A multipath ghost suppression method for UAV-mounted through-wall radar based on frequency domain filtering

Abstract

The present invention discloses a multipath ghost suppression method for a UAV-mounted through-wall radar based on frequency domain filtering, comprising: proposing a multipath ghost suppression method based on azimuth frequency domain filtering. Multipath reflection of electromagnetic waves indoors can lead to multipath ghosts in the imaging results, causing false alarms and seriously affecting the performance of moving target detection. In order to solve this problem, the present invention analyzes the difference between multipath echoes and direct path echoes in the range Doppler domain: multipath echoes appear as high-frequency components in the range Doppler domain. Then, a multipath clutter suppression method based on azimuth frequency domain filtering is proposed. Finally, the detection and imaging of moving targets inside buildings is realized by a back-projection algorithm. The present invention simulates and verifies the effectiveness and robustness of the proposed method. Compared with other ghost suppression methods, the present invention achieves multipath ghost suppression without destroying the phase information of the moving target, providing technical support for the detection and positioning of moving targets inside buildings.

Description

Technical Field

[0001] The present invention relates to the field of radar signal processing, and in particular to a method for suppressing multipath ghosting of a through-wall radar carried by an unmanned aerial vehicle. Background Art

[0002] Through-the-wall radar uses electromagnetic waves in the L / S band to detect dangerous moving targets indoors, and has been widely used in urban street fighting, rescue, law enforcement and arrest. Multi-channel through-the-wall radar on drones takes advantage of the flexible deployment, rapid response and wide-area coverage of drones to achieve long-range, precise, non-contact detection and positioning of moving targets, and is particularly suitable for complex environments and inaccessible areas. However, multiple reflections of electromagnetic waves in closed spaces may cause false targets to appear in the imaging results, thereby generating false alarms. The multipath ghost suppression method for through-the-wall radar on drones proposed in the present invention aims to propose a technology that can retain the energy of moving targets while suppressing multipath ghosts and reducing the false alarm rate of indoor moving target detection.

[0003] In recent years, the problem of suppressing multipath ghosting has received great attention. The existing research methods in academia can be divided into three categories. The first type of method is based on multipath utilization. For example, P. Setlur et al. mapped the multipath ghost back to the real imaging position of the target by applying specific weighting functions and point spread functions. The second type of method relies on the theoretical framework of compressed sensing. The core concept of this type of method is to utilize the group sparsity of multipath components during signal transmission to achieve accurate reconstruction of scenes in complex environments and effectively distinguish between real targets and multipath interference caused by obstacles such as walls. The third type of method utilizes the azimuth-related characteristics of ghosts. This type of method includes multipath ghost suppression based on array rotation, multi-angle observation, and sub-aperture image fusion.

[0004] Multipath mitigation methods based on multipath utilization and compressed sensing theoretical frameworks require high accuracy of the multipath model and are computationally complex, thus facing challenges in real-time imaging applications. Ghost mitigation methods that exploit azimuth-correlation characteristics can significantly suppress multipath ghosting when imaging stationary targets. However, since the imaging results of moving targets are also dependent on the position of the antenna array, these methods will lose some energy from the moving target, thereby reducing the signal-to-noise ratio.

[0005] Based on the above research, we believe that existing methods mainly focus on multipath ghost suppression for stationary target imaging and do not consider how to separate moving targets from ghosts. To address this issue, we propose a new multipath ghost suppression method. Our method first analyzes that multipath echoes appear as high-frequency signals in the range Doppler domain. Then, through frequency domain filtering and back projection (BP) techniques, we filter out multipath signals and image moving targets. Simulation results show that the proposed method can improve the signal-to-noise ratio of the imaging results. Summary of the Invention

[0006] The present invention provides a method for suppressing multipath ghosting of a UAV-mounted through-wall radar based on frequency domain filtering, which can solve the difficult technical problem of false alarms caused by multipath ghosting generated by multiple reflections of electromagnetic waves in a closed space when the UAV-mounted through-wall radar detects indoor moving targets.

[0007] A method for suppressing multipath ghosting of an airborne through-wall radar based on frequency domain filtering, comprising:

[0008] Step S1: obtaining raw data of a moving target echo from a wall-penetrating radar carried by a UAV, performing range compression on the raw data, and transforming the range-compressed echo data into a range Doppler domain through an azimuth Fourier transform;

[0009] Step S2: construct a low-pass filter using a rectangular gate function, set a suitable cutoff frequency, and multiply the rectangular gate function by the echo signal in the range-Doppler domain to filter out multipath signals;

[0010] Step S3: The frequency domain filtering result is transformed into the two-dimensional time domain through the azimuth inverse Fourier transform, and the BP algorithm is used to complete the imaging of the moving target.

