A distributed radar two-dimensional high-resolution imaging configuration design method

Abstract

The present invention discloses a method for designing a two-dimensional high-resolution imaging configuration of a distributed radar. First, a distributed radar echo model is established to analyze the mapping relationship between the geometric configuration and the echo wavenumber spectrum. Then, the wavenumber spectrum is expanded in the range and azimuth directions in the wavenumber domain to quickly obtain the wavenumber spectrum distribution under the two-dimensional high-resolution imaging requirements. Finally, according to the flight speed of the radar platform and the initial configuration relationship between the main transmitter and the main receiver, the configuration positions of multiple slave receivers are solved to realize the configuration design of the two-dimensional high-resolution imaging of the distributed radar. The distributed radar configuration designed by the method of the present invention utilizes the distribution characteristics of the radar echo in the wavenumber domain to solve the spatial configuration of the bandwidth of the extended wavenumber spectrum, which can effectively improve the two-dimensional imaging resolution in the range and azimuth directions, and can obtain a two-dimensional high-resolution radar image at a lower transmission signal bandwidth and synthetic aperture time.

Description

Technical Field

[0001] The invention belongs to the field of radar detection and imaging, and in particular relates to a distributed radar two-dimensional high-resolution imaging configuration design method. Background Art

[0002] Distributed radar can obtain information about targets in different detection frequency bands and detection angles by separating the transceiver stations under all-day and all-weather conditions, and can quickly obtain two-dimensional high-resolution imaging results of the target by fusing multiple echo data information.

[0003] In order to improve the imaging resolution of distributed radar along azimuth in a short time, the document "Junyu Zhu, Deqing Mao, Yongchao Zhang, et al. A topology design method based on wavenumber spectrum generation for multistatic synthetic aperture radar. 2021 IEEE International Geoscience and Remote Sensing Symposium, pp. 5453–5456" proposed a distributed radar configuration design method based on wavenumber spectrum growth. By generating a wavenumber spectrum along the azimuth direction, a new wavenumber spectrum distribution is obtained, and then the geometric configuration of the radar platform is calculated. However, this method is only applicable to short-term high-resolution imaging in the target azimuth direction. The document "Deqing Mao, Yongchao Zhang, Jifang Pei, et al. Forward looking geometric configuration optimization design for spaceborne-airborne multistatic synthetic aperture radar. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, vol. 14, pp. 8033–8047, 2021" proposes a distributed radar configuration optimization design method based on genetic algorithm. The optimized geometric configuration is obtained by using a multi-objective optimization method, which simultaneously meets multiple application requirements such as short-time azimuth high resolution, two-dimensional resolution balance, and regular point spread function. However, the computational complexity of this method is relatively high. Summary of the invention

[0004] In order to solve the above technical problems, the present invention proposes a distributed radar two-dimensional high-resolution imaging configuration design method, the purpose of which is to improve the two-dimensional imaging resolution of the distributed radar system through distributed radar configuration design and realize short-time and low-bandwidth two-dimensional high-resolution imaging.

[0005] The technical solution of the present invention is: a distributed radar two-dimensional high-resolution imaging configuration design method, the specific steps are as follows:

[0006] Step 1: Establish the distributed radar echo model.

[0007] In the method of the present invention, the distributed radar system includes 1 transmitter and N receivers. The Cartesian coordinates of the transmitter and the receiver are (x T ,y T ,z T ) and (x Rn ,y Rn ,z Rn ), where T represents the transmitter, R n represents the nth receiver, n=1,2,...,N. Let the speeds of the transmitter and receiver be v T =(v xT ,v yT ,0) and v Rn =(v xRn ,v yRn ,0),v xT , v xRn Represent the transmitter T and the receiver R respectively n Flight speed along the x-axis, v yT , v yRn Represent the transmitter T and the receiver R respectively n The flight speed along the y-axis, and the speed of the transmitter and the receiver are the same, that is, ||v T ||=||v Rn ||, the reference target point is located at the origin O, and the coordinates of the observed target P are (x P ,y P ,z P ).

