CN111781589A - Time-frequency analysis method for improving time-frequency resolution of micro cone target - Google Patents

Time-frequency analysis method for improving time-frequency resolution of micro cone target Download PDF

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CN111781589A
CN111781589A CN202010368491.0A CN202010368491A CN111781589A CN 111781589 A CN111781589 A CN 111781589A CN 202010368491 A CN202010368491 A CN 202010368491A CN 111781589 A CN111781589 A CN 111781589A
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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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    • 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 time-frequency analysis method for improving the time-frequency resolution of a micro cone target. The method comprises the following steps: firstly, a geometric model of a ballistic missile target is established, then a single frequency pulse is transmitted to the target, the echo of the target is received, and a time-frequency distribution diagram of the target is obtained by performing time-frequency analysis on the echo of the target, so that the geometric shape parameters and the micro-motion parameters of the micro-motion cone target can be estimated, and the method has great significance for target identification. In order to obtain the time-frequency distribution map of the target, a time-frequency transformation method is required to be applied to the echo signal of the target for time-frequency analysis, and the quality of the time-frequency transformation method determines the time-frequency resolution of the time-frequency distribution map, which directly affects the precision of subsequent parameter estimation. The invention introduces synchronous compressed Wavelet Transform (SWT) to carry out time-frequency analysis on the micro-motion target echo, and has higher time-frequency resolution compared with other time-frequency Transform methods.

Description

Time-frequency analysis method for improving time-frequency resolution of micro cone target
Technical Field
The invention belongs to the technical field of signal processing, and particularly relates to a time-frequency analysis method for improving time-frequency resolution of a cone warhead target.
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 time-frequency analysis method for cone warhead target echoes.
The technical solution for realizing the purpose of the invention is as follows: a time-frequency analysis method for improving time-frequency resolution of a cone warhead target comprises the following steps:
step 1, establishing a cone trajectory missile warhead target geometric model;
step 2, transmitting a single frequency pulse with duration t to the ballistic missile target, and receiving the echo of the ballistic missile target within the period t;
and 3, performing synchronous compression wavelet time-frequency transformation on the received echoes to obtain a time-frequency graph of the ballistic missile target echoes.
Step 4, extracting an instantaneous micro Doppler frequency curve of the target according to the time-frequency diagram;
and 5, estimating cone target parameters according to the extracted target instantaneous micro Doppler frequency curve.
Further, the establishment of the geometric model of the ballistic missile target in step 1 specifically comprises the following steps:
step 1.1, the cone top instantaneous micro Doppler theoretical curve of the ballistic missile target echo is as follows:
Figure BDA0002477311930000021
the cone top instantaneous micro-Doppler theoretical curve of the ballistic missile target echo is as follows:
Figure BDA0002477311930000022
wherein t is time, λ is wavelength at current frequency, ω is precession frequency, H is height of ballistic missile target, H is height of centroid of ballistic missile target, γ is radar line-of-sight angle, θ is precession angle, r is radius of ballistic missile, β is attitude angle, cos β (t) is cos γ cos θ -sin γ sin θ sin (ω t);
the synchronous compression wavelet transform described in the step three is specifically as follows:
assume that the continuous wavelet transform of a single harmonic signal s (t) ═ a cos (ω t) is:
Figure BDA0002477311930000023
wherein a and b are respectively a scale factor and a translation factor,
Figure BDA0002477311930000024
is that
Figure BDA0002477311930000025