[0011] The specific method of step S1 is:

[0012] Consider a closed space surrounded by four walls. The front and back walls are parallel to the x-axis, the left and right side walls are parallel to the y-axis, and the inner surface of the right wall is at x = x. w The target P is located in a closed space, and its azimuth and range velocities are v x and v y The dual-channel radar onboard a UAV flies along the x-axis at a speed of V. The antenna array consists of a transmitting antenna and two receiving antennas. The antenna elements are evenly spaced along the x-axis, and the element spacing is d. Let the slow time moment t a = 0, the transmitting antenna is at the origin, the coordinates of the target P are (x0, y0), and the coordinates of the mirror image point P1 of point P on the right wall are (2x w -x0,y0). t a At this moment, the position of the transmitting antenna is (Vt a ,0), the position of the receiving antenna n(n∈{1,2}) is (Vt a -nd,0). The radar transmits a linear frequency modulation signal

[0013]

[0014] where rect(·), t, T p 、f c , K rRepresent the gate function, fast time variable, pulse width, signal center frequency and modulation frequency respectively. The echo signal received by the radar consists of direct path echo and multipath echo, which can be expressed as

[0015] s r,n (t,t a )=s D,n (t,t a )+s M,n (t,t a ) (2)

[0016] Among them, s D,n (t,t a ) and s M,n (t,t a ) are the range compression results of the direct path echo and the first-order side wall multipath echo received by the nth receiving antenna, respectively.

[0017] In step S1, the specific method for further analyzing the signal propagation path lengths of the direct path echo and the multipath echo is:

[0018] Compared with the distance between the radar and the target, the radar channel spacing d is very small. According to the equivalent phase center principle, the propagation path length of the direct path echo can be obtained as

[0019]

[0020] Then the direct path echo is

[0021]

[0022] where w D,n (t a ) is the azimuth gate function of the direct path echo, B = K r T p is the signal bandwidth, c is the speed of light, λ=c / f c is the wavelength corresponding to the center frequency. Without loss of generality, here we only consider the multipath echo generated by the right wall reflection, and its signal propagation path length is

[0023]

[0024] The multipath echo is

[0025]

[0026] where w M,n (t a ) is the azimuth gate function of the multipath echo on the right wall. Taylor expansion of (3) yields

[0027]

[0028] in

[0029]

[0030] Similarly, Taylor expansion of (5) yields

[0031]

[0032] in

[0033]

[0034] In step S1, the specific method of suppressing the stationary target echo in the echo data is:

[0035] The dual-channel echo data is processed by the Displaced Phase Center Antenna (DPCA) to eliminate the stationary target, so that the direct path echo only contains the moving target echo. At this time, the received echo signal consists of the moving target echo and the multipath echo. After distance compression, it can be expressed as

[0036]

[0037] In step S1, the specific method of transforming the echo data after range compression into the range Doppler domain to further analyze the characteristic differences between the direct path echo and the multipath echo is:

[0038] Transform (11) to Fourier transform.

[0039]

[0040] According to the stationary phase principle, the expression of echo data in the range Doppler domain can be obtained as follows:

[0041]

[0042] in and They are the azimuth gate functions of the direct path echo and multipath echo in the range Doppler domain, and the corresponding Doppler center frequencies are and Substituting (8) and (10) into the Doppler center frequency expressions of the direct path echo and multipath echo respectively, we can obtain

[0043]

[0044] Since x0<2x w -x0, x0<R1<R2 and the target speed is much smaller than the platform speed, so

[0045] f D,c ≈0(16)

[0046]

[0047] That is, the Doppler center frequency of the direct path echo is approximately 0, while the Doppler center frequency of the multipath echo corresponds to a larger value. In other words, the direct path echo mainly appears as a low-frequency signal in the range Doppler domain, while the multipath echo mainly appears as a high-frequency signal. This conclusion can be further verified by analyzing the range migration characteristics of the direct path echo and the multipath echo. From (13), it can be seen that the fast time variable t is the azimuth frequency f a The range migration increases with increasing Doppler frequency. When the radar approaches the right wall, the first-order ghost reflection path generated by the right wall disappears; correspondingly, when the radar approaches the left wall, the first-order ghost reflection path generated by the left wall disappears. Therefore, after range compression, the multipath echo gradually weakens and disappears as it approaches the lowest point of the parabola. In the range-Doppler domain, the energy of the multipath reflection is primarily concentrated in areas exhibiting large range migration characteristics, manifesting as high-frequency components. Conversely, the low-frequency portion of the echo signal primarily originates from the direct path echo.

