CN113221314B - Modeling method for radar echo signal caused by angular motion initial disturbance of spinning tail fin projectile - Google Patents

Modeling method for radar echo signal caused by angular motion initial disturbance of spinning tail fin projectile Download PDF

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CN113221314B
CN113221314B CN202110271117.3A CN202110271117A CN113221314B CN 113221314 B CN113221314 B CN 113221314B CN 202110271117 A CN202110271117 A CN 202110271117A CN 113221314 B CN113221314 B CN 113221314B
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宫志华
段鹏伟
陈春江
冷雪冰
田珂
田家磊
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Abstract

The invention relates to a modeling method of radar echo signals of angular motion initial disturbance of a spinning tail wing projectile, which is characterized by comprising the following specific steps of: establishing a kinetic equation of the spinning tail wing projectile; solving a homogeneous differential equation of the projectile re-attack angle; determining an angular motion mode of the spinning tail fin projectile; determining a relevant coordinate system definition; calculating the distance from a scattering point of the projectile to the radar; a radar echo Doppler signal; the method is characterized in that the change mechanism of the angular motion between the bullet axis and the velocity vector of the spinning tail bullet in the space motion process is analyzed, and then the change mechanism is converted into the projection transformation of radar measurement information on the motion, and a theoretical basis is provided for identifying the motion characteristic, the aerodynamic characteristic and the structural characteristic of a target by utilizing the radar measurement information.

Description

Modeling method for radar echo signal caused by angular motion initial disturbance of spinning tail fin projectile
Technical Field
The invention relates to a modeling method of radar echo signals caused by the angular motion initial disturbance of a spinning tail projectile, which is a modeling and simulation technology of micro Doppler signals generated by radar echoes by the angular motion of the spinning tail projectile in the aspects of ballistics, electromagnetism, weapon tests and the like, and belongs to the field of radar echo signal modeling and simulation.
Background
The flight motion of the projectile in the air comprises the mass center motion and the rotation around the center, and the core of the motion model of the spinning empennage projectile constructed according to the motion model is the kinematics and the kinetic equation of the mass center motion and the rotation around the center of the projectile. The projectile rotates around the center to determine the flight stability of the projectile, and the methods for realizing the flight stability of the projectile mainly comprise rotation stability and tail fin stability.
In the field of radar measurement, the movement of the mass center of a projectile belongs to translation, comprises motion components such as radial velocity, radial acceleration or high-order acceleration and the like, and is a main component of radar measurement of the Doppler effect of a moving target (the flying principle and application of Bomb and rocket [ M ]. Beijing: the publisher of Beijing university of science and engineering, 2018.). The shot moves around the center, and the shot comprises spinning, coning, rolling, vibration and other motion components, so that a radar target Doppler signal is subjected to micro modulation, and the radar target Doppler signal is usually taken as 'noise' or 'residual error' to be strictly eliminated during ballistic time domain data processing.
In the early century, the radial Micro-motion (Micro-motion) effect of a moving target, excluding centroid translation, was analyzed by v.c. Chen using microwave radar measurement and defined as after Micro-Doppler (Chen v.c. analysis of radio Micro-Doppler with time-frequency transforms [ J ]. Proceedings of the 10th IEEE work hop on Statistical Signal and Array processing, usa, 2000.), the field of radar target detection and identification has become a research hotspot of the international and foreign academic communities (William Z L, alan a g.overview of the linear Laboratory based failure of systematic project [ J ]. Linear Laboratory Journal,2002,13 (1): 932.) (advance of radar target identification technology in the missile defense system of Liu Yongxiang, li Xiang, zhuzhgzhao. System engineering and electronics, 2006,28 (8): 1188-1193.).
There are many research achievements for micro-motion identification of ground, air and high-altitude targets, and classification and accurate identification of ground moving targets such as tank armored vehicles and the like can be realized by using micro-doppler features (barbarbarbarboss s. Doppler-rate filtering for detecting moving targets with Synthetic apertures radars [ a ]. Proceedings of the SPIE on Millimeter Wave and Synthetic Aperture Radar [ C ]. Orlando, USA: SPIE Press, 1989.140-147.) (yellow key, plum, yellow dawn, etc.. Tank target parameter estimation and identity identification based on micro-doppler features [ J ]. Electronic and informatics newspaper, 2010,32 (5): 1050-1055.); the micro Doppler spectrum of the helicopter rotor can be analyzed and judged by adopting millimeter wave Radar to analyze and judge the motion state of the helicopter (Nalecz M, andrianik R, wojtkiewicz A. Micro-Doppler analysis of signal received by FMCW Radar [ A ]. Proceedings of International radio Symposium [ C ]. Dresden, germany: IEEE Press, 2003.231-235.) (Chenpeng, strength, waisward, etc.. The micro Doppler characteristic analysis of the helicopter rotor [ J ]. Infrared and laser engineering, 2015,44 (1): 118-121.); especially in a missile defense system, the micro-motion characteristic information becomes an important auxiliary means for target identification, and the research result of the micro-motion characteristic of the ballistic missile can effectively provide basis for identifying threat targets in the middle of a ballistic missile (Yanggui, wang Han, zhang Yu and the like. The change characteristic [ J ] of the micro-motion characteristic parameter of the ballistic missile along with the signal to noise ratio of radar echo is communicated with information, 2017,175 (7): 10-12.) (Wangwulin, chenyili, rawarong Jun. The research of the micro-motion characteristic of the middle section of the ballistic missile [ J ]. System engineering and electronic technology, 2016,38 (3): 487-492.).
However, the above researches do not relate to the simulation and modeling of radar echo signals of ballistic straight-line section projectiles subjected to initial disturbance.
