阅读说明：本技术 基于乘积变尺度周期吕分布的机动目标相参检测方法及装置 (Maneuvering target coherent detection method and device based on product variable-scale periodic Lu distribution ) 是由 靳科 黄洁 张红敏 党同心 王建涛 于 2019-09-30 设计创作，主要内容包括：本发明属于雷达信号处理技术领域,特别涉及一种基于乘积变尺度周期吕分布的机动目标相参检测方法及装置,包含：依据雷达发射线性调频信号,获取多普勒模糊目标信号模型；针对多普勒模糊目标信号模型,利用离散傅里叶变换消除多普勒模糊和耦合,获取不同距离频率下的吕分布结果；并针对吕分布结果通过乘积操作,以实现机动目标相参检测。本发明具有良好的交叉项抑制性能,适用于多目标探测及参数估计；在不增加PRF或改变其他系统参数的情况下,通过进行频谱周期延拓估计模糊多普勒频率,能够较好实现对具有恒定速度的多普勒模糊目标的探测,可通过快速傅里叶变换FFT和快速傅里叶反变换IFFT实现无搜索参数估计,在低信噪比下实现有效探测机动目标。(The invention belongs to the technical field of radar signal processing, and particularly relates to a maneuvering target coherent detection method and device based on product variable-scale periodic distribution, which comprises the following steps: acquiring a Doppler fuzzy target signal model according to a linear frequency modulation signal transmitted by a radar; aiming at a Doppler fuzzy target signal model, eliminating Doppler fuzzy and coupling by utilizing discrete Fourier transform to obtain a Lu distribution result under different distance frequencies; and aiming at the Lu distribution result, the mobile target coherent detection is realized through product operation. The method has good cross item inhibition performance, and is suitable for multi-target detection and parameter estimation; under the condition of not increasing PRF or changing other system parameters, the detection of the Doppler fuzzy target with constant speed can be better realized by carrying out spectrum period continuation estimation on the fuzzy Doppler frequency, the non-search parameter estimation can be realized by Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT), and the effective detection of the maneuvering target can be realized under the condition of low signal-to-noise ratio.)

1. A maneuvering target coherent detection method based on product variable-scale periodic Lu distribution is characterized by comprising the following steps:

acquiring a Doppler fuzzy target signal model according to a linear frequency modulation signal transmitted by a radar;

aiming at a Doppler fuzzy target signal model, eliminating Doppler fuzzy and coupling by utilizing discrete Fourier transform to obtain a Lu distribution result under different distance frequencies; and aiming at the Lu distribution result, the mobile target coherent detection is realized through product operation.

2. The method as claimed in claim 1, wherein the method comprises obtaining the received signal with non-linear variation in slow time by setting the instantaneous slant range of the maneuvering target moving at a constant acceleration from the radar according to the chirp signal emitted from the radar; and Fourier transform is carried out on the received signal along the fast time to obtain a Doppler fuzzy target signal model.

3. The method as claimed in claim 1, wherein the symmetric instantaneous autocorrelation function is set according to a Doppler fuzzy target signal model; the distribution of the symmetrical instantaneous autocorrelation function is obtained by setting slow time and delay variables; and estimating the fuzzy Doppler frequency by carrying out periodic continuation on the discrete Fourier transform main value interval, and eliminating the coupling between the distance frequency and the slow time by utilizing the signal variable scale factor to obtain the distribution results of the Lu under different distance frequencies.

4. The method as claimed in claim 3, wherein the periodic integer of the periodic prolongation is obtained by presetting the velocity observation range to expand the Doppler frequency range.

5. The method of claim 3, wherein the distance frequency-dependent scaling factor is set to cancel the coupling between the distance frequency and the slow time.

6. The method as claimed in claim 1 or 3, wherein the multiplication operation is performed on the distribution result of the mechanical target at different distance frequencies, and coherent accumulation on the mechanical target is realized by coherent enhancement of spectral peaks and suppression of grating lobes.

7. The method as claimed in claim 6, wherein a cost function for estimating the motion parameters of the maneuvering target is constructed according to the result of the coherence enhanced spectrum peak; and the coherent accumulation detection of the maneuvering target is realized through a phase compensation function.

8. The method as claimed in claim 7, wherein the moving object motion parameters include velocity and acceleration.

9. The method of claim 7, wherein the phase compensation function is constructed using the estimated motion parameters to eliminate linear range, range-bending, and doppler frequency shifts; and realizing coherent accumulation of the maneuvering target through discrete Fourier transform and inverse discrete Fourier transform according to the phase compensation function, the slow time and the distance frequency.