[0048] The specific method of step S2 is:

[0049] We suppress multipath signals by performing low-pass filtering in the range Doppler domain. The ideal low-pass filter is represented by a gate function in the frequency domain.

[0050]

[0051] Among them F z is the cutoff frequency, which needs to be set empirically according to the changes in pulse repetition frequency and imaging scene. Multiply (13) by (18) to get

[0052]

[0053] After filtering, the direct path signal is retained, while the multipath signal is suppressed.

[0054] The specific method of step S3 is:

[0055] The frequency domain filtering result is transformed into the two-dimensional time domain through the azimuth inverse Fourier transform, and the BP algorithm is used to complete the imaging of the moving target. filter,n (t,f a ) performs an inverse Fourier transform in azimuth direction to obtain an echo expression similar to (4), except that the gate function is narrower. Let the coordinates of the projected pixel be (x, y), then the distance from the pixel to the antenna is

[0056]

[0057] Taylor expansion of (20) yields

[0058]

[0059] in

[0060]

[0061] The BP imaging result is

[0062]

[0063] According to the stationary phase principle,

[0064]

[0065] From (24), we can see that the larger the difference between q2 and a2, the wider the gate function, that is, the more serious the defocus of the imaging result. Let q1-a1=0, and the azimuth imaging position center is

[0066]

[0067] where v r =(v x x0+v y y0) / R0 is the radial velocity of the target, t a = 0 when the slant distance between the moving target and the radar. Therefore, the imaging position in the range direction is

[0068]

[0069] When v x =v y =0, that is, when P is a stationary target, from (25) and (26) we can get x=x0, y=y0, that is, the imaging position of the stationary target is its real position.

[0070] Beneficial effects:

[0071] (1) The present invention proposes a method for suppressing multipath ghosting in UAV-mounted through-wall radars based on frequency domain filtering, which is different from traditional multipath ghosting suppression technologies. This technology does not require complex calculations and large amounts of data processing, has higher processing efficiency, and can quickly achieve multipath ghosting suppression;

[0072] (2) The present invention proposes a method for suppressing multipath ghosting of UAV-mounted wall-penetrating radar based on frequency domain filtering, which is different from the traditional multipath ghosting suppression technology. The UAV-mounted radar used in this technology can perform large-scale search and detection. This makes the technology not restricted by the ground environment, floor height, etc., and has a very large effective search range;

[0073] (3) This invention proposes a method for suppressing multipath ghosting in UAV-mounted through-wall radars based on frequency domain filtering. This method is different from traditional multipath ghosting suppression techniques. This method does not require image multiplication, preserves the phase information of moving targets, and is more conducive to the positioning of moving targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 A flow chart of a method for suppressing multipath ghosting of a UAV-mounted through-wall radar based on frequency domain filtering provided by the present invention;

[0075] Figure 2 This is a schematic diagram of the modeling method for multipath ghost suppression of UAV-mounted wall-penetrating radar based on frequency domain filtering provided by the present invention;

[0076] Figure 3 A schematic diagram of the radar antenna array structure of a multipath ghost suppression method for UAV-mounted through-wall radar based on frequency domain filtering provided by the present invention;

[0077] Figure 4 A schematic diagram of a simulation scenario for a method for suppressing multipath ghosting of a UAV-mounted wall-penetrating radar based on frequency domain filtering provided by the present invention;

[0078] Figure 5 This is a schematic diagram of the results of a multipath ghost suppression method for UAV-mounted wall-penetrating radar based on frequency domain filtering provided by the present invention. DETAILED DESCRIPTION

[0079] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0080] like Figure 1 The method for suppressing multipath virtual images of a UAV-mounted through-wall radar based on frequency domain filtering is shown, comprising:

[0081] Step S1: Obtain the raw data of the moving target echo from the UAV-mounted wall-penetrating radar, perform range compression on the raw data, and transform the range-compressed echo data into the range Doppler domain through azimuth Fourier transform. The specific method is as follows:

