmm,xIs estimated optimally
Figure BDA0001896205020000041
(3) Method for calculating initial velocity of rotating projectile at muzzle
The estimate of the total projectile velocity out of the chamber is expressed as:
Figure BDA0001896205020000042
in the above formula (7), D is the caliber size of the rotating projectile, gammagIs the size of the winding angle of the rifling,the size of the wrap angle is determined by the type of gun system, and if the type of the rotating projectile is known, the initial velocity v of the muzzle0Angular velocity omega with rotating elastic shaftxThere is a mutual correspondence;
thus, the optimal estimation of the resulting magnetometric roll angular rate using the discrete kalman filter-based algorithm described previously
Figure BDA0001896205020000043
Obtaining the initial total velocity v of the muzzle of the rotary projectile through table lookup0；
(4) Method for resolving initial attitude of muzzle of rotating projectile
The three-axis accelerometer strapdown installs the bullet coordinate system, and before the gun launches, each axle acceleration measurement output is the projection component of gravity component in bullet coordinate system, and its expression is:
Figure BDA0001896205020000044
in the above-mentioned formula (8),
Figure RE-GDA0002693572350000011
and
Figure RE-GDA0002693572350000012
represented as X, Y and Z-axis accelerometer measurement outputs, respectively; [0, -g,0]TIs the gravity projection component under the navigation coordinate system;
Figure RE-GDA0002693572350000013
transforming a direction cosine matrix for the rotating projectile attitude;
Figure BDA0001896205020000048
Figure BDA0001896205020000051
according to the projection relation of the formula (8), the pitch angle and the roll angle of the rotating projectile before the gun is launched are obtained; assuming that the yaw angle and the pitch angle of the projectile body are unchanged and the yaw angle is zero when the rotating projectile moves in the bore, the calculation formulas of the initial pitch angle and the roll angle before ignition when the projectile body is rotationally ejected out of the muzzle are respectively as follows:
Figure BDA0001896205020000052
Figure BDA0001896205020000053
if the time required for the rotating bomb to move in the bore is tau seconds, the obtained magnetic roll angle rate is estimated by using the filter
Figure BDA0001896205020000054
The roll angle of the projectile opening of the rotary projectile is obtained through integral calculation, and the calculation formula of the initial roll angle (when the projectile is discharged from the projectile opening) of the projectile body is as follows:
Figure BDA0001896205020000055
therefore, measurement and calculation of the three-dimensional attitude angle of the initial yaw angle, the pitch angle and the roll angle of the rotary projectile muzzle are finally completed through the above formulas (10) to (12);
(5) and projectile body three-dimensional attitude information obtained by utilizing muzzle initial attitude calculation (
Figure BDA0001896205020000056
θ0And gamma0) Then, each initial velocity component (v) at the time of rotating and ejecting the muzzle is calculated according to the following velocity projection formula (13)0,x，v0,yAnd v0,z)。
Figure BDA0001896205020000057
And the calculation step is used for measuring and calculating each initial velocity component when the gun muzzle is ejected in a rotating mode.
The method has the following advantages:
1. compared with the traditional gyroscope measurement scheme, the invention adopts the combination scheme of measuring by using the three-axis accelerometer and the single-axis magnetic sensor, is more suitable for the application environment of three-high severe missile-borne test under high overload, high spin and high dynamic conditions, and the measurement system has higher survivability and reliability.
2. The measuring method can simultaneously complete the measurement of the three-dimensional initial speed and the three-dimensional initial attitude of the muzzle, and realizes the acquisition of all parameters of the initial parameters of the muzzle.
3. The measuring scheme provided by the invention has the advantages of simplicity, easiness in implementation, high performance ratio and the like.
Drawings
Figure 1 shows a schematic view of a missile-borne sensor installation scheme.
Fig. 2 shows a navigation reference coordinate system.
Detailed Description
The following detailed description of specific embodiments of the invention refers to the accompanying drawings.