Disclosure of Invention
The invention aims to provide a modeling method of an angular motion initial disturbance radar echo signal of a spinning tail projectile, which is in the field of conventional weapon test identification, on the premise of a dynamics and kinematics model of the micromotion of the projectile, focuses on the signal level mapping relation of angular motion to a measurement radar caused by the influence of initial disturbance on the straight-line segment of the projectile in a trajectory, establishes a quantitative relation between micro Doppler and projectile parameters and a micromotion echo model, and can provide a reference basis for interpreting radar signals and accurately identifying target motion parameters; on the basis of representing the dynamic equation of the spin tail projectile by a second-order variable coefficient differential equation of the projectile counterattack angular motion, various micromotions generated by the spin tail projectile under the influence of initial disturbance in a trajectory straight-line segment are analyzed and researched, a quantitative relation between micro Doppler and projectile parameters and a micromotion echo model are established, and a radar echo signal modeling system is perfected.
The technical scheme of the invention is realized as follows: a modeling method for radar echo signals of angular motion initial disturbance of a spinning tail projectile is characterized by comprising the following specific steps:
the method comprises the following steps: establishing a kinetic equation of the spinning tail projectile;
according to the ballistics theory, the kinetic equation of the spinning tail projectile can be expressed by a second-order variable coefficient differential equation of the complex attack angle motion
Figure GDA0004036388940000031
Delta is the angle of attack of the projectile flying in the air and can be expressed by complex numbers;
Figure GDA0004036388940000041
wherein k is zz Is the equatorial damping moment, b y As a lifting force, b x G is the local gravity acceleration, theta is the scalar value of the attack angle of the projectile, and v is the flight speed of the projectile;
M＝k z ，k z determining the frequency of attitude motion for the static moment;
Figure GDA0004036388940000042
c is the polar moment of inertia,
Figure GDA0004036388940000043
the autorotation speed of the projectile, A is the equator moment of inertia, and v is the ratio of the flight speed;
Figure GDA0004036388940000044
b y is a lifting force, k y Is the magnus moment;
Figure GDA0004036388940000045
disturbance terms for the angle of attack motion of the projectile caused by ballistic curvature;
Figure GDA0004036388940000046
the disturbance term of the projectile attack angle motion caused by the asymmetry of the projectile structure is used;
Figure GDA0004036388940000047
the method comprises the following steps of (1) obtaining a perturbation term of projectile attack angle movement caused by projectile pneumatic asymmetry;
Figure GDA0004036388940000048
is the term for the perturbation of the projectile angle of attack caused by the vertical gas flow.
| | Δ | | is the angle between the space missile axis and the velocity vector, Δ' and Δ ″ are the first and second derivatives of the complex angle of attack on the ballistic arc length s, Δ = Δ | | when the starting condition is s =0 0 ，
Figure GDA0004036388940000049
Δ 0 Is the initial value of the re-attack angle of the projectile,
Figure GDA00040363889400000410
represents delta 0 First derivative of time t, v 0 For the initial velocity of the projectile, the equation and its initial conditions reflect the angular of attack motion of the projectile caused by various factors, wherein H represents the damping motion and is mainly determined by the equatorial damping moment k zz And a lift force b y And resistance b x Etc.; m major and static moment k z In relation, the frequency of the gesture motion depends mainly on this term; t main and lift b y And Magnus moment k y In relation, it affects flight stability; pThe ratio of the autorotation speed to the flight speed of the projectile is obtained;
step two: solving a uniform differential equation of the complex attack angle of the projectile;
solving a homogeneous differential equation of a complex attack angle of the projectile according to the angular motion characteristic that the projectile is only disturbed by the initial disturbance in the straight line segment;
Δ″+(H-iP)Δ′-(M+iPT)Δ＝0
the characteristic root of this equation for the complex angle of attack Δ is
l 1 ＝λ 1 +iω 1 ，l 2 ＝λ 2 +iω 2
In the formula of lambda 1 ,λ 2 Called damping index, ω 1 ,ω 2 Modal angular frequency referred to as the ballistic arc length s; the angle of attack is solved as
Figure GDA0004036388940000051
In the formula, C 1 ,C 2 Is a undetermined coefficient, is a complex number, and can be written as
Figure GDA0004036388940000052
Constant k 1 ,k 2 Is a real number and, therefore,
Figure GDA0004036388940000053
is an initial phase, determined by an initial condition; the solution to the angle of attack can be written as
Figure GDA0004036388940000054
In the formula (I), the compound is shown in the specification,
Figure GDA0004036388940000055
wherein k is 1 ,k 2 And
Figure GDA0004036388940000056
determined by initial conditions;
two complex numbers at the right end of the above formula are modal vectors, K 1 ,K 2 Referred to as modal amplitudes. According to the vector representation method of the complex number,
Figure GDA0004036388940000057
representing a mode of 1 and an argument of phi 1 ，Φ 2 When the argument is at an angular frequency ω, respectively 1 ,ω 2 When the unit modulus complex number is changed, the vector end of the unit modulus complex number draws a circle on the complex number plane;
step three: determining a spinning tail projectile angular motion mode;
when the ballistic arc length s =0, delta = delta 0 ，Δ′＝Δ′ 0 In conjunction with the angle of attack resolution, the undetermined coefficient C can be resolved 1 ,C 2 Is composed of
Figure GDA0004036388940000058
Therefore, modeling of radar echo signals caused by initial disturbance in a fast and slow two-circle motion mode is determined;
step four: determining a relevant coordinate system definition;
by combining the ballistics theory and the definition of a measurement radar related coordinate system, the geometric relation of the projectile linear segment angular motion space can be established, and four coordinate systems oriented according to the right-hand rule are introduced by taking radar tail-pursuit type tracking as an example, wherein the coordinate systems comprise a radar coordinate system Q-UVW and a gun position coordinate system O 1 -XYZ, a reference coordinate system O-XYZ and a missile axis coordinate system O- ξ η ζ, the gun location coordinate system taking the gun muzzle center as an origin O 1 Horizontal axis O 1 x is the intersection line of the shooting surface and the horizontal plane of the muzzle, the forward direction is positive, and the vertical axis O is 1 y in the shooting plane and with the horizontal axis O 1 The z phase is vertical; the radar coordinate system takes the center of a station as an original point Q, a horizontal shaft QU points to the true north direction in a horizontal plane, and QV is the direction of a plumb line and is vertical to a horizontal shaft QW; the reference coordinate system takes the center of mass of the projectile as an origin O and is always parallel to the radar coordinate system; the origin of the bullet axis coordinate system is on the center of mass of the bullet, the O xi axis is positive along the bullet axis, the O eta axis is positive in the direction vertical to the bullet axis, and the O zeta axis is determined by the right hand ruleDetermining;
