CN111965614B - Maneuvering weak target detection method based on dynamic programming and minimum image entropy - Google Patents

Abstract

The invention provides a mobile weak target detection method based on dynamic programming and minimum image entropy. First, the dynamic programming method is used to quickly search for the most likely weak target, that is, the trajectory with the largest echo energy; then the target signal is extracted and FFT is performed to obtain its Spectrum, using image entropy as the cost function, uses Newton's method to iteratively search for high-order components of the target to minimize the image entropy of the spectrum, and finally uses CA-CFAR to determine the threshold, and compare the compensated spectrum maximum with the detection threshold to judge Whether the target exists or not provides an effective means for the detection of maneuvering weak targets in the radar; it can be seen that the present invention uses the DP technology to find the possible trajectory of the target, runs faster, and can correct the distance migration caused by the target maneuvering , realizes the coherent accumulation of signals, runs fast and can compensate for the motion components of any order, and has higher detection efficiency and accuracy in the detection of maneuvering weak targets in radar.

Description

A mobile weak target detection method based on dynamic programming and minimum image entropy

technical field

The invention belongs to the technical field of radar detection, and in particular relates to a mobile weak target detection method based on dynamic programming (Dynamic Programming, DP) and minimum image entropy (Minimum Image Entropy, MIE).

Background technique

Long-term coherent accumulation methods are often used to detect weak targets. However, during the accumulation process, the target may move, resulting in the occurrence of range migration and Doppler frequency migration, which makes it difficult to effectively accumulate and detect the energy of weak targets.

In the traditional coherent accumulation method, Keystone transform is a commonly used method to solve the distance migration of the target. The basic principle of Keystone transform is to decouple the Doppler frequency and time delay of the target echo signal through slow time scale transformation, so as to eliminate the influence of distance migration. However, the Keystone transform is only suitable for eliminating distance migration in the case of uniform motion. When the target is maneuvering, the Keystone transform can only eliminate part of the distance migration caused by the initial velocity, but cannot eliminate the distance migration caused by the high-order motion components of the target. In addition, Keystone transform also has defects such as a large amount of calculation and the need to estimate the target velocity in advance.

For the Doppler frequency migration caused by maneuvering, a coherent accumulation method using Fractional Fourier transform (FrFT) and Generalized Radon-Fourier Transform (GRFT) for higher-order phase compensation is proposed. FrFT is an extension of the traditional Fourier transform, which can compensate for higher-order phases by transforming the signal into the fractional frequency domain to eliminate the effects of the quadratic phase. However, FrFT can only compensate for phase changes caused by acceleration, and cannot do anything for jerk and higher-order motion components. GRFT is similar to the exhaustive method. It realizes coherent accumulation by jointly searching for motion component parameters such as velocity, acceleration, and jerk. It can compensate for the phase change caused by any high-order component, but it involves a joint search of multiple parameters. often unacceptable.

Therefore, for radar maneuvering weak target detection, a coherent accumulation detection algorithm that can efficiently compensate for the high-order motion of the target is urgently needed.

SUMMARY OF THE INVENTION

In order to solve the above problems, the present invention provides a mobile weak target detection method based on dynamic programming and minimum image entropy. Firstly, the dynamic programming is used to search the trajectory, and the high-order motion components of the target are quickly and iteratively searched, so as to realize the coherent accumulation of signals and the running speed. It is fast and can compensate any order of motion components, which can effectively improve the detection efficiency and accuracy of maneuvering weak targets in radar.

A mobile weak target detection method based on dynamic programming and minimum image entropy, comprising the following steps:

S1: Receive the K-frame radar echo signal, and use the dynamic programming method to obtain the trajectory of the weak target with the largest echo energy from the K-frame radar echo signal, wherein each frame of the radar echo signal corresponds to a frame of a one-dimensional range image, and The one-dimensional range image includes a plurality of distance units, and the trajectory is composed of the distance units where the weak target is located in each frame of the one-dimensional range image;

S2: Extract the echo data corresponding to each distance unit where the weak target is located, and then construct the trajectory echo signal s _DP (k) corresponding to the weak target according to the extracted echo signal:

Among them, _Ar is the set target amplitude, λ is the radar wavelength, T is the pulse repetition period of the radar, a ₁ ~ a _H are the undetermined coefficients, and h=1,2,...,H, H is the set order , j is the imaginary part, k=1,2,...,K;

