Method and system for extracting poles of multiple radar targets based on short-time matrix pencil method

Abstract

The invention discloses a method and a system for extracting poles of multiple radar targets based on a short-time matrix beam method, relates to the technical field of radar target identification, and aims to solve the problem that the existing matrix beam method is suitable for extracting poles from time domain echo data of a single target, and when multiple targets exist in the incident direction of radar electromagnetic waves, the extracted poles are disordered and unsystematic. In order to solve the problems that in the prior art, in the prior art, the pole information of each target cannot be reflected, one-dimensional range profile information and a short-time matrix method are combined, the pole information between the targets can be distinguished on a time-frequency diagram through the one-dimensional range profile information, and extraction of the pole information of each target in the incident direction of radar electromagnetic waves is facilitated.

Description

Technical Field

[0001] The present invention relates to the technical field of radar target recognition, in particular to a method and system for extracting poles of multiple radar targets based on a short-time matrix bundle method. Background Art

[0002] The natural resonance of a target is considered to be an electrical property. Different targets have different electrical properties, and the target can be identified by this electrical property. By irradiating a target as a scatterer with a short pulse, the various natural resonances of the target can be excited. The scattered energy generated by the induced current or magnetic induced current on the scatterer consists of two different parts: early response and late response, which correspond to two different phenomena. The early response corresponds to the specular reflection generated by the local scattering center of the scatterer. This specular reflection is very sensitive to the incident angle and is not suitable for target identification. In contrast, the late response corresponds to the global resonance generated after the detection pulse completely passes through the target. These complex natural resonances (CNRs) are independent of direction and only related to the geometric and physical properties of the object, which are very suitable for target identification. In order to identify the target, it is necessary to extract these complex natural resonances that reflect the characteristics of the target.

[0003] The matrix beam method (MPM) is a commonly used method for extracting complex natural resonance frequencies. However, its disadvantage is that it requires the prediction of the start time of the late response. The matrix beam method operates on the late response of the target echo, which requires the early response and late response of the target echo to be distinguished in advance. The late response can be regarded as the sum of a series of exponential functions, and the information it carries is only related to the object itself. In addition, in practical applications, the real part of CNRs is highly sensitive to noise, which will affect the extraction of pole information, or more accurately, the real part of the pole information. Compared with the real part, the imaginary part is less affected by noise. Compared with the matrix beam method, the short-time matrix beam method can avoid these shortcomings to some extent.

[0004] The commonly used matrix beam method is suitable for extracting poles from the time domain echo data of a single target. When there are multiple targets in the incident direction of the radar electromagnetic wave, the extracted poles are disorganized and cannot reflect the pole information of each target. Summary of the invention

[0005] The purpose of the present invention is to propose a method and system for extracting poles of multiple radar targets based on the short-time matrix beam method, aiming at the existing matrix beam method, which is suitable for extracting poles from time-domain echo data of a single target. When there are multiple targets in the incident direction of radar electromagnetic waves, the extracted poles are disorderly and cannot reflect the pole information of each target.

[0006] The technical solution adopted by the present invention to solve the above technical problems is:

[0007] The method for extracting the poles of multiple radar targets based on the short-time matrix beam method comprises the following steps:

[0008] Step 1: Obtain the frequency domain echo signal of the target group in the incident direction of the radar electromagnetic wave, and use the inverse Fourier transform to obtain the time domain echo signal of the target group;

[0009] Step 2: Based on the time domain echo signal of the target group, a sliding time window is introduced. Then, on the entire time domain echo signal, the time window is moved at intervals of a set time step, and the matrix bundle method is used to obtain multiple groups of poles and the residuals corresponding to the poles;

[0010] Step 3: Combine each group of poles and the residuals corresponding to the poles to obtain time-frequency space information;

[0011] Step 4: Based on the time-frequency-space information, select the poles that converge to a straight line and use them as the pole extraction results of the radar target.