step five: calculating the distance from a scattering point of the projectile to the radar;
decomposing the angular motion of the projectile into the motion superposition of three degrees of freedom, namely autorotation of a polar axis of the projectile, nutation fast circular motion of the polar axis around a moment vector of the gyroscope momentum and precession slow circular motion of the moment vector of the gyroscope momentum around a speed vector line; starting from the superposition of three motions of projectile spinning, nutation and precession, establishing a projectile target strong scattering point radar echo signal model;
in the electromagnetic scattering, a strong scattering center with a discontinuous curvature as a target, in the spinning tail projectile, two representative scattering points of a projectile vertex and a tail scattering point can be taken to model a radar echo signal, wherein the spinning angular velocity is omega 'in a missile axis coordinate system' s ＝(ω sξ ,ω sη ,ω sζ ) T And the nutation angular velocity is ω' n ＝(ω nξ ,ω nη ,ω nζ ) T And the precession angular velocity is ω' c ＝(ω cξ ,ω cη ,ω cζ ) T Scalar of angular velocity omega s ＝||ω′ s ||、Ω n ＝||ω′ n And omega c ＝||ω′ c If the unit angular velocity of each rotation angular velocity in the reference coordinate system is ω |, respectively s ＝R init ·ω′ s /Ω s 、ω n ＝R init ·ω′ n /Ω n And omega c ＝R init ·ω′ c /Ω c ，R init From an initial Euler angle
Figure GDA0004036388940000071
Determining, i.e. clockwise rotation of the local coordinate system O-xyz about the z-axis respectively
Figure GDA0004036388940000072
Clockwise rotation theta around the x-axis e And then rotate clockwise phi around the z-axis e Then the coordinate system is transformed into a reference coordinate system O-XYZ; the expression is
Figure GDA0004036388940000073
From the above analysis, the angular motion of the projectile can be described as: at the time t, firstly, a scattering point P on the projectile makes spinning motion around a projectile axis O xi, and then a coordinate P is changed into a coordinate
Figure GDA0004036388940000074
R spin Is a matrix of spin rotations, and is,
Figure GDA0004036388940000075
the initial vector of a scattering point P before transmission in a radar coordinate system is related to the transmitted angle and direction; then the elastic axis O xi does nutation motion around the gyro moment vector line OG axis, and the P coordinate becomes
Figure GDA0004036388940000076
R nut A nutating rotation matrix; finally, gyro moment vector line OG is axially wound on velocity vector line V 0 Precession, then the P coordinate becomes
Figure GDA0004036388940000077
R con For a precessional rotation matrix, the distance from point P on the projectile to the radar at time t is
Figure GDA0004036388940000078
Wherein each rotation matrix is represented by a rotation formula around a vector axis according to Euler-Rodrigues
Figure GDA0004036388940000079
Figure GDA00040363889400000710
Figure GDA00040363889400000711
Wherein the content of the first and second substances,
Figure GDA00040363889400000712
and
Figure GDA00040363889400000713
are respectively omega s 、ω n And omega c The corresponding oblique symmetric matrix;
step six: a radar echo Doppler signal;
the radar is set to transmit a single carrier frequency continuous wave signal in the form of
s＝exp(j2πf 0 t)
Wherein f is 0 Is the carrier frequency. The echo of the scattering point P is s P ＝σexp(j2πf 0 (t- τ)), where σ is a scattering coefficient, τ is a time delay of the scattering point P, and τ =2R is satisfied P (t)/c；
Taking the transmitted signal formula as a reference signal, and performing coherent processing on the reference signal formula and a target echo to obtain a coherent phase signal
Figure GDA0004036388940000081
Wherein, the phase term phi (t) =4 pi f 0 R P (t)/c, deriving the phase term with respect to time t to obtain the Doppler frequency of the echo as
Figure GDA0004036388940000082
Wherein, the first and the second end of the pipe are connected with each other,
Figure GDA0004036388940000083
is composed of
Figure GDA0004036388940000084
When the target is located in the radar far field, n ≈ R 0 /||R 0 | |, which is a unit vector of LOS in the radar sight line direction;
the Doppler frequency caused by the translation of the target can be obtained as follows:
Figure GDA0004036388940000085
the shot scattering point causes micro-doppler frequency by the shot angular motion:
Figure GDA0004036388940000086
from the above formula, the expression of the shot radar echo micro doppler frequency caused by the angular motion of the missile axis in space is relatively complex. Through analysis, the change of the radar micro Doppler frequency along with time has periodicity, and the movement period T of the ejection scattering point A top For a period of nutation T s And precession period T c The least common multiple of; motion period T of tail scattering point P bom Is the spin period T s Precession period T c And period of nutation T u The following relationship holds true for the least common multiple of (c):
T t o p ＝k 1 T c ＝k 2 T u ,T b o m ＝k 1 T c ＝k 2 T u ＝k 3 T s k 1 ,k 2 ,k 3 ∈N
wherein N is a natural number set.
The method has the advantages that the radar echo characteristics of the micro-motion target reflect the fine characteristics of the target, such as structural characteristics, electromagnetic scattering characteristics, motion characteristics and the like, the change mechanism of the angular motion between the elastic axis and the velocity vector of the spinning tail wing projectile in the space motion process is analyzed, the change mechanism is further converted into the projection transformation of radar measurement information on the motion, and the theoretical basis is provided for identifying the motion characteristics, the pneumatic characteristics and the structural characteristics of the target by utilizing the radar measurement information. The method is characterized in that a quantitative relation between micro Doppler and projectile parameters is established for the conditions that the angular motion of the spinning tail projectile is influenced by initial disturbance in a straight line segment of a trajectory, a radar micro Doppler echo signal modeling method is provided, the defect of research on the spatial motion of the spinning tail projectile influenced by the initial disturbance in the straight line segment is overcome, a radar micro Doppler signal modeling system is perfected, and theoretical support is provided for the research on the micro Doppler effect of the spinning tail projectile on radar echo signals.
