CN108387882B - A Design Method of MTD Filter Bank Based on Second-Order Cone Optimization Theory - Google Patents

Abstract

The invention belongs to the field of signal processing, and discloses a method for designing an MTD filter bank based on the second-order cone optimization theory. and power and calculate the covariance matrix of the interference: obtain the noise power of the radar and calculate the covariance matrix of the ground clutter, interference and noise; adopt a method similar to the minimum variance undistorted response, with a linear constraint on the center frequency of the filter; Under the condition of limiting the side lobe level of the filter's amplitude-frequency response, modify the above linear constraints; convert it into an easy-to-solve second-order cone programming real number problem; design an MTD filter based on the second-order cone programming theory. The lobe level is free to form a deeper notch in the strong interference frequency area or the weather clutter area, which overcomes the problem of filter distortion near zero frequency and enhances the advantages of low-speed moving target detection.

Description

A Design Method of MTD Filter Bank Based on Second-Order Cone Optimization Theory

technical field

The invention belongs to the technical field of signal processing, and in particular relates to an MTD (Moving Target Detection) filter bank design method based on the second-order cone optimization theory, which is used for radar to suppress clutter and realize radar detection of targets

Background technique

Effective suppression of clutter signals is the premise and foundation of normal target detection for radar systems. Among the adaptive clutter suppression methods, moving target detection MTD is a commonly used technique. The moving target detection MTD filter uses a filter bank composed of multiple band-pass filters to filter the radar echo, and then detects the output of the filter bank to find the target.

The easiest way to realize the moving target detection MTD filter bank is to use the discrete Fourier transform DFT filter bank. The moving target display MTI processing is added before the discrete Fourier transform DFT filter bank, so that the ground clutter can be eliminated by the moving target display MTI first, and then the discrete Fourier transform DFT filter bank is used for filtering processing. Lie Transform DFT filter banks can be implemented with Fast Fourier Transform FFT. Because the fast Fourier transform (FFT) can save a lot of computation, this method is still widely used, especially when the order of the MTD filter bank for moving target detection is large. However, since the order of the fast Fourier transform FFT must be an integer power of 2, the application of the moving target display MTI plus fast Fourier transform FFT implementation method is limited, and the discrete Fourier transform DFT filter The group is located behind the MTI displayed by the moving target, and each filter gain of the filter bank is modulated by the frequency response of the MTI filter displayed by the moving target;

At present, the commonly used implementation method of MTD filter bank for moving target detection is to use limited-length impulse response FIR filter bank. For each filter in the finite-length impulse response FIR filter bank, its amplitude and frequency response must have a deep null near the zero frequency to suppress clutter, which is mainly ground clutter. Adaptive moving target detection MTD filter. However, the conventional adaptive MTD filter has no constraint on the side lobe and has a high side lobe level, which is easy to cause mutual influence between the targets of different filters in the filter bank, which will bring false alarms. Even the windowing method often fails to meet the requirements. When the center frequency of the filter is close to zero frequency, the performance of the windowing method is seriously degraded, the filter is distorted, and the windowing cannot form a wide notch in a specific frequency band, suppressing occupation Clutter and interference in a certain frequency range.

SUMMARY OF THE INVENTION

In view of the above problems, the purpose of the present invention is to provide a MTD filter bank design method based on the second-order cone optimization theory, to solve the problem that the performance of the moving target detection MTD filter in the prior art is seriously degraded when the center frequency is close to the zero frequency. , the problem of filter distortion, and the problem that the windowing method cannot make the filter form a wide notch in a specific frequency band such as weather clutter or strong interference.

The basic idea of implementing the present invention is to firstly calculate the covariance matrix of ground clutter by searching the clutter power spectrum variance and clutter power of the radar working scene in order to form a deeper null. At the same time, the covariance matrix of interference and the covariance matrix of noise are calculated. The filter center frequency is then linearly constrained according to the design model using a method similar to Minimum Variance Distortion Response (MVDR) in the field of adaptive beamforming. Under the conditions of limiting the side lobe level of the filter's amplitude-frequency response and suppressing meteorological clutter and strong interference occupying a certain frequency band, a quadratic constraint is added on the basis of the above-mentioned linear constraints. Finally, it is converted into a second-order cone programming (SOCP) problem, and the desired FIR filter coefficients are simply and efficiently designed through the SeDuMi toolbox of MATLAB.