10. A mobile target coherent detection device based on product variable-scale periodic distribution is characterized by comprising: a signal model building module and a target coherent detection module, wherein,

the signal model building module is used for acquiring a Doppler fuzzy target signal model according to the linear frequency modulation signals transmitted by the radar;

the target coherent detection module is used for eliminating Doppler ambiguity and coupling by using discrete Fourier transform aiming at a Doppler ambiguity target signal model and acquiring a Lu distribution result under different distance frequencies; and aiming at the Lu distribution result, the mobile target coherent detection is realized through product operation.

Technical Field

The invention belongs to the technical field of radar signal processing, and particularly relates to a maneuvering target coherent detection method and device based on product variable-scale periodic distribution.

Background

The rapid development of stealth airplanes and Unmanned Aerial Vehicles (UAVs) in recent years has placed increasing demands on radar maneuvering weak target detection. To detect such low radar cross-sectional area RCS targets, long-term coherent accumulation is a preferred approach. Unfortunately, the resulting problems include not only linear range migration LRM, range bending and doppler frequency migration DFM, but also doppler frequency ambiguity due to high target speed or radar low pulse repetition frequency PRF. These adverse factors will severely affect the detection performance of traditional accumulation algorithms (e.g. MTD). Therefore, how to effectively detect a maneuvering target with doppler ambiguity becomes a hot topic in the field of radar signal processing.

Linear range migration LRM will cause the target envelope to span cell migration. The existing Keystone transformation KT, Radon-Fourier transformation, variable-scale Fourier inverse transformation SCIFT, frequency domain deskew-Keystone transformation FDDKT, axis rotation MTD (AR-MTD) and improved coordinate rotation transformation MLRT and the like all provide LRM elimination. However, they suffer from severe cumulative performance loss due to neglect of the range bending and DFM effects caused by target acceleration. In order to solve the problems, a representative method comprises search algorithms such as generalized RFT (generalized RFT), namely GRFT, Radon Lu distribution algorithm RLVD, KT and Lu distribution algorithms KT-LVD, KT and linear regular transformation KT-LCT, improved axis rotation transformation and Lu distribution MART-LVT, and improved axis rotation and fractional order Fourier transformation IAR-FRFT, and the algorithms show excellent detection performance under low signal-to-noise ratio (SNR) through parameter search; however, the great computational complexity makes it unacceptable in practical applications. In addition, compared with the search algorithm, the non-search algorithms including the adjacent cross-correlation function ACCF, the symmetric autocorrelation function-variable scale Fourier transform SAF-SFT, the frequency second-order phase difference FD-SoPD, the three-dimensional variable scale transform TDST and the like can obtain lower computational complexity but at the expense of anti-noise performance. Therefore, a processing scheme capable of effectively balancing complexity and detection performance is needed to achieve detection of a radar maneuvering target.

Disclosure of Invention

Therefore, the invention provides the Doppler fuzzy maneuvering target coherent detection method and device based on the product variable-scale periodic distribution, which are suitable for Doppler fuzzy maneuvering target detection, can better inhibit cross terms in maneuvering target coherent detection, and improve the accuracy and efficiency of maneuvering target detection.

According to the design scheme provided by the invention, the Doppler fuzzy maneuvering target coherent detection method based on the product variable-scale periodic Lu distribution comprises the following contents:

acquiring a Doppler fuzzy target signal model according to a linear frequency modulation signal transmitted by a radar;

aiming at a Doppler fuzzy target signal model, eliminating Doppler fuzzy and coupling by utilizing discrete Fourier transform to obtain a Lu distribution result under different distance frequencies; and aiming at the Lu distribution result, the mobile target coherent detection is realized through product operation.

As the mobile target coherent detection method, further, a receiving signal which changes in a non-linear way in a slow time is obtained by setting the instantaneous slope distance of the mobile target moving at a constant acceleration from the radar according to a linear frequency modulation signal transmitted by the radar; and Fourier transform is carried out on the received signal along the fast time to obtain a Doppler fuzzy target signal model.

As a coherent detection method for a maneuvering target in the embodiment of the invention, further, a symmetrical instantaneous autocorrelation function is set according to a Doppler fuzzy target signal model; the distribution of the symmetrical instantaneous autocorrelation function is obtained by setting slow time and delay variables; and estimating the fuzzy Doppler frequency by carrying out periodic continuation on the discrete Fourier transform main value interval, and eliminating the coupling between the distance frequency and the slow time by utilizing the signal variable scale factor to obtain the distribution results of the Lu under different distance frequencies.