S3: Perform phase compensation and Fourier transform on the track echo signal s _DP (k) to obtain the compensated spectrum S (m):

为相位补偿量，且

Among them, m is the frequency point,

is the phase compensation amount, and

S4: Obtain the image entropy E of the spectrum S(m):

Among them, C is the setting constant;

S5: Construct the following objective function according to the image entropy E:

where a=[a ₂ ,..., _{ah ,...,a H ]} ;

S6: set a ₁ =0, and then use Newton's method to solve the objective function to obtain the values of the undetermined coefficients a ₁ to a _H , thereby obtaining the final spectrum _Send (m);

S7: Obtain the peak value _Send (m ₀ ) of the spectrum _Send (m), where m ₀ is the frequency point where the peak value _Send (m ₀ ) is located;

S8: Determine whether | _{S end} (m ₀ )| ² is smaller than the set CA-CFAR threshold VT , if smaller, the weak target is a false alarm target, if not, then the weak target is a real target.

Further, the use of the dynamic programming method to obtain the trajectory of the weak target with the largest echo energy from the K-frame radar echo signal includes the following steps:

S11: Initial value of the setpoint function

为第1帧雷达回波信号对应的一维距离像中第n个距离单元的状态，且状态包括有目标和无目标，

为第1帧雷达回波信号对应的一维距离像中第n个距离单元的雷达回波信号幅值的平方；in,

is the state of the nth range unit in the one-dimensional range image corresponding to the first frame of radar echo signal, and the state includes target and no target,

is the square of the radar echo signal amplitude of the nth range unit in the one-dimensional range image corresponding to the first frame radar echo signal;

其中，每个阶段均获取一帧雷达回波信号：S12: According to the initial value of the value function corresponding to each distance unit in the first stage, use the following formula to perform iterative calculation to obtain the value function corresponding to each distance unit from the second stage to the Kth stage

Among them, each stage obtains a frame of radar echo signal:

为第k帧雷达回波信号对应的一维距离像中第n个距离单元的状态，且状态包括有目标和无目标，k＝1,2,…,K，

为第n个距离单元的雷达回波信号幅值的平方，

为第k-1阶段的所有状态中最有可能转移到状态

的状态，且

为第k-1阶段中所有可能转移到状态

的状态的集合，max为取最大值函数，arg表示将

取最大值时对应的状态作为

in,

is the state of the nth range unit in the one-dimensional range image corresponding to the kth frame radar echo signal, and the state includes target and no target, k=1,2,...,K,

is the square of the radar echo signal amplitude of the nth range unit,

is the most probable transition to state among all states in stage k-1

state, and

for all possible transition states in stage k-1

The set of states, max is the function of taking the maximum value, arg indicates that the

The corresponding state when the maximum value is taken as

其中，n₀为状态

所在的距离单元的序号；S13: Record the state corresponding to the maximum value of the value function obtained in the Kth stage as

Among them, n ₀ is the state

The serial number of the distance unit where it is located;

获取第K-1阶段中最有可能转移到状态

的状态

然后再获取第K-2阶段中最有可能转移到状态

的状态

以此类推，直到回溯到第1阶段，得到回波能量最大的弱目标的轨迹。S14: Based on the state of the Kth stage

Get the most likely transition to state in stage K-1

status

Then get the most likely transition to state in stage K-2

status

And so on, until backtracking to the first stage, the trajectory of the weak target with the largest echo energy is obtained.

Further, the setting method of the described setting constant C is:

Further, the setting method of the CA- _CFAR threshold VT is:

Among them, _Pfa is the set false alarm rate, r=1,2,...,R, R is the number of reference frequency points, _Send (m _r ) is the frequency spectrum value on the reference frequency point m _r , where, all The method for obtaining the reference frequency points is as follows:

Take the frequency point m ₀ as the center, and take the set number of frequency points on the left and right sides as the protection frequency point;

Take the outermost protection frequency points on the left and right sides as the starting point and extend to the left and right sides respectively, and use the set number of frequency points on the left and right sides as the reference frequency points.