[0082] Consider a closed space surrounded by four walls, such as Figure 2 The front and back walls are parallel to the x-axis, the left and right side walls are parallel to the y-axis, and the inner surface of the right wall is at x=x w The target P is located in a closed space, and its azimuth and range velocities are v x and v y The dual-channel radar on the UAV flies along the x-axis at a speed of V. Figure 3 As shown, the antenna array consists of one transmitting antenna and two receiving antennas. The antenna elements are evenly spaced along the x-axis, and the element spacing is d. a= 0, the transmitting antenna is at the origin, the coordinates of the target P are (x0, y0), and the coordinates of the mirror image point P1 of point P on the right wall are (2x w -x0,y0). t a At this moment, the position of the transmitting antenna is (Vt a ,0), the position of the receiving antenna n(n∈{1,2}) is (Vt a -nd,0). The radar transmits a linear frequency modulation signal

[0083]

[0084] where rect(·), t, T p 、f c , K r Represent the gate function, fast time variable, pulse width, signal center frequency and modulation frequency respectively. The echo signal received by the radar consists of direct path echo and multipath echo, which can be expressed as

[0085] s r,n (t,t a )=s D,n (t,t a )+s M,n (t,t a ) (28)

[0086] where s D,n (t,t a ) and s M,n (t,t a ) are the range compression results of the direct path echo and the first-order side wall multipath echo received by the nth receiving antenna, respectively.

[0087] Compared with the distance between the radar and the target, the radar channel spacing d is very small. According to the equivalent phase center principle, the propagation path length of the direct path echo can be obtained as

[0088]

[0089] Then the direct path echo is

[0090]

[0091] where w D,n (t a ) is the azimuth gate function of the direct path echo, B = K r T p is the signal bandwidth, c is the speed of light, λ=c / f c is the wavelength corresponding to the center frequency. Without loss of generality, here we only consider the multipath echo generated by the right wall reflection, and its signal propagation path length is

[0092]

[0093] The multipath echo is

[0094]

[0095] where w M,n (t a ) is the azimuth gate function of the multipath echo on the right wall.

[0096] Expand (29) by Taylor to get

[0097]

[0098] in

[0099]

[0100] Similarly, Taylor expansion of (31) yields

[0101]

[0102] in

[0103]

[0104] The dual-channel echo data can be processed by the Displaced Phase Center Antenna (DPCA) to eliminate the stationary target, so that the direct path echo only contains the moving target echo. At this time, the received echo signal consists of the moving target echo and the multipath echo. After distance compression, it can be expressed as

[0105]

[0106] We transform the echo data after range compression into the range Doppler domain to further analyze the characteristic differences between the direct path echo and the multipath echo, and transform the azimuth Fourier transform of (37) to obtain

[0107]

[0108] According to the stationary phase principle, the expression of echo data in the range Doppler domain can be obtained as follows:

[0109]

[0110] in and They are the azimuth gate functions of the direct path echo and multipath echo in the range Doppler domain, and the corresponding Doppler center frequencies are and Substituting (34) and (36) into the Doppler center frequency expressions of the direct path echo and multipath echo respectively, we can obtain

[0111]

[0112] Since x0<2x w -x0, x0<R1<R2 and the target speed is much smaller than the platform speed, so

[0113] f D,c ≈0(42)

[0114]

[0115] That is, the Doppler center frequency of the direct path echo is approximately 0, while the Doppler center frequency of the multipath echo corresponds to a larger value. In other words, the direct path echo appears primarily as a low-frequency signal in the range Doppler domain, while the multipath echo appears primarily as a high-frequency signal.

[0116] This conclusion can be further verified by analyzing the range migration characteristics of direct path echo and multipath echo. From (39), we can see that the fast time variable t is the azimuth frequency f a The range migration increases with increasing Doppler frequency. When the radar approaches the right wall, the first-order ghost reflection path generated by the right wall disappears; correspondingly, when the radar approaches the left wall, the first-order ghost reflection path generated by the left wall disappears. Therefore, after range compression, the multipath echo gradually weakens and disappears as it approaches the lowest point of the parabola. In the range-Doppler domain, the energy of the multipath reflection is primarily concentrated in areas exhibiting large range migration characteristics, manifesting as high-frequency components. Conversely, the low-frequency portion of the echo signal primarily originates from the direct path echo.

