CN110398730B - Coherent detection method of maneuvering target based on coordinate rotation and non-uniform Fourier transform - Google Patents

Abstract

The invention belongs to the technical field of radar target signal estimation, and particularly relates to a maneuvering target coherent detection method based on coordinate rotation and non-uniform Fourier transform, which comprises the following steps: aiming at radar signals, establishing a maneuvering target signal model; and performing range migration processing on the maneuvering target signal model, and estimating target motion parameters through coordinate rotation and non-uniform Fourier transform. The method can relieve the contradiction between the calculation complexity and the detection performance, eliminates QRM by utilizing second-order Keystone transform (SoKT), and constructs a phase compensation function by combining the relation between the rotation angle and the Doppler frequency; and simulation experiments verify that compared with the existing representative algorithm, the method can obtain nearly ideal detection performance with lower operation complexity and has stronger application prospect.

Description

Coherent detection method of maneuvering target based on coordinate rotation and non-uniform Fourier transform

technical field

The invention belongs to the technical field of radar target signal estimation, in particular to a coherent detection method for maneuvering targets based on coordinate rotation and non-uniform Fourier transform.

Background technique

In recent years, with the rapid development of stealth aircraft and unmanned aerial vehicles (UAVs), higher and higher requirements have been put forward for radar maneuverable weak target detection. To detect such low radar cross section (RCS) targets, long-term coherent accumulation is an indispensable means. Unfortunately, due to the high mobility of the above-mentioned targets, linear range migration (LRM), quadratic range migration (QRM), and Doppler frequency migration) (DFM) are inevitable for the target during the accumulation time. These unfavorable factors will seriously affect the detection performance of traditional accumulation algorithms such as MTD. Therefore, how to robustly detect maneuvering weak targets has become a hot topic in the field of radar signal processing.

The LRM will cause the target envelope to migrate across distance cells. To eliminate LRM, many successful algorithms have been proposed, such as Scale-Inverse Fourier Transform (SCIFT), Keystone Transform (KT), Modified Coordinate Rotation Transform (MLRT), and Radon-Fourier Transform. These algorithms can achieve satisfactory detection capability with moderate computational complexity. However, they will suffer severe cumulative performance loss due to ignoring the QRM and DFM effects caused by target acceleration. In order to solve this problem, researchers have spent a lot of energy and developed many methods, which can be roughly divided into two categories: (a) search-like algorithms, representative methods include generalized Radon-Fourier transform (GRFT), KT and Lv Distribution Algorithm (KT-LVD), KT and Linear Regular Transform (KT-LCT), Modified Axis Rotation Transform and Lv Distribution (MART-LVT), Modified Axis Rotation and Fractional Fourier Transform (IAR-FRFT) , and the Radon-Lu distribution (RLVD). These algorithms demonstrate superior detection performance at low signal-to-noise ratio (SNR) through parametric search. However, the huge computational complexity makes it unacceptable in practical applications. (b) Non-search-type algorithms, typical methods include symmetric autocorrelation function-scale-variable Fourier transform (SAF-SFT), three-dimensional scale-variant transform (TDST), frequency second-order phase difference (FD-SoPD), and phase Adjacent Cross-Correlation Function (ACCF). These algorithms reduce the coupling order through correlation operations, which greatly reduces the computational burden. However, the correlation is a non-linear operation, which causes cross-term interference under multiple targets and reduces the anti-noise performance.

SUMMARY OF THE INVENTION

To this end, the present invention provides a coherent detection method and device for maneuvering targets based on coordinate rotation and non-uniform Fourier transform, which alleviates the contradiction between computational complexity and detection performance, and achieves near-ideal results with lower computational complexity. The detection performance has strong application prospects.

According to the design scheme provided by the present invention, a coherent detection method for maneuvering targets based on coordinate rotation and non-uniform Fourier transform includes the following contents:

A) For the radar signal, establish a maneuvering target signal model;

B) The distance migration process is performed on the maneuvering target signal model, and the target motion parameters are jointly estimated by coordinate rotation and non-uniform Fourier transform.

The above-mentioned, A) establish a maneuvering target signal model, including the following content: Assuming that the radar transmits a chirp signal, the maneuvering target moves with a constant acceleration, and obtains the target distance from the radar according to the slow time variable, the target initial slant range, the radial velocity and the acceleration. Instantaneous slant range; according to the instantaneous slant range, target radial velocity, signal amplitude and bandwidth, the radar received signal is obtained; the Fourier transform of the radar received signal along the fast time axis is performed to obtain the maneuvering target signal model.

As mentioned above, B) the middle-range migration processing includes the elimination processing of the three effects of linear range migration, quadratic range migration and Doppler frequency migration.

Preferably, in B), the second-order Keystone transform is used to eliminate the second-order distance migration caused by the acceleration of the maneuvering target.