Further, the use of Newton's method to solve the objective function to obtain the values of the undetermined coefficients a ₁ to a _H specifically includes the following steps:

S61: Set the initial value of a=[a ₂ ,...,a _h ,...,a _H ] to 0 to obtain the initial value of the image entropy E, and then perform a coefficient update operation on the initial value of the image entropy E, Obtain the updated undetermined coefficients a ₂ to a _H ; wherein, the coefficient update operation is specifically:

S61a: Using a ₂ to a _H as variables respectively, obtain the first-order partial derivatives of the to-be-determined coefficients a ₂ to a _H of the image entropy E

Among them, Imag represents the imaginary part, * represents the conjugate;

再获取图像熵E对待定系数a₂～a_H的二阶偏导数

S61b: Based on the image entropy E, the first-order partial derivatives of the to-be-determined coefficients a ₂ to a _H

Then obtain the second-order partial derivatives of the image entropy E of the coefficients a ₂ to a _H to be determined

且l表示二阶偏导数中相位补偿量

的序号；in,

And l represents the phase compensation amount in the second-order partial derivative

the serial number;

S61c: Calculate the cross term in the second partial derivative according to whether k and l are equal

Among them, when k=l:

Among them, Re represents the real part, and IDFT represents the inverse discrete Fourier transform;

When k≠l:

与二阶偏导数

分别记为

与

然后根据

与

更新待定系数a₂～a_H：S61d: Convert the first partial derivative

with the second partial derivative

are recorded as

and

then according to

and

Update the undetermined coefficients a ₂ to a _H :

为待定系数a_h在第i+1次迭代中得到的迭代值，

为待定系数a_h在第i次迭代中得到的迭代值，i为迭代次数，且i＝0,1,2,…,I，I为设定的迭代次数上限值，

为a＝[a₂,...,a_h,...,a_H]的初始值0；in,

is the iterative value of the undetermined coefficient a _h obtained in the i+1th iteration,

is the iteration value of the undetermined coefficient a _h obtained in the ith iteration, i is the number of iterations, and i=0, 1, 2,..., I, and I is the upper limit of the set number of iterations,

is the initial value of a=[a ₂ ,...,a _h ,...,a _H ];

S62: Determine whether the updated undetermined coefficients a ₂ to a _H meet the iteration termination condition. If any of the iteration termination conditions are met, the undetermined coefficients a ₂ to a _H obtained in this iteration are the final values. Then enter step S63, wherein, the iteration termination condition is:

与0的差值绝对值均小于设定阈值；The first derivative corresponding to each undetermined coefficient a ₂ ～a _H

The absolute value of the difference from 0 is less than the set threshold;

The number of iterations reaches the upper limit of the number of iterations I;

S63: Use the updated undetermined coefficients a ₂ to a _H to update the image entropy E, and then perform a coefficient update operation on the updated image entropy E again to obtain the second updated undetermined coefficients a ₂ to a _H ; and so on, Until the updated undetermined coefficients a ₂ to a _H reach the iteration termination condition.

Beneficial effects:

The invention provides a mobile weak target detection method based on dynamic programming and minimum image entropy. First, the dynamic programming method is used to quickly search for the most likely weak target, that is, the trajectory with the largest echo energy; then the target signal is extracted and FFT is performed to obtain its Spectrum, using image entropy as the cost function, uses Newton's method to iteratively search for high-order components of the target to minimize the image entropy of the spectrum, and finally uses CA-CFAR to determine the threshold, and compare the compensated spectrum maximum with the detection threshold to judge Whether the target exists or not provides an effective means for the detection of maneuvering weak targets in the radar; compared with the existing distance migration correction methods such as Keystone transformation, the present invention uses the DP technology to find the possible trajectory of the target, and the running speed is faster , and can correct the distance migration caused by the target maneuver; compared with the existing phase compensation methods such as FrFT and GRFT, the present invention minimizes the image entropy of the signal spectrum and quickly iteratively searches for the high-order motion components of the target, thereby realizing the phase compensation of the signal. The parameters are accumulated, the running speed is fast, and the motion component of any order can be compensated. In conclusion, the present invention has higher detection efficiency and higher accuracy in the detection of maneuvering weak targets in the radar.

Description of drawings

Fig. 1 is a kind of flow chart of the mobile weak target detection method based on dynamic programming and minimum image entropy provided by the present invention;

2 is a schematic diagram of a distance-time plane of a radar echo provided by the present invention;

3 is a schematic diagram of an initial spectrum provided by the present invention;

Fig. 4 is the schematic diagram that the high-order motion component provided by the present invention utilizes Newton's method to iterate;

FIG. 5 is a schematic diagram of a spectrum provided by the present invention after being processed by DP-MIE.