As the maneuvering target coherent detection method in the embodiment of the invention, further, a period integer of period extension is obtained by presetting a speed observation range to expand a doppler frequency range.

As a maneuvering target coherent detection method in the embodiment of the invention, further, coupling between the range frequency and the slow time is eliminated by setting a variable scale factor depending on the range frequency.

As the maneuvering target coherent detection method in the embodiment of the invention, further, product operation is carried out on the Lu distribution results under different distance frequencies, and coherent accumulation on the maneuvering target is realized by coherent enhancement of a spectral peak and suppression of grating lobes.

As a mobile target coherent detection method in the embodiment of the invention, further, a cost function for estimating mobile target motion parameters is constructed according to a coherent enhancement spectrum peak result; and the coherent accumulation detection of the maneuvering target is realized through a phase compensation function.

As the maneuvering target coherent detection method in the embodiment of the invention, further, the maneuvering target motion parameters include speed and acceleration.

As the maneuvering target phase-coherent detection method in the embodiment of the invention, a phase compensation function is further constructed by utilizing the estimated motion parameters to eliminate linear distance migration, distance bending and Doppler frequency migration; and realizing coherent accumulation of the maneuvering target through discrete Fourier transform and inverse discrete Fourier transform according to the phase compensation function, the slow time and the distance frequency.

Further, the present invention also provides a doppler fuzzy maneuvering target coherent detection device based on the product variable scale periodic lu distribution, including: a signal model building module and a target coherent detection module, wherein,

the signal model building module is used for acquiring a Doppler fuzzy target signal model according to the linear frequency modulation signals transmitted by the radar;

the target coherent detection module is used for eliminating Doppler ambiguity and coupling by using discrete Fourier transform aiming at a Doppler ambiguity target signal model and acquiring a Lu distribution result under different distance frequencies; and aiming at the Lu distribution result, the mobile target coherent detection is realized through product operation.

The invention has the beneficial effects that:

in the invention, a Doppler fuzzy target signal model is obtained according to a linear frequency modulation signal transmitted by a radar; aiming at a Doppler fuzzy target signal model, eliminating Doppler fuzzy and coupling by utilizing discrete Fourier transform to obtain a Lu distribution result under different distance frequencies; the method realizes the coherent detection of the maneuvering target by product operation aiming at the Lu distribution result, has good cross term inhibition performance, and is suitable for multi-target detection and parameter estimation; under the condition of not increasing PRF or changing other system parameters, the detection of the Doppler fuzzy target with constant speed can be better realized by carrying out spectrum period continuation estimation on the fuzzy Doppler frequency, the non-search parameter estimation can be realized by Fast Fourier Transform (FFT) and Inverse Fast Fourier Transform (IFFT), and the maneuvering target can be effectively detected under the condition of low signal-to-noise ratio. Furthermore, the effectiveness of the technical scheme of the invention is verified through simulation experiments and actual measurement data, and the method has better application value.

Description of the drawings:

FIG. 1 is a schematic flow chart of a coherent detection method for a maneuvering target in an embodiment;

FIG. 2 is a schematic diagram of a coherent detection device for a maneuvering target in an embodiment;

FIG. 3 is a diagram illustrating DFT period extension in an embodiment;

FIG. 4 is a schematic diagram of a scaling process in an embodiment;

FIG. 5 is a diagram showing simulation results of Doppler spectrum peaks (no overlap and overlap) in the embodiment;

FIG. 6 is a schematic diagram of an implementation process of a variable scale period DFT based on CZT in the embodiment;

FIG. 7 is a diagram illustrating the comparison of computational complexity of different algorithms in the embodiment;

FIG. 8 is a schematic diagram of coherent accumulation simulation of a single maneuvering target in an embodiment;

FIG. 9 is a schematic diagram of coherent accumulation simulation of two maneuvering targets in the embodiment;

FIG. 10 is a comparison of the detection performances of different algorithms in the examples;

FIG. 11 is a diagram showing the result of measured data of radar in the embodiment.

The specific implementation mode is as follows:

in order to make the objects, technical solutions and advantages of the present invention clearer and more obvious, the present invention is further described in detail below with reference to the accompanying drawings and technical solutions.

For the problem of coherent accumulation of a maneuvering target with doppler blur, an embodiment of the present invention, as shown in fig. 1, provides a doppler blur maneuvering target coherent detection method based on product variable scale periodic distribution, including:

s101) acquiring a Doppler fuzzy target signal model according to a linear frequency modulation signal transmitted by a radar;

s102) eliminating Doppler ambiguity and coupling by using discrete Fourier transform aiming at a Doppler ambiguity target signal model, and obtaining a Lu distribution result under different distance frequencies; and aiming at the Lu distribution result, the mobile target coherent detection is realized through product operation.