[0008] The transmitter radiates a linear frequency modulation signal (LFM), and the receiver R n The received echo signal is first pulse compressed, and then correlated with the echo signal of the reference point O to obtain the range frequency domain expression of the echo:

[0009]

[0010] Among them, rect(·) represents the rectangular window function, A n ,f t ,τ,Ta ,K r ,T r ,c and f c They represent echo amplitude, range frequency variable, slow time, synthetic aperture time, frequency modulation rate, pulse width, electromagnetic wave propagation speed and carrier frequency respectively. P (τ) = r TP (τ)+r RnP (τ) represents the transmitter T and the receiver R n The distance history relative to the target point P, r TP (τ), r RnP (τ) represents the transmitter T and the receiver R n The distance history relative to the target point P. O (τ) = r TO (τ)+r RnO (τ) represents the transmitter T and the receiver R n The distance history relative to the reference point O, r TO (τ), r RnO (τ) represents the transmitter T and the receiver R n Range history relative to a reference point O. All radar platforms have the same synthetic aperture time T a .

[0011] Step 2: Projection of distributed radar echo in wave number domain.

[0012] In the far field case, the distance history difference between the target point P and the reference point O can be approximately expressed as:

[0013]

[0014] Among them, x T (τ), x Rn (τ) represents the transmitter T and the receiver R at time τ respectively n The x-coordinate, y- T (τ), y Rn (τ) represents the transmitter T and the receiver R at time τ respectively n The y coordinate, x P and P They represent the x-coordinate and y-coordinate of the observed target P in step 1 respectively.

[0015] Define the receiver R n The wave number variables k of the echo along the x-axis and y-axis in the wave number domain xn , k yn for:

[0016]

[0017] Among them, k(f t)=2π(f c +f t ) / c. According to the echo expression obtained in step 1, the receiver R n The wavenumber spectrum of the echo projected into the wavenumber domain is:

[0018] S n (k xn ,k yn )=A n exp[j(x P k xn +y P k yn )] (4)

[0019] Step 3: Distance to wavenumber spectrum expansion,

[0020] Given a transmitter T and a receiver R n-1 In order to improve the distance bandwidth of the wave number spectrum, the receiver R n-1 and receiver R n The edges of the wavenumber spectrum along the slow time τ direction should overlap as much as possible to maximize the expansion f t The wave number spectrum in the direction of τ. Let the vertices of the edge of the wave number spectrum τ coincide, and we can get the following relationship:

[0021]

[0022] Among them, τ start represents the slow time at the start of the synthetic aperture, τ end represents the slow time at the end of the synthetic aperture, B r =K r T r represents the transmitter signal bandwidth. Combining the above equation with equation (3) in step 2, we can get the receiver R n The starting and ending point configuration solutions of signal accumulation are:

[0023] [x Rn (τ i ),y Rn (τ i ),z Rn (τ i )]=r RnO (τ i ) i (6)

[0024] Where i = start, end, start represents R n The configuration starting point, end represents R n The configuration endpoint, Represents the direction vector of the distance extension configuration. When i = start, U iIndicates the direction vector of the distance extension starting point configuration; when i = end, U i A direction vector representing the distance from the extended end configuration. Respectively represent the receiver R n In τ i The configuration coordinates along the x, y, and z axes at all times, and:

[0025]

[0026] Step 4: Azimuthal wavenumber spectrum expansion.