[0012] Furthermore, the frequency domain echo signal of the target group is expressed as:

[0013]

[0014] Among them, S r (w) and S(w) represent the frequency domain forms of the echo signal and the transmitted signal respectively, U1(W) and U2(w) represent the frequency domain forms of u1(t) and u2(t) respectively, u1(t) and u2(t) represent the modulation of the transmitted signal by the first and second objects respectively, R1 represents the distance between the first object and the transmitting source, R represents the distance between the two objects in the incident direction of the radar electromagnetic wave, j represents the imaginary unit, w represents the angular frequency, and c represents the speed of light.

[0015] Furthermore, the time domain echo signal of the target group is expressed as:

[0016]

[0017] Among them, s1(t) and s2(t) represent the echo signals of the first and second objects respectively.

[0018] Furthermore, the specific steps of step 2 are:

[0019] First, a time-dependent constant of length T is applied along the time direction. w The sliding window is used to intercept the signal starting from time T in the time domain echo signal. Then the late response y after windowing is T (t) is expressed as:

[0020]

[0021] Then, the matrix bundle method is applied to each window response, and the windowed late response y is calculated on a logarithmic scale. T The residual information of (t) is expressed as:

[0022]

[0023] in, Represents the residual information of the i-th order pole of the windowed signal, α i Indicates the attenuation of the signal, w i The imaginary resonant frequency representing the pole information, Re represents the real part, and t represents T and T+T w Any moment in between.

[0024] Furthermore, the residual information of the i-th order pole of the windowed signal It is expressed as:

[0025]

[0026] Among them, S i represents the i-th order pole of the signal, R i Represents the residual information of the i-th order pole.

[0027] A pole extraction system for multiple radar targets based on a short-time matrix beam method, the system comprising an echo signal module, a time window module and a pole extraction module;

[0028] The echo signal module is used to obtain the frequency domain echo signal of the target group in the incident direction of the radar electromagnetic wave, and obtain the time domain echo signal of the target group by inverse Fourier transforming the frequency domain echo signal of the target group;

[0029] The time window module is used to introduce a sliding time window based on the time domain echo signal of the target group, and then move the time window on the entire time domain echo signal at intervals of a set time step, and use a matrix bundle method to obtain multiple groups of poles and residuals corresponding to the poles;

[0030] The pole extraction module is used to combine each group of poles and the residuals corresponding to the poles to obtain time-frequency space information, and based on the time-frequency space information, select the poles that converge to a straight line and use them as the pole extraction results of the radar target.

[0031] Furthermore, the frequency domain echo signal of the target group is expressed as:

[0032]

[0033] Among them, S r(w) and S(w) represent the frequency domain forms of the echo signal and the transmitted signal respectively, U1(W) and U2(w) represent the frequency domain forms of u1(t) and u2(t) respectively, u1(t) and u2(t) represent the modulation of the transmitted signal by the first and second objects respectively, R1 represents the distance between the first object and the transmitting source, R represents the distance between the two objects in the incident direction of the radar electromagnetic wave, j represents the imaginary unit, w represents the angular frequency, and c represents the speed of light.

[0034] Furthermore, the time domain echo signal of the target group is expressed as:

[0035]

[0036] Among them, s1(t) and s2(t) represent the echo signals of the first and second objects respectively.

[0037] Furthermore, the time window module specifically performs the following steps:

[0038] First, a time-dependent constant of length T is applied along the time direction. w The sliding window is used to intercept the signal starting from time T in the time domain echo signal. Then the late response y after windowing is T (t) is expressed as:

[0039]

[0040] Then, the matrix bundle method is applied to each window response, and the windowed late response y is calculated on a logarithmic scale. T The residual information of (t) is expressed as:

[0041]

[0042] in, Represents the residual information of the i-th order pole of the windowed signal, α i Indicates the attenuation of the signal, w i The imaginary resonant frequency representing the pole information, Re represents the real part, and t represents T and T+T w Any moment in between.

[0043] Furthermore, the residual information of the i-th order pole of the windowed signal It is expressed as:

[0044]

[0045] Among them, S i represents the i-th order pole of the signal, R i Represents the residual information of the i-th order pole.