The fuzzy Doppler frequency estimation is realized through discrete Fourier transform and product operation, range migration and Doppler frequency migration are compensated, the cross term suppression performance is good, the method is suitable for multi-target detection and parameter estimation, and a maneuvering target with Doppler ambiguity can be effectively detected.

As a coherent detection method for a maneuvering target in the embodiment of the invention, further, a received signal which changes in a non-linear manner within a slow time is obtained by setting an instantaneous slope distance from the maneuvering target moving at a constant acceleration to the radar according to a chirp signal transmitted by the radar; and Fourier transform is carried out on the received signal along the fast time to obtain a Doppler fuzzy target signal model.

Assuming that the radar transmits a chirp modulated (LFM) signal,

wherein the content of the first and second substances,

in order to be a function of the window,

for fast time variables, T_pAnd f_cRespectively representing pulse duration and signal carrier frequency, k_r＝B/T_pFrequency modulation slope, and B radar signal bandwidth.

Assuming a moving target moves at a constant acceleration, its instantaneous slope distance R (t) from the radar_m) Satisfy the requirement of

Wherein R is₀V and a are the initial slope, radial velocity and acceleration of the target, respectively. t is t_m＝mT_m(m＝1,2,...,N_a) Representing a slow time variable, T_mIs the pulse repetition time, N_aTo accumulate the number of pulses.

Neglecting the effects of noise, the received signal after pulse pressure can be expressed as:

wherein A is_cAnd c are signal amplitude and propagation velocity, respectively.

The formula (3) can be substituted into the formula (4)

Wherein λ ═ c/f_cIs the signal wavelength.

As can be seen from equation (5), the signal envelope varies nonlinearly with slow time. The LRM appears linearly when the offset caused by the velocity exceeds a distance resolution unit Δ r — c/2B. Range bending may also be observed if the target is more maneuverable (i.e., has greater acceleration).

Fourier Transform (FT) is performed on equation (5) along a fast time to obtain

Wherein f is_rIs the distance frequency relative to the fast time.

Obviously, f_rAnd t_mCoupling between them is the essential cause of range migration. The doppler frequency of the target is defined as:

due to the acceleration, the doppler frequency changes linearly with the slow time, i.e. the DFM phenomenon occurs, thereby causing the target energy to be severely dispersed in the doppler domain. Also, doppler ambiguity can occur at high target speeds or low radar PRF^[35,36]I.e. by

|f_d,T|＞f_p/2 (8)

Wherein f is_p＝1/T_mRepresenting the PRF.

At this point, the signal is undersampled along the slow time dimension, which creates great difficulty in target velocity estimation. Therefore, in order to effectively detect a moving object at a low signal-to-noise ratio, elimination of the coupling term, DFM, doppler ambiguity must be considered.

As a coherent detection method for a maneuvering target in the embodiment of the invention, further, a symmetrical instantaneous autocorrelation function is set according to a Doppler fuzzy target signal model; the distribution of the symmetrical instantaneous autocorrelation function is obtained by setting slow time and delay variables; and estimating the fuzzy Doppler frequency by carrying out periodic continuation on the discrete Fourier transform main value interval, and eliminating the coupling between the distance frequency and the slow time by utilizing the signal variable scale factor to obtain the distribution results of the Lu under different distance frequencies.

Further, a period integer of the period extension is acquired by presetting a speed observation range to expand the Doppler frequency range. Preferably, the coupling between range frequency and slow time is eliminated by setting a distance frequency dependent scaling factor. And performing product operation on the Lu distribution results at different distance frequencies, and realizing coherent accumulation on the maneuvering target by means of coherent enhancement of a spectral peak and suppression of grating lobes. Constructing a cost function for estimating the motion parameters of the maneuvering target according to the result of the coherent enhancement spectrum peak; and the coherent accumulation detection of the maneuvering target is realized through a phase compensation function. The maneuvering target motion parameters include velocity and acceleration. Constructing a phase compensation function by utilizing the estimated motion parameters to eliminate linear range migration, range bending and Doppler frequency migration; and realizing coherent accumulation of the maneuvering target through discrete Fourier transform and inverse discrete Fourier transform according to the phase compensation function, the slow time and the distance frequency.