[0117] Step S2: Use the rectangular gate function to construct a low-pass filter, set a suitable cutoff frequency, and multiply the rectangular gate function by the echo signal in the range Doppler domain to filter out the multipath signal. The specific method is as follows:

[0118] We suppress multipath signals by performing low-pass filtering in the range Doppler domain. The ideal low-pass filter is represented by a gate function in the frequency domain.

[0119]

[0120] Among them F z is the cutoff frequency, which needs to be set empirically according to the changes in pulse repetition frequency and imaging scene. Multiply (39) by (44) to get

[0121]

[0122] After filtering, the direct path signal is retained, while the multipath signal is suppressed.

[0123] Step S3: transform the frequency domain filtering result into the two-dimensional time domain through the azimuth inverse Fourier transform, and use the BP algorithm to complete the imaging of the moving target. The specific method is as follows:

[0124] The frequency domain filtering result is transformed into the two-dimensional time domain through the azimuth inverse Fourier transform, and the BP algorithm is used to complete the imaging of the moving target. filter,n (t,f a ) performs an azimuth inverse Fourier transform to obtain an echo expression similar to (30), the difference being that the gate function is narrower.

[0125] Assume the coordinates of the projected pixel point are (x, y), then the distance from the pixel point to the antenna is

[0126]

[0127] Expand (46) Taylor to get

[0128]

[0129] in

[0130]

[0131] The BP imaging result is

[0132]

[0133] According to the stationary phase principle,

[0134]

[0135] From (50), we can see that the larger the difference between q2 and a2, the wider the gate function, that is, the more serious the defocus of the imaging result. Let q1-a1=0, and the center of the azimuth imaging position is

[0136]

[0137] where v r =(v x x0+v y y0) / R0 is the radial velocity of the target, t a = 0 when the slant distance between the moving target and the radar. Therefore, the imaging position in the range direction is

[0138]

[0139] When v x =v y =0, that is, when P is a stationary target, from (51) and (52) we can get x=x0, y=y0, that is, the imaging position of the stationary target is its real position.

[0140] This invention demonstrates a method for suppressing multipath ghosts in UAV-mounted through-the-wall radars based on frequency domain filtering, which is significantly different from traditional multipath ghost suppression technologies. The present invention abandons complex computational processes and huge data processing requirements, achieves a leap in processing efficiency, and ensures rapid and effective suppression of multipath ghosts. In addition, this technology relies on the radar carried by the UAV platform, giving it a wide-coverage search and detection capability, regardless of the complex and changeable ground environment or floor height restrictions, greatly expanding the effective search area. More importantly, this technology avoids the image multiplication step, thereby protecting the integrity of the phase information of the moving target, laying a solid foundation for the subsequent precise positioning of the moving target. In summary, this invention is of great significance in the suppression of multipath ghosts in through-the-wall radars, and provides a reliable solution for reducing the false alarm rate of moving target detection.

[0141] In order to verify the effectiveness of the proposed method, this section uses the electromagnetic field simulation software gprMax for simulation verification. The simulation scenario is as follows Figure 4 As shown in the figure, the black borders represent the four walls. The two stationary targets are located near the left and right walls, respectively, and the moving target moves perpendicular to the radar. The antenna array consists of one transmitting antenna and two receiving antennas, with a spacing of 0.15m. The main simulation parameters are shown in Table 1.

[0142] Table 1 Simulation parameter settings

[0143]

[0144] Step S1 is executed to analyze the characteristic differences between the direct path echo and the multipath echo in the range Doppler domain.

[0145] Execute step S2 to set a suitable low-pass filter to filter out multipath signals.

[0146] Execute step S3 to complete imaging of the moving target using the BP algorithm.

[0147] In order to highlight the superiority of the proposed algorithm, the proposed method is compared with the subaperture imaging algorithm and the CF weighted method. The improvement factor (IF) is used as an indicator to measure the multipath ghost suppression effect. The imaging results of different methods are shown in Figure 2. Figure 5 As shown, (a) is the imaging result of direct BP; (b) is the result after CF weighting of (a); (c) is the result of sub-aperture image fusion; (d) is the imaging result of the proposed method. Figure 5It can be seen that the moving target is defocused in the direct BP imaging results, and the detection of multipath ghost moving targets is interfered with; the CF weighted method and sub-aperture imaging algorithm can suppress weak focus points while enhancing the intensity of strong focus points, and perform well in multipath ghost suppression in static scenes. However, for scenes with moving targets, due to the defocus phenomenon in the imaging results of moving targets, these two methods will also suppress the energy of the moving targets to a certain extent, thereby reducing the signal-to-noise ratio; compared with the sub-aperture imaging method, the proposed method does not require image multiplication, which can keep the phase information of the moving target intact, and is more conducive to completing the moving target positioning on this basis.