Detailed ways

In order to make those skilled in the art better understand the solutions of the present application, the following will clearly and completely describe the technical solutions in the embodiments of the present application with reference to the accompanying drawings in the embodiments of the present application.

As shown in FIG. 1, the present invention provides a coherent accumulation detection algorithm combining dynamic programming and minimum image entropy. First, the dynamic programming algorithm is used to search for possible target trajectories and correct distance migration; then the trajectory echoes are extracted and FFT is performed. To obtain its spectrum, the image entropy is used as the cost function for the spectrum, and the high-order motion components such as acceleration and jerk are quickly and iteratively searched by the Newton method to minimize the image entropy of the spectrum; finally, the searched high-order motion parameters are used to compensate the target. The high-order phase of the signal, completes the coherent accumulation, and uses the Cell-average constant false alarm (CA-CFAR) detection method to set the threshold to complete the weak target detection. The overall process includes the following steps:

S1: Receive the K-frame radar echo signal, and use the dynamic programming method to obtain the trajectory of the weak target with the largest echo energy from the K-frame radar echo signal, wherein each frame of the radar echo signal corresponds to a frame of a one-dimensional range image, and The one-dimensional range image includes a plurality of distance units, and the trajectory is composed of distance units where the weak target is located in each frame of the one-dimensional range image.

It should be noted that the dynamic programming method searches for the trajectory recursively through the energy of the echo signal on the distance-time plane, which can quickly screen out the trajectory with higher energy as the possible trajectory of the target. The following are the specific implementation steps for DP technology to quickly search for possible trajectories of targets:

S11: Initial value of the setpoint function

为第1帧雷达回波信号对应的一维距离像中第n个距离单元的状态，且状态包括有目标和无目标，

为第1帧雷达回波信号对应的一维距离像中第n个距离单元的雷达回波信号幅值的平方；in,

is the state of the nth range unit in the one-dimensional range image corresponding to the first frame of radar echo signal, and the state includes target and no target,

is the square of the radar echo signal amplitude of the nth range unit in the one-dimensional range image corresponding to the first frame radar echo signal;

以实现值函数的积累，其中，每个阶段均获取一帧雷达回波信号：S12: According to the initial value of the value function corresponding to each distance unit in the first stage, use the following formula to perform iterative calculation to obtain the value function corresponding to each distance unit from the second stage to the Kth stage

To achieve the accumulation of the value function, in which each stage obtains a frame of radar echo signal:

也称为代价函数或累积观测量，其记录的是沿某一轨迹(此轨迹，第k阶段的状态为

)的观测值的非相干累积值；

为第k帧雷达回波信号对应的一维距离像中第n个距离单元的状态，且状态包括有目标和无目标，k＝1,2,…,K；

为第n个距离单元的雷达回波信号幅值的平方，也表示对状态

的观测值；

为第k-1阶段的所有状态中最有可能转移到状态

的状态，且初始化时设置为0，即

用于表示轨迹起点；

为第k-1阶段中所有可能转移到状态

的状态的集合，max为取最大值函数，arg表示将

取最大值时对应的状态作为

in,

Also known as a cost function or cumulative observations, it records the state along a trajectory (this trajectory, the state of the kth stage is

) is the incoherent cumulative value of the observations;

is the state of the nth range unit in the one-dimensional range image corresponding to the kth frame radar echo signal, and the state includes target and no target, k=1,2,...,K;

is the square of the amplitude of the radar echo signal of the nth distance unit, and also represents the

the observed value;

is the most probable transition to state among all states in stage k-1

state, and is set to 0 during initialization, that is

Used to indicate the starting point of the trajectory;

for all possible transition states in stage k-1

The set of states, max is the function of taking the maximum value, arg indicates that the

The corresponding state when the maximum value is taken as

其中，n₀为状态

所在的距离单元的序号。S13: Record the state corresponding to the maximum value of the value function obtained in the Kth stage as

Among them, n ₀ is the state

The serial number of the distance unit where it is located.