In order to achieve the above object, the present invention adopts the following technical solutions to achieve.

A method for designing an MTD filter bank based on the second-order cone optimization theory, the MTD filter is used for radar to suppress clutter and detect targets, and the method comprises the following steps:

Step 1, set the working parameters of the radar, the working parameters of the radar include the pulse repetition frequency and the accumulated pulse number of the radar; wherein, the pulse repetition frequency is used to determine the center frequency of each filter in the MTD filter bank, so The number of accumulated pulses is used to determine the order of the MTD filter bank;

Step 2, set the radar working scene to include target, ground clutter, interference and noise; obtain the ground clutter power spectrum variance and ground clutter power of the radar working scene, and obtain the covariance matrix of ground clutter; obtain the radar working scene The interference signal frequency and the interference signal power are calculated to obtain the covariance matrix of the interference; the noise power of the radar is obtained, and the covariance matrix of the noise is obtained by calculation;

Step 3, obtain a comprehensive covariance matrix of ground clutter, interference and noise according to the covariance matrix of the ground clutter, the covariance matrix of the interference and the covariance matrix of the noise;

Step 4, according to the comprehensive covariance matrix of the ground clutter, interference and noise, carry out the first linear constraint on the center frequency of each filter, and obtain the first optimization expression;

Step 5, set the amplitude-frequency response sidelobe limit level of the filter, and the weather clutter or interference limit level, carry out secondary constraints to the first optimization expression, and obtain the second optimization expression;

Step 6, the second optimization expression is converted into a second-order cone programming real number expression, and the second-order cone programming real number expression is solved to obtain the weight vector of the filter; thereby obtain each in the MTD filter bank. The weight vector of the filter.

Compared with the prior art, the present invention has the following advantages: (1) The method of the present invention is essentially to solve a second-order cone optimization problem, and the interior point method can be used to solve the problem effectively, and the calculation amount is small. (2) Since the method of the present invention adds the condition of constraining the side lobe level and restricting the strong interference or weather clutter when establishing the constraint condition of the filter center frequency, the filter designed by the method of the present invention has a lower side lobe voltage. Flat, and free to form deep notches in strong interference frequency areas or weather clutter areas. (3) The second-order stack optimization problem is solved by using the SeDuMi toolbox of MATLAB, which overcomes the problem that the filter is distorted when the center frequency of the filter is close to the zero frequency in the conventional windowing method. Even when the center frequency of the filter designed by the method of the invention is close to zero frequency, the filter will not be distorted, and the detection ability of the filter for low-speed moving objects is enhanced.

Description of drawings

In order to explain the embodiments of the present invention or the technical solutions in the prior art more clearly, the following briefly introduces the accompanying drawings that need to be used in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are only These are some embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained according to these drawings without creative efforts.

1 is a schematic flowchart of a method for designing an MTD filter bank based on the second-order cone optimization theory provided by an embodiment of the present invention;

Fig. 2 is the MTD filter using the design of the present invention, it forms the deep notch schematic diagram of -60dB in weather clutter or strong interference area, and the side lobe level is controlled at -40dB simultaneously;

Fig. 3 is the contrast schematic diagram of the MTD filter designed using the present invention and the traditional windowing method under the condition that the center frequency is far from zero frequency;

Fig. 4 is the contrast schematic diagram of the MTD filter designed using the present invention, traditional windowing method and digital synthesis method under the condition that the center frequency is close to zero frequency;

5 is a comparison diagram of the designed MTD filter using the present invention, the traditional windowing method and the digital synthesis method under the condition that the center frequency is further close to the zero frequency, and a partial amplification is performed near the center frequency.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

An embodiment of the present invention provides a method for designing an MTD filter bank based on the second-order cone optimization theory. The MTD filter is used for radar to suppress clutter and detect targets. As shown in FIG. 1 , the method includes the following steps:

Step 1, set the working parameters of the radar, the working parameters of the radar include the pulse repetition frequency and the accumulated pulse number of the radar; wherein, the pulse repetition frequency is used to determine the center frequency of each filter in the MTD filter bank, so The number of accumulated pulses is used to determine the order of the MTD filter bank. The ground radar used in the example of the present invention transmits and receives a public equidistant line array.

