CN114488125A - Method for optimizing precession cone target parameters by using spatial mapping - Google Patents

Method for optimizing precession cone target parameters by using spatial mapping Download PDF

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CN114488125A
CN114488125A CN202011263520.3A CN202011263520A CN114488125A CN 114488125 A CN114488125 A CN 114488125A CN 202011263520 A CN202011263520 A CN 202011263520A CN 114488125 A CN114488125 A CN 114488125A
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陈如山
丁大志
樊振宏
何姿
李猛猛
张�杰
张晓杰
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Nanjing University of Science and Technology
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract

The invention discloses a method for optimizing a precession cone target parameter by utilizing spatial mapping. The method estimates the geometric parameters and the micromotion parameters of the space cone target by using a space mapping optimization method. The method comprises the following specific steps: firstly, a coarse model and a fine model of the space-advance mapping are established, wherein the coarse model is a scattering center model, the accuracy of the coarse model is poor, but the calculation speed is high. The fine model is a full-wave electromagnetic simulation rotational symmetry body moment method (Bornom), the simulation precision is high, but the calculation is time-consuming, and the resource consumption is large. The basic idea of the invention is to establish a mapping relation between the coarse model and the fine model, and to convert the parameter updating and optimizing of the fine model into the parameter updating and optimizing of the coarse model, because the efficiency can be greatly improved by updating the parameter calculation model in the coarse model. The invention finally uses the gradient descent method to search more accurate solution around the accurate solution, and compared with the existing estimation method, the method can effectively improve the accuracy of cone target parameter estimation.