The conjugate of ψ (t) is called the mother wavelet function. Common mother wavelet functions are: morlet wavelets, bump wavelets, Gauss wavelets, and the like. The time-frequency distribution diagram obtained by different wavelet functions also has difference. According to Plancherel's theorem, the above formula can be expressed in the frequency domain as:
Figure BDA0002477311930000026
wherein,
Figure BDA0002477311930000027
fourier transform of S (t), here:
Figure BDA0002477311930000028
substituting the above equation can result in:
Figure BDA0002477311930000029
if ψ (ξ) converges to around ξ ═ 0, the wavelet coefficient Ws(a, b) is concentrated on the scale factor a ═ ω0Near/ω. At this time, no energy is diffused near the instantaneous frequency, and the time-frequency resolution is higher. However, in practice in the time scale plane, Ws(a, b) in a ═ ω0Diffusion phenomena often exist near/omega, and the time frequency spectrum of wavelet transformation is blurred. For arbitrary (a, b), Ws(a, b) ≠ 0 calculating the instantaneous frequency ω of the signal S (t)s(a, b), i.e. the time derivative:
Figure BDA00024773119300000210
mapping (a, b) to (ω)s(a, b), b) mapping the continuous wavelet transform from the time-scale plane onto the time-frequency plane. In the discrete synchronous compression wavelet transform, a, b and omega are dispersed, and when the frequency omega and the scale a are discrete variables, the wavelet coefficient Ws(a, b) at Point a onlykIs calculated by compressing the center frequency omega in the time-frequency domainlIn the vicinity of [ omega ]l-0.5*Δω,ωl+0.5*Δω]Wavelet coefficient W ofs(a, b) wherein ak-ak-1＝Δa,ωk-ωk-1Δ ω, we obtain:
Figure BDA0002477311930000031
the above equation is discrete synchronous compression wavelet transform, and the continuous synchronous compression wavelet transform can be written as:
Figure BDA0002477311930000032
wherein,
Figure BDA0002477311930000033
let Zk＝{(a,b):|aω'k(b) -1| > Δ }, when (a, b) ∈ ZkThe method comprises the following steps:
Figure BDA0002477311930000034
the SWT transform can obtain the frequency corresponding to each scale by solving the time partial derivative. After SWT processing, the signal energy divergence condition can be greatly improved, and the time-frequency resolution is obviously improved
The cone target parameter estimation method described in the fifth step is concretely as follows;
when the cone bottom instantaneous micro Doppler theoretical curve changes T/2 along with the time, the cone bottom instantaneous micro Doppler theoretical curve
Figure BDA0002477311930000035
Comprises the following steps:
Figure BDA0002477311930000036
wherein,
Figure BDA0002477311930000037
t is a precession period; will f is2(t) and
Figure BDA0002477311930000038
adding to obtain an objective function g (t):
Figure BDA0002477311930000039
wherein:
cos β(t)＝cos γ cos θ-sin γ sin θ sin(ωt)
Figure BDA00024773119300000310
performing least square on the target curve and the target function to obtain the radius and the precession angle of the trajectory missile target, wherein the formula is as follows:
Figure BDA00024773119300000311
wherein:
G(t)＝f2(t1)+f2(t2)
Figure BDA0002477311930000041
wherein G (t) is a target curve, f2(t1) Represents the cone bottom instantaneous micro Doppler curve oneFirst half of a period, f2(t2) Representing the second half period of the cone bottom instantaneous micro-Doppler curve in one period;
Figure BDA0002477311930000042
for the angle of precession to be estimated,
Figure BDA0002477311930000043
for the ballistic missile radius to be estimated, g (t | θ, r) is the objective function, where θ and r are the parameters to be searched. The height and the centroid height of the ballistic missile target are obtained by using the maximum values of the cone top instantaneous micro-Doppler curve and the cone bottom instantaneous micro-Doppler curve, and the formula is as follows:
Figure BDA0002477311930000044
Figure BDA0002477311930000045
wherein λ is the wavelength at the current frequency, ω is the precession frequency, H is the height of the ballistic missile target, H is the height of the center of mass of the ballistic missile target, γ is the radar line-of-sight angle, θ is the precession angle, r is the radius of the ballistic missile, f is the distance between the target and the radar line-of-sight angle, f2(t)maxIs the maximum value, f, of the cone bottom instantaneous micro-Doppler curve1(t)maxThe maximum value of the cone top instantaneous micro-Doppler curve.