如下式所示：It should be noted that this step is to filter the value function, find the largest value function in the Kth stage, and obtain the state corresponding to this value function

As shown in the following formula:

获取第K-1阶段中最有可能转移到状态

的状态

然后再获取第K-2阶段中最有可能转移到状态

的状态

以此类推，直到回溯到第1阶段，得到回波能量最大，也即值函数总和最大的弱目标的轨迹。S14: Based on the state of the Kth stage

Get the most likely transition to state in stage K-1

status

Then get the most likely transition to state in stage K-2

status

By analogy, until backtracking to the first stage, the trajectory of the weak target with the largest echo energy, that is, the largest sum of the value functions, is obtained.

Further, the backtracking process is expressed by the formula as follows:

的轨迹在第k阶段的状态。Among them, Track(k) indicates that the final state is

The state of the trajectory in the kth stage.

S2: Extract the echo data corresponding to each distance unit where the weak target is located, and then construct the trajectory echo signal s _DP (k) corresponding to the weak target according to the extracted echo signal:

Among them, _Ar is the set target amplitude, λ is the radar wavelength, T is the pulse repetition period of the radar, a ₁ ~ a _H are the undetermined coefficients, a _h represents the h-th order motion component of the target, and the first order is the speed, The second order is the acceleration, the third order is the jerk, and so on, and h=1,2,…,H, H is the set order, j is the imaginary part, k=1,2,…,K.

S3: Perform phase compensation and Fourier transform on the track echo signal s _DP (k) to obtain the compensated spectrum S (m):

为相位补偿量，且

Among them, m is the frequency point,

is the phase compensation amount, and

That is to say, after the dynamic programming process, the range migration of the weak target has been corrected and the target signal s _DP (k) has been extracted, which needs to be phase compensated, then the compensated spectrum S can be obtained by using FFT (m).

S4: Obtain the image entropy E of the spectrum S(m):

where C is a set constant equal to the total energy of the signal sequence, and

It should be noted that the image entropy can represent the chaos and complexity of the image. The larger the entropy value is, the more disordered (defocused), random, and complex the image is; on the contrary, the smaller the image entropy is, the more ordered (focused), regular, and simple the image is. When the entropy value reaches the theoretical minimum value of 0, the image energy is completely focused on one point. In radar data processing, if the target signal Doppler migration compensation is not performed, when the target has high-order motion components, MTD processing is performed directly on the target echo signal, and the energy of the target will be divergent in the spectrum (entropy large value), cannot be ideally focused on a certain frequency. This results in a decrease in the pulse accumulation gain, which is not conducive to subsequent target detection. If the MTD processing is performed after the compensation of the high-order motion components is completed, a good focus spectrum (with a small entropy value) can be obtained. Therefore, the present invention takes the image entropy as the cost function, and then quickly and iteratively searches for high-order motion components such as acceleration and jerk through the Newton method to minimize the image entropy of the spectrum; order phase, complete the coherent accumulation, and use the CA-CFAR detection method to set the threshold to complete the detection of weak targets, see steps S5 to S8 for details:

S5: Construct the following objective function according to the image entropy E:

where a=[a ₂ ,...,ah ,...,a _H ] _.

满足

时，频谱的图像熵E最小，因此，以图像熵E为代价函数，高阶运动分量a₂,...,a_h,...,a_H为需要优化的变量，进行频谱图像熵E的优化，得到如上目标函数。It should be noted that when

Satisfy

When , the image entropy E of the spectrum is the smallest. Therefore, the image entropy E is used as the cost function, and the high-order motion components a ₂ ,...,a _h ,...,a _H are the variables that need to be optimized, and the spectrum image entropy E is calculated. optimization to obtain the above objective function.

S6: Set a ₁ =0, and then use Newton's method to solve the objective function to obtain the values of the undetermined coefficients a ₁ to a _H , thereby obtaining the final spectrum _Send (m), which specifically includes the following steps:

S61: Set the initial value of a=[a ₂ ,...,a _h ,...,a _H ] to 0 to obtain the initial value of the image entropy E, and then perform a coefficient update operation on the initial value of the image entropy E, Obtain the updated undetermined coefficients a ₂ to a _H ; wherein, the coefficient update operation is specifically:

S61a: Using a ₂ to a _H as variables respectively, obtain the first-order partial derivatives of the to-be-determined coefficients a ₂ to a _H of the image entropy E

Among them, Imag represents the imaginary part, * represents the conjugate;

再获取图像熵E对待定系数a₂～a_H的二阶偏导数

S61b: Based on the image entropy E, the first-order partial derivatives of the to-be-determined coefficients a ₂ to a _H