Step 2, set the radar working scene to include target, ground clutter, interference and noise; obtain the ground clutter power spectrum variance and ground clutter power of the radar working scene, and obtain the covariance matrix of ground clutter; obtain the radar working scene The interference signal frequency and interference signal power are calculated to obtain the interference covariance matrix; the noise power of the radar is obtained, and the noise covariance matrix is obtained by calculation.

By searching the ground clutter power spectrum variance and ground clutter power table of different scenarios, the power spectrum variance and ground clutter power of ground clutter in the radar working scene are obtained;

(2a) Using the Gaussian power spectral density formula to calculate the ground clutter power spectral density of the radar working scene; (2b) Using the Wienersinchin formula to calculate the element value of the ground clutter covariance matrix.

In the step 2, the interference signal frequency and the interference signal power of the radar working scene are obtained, and the interference covariance matrix is obtained by calculation; the noise power of the radar is obtained, and the noise covariance matrix is obtained by calculation, which specifically includes the following sub-steps:

计算得到干扰的协方差矩阵

其中，a(f_p)为干扰信号在干扰信号频率f_p处的导频矢量，上标H表示共轭转置。(2a) Obtain the jamming signal frequency f _p and jamming signal power of the radar working scene

Calculate the covariance matrix of the interference

Among them, a(f _p ) is the pilot frequency vector of the interference signal at the frequency f _p of the interference signal, and the superscript H represents the conjugate transpose.

(2b) Obtain the noise power δ _n ² of the radar, and calculate the covariance matrix R _n =δ _n ² I of the noise; wherein, I represents the identity matrix.

Step 3: Obtain a comprehensive covariance matrix of ground clutter, interference and noise according to the covariance matrix of the ground clutter, the covariance matrix of the interference, and the covariance matrix of the noise.

In order to make the filter form a deeper depression at zero frequency, it is necessary to comprehensively calculate the comprehensive covariance matrix of noise, ground clutter and interference. The step 3 is specifically:

According to the covariance matrix R _c of the ground clutter, the covariance matrix R _i of the interference and the covariance matrix R _n of the noise, the comprehensive covariance matrix R of the ground clutter, interference and noise is obtained:

表示干扰信号功率，a(f_p)为干扰信号在干扰信号频率f_p处的导频矢量，上标H表示共轭转置。Among them, δ _n ² represents the noise power of the radar, I represents the identity matrix,

represents the power of the interference signal, a(f _p ) is the pilot vector of the interference signal at the frequency f _p of the interference signal, and the superscript H represents the conjugate transpose.

Step 4: Perform a first linear constraint on the center frequency of each filter according to the comprehensive covariance matrix of the ground clutter, interference and noise to obtain a first optimization expression.

A method similar to the minimum variance undistorted response is used to linearly constrain the center frequency of the filter. Step 4 is as follows:

According to the comprehensive covariance matrix R of the ground clutter, interference and noise, a first linear constraint is performed on the center frequency of the filter, and the first optimization expression is obtained as follows:

sth ^H a(f ₀ )=1

N表示雷达天线包含的阵元个数，Tr为雷达脉冲重复周期，

表示表达式h^HRh最小时h的值，s.t.表示约束条件，上标H表示共轭转置。Among them, h is the weight vector of the filter, f ₀ is the center frequency of the filter, a(f ₀ ) is the pilot frequency vector of the filter at f ₀ ,

N represents the number of array elements contained in the radar antenna, Tr is the radar pulse repetition period,

represents the value of h when the expression h ^H Rh is minimum, st represents the constraint condition, and the superscript H represents the conjugate transpose.