Drawings
FIG. 1 is a time-frequency diagram of a radar micro Doppler echo signal generated by the angular motion initial disturbance of a spinning tail projectile generated by modeling simulation of the invention.
Fig. 2 is a time-frequency diagram of a micro doppler signal obtained by Gabor transform of the micro doppler signal in fig. 1 according to the present invention.
FIG. 3 is a shot angle of attack curve calculated from simulation data in accordance with the present invention.
Fig. 4 is a doppler time-frequency diagram obtained by actual measurement of the projectile of the present invention.
FIG. 5 is a simulation time-frequency diagram for matching the time-frequency signal of the actual measured projectile according to the prior conditions of the actual size, the projectile coefficient, the flying speed, etc. of the projectile.
Detailed Description
The invention is further described with reference to the following figures and examples: a modeling method for radar echo signals caused by the initial disturbance of angular motion of a spinning tail fin projectile takes radar related parameters, translation parameters and micro-motion parameters of the spinning tail fin projectile in the air and scattering characteristic parameters of the projectile as main input, and after the relation between a radar and a target is determined, the change of the angular motion between a projectile axis and a velocity vector in the space motion process of the projectile is converted into the projection transformation of radar measurement information on the micro-motion, and a micro Doppler signal model generated by the angular motion of the spinning tail fin projectile on the radar is established. The specific implementation steps are as follows:
the method comprises the following steps: establishing a kinetic equation of the spinning tail projectile;
according to the ballistics theory, the kinetic equation of the spinning tail projectile can be expressed by a second-order variable coefficient differential equation of the complex attack angle motion
Figure GDA0004036388940000101
Delta is the angle of attack of the projectile flying in the air and can be expressed by complex numbers;
Figure GDA0004036388940000102
wherein k is zz Is the equatorial damping moment, b y Is a lifting force, b x G is the local gravity acceleration, theta is the scalar value of the attack angle of the projectile, and v is the flight speed of the projectile;
M＝k z ，k z determining the frequency of attitude motion for the static moment;
Figure GDA0004036388940000103
c is the moment of inertia of the pole,
Figure GDA0004036388940000104
the autorotation speed of the projectile, A is the equator moment of inertia, and v is the ratio of the flight speed;
Figure GDA0004036388940000105
b y is a lifting force, k y Is the magnus moment;
Figure GDA0004036388940000111
the disturbance term of the projectile attack angle motion caused by ballistic bending;
Figure GDA0004036388940000112
the disturbance term of the projectile attack angle motion caused by the asymmetry of the projectile structure is used;
Figure GDA0004036388940000113
is pneumatically asymmetric by the projectileThe disturbance term caused to the angle of attack motion of the projectile;
Figure GDA0004036388940000114
is the term for the perturbation of the projectile angle of attack caused by the vertical gas flow.
| | Δ | | is the angle between the space missile axis and the velocity vector, Δ' and Δ ″ are the first and second derivatives of the complex angle of attack on the ballistic arc length s, Δ = Δ | | when the starting condition is s =0 0 ，
Figure GDA0004036388940000115
Δ 0 Is the initial value of the re-attack angle of the projectile,
Figure GDA0004036388940000116
represents delta 0 First derivative of time t, v 0 The initial speed of the pill is. The equation and its starting conditions reflect the angular motion of the projectile due to various factors. Wherein H represents the damping movement, mainly dependent on the equatorial damping moment k zz And a lifting force b y And resistance b x Etc.; m major and static moment k z In relation, the frequency of the gesture motion depends mainly on this term; t main and lift b y And Magnus moment k y Related, it affects flight stability; p is the ratio of the autorotation speed and the flight speed of the projectile.
Step two: solving a homogeneous differential equation of the projectile re-attack angle;
and solving a homogeneous differential equation of the complex attack angle of the projectile according to the angular motion characteristic that the projectile is only disturbed by the initial disturbance in the straight line segment.
Δ″+(H-iP)Δ′-(M+iPT)Δ＝0
The characteristic root of this equation for the complex angle of attack Δ is
l 1 ＝λ 1 +iω 1 ，l 2 ＝λ 2 +iω 2
In the formula, λ 1 ,λ 2 Called damping index, ω 1 ,ω 2 Referred to as modal angular frequency to ballistic arc length s.
Then the angle of attack is solved as
Figure GDA0004036388940000117
In the formula, C 1 ,C 2 Is a undetermined coefficient, is a complex number, and can be written as
Figure GDA0004036388940000118
Constant k 1 ,k 2 Is a real number and is,
Figure GDA0004036388940000121
is the initial phase, determined by the starting conditions. The solution to the angle of attack can be written as
Figure GDA0004036388940000122
In the formula (I), the compound is shown in the specification,
Figure GDA0004036388940000123
wherein k is 1 ,k 2 And
Figure GDA0004036388940000124
determined by the initial conditions.
Two complex numbers at the right end of the above formula are modal vectors, K 1 ,K 2 Referred to as modal amplitude. According to the vector representation of the complex number,
Figure GDA0004036388940000125
representing a mode of 1 and an argument of phi 1 ，Φ 2 When the argument is at an angular frequency ω, respectively 1 ,ω 2 When changed, the edge of the unit modulus complex number will draw a circle on the complex number plane.
Step three: determining an angular motion mode of the spinning tail fin projectile;
when the ballistic arc length s =0, delta = delta 0 ，Δ′＝Δ′ 0 In conjunction with the angle of attack solution, the undetermined coefficient C can be solved 1 ,C 2 Is composed of
Figure GDA0004036388940000126
Therefore, it is determined that radar echo signals caused by initial disturbances are modeled in fast and slow two-circle motion modes.
Step four: determining a relevant coordinate system definition;
by combining the ballistics theory and the definition of a relative coordinate system of a measuring radar, a geometrical relationship of the projectile linear segment angular motion space can be established, taking radar tail-chasing tracking as an example, as shown in fig. 1.