Preferably, the second-order Keystone transform eliminates the quadratic distance migration process, including the following content: scaling the slow time of each distance frequency unit, and bringing the scaled slow time variable into the maneuvering target signal model; The signal model of the maneuvering target is simplified and represented by Taylor expansion, and inverse Fourier transform is performed along the range frequency to complete the secondary coupling between the Doppler frequency and the slow time variable, and correct the secondary range migration caused by the maneuvering target. effect.

Preferably, in B), jointly estimating the target motion parameters includes the following contents: the maneuvering target signal model is represented as a discrete form in the coordinate system; by introducing coordinate rotation transformation, the residual linear distance migration effect is eliminated, and the signal energy is extracted along the azimuth direction , and use the rotation angle to estimate the equivalent velocity, unambiguous velocity and true velocity of the maneuvering target; build a phase compensation function based on the estimated unambiguous velocity, and multiply the extracted signal energy to compensate the linear phase term; The Lie transform is used for parameter estimation.

Preferably, in the parameter estimation using the non-uniform Fourier transform, the non-uniform Fourier transform is first performed on the result of the multiplication operation, and according to the non-uniform Fourier transform, it is determined that the energy accumulation of the maneuvering target is a single peak. This single peak situation estimates the maneuvering target acceleration.

Preferably, a phase compensation function is constructed according to the estimated target speed and acceleration; slow-time Fourier transform and inverse range-frequency Fourier transform are performed on the maneuvering target signal model to complete coherent accumulation; The distance-Doppler domain of a single spectral peak; complete target detection through a single spectral peak-to-peak value.

Preferably, for a single spectral peak-to-peak value, target detection is completed by using constant false alarm. If the peak value exceeds the adaptive threshold, it is determined that there is a moving target, and the parameters of the moving target are obtained; if the peak value is less than the threshold, it is determined that no moving target is detected.

Further, the present invention also provides a coherent detection device for maneuvering targets based on coordinate rotation and non-uniform Fourier transform, comprising: a model building module and a joint estimation module, wherein,

A model building module is used to build a maneuvering target signal model for radar signals;

The joint estimation module is used to process the distance migration of the maneuvering target signal model, and jointly estimate the target motion parameters through coordinate rotation and non-uniform Fourier transform.

Beneficial effects of the present invention:

The present invention establishes a maneuvering target signal model for radar signals; performs distance migration processing on the maneuvering target signal model, and jointly estimates target motion parameters through coordinate rotation and non-uniform Fourier transform, thereby effectively alleviating the difference between computational complexity and detection performance And use the second-order Keystone transform (SoKT) to eliminate the QRM, and combine the relationship between the rotation angle and the Doppler frequency to construct a phase compensation function, which can be compared with the existing representative algorithms. to obtain near-ideal detection performance. Finally, the effectiveness of the technical solution of the present invention is further verified through the simulation and measured radar data processing results.

Description of drawings:

1 is a flowchart of a coherent detection method in an embodiment;

2 is a schematic diagram of a coherent detection device in an embodiment;

Fig. 3 is the LRT-NuFFT algorithm flow chart in the embodiment;

4 is a schematic diagram of a comparison of algorithm computational complexity in an embodiment;

5 is a schematic diagram of a coherent accumulation simulation result of a single maneuvering target in the embodiment;

6 is a schematic diagram of the multi-target coherent accumulation simulation result of the LRT-NuFFT algorithm in the embodiment;

Fig. 7 is the variation curve of target detection probability with SNR in the embodiment;

FIG. 8 is a schematic diagram of the UAV measured data processing result in the embodiment.

Detailed ways:

In order to make the objectives, technical solutions and advantages of the present invention clearer and more comprehensible, the present invention will be described in further detail below with reference to the accompanying drawings and technical solutions.

Long-term coherent accumulation can significantly improve the radar's ability to detect and estimate motion parameters of maneuvering targets. However, linear range migration (LRM), quadratic range migration (QRM) and Doppler frequency migration (DFM) during coherent processing severely degrade radar detection and estimation performance. In view of this, in the embodiment of the present invention, referring to FIG. 1 , a method for coherent detection of a maneuvering target based on coordinate rotation and non-uniform Fourier transform is provided, including the following contents:

S101) for the radar signal, establish a maneuvering target signal model;

S102) Perform distance migration processing on the maneuvering target signal model, and jointly estimate target motion parameters through coordinate rotation and non-uniform Fourier transform.

Further, in the embodiment of the present invention, it is assumed that the radar transmits a linear frequency modulation signal, the maneuvering target moves at a constant acceleration, and the instantaneous slope distance of the target from the radar is obtained according to the slow time variable, the initial slope distance of the target, the radial velocity and the acceleration; The distance, target radial velocity, signal amplitude and bandwidth are obtained to obtain the radar received signal; Fourier transform is performed on the radar received signal along the fast time axis to obtain the maneuvering target signal model.

The radar transmits a linear frequency modulation (LFM) signal,

in,

和γ分别表示快时间变量和调频斜率。T _p and f _c are pulse duration and signal carrier frequency,

and γ denote fast time variable and FM slope, respectively.