Description

Method for optimizing precession cone target parameters by using spatial mapping
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a method for optimizing a precession cone target parameter by utilizing spatial mapping.
Background
When the ballistic missile flies at high speed in the air, the spinning motion keeps the attitude stability, and the transverse interference can convert the spinning motion into a precession form, wherein the spinning motion refers to the rotation motion of the ballistic missile around a self symmetrical axis, and the precession refers to the rotation of the ballistic missile around a cone rotation axis while spinning.
Spatial target recognition is a crucial link in ballistic missile defense systems. The middle-segment flight has the longest duration in the process of ballistic missile flight, the space environment is relatively simple, and the target at the moment is represented by that the target rotates around the mass center in a small range while translating. Precession may reflect more target features, such as target size and mass distribution, which are important for true and false target identification, and therefore, target parameter estimation using precession is increasingly studied.
When the target precesses, the radar echo reflected by the target is modulated, and the modulation is embodied in two aspects: macro modulation and micro doppler frequency modulation. The microspur modulation is mainly proposed for broadband radar and is represented by periodic variation of the position of a target scattering center on an echo one-dimensional range profile sequence. The macro modulation is caused by the change of a target scattering center relative to the radar distance, can be used for estimating the size and the precession parameters of a target, and most of the existing methods utilize a one-dimensional range profile sequence to estimate the parameters. While micro-doppler frequency modulation is mainly proposed for narrow-band radar, which is manifested as a change in the velocity of the scattering center of the target relative to the radar. Compared with the microspur change, the micro-Doppler frequency has the advantages that the requirement on the radar bandwidth is low, and the frequency change amplitude is larger due to the short wavelength of electromagnetic waves, so that the micro-Doppler frequency is easier to extract and utilize. However, the two methods can not eliminate the influence of the centroid height parameter on the estimation of the structural parameters of the ballistic missile, so that the estimation error of the target of the ballistic missile is large.
Disclosure of Invention
The invention aims to provide a method for optimizing a precession cone target parameter by using spatial mapping.
The technical solution for realizing the purpose of the invention is as follows: a method for optimizing precession cone target parameters by using spatial mapping comprises the following steps:
step 1, establishing a geometric diffraction scattering center model,
step 2, obtaining the optimal parameter vector of the coarse model
Figure BDA0002775400130000011
Order to
Figure BDA0002775400130000012
Step 3, initializing matrix B(1)Is as follows I, according to B(i)h(i)＝-f(i)Solving for incremental step length h(i)；
Step 4, updating the parameter vector of the detailed model
Figure BDA0002775400130000021
Step 5, substituting the parameter vector of the fine model into the fine model for simulation, and stopping the algorithm if the error requirement is met;
step 6, obtaining a rough model parameter vector according to the parameter extraction process
Figure BDA0002775400130000022
Computing residual vectors
Figure BDA0002775400130000023
Step 7, updating the matrix B(i+1)And i +1, turning to the step 2 until the fine model simulation meets the requirements.
Further, the scattering center model in step 1 is specifically as follows:
the scattering center theory relies on establishing an accurate model, and the existing scattering center model mainly comprises an ideal point model, a geometric diffraction model (GTD) and an attribute scattering center model. The present invention employs a GTD model based on the characteristics of the warhead cone target.
Radar system for sweeping frequency and angleObserving the target with the formula, f ═ f0…fN-1For transmitting signal frequency sweep, N is the number of frequency points. Theta is equal to theta0…θM-1For all observation angles, M is the total number of sweep angles.
The mathematical expression for the GTD model is as follows:
Figure BDA0002775400130000024
wherein y (f, theta) represents a two-dimensional echo received by the radar, K represents the number of scattering centers, and si,xi,yiRepresenting amplitude information and position information of the ith scattering center, f0Denotes the center frequency, c is the speed of light, αiIs a frequency dependent factor, because when the signal bandwidth is larger, the scattering information of the target has a certain relation with the emission frequency of the signal, different scattering types are represented by the value of the frequency dependent factor,
the detailed model described in step 4, namely the rotational symmetry moment method, is as follows:
the core idea of the rotational symmetric body moment method is that a Fourier series is utilized to expand circumferential current, and an original three-dimensional problem is converted into a two-dimensional half space to be solved by combining the structural characteristics of a target, firstly, a basis function of a group of half domain and half universes is defined to expand surface current of the rotational symmetric body target, and the specific expression is as follows:
Figure BDA0002775400130000025
wherein the content of the first and second substances,
Figure BDA0002775400130000026
respectively representing alpha-th mode number
Figure BDA0002775400130000027
The nth basis function in the direction of the vector,
Figure BDA0002775400130000028
the expansion coefficients of the corresponding basis functions are respectively represented, and N represents the number of all the basis functions in the direction of the target bus. Specific expressions of the two types of basis functions are given below:
Figure BDA0002775400130000029
Figure BDA00027754001300000210
then, by using a Galileo test method, the conjugate of the basis function is selected as a test function, and the specific expression is as follows:
Figure BDA0002775400130000031
Figure BDA0002775400130000032
where β represents the number of modes corresponding to the test function. And finally substituting the formula into an integral equation to obtain:
Figure BDA0002775400130000033
wherein the impedance matrix can be expressed as:
Figure BDA0002775400130000034
the right vector can be expressed as:
Figure BDA0002775400130000035
through the process, the accurate solution of the current coefficient of the target surface of the rotational symmetric body can be realized.