Then obtain the second-order partial derivatives of the image entropy E of the coefficients a ₂ to a _H to be determined

且l表示二阶偏导数中相位补偿量

的序号；in,

And l represents the phase compensation amount in the second-order partial derivative

the serial number;

S61c: Calculate the cross term in the second partial derivative according to whether k and l are equal

Among them, when k=l:

Among them, Re represents the real part, and IDFT represents the inverse discrete Fourier transform;

When k≠l:

与二阶偏导数

分别记为

与

然后根据

与

更新待定系数a₂～a_H：S61d: Convert the first partial derivative

with the second partial derivative

are recorded as

and

then according to

and

Update the undetermined coefficients a ₂ to a _H :

为待定系数a_h在第i+1次迭代中得到的迭代值，

为待定系数a_h在第i次迭代中得到的迭代值，i为迭代次数，且i＝0,1,2,…,I，I为设定的迭代次数上限值，

为a＝[a₂,...,a_h,...,a_H]的初始值0；in,

is the iterative value of the undetermined coefficient a _h obtained in the i+1th iteration,

is the iteration value of the undetermined coefficient a _h obtained in the ith iteration, i is the number of iterations, and i=0, 1, 2,..., I, and I is the upper limit of the set number of iterations,

is the initial value of a=[a ₂ ,...,a _h ,...,a _H ];

S62: Determine whether the updated undetermined coefficients a ₂ to a _H meet the iteration termination condition. If any of the iteration termination conditions are met, the undetermined coefficients a ₂ to a _H obtained in this iteration are the final values. Then enter step S63, wherein, the iteration termination condition is:

与0的差值绝对值均小于设定阈值；The first derivative corresponding to each undetermined coefficient a ₂ ～a _H

The absolute value of the difference from 0 is less than the set threshold;

The number of iterations reaches the upper limit of the number of iterations I;

S63: Use the updated undetermined coefficients a ₂ to a _H to update the image entropy E, and then perform a coefficient update operation on the updated image entropy E again to obtain the second updated undetermined coefficients a ₂ to a _H ; and so on, Until the updated undetermined coefficients a ₂ to a _H reach the iteration termination condition.

S7: Obtain the peak value _Send (m ₀ ) of the spectrum _Send (m), where m ₀ is the frequency point where the peak value _Send (m ₀ ) is located;

S8: Determine whether | _{S end} (m ₀ )| ² is smaller than the set CA-CFAR threshold VT , if smaller, the weak target is a false alarm target, if not, then the weak target is a real target.

The setting method of the CA- _CFAR threshold VT is:

Among them, _Pfa is the set false alarm rate, r=1,2,...,R, R is the number of reference frequency points, _Send (m _r ) is the frequency spectrum value on the reference frequency point m _r , where, all The method for obtaining the reference frequency points is as follows:

Take the frequency point m ₀ as the center, and take the set number of frequency points on the left and right sides as the protection frequency point;

Take the outermost protection frequency points on the left and right sides as the starting point and extend to the left and right sides respectively, and use the set number of frequency points on the left and right sides as the reference frequency points.

To verify the validity of the accumulation detection method described above. Based on the simulation experimental data, the present invention adopts the mobile weak target detection algorithm combining dynamic programming and minimum image entropy described in the present invention to complete the detection of the mobile weak target. The parameters of the simulation are shown in Table 1:

Table 1 Simulation parameters

parameter value radar wavelength 0.02m Radar center frequency 16GHz Radar bandwidth 800MHz pulse repetition frequency 500Hz distance unit width 0.12m Target motion component [a₁,a₂,a₃] [0.8,0.3,0.1] target signal-to-noise ratio 3dB

The distance-time plane of the radar echo is shown in Figure 2, with a total of 500 pulses of radar echo data. The target begins to appear at 540m, and obvious maneuvering occurs during the movement.

Step 1, DP finds the target trajectory:

The multi-frame one-dimensional range image data is modulo calculated, and the signal energy is used as the value function and the recursive accumulation is performed to obtain the target trajectory. The number of state transitions in dynamic programming is set to 3, a total of 500 frames are accumulated recursively, and the state of the highest value function is selected as the possible trajectory of the target.