The maneuvering target moves with constant acceleration, and its instantaneous slope distance R(t _m ) from the radar satisfies

Among them, R ₀ , v and a are the initial slope distance, radial velocity and acceleration of the target, respectively. t _m =mT (m=1,2,...,N _a ) represents the slow time variable, T is the pulse repetition time, and _Na is the number of accumulated pulses.

Ignoring the effect of noise, the received signal after the pulse pressure can be expressed as:

Among them, A _c and B are the signal amplitude and bandwidth, respectively.

Substitute equation (2) into equation (3) to get

Among them, λ=c/f _c is the signal wavelength.

Doppler ambiguity often occurs due to the low pulse repetition frequency of the radar and the high velocity of the target. Therefore, the radial velocity of the target can be expressed as

v=N _b v _b +v ₀ (5)

Among them, v _b =λf _p /2 and f _p represent the radar blind speed and pulse repetition frequency, respectively. N _b is the target Doppler ambiguity number, v ₀ is the blur-free velocity and satisfies -v _b /2≦v ₀ <v _b / ² .

Inserting equation (5) into equation (4), we can get:

In the above formula, the equation exp(-j2πf _c N _b v _b t _m /c)=1 is used.

From equation (6), it can be observed that the signal envelope changes nonlinearly with slow time. When the offset exceeds one range resolution unit Δr=c/2B within the accumulation time, the LRM effect follows. The QRM effect can also be observed if the target is highly maneuverable (ie, has a high acceleration). Taking the Fourier transform (FT) of Equation (6) along the fast time axis, we can get

的多普勒频率。式(7)表明，f_r和t_m之间的耦合关系是造成LRM和QRM的根本原因。目标带来的多普勒频率被定义为：Among them, _fr is relative to

the Doppler frequency. Equation (7) shows that the coupling relationship between _fr and _tm is the root cause of LRM and QRM. The Doppler frequency brought by the target is defined as:

Due to the acceleration of the target, a linear Doppler shift occurs by an amount of 2at _m /λ. If this value exceeds the Doppler resolution unit 1/N _a T, the DFM effect occurs and causes the Doppler domain energy to diverge. Therefore, in order to detect maneuvering targets at low signal-to-noise ratios, the effects of LRM, QRM and DFM must be effectively eliminated. Therefore, in the embodiment of the present invention, the range migration process includes three effects of linear range migration, quadratic range migration, and Doppler frequency migration.

Further, in the embodiment of the present invention, the second-order Keystone transform is used to eliminate the second-order distance migration caused by the acceleration of the maneuvering target. Preferably, the second-order Keystone transform eliminates the quadratic distance migration process, including the following content: scaling the slow time of each distance frequency unit, and bringing the scaled slow time variable into the maneuvering target signal model; The signal model of the maneuvering target is simplified and represented by Taylor expansion, and inverse Fourier transform is performed along the range frequency to complete the secondary coupling between the Doppler frequency and the slow time variable, and correct the secondary range migration caused by the maneuvering target. effect.

The second-order Keystone transform (SoKT) is used to eliminate the second-order coupling caused by the target acceleration. SoKT scales the slow time for each distance frequency unit and can be expressed as

where _ta is the scaled slow time variable.

Substitute equation (9) into equation (7) to get:

For narrowband radar systems, the first-order Taylor expansion is usually satisfied:

Therefore, Equation (10) can be simplified as

where V _e =N _b v _b +v ₀ /2 is defined as the equivalent velocity of the target.

Taking the inverse Fourier transform ( _IFT ) along the range frequency fr of equation (12), we can get

表示对应于

的距离轴。in

means corresponding to

distance axis.

It can be observed from equations (12) and (13) that _SoKT eliminates the quadratic coupling between fr and _tm . Therefore, the QRM effect caused by the target is effectively corrected.

Further, in this embodiment of the present invention, jointly estimating target motion parameters includes the following contents: expressing the maneuvering target signal model as a discrete form in a coordinate system; by introducing coordinate rotation transformation, the residual linear distance migration effect is eliminated, and extraction along the azimuth direction is performed. signal energy, and use the rotation angle to estimate the equivalent speed, unambiguous speed and true speed of the maneuvering target; build a phase compensation function based on the estimated unambiguous speed, and multiply the extracted signal energy to compensate the linear phase term; Uniform Fourier Transform for parameter estimation. Preferably, in the parameter estimation using the non-uniform Fourier transform, the non-uniform Fourier transform is first performed on the result of the multiplication operation, and according to the non-uniform Fourier transform, it is determined that the energy accumulation of the maneuvering target is a single peak. This single peak situation estimates the maneuvering target acceleration.

The residual LRM and QFM in Eq. (13) bring enormous difficulties to the coherent accumulation. In the embodiment of the present invention, it is proposed to comprehensively utilize LRT and NuFFT to eliminate LRM and QFM. Note that ta ₌ mT, _fs =KB, where _fs is the signal sampling rate and K is the oversampling rate. Therefore, there are r=ρn, R ₀ =ρn _R0 , where ρ=c/2f _s distance sampling unit, n and n _R0 are the distance unit identification bits of r and R ₀ respectively. Equation (13) can be expressed as a discrete form in the (n,m) coordinate system, namely

To compensate for the LRM effect caused by the equivalent velocity, LRT is introduced, which is defined as a coordinate rotation operation as shown below,

为旋转角度。Among them, (m',n') is the coordinate after rotation,

is the rotation angle.