[0046] The beneficial effects of the present invention are:

[0047] The present application combines one-dimensional range profile information with the short-time matrix method. The pole information between each target can be distinguished on the time-frequency diagram through the one-dimensional range profile information, which is more conducive to extracting the pole information of each target in the incident direction of the radar electromagnetic wave. BRIEF DESCRIPTION OF THE DRAWINGS

[0048] Figure 1 It is frequency domain data between 0.01GHz and 5GHz;

[0049] Figure 2 is the time domain data obtained after inverse Fourier transform;

[0050] Figure 3 The pole diagram is obtained by using the matrix bundle method to extract pole information using the entire time domain data;

[0051] Figure 4 is the time-frequency space diagram of the imaginary part of the pole;

[0052] Figure 5 It is a time-frequency space diagram of the residual logarithm;

[0053] Figure 6 A schematic diagram of two spheres with radii of 0.075m and 0.05m placed 2m apart in the incident direction of electromagnetic waves;

[0054] Figure 7 This is a frequency domain data diagram of two spheres with radii of 0.075m and 0.05m placed 2m apart in the incident direction of the electromagnetic wave;

[0055] Figure 8 This is a schematic diagram of time domain data of two spheres with radii of 0.075m and 0.05m placed 2m apart in the incident direction of electromagnetic waves;

[0056] Fig. 9 The spectrum diagrams are of two conducting spheres with different radii;

[0057] Fig.10 is the polar diagram of two conducting spheres of different radii;

[0058] Fig.11 It is a schematic diagram of the imaginary part of the pole with the time domain waveform in the relationship between the imaginary part of the pole and the time index;

[0059] Fig.12 It is a schematic diagram of the imaginary part of the pole obtained after processing the relationship between the imaginary part of the pole and the time index;

[0060] Fig.13 It is a schematic diagram of the imaginary part of the pole of a sphere with a radius of 0.075 meters;

[0061] Fig.14 It is a schematic diagram of the imaginary part of the pole of a sphere with a radius of 0.05 meters;

[0062] Fig.15 It is a schematic diagram of the relationship between the logarithm of the residual of the extreme point and the time index in the entire time domain;

[0063] Fig.16 It is a schematic diagram of a conducting sphere with a radius of 0.075 meters;

[0064] Fig.17 Schematic diagram of a conducting sphere with a radius of 0.05 meters. DETAILED DESCRIPTION

[0065] It should be particularly noted that, in the absence of conflict, the various embodiments disclosed in this application can be combined with each other.

[0066] Specific implementation method 1: The method for extracting the poles of multiple radar targets based on the short-time matrix beam method described in this implementation method includes the following steps:

[0067] Step 1: Obtain the frequency domain echo signal of the target group in the incident direction of the radar electromagnetic wave, and use the inverse Fourier transform to obtain the time domain echo signal of the target group;

[0068] Take two targets in the incident direction of the radar electromagnetic wave as an example. This two-target model is used in the following analysis. Assuming that the transmitted signal is s(t), the two objects are separated by R in the incident direction of the radar electromagnetic wave, and the distance between the first object and the transmitting source is R1, then the received echo signal s r The time domain expression of (t) can be expressed as:

[0069]

[0070] Among them, s1(t) and s2(t) represent the echo signals of the first and second objects respectively, and u1(t) and u2(t) represent the modulation of the first and second objects on the transmitted signal respectively.

[0071] Echo signal r The frequency domain expression of (t) is s r (w) is:

[0072]

[0073] Among them, S r (w) and S(w) represent the frequency domain forms of the echo signal and the transmitted signal, respectively. U1(W) and U2(w) are the frequency domain forms of u1(t) and u2(t), respectively. The third term It is only related to the distance R between the two objects in the incident direction of the radar electromagnetic wave, and affects the envelope of the echo signal. Looking only at the amplitude of the third term, it can be expressed as:

[0074]

[0075] From the frequency domain expression, we can know that the amplitude of the group target echo signal in the frequency domain can be expressed as a signal whose envelope is a cosine signal. From the time domain expression, we can know that the group target echo signal s r (t) can be represented in the time domain as the superposition of two transmitted signals s1(t) and s2(t) after being modulated by the target.