[0148] The IFs of the processing results of different methods are shown in Table 2. It can be seen from Table 2 that the CF weighted method fails in multipath suppression of moving targets, and the proposed method has the best multipath ghost suppression effect.

[0149] Table 2 IF of the results of different methods

[0150]

[0151] Compared with the traditional method, the processing result of the present invention basically filters out the multipath echo, and has a better focusing effect on the moving target, which well completes the task of multipath ghost suppression of the wall-penetrating radar.

[0152] The above specific embodiments merely illustrate the design principles of the present invention. The shapes and names of the components described herein may vary and are not limiting. Therefore, those skilled in the art may modify or substitute equivalents for the technical solutions described in the above embodiments. Such modifications and substitutions, without departing from the inventive spirit and technical solutions of the present invention, shall fall within the scope of protection of the present invention.

Claims

1. A method for suppressing multipath ghosting of UAV-mounted through-wall radar based on frequency domain filtering, characterized in that: include: Step S1: obtaining raw data of a moving target echo from a wall-penetrating radar carried by a UAV, performing range compression on the raw data, and transforming the range-compressed echo data into a range Doppler domain through an azimuth Fourier transform; Consider a closed space surrounded by four walls, with the front and back walls parallel to the x-axis, the left and right side walls parallel to the y-axis, and the inner surface of the right wall at ;Target Located in a closed space, its azimuth and range velocities are and The dual-channel radar on the UAV flies along the x-axis at a speed of V. The antenna array consists of a transmitting antenna and two receiving antennas. The antenna elements are evenly spaced along the x-axis, and the element spacing is d. Let the slow time be When the transmitting antenna is at the origin, the target The coordinates are ,point About the mirror point of the right wall The coordinates are ; At time , the position of the transmitting antenna is , receiving antenna The location is ;The radar transmits a linear frequency modulation signal (1) in 、 、 、 、 Represent the gate function, fast time variable, pulse width, signal center frequency and modulation rate respectively; the echo signal received by the radar consists of direct path echo and multipath echo, which are expressed as (2) in, and are the range compression results of the direct path echo and the first-order side wall multipath echo received by the nth receiving antenna; The propagation path length of the direct path echo is (3) The direct path echo is (4) in is the azimuth gating function of the direct path echo, is the signal bandwidth, is the speed of light, is the wavelength corresponding to the center frequency; To maintain generality, we only consider the multipath echo generated by the right wall reflection, and the signal propagation path length is (5) Multipath echo is (6) in is the azimuth gate function of the multipath echo on the right wall; The expression of echo data in the range Doppler domain is: (7) in is the Doppler frequency variable, and They are the azimuth gate functions of the direct path echo and multipath echo in the range Doppler domain, and the corresponding Doppler center frequencies are and , 、 and They are the direct path echo signal propagation length exist The constant term, linear term coefficient and quadratic term coefficient of the Taylor expansion at , 、 and They are the propagation lengths of multipath echo signals exist The constant term, linear term coefficient and quadratic term coefficient of the Taylor expansion at ; Step S2: construct a low-pass filter using a rectangular gate function, set a suitable cutoff frequency, and multiply the rectangular gate function by the echo signal in the range-Doppler domain to filter out multipath signals; Multiply the range Doppler domain echo signal by the low-pass filter to obtain (8) in It is the cutoff frequency of the ideal low-pass filter, which determines the Doppler bandwidth of the filtered signal. It is necessary to set the empirical value according to the changes in the pulse repetition frequency and the imaging scene. It is the azimuth gate function of the direct path echo in the range-Doppler domain after filtering. The corresponding Doppler center frequency is 0. After filtering, the direct path signal is retained, while the multipath signal is suppressed. Step S3: transform the frequency domain filtering result into the two-dimensional time domain through azimuth inverse Fourier transform, and use the BP algorithm to complete the imaging of the moving target; The moving target imaging result after suppressing multipath ghost is expressed as (9) in is the azimuth gate function that represents the target focusing effect, is the distance from the projected pixel to the antenna, 、 and They are exist The constant term, linear term coefficient, and quadratic term coefficient of the Taylor expansion at .

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