Substitute equation (15) into equation (14) to get:

或者等效地

式(16)中的LRM将被校正，即，when

or equivalently

The LRM in equation (16) will be corrected, i.e.,

As shown in equation (17), the target energy is concentrated in the same distance unit. The signal energy is then extracted in the azimuth direction. For a particular distance unit, the extracted signal can be expressed as:

Obviously, s _azi (m') is a chirp signal. LVT is used to complete coherent accumulation and motion parameter estimation. Although it exhibits satisfactory accumulation performance and anti-noise performance, the huge computational load is daunting.

In the embodiment of the present invention, it can be noticed from equations (17) and (18) that the target's equivalent velocity _Ve , unambiguous velocity v ₀ and true velocity v can be estimated simultaneously by using the rotation angle, that is,

According to equation (12), the unambiguous velocity can be solved by

为目标的多普勒模糊数。所以目标的真实速度估计为Among them, ROUND( ) is the rounding function,

is the Doppler fuzzy number of the target. So the true velocity of the target is estimated as

构建新的相位补偿函数，using the estimated

Build a new phase compensation function,

The linear phase term can be compensated by multiplying equation (22) by equation (18). Then, energy accumulation and parameter estimation can be done using efficient NuFFT:

为对应于(m′T)²的频率变量。where p( ) represents the impulse response function of NuFFT,

is the frequency variable corresponding to (m'T) ² .

It can be seen from equation (23) that the target energy is accumulated as a single peak value, and the acceleration of the target can be estimated from its position as:

Further, in the embodiment of the present invention, a phase compensation function is constructed according to the estimated target speed and acceleration; the slow-time Fourier transform and the inverse range-frequency Fourier transform are performed on the maneuvering target signal model to complete the coherent accumulation; Range-Doppler domain single spectral peak after accumulation of signals received by maneuvering targets; target detection is accomplished through a single spectral peak-to-peak value. Preferably, for a single spectral peak-to-peak value, target detection is completed by using constant false alarm. If the peak value exceeds the adaptive threshold, it is determined that there is a moving target, and the parameters of the moving target are obtained; if the peak value is less than the threshold, it is determined that no moving target is detected.

Based on the estimated target velocity and acceleration, a phase compensation function is constructed to eliminate the effects of LRM, QRM, and DFM:

Finally, perform slow time FT and distance frequency IFT on equation (7) to complete the coherent accumulation:

where A _CI is the complex amplitude and f _d is the Doppler frequency corresponding to the slow time t _m .

In Equation (26), the received signal of the maneuvering target is accumulated as a single spectral peak in the range-Doppler domain, whose peak is |S _CI (2R ₀ /c,-2v ₀ /λ)|. Then, the constant false alarm (CFAR) technique can be used for object detection:

和

否则，如果|S_CI(2R₀/c,-2v₀/λ)|小于门限η，则没有检测到运动目标。If the peak value exceeds the adaptive threshold η, it means that there is a moving target, and the motion parameter is

and

Otherwise, if |S _CI (2R ₀ /c,-2v ₀ /λ)| is less than the threshold η, no moving object is detected.

Suppose that Q targets are observed during the coherent accumulation time. Similar to equation (14), the signal can be expressed as:

Perform LRT on equation (28), we can get:

时，第i个目标的LRM被校正，然而其余q-1个目标的LRM仍然存在，即when

When , the LRM of the ith target is corrected, but the LRMs of the remaining q-1 targets still exist, namely

Then, extract the bearing signal along the distance unit n _R0,i to get:

in,

Similar to equations (19)-(22), the phase compensation function is constructed according to the rotation angle of rotation

Multiplying equations (31) and (33) and performing NuFFT to focus the target energy and estimate the acceleration, we get:

Note that only the ith target energy is aggregated into a single peak, while the other target energies are divergent, mainly due to the following two reasons: (a) The envelopes of the other q-1 targets are distributed between different distance cells (b) The linear phase term exp(-j4πv _0,q m'T/λ) in equation (32) cannot be canceled by the phase compensation function H ₁ (m'), so NuFFT cannot gather its energy.

Finally, the coherent accumulation and parameter estimation of the ith target can be completed, but the remaining q-1 targets cannot be focused using the parameters of the ith target.

LRT-NuFFT realizes LRM correction by rotation angle search. However, the LRT process requires a large number of interpolation operations, which obviously inevitably causes numerical errors. In addition, the rotation angle is not a natural representation of the target motion parameters. Because, in order to solve this problem, an implementation form of LRT-NuFFT without interpolation, that is, velocity search-NuFFT (VS-NuFFT) is also provided in the embodiments of the present invention.