[0076] Step 2: Based on the time domain echo signal of the target group, a sliding time window is introduced, and then the time window is moved at intervals of the set time step on the entire time domain echo signal, and the matrix bundle method is used to obtain multiple groups of poles and the residuals corresponding to the poles;

[0077] Step 3: The multiple groups of poles and the residuals corresponding to the poles obtained in step 2 are processed in time order to obtain the time-frequency space information of each group of poles and residuals and time indicators;

[0078] The combination of each set of poles and residuals obtained in step 2 and the time index on the corresponding time period can form a time-frequency space. The late time starts when the extracted poles converge to a stable value, and the residual of the complex natural resonance decreases with the time index on a logarithmic scale, and its slope is the real part of the complex natural resonance.

[0079] In general, the signal model of the electromagnetic energy scattering response y(t) of a single object can be expressed as:

[0080]

[0081] Among them, S i is the i-th order pole of the signal, M is the total number of poles in the signal, R i is the residual information of the i-th order pole.

[0082] Take a perfect electrical conductor sphere with a radius of 0.05 meters as an example. Figure 1 and Figure 2 Shown are the frequency domain data between 0.01 GHz and 5 GHz and the time domain data obtained after inverse Fourier transform.

[0083] Use the entire time domain data to perform matrix bundle method to extract pole information, and get Figure 3 The pole diagram is shown in Figure 1. It can be seen from the figure that 5 poles are extracted in this frequency band, 4 of which match the theoretical poles perfectly.

[0084] For the short-time matrix beam method, a matrix with a length of T is applied along the time direction. w The sliding window of the time window intercepts the signal starting from time T in the time domain echo signal, then the late response y after windowing T (t):

[0085]

[0086] in, is the residual information of the i-th order pole of the windowed signal, α i is the real part attenuation factor of the pole information, indicating the attenuation degree of the signal, w i is the imaginary resonance frequency of the pole information. Re represents the real part, and t is T and T+T w Any moment in between.

[0087]

[0088] Then, the matrix bundle method is applied to each window response. In logarithmic scale, the residual information of the late response after windowing is It can be expressed as:

[0089]

[0090] Among them, the logarithmic magnitude of the residual The indicator decreases linearly over time with a slope of α i In order to obtain the damping factor, it is necessary to find the logarithmic slope of the residual on the time-frequency scale.

[0091] The specific operation is as follows: Figure 1 Extract multiple segments from the time domain waveform in Figure 2 The time domain sampling interval in is 0.1ns, which can be divided into 0-5ns, 0.1ns-5.1ns, 0.2ns-5.2ns, and so on. The matrix bundle method is used to extract the poles and the corresponding residual information in each time period, and then the time-frequency space is formed. Figure 4 and Figure 5 The figure shows the time-frequency space formed by the imaginary part of the poles, where time refers to time and frequency refers to the imaginary part of the poles, i.e. the resonant frequency. When the ordinate in the figure is 0, there are 5 corresponding points, representing that 5 poles are extracted from the time period of 0-5ns, and the abscissa is the resonant frequency corresponding to the poles; when the ordinate in the figure is 1.5, there are 4 corresponding points, representing that 4 poles are extracted from the time period of 1.5ns-6.5ns, and the 5th pole is not extracted because of its large attenuation compared to the first 4 poles, and the abscissa is the resonant frequency corresponding to the pole; other cases can be deduced by analogy, the imaginary parts of the poles in different time periods converge to the vertical line in the figure in the time-frequency space, and this vertical line is the imaginary part of the pole of the corresponding object. Figure 5 The figure shows the time-frequency space formed by the logarithmic value of the residual, where time refers to time and frequency refers to the logarithmic value of the residual. When the horizontal axis in the figure is 0, the logarithmic values ​​of the residual corresponding to 5 poles are extracted, and the logarithmic values ​​of the residual in different time periods are fitted into a straight line. A total of 5 straight lines are fitted, and the slope of the straight line is the real part of the target pole.

[0092] Step 4: Analyze and process the time-frequency space of the multiple groups of poles and the corresponding residual data and time indicators obtained in step 3, distinguish the positions of each target pole information, and extract the target pole information at the corresponding position.