Further, based on the above method, an embodiment of the present invention further provides a doppler fuzzy maneuvering target coherent detection apparatus based on product variable-scale periodic lv distribution, as shown in fig. 2, including: a signal model construction module 101 and a target coherent detection module 102, wherein,

the signal model building module 101 is used for obtaining a Doppler fuzzy target signal model according to a linear frequency modulation signal transmitted by a radar;

the target coherent detection module 102 is configured to eliminate doppler ambiguity and coupling by using discrete fourier transform for a doppler ambiguity target signal model, and obtain a lv distribution result at different distance frequencies; and aiming at the Lu distribution result, the mobile target coherent detection is realized through product operation.

To estimate the center frequency and chirp rate of the LFM signal. The Symmetric Instantaneous Autocorrelation Function (SIAF) of equation (6) is defined as

Where denotes the complex conjugate and τ is the delay variable.

As can be seen from equation (9), the slow time t_mCoupled to the time delay tau. To eliminate this coupling term, the following variable substitutions may be made:

where h is a variable scale factor, t_nIs a new slow time variable.

The formula (10) is brought into the formula (9)

H-1 may be employed to balance the resolution and range of chirp rate estimation. Within a certain distance frequency unit, to time delay tau and slow time t_nPerforming two-dimensional DFT to obtain R_s(t_n,τ；f_r) LVD of (i.e.

Wherein v is₀＝mod(v,v_b) Is a non-fuzzy speed, v_b＝λf _p2 is blind speed, n_b＝Round(v/v_b) Represents the Doppler ambiguity of the target, where Round (-) is an upward integer function, f_d∈[-f_p/2,f_p/2) is the Doppler frequency variation with respect to the time delay τ, and γ is with respect to the slow time t_nThe chirp rate variation of (c).

In equation (12), the signal coherently accumulates as one spectral peak along the slow time in the center frequency-tone frequency (CFCR) domain. However, due to Doppler ambiguity and f_rAnd t_mThe coupling between them causes the spectral peak to erroneously estimate the target motion parameter, resulting in that the LVD is no longer applicable.

Doppler frequency estimation is achieved by DFT of the time delay, so the Doppler frequency is naturally limited to f_d∈[-f_p/2,f_pAnd/2). When frequency ambiguity occurs, the Doppler frequency of the target will exceed the main value interval of DFT, i.e.

Therefore, only the aliasing frequency can be measured by equation (12). In other words, the frequency of the DFTThe range is insufficient to support observations of ambiguous doppler frequencies.

It is well known that DFT can be repeated periodically (extended) with a repetition period f_pI.e. by

L_R(f_d,γ；f_r)＝L_R(f_d+q·f_p,γ；f_r),q∈Z (13)

Wherein q represents a periodic integer.

In practical applications, the periodicity of the DFT is usually ignored and only its main value interval is used. Thus, without changing the PRF or other system parameters, one of the most straightforward ways to measure the ambiguous doppler frequency is to reintroduce the redundancy period of the DFT to spread the frequency range. Fig. 3 shows a schematic diagram of frequency estimation, wherein the true frequency of the single frequency signal is 160Hz and the sampling rate is 100 Hz. Under traditional DFT, aliasing frequencies are only available at-40 Hz due to frequency ambiguity. But true frequencies are also observed when the frequency range is periodically extended from-50, 50) Hz to-250, 250 Hz. In the embodiment of the present invention, the period lvd (plvd) extended by the period may be defined as

Wherein the content of the first and second substances,

indicating the doppler frequency after the period extension. In order to be able to observe the ambiguous Doppler frequencies, we should have q > 2n_b. However, since the target speed is unknown, in practical application, the speed observation range can be determined first, and then the continuation integer q is obtained.

After PLVD, the blurred doppler frequency of the target is already observable. However, since f_rAnd t_mThe doppler spectrum peaks will give erroneous velocity and acceleration values. At this time, the PLVD needs to be modified into a variable-scale PLVD (splvd) to eliminate the influence of the coupling, which is defined as:

wherein ξ (f)_r)＝(f_r+f_c)/f_cTo depend on f_rThe variable scale factor of (2).

As can be seen from equation (15), when i ═ 0, the spectral peak in the CFCR domain will give the correct center frequency and frequency modulation, i.e., f_d0＝-2v/λ，γ₀＝-2a/λ。

FIG. 4 emulates three single frequency signals(s)₁，s₂And s₃) The scaling process of (1). The true frequency of the signal is 160Hz and the sampling rate is 100 Hz. The variable scale factors of the three signals are xi respectively₁＝1.1，ξ ₂1 and xi₃0.9. Therefore, s can only be estimated from the results of the periodic DFT before scaling₁And s₃I.e. 176Hz, 144 Hz. After scaling, the three signals can be estimated to the correct frequency.