Four coordinate systems oriented according to the right-hand rule are introduced, including a radar coordinate system Q-UVW and a gun position coordinate system O 1 -XYZ, a reference coordinate system O-XYZ and a spring axis coordinate system O- ξ η ζ. The coordinate system of the gun position takes the center of the gun muzzle as the origin O 1 Horizontal axis O 1 x is the intersection line of the shooting surface and the horizontal plane of the muzzle, the forward direction is positive, and the vertical axis O is 1 y in the shooting plane and with the horizontal axis O 1 z is vertical; the radar coordinate system takes the center of a station as an original point Q, a horizontal shaft QU points to the true north direction in a horizontal plane, and QV is the direction of a plumb line and is vertical to a horizontal shaft QW; the reference coordinate system takes the center of mass of the projectile as an origin O and is always parallel to the radar coordinate system; the origin of the bullet axis coordinate system is on the center of mass of the bullet, the O xi axis is positive along the bullet axis, the O eta axis is positive in the direction vertical to the bullet axis, and the O zeta axis is determined by a right-hand rule.
Step five: calculating the distance from a scattering point of the projectile to the radar;
the angular motion of the projectile is decomposed into the superposition of the motions of three degrees of freedom, namely autorotation of a polar axis of the projectile, nutation fast circular motion of the polar axis around a moment vector of a gyroscope momentum and precession slow circular motion of the moment vector of the gyroscope around a speed vector line. Starting from the superposition of the projectile spinning motion, the nutation motion and the precession motion, a projectile target strong scattering point radar echo signal model is established.
The curvature discontinuity in the electromagnetic scattering is the strong scattering center of the target, and for spinning tail projectile, the vertex of the projectile body, the conical column joint part and the tail scattering point are the strong scattering center of the target, and the vertex of the projectile body and the tail scattering point can be takenTwo representative scatter points model the radar echo signal. In the missile axis coordinate system, the spinning angular velocity is omega' s ＝(ω sξ ,ω sη ,ω sζ ) T The nutation angular velocity is ω' n ＝(ω nξ ,ω nη ,ω nζ ) T And the precession angular velocity is ω' c ＝(ω cξ ,ω cη ,ω cζ ) T Scalar of angular velocity omega s ＝||ω′ s ||、Ω n ＝||ω′ n And omega c ＝||ω′ c If the unit angular velocity of each rotation angular velocity in the reference coordinate system is ω |, respectively s ＝R init ·ω′ s /Ω s 、ω n ＝R init ·ω′ n /Ω n And omega c ＝R init ·ω′ c /Ω c 。R init From an initial Euler angle
Figure GDA0004036388940000131
Determining, i.e. clockwise rotation of the local coordinate system O-xyz about the z-axis respectively
Figure GDA0004036388940000132
Clockwise rotation theta around the x-axis e And then rotate clockwise phi around the z-axis e And transformed into the reference coordinate system O-XYZ. The expression is
Figure GDA0004036388940000133
From the above analysis, the angular motion of the projectile can be described as: at the time t, firstly, a scattering point P on the projectile makes spinning motion around a projectile axis O xi, and then a coordinate P is changed into a coordinate
Figure GDA0004036388940000141
R spin Is a matrix of spin rotations, and is,
Figure GDA0004036388940000142
is an initial vector of the scattering point P before transmission in a radar coordinate system,relative to the angle and direction of the shot; then the elastic axis O xi does nutation motion around the gyro moment vector line OG axis, and the P coordinate becomes
Figure GDA0004036388940000143
R nut Is a nutating rotation matrix; finally, gyro moment vector line OG is axially wound around velocity vector line V 0 Precession, then the P coordinate becomes
Figure GDA0004036388940000144
R con Is a precessional rotation matrix. The distance from point P on the projectile to the radar at time t is
Figure GDA0004036388940000145
Wherein each rotation matrix is represented by a rotation formula around a vector axis according to Euler-Rodrigues
Figure GDA0004036388940000146
Figure GDA0004036388940000147
Figure GDA0004036388940000148
Wherein the content of the first and second substances,
Figure GDA0004036388940000149
and
Figure GDA00040363889400001410
are each omega s 、ω n And ω c The corresponding oblique symmetric matrix.
Step six: a radar echo Doppler signal;
the radar is set to transmit a single carrier frequency continuous wave signal in the form of
s＝exp(j2πf 0 t)
Wherein f is 0 Is the carrier frequency. The echo of the scattering point P is s P ＝σexp(j2πf 0 (t- τ)), where σ is a scattering coefficient, τ is a time delay of the scattering point P, and τ =2R is satisfied P (t)/c。
Taking the transmitted signal formula as a reference signal, and performing coherent processing on the reference signal formula and a target echo to obtain a coherent phase signal
Figure GDA00040363889400001411
Wherein, the phase term phi (t) =4 pi f 0 R P (t)/c. The phase term is derived with respect to time t to obtain the Doppler frequency of the echo as
Figure GDA0004036388940000151
Wherein the content of the first and second substances,
Figure GDA0004036388940000152
is composed of
Figure GDA0004036388940000153
The unit vector of (2). When the target is located in the far field of the radar, n ≈ R 0 /||R 0 And | l is a unit vector of the LOS in the radar sight line direction.
The Doppler frequency caused by the translation of the target can be obtained as follows:
Figure GDA0004036388940000154
the shot scattering point causes micro-doppler frequency by the shot angular motion:
Figure GDA0004036388940000155
as can be seen from the above formula, the elastic shaftThe expression of the shot radar echo micro-doppler frequency caused by the angular motion in space is complex. Through analysis, the change of the radar micro Doppler frequency along with time has periodicity, and the movement period T of the ejection scattering point A top For a period of nutation T s And precession period T c The least common multiple of; motion period T of tail scattering point P bom Is the spin period T s Precession period T c And period of nutation T u The following relationship holds true for the least common multiple of (c):
T top ＝k 1 T c ＝k 2 T u ,T bom ＝k 1 T c ＝k 2 T u ＝k 3 T s k 1 ,k 2 ,k 3 ∈N
wherein N is a natural number set.
Firstly, setting radar parameters including radar position, system, frequency, sampling time, sight line vector, window function and the like; then, setting various motion parameters of the spinning tail projectile, including translation speed, spinning frequency, nutation frequency, precession frequency, nutation angle, precession angle and the like; and finally, setting the number of the strong scattering points of the projectile, the positions of the points on the projectile body and the like. The setting of the parameters has no special requirements and is set only aiming at the general indexes.