[0093] Step 3 gives the short-time matrix bundle method for extracting poles for a single target, such as Figure 4 and Figure 5 As shown in the figure, when the time-frequency space of the imaginary part of the extracted multiple groups of poles can form a stable and convergent vertical line, it means that the time domain data in the corresponding time period is the late response of the target. This phenomenon also applies to the time-frequency space of multiple targets. When the time-frequency space of the imaginary part of the pole converges to a stable vertical line for the first time, it corresponds to the pole information of the first target. Thereafter, as the time window slides, the time window will contain two target responses at the same time. At this time, the time-frequency space of the imaginary part of the pole will diverge and no longer converge to the original vertical line. When the time window slides to contain only the response of the second target, the time-frequency space of the imaginary part of the pole will converge to the new vertical line again, corresponding to the pole of the second target. For a more detailed description, please refer to the description in the specific process (4).

[0094] Taking a model in which two spheres with different radii are placed two meters apart in the direction of incident radar electromagnetic waves (the radius of the sphere placed in front is 0.075 meters, and the radius of the sphere placed in the back is 0.05 meters) as an example, the effect of this application on extracting the pole information of each sphere is demonstrated.

[0095] Specific process:

[0096] (1) The electromagnetic simulation software FEKO can be used to solve various types of electromagnetic field analysis, involving any shape of electrically large objects composed of complex metal and dielectric structures. FEKO software is used to establish a model in which two spheres with different radii are placed two meters apart in the direction of incident radar electromagnetic waves (the radius of the sphere placed in front is 0.075 meters, and the radius of the sphere placed in the back is 0.05 meters); the frequency is set to 0.01 GHz to 5 GHz, the frequency points are set to 500, and the frequency interval is 10 MHz; the electromagnetic wave incident angle is set to θ = 90°, φ = 0°, such as Figure 6 As shown;

[0097] (2) The frequency domain data and time domain data obtained by using the simulation model in (1) are as follows Figure 7and Figure 8 When the two objects are two meters apart in the direction of the transmitted signal, the frequency period of the frequency domain signal envelope can be deduced to be 75MHz according to the formula m(f) in step 1 of Section 4, which is reflected in the frequency domain as 75MHz between the two peaks; accordingly, if the distance between the two targets is unknown in advance, the distance information between the two targets can also be obtained based on the spacing between the peaks of the frequency domain data.

[0098] (3) Reasonably set the length and step of the time window. Now set the length of the time window to 60 times the sampling interval, set the time window moving step to the time domain sampling interval, and use the short-time matrix bundle method to extract the pole information. In order to compare the pole information extracted by the short-time matrix bundle method, we give Fig. 9 and Fig.10 RCS data and pole data of two spheres of corresponding radius are shown.

[0099] (4) Display the multiple sets of pole data obtained in (3) in time sequence in a time-frequency diagram, such as Fig.11 and Fig.12 The figure shows the relationship between the imaginary part of the pole and the time index. The vertical line in the figure represents the imaginary part of the theoretical pole. Fig.11 There are both time domain signals with multiple changes (blue curve) and imaginary part information of the poles, which is to facilitate the observation of the influence of time domain signals on the extracted poles; Fig.12It is the pole imaginary part information after data processing, excluding some unreasonable pole information. The figure can be divided into 4 parts. When the time index is from 0ns to 60ns, the time window changes from containing the first time domain fluctuation part and part of the time domain flat part to only containing the time domain flat part. In this time index period, the change of the pole imaginary part is the same as that of a single object; when the time index is from 60ns to 80ns, the time window contains part of the time domain flat part and the first peak part of the second time domain fluctuation part, and part of the pole imaginary part of the first object begins to converge again. One possible reason is that the first peak part of the second time domain fluctuation part is not caused by the second object but by the first object. It may be that the electromagnetic wave reflected back by the second object re-irradiates the first object. When the time index is from 80ns to 130ns, the time window includes part of the time domain flat part, the first peak part and the second peak part of the second time domain fluctuation part. Although the pole converges, it does not converge to the theoretical pole. This is because the time window includes both the first peak and the second peak of the second time domain fluctuation part. It is speculated that the first peak is caused by the first object, and the second peak is caused by the second object, that is, the time domain waveforms of the two objects are included at the same time, so the pole does not converge to the theoretical pole; after 130ns, only the time domain response of the second object is included, and the changes in the pole extracted by a single object reappear.