Considering the coordinate rotation transformation in equation (16), it can be rewritten as:

为搜索的旋转角度。in,

is the rotation angle of the search.

FT of Eq. (35) along the fast time can be obtained:

It can be seen from equation (36) that the LRT operation can be realized by phase compensation in the range frequency domain, where the compensation function is

When V _s =V _e , the coupling relationship between _fr and m' is eliminated. Performing IFT on Eq. (36) along the distance frequency, we can get:

It is worth noting that, according to the Doppler frequency resolution, the velocity search interval should be less than Δv=λ/2N _a T.

Further, based on the above method, an embodiment of the present invention also provides a coherent detection device for maneuvering targets based on coordinate rotation and non-uniform Fourier transform, as shown in FIG. 2 , including: a model building module 101 and a joint estimation Module 102, wherein,

The model establishment module 101 is used for establishing a maneuvering target signal model according to the radar signal;

The joint estimation module 102 is used for performing distance migration processing on the maneuvering target signal model, and jointly estimating target motion parameters through coordinate rotation and non-uniform Fourier transform.

In order to further verify the validity of the present invention, the technical solution of the present invention is explained below in conjunction with the specific implementation algorithm and simulation experiment:

Referring to Figure 3, the specific steps of the LRT-NuFFT algorithm can be designed as follows:

Step 1: Pulse compression of the radar echo to get

Step 2: Distance FT. SoKT eliminates QRM. Get s _SoKT (n,m) from the distance IFT;

搜索间隔

应小于arctan(λ/2N_aρ)；Step 3: Determine the rotation angle search range according to the detected speed range

search interval

Should be less than arctan(λ/2N _a ρ);

Step 4: Under a certain rotation angle, perform LRT on formula (17), and then obtain the rotated signal s _rot (n′,m′);

Step 5: Construct the phase compensation function H ₁ (m′) according to the rotation angle, as shown in equations (19) to (22). Extract the slow time signal to get s _azi (m');

Step 6: perform NuFFT on s _azi (m′)·H ₁ (m′) to achieve signal energy accumulation and estimate acceleration, as shown in equation (23);

Step 7: The output of NuFFT reaches its maximum value when the initial distance and the search angle match the true value of the target. Estimate the target speed and acceleration according to equations (21) to (24);

Step 8: Construct another phase compensation function H ₂ (f _r , t _m ) using the estimated motion parameters to realize coherent accumulation, as shown in equations (25) and (26).

和无模糊速度v₀之间的关系，创新性地构造了相位补偿然后。因此，随后的能量积累和加速度估计可以通过NuFFT快速实现，这极大地缓解了计算LVT算法的计算负担。相比于MART-LVT、KT-LVD、TDST、SAF-SFT和ACCF算法，本发明实施例中所提LRT-NuFFT算法没有涉及非线性操作，因此，该算法不会出现交叉项，并且满足线性性质；虽然LVD、TDST、SAF-SFT和ACCF具有令人满意的交叉项抑制能力，但弱目标仍然容易淹没在强目标引起的交叉项中。旋转角度搜索等效于速度搜索，所以插值过程可以利用FT、相位补偿和IFT实现，这就避免引入数值误差；另外，速度搜索比角度搜索更为直观，其结果也是目标运动参数的自然表达；在搜索间隔方面，角度的均匀搜索对应于速度的非均匀采样，在小角度下二者近似相等，但在大角度下二者呈现出明显差异。Compared with the existing MART-LVT and LRT-NuFFT algorithms, the improvements and advantages are: (1) In MART-LVT, the QRM effect caused by the target acceleration is ignored, which will cause accumulation in some specific scenarios performance loss. In LRT-NuFFT, SoKT is used to eliminate the QRM first, which makes the algorithm more suitable for high maneuvering target detection. (2) Unlike MART-LVT, LRT-NuFFT utilizes the rotation angle

and the relationship between the unambiguous velocity v ₀ , the phase compensation is innovatively constructed and then. Therefore, the subsequent energy accumulation and acceleration estimation can be quickly realized by NuFFT, which greatly relieves the computational burden of calculating the LVT algorithm. Compared with the MART-LVT, KT-LVD, TDST, SAF-SFT, and ACCF algorithms, the LRT-NuFFT algorithm proposed in the embodiment of the present invention does not involve nonlinear operations. Therefore, the algorithm does not have cross terms and satisfies linearity. Properties; although LVD, TDST, SAF-SFT and ACCF have satisfactory cross-term suppression, weak targets are still easily submerged in cross-terms induced by strong targets. The rotation angle search is equivalent to the speed search, so the interpolation process can be realized by FT, phase compensation and IFT, which avoids the introduction of numerical errors; in addition, the speed search is more intuitive than the angle search, and the result is also a natural expression of the target motion parameters; In terms of search interval, the uniform search of the angle corresponds to the non-uniform sampling of the velocity, and the two are approximately equal at small angles, but they show significant differences at large angles.