A rotary projectile muzzle initial attitude and speed combined measurement method based on a three-axis accelerometer and a single-axis magnetic sensor comprises the following steps:
1. scheme for measuring initial parameters of rotating projectile muzzle
The missile-borne sensor mainly comprises a triaxial accelerometer and a uniaxial magnetic sensor, and the measuring and mounting scheme of the missile-borne sensor is shown in figure 1. Coordinate system (OX)bYbZb) And a bullet coordinate system is defined as the upper front part and the right part, and the relationship of the right hand is met. The three-axis accelerometer is completely strapdown mounted on the projectile coordinate system, the directions of all sensitive axes of the accelerometer are consistent with those of all axes of the projectile coordinate system, and the X, Y and Z-axis accelerometer are used for measuring output respectively
Figure BDA0001896205020000061
And
Figure BDA0001896205020000062
showing that each accelerometer is used to measure an acceleration component within the projectile. And the single-axis magnetic sensor and the projectile rolling axis XbComplete strapdown mounting of shafts, single-shaft magnetic transmissionSensing roll rate information of spinning projectile, and measuring output MxAnd (4) showing.
The invention selects a launching coordinate system as a spinning projectile navigation reference coordinate system (OX)nYnZn) As shown in fig. 2, in this example,
Figure BDA0001896205020000071
the yaw angle of the projectile body, the pitch angle theta of the projectile body and the roll angle gamma of the projectile body are shown.
2. Magnetic rolling rate measurement and filtering estimation method thereof
2.1 method for acquiring rolling angle rate observed quantity of spinning projectile
Because the rotating projectile makes high-speed self-rotating motion in the bore of the cannon, the magnetic sensor which is connected with the projectile axis in a strapdown mode also makes self-rotating motion along with the projectile body, and the magnetic sensor can generate induced voltage in a magnetic field. According to the law of electromagnetic induction, the output voltage of a magnetic sensor installed on a missile shaft in a strapdown mode can be derived to meet the following equation:
Figure BDA0001896205020000072
in the above formula (1), phimIs the maximum magnetic flux in the bore of the gun, N is the number of turns of the coil, and is psimFlux linkage, omegaxIs the angular rate of projectile spin.
The magnetic measurement output equation of the formula (1) shows that the projectile body roll rate (omega)x) And the output of the magnetic sensor can be used for carrying out reverse calculation. Thus, the present invention utilizes a strapdown mounted magnetic measurement output (M) at the roll axisx) Estimating projectile roll rate (ω)m,x)。
2.2 elastomer roll angular rate filter
Due to the existence of adverse factors such as external magnetic interference, error parameters of the sensor, noise of a measuring circuit and the like, the actual measurement output of the strap-down magnetic sensor always has measurement errors. Thus, the output (M) is measured with a magnetic sensorx) Estimated projectile roll rate (ω)m,x) There is always a certain error, and its measurement error equation can be expressedComprises the following steps:
ωm,x＝ωi,x+nx(2)
in the above formula (2), ω ism,xEstimating the resulting roll rate, ω, for measurementi,xFor ideal roll angular rate, nxTo measure noise.