Step 5: Set the amplitude-frequency response side lobe limit level of the filter and the weather clutter or interference limit level, and perform secondary constraints on the first optimization expression to obtain a second optimization expression.

Step 5 is specifically:

Set the amplitude-frequency response side lobe limit level ε ₁ of the filter, and the weather clutter or interference limit level ε ₂ , perform secondary constraints on the first optimization expression, and obtain the second optimization expression as follows:

sth ^H a(f ₀ )=1

||h ^H a(f _i )|| ² ≤ε ₁ i=1,2,…,K

||h ^H a(f _j )|| ² ≤ε ₂ j=K+1,2,…,L

表示表达式h^HRh最小时h的值，s.t.表示约束条件，f_i表示滤波器旁瓣区的第i个采样频率，i＝1,2,…,K，K表示滤波器旁瓣区总的采样频率个数，a(f_i)表示滤波器在频率f_i处的导频矢量，f_j表示干扰区的第j个采样频率，j＝K+1,2,…,L，L表示滤波器旁瓣区和干扰区总的采样频率个数，a(f_j)表示干扰信号在频率f_j处的导频矢量，||·||²表示求模值的平方。Among them, h is the weight vector of the filter, f ₀ is the center frequency of the filter, a(f ₀ ) is the pilot frequency vector of the filter at f ₀ ,

Represents the value of h when the expression h ^H Rh is the smallest, st represents the constraint condition, f _i represents the ith sampling frequency of the filter side lobe region, i=1, 2,...,K, K represents the total filter side lobe region The number of sampling frequencies of , a(f _i ) represents the pilot vector of the filter at frequency f _i , f _j represents the jth sampling frequency of the interference area, j=K+1,2,...,L, L represents The total number of sampling frequencies in the filter sidelobe region and the interference region, a(f _j ) represents the pilot vector of the interference signal at the frequency f _j , and ||·|| ² represents the square of the modulo value.

Step 6, the second optimization expression is converted into a second-order cone programming real number expression, and the second-order cone programming real number expression is solved to obtain the weight vector of the filter; thereby obtain each in the MTD filter bank. The weight vector of the filter.

Through matrix operations, the original problem is further transformed into an easy-to-solve second-order cone programming real number problem. Step 6 is as follows:

(6a) Perform Cholesky decomposition on the comprehensive covariance matrix R of the ground clutter, interference and noise to obtain R=U ^H U, where U represents the decomposition matrix, let τ be the first intermediate variable, and ||Uh| |≤τ;

Then the second optimized expression is converted into the following third optimized expression:

sth ^H a(f ₀ )=1

||Uh||≤τ

||h ^H a(f _i )|| ² ≤ε ₁ i=1,2,…,K

||h ^H a(f _j )|| ² ≤ε ₂ j=K+1,2,…,L

表示使得τ最小时，τ和h的取值，||·||²表示求模值的平方；in,

Represents the value of τ and h when τ is minimized, and ||·|| ² represents the square of the modulus value;

第五中间变量

第六中间变量y₄＝h；(6b) Let the second intermediate variable y=[y ₁ , y ₂ , y ₃ , y ₄ ^T ] ^T , the third intermediate variable y ₁ =τ, and the fourth intermediate variable

fifth intermediate variable

sixth intermediate variable y ₄ =h;

Then the third optimization expression is simplified to the following second-order cone programming expression:

sth ^H a(f ₀ )=1

||Uy ₄ ||≤y ₁

||h ^H a(f _i )||≤y ₂ i=1,2,…,K

||h ^H a(f _j )||≤y ₃ j=K+1,2,…,L

表示使得y₁最小时y的值，||·||表示求模值；in,

Indicates the value of y when y ₁ is minimized, and || · || represents the modulo value;

(6c) Convert the second-order cone programming expression into a second-order cone programming real expression:

第八中间变量

第九中间变量

第十中间变量

变量l＝0,1,…,L，则根据所述二阶锥规划表达式对应得到如下等价关系：Let the seventh intermediate variable

Eighth Intermediate Variable

Ninth Intermediate Variable

Tenth Intermediate Variable

If the variable l=0,1,...,L, the following equivalent relation is obtained according to the second-order cone programming expression:

第十二中间变量b＝[1,0,…,0]^T，从而得到二阶锥规划实数表达式如下：and let the eleventh intermediate variable

The twelfth intermediate variable b=[1,0,…,0] ^T , so the real number expression of the second-order cone programming is obtained as follows:

表示使得

最小时的

值；in,

means to make

the smallest

value;

(6d) Solve the real number expression of the second-order cone programming to obtain the weight vector h of the filter, so as to determine the MTD filter bank.

Specifically, use the SeDuMi toolbox in Matlab to design the MTD filter based on the second-order cone programming theory, and construct the core function sedumi(Att,bt,ct,K) that calls SeDuMi according to the above-mentioned simplified second-order cone programming problem. , and then call the sedumi function to design an MTD filter based on the second-order cone programming theory.

The effects of the present invention will be further described below in conjunction with the accompanying drawings.

1. Simulation conditions:

The software running system of the simulation experiment of the present invention is a 64-bit windows operating system, and the simulation software is MATLAB (R2015b).

其中MTD滤波器组中一个滤波器中心频率f₀＝800Hz，旁瓣限制电平ε₁＝1×10^-4，气象杂波或强干扰区限制电平ε₂＝1×10^-6，主瓣区域为中心频率前后各拓展60Hz，噪声功率为1。干扰频率为1600Hz，干噪比INR＝20dB，得到仿真图2。The parameters for simulating the MTD filter bank of the present invention are: radar pulse repetition frequency PRF=2000Hz, MTD filter bank length N=64, clutter power C _g =1×10 ⁷ , clutter spectrum width

Among them, the center frequency of one filter in the MTD filter bank is f ₀ =800Hz, the side lobe limit level ε ₁ =1×10 ^-4 , the weather clutter or strong interference area limit level ε ₂ =1×10 ^-6 , the main The lobe area is extended by 60Hz before and after the center frequency, and the noise power is 1. The interference frequency is 1600Hz, and the interference-to-noise ratio INR=20dB, and the simulation Figure 2 is obtained.

Without considering the weather clutter or strong interference, the center frequency f ₀ =500Hz of the filter is modified, and other parameters remain unchanged. The SOCP method of the present invention is used to design the filter and the 40dB Chebyshev window adding method is used respectively. Design the filter and get the simulation Figure 3.

Other parameters remain unchanged, the center frequency of the filter is close to zero frequency, f ₀ =80Hz, the SOCP method of the present invention is used to design the filter, the 40dB Chebyshev window method is used to design the filter, and the digital synthesis method is used to design the filter. filter, get the simulation in Figure 4.

Considering meteorological clutter or strong interference, other parameters remain unchanged, the center frequency of the filter is further closer to the zero frequency f ₀ =60Hz, and a deep notch with a width of 200Hz is formed near the interference frequency 1600Hz. The SOCP method is used to design the filter, the 40dB Chebyshev window method is used to design the filter, and the digital synthesis method is used to design the filter, and the simulation diagram 5 is obtained.

2. Simulation content and result analysis:

FIG. 2 is a spectrum diagram of an MTD filter designed by the method of the present invention. The abscissa represents the Doppler frequency, and the ordinate represents the normalized amplitude value of the filter designed by the present invention. It can be seen from Figure 2 that the filter forms a deep notch of -60dB in the weather clutter or strong interference area, and the side lobe level is controlled at -40dB, so the filter designed by the method of the present invention has a lower side lobe voltage. Flat, and can form deep notches at specified frequencies to suppress interference.

3 is a spectrum diagram of a filter designed by the method of the present invention and a filter designed by a 40dB Chebyshev window windowing method without considering meteorological clutter or strong interference. It can be seen from FIG. 3 that the traditional windowing method and the method of the present invention have similar filtering performance when the center frequency is not close to the zero frequency. The essence of designing the MTD filter by the method of the present invention is to solve a second-order cone programming problem, and the interior point method can be used to solve the problem effectively, and the calculation amount is small.