The calculation amount of the LRT-NuFFT algorithm is analyzed below and compared with the representative MART-LVT, KT-LVD, TDST, SAF-SFT and MLRT algorithms:

N_F、N_r和N_a分别表示角度搜索数、折叠因子搜索数、距离单元数和脉冲数。Assumption

_NF , N _r and _Na represent the number of angle searches, the number of folding factor searches, the number of distance cells and the number of pulses, respectively.

和LVT操作

因此，总计算量在

量级。The main steps of the MART-LVT algorithm include the MART operation

and LVT operation

Therefore, the total computation is

magnitude.

因此，总计算量约在

量级。For the KT-LVD algorithm, the main steps include folding factor search (O(N _F N _r )) and LVD operations

Therefore, the total computation is about

magnitude.

和

来计算两步变尺度傅里叶变换(SFT)。因此，总计算量约在

量级。For the TDST algorithm, it is required

and

to compute the two-step scaled Fourier transform (SFT). Therefore, the total computation is about

magnitude.

因此总计算量在O(3N_a(N_a+N_r)log₂N_a)量级。The main steps of the SAF-SFT algorithm include two-step SFT operations, whose computational complexity is O(3N _a N _r log ₂ N _a ) and

Therefore, the total computational effort is on the order of O(3N _a (N _a +N _r )log _{2 Na} ).

量级。It can be easily concluded that the computational cost of MLRT is

magnitude.

Different from the MART-LVT algorithm, the algorithm proposed in the embodiment of the present invention uses phase compensation and NuFFT to reduce the computational complexity. Therefore, the total computation amount is also about

N_KT＝10，图4直观地给出了算法计算量曲线。显然，LRT-NuFFT算法比MART-LVT、KT-LVD和TDST有更低的计算量。The calculation amount of the above algorithm is given in Table 1. Assumption

N _KT =10, and Fig. 4 intuitively shows the calculation curve of the algorithm. Obviously, the LRT-NuFFT algorithm has lower computational complexity than MART-LVT, KT-LVD and TDST.

Table 1 Computational complexity of different algorithms

The algorithm of the present invention is analyzed below in conjunction with the radar simulation data, and the simulated radar parameters are shown in Table 2:

Table 2 Simulation radar parameters

First, a single objective is used to evaluate the coherent accumulation ability of the proposed algorithm. The target motion parameters are: R ₀ =150km, v=150m/s, a=8m/s ² . Figure 5(a) shows the pulse compression results, where the signal-to-noise ratio is -10dB. Obviously, the target trajectory is overwhelmed by strong noise and cannot be observed. In addition, Fig. 5(b) presents the accumulation results of MLRT. Since QRM and DFM are not considered, MLRT cannot detect maneuvering targets. Figure 5(c) and Figure 5(d) show the accumulated results of the SAF-SFT and TDST algorithms, respectively. Because the nonlinear transformation loses some signal energy, the output of both algorithms is still drowned in noise. In contrast, MART-LVT and LRT-NuFFT are able to accumulate the target as a single peak at the corresponding position in the range-Doppler domain, as shown in Fig. 5(e) and Fig. 5(f). This simulation experiment shows the coherent accumulation ability of the proposed algorithm in a low signal-to-noise ratio environment.

利用该参数可以分别校正两目标的LRM，如图6(c)和图6(d)所示。通过NuFFT，Tr1和Tr2的加速度能够在相应距离单元中估计出来，得到

如图6(e)和图6(f)所示。最后，图6(g)和图6(h)分别给出了两目标的相参积累结果。该仿真实验验证了所提算法对多目标的积累能力。Second, the accumulation performance under multi-objective is analyzed. The motion parameter settings of the two maneuvering targets (Tr1 and Tr2) are given in Table 3. Figure 6(a) shows the pulse compression results. Figure 6(b) shows the velocity search results, where two distinct spectral peaks give the equivalent velocity of Tr1 and Tr2. From this, it is estimated that the true speeds of Tr1 and Tr2 are:

Using this parameter, the LRMs of the two targets can be corrected respectively, as shown in Fig. 6(c) and Fig. 6(d). Through NuFFT, the accelerations of Tr1 and Tr2 can be estimated in the corresponding distance units, obtaining

As shown in Figure 6(e) and Figure 6(f). Finally, Figure 6(g) and Figure 6(h) show the coherent accumulation results of the two targets, respectively. The simulation experiment verifies the accumulation ability of the proposed algorithm for multiple targets.

Table 3 Simulation parameters of two maneuvering targets

It is worth noting that many spurious peaks can be observed in Fig. 6(b), and these spurious peaks are spaced at a half-blind speed. Therefore, these spurious peaks are called half-blind velocity side lobes (HBSSLs). In practical situations, weak targets may be submerged in HBSSLs of strong targets, which can be handled by the CLEAN algorithm.