[0100] Fig.13 The imaginary part of the pole in corresponds to the imaginary part of the spherical pole with a radius of 0.075 meters. Fig.14 The imaginary part of the pole in corresponds to the imaginary part of the pole of a sphere with a radius of 0.05 meters, which can be compared with the result given in step (3) to verify the accuracy of pole extraction.

[0101] like Fig.15 The figure shows the relationship between the logarithm of the residual error of the pole and the time index. It can still be divided into 4 sections, and the first and last sections are analyzed. The first section corresponds to a conductor sphere with a radius of 0.075 meters. Only the first 5 poles are listed here. The first 4 poles are relatively stable and the straight line fitting effect is better, while the 5th order is more scattered, corresponding to the poor stability of the high-order poles. The tail end corresponds to the case of a radius of 0.05 meters. The straight line fitting effect of the first 4 poles is better, and the fitting effect of the 5th pole is poor.

[0102] Effect comparison: Compared with the matrix bundle method for extracting pole information, the short-time matrix bundle method for extracting pole information is not affected by the number of targets, and the instability of the real part of the high-order pole can be reduced by curve fitting. It is worth noting that in step (4), the change of the imaginary part of the pole with the time domain signal and the specific analysis are given. According to the description in the specific analysis, the step of extracting the pole in the transition part between the two targets in the time domain echo signal can be omitted, thereby further reducing the amount of data.

[0103] The purpose of this application is to solve the problem that when there are multiple targets at the same time in the incident direction of the radar electromagnetic wave, the received echo signal contains the echo signals of multiple targets, which can no longer be expressed as the sum of a series of exponential functions, thereby causing the matrix beam method to fail to extract pole information.

[0104] The late response of a single target can be regarded as the sum of a series of exponential functions. The matrix beam method can extract the attenuation factor and frequency of each exponential function in the late response. However, when there are multiple targets in the incident direction of the radar electromagnetic wave, the matrix beam method fails. The short-time matrix beam method can still extract the pole information on the corresponding time window by moving the time window, that is, it can solve the problem of echo signals of multiple targets in the radar echo signal. For the pole extraction of a single target only, the matrix beam method extracts the entire time domain signal. Although more pole information can be extracted, the extracted high-order poles often have slight deviations due to the instability of the attenuation factor. The short-time matrix beam method divides the time domain signal into multiple segments. By averaging the pole information of multiple segments, the instability of the high-order poles can be reduced. In addition, because the time window of the short-time matrix beam method is sliding, it can be seen that the pole information changes with the change of the time domain waveform, which can indirectly reflect the proportion of each pole in the pole set, providing more favorable conditions for subsequent pole screening.

[0105] It should be noted that the specific implementation is only an explanation and description of the technical solution of the present invention, and cannot be used to limit the scope of protection of the rights. Any partial changes made according to the claims and description of the present invention should still fall within the scope of protection of the present invention.

Claims

1. A method for extracting the poles of multiple radar targets based on the short-time matrix beam method, characterized in that The following steps are included: Step 1: Obtain the frequency domain echo signal of the target group in the incident direction of the radar electromagnetic wave, and use the inverse Fourier transform to obtain the time domain echo signal of the target group; Step 2: Based on the time domain echo signal of the target group, a sliding time window is introduced. Then, on the entire time domain echo signal, the time window is moved at intervals of a set time step, and the matrix bundle method is used to obtain multiple groups of poles and the residuals corresponding to the poles; Step 3: Combine each group of poles and the residuals corresponding to the poles to obtain time-frequency space information; Step 4: Based on the time-frequency-space information, select the poles that converge to a straight line and use them as the pole extraction results of the radar target.

2. The method for extracting the poles of multiple radar targets based on the short-time matrix beam method according to claim 1, characterized in that The frequency domain echo signal of the target group is expressed as: Among them, S r (w) and S(w) represent the frequency domain forms of the echo signal and the transmitted signal respectively, U1(W) and U2(w) represent the frequency domain forms of u1(t) and u2(t) respectively, u1(t) and u2(t) represent the modulation of the transmitted signal by the first and second objects respectively, R1 represents the distance between the first object and the transmitting source, R represents the distance between the two objects in the incident direction of the radar electromagnetic wave, j represents the imaginary unit, w represents the angular frequency, and c represents the speed of light.