[0027] The step 2 (3) is expressed as follows:

[0028]

[0029] in represents the azimuth component of the wave number variable along the x-axis at receiver n, represents the azimuth component of the wavenumber variable along the y-axis at receiver n, and:

[0030]

[0031] In order to increase the azimuth bandwidth of the wavenumber spectrum, the receiver R n-1 and receiver R n Wave number spectrum along the distance frequency f t The edges of the direction should overlap as much as possible to maximize the expansion of the azimuthal wavenumber spectrum. Combining formula (8), the following relationship can be obtained:

[0032]

[0033] The τ direction of the azimuth wavenumber spectrum is related to the flight direction of the receiver. A good azimuth expansion of the wavenumber spectrum must satisfy the receiver R n-1 and receiver R n The τ direction of the wave number spectrum is parallel, and the following relationship can be obtained:

[0034]

[0035] Combining equations (10), (11) and (8), we can get the receiver R n The configuration solution is:

[0036]

[0037] in, represents the direction vector of the azimuth extension starting point configuration, Respectively represent the receiver R n The flight speed along the x, y, and z directions at the starting point, represents the direction vector of the azimuthally extended endpoint configuration, Respectively represent the receiver R n The flight speed in the x, y, and z directions at the end point, and:

[0038]

[0039]

[0040]

[0041]

[0042]

[0043] Step 5: Configuration solution and two-dimensional high-resolution imaging.

[0044] Based on the configuration solutions obtained in steps 3 and 4, combined with the constraints on the receiver velocity in step 1, the final configuration result is further solved. According to the description in step 1, v zT =0,v zRn =0 and ||v T ||=||v Rn ||, from this we can get:

[0045]

[0046] And there are:

[0047]

[0048] Combining equations (6) and (12), we can obtain:

[0049]

[0050] Among them, W in formula (16) has different meanings according to the range expansion and azimuth expansion. When the range wavenumber spectrum expansion of step 3 is performed, W=U; when the azimuth wavenumber spectrum expansion of step 4 is performed, W=V. According to the above steps, the distributed radar configuration that can achieve wavenumber spectrum expansion can be calculated. For different speed constraints, the above method can still be used for calculation and solution.

[0051] According to the radar configuration solved above, the distributed radar echo data is obtained by step 1 and step 2, and the projection of the distributed radar echo data in the wavenumber domain is completed. Then, the two-dimensional Fourier transform is performed on the multiple echo wavenumber spectrum data shown in formula (4), and the two-dimensional high-resolution imaging result under the design configuration of the method of the present invention can be obtained as follows:

[0052]

[0053] Beneficial effects of the present invention: The method of the present invention first establishes a distributed radar echo model, analyzes the mapping relationship between the geometric configuration and the echo wavenumber spectrum, then expands the wavenumber spectrum in the range and azimuth directions in the wavenumber domain, and quickly obtains the wavenumber spectrum distribution under the two-dimensional high-resolution imaging requirements. Finally, according to the flight speed of the radar platform and the initial configuration relationship between the main transmitter and the main receiver, the configuration positions of multiple slave receivers are solved to realize the configuration design of distributed radar two-dimensional high-resolution imaging. The distributed radar configuration designed by the method of the present invention utilizes the distribution characteristics of radar echoes in the wavenumber domain to solve the spatial configuration of the extended wavenumber spectrum bandwidth, which can effectively improve the two-dimensional imaging resolution in the range and azimuth directions, and can obtain a two-dimensional high-resolution radar image at a lower transmission signal bandwidth and synthetic aperture time. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 The present invention is a flow chart of a distributed radar two-dimensional high-resolution imaging configuration design method.

[0055] Figure 2 Schematic diagram of the distributed radar configuration in an embodiment of the present invention.

[0056] Figure 3 The receiver R in the embodiment of the present invention n Schematic diagram of the wavenumber spectrum distribution.

[0057] Figure 4 4 is a distribution diagram of the wave number spectrum in the case of 1 transmitter and 4 receivers in an embodiment of the present invention.