Compared with the prior art, the invention has the following remarkable advantages: (1) the time-frequency resolution of the target time-frequency distribution graph is improved by compressing the instantaneous micro Doppler frequency (2), and the precision of parameter estimation can be effectively improved by estimating the geometric parameters and the micro-motion parameters of the cone target by the method.
Drawings
Figure 1 is a schematic view of the precession of a ballistic missile target of the present invention.
Figure 2 is a graphical representation of the two-dimensional parameters of the ballistic missile target of the present invention.
Fig. 3 is a blunt-tipped flat-bottomed conical bullet model.
Fig. 4 is a target transform time-frequency diagram.
Figure 5 is a graph of target theoretical micro-doppler.
FIG. 6 is a comparison graph of the micro-Doppler curves of cone top strong scattering points.
FIG. 7 is a comparison graph of the micro-Doppler curves of the strong scattering points at the cone bottom.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
With reference to the attached drawing 1, the time-frequency analysis method for improving the time-frequency resolution of the cone warhead target of the invention comprises the following steps:
step 1, establishing a cone trajectory missile warhead target geometric model:
step 1.1, a target precession model of a middle-section ballistic missile trajectory missile is shown in fig. 1, wherein OXYZ is a translational coordinate system, Oxyz is a satellite coordinate system, a warhead makes spinning motion around a symmetric axis Oz at an angular velocity omega, and a spinning axis Oz makes coning motion around a precession axis OZ at an angular velocity omega; LOS is the radar sight line direction, beta is the included angle between the radar sight line and the target central axis, theta is the precession angle, the included angle between the radar sight line and the precession axis is gamma, the geometric parameters of the ballistic missile model are set as shown in figure 3, the height of the ballistic missile is H, the radius of the bottom surface is r, the O point is the target mass center, and the height from the bottom surface is H, then:
the cone top instantaneous micro-Doppler theoretical curve of the ballistic missile target echo is as follows:
Figure BDA0002477311930000051
the cone top instantaneous micro-Doppler theoretical curve of the ballistic missile target echo is as follows:
Figure BDA0002477311930000052
wherein t is time, λ is wavelength at current frequency, ω is precession frequency, H is height of ballistic missile target, H is height of centroid of ballistic missile target, γ is radar line-of-sight angle, θ is precession angle, r is radius of ballistic missile, β is attitude angle, cos β (t) is cos γ cos θ -sin γ sin θ sin (ω t);
step 2, transmitting a single frequency pulse with duration t to the ballistic missile target, and receiving the echo of the ballistic missile target within the period t;
and 3, performing synchronous compression wavelet time-frequency transformation on the received echoes to obtain a time-frequency graph of the ballistic missile target echoes. The method comprises the following specific steps:
step 3.1, assuming that the continuous wavelet transform of a single harmonic signal s (t) ═ a cos (ω t) is:
Figure BDA0002477311930000053
wherein a and b are respectively a scale factor and a translation factor,
Figure BDA0002477311930000054
is that
Figure BDA0002477311930000055
The conjugate of ψ (t) is called the mother wavelet function. Common mother wavelet functions are: morlet wavelets, bump wavelets, Gauss wavelets, and the like. The time-frequency distribution diagram obtained by different wavelet functions also has difference. According to Plancherel's theorem, the above formula can be expressed in the frequency domain as:
Figure BDA0002477311930000056
wherein,
Figure BDA0002477311930000057
fourier transform of S (t), here:
Figure BDA0002477311930000058
substituting the above equation can result in:
Figure BDA0002477311930000059