4 is a spectrum diagram of designing a filter using the method of the present invention, the 40dB Chebyshev window windowing method and the digital synthesis method respectively without considering weather clutter or strong interference and the center frequency of the filter is close to zero frequency. As can be seen from Figure 4, the FIR filter designed by the 40dB Chebyshev windowing method has obvious distortion when the center frequency is close to zero frequency, and the performance of the digital synthesis method and the SOCP method of the present invention is relatively stable.

Fig. 5 is the frequency spectrum of adopting the SOCP method of the present invention, the 40dB Chebyshev window windowing method and the digital synthesis method to design the filter under the situation that the center frequency of the filter is further approached to zero frequency in consideration of meteorological clutter or strong interference picture. As can be seen from Figure 4, the FIR filter designed by the 40dB Chebyshev windowing method and the digital synthesis method has obvious distortion, and the center frequency is shifted to the left instead of the set 60Hz. The performance of the method of the invention is relatively stable, and the filter will not be distorted even when the center frequency of the filter is close to the zero frequency. And while limiting the side lobe level, it can freely form deeper notches in the strong interference frequency region or the weather clutter region.

Those of ordinary skill in the art can understand that all or part of the steps of implementing the above method embodiments can be completed by program instructions related to hardware, the aforementioned program can be stored in a computer-readable storage medium, and when the program is executed, the execution includes: The steps of the above method embodiments; and the aforementioned storage medium includes: ROM, RAM, magnetic disk or optical disk and other media that can store program codes.

The above are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention. should be included within the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims (3)

1. a MTD filter bank design method based on second-order cone optimization theory, described MTD filter is used for radar suppression clutter and detection target, it is characterized in that, described method comprises the steps: Step 1, set the working parameters of the radar, the working parameters of the radar include the pulse repetition frequency and the accumulated pulse number of the radar; wherein, the pulse repetition frequency is used to determine the center frequency of each filter in the MTD filter bank, so The number of accumulated pulses is used to determine the order of the MTD filter bank; Step 2, set the radar working scene to include target, ground clutter, interference and noise; obtain the ground clutter power spectrum variance and ground clutter power of the radar working scene, and obtain the covariance matrix of ground clutter; obtain the radar working scene The interference signal frequency and the interference signal power are calculated to obtain the covariance matrix of the interference; the noise power of the radar is obtained, and the covariance matrix of the noise is obtained by calculation; Step 3, obtain a comprehensive covariance matrix of ground clutter, interference and noise according to the covariance matrix of the ground clutter, the covariance matrix of the interference and the covariance matrix of the noise; Step 4, according to the comprehensive covariance matrix of the ground clutter, interference and noise, carry out the first linear constraint on the center frequency of each filter, and obtain the first optimization expression; The step 4 is specifically: According to the comprehensive covariance matrix R of the ground clutter, interference and noise, a first linear constraint is performed on the center frequency of the filter, and the first optimization expression is obtained as follows:

sth ^H a(f ₀ )=1 Among them, h is the weight vector of the filter, f ₀ is the center frequency of the filter, a(f ₀ ) is the pilot frequency vector of the filter at f ₀ ,

N represents the number of array elements contained in the radar antenna, Tr is the radar pulse repetition period,

Represents the value of h when the expression h ^H Rh is the smallest, st represents the constraint condition, and the superscript H represents the conjugate transpose; Step 5, set the amplitude-frequency response sidelobe limit level of the filter, and the weather clutter or interference limit level, carry out secondary constraints to the first optimization expression, and obtain the second optimization expression; The step 5 is specifically: Set the amplitude-frequency response sidelobe limit level ε ₁ of the filter, and the weather clutter or interference limit level ε ₂ , and perform quadratic constraints on the first optimization expression, and obtain the second optimization expression as follows:

sth ^H a(f ₀ )=1 ||h ^H a(f _i )|| ² ≤ε ₁ i=1, 2,...,K ||h ^H a(f _j )|| ² ≤ε ₂ j=K+1,2,...,L Among them, h is the weight vector of the filter, f ₀ is the center frequency of the filter, a(f ₀ ) is the pilot frequency vector of the filter at f ₀ ,