[0058] Figure 5 4 is a comparison diagram of imaging results in an embodiment of the present invention. DETAILED DESCRIPTION

[0059] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0060] The present invention adopts the method of simulation experiment to verify the effectiveness of the proposed method. All the steps and conclusions of the present invention are verified on the MATLAB R2021a simulation platform. Figure 1 As shown, a flow chart of a distributed radar two-dimensional high-resolution imaging configuration design method of the present invention, the specific steps are as follows:

[0061] Step 1: Establish the distributed radar echo model.

[0062] In this embodiment, the configuration of the distributed radar system is as follows: Figure 2 This embodiment includes 1 transmitter and 4 receivers, and the radar system parameters are shown in Table 1.

[0063] Table 1

[0064]

[0065] Given a transmitter T and a receiver R 1 The configuration (x T ,y T ,z T ) and (x R1 ,y R1 ,z R1 ), and the speed parameter v T and v R1 , as shown in Table 2. Transmitter T and receiver R n The speed satisfies the constraint ||v T ||=||v Rn ||, where n=1,2,3,4.

[0066] Table 2

[0067]

[0068] The transmitter radiates LFM signal, and the receiver R n The received echo signal is subjected to pulse compression and correlation processing, and the range frequency domain expression is obtained as follows:

[0069]

[0070] Among them, rect(·) represents the rectangular window function, A n ,f t ,τ,T a ,K r ,T r ,c and f c They represent echo amplitude, range frequency variable, slow time, synthetic aperture time, frequency modulation rate, pulse width, electromagnetic wave propagation speed and carrier frequency respectively. P (τ) = r TP (τ)+r RnP (τ) represents the transmitter T and the receiver R n The distance history relative to the target point P, r TP (τ), r RnP (τ) represents the transmitter T and the receiver R n The distance history relative to the target point P. O (τ) = r TO (τ)+r RnO (τ) represents the transmitter T and the receiver R n The distance history of O relative to the reference, r TO (τ), r RnO (τ) represents the transmitter T and the receiver R n Distance history relative to a reference point O.

[0071] Step 2: Projection of distributed radar echo in wave number domain.

[0072] In the far field case, the distance history difference between the target point P and the reference point O can be approximately expressed as:

[0073]

[0074] Among them, x T (τ), x Rn (τ) represents the transmitter T and the receiver R at time τ respectively n The x-coordinate, y- T (τ), y Rn (τ) represents the transmitter T and the receiver R at time τ respectively n The y coordinate of

[0075] Define the receiver R n The wave number variables k of the echo along the x-axis and y-axis in the wave number domain xn , k yn for:

[0076]

[0077] Among them, k(f t )=2π(f c +f t ) / c, apply the projection rule of the above formula to the phase term in step 1 (18), and obtain the receiver R n The wave number spectrum of

[0078] S n (k xn ,k yn )=A n exp[j(x P k xn +y P k yn )] (twenty one)

[0079] Receiver n The wave number spectrum distribution is as follows Figure 3 shown.

[0080] Step 3: Distance to wavenumber spectrum expansion,

[0081] According to step 2, let n = 2, and get the receiver R 1 and R 2 The wave number spectrum expression S 1 (k x1 ,k y1 ) and S 2 (k x2 ,k y2 ), let the wave number spectrum S1 and S 2 The vertices of the edge in the direction of the slow time τ coincide with each other, and the following equation is obtained:

[0082]

[0083] Among them, τ start represents the slow time at the start of the synthetic aperture, τ end represents the slow time at the end of the synthetic aperture, B r =K r T r represents the transmitter signal bandwidth, and the expanded wavenumber spectrum is as follows Figure 4 As shown in the figure, WS1 and WS2 are receivers R 1 and receiver R 2 According to the parameters given in Table 2, the receiver R is calculated by equation (20): 1 The wave number variable is substituted into the above formula to obtain the receiver R 2 The configuration solution that needs to be satisfied is:

[0084]

[0085] Where i = start, end, start represents R n The configuration starting point, end represents R n The configuration endpoint of , and:

[0086]

[0087] Step 4: Azimuthal wavenumber spectrum expansion.