if ψ (ξ) converges to around ξ ═ 0, the wavelet coefficient Ws(a, b) is concentrated on the scale factor a ═ ω0Near/ω. At this time, no energy is diffused near the instantaneous frequency, and the time-frequency resolution is higher. However, in practice in the time scale plane, Ws(a, b) in a ═ ω0Diffusion phenomena often exist near/omega, and the time frequency spectrum of wavelet transformation is blurred. For arbitrary (a, b), Ws(a, b) ≠ 0 calculating the instantaneous frequency ω of the signal S (t)s(a, b), i.e. the time derivative:
Figure BDA0002477311930000061
mapping (a, b) to (ω)s(a, b), b) mapping the continuous wavelet transform from the time-scale plane onto the time-frequency plane. In the discrete synchronous compression wavelet transform, a, b and omega are dispersed, and when the frequency omega and the scale a are discrete variables, the wavelet coefficient Ws(a, b) at Point a onlykIs calculated by compressing the center frequency omega in the time-frequency domainlIn the vicinity of [ omega ]l-0.5*Δω,ωl+0.5*Δω]Wavelet coefficient W ofs(a, b) wherein ak-ak-1＝Δa,ωk-ωk-1Δ ω, we obtain:
Figure BDA0002477311930000062
the above equation is discrete synchronous compression wavelet transform, and the continuous synchronous compression wavelet transform can be written as:
Figure BDA0002477311930000063
wherein,
Figure BDA0002477311930000064
let Zk＝{(a,b):|aω'k(b) -1| > Δ }, when (a, b) ∈ ZkThe method comprises the following steps:
Figure BDA0002477311930000065
the SWT transform can obtain the frequency corresponding to each scale by solving the time partial derivative. After SWT processing, the signal energy divergence condition can be greatly improved, and the time-frequency resolution is obviously improved.
And 4, extracting the instantaneous micro Doppler frequency curve of the target according to the time-frequency diagram.
And 5, estimating cone target parameters according to the extracted target instantaneous micro Doppler frequency curve. The method comprises the following specific steps:
step 5.1, after the cone bottom instantaneous micro Doppler theoretical curve changes T/2 along with the time, the cone bottom instantaneous micro Doppler theoretical curve
Figure BDA0002477311930000066
Comprises the following steps:
Figure BDA0002477311930000067
wherein,
Figure BDA0002477311930000068
t is a precession period; will f is2(t) and
Figure BDA0002477311930000069
adding to obtain an objective function g (t):
Figure BDA00024773119300000610
wherein:
cos β(t)＝cos γ cos θ-sin γ sin θ sin(ωt)
Figure BDA00024773119300000611
performing least square on the target curve and the target function to obtain the radius and the precession angle of the trajectory missile target, wherein the formula is as follows:
Figure BDA0002477311930000071
wherein:
G(t)＝f2(t1)+f2(t2)
Figure BDA0002477311930000072
wherein G (t) is a target curve, f2(t1) Representing the first half of a period, f, of a cone-bottom instantaneous micro-Doppler curve2(t2) Representing the second half period of the cone bottom instantaneous micro-Doppler curve in one period;
Figure BDA0002477311930000073
for the angle of precession to be estimated,
Figure BDA0002477311930000074
for the ballistic missile radius to be estimated, g (t | θ, r) is the objective function, where θ and r are the parameters to be searched. The height and the centroid height of the ballistic missile target are obtained by using the maximum values of the cone top instantaneous micro-Doppler curve and the cone bottom instantaneous micro-Doppler curve, and the formula is as follows:
Figure BDA0002477311930000075
Figure BDA0002477311930000076
wherein λ is the wavelength at the current frequency, ω is the precession frequency, H is the height of the ballistic missile target, H is the height of the center of mass of the ballistic missile target, γ is the radar line-of-sight angle, θ is the precession angle, r is the radius of the ballistic missile, f is the distance between the target and the radar line-of-sight angle, f2(t)maxIs the maximum value, f, of the cone bottom instantaneous micro-Doppler curve1(t)maxThe maximum value of the cone top instantaneous micro-Doppler curve.