Step 2, extract the trajectory echo, and use Newton's method to iteratively optimize its spectral image entropy:

Extract the echo signal of the target, set the initial value of each order motion compensation amount a ₁ , a ₂ , a ₃ to 0, use the initial value to compensate and do FFT to obtain its spectrum, its initial spectrum distribution is shown in Figure 3. It can be seen that the spectrum of the target is divergent, and the signal-to-noise ratio is very low about 9dB, which is difficult to detect. Using Newton's method, the high-order components a ₂ , a ₃ are iterated for a total of 1000 iterations, as shown in Figure 4, and finally a ₂ , a ₃ gradually converge to the true value [0.3, 0.1]. Finally, the iterative motion components are used to detect the spectrum after compensation. As shown in Figure 5, the signal-to-noise ratio of the target spectrum is greatly enhanced, reaching 27.2dB, which takes 9s in total.

We use the theoretically optimal coherent accumulation algorithm: GRFT to perform third-order motion search compensation, and perform accumulation detection under the same hardware conditions. After accumulation, the weak target signal-to-noise ratio is 28.3dB, but it takes 4300s. The specific comparison results of the two methods are shown in Table 2:

Table 2 Comparison of DP-MIE and GRFT examples

Evaluation indicators DP-MIE GRFT cumulative signal-to-noise ratio 27.2dB 28.3dB Operation time 9s 4300s

It can be seen that the method of the present invention loses a very small accumulation gain, but greatly improves the operation efficiency, and verifies the real-time performance and effectiveness.

The method of the present invention can be applied to the long-term coherent accumulation of radar, so as to realize the efficient detection of maneuvering weak targets.

Of course, the present invention can also have other various embodiments. Without departing from the spirit and essence of the present invention, those skilled in the art can of course make various corresponding changes and deformations according to the present invention, but these corresponding Changes and deformations should belong to the protection scope of the appended claims of the present invention.

Claims (4)

1. A maneuvering weak target detection method based on dynamic programming and minimum image entropy is characterized by comprising the following steps:

s1: receiving K frames of radar echo signals, and acquiring a track of a weak target with the maximum echo energy from the K frames of radar echo signals by adopting a dynamic programming method, wherein each frame of radar echo signal corresponds to one frame of one-dimensional range profile, the one-dimensional range profile comprises a plurality of range units, and the track is formed by the range units of the weak target in each frame of one-dimensional range profile; the method for acquiring the track of the weak target with the maximum echo energy from the K frames of radar echo signals by adopting the dynamic programming method comprises the following steps:

s11: initial value of the set-point function

Wherein,

the state of the nth range cell in the one-dimensional range profile corresponding to the 1 st frame of radar echo signal is shown, and the state comprises a target and no target,

the square of the amplitude of the radar echo signal of the nth range unit in the one-dimensional range profile corresponding to the 1 st frame of radar echo signal is obtained;

s12: according to the initial value of the value function corresponding to each distance unit in the 1 st stage, iterative calculation is carried out by adopting the following formula to obtain the value function corresponding to each distance unit from the 2 nd stage to the K th stage

Wherein, every stage all acquires a frame radar echo signal:

wherein,

the state of the nth range cell in the one-dimensional range profile corresponding to the kth frame radar echo signal is shown, and the state includes a target and no target, K is 1,2, …, K,

is the square of the amplitude of the radar echo signal of the nth range unit,

is the most probable transition to the state in all the states of the k-1 stage

A state of (1), and

all possibilities in the k-1 stageTransition to a State

Max is a function taking the maximum value, arg denotes the number of states that will be processed

Taking the corresponding state at the time of maximum value as

Representation collection

The value function corresponding to all the states;

s13: recording the state corresponding to the maximum value of the value function obtained in the K stage as

Wherein n is ₀ Is in a state

The serial number of the located distance unit;

s14: based on the state of the K stage

Obtaining the most probable transition to State in stage K-1

State of (1)

Then, the most possible transition to the state in the K-2 stage is obtained

State of (1)

In this way, until the stage 1 is traced back, the track of the weak target with the maximum echo energy is obtained;

s2: extracting echo data corresponding to each distance unit where the weak target is located, and then constructing a track echo signal s corresponding to the weak target according to the extracted echo signals _DP (k)：