[0088] According to step 4 of the invention, in step 2, the receiver R 1 and receiver R 3 Wave number spectrum along the distance frequency f t Under the condition that the edges of the directions coincide, the following relationship can be obtained:

[0089]

[0090] Assuming that the extension direction of the azimuthal wavenumber spectrum is consistent, the following relationship can be obtained:

[0091]

[0092] The expanded wavenumber spectrum is as follows Figure 4 As shown in the figure, WS1 and WS3 are receivers R 1 and receiver R 3 Combining equations (25), (26) and (8), we can get the receiver R n The configuration solution is:

[0093]

[0094] Among them, start represents R 3 The configuration starting point, end represents R 3 The configuration endpoint of , and:

[0095]

[0096]

[0097]

[0098]

[0099]

[0100] Based on the receiver R calculated in step 3 2 Parameters, and then using step 4, the receiver R 4 Relative to the receiver R 2 The azimuth expansion result is as follows: Figure 4 As shown in the figure, WS2 and WS4 are receivers R 2 and receiver R 4 The wavenumber spectrum distribution of .

[0101] Step 5: Configuration solution and two-dimensional high-resolution imaging.

[0102] According to step 5 described in the invention, the receiver R is solved by combining the speed constraint of step 1 with the configuration solution of step 3 and step 4. 2 , R 3 and R 4 The configuration result is:

[0103]

[0104] The flight speed is:

[0105]

[0106] By using the geometric configurations shown in (29) and (30) after design, the distributed radar echo data is generated by step one and step two, and the projection of the distributed radar echo data in the wavenumber domain is completed. Then, the two-dimensional Fourier transform is performed on the multiple echo wavenumber spectrum data shown in formula (21), and the two-dimensional high-resolution imaging result under the design configuration of the method of the present invention can be obtained:

[0107]

[0108] The simulation imaging results are as follows Figure 5 As shown, Figure 5The imaging results of the above-mentioned solution configuration include 5 point target simulation imaging results. Figure 5 (a) is the imaging result of 1 transmit and 1 receive, the range resolution of the center point target is 0.79m, and the azimuth resolution is 0.83m. Figure 5 (b) is the imaging result in the case of 1 transmission and 4 receptions, in which the range resolution of the central point target is 0.40m and the azimuth resolution is 0.41m. It can be seen that the method of the present invention designs the configuration of the distributed radar through wavenumber spectrum analysis. Compared with the bistatic radar with 1 transmission and 1 reception, under the same signal bandwidth and synthetic aperture time, the range and azimuth imaging resolution are doubled.