Another problem arising from PLVD is the grating lobes in the doppler domain, the presence of which poses great difficulties in the discrimination and estimation of the true doppler frequency. However, an advantageous condition can be noted from fig. 4: after SPLVD, only the spectral peaks of the real frequency are aligned, and the spectral peaks of the grating lobes are staggered in position. When i is 0, the spectral peaks of different range frequencies all point to the true doppler frequency, i.e. the real doppler frequency

However, for different distance frequencies, different scaling factors ξ are set. At this time, the repetition period between grating lobes is

Therefore, grating lobes at different range frequencies are staggered due to different repetition periods, i.e. when i ≠ 0, grating lobes at different range frequencies will indicate different doppler frequencies.

In the above method for identifying true doppler frequency to eliminate spurious spectral peaks, the product splvd (psplvd) can be designed to coherently enhance the true spectral peaks and suppress grating lobes. The method carries out product operation on SPLVD results under different distance frequencies, and the product operation is defined as:

wherein A is_PSPIs the amplitude.

In this way, the amplitude of the grating lobes will be greatly reduced, resulting in a single spectral peak indicating the correct tune frequency and the ambiguous doppler frequency. The velocity and the acceleration of the target can be estimated by constructing a cost function:

using the estimated motion parameters, a phase compensation function of the following formula can be constructed to eliminate LRM, range warping and DFM.

Finally, respectively for t_mAnd f_rAnd performing DFT and Inverse DFT (IDFT), namely realizing coherent accumulation on the maneuvering target.

Similar to equation (6), K target received signals can be expressed in the range frequency domain as

SIAF of formula (22) is

Wherein the content of the first and second substances,

according to the euler formula:

can obtain the product

As can be seen from equation (27), after the variable replacement and DFT, the cosine function will have difficulty in coherent accumulation, and the oscillation term occurs. However, self terms can accumulate as spectral peaks in the CFCR domain. Only when R is_0,d＝R_0,p，v_d＝v_pAnd a_d＝a_pThe cosine term will be eliminated, but the cross term becomes the self term at this time. Therefore, the cross terms of the SIAF cannot achieve coherent accumulation.

Based on the above contents, the multi-objective coherent detection content can be designed as follows:

the PSPLVD results in the case of two maneuvering targets are considered as follows, and can be obtained on the same principle as for the case of multiple targets.

Ignoring the cross terms of SIAF, the SPLVD results for both targets can be written as:

the results of the PSPLVD can be considered in the following three cases.

Case 1: the acceleration of the two objects being different, i.e. a₁≠a₂. At this point, we can easily obtain the PSPLVD results as:

case 2: the acceleration of both objects being the same, i.e. a₁＝a₂. But instead of the other end of the tube

There is no overlap of the doppler spectrum peaks.

FIG. 5(a) simulates two single-frequency signals s₁And s₂The scaling results of (a). The frequencies of the two signals are 160Hz and 140Hz, respectively. The sampling rate was 100 Hz. The scale-varying factor is set to xi₁＝1.1，ξ ₂1 and xi₃0.9. After scaling, the true frequencies of each signal are aligned, but the false spectral peaks are staggered. Therefore, the result of PSPLVD can also be expressed by equation (29).

Case 3: the acceleration of both objects being the same, i.e. a₁＝a₂. But instead of the other end of the tube

There is overlap of the doppler spectrum peaks.

FIG. 6(b) simulates two single-frequency signals s₁And s₂The scaling results of (a). The frequencies of the two signals are 160Hz and 60Hz, respectively. The sampling rate was 100 Hz. The scale-varying factor is set to xi₁＝1.1，ξ ₂1 and xi₃0.9. After scaling, only s₁A spurious spectral peak of and s₂The true spectral peaks of (a) align. Similarly, only s₂A spurious spectral peak of and s₁The true spectral peaks of (a) align. Since the period spacing between grating lobes depends on the scaling factor, no overlap of other spurious spectral peaks will occur. Thus, the result of the PSPLVD in this case is

After the product operation, the grating lobe will not realize coherent accumulation like the real Doppler spectrum peak. When the echo amplitudes of the two maneuvering targets are greatly different, the two maneuvering targets can be usedConsider the use of CLEAN^[37]The strong and weak target components are separated because the weak target may be suppressed after the multiplication operation.

The variable substitution is realized by a variable-Scale Fourier Transform (SFT). Fuse variable substitutions into SPLVD, the process becomes

Wherein

ζ＝h·τ·ξ(f_r) (32)

Equation (31) defines a two-dimensional SFT, for τ and t_mThe variable scale factors of the dimension are xi (f) respectively_r) And ζ. Considering the scalability and spectral refinement of the Chirp-Z transform (CZT)^[38]The SPLVD process can be quickly implemented by FFT and IFFT.