In order to improve the measurement accuracy of the roll angle rate of the magnetic measurement projectile body, the Kalman filter is adopted to carry out optimal filtering estimation on the magnetic measurement roll rate so as to improve the roll angle rate accuracy. The filter designed by the invention selects the roll angle rate omegaxAs the state variable X ═ ω of the systemxThe equation of state can be expressed as:
X(k)＝X(k-1)+w(k-1)(3)
in the above formula (3), w(k-1)Assuming zero mean Gaussian white noise, satisfy E [ w (t)]＝0， E[w(t),wT(τ)]＝Q(t)(t-τ)。
Selecting the magnetic rolling angle rate (omega) obtained by reverse-deducing calculation according to the formula (1)x) Observed variable z (t) ═ ω as a filter systemm,xThe observation equation can be expressed as:
z(t)＝X(t)+v(t) (4)
in the above formula (4), v (t) is the measured noise of the system, and v (t) is assumed to be white Gaussian noise and satisfies E [ v (t)]＝0，E[v(t),vT(τ)]＝R(t)(t-τ)。
Therefore, the designed filter of the invention constructs a system filtering equation set by the state equation (3) and the observation equation (4) together, and adopts a filter based on a discrete kalman filtering algorithm to carry out the optimal estimation of the roll rate, wherein the filtering algorithm comprises the following two processes of time updating and measurement updating:
(1) and (3) time updating process:
Figure BDA0001896205020000081
(2) and (3) measurement updating process:
Figure BDA0001896205020000091
in the above formula, K(k)Representing the filter gain; hkIs a measured value; rkTo measure noise; qk-1Is the system noise; p(k,k-1)Estimating a variance for the system at a previous time; p(k)The system variance at the current moment; i is a unit array; p(k-1)Estimating a variance for the system; hk TIs a measuring array; k is the sampling instant.
Therefore, the projectile roll angular rate omega is finally completed through a discrete kalman filtering algorithmm,xIs estimated optimally
Figure BDA0001896205020000092
3. Method for calculating initial speed of rotating projectile at muzzle
Because the projectile flies by means of inertia after being ejected out of the muzzle in a rotating way, the initial speed of the projectile out of the muzzle directly determines the flying distance or range of the projectile. However, the flight distance of the projectile spinning one circle in the bore is irrelevant to the initial velocity, and is mainly determined by the type of the gun system, the winding angle of rifling in the gun, the caliber of the projectile and the like. The estimate of the total projectile velocity out of the chamber can be expressed as:
Figure BDA0001896205020000093
in the above formula (7), D is the caliber size of the rotating projectile, gammagThe winding angle of the rifling is determined by the type of gun system, and the initial velocity v of the muzzle is known0Angular velocity omega with rotating elastic shaftxThere is a mutual correspondence.
Therefore, the invention utilizes the discrete kalman filter algorithm to optimally estimate the obtained magnetic roll rate
Figure BDA0001896205020000094
Obtaining the initial total velocity v of the muzzle of the rotary projectile through table lookup0. The accurate corresponding relation between the initial speed and the roll angular speed is provided by artillery manufacturing enterprisesAnd stored in the missile-borne measurement system in advance.
4. Method for resolving initial attitude of rotating projectile at muzzle
In the measuring scheme of the missile-borne sensor, a triaxial accelerometer is strapdown-mounted with a missile coordinate system. Before the artillery is launched, the acceleration measurement output of each axis is a projection component of the gravity component in a projectile coordinate system, which can be expressed as:
Figure BDA0001896205020000101
in the above-mentioned formula (8),
Figure RE-GDA0002693572350000014
and
Figure RE-GDA0002693572350000015
represented as X, Y and Z-axis accelerometer measurement outputs, respectively; [0, -g,0]TIs the gravity projection component under the navigation coordinate system;
Figure RE-GDA0002693572350000016
the direction cosine matrix is transformed for the spinning projectile attitude.
Figure BDA0001896205020000105
From the projection relationship of equation (8), the pitch and roll angles of the spinning projectile prior to firing of the artillery can be derived. The invention assumes that the yaw angle and the pitch angle of the projectile body are not changed and the yaw angle is zero when the rotating projectile moves in the bore. Therefore, the calculation formulas of the initial pitch angle and the rolling angle before ignition when the muzzle is ejected in a rotating mode are respectively as follows:
Figure BDA0001896205020000106
Figure BDA0001896205020000107
if the rotating bullet is in the chamberIf the time required for movement is tau seconds, the obtained magnetic rolling angle rate is estimated by using the filter
Figure BDA0001896205020000108
The roll angle of the projectile opening of the rotary projectile is obtained through integral calculation, and the calculation formula of the initial roll angle (when the projectile is discharged from the projectile opening) of the projectile body is as follows:
Figure BDA0001896205020000109
therefore, the measurement calculation of the three-dimensional attitude angle of the initial yaw angle, the pitch angle and the roll angle of the rotating projectile muzzle is finally completed through the above equations (10) to (12).