Claims

1. A method for designing a configuration of a distributed radar for two-dimensional high-resolution imaging, the specific steps are as follows: Step 1: Establish the echo model of the distributed radar, The distributed radar system consists of 1 transmitter and N receivers. The Cartesian coordinates of the transmitter and receiver are (x T ,y T ,z T ) and (x Rn ,y Rn ,z Rn ), T represents the transmitter, R n represents the nth receiver, n=1,2,...,N, let the speed of the transmitter and receiver be v T =(v xT ,v yT ,0) and v Rn =(v xRn ,v yRn ,0),v xT ,v xRn Represent the transmitter T and the receiver R respectively n Flight speed along the x-axis, v yT ,v yRn Represent the transmitter T and the receiver R respectively n The flight speed along the y-axis, and the speed of the transmitter and the receiver are the same, that is, ||v T ||=||v Rn ||, the reference target point is located at the origin O, and the coordinates of the observed target P are (x P ,y P ,z P ); The transmitter radiates a linear frequency modulation signal (LFM), and the receiver R n The received echo signal is first pulse compressed, and then correlated with the echo signal of the reference point O to obtain the range frequency domain expression of the echo: where, rect(·) represents the rectangular window function, A n ,f t ,τ,T a ,K r ,T r ,c and f c They represent echo amplitude, range frequency variable, slow time, synthetic aperture time, modulation frequency, pulse width, electromagnetic wave propagation speed and carrier frequency, respectively. P (τ) = r TP (τ)+r RnP (τ) represents the transmitter T and the receiver R n The distance history relative to the target point P, r TP (τ), r RnP (τ) represents the transmitter T and the receiver R n The distance history relative to the target point P, r O (τ) = r TO (τ)+r RnO (τ) represents the transmitter T and the receiver R n The distance history relative to the reference point O, r TO (τ), r RnO (τ) represents the transmitter T and the receiver R n The distance history relative to the reference point O; Step 2: Project the echo of the distributed radar into the wavenumber domain, In the far-field case, the range history difference between the target point P and the reference point O is approximately expressed as: Among them, x T (τ), x Rn (τ) represents the transmitter T and the receiver R at time τ respectively n The x-coordinate, y- T (τ), y Rn (τ) represents the transmitter T and the receiver R at time τ respectively n The y coordinate of Define the receiver R n The wave number variables k of the echo along the x-axis and y-axis in the wave number domain xn , k yn for: Among them, k(f t )=2π(f c +f t ) / c, receiver R n The wavenumber spectrum of the echo projected into the wavenumber domain is: S n (k xn ,k yn )=A n exp[j(x P k xn +y P k yn )] (4) Step 3: Expand the range wavenumber spectrum, Let the vertices of the side where the wavenumber spectrum τ is located coincide, and the following relationship is obtained: Among them, τ start represents the slow time at the start of the synthetic aperture, τ end represents the slow time at the end of the synthetic aperture, B r =K r T r represents the transmitter signal bandwidth. Combining equation (5) with equation (3), we can get the receiver R n The starting and ending point configuration solutions of signal accumulation are: [x] Rn (t i ),y Rn (t i ),z Rn (t i )]=r RnO (t i )U i (6) Where i = start, end, start represents R n The configuration starting point, end represents R n The configuration endpoint, Represents the direction vector of the distance extension configuration. When i = start, U i Indicates the direction vector of the distance extension starting point configuration; when i = end, U i represents the direction vector from the extended end point configuration, Respectively represent the receiver R n In τ i The configuration coordinates along the x, y, and z axes at all times, and: Step 4: Expand the azimuth wavenumber spectrum, Express Equation (3) in the following form: in, represents the azimuth component of the wave number variable along the x-axis at receiver n, represents the azimuth component of the wavenumber variable along the y-axis at receiver n, and: Combining Equation (8), the following relationship can be obtained: Satisfy the receiver R n-1 and receiver R n The τ direction of the wave number spectrum is parallel, and the following relationship can be obtained: Combining equations (10), (11) and (8), we can get the receiver R n The configuration solution is: in, represents the direction vector of the azimuth extension starting point configuration, Respectively represent the receiver R n The flight speed along the x, y, and z directions at the starting point, represents the direction vector of the azimuthally extended endpoint configuration, Respectively represent the receiver R n The flight speed in the x, y, and z directions at the end point, and: Step 5: Solve the configuration and perform two-dimensional high-resolution imaging, According to the description in step 1, v zT =0,v zRn =0 and ||v T ||=||v Rn ||, from this we can get: and there is: Combining Equation (6) and (12), we can get: where, W in Equation (16) has different meanings according to the range expansion and azimuth expansion. When performing the range wavenumber spectrum expansion in Step 3, W = U; when performing the azimuth wavenumber spectrum expansion in Step 4, W = V. The echo data of the distributed radar are obtained from Step 1 and Step 2, and the projection of the echo data of the distributed radar in the wavenumber domain is completed. Then, by performing a two-dimensional Fourier transform on the multiple echo wavenumber spectrum data shown in Equation (4), the two-dimensional high-resolution imaging result can be obtained as:

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