For discrete signals x (N), N ═ 0,1, …, N_a-1, with a variable scale period DFT of

In formula (33), we have

Wherein

Representing the sampling interval of the digital angular frequency.

Here, we use the Bluestein equation:

by bringing formula (34) into formula (33)

Wherein the content of the first and second substances,representing a convolution operation.

When in useThe calculation procedure is the same as that shown in equations (33) to (35).

The calculation process of equation (35) is shown in fig. 6. Therefore, both the scale-variable period DFT and SPLVD can be efficiently calculated using FFT and IFFT.

The computational complexity of the different algorithms is analyzed as follows: four representative algorithms, MLRT, SAF-SFT, GRFT and RLVD, were used for comparison.

Suppose M_a、M_v、M_θ、N_rAnd N_aThe calculation complexity of obtaining the MLRT is O (M) by respectively representing the number of acceleration searches, the number of velocity searches, the number of rotation angle searches, the number of distance cells and the number of pulses_θN_rN_alog₂N_a) Magnitude.

For SAF-SFT, the calculated amounts of generalized KT, SAF and SFT are O (N), respectively_rN_alog₂N_a)、

And O (N)_rN_alog₂N_r)^[31]. Therefore, the calculation complexity of SAF-SFT is

GRFT realizes coherent accumulation by searching motion parameters of a target. The computational complexity of GRFT is therefore about O (N)_rM_vM_aN_a)。

The RLVD algorithm firstly searches the motion trail of the target and then realizes the coherent accumulation through the LVD. Thus, RLVD is calculated to be approximately

For PSPLVD at each range frequency, the complexity of SIAF and SPLVD is calculatedAre respectively asAnd

therefore, the calculation amount of the algorithm provided by the embodiment of the invention is about

Table 1 lists the computational complexity of the above algorithm. When q is 10, M_a＝M_v＝M_θ＝qN_aAnd N_r＝N_aUnder the assumption that fig. 7 visually depicts the calculated quantity curves of the different algorithms. Obviously, the GRFT and RLVD algorithms have higher computational complexity due to multi-dimensional parameter search. MLRT and SAF-SFT algorithms are less computationally intensive than the algorithms herein, but MLRT is not suitable for maneuvering target detection and SAF-SFT has poor detection performance at low signal-to-noise ratios.

TABLE 1 computational complexity of different algorithms

In order to verify the effectiveness of the technical scheme of the invention, further explanation is made below through simulation values and actual measurement experiment results:

the radar simulation parameters are shown in table 2.

TABLE 2 simulated Radar parameters

First, fig. 8 shows the coherent integration result of a single maneuvering target, where the target motion parameter is r 150km, v 200m/s, and a 10m/s². The signal-to-noise ratio after pulse compression is 3 dB. The period integer is chosen to be q-12 to ensure a speed range of v e-225,225) m/s. Fig. 8(a) shows the motion trace of the object after pulse pressure. Due to the high speed of the target, the LRM effect can be seen clearly. FIG. 8(b) shows f_rSPLVD results at 0. Obviously, the Doppler frequency is subjected to periodic prolongation, and q-1 grating lobes can be observed besides the real spectral peak. The true LVD spectral peaks indicate the velocity and acceleration of the target. After the product operation, the grating lobes are greatly suppressed while the true LVD spectral peaks are enhanced, as shown in fig. 8 (c). The result shows that the PSPLVD can accurately estimate the motion parameters of the target. Finally, FIG. 8(d) shows the coherent integration results.

Coherent integration performance of multiple maneuvering targets (Tr1 and Tr2), target motion parameters are given in table 3. Fig. 9 shows coherent accumulation and parameter estimation results.

TABLE 3 two maneuvering target motion parameters

Fig. 9(a) shows the pulse compression result. FIGS. 9(b) and 7(c) show the values at f_r1MHz and f_rSPLVD results at 500 kHz. After SPLVD, only the spectral peaks of the true Doppler frequency are aligned, and the grating lobes are staggered. FIG. 9(d) shows the results of PSPLVD. As with the expected results, two sharp spectral peaks can be observed in the CFCR domain. From the peak position we estimate the motion parameters of the target as:also, the figure illustrates that the cross terms of the LVD and product operations do not achieve energy accumulation like the self terms. Finally, using the estimated parameters, coherent accumulation was performed for Tr1 and Tr2, respectively, and the results are shown in fig. 9(e) and 9 (f).