Examples
The typical simulation of electromagnetic scattering is performed in the embodiment, the simulation is realized on a personal computer with a main frequency of 2.5GHz and a memory of 4GB, the target height of the cone head is 1.2m, the radius of the bottom surface is 0.25m, and the precession angle is 10 degrees. Other simulation parameters were: the target precession period is 2s, the radar line-of-sight angle is 35 degrees, the sampling frequency is 500Hz, and the sampling time is 2 s. Table 1 shows the results of estimating parameters by using the method of the present invention to estimate the instantaneous micro doppler frequency. In order to verify the correctness of the method, the result of short-time Fourier transform is compared.
TABLE 1
θ(°) H(m) h(m) r(m)
True value 10 1.2 0.2 0.25
Estimated value 10.3 1.2008 0.2203 0.23
Estimation error (Absolute) 0.3 0.0008 0.0203 0.02
Estimation error (relative) 3％ 0.4％ 10.15％ 8％
From the estimation results in table 1, it can be seen that the estimation error of the target structural parameter is about 0.02m, the estimation error of the precession angle is within 0.5 °, and the estimation accuracy of the method is relatively high when no noise interference exists. The result of the parameters estimated from the time-frequency diagram obtained by STFT transformation is as follows: the error is higher than the SWT conversion by more than 10%, and the comparison of the micro Doppler frequency curves of fig. 6 and fig. 7 also shows that the curve of SWT is better matched with the theoretical curve, thus showing the effectiveness of the method provided by the invention.

Claims (4)

1. A time-frequency analysis method for improving the time-frequency resolution of a micro cone target is characterized by comprising the following steps:
step 1, establishing a cone trajectory missile warhead target geometric model,
step 2, transmitting a single frequency pulse with duration t to the ballistic missile target, and receiving the echo of the ballistic missile target within the period t;
step 3, performing synchronous compression wavelet time-frequency transformation on the received echoes to obtain a time-frequency graph of the ballistic missile target echoes;
step 4, extracting an instantaneous micro Doppler frequency curve of the target according to the time-frequency diagram;
and 5, estimating cone target parameters according to the extracted target instantaneous micro Doppler frequency curve.
2. The time-frequency analysis method for improving the time-frequency resolution of the micro-motion cone target according to claim 1, wherein the establishment of the geometric model of the ballistic missile target in the step 1 is as follows:
the cone top instantaneous micro Doppler theoretical curve of the bullet target echo of the ballistic missile cone is as follows:
Figure FDA0002477311920000011
the cone top instantaneous micro Doppler theoretical curve of the bullet target echo of the ballistic missile cone is as follows:
Figure FDA0002477311920000012
wherein t is time, λ is wavelength at current frequency, ω is precession frequency, H is height of ballistic missile target, H is height of centroid of ballistic missile target, γ is radar line-of-sight angle, θ is precession angle, r is radius of ballistic missile, β is attitude angle, cos β (t) is cos γ cos θ -sin γ sin θ sin (ω t).