The target detection performance of the proposed algorithm is evaluated by Monte Carlo experiments, where the signal-to-noise ratio varies from -25dB to 5dB after pulse compression. At each signal-to-noise ratio, 500 independent Monte Carlo experiments were performed. The false alarm rate is set to P _fa =10 ^-6 . Five representative algorithms (MART-LVT, KT-LVD, TDST, SAF-SFT, and MLRT) were used for comparison. The target detection probability curve is shown in Figure 7. Obviously, the LRT-NuFFT algorithm can obtain nearly ideal detection performance. This is because LRT-NuFFT effectively removes the influence of LRM, QRM and DFM effects. MART-LVT and KT-LVD suffer some performance penalty due to ignoring QRM due to target acceleration. The detection thresholds of the TDST and SAF-SFT algorithms are 3dB and 6dB higher than the ideal case, respectively, which indicates that the bilinear transform will lose a lot of signal energy and deteriorate the anti-noise performance. MLRT does not take into account the QRM and DFM effects, so the detection performance is the worst.

The algorithm in the embodiment of the present invention is further described below with reference to the DJI Phantom 3 commercial drone, and the data is collected in a certain campus. Figures 8(a) and 8(b) show the experimental scenario and the frequency modulated continuous wave (FMCW) radar system used. Radar parameters are listed in Table 4. In order to obtain Doppler blur of the target, the PRF of the radar is artificially lowered.

Table 4 FMCW radar system parameters

真实速度为

经过相位补偿，LRM被有效校正，通过NuFFT获得了UAV的加速度，即

分别如图8(e)和图8(f)所示。图8(g)给出了LRT-NuFFT的积累结果，可以看出在距离—多普勒域中形成了聚焦良好的谱峰。同时，在图8(h)和图8(i)中给出了MTD和MLRT的积累结果以供参考。但是可以看到，目标的能量分散在多个距离和多普勒单元中，给目标检测制造了困难；进一步验证了本发明实施例中，所提LRT-NuFFT算法能够以较低的计算量获得近乎理想的检测性能，通过UAV实验结果验证了本发明实施例中技术方案的有效性。Figure 8(c) shows the target motion trajectory after pulse compression. During the coherent accumulation time of 0.92s, the UAV moved more than 7 distance units, causing a severe distance migration phenomenon. Figure 8(d) presents the equivalent velocity estimation results. The speed search range is set to [-10,10]m/s, and the search interval is 0.01m/s. The equivalent velocity of the UAV can be derived from the peak position as

The true speed is

After phase compensation, the LRM is effectively corrected, and the acceleration of the UAV is obtained through NuFFT, namely

As shown in Fig. 8(e) and Fig. 8(f), respectively. Figure 8(g) shows the accumulation result of LRT-NuFFT, and it can be seen that well-focused spectral peaks are formed in the range-Doppler domain. Meanwhile, the accumulated results of MTD and MLRT are presented in Fig. 8(h) and Fig. 8(i) for reference. However, it can be seen that the energy of the target is dispersed in multiple range and Doppler units, which makes target detection difficult; it is further verified that in the embodiment of the present invention, the proposed LRT-NuFFT algorithm can be obtained with a low amount of calculation. The detection performance is almost ideal, and the effectiveness of the technical solutions in the embodiments of the present invention is verified by the UAV experimental results.

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

Based on the above method, an embodiment of the present invention further provides a server, including: one or more processors; and a storage device for storing one or more programs, when the one or more programs are stored by the one or more programs The execution of the one or more processors causes the one or more processors to implement the above-described method.

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

The implementation principle and technical effects of the device provided by the embodiment of the present invention are the same as those of the foregoing method embodiment. For brief description, for the parts not mentioned in the device embodiment, reference may be made to the corresponding content in the foregoing method embodiment.

Those skilled in the art can clearly understand that, for the convenience and brevity of description, for the specific working process of the system and device described above, reference may be made to the corresponding process in the foregoing method embodiments, which will not be repeated here.

In all examples shown and described herein, any specific value should be construed as illustrative only and not limiting, as other examples of example embodiments may have different values.

It should be noted that like numerals and letters refer to like items in the following figures, so once an item is defined in one figure, it does not require further definition and explanation in subsequent figures.

The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of code that contains one or more functions for implementing the specified logical function(s) executable instructions. It should also be noted that, in some alternative implementations, the functions noted in the blocks may occur out of the order noted in the figures. For example, two blocks in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It is also noted that each block of the block diagrams and/or flowchart illustrations, and combinations of blocks in the block diagrams and/or flowchart illustrations, can be implemented in dedicated hardware-based systems that perform the specified functions or actions , or can be implemented in a combination of dedicated hardware and computer instructions.

The functions, if implemented in the form of software functional units and sold or used as stand-alone products, may be stored in a processor-executable non-volatile computer-readable storage medium. Based on such understanding, the technical solution of the present invention can be embodied in the form of a software product in essence, or the part that contributes to the prior art or the part of the technical solution. The computer software product is stored in a storage medium, including Several instructions are used to cause a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes: U disk, mobile hard disk, Read-Only Memory (ROM, Read-Only Memory), Random Access Memory (RAM, Random Access Memory), magnetic disk or optical disk and other media that can store program codes .