Radar main parameter setting:
1) A single carrier frequency continuous wave radar;
2) Carrier frequency f 0 ＝10GHz；
3) Sampling interval f s ＝20000Hz；
4) Taking the radar position as a coordinate origin;
5) And (4) tracking in a tail-pursuit mode.
Setting main parameters of the projectile:
1) A translation velocity vector (200, 200, 200) m/s;
2) Spin frequency omega s ＝300πrad/s；
3) Precession frequency omega c ＝4πrad/s；
4) Nutation frequency omega s ＝20πrad/s；
5) Nutation angle phi =1.2 °;
6) Precession angle ψ =8.2 °.
Setting the scattering characteristics of the spinning tail projectile:
1) Selecting shot tip scattering points and 2 empennage scattering points for calculation;
2) The missile axis coordinate system positions of the scattering points are that the missile top scattering point P1 is (0.5, 0) m, the empennage scattering point P2 is (-0.3, 0.06, 0) m, the empennage scattering point P3 is (-0.3,
-0.06，0)m；
secondly, a radar coordinate system, a missile coordinate system and a reference coordinate system are determined, the conversion relation among the coordinate systems is calculated through an Euler rotation transformation matrix, and a rotation matrix rotating around a vector axis is calculated.
Each rotation matrix is a function of the Euler-Rodrigues rotation formula around the vector axis
Figure GDA0004036388940000171
Figure GDA0004036388940000172
Figure GDA0004036388940000173
And thirdly, calculating a distance expression of each scattering point relative to the continuous wave radar under superposition of multiple motions of translation, spin, nutation, precession and the like of the projectile, and separating out the Doppler signals born by the radar signals.
Figure GDA0004036388940000174
Finally, separating Doppler signals generated by translation and micromotion and carrying out time-frequency analysis,
the translational Doppler signal is:
Figure GDA0004036388940000175
micro-doppler signal:
Figure GDA0004036388940000176
the results of the modeling simulation are shown in fig. 1. The horizontal axis is time, and the simulation time length is 4 seconds; the vertical axis is the frequency amplitude of micro Doppler; the solid curve with smaller amplitude in the graph is a micro Doppler signal generated by a scattering point of the bullet tip; the curves with larger amplitudes and overlapping are doppler signals generated by two different tail scattering points. The two vertical lines show the period of the time-frequency signal, which is completely consistent with the theoretical calculation value.
Fig. 2 is a time-frequency diagram of a micro doppler signal obtained by Gabor transform of the micro doppler signal in fig. 1; the horizontal axis is time, and the simulation time length is 4 seconds; the vertical axis is the frequency amplitude of micro Doppler; the curve with the highest central brightness in the graph is a micro Doppler signal generated by a bullet point scattering point; the curves with lower brightness and sinusoidal variation are Doppler signals generated by two different tail scattering points respectively.
Therefore, modeling of the radar echo signal of the initial disturbance of the angular motion of the spinning tail projectile is completed.
In order to verify the correctness of the model, parameter extraction comparison and model matching verification are carried out on the micro Doppler signals.
And calculating the projectile attack angle of the simulation data, and performing matching simulation on the actually measured projectile time-frequency diagram to verify the correctness of modeling.
The calculated result is compared with the matching simulation, and as shown in fig. 3, a shot attack angle curve is calculated through simulation data. The horizontal axis is time, and the simulation time length is 4 seconds; the vertical axis is the attack angle amplitude of the projectile; the peak value is equal to the theoretical calculation value, and the change rule of the peak value is consistent with the change rule of the projectile attack angle in ballistics. For example, fig. 4 is a doppler time-frequency diagram obtained by actual measurement of the projectile, and fig. 5 is a matching simulation time-frequency diagram of the actual measurement projectile time-frequency signal according to the prior conditions such as the actual size, the projectile form coefficient, and the flying speed of the projectile. Because the actual parameters of the projectile are related, the projectile belongs to military secrets, and the scales and coordinates of the transverse and longitudinal axes, namely the time axis and the frequency axis, of the two figures are cut. By comparing fig. 4 and fig. 5, the correctness and validity of the model are verified.
From parameter comparison and simulation verification, the radar echo signal model generated by the angular motion initial disturbance of the spinning tail projectile obtained by the method conforms to the ballistics theory, the attack angle change between the projectile axis and the velocity vector of the projectile conforms to the actual situation of the angular motion change of the projectile, and the correctness of the established model is verified.