Represents the value of h when the expression h ^H Rh is the smallest, st represents the constraint condition, f _i represents the ith sampling frequency of the filter side lobe region, i=1, 2, ..., K, K represents the total filter side lobe region The _number of _{sampling frequencies} of the The total number of sampling frequencies in the filter sidelobe region and the interference region, a(f _j ) represents the pilot vector of the interference signal at the frequency f _j , ||·|| ² represents the square of the modulo value; Step 6, the second optimization expression is converted into a second-order cone programming real number expression, and the second-order cone programming real number expression is solved to obtain the weight vector of the filter; thereby obtain each in the MTD filter bank. the weight vector of the filter; The step 6 is specifically: (6a) Perform Cholesky decomposition on the comprehensive covariance matrix R of the ground clutter, interference and noise to obtain R=U ^H U, where U represents the decomposition matrix, let τ be the first intermediate variable, and ||Uh| |≤τ; Then the second optimized expression is converted into the following third optimized expression:

sth ^H a(f ₀ )=1 ||Uh||≤τ ||h ^H a(f _i )|| ² ≤ε ₁ i=1, 2,...,K ||h ^H a(f _j )|| ² ≤ε ₂ j=K+1,2,...,L in,

Represents the value of τ and h when τ is minimized, and ||·|| ² represents the square of the modulus value; (6b) Let the second intermediate variable y=[y ₁ , y ₂ , y ₃ , y ₄ ^T ] ^T , the third intermediate variable y ₁ =τ, the fourth intermediate variable

fifth intermediate variable

sixth intermediate variable y ₄ =h; Then the third optimization expression is simplified to the following second-order cone programming expression:

sth ^H a(f ₀ )=1

||Uy ₄ ||≤y ₁ ||h ^H a(f _i )||≤y ₂ i=1, 2,...,K ||h ^H a(f _j )||≤y ₃ j=K+1,2,...,L in,

Indicates the value of y when y ₁ is minimized, and || · || represents the modulo value; (6c) Convert the second-order cone programming expression into a second-order cone programming real expression: Let the seventh intermediate variable

Eighth Intermediate Variable

Ninth Intermediate Variable

Tenth Intermediate Variable

If the variable l=0, 1, ..., L, the following equivalent relation can be obtained according to the second-order cone programming expression:

and let the eleventh intermediate variable

The twelfth intermediate variable b=[1, 0, ^.

in,

means to make

the smallest

value; (6d) Solve the real number expression of the second-order cone programming to obtain the weight vector h of the filter, so as to determine the MTD filter bank. 2. a kind of MTD filter bank design method based on second-order cone optimization theory according to claim 1, is characterized in that, in described step 2, obtains the jamming signal frequency and jamming signal power of radar working scene, calculates to obtain The covariance matrix of interference; obtain the noise power of the radar, and calculate the covariance matrix of the noise, which includes the following sub-steps: (2a) Obtain the jamming signal frequency f _p and jamming signal power of the radar working scene

Calculate the covariance matrix of the interference

Among them, a(f _p ) is the pilot frequency vector of the interference signal at the frequency f _p of the interference signal, and the superscript H represents the conjugate transpose; (2b) Obtain the noise power δ _n ² of the radar, and calculate the covariance matrix R _n =δ _n ² I of the noise; wherein, I represents the identity matrix. 3. a kind of MTD filter bank design method based on second-order cone optimization theory according to claim 1, is characterized in that, described step 3 is specifically: According to the covariance matrix R _c of the ground clutter, the covariance matrix R _i of the interference and the covariance matrix R _n of the noise, the comprehensive covariance matrix R of the ground clutter, interference and noise is obtained:

Among them, δ _n ² represents the noise power of the radar, I represents the identity matrix,

represents the power of the interference signal, a(f _p ) is the pilot vector of the interference signal at the frequency f _p of the interference signal, and the superscript H represents the conjugate transpose.

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