Finally, it should be noted that the above-mentioned embodiments are only specific implementations of the present invention, and are used to illustrate the technical solutions of the present invention, but not to limit them. The protection scope of the present invention is not limited thereto, although referring to the foregoing The embodiment has been described in detail the present invention, and those of ordinary skill in the art should understand: any person skilled in the art who is familiar with the technical field of the present invention can still modify the technical solutions described in the foregoing embodiments within the technical scope disclosed by the present invention. Or can easily think of changes, or equivalently replace some of the technical features; and these modifications, changes or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should be covered in the present invention. within the scope of protection. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims (4)

1. A maneuvering target coherent detection method based on coordinate rotation and non-uniform Fourier transform is characterized in that,

A) aiming at radar signals, establishing a maneuvering target signal model;

B) carrying out range migration processing on the maneuvering target signal model, and jointly estimating target motion parameters through coordinate rotation and non-uniform Fourier transform;

A) the method for establishing the maneuvering target signal model comprises the following steps: assuming that the radar transmits a linear frequency modulation signal, the maneuvering target moves at constant acceleration, and the instantaneous slope distance of the target from the radar is obtained according to the slow time variable, the initial slope distance of the target, the radial speed and the acceleration; obtaining radar receiving signals according to the instantaneous slope distance, the target radial speed, the signal amplitude and the bandwidth;

fourier transformation is carried out on the radar receiving signals along a fast time axis to obtain a maneuvering target signal model, and the maneuvering target signal model is expressed as follows:

wherein f is_rIs relative to

Doppler frequency of f_cIs the carrier frequency of the signal and,

representing a fast time variable, t_mDenotes a slow time variable, A_fAnd B is the signal amplitude and bandwidth, v, respectively_b＝λf_pA/2 and f_pRespectively representing radar blind speed and pulse repetition frequency, N_bIs a target Doppler ambiguity number, v₀For no blurring speed, R₀And a is the initial slope and acceleration of the target, respectively, and λ ═ c/f_cIs the signal wavelength;

B) the intermediate range migration treatment comprises elimination treatment of linear range migration, secondary range migration and Doppler frequency migration;

B) in the method, second-order Keystone transformation is adopted to eliminate secondary range migration caused by maneuvering target acceleration; the second-order Keystone transformation eliminates the secondary range migration process, and comprises the following contents: scaling the slow time of each distance frequency unit, and bringing the scaled slow time variable into a maneuvering target signal model; simplifying and expressing a maneuvering target signal model obtained after scaling through Taylor expansion, performing Fourier inverse transformation along range frequency, completing secondary coupling between Doppler frequency and slow time variable, and correcting a secondary range migration effect caused by a maneuvering target;

B) in the method, the jointly estimated target motion parameters include the following: representing the maneuvering target signal model as a discrete form under a coordinate system; eliminating residual linear distance migration effect by introducing coordinate rotation transformation, extracting signal energy along the azimuth direction, and estimating the equivalent speed, the unambiguous speed and the real speed of the maneuvering target by using the rotation angle; constructing a phase compensation function according to the estimated non-fuzzy speed, and multiplying the phase compensation function by the extracted signal energy to compensate a linear phase term; carrying out parameter estimation by utilizing non-uniform Fourier transform;

in the parameter estimation by utilizing the non-uniform Fourier transform, firstly, the non-uniform Fourier transform is carried out on the multiplication result, the situation that the energy of the maneuvering target is accumulated into a single peak value is judged according to the non-uniform Fourier transform, and the acceleration of the maneuvering target is estimated from the single peak value situation, wherein the non-uniform Fourier transform is expressed as:

the maneuvering target acceleration estimate is expressed as:

p (-) represents the impulse response function of the non-uniform fourier transform,

to correspond to (m' T)²Is the rotated coordinate, n_R0Is R₀T is the pulse repetition time and K is the over-sampling rate.

2. The method for coherent detection of maneuvering targets based on coordinate rotation and non-uniform Fourier transform according to claim 1, characterized in that a phase compensation function is constructed according to the estimated target speed and acceleration; carrying out slow time Fourier transform and range frequency Fourier inverse transform on the maneuvering target signal model to complete coherent accumulation; obtaining a single spectral peak of a distance-Doppler domain after the mobile target receiving signal is accumulated; target detection is accomplished by a single spectral peak.

3. The method for detecting the coherent moving target based on the coordinate rotation and the non-uniform Fourier transform as claimed in claim 1 or 2, wherein the target detection is completed by using a constant false alarm for a single spectral peak value, and if the peak value exceeds a self-adaptive threshold, a moving target is determined to exist, and a moving target parameter is obtained; and if the peak value is smaller than the threshold, judging that the moving target is not detected.

4. A mobile object coherent detection device based on coordinate rotation and non-uniform Fourier transform, which is realized based on the method of claim 1 and comprises the following steps: a model building module and a joint estimation module, wherein,

the model establishing module is used for establishing a maneuvering target signal model aiming at the radar signal;

and the joint estimation module is used for carrying out range migration processing on the maneuvering target signal model and estimating target motion parameters through coordinate rotation and non-uniform Fourier transform.

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