Claims (1)

1. A modeling method for radar echo signals of angular motion initial disturbance of a spinning tail projectile is characterized by comprising the following specific steps:
the method comprises the following steps: establishing a kinetic equation of the spinning tail wing projectile;
according to the ballistics theory, the kinetic equation of the spinning tail projectile can be expressed by a second-order variable coefficient differential equation of the complex attack angle motion
Figure FDA0004040291330000011
Delta is the angle of attack of the projectile flying in the air and can be expressed by complex numbers;
Figure FDA0004040291330000012
wherein k is zz Is the equatorial damping moment, b y As a lifting force, b x G is the local gravity acceleration, theta is the scalar value of the attack angle of the projectile, and v is the flight speed of the projectile;
M＝k z ，k z determining the frequency of the attitude motion for the static moment;
Figure FDA0004040291330000013
c is the polar moment of inertia,
Figure FDA0004040291330000014
the autorotation speed of the projectile, A is the equator moment of inertia, and v is the ratio of the flight speed;
Figure FDA0004040291330000015
b y is a lifting force, k y Is the magnus moment;
Figure FDA0004040291330000016
disturbance terms for the angle of attack motion of the projectile caused by ballistic curvature;
Figure FDA0004040291330000017
the disturbance term of the angle of attack motion of the projectile caused by the asymmetry of the structure of the projectile is included;
Figure FDA0004040291330000018
the method comprises the following steps of (1) obtaining a perturbation term of projectile attack angle movement caused by projectile pneumatic asymmetry;
Figure FDA0004040291330000019
is the disturbance term to the projectile angle of attack caused by the vertical airflow;
| Δ | is the angle between the spatial axis of the projectile and the velocity vector, Δ' and Δ ″ are the first and second derivatives of the complex angle of attack to the ballistic arc length s, Δ = when the starting condition is s =0 0 ，
Figure FDA00040402913300000110
Δ 0 Is the initial value of the re-attack angle of the projectile,
Figure FDA00040402913300000111
represents delta 0 First derivative of time t, v 0 The initial speed of the pill is; the equation and the initial conditions thereof can reflect the angle of attack motion of the projectile caused by various factors; wherein H represents the damping movement, mainly dependent on the equatorial damping moment k zz And a lifting force b y And resistance b x (ii) a M main and static moment k z In relation, the frequency of the gesture motion depends mainly on this term; t main and lift b y And Magnus moment k y In relation, it affects flight stability; p is the ratio of the autorotation speed and the flight speed of the projectile;
step two: solving a homogeneous differential equation of the projectile re-attack angle;
solving a homogeneous differential equation of a complex attack angle of the projectile according to the angular motion characteristic that the projectile is only disturbed by the initial disturbance in the straight line segment;
Δ″+(H-iP)Δ′-(M+iPT)Δ＝0
the characteristic root of this equation for the complex angle of attack Δ is
l 1 ＝λ 1 +iω 1 ，l 2 ＝λ 2 +iω 2
In the formula of lambda 1 ,λ 2 Called damping index, ω 1 ,ω 2 Modal angular frequency referred to as the ballistic arc length s; the angle of attack is solved as
Figure FDA0004040291330000021
In the formula, C 1 ,C 2 Is a undetermined coefficient, is a complex number, and can be written as
Figure FDA0004040291330000022
Constant k 1 ,k 2 Is a real number and is,
Figure FDA0004040291330000023
is an initial phase and is determined by an initial condition; the solution to the angle of attack can be written as
Figure FDA0004040291330000024
In the formula (I), the compound is shown in the specification,
Figure FDA0004040291330000025
wherein k is 1 ,k 2 And
Figure FDA0004040291330000026
determined by initial conditions;
two complex numbers at the right end of the above formula are modal vectors, K 1 ,K 2 Referred to as modal amplitude; according to the vector representation of the complex number,
Figure FDA0004040291330000027
representing a mode of 1 and an argument of phi 1 ，Φ 2 When the argument is at an angular frequency ω, respectively 1 ,ω 2 When the unit modulus complex number is changed, the vector end of the unit modulus complex number draws a circle on the complex number plane;
step three: determining an angular motion mode of the spinning tail fin projectile;
Δ = Δ when ballistic arc length s =0 0 ，Δ′＝Δ′ 0 In conjunction with the angle of attack resolution, the undetermined coefficient C can be resolved 1 ,C 2 Is composed of
Figure FDA0004040291330000031
Therefore, modeling of radar echo signals caused by initial disturbance in a fast and slow two-circle motion mode is determined;
step four: determining a relevant coordinate system definition;
four coordinate systems oriented according to the right-hand rule are introduced, including a radar coordinate system Q-UVW and a gun position coordinate system O 1 -XYZ, a reference coordinate system O-XYZ and a missile axis coordinate system O-xi eta zeta, wherein the gun position coordinate system takes the center of the gun muzzle as an original point O 1 Horizontal axis O 1 x is the intersection line of the shooting surface and the horizontal plane of the muzzle, the forward direction is positive, and the vertical axis O is 1 y in the shooting plane and with the horizontal axis O 1 z is vertical; the radar coordinate system takes a station center as an origin Q, a horizontal axis QU points to the true north direction in a horizontal plane, and QV is a plumb line direction and is vertical to a horizontal axis QW; the reference coordinate system takes the center of mass of the projectile as an origin O and is always parallel to the radar coordinate system; the origin of a bullet axis coordinate system is on the center of mass of the bullet, the O xi axis is positive along the bullet axis, the O eta axis is positive vertical to the bullet axis, and the O zeta axis is determined by a right-hand rule;
step five: calculating the distance from a scattering point of the projectile body to the radar;
the angular motion of the projectile is decomposed into the motion superposition of three degrees of freedom, namely autorotation of a polar axis of the projectile, nutation fast circular motion of the polar axis around a moment vector of a gyroscope momentum, and precession slow circular motion of the moment vector of the gyroscope around a speed vector line; starting from the superposition of three motions of projectile spinning, nutation and precession, establishing a projectile target strong scattering point radar echo signal model;