3. The method for extracting the poles of multiple radar targets based on the short-time matrix beam method according to claim 2 is characterized in that The time domain echo signal of the target group is expressed as: Among them, s1(t) and s2(t) represent the echo signals of the first and second objects respectively.

4. The method for extracting the poles of multiple radar targets based on the short-time matrix beam method according to claim 1 is characterized in that The specific steps of step 2 are: First, a time-dependent constant of length T is applied along the time direction. w The sliding window is used to intercept the signal starting from time T in the time domain echo signal. Then the late response y after windowing is T (t) is expressed as: Then, the matrix bundle method is applied to each window response, and the windowed late response y is calculated on a logarithmic scale. T The residual information of (t) is expressed as: in, Represents the residual information of the i-th order pole of the windowed signal, α i Indicates the attenuation of the signal, w i The imaginary resonant frequency representing the pole information, Re represents the real part, and t represents T and T+T w Any moment in between.

5. The method for extracting the poles of multiple radar targets based on the short-time matrix beam method according to claim 4 is characterized in that The residual information of the i-th order pole of the windowed signal It is expressed as: Among them, S i represents the i-th order pole of the signal, R i Represents the residual information of the i-th order pole.

6. A pole extraction system for multiple radar targets based on the short-time matrix beam method, characterized in that The system includes an echo signal module, a time window module and a pole extraction module; The echo signal module is used to obtain the frequency domain echo signal of the target group in the incident direction of the radar electromagnetic wave, and obtain the time domain echo signal of the target group by inverse Fourier transforming the frequency domain echo signal of the target group; The time window module is used to introduce a sliding time window based on the time domain echo signal of the target group, and then move the time window on the entire time domain echo signal at intervals of a set time step, and use a matrix bundle method to obtain multiple groups of poles and residuals corresponding to the poles; The pole extraction module is used to combine each group of poles and the residuals corresponding to the poles to obtain time-frequency space information, and based on the time-frequency space information, select the poles that converge to a straight line and use them as the pole extraction results of the radar target.

7. The pole extraction system for multiple radar targets based on the short-time matrix beam method according to claim 6 is characterized in that The frequency domain echo signal of the target group is expressed as: Among them, S r (w) and S(w) represent the frequency domain forms of the echo signal and the transmitted signal respectively, U1(W) and U2(w) represent the frequency domain forms of u1(t) and u2(t) respectively, u1(t) and u2(t) represent the modulation of the transmitted signal by the first and second objects respectively, R1 represents the distance between the first object and the transmitting source, R represents the distance between the two objects in the incident direction of the radar electromagnetic wave, j represents the imaginary unit, w represents the angular frequency, and c represents the speed of light.

8. The pole extraction system for multiple radar targets based on the short-time matrix beam method according to claim 7 is characterized in that The time domain echo signal of the target group is expressed as: Among them, s1(t) and s2(t) represent the echo signals of the first and second objects respectively.

9. The pole extraction system for multiple radar targets based on short-time matrix beam method according to claim 1 is characterized in that The time window module specifically performs the following steps: First, a time-dependent constant of length T is applied along the time direction. w The sliding window is used to intercept the signal starting from time T in the time domain echo signal. Then the late response y after windowing is T (t) is expressed as: Then, the matrix bundle method is applied to each window response, and the windowed late response y is calculated on a logarithmic scale. T The residual information of (t) is expressed as: in, Represents the residual information of the i-th order pole of the windowed signal, α i Indicates the attenuation of the signal, w i The imaginary resonant frequency representing the pole information, Re represents the real part, and t represents T and T+T w Any moment in between.

10. The pole extraction system for multiple radar targets based on short-time matrix beam method according to claim 9, characterized in that The residual information of the i-th order pole of the windowed signal It is expressed as: Among them, S i represents the i-th order pole of the signal, R i Represents the residual information of the i-th order pole.

Images