5. Method for calculating initial speed of rotating projectile at muzzle
The steps of measuring and resolving the initial velocity of the muzzle of the spinning projectile mainly comprise the following steps:
estimating the optimal magnetic rolling rate according to a filter
Figure BDA0001896205020000111
The size is calculated by the formula (7) of the total velocity calculation of the muzzle of the rotating projectile in a reverse mode to obtain the initial total velocity v of the projectile0。
Projectile body three-dimensional attitude information obtained by utilizing muzzle initial attitude calculation (
Figure BDA0001896205020000112
θ0And gamma0) Then, each initial velocity component (v) at the time of rotating and ejecting the muzzle is calculated according to the following velocity projection formula (13)0,x， v0,yAnd v0,z)。
Figure BDA0001896205020000113
And the calculation step is used for measuring and calculating each initial velocity component when the gun muzzle is ejected in a rotating mode.
Therefore, the invention finally realizes the initial attitude of the rotating projectile muzzle simultaneously according to the attitude measurement method and the speed measurement method
Figure BDA0001896205020000114
θ0And gamma0) And initial velocity (v)0,x，v0,yAnd v0,z) And (4) solving joint measurement.
It should be noted that modifications and applications may occur to those skilled in the art without departing from the spirit and scope of the invention.

Claims (1)

1. A method for measuring initial parameters of a rotating projectile muzzle based on magnetic rolling is characterized by comprising the following steps: the method comprises the following steps:
(1) scheme for measuring initial parameters of gun muzzle of rotating projectile
Projectile coordinate system OXbYbZbThe front part, the upper part and the right part are defined and accord with the right-hand relationship;
the three-axis accelerometer is completely installed in a missile body coordinate system in a strapdown mode, the directions of all sensitive axes of the accelerometer are consistent with the directions of all axes of the missile body coordinate system, and the X, Y and the Z-axis accelerometer are used for measuring output respectively
Figure FDA0002693572340000011
And
Figure FDA0002693572340000012
showing that each accelerometer is used to measure an acceleration component in the projectile;
single-shaft magnetic sensor and projectile rolling axis XbThe axis is completely installed in a strapdown way, the single-axis magnetic sensor is used for measuring the roll angle rate information of the spinning projectile, and the measurement output of the single-axis magnetic sensor is MxRepresents;
selecting a launching coordinate system as a rotating missile navigation reference coordinate system OXnYnZnWherein
Figure FDA0002693572340000013
The yaw angle of the projectile body is theta, the pitch angle of the projectile body is theta, and gamma is the roll angle of the projectile body;
(2) magnetic survey roll rate and filtering estimation method thereof
2.1 method for acquiring rolling angle rate observed quantity of spinning projectile
According to the electromagnetic induction law, the output voltage of the single-shaft magnetic sensor installed on the elastic shaft in a strapdown mode meets the following equation:
Figure FDA0002693572340000014
in the above formula (1), phimIs the maximum magnetic flux in the bore of the gun, N is the number of turns of the coil, psimIs a flux linkage, omegaxIs the angular rate of projectile self-rotation;
magnetic measurement output M mounted on rolling shaft by utilizing strapdownxEstimating projectile roll rate ωm,x；
2.2 elastomer roll angular rate filter
Measuring output M with a magnetic sensorxEstimated projectile roll rate omegam,xThere is an error, and the measurement error equation is expressed as:
ωm,x＝ωi,x+nx(2)
in the above formula (2), ω ism,xEstimating the resulting roll rate, ω, for measurementi,xFor ideal roll rate, nxTo measure noise;
selecting roll angle rate omega by filterxAs the state variable X ═ ω of the systemxThe equation of state is expressed as:
X(k)＝X(k-1)+w(k-1)(3)
in the above formula (3), w(k-1)Is assumed to be zero mean gaussian white noise;
selecting a magnetic rolling angle rate omega obtained by reverse-push calculation according to the formula (1)m,xObserved variable z (t) ═ ω as a filter systemm,xThe observation equation is expressed as:
z(t)＝X(t)+v(t) (4)
in the above formula, v (t) is the measurement noise of the system;
therefore, the filter jointly constructs a system filtering equation set by the state equation (3) and the observation equation (4), and adopts a filter based on a discrete kalman filtering algorithm to perform optimal estimation on the roll rate, wherein the filtering algorithm comprises the following two processes of time updating and measurement updating:
2.2.1, time update process:
Figure FDA0002693572340000021
2.2.2, measurement updating process:
Figure FDA0002693572340000022
in the above formula, K(k)Representing the filter gain; hkIs a measured value; rkTo measure noise; qk-1Is the system noise; p(k/k-1)Estimating a variance for the system at a previous time; p(k)The system variance at the current moment; i is a unit array; p(k-1)Estimating a variance for the system;
Figure FDA0002693572340000031
is a measuring array;
therefore, the projectile roll angular rate omega is finally completed through a discrete kalman filtering algorithmm,xIs estimated optimally
Figure FDA0002693572340000032
(3) Method for calculating initial velocity of rotating projectile at muzzle
The estimate of the total projectile velocity out of the chamber is expressed as:
Figure FDA0002693572340000033
in the above formula (7), D is the caliber size of the rotating projectile, gammagThe winding angle of the rifling is determined by the type of gun system, and the initial velocity v of the muzzle is known0And a rotary elastic shaftAngular velocity of (a) < omega >xThere is a mutual correspondence;
thus, the optimal estimation of the resulting magnetometric roll rate using the aforementioned discrete kalman filter-based algorithm
Figure FDA0002693572340000034
Obtaining the initial total velocity v of the muzzle of the rotary projectile through table lookup0；
(4) Method for resolving initial attitude of muzzle of rotating projectile
The three-axis accelerometer strapdown installs the bullet coordinate system, and before the gun launches, each axle acceleration measurement output is the projection component of gravity component in bullet coordinate system, and its expression is:
Figure FDA0002693572340000035
in the above-mentioned formula (8),
Figure FDA0002693572340000036
and
Figure FDA0002693572340000037
represented as X, Y and Z-axis accelerometer measurement outputs, respectively; [0, -g,0]TIs the gravity projection component under the navigation coordinate system;
Figure FDA0002693572340000038
transforming a direction cosine matrix for the rotating projectile attitude;
Figure FDA0002693572340000041
according to the projection relation of the formula (8), the pitch angle and the roll angle of the rotating projectile before the gun is launched are obtained; assuming that the yaw angle and the pitch angle of the projectile body are unchanged and the yaw angle is zero when the rotating projectile moves in the bore, the calculation formulas of the initial pitch angle and the roll angle when the projectile body is rotationally ejected out of the muzzle are respectively as follows:
Figure FDA0002693572340000042
Figure FDA0002693572340000043
if the time required for the rotating bomb to move in the bore is tau seconds, the magnetic roll angle rate obtained by the filter estimation is used
Figure FDA0002693572340000044
The rolling angle of the muzzle of the rotating projectile is obtained through integral calculation, and the calculation formula of the initial rolling angle of the projectile body is as follows:
Figure FDA0002693572340000045
therefore, measurement and calculation of the three-dimensional attitude angle of the initial yaw angle, the pitch angle and the roll angle of the rotary projectile muzzle are finally completed through the above formulas (10) to (12);
(5) and calculating the three-dimensional attitude information of the projectile body by utilizing the initial attitude of the muzzle
Figure FDA0002693572340000046
θ0And gamma0Then, each initial velocity component v at the time of rotating and ejecting the muzzle is calculated according to the following velocity projection formula (13)0,x、v0,yAnd v0,z；
Figure FDA0002693572340000047
And the calculation step is used for measuring and calculating each initial velocity component when the gun muzzle is ejected in a rotating mode.
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