3. The time-frequency analysis method for improving the time-frequency resolution of a jogging cone target according to claim 1, wherein the synchronous compression wavelet transform of step 3: the method comprises the following specific steps:
assume that the continuous wavelet transform of a single harmonic signal s (t) ═ Acos (ω t) is:
Figure FDA0002477311920000013
wherein a and b are respectively a scale factor and a translation factor,
Figure FDA0002477311920000014
is that
Figure FDA0002477311920000015
Is referred to as the mother wavelet function; according to Plancherel's theorem, the above formula can be expressed in the frequency domain as:
Figure FDA0002477311920000016
wherein,
Figure FDA0002477311920000017
fourier transform of S (t), here:
Figure FDA0002477311920000018
substituting the formula to obtain:
Figure FDA0002477311920000021
for arbitrary (a, b), Ws(a, b) ≠ 0 calculating the instantaneous frequency ω of the signal S (t)s(a, b), i.e. the time derivative:
Figure FDA0002477311920000022
mapping (a, b) to (ω)s(a, b), b) mapping the continuous wavelet transform from the time-scale plane onto the time-frequency plane. In the discrete synchronous compression wavelet transform, a, b and omega are dispersed, and when the frequency omega and the scale a are discrete variables, the wavelet coefficient Ws(a, b) at Point a onlykIs calculated by compressing the center frequency omega in the time-frequency domainlIn the vicinity of [ omega ]l-0.5*Δω,ωl+0.5*Δω]Wavelet coefficient W ofs(a, b) wherein ak-ak-1＝Δa,ωk-ωk1Δ ω, we obtain:
Figure FDA0002477311920000023
the above equation is discrete synchronous compression wavelet transform, and the continuous synchronous compression wavelet transform is written as:
Figure FDA0002477311920000024
wherein,
Figure FDA0002477311920000025
order to
Figure FDA0002477311920000026
When (a, b) ∈ ZkThe method comprises the following steps:
Figure FDA0002477311920000027
the SWT transform can obtain the frequency corresponding to each scale by solving the time partial derivative.
4. The time-frequency analysis method for improving the time-frequency resolution of the micro-motion cone target according to claim 1, wherein the cone target parameter estimation method of step 5 comprises: the method comprises the following specific steps:
when the cone bottom instantaneous micro Doppler theoretical curve changes T/2 along with the time, the cone bottom instantaneous micro Doppler theoretical curve
Figure FDA0002477311920000028
Comprises the following steps:
Figure FDA0002477311920000029
wherein,
Figure FDA00024773119200000210
t is a precession period; will f is2(t) and
Figure FDA00024773119200000211
adding to obtain an objective function g (t):
Figure FDA0002477311920000031
wherein:
cosβ(t)＝cosγcosθ-sinγsinθsin(ωt)
Figure FDA0002477311920000032
performing least square on the target curve and the target function to obtain the radius and the precession angle of the trajectory missile target, wherein the formula is as follows:
Figure FDA0002477311920000033
wherein:
G(t)＝f2(t1)+f2(t2)
Figure FDA0002477311920000034
wherein G (t) is a target curve, f2(t1) Representing the first half of a period, f, of a cone-bottom instantaneous micro-Doppler curve2(t2) Representing the second half period of the cone bottom instantaneous micro-Doppler curve in one period;
Figure FDA0002477311920000035
for the angle of precession to be estimated,
Figure FDA0002477311920000036
for the ballistic missile radius to be estimated, g (t | θ, r) is the objective function, where θ and r are the parameters to be searched. The height and the centroid height of the ballistic missile target are obtained by using the maximum values of the cone top instantaneous micro-Doppler curve and the cone bottom instantaneous micro-Doppler curve, and the formula is as follows:
Figure FDA0002477311920000037
Figure FDA0002477311920000038
wherein λ is the wavelength at the current frequency, ω is the precession frequency, H is the height of the ballistic missile target, H is the height of the center of mass of the ballistic missile target, γ is the radar line-of-sight angle, θ is the precession angle, r is the radius of the ballistic missile, f is the distance between the target and the radar line-of-sight angle, f2(t)maxIs the maximum value, f, of the cone bottom instantaneous micro-Doppler curve1(t)maxThe maximum value of the cone top instantaneous micro-Doppler curve.
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CN113296065A (en) * 2021-04-15 2021-08-24 中国人民解放军63921部队 Simulation method for micro cone target radar echo signal
CN113296065B (en) * 2021-04-15 2023-01-20 中国人民解放军63921部队 Simulation method for micro cone target radar echo signal
CN113625245A (en) * 2021-08-17 2021-11-09 哈尔滨工业大学 Ballistic missile middle-section target precession parameter estimation method
CN113625245B (en) * 2021-08-17 2023-11-07 哈尔滨工业大学 Method for estimating middle-stage target precession parameters of ballistic missile

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