Compared with the prior art, the invention has the following remarkable advantages: (1) the cone target parameter estimation precision can be obviously improved by a space mapping optimization method. (2) The method does not need to extract an instantaneous micro Doppler frequency curve from a target time frequency graph, thereby reducing errors.
Drawings
FIG. 1 is a diagram of the cone target location in the present invention.
Figure 2 is a graph comparing scattering center echo with actual echo in the present invention.
FIG. 3 is the first fine model response in the present invention.
Fig. 4 is a fourth fine model response in the present invention.
FIG. 5 is the final fine model response in the present invention.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
The method of the invention estimates the geometric parameters and the micro-motion parameters of the space cone target by using a space mapping optimization method. The method comprises the following specific steps: firstly, a coarse model and a fine model of space mapping are established, wherein the coarse model is a scattering center model, the accuracy of the coarse model is poor, but the calculation speed is high. The fine model is a full-wave electromagnetic simulation rotational symmetry body moment method (Bornom), the simulation precision is high, but the calculation is time-consuming, and the resource consumption is large. The basic idea of the invention is to establish a mapping relation between a coarse model and a fine model, and convert the parameter updating and optimizing of the fine model into the updating and optimizing of the coarse model parameters, because the efficiency can be greatly improved by updating the parameter calculation model in the coarse model; and finally, searching a more accurate solution around the accurate solution by using a gradient descent method.
With reference to fig. 1-5, the present invention provides a method for optimizing a precession cone target parameter by using spatial mapping, which comprises the following steps:
step 1, establishing a geometric diffraction scattering center model,
the scattering center theory relies on establishing an accurate model, and the existing scattering center model mainly comprises an ideal point model, a geometric diffraction model (GTD) and an attribute scattering center model. The present invention employs a GTD model based on the characteristics of the warhead cone target.
The radar system observes the target in a mode of frequency sweep and angle sweep, and f is f0…fN-1For transmitting signal frequency sweep, N is the number of frequency points. Theta is equal to theta0…θM-1For all observation angles, M is the total number of sweep angles.
The mathematical expression for the GTD model is as follows:
Figure BDA0002775400130000041
wherein y (f, theta) represents a two-dimensional echo received by the radar, K represents the number of scattering centers, and si,xi,yiRepresenting amplitude information and position information of the ith scattering center, f0Denotes the center frequency, c is the speed of light, αiIs a frequency dependent factor, because when the signal bandwidth is larger, the scattering information of the target has a certain relation with the emission frequency of the signal, different scattering types are represented by the value of the frequency dependent factor,
step 2, obtaining the optimal parameter vector of the coarse model
Figure BDA0002775400130000042
Order to
Figure BDA0002775400130000043
Step 3, initializing matrix B(1)Is as follows I, according to B(i)h(i)＝-f(i)Solving for incremental step length h(i)；
Step 4, updating the parameter vector of the detailed model
Figure BDA0002775400130000044
The core idea of the rotational symmetric body moment method is that a Fourier series is utilized to expand circumferential current, and an original three-dimensional problem is converted into a two-dimensional half space to be solved by combining the structural characteristics of a target, firstly, a basis function of a group of half domain and half universes is defined to expand surface current of the rotational symmetric body target, and the specific expression is as follows:
Figure BDA0002775400130000045
wherein the content of the first and second substances,
Figure BDA0002775400130000046
respectively representing alpha-th mode number
Figure BDA0002775400130000047
The n-th basis function in the direction,
Figure BDA0002775400130000048
the expansion coefficients of the corresponding basis functions are respectively represented, and N represents the number of all the basis functions in the direction of the target bus. Specific expressions of the two types of basis functions are given below:
Figure BDA0002775400130000051
Figure BDA0002775400130000052
then, by using a Galileo test method, the conjugate of the basis function is selected as a test function, and the specific expression is as follows:
Figure BDA0002775400130000053
Figure BDA0002775400130000054
where β represents the number of modes corresponding to the test function. And finally substituting the formula into an integral equation to obtain:
wherein the impedance matrix can be expressed as:
Figure BDA0002775400130000055
the right vector can be expressed as:
Figure BDA0002775400130000056
through the analysis process, the accurate solution of the current coefficient of the target surface of the rotational symmetric body is basically realized.
Step 5, substituting the parameter vector of the fine model into the fine model for simulation, and stopping the algorithm if the error requirement is met;
step 6, obtaining a rough model parameter vector according to the parameter extraction process
Figure BDA0002775400130000057
Computing residual vectors
Figure BDA0002775400130000058
Step 7, updating the matrix B(i+1)And i +1, turning to the step 2 until the fine model simulation meets the requirements.
Examples
The method is described by taking a cone warhead with H being 1.0m, r being 0.25m and theta being 18 degrees as an example, the target precesses in the space, the position of the cone target in a coordinate system is assumed to be shown in FIG. 1, and the coordinate of the point P1 is (x)1,y1) The coordinate of the point P2 is (x)2,y2) The target precession angle is θ, and the variables to be optimized are the five parameters. The height and radius of the target may be defined by H ═ x1-x2，r＝y2-y1And (4) obtaining.
The parametric variations of the fine model during the optimization are given in the following table.
TABLE 1 Fine model parameter values
Figure BDA0002775400130000061
The final estimate yielded a precession cone height of 0.9997 with a relative error of 0.03%, a base radius estimate of 0.2479 with a relative error of 0.84%, a precession angle estimate of 18.0074 °, and a relative error of 0.04%. It can be seen that the accuracy of the estimation by the method of the present invention is already very high, whereas the accuracy of the estimation by the previous method is between 5% and 15%.