the discontinuous part of curvature in the electromagnetic scattering is a strong scattering center of a target, and for a spinning empennage projectile, the top point of the projectile body, the conical column combination part and the empennage scattering point are the strong scattering center of the target, and two representative scattering points, namely the top point of the projectile body and the empennage scattering point, can be used for modeling a radar echo signal; in the missile axis coordinate system, the spinning angular velocity is omega' s ＝(ω sξ ,ω sη ,ω sζ ) T And the nutation angular velocity is ω' n ＝(ω nξ ,ω nη ,ω nζ ) T And the precession angular velocity is ω' c ＝(ω cξ ,ω cη ,ω cζ ) T Scalar of angular velocity omega s ＝||ω′ s ||、Ω n ＝||ω′ n And omega c ＝||ω′ c If the unit angular velocity of each rotation angular velocity in the reference coordinate system is ω |, respectively s ＝R init ·ω′ s /Ω s 、ω n ＝R init ·ω′ n /Ω n And omega c ＝R init ·ω′ c /Ω c ；R init From an initial Euler angle
Figure FDA0004040291330000041
Determining, i.e. clockwise rotation of the local coordinate system O-xyz about the z-axis respectively
Figure FDA0004040291330000042
Clockwise rotation theta around the x-axis e And then rotate clockwise around the z-axis by phi e Then the coordinate system is transformed into a reference coordinate system O-XYZ; the expression is
Figure FDA0004040291330000043
From the above analysis, the angular motion of the projectile can be described as: at the time t, firstly, a scattering point P on the projectile makes spinning motion around a projectile axis O xi, and then a coordinate P is changed into a coordinate
Figure FDA0004040291330000044
R spin Is a matrix of spin rotations, and is,
Figure FDA0004040291330000045
the initial vector of a scattering point P before transmission in a radar coordinate system is related to the transmitted angle and direction; then the elastic axis O xi does nutation motion around the gyro moment vector line OG axis, and the P coordinate becomes
Figure FDA0004040291330000046
R nut Is a nutating rotation matrix; finally, gyro moment vector line OG is axially wound around velocity vector line V 0 Precession, then P coordinate becomes
Figure FDA0004040291330000047
R con Is a precessional rotation matrix; the distance from point P on the projectile to the radar at time t is
Figure FDA0004040291330000048
Wherein each rotation matrix is represented by a rotation formula around a vector axis according to Euler-Rodrigues
Figure FDA0004040291330000051
Figure FDA0004040291330000052
Figure FDA0004040291330000053
Wherein the content of the first and second substances,
Figure FDA0004040291330000054
and
Figure FDA0004040291330000055
are each omega s 、ω n And omega c A corresponding skew symmetric matrix;
step six: a radar echo Doppler signal;
the radar is set to transmit a single carrier frequency continuous wave signal in the form of
s＝exp(j2πf 0 t)
Wherein, f 0 Is the carrier frequency; the echo of the scattering point P is s P ＝σexp(j2πf 0 (t- τ)), where σ is a scattering coefficient, τ is a time delay of the scattering point P, and τ =2R is satisfied P (t)/c；
Taking the transmitted signal formula as a reference signal, and performing coherent processing on the reference signal formula and a target echo to obtain a coherent phase signal
Figure FDA0004040291330000056
Wherein, the phase term phi (t) =4 pi f 0 R P (t)/c; the phase term is derived with respect to time t to obtainDoppler frequency of the wave is
Figure FDA0004040291330000057
Wherein the content of the first and second substances,
Figure FDA0004040291330000058
is composed of
Figure FDA0004040291330000059
When the target is located in the far field of the radar, n ≈ R 0 /||R 0 | |, which is a unit vector of LOS in the radar sight line direction;
the Doppler frequency caused by the translation of the target can be obtained as follows:
Figure FDA0004040291330000061
the shot scattering point causes a micro doppler frequency from the shot angular motion:
Figure FDA0004040291330000062
the expression of the shot radar echo micro Doppler frequency caused by the angular motion of the shot axis in the space is complex; through analysis, the change of the radar micro Doppler frequency along with time has periodicity, and the movement period T of the scattering point A on the missile top top For a period of nutation T s And precession period T c The least common multiple of; period T of motion P of scattering point of empennage bom Is the spin period T s Precession period T c And period of nutation T u The following relationship holds true for the least common multiple of (c):
T top ＝k 1 T c ＝k 2 T u ,T bom ＝k 1 T c ＝k 2 T u ＝k 3 T s k 1 ,k 2 ,k 3 ∈N
wherein N is a natural number set.
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Publication number Priority date Publication date Assignee Title
CN115453514B (en) * 2022-08-03 2024-05-10 西安电子工程研究所 Sight correction method for gun external trajectory initial speed measurement radar

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103453806A (en) * 2013-08-15 2013-12-18 冷雪冰 Projectile nutation angle extraction method based on radar Doppler data
CN103743298A (en) * 2014-01-06 2014-04-23 常华俊 Projectile revolution extraction method based on continuous wave radar
CN104007430A (en) * 2014-05-29 2014-08-27 西安电子科技大学 Precession target micro-Doppler extracting method based on instant frequency modulation rate estimation
CN105571412A (en) * 2015-12-11 2016-05-11 中国人民解放军63850部队 Projectile procession period extraction method based on Hilbert conversion
CN108008368A (en) * 2016-10-27 2018-05-08 北京遥感设备研究所 A kind of object localization method based on echo Doppler Information revision angle error

Family Cites Families (3)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US4589610A (en) * 1983-11-08 1986-05-20 Westinghouse Electric Corp. Guided missile subsystem
CN104459662B (en) * 2014-11-27 2017-01-25 北京环境特性研究所 Micro-motion target characteristic extraction method and system based on wavelet multi-scale analysis
CN109031219B (en) * 2018-06-14 2022-05-24 西安电子科技大学 Broadband radar trajectory target micro-motion geometric parameter estimation method based on phase ranging

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN103453806A (en) * 2013-08-15 2013-12-18 冷雪冰 Projectile nutation angle extraction method based on radar Doppler data
CN103743298A (en) * 2014-01-06 2014-04-23 常华俊 Projectile revolution extraction method based on continuous wave radar
CN104007430A (en) * 2014-05-29 2014-08-27 西安电子科技大学 Precession target micro-Doppler extracting method based on instant frequency modulation rate estimation
CN105571412A (en) * 2015-12-11 2016-05-11 中国人民解放军63850部队 Projectile procession period extraction method based on Hilbert conversion
CN108008368A (en) * 2016-10-27 2018-05-08 北京遥感设备研究所 A kind of object localization method based on echo Doppler Information revision angle error

Non-Patent Citations (7)

* Cited by examiner, † Cited by third party
Title
extracting method of projectile spin speed based on hilbert-huang transform;Duan Peng-wei等;《Joint international mechanical,electronic and information technology conference 2015》;20151231;全文 *
基于chirplet的弹道目标逆合成孔径雷达回波分解;金光虎等;《电子与信息学报》;20101231(第10期);22-26页 *
基于时间分段信号的弹道导弹目标微多普勒调制周期估计;刘丽华等;《信号处理》;20100225(第02期);165-167页 *
基于移动散射点模型的雷达回波仿真及分析;薛爱军等;《计算机科学》;20130915(第09期);207-209页 *
底部刻槽旋转稳定弹丸的飞行初始段回波建模;张若禹等;《系统仿真学报》;20090105(第01期);58-61页 *
弹道中段目标回波平动补偿与微多普勒提取;杨有春等;《中国科学:信息科学》;20130920(第09期);112-122页 *
膛内运动弹丸微多普勒建模与仿真;陈曦等;《现代雷达》;20130815(第08期);全文 *

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