Wherein A is _r For a set target amplitude, λ is the radar wavelength, T is the pulse repetition period of the radar, a ₁ ～a _H H is 1,2, …, H is a set order, j is an imaginary part, K is 1,2, …, K;

s3: for the track echo signal s _DP (k) Performing phase compensation and fourier transform to obtain a compensated spectrum s (m):

wherein m is a frequency point,

is a phase compensation amount, and

s4: obtaining the image entropy E of the spectrum s (m):

wherein C is a set constant;

s5: the following objective function is constructed according to the image entropy E:

wherein a ═ a ₂ ,...,a _h ,...,a _H ]；

S6: let a be ₁ When the value is equal to 0, then the objective function is solved by adopting Newton method to obtain undetermined coefficient a ₁ ～a _H To obtain the final spectrum S _end (m)；

S7: obtaining a spectrum S _end (m) peak value S _end (m ₀ ) Wherein m is ₀ Is a peak value S _end (m ₀ ) The frequency point of the position;

s8: determine | S _end (m ₀ )| ² Whether the threshold value is less than the set CA-CFAR threshold value V _T If the weak target is smaller than the target, the weak target is a false alarm target, and if the weak target is not smaller than the target, the weak target is a real target.

2. The method for detecting the maneuvering weak target based on the dynamic programming and the minimum image entropy as claimed in claim 1, characterized in that the setting method of the setting constant C is as follows:

3. the method for detecting maneuvering weak targets based on dynamic programming and minimum image entropy as claimed in claim 1, characterized in that the CA-CFAR threshold V is _T The setting method comprises the following steps:

wherein, P _fa In order to set the false alarm rate, R is 1,2, …, R is the number of reference frequency points, S _end (m _r ) Is a reference frequency point m _r The reference frequency point obtaining method comprises the following steps:

at frequency point m ₀ Taking a set number of frequency points on the left side and the right side of the center as protection frequency points;

the protection frequency points at the outermost peripheries of the left side and the right side are respectively taken as starting points and extend to the left side and the right side, and the frequency points with the set number on the left side and the right side are taken as reference frequency points.

4. The maneuvering weak target detection method based on dynamic programming and minimum image entropy as claimed in claim 1, characterized in that the objective function is solved by Newton method to obtain undetermined coefficient a ₁ ～a _H The value of (b) specifically comprises the following steps:

s61: let a be [ a ] ₂ ,...,a _h ,...,a _H ]Is 0, the initial value of the image entropy E is obtained, then the coefficient updating operation is executed on the initial value of the image entropy E, and the updated undetermined coefficient a is obtained ₂ ～a _H (ii) a Wherein the coefficient updating operation specifically comprises:

s61 a: respectively with a ₂ ～a _H For variable, obtaining image entropy E to-be-determined coefficient a ₂ ～a _H First partial derivative of

Wherein, Imag represents an imaginary part, and one represents conjugation;

s61 b: treating a fixed coefficient a based on image entropy E ₂ ～a _H First partial derivative of

Obtaining the entropy E of the image to be determinedCoefficient a ₂ ～a _H Second partial derivative of

Wherein,

and l represents the amount of phase compensation in the second partial derivative

The serial number of (2);

s61 c: calculating the cross term in the second partial derivative according to whether k and l are equal

Wherein when k is l:

wherein Re represents a real part, and IDFT represents inverse discrete Fourier transform;

when k ≠ l:

s61 d: the first partial derivative

And second partial derivative

Are respectively marked as

Then according to

And

updating the undetermined coefficient a ₂ ～a _H ：

Wherein,

is a coefficient to be determined _h The iteration value obtained in the (i + 1) th iteration,

is a coefficient to be determined _h The iteration value obtained in the ith iteration, I is the iteration number, and I is 0,1,2, …, I is the set upper limit value of the iteration number,

is a ═ a ₂ ,...,a _h ,...,a _H ]0;

s62: judging the updated undetermined coefficient a ₂ ～a _H Whether the iteration termination condition is met or not, if any iteration termination condition is met, the undetermined coefficient a obtained by the iteration is obtained ₂ ～a _H If the values are not satisfied, the step S63 is entered, where the iteration termination condition is:

each coefficient to be determined a ₂ ～a _H Corresponding first derivative

The absolute values of the difference values with 0 are all smaller than a set threshold value;

the iteration times reach an iteration time upper limit value I;

s63: adopting the updated undetermined coefficient a ₂ ～a _H Updating the image entropy E, and then re-executing the coefficient updating operation on the updated image entropy E to obtain a secondary updated undetermined coefficient a ₂ ～a _H (ii) a And so on until the updated undetermined coefficient a ₂ ～a _H An iteration end condition is reached.

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