Claims (3)

1. A method for optimizing a precession cone target parameter by using spatial mapping is characterized by comprising the following specific steps:
step 1, establishing a geometric diffraction scattering center model;
step 2, obtaining the optimal parameter vector of the coarse model
Figure FDA0002775400120000011
Order to
Figure FDA0002775400120000012
Step 3, initializing matrix B(1)Is as follows I, according to B(i)h(i)＝-f(i)Solving for incremental step length h(i)；
Step 4, updating the parameter vector of the detailed model
Figure FDA0002775400120000013
Step 5, substituting the parameter vector of the fine model into the fine model for simulation, and stopping the algorithm if the error requirement is met;
step 6, obtaining a rough model parameter vector according to the parameter extraction process
Figure FDA0002775400120000014
Computing residual vectors
Figure FDA0002775400120000015
Step 7, updating the matrixB(i+1)And i +1, turning to the step 2 until the fine model simulation meets the requirements.
2. The method for optimizing the parameters of a precession cone target according to claim 1, wherein the scattering center model is established in step 1, specifically as follows:
establishing a geometric diffraction model GTD according to the characteristics of the warhead cone target; the radar system observes the target in a mode of frequency sweep and angle sweep, and f is f0…fN-1For the frequency sweep of the transmitted signal, N is the number of frequency points, and theta is equal to theta0…θM-1For all observation angles, M is the total number of sweep angles;
the mathematical expression for the GTD model is as follows:
Figure FDA0002775400120000016
wherein y (f, theta) represents a two-dimensional echo received by the radar, K represents the number of scattering centers, and si,xi,yiRepresenting amplitude information and position information of the ith scattering center, f0Denotes the center frequency, c is the speed of light, αiThe frequency dependent factor is used to represent different scattering types.
3. The method for optimizing a precession cone target parameter using spatial mapping as claimed in claim 1, wherein said fine model of step 4 is a full-wave electromagnetic simulation rotational symmetry method, specifically as follows:
firstly, defining a surface current of a set of half-component domain and half-global basis function expansion rotational symmetry body target, wherein the specific expression is as follows:
Figure FDA0002775400120000017
wherein the content of the first and second substances,
Figure FDA0002775400120000018
respectively representing alpha-th mode number
Figure FDA0002775400120000019
The nth basis function in the direction of the vector,
Figure FDA00027754001200000110
respectively representing the expansion coefficients of the corresponding basis functions, and N represents the number of all the basis functions in the direction of the target bus; specific expressions of the two types of basis functions are given below:
Figure FDA0002775400120000021
Figure FDA0002775400120000022
then, by using a Galileo test method, the conjugate of the basis function is selected as a test function, and the specific expression is as follows:
Figure FDA0002775400120000023
Figure FDA0002775400120000024
wherein, beta represents the corresponding mode number of the test function; and finally substituting the formula into an integral equation to obtain:
Figure FDA0002775400120000025
wherein the impedance matrix is represented as:
Figure FDA0002775400120000026
the right vector is represented as:
Figure FDA0002775400120000027
through the analysis process, the accurate solution of the current coefficient of the target surface of the rotational symmetric body is realized.
CN202011263520.3A 2020-11-12 2020-11-12 Method for optimizing precession cone target parameters by using spatial mapping Pending CN114488125A (en)

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