The detection performance of the algorithm on the maneuvering target is researched through Monte Carlo simulation. Meanwhile, four representative algorithms (GRFT, RLVD, SAF-SFT, and MLRT) were used for comparison. The signal-to-noise ratio after pulse compression varies from-20 dB to 10 dB. For each signal-to-noise ratio, 500 monte carlo experiments were performed. False alarm rate is set to P_fa＝10^-6. The detection probability curve is shown in fig. 10. GRFT and RLVD can obtain the optimal detection performance through multi-dimensional parameter search. The algorithm is due to formula(9) The nonlinear autocorrelation function of (a) loses about 3dB of detection performance. SAF-SFT loses a significant amount of signal energy when auto-correlating the range frequency. The low computational complexity of the algorithm comes at the expense of probing performance. MLRT results in the worst detection performance because it ignores the acceleration of the target. By comprehensively considering the anti-noise performance and the calculation complexity, the algorithm is more suitable for the coherent detection of the maneuvering target with Doppler ambiguity.

The technical scheme of the invention is further verified by a commercial unmanned aerial vehicle 3 Xinjiang spirit, and data is collected in a school. Fig. 11(a) and 9(b) show an experimental scenario and the Frequency Modulated Continuous Wave (FMCW) radar system used. The radar parameters are listed in table 4. It is worth mentioning that in order to obtain the LRM effect and doppler ambiguity, the radar bandwidth can be artificially increased and the PRF of the radar can be decreased.

TABLE 4 FMCW Radar System parameters

Fig. 11(c) shows the pulse compression result. Within the coherent accumulation time, the drone moves more than 7 range cells, causing severe range migration phenomena. Fig. 11(d) shows the SPLVD result, where the period integer q is 12. Thus, 12 well-focused spectral peaks can be observed in the CFCR domain. Of these spectral peaks, only one LVD spectral peak indicates the true doppler center frequency and tone frequency of the target. Through the product operation, grating lobes, noise and clutter are greatly suppressed and the true spectral peak is enhanced, as shown in fig. 11 (e). The motion parameters of the unmanned aerial vehicle can be estimated from the spectral peak positions

Fig. 11(f) shows the coherent accumulation result obtained by the algorithm of the present invention, and it can be seen that the target energy achieves good focusing in the range-doppler domain. At the same time, FIG. 11(g) and 11(h) show the coherent accumulation results of MTD and MLRT, respectively, for comparison. It is clear, however, that the energy of the target is spread over a number of range or velocity bins, causing difficulties in target detection. The actual measurement experiment further verifies the effectiveness of the technical scheme of the invention in the detection of the motor target.

Unless specifically stated otherwise, the relative steps, numerical expressions, and values of the components and steps set forth in these embodiments do not limit the scope of the present invention.

Based on the foregoing method, an embodiment of the present invention further provides a server, including: one or more processors; a storage device for storing one or more programs which, when executed by the one or more processors, cause the one or more processors to implement the method described above.

Based on the above method, the embodiment of the present invention further provides a computer readable medium, on which a computer program is stored, wherein the program, when executed by a processor, implements the above method.

The device provided by the embodiment of the present invention has the same implementation principle and technical effect as the method embodiments, and for the sake of brief description, reference may be made to the corresponding contents in the method embodiments without reference to the device embodiments. It is clear to those skilled in the art that, for convenience and brevity of description, the specific working processes of the system and the apparatus described above may refer to the corresponding processes in the foregoing method embodiments, and are not described herein again. In all examples shown and described herein, any particular value should be construed as merely exemplary, and not as a limitation, and thus other examples of example embodiments may have different values.

The functions, if implemented in the form of software functional units and sold or used as a stand-alone product, may be stored in a non-volatile computer-readable storage medium executable by a processor. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device) to execute all or part of the steps of the method according to the embodiments of the present invention. And the aforementioned storage medium includes: a U-disk, a removable hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk or an optical disk, and other various media capable of storing program codes.

Finally, it should be noted that: the above-mentioned embodiments are only specific embodiments of the present invention, which are used for illustrating the technical solutions of the present invention and not for limiting the same, and the protection scope of the present invention is not limited thereto, although the present invention is described in detail with reference to the foregoing embodiments, those skilled in the art should understand that: any person skilled in the art can modify or easily conceive the technical solutions described in the foregoing embodiments or equivalent substitutes for some technical features within the technical scope of the present disclosure; such modifications, changes or substitutions do not depart from the spirit and scope of the embodiments of the present invention, and they should be construed as being included therein. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.