A Method for Target Range-Doppler Walk Correction Based on Panoramic Radar

Abstract

The present invention discloses a method for target range-Doppler walk correction based on a wide-swath radar, comprising the following steps: S1. Establish a geometric scene with the radar as the origin to obtain the instantaneous range of the target; S2. Perform pulse compression on the instantaneous range of the target to obtain a range compression result; S3. Perform Fourier transform on the range compression result in the fast time domain; S4. Perform slow time-fast time frequency decoupling on the range compression result after Fourier transform; S5. Perform inverse Fourier transform on the frequency decoupling result in the fast time domain; S6. Perform range-Doppler domain transformation on the decoupling result after inverse Fourier transform, and then perform phase walk compensation to obtain a relational expression between the target range-Doppler domain result and the phase walk to be estimated; S7. Use an iterative method of coordinate descent to solve the optimal solution of the relational expression between the target range-Doppler domain result and the phase walk to be estimated.

Description

Technical Field

[0001] The present invention relates to the technical field of radar antennas, and particularly relates to a method for correcting target range-Doppler walk based on a wide-swath radar. Background Art

[0002] The wide-swath radar is based on array antenna technology, makes full use of the antenna aperture, and realizes simultaneous multi-beams. The beams in the entire detection airspace gaze at the target, so that long-time coherent accumulation can be achieved, the utilization rate of the radar transmission power is improved, and the detection ability of the radar for weak targets is enhanced. For a conventional beam scanning radar, the dwell time of the beam at each pointing is limited, and the number of echo signals available for coherent accumulation is limited. In order to further improve the detection probability, only the information of multiple scanning cycles can be used for non-coherent accumulation. It has been proved that non-coherent accumulation always causes accumulation loss, and the obtained signal-to-noise ratio is lower than that of coherent accumulation. For a wide-swath radar, long-time coherent accumulation, and the accumulation time only depends on the system correlation and the target motion characteristics, and is not affected by the beam scanning time, which can greatly improve the accumulation gain and the target detection performance of the radar. However, long-time coherent accumulation will increase the range walk and Doppler walk of the target, resulting in the defocusing of the target in the range-Doppler domain (across range and Doppler cells), which affects the radar detection performance.

[0003] Only by effectively compensating the target range and Doppler walk can the long-time coherent accumulation characteristics of the wide-swath radar be better reflected. At present, many domestic and foreign experts and scholars have studied the compensation methods for target range walk and Doppler walk. The literature "A Compensation Method for Multiple High-Speed Moving Targets" (Journal of Air Force Early Warning Academy, 2018, 32(6)) proposes to use the Radon transform to roughly estimate the target speed, then use the minimum entropy criterion to search for the target precise speed and construct a compensation function to compensate for the range walk. This method mainly focuses on the walk correction of high-speed targets and has not corrected the Doppler walk; the literature "Moving Target Detection Algorithm Based on Fractional Fourier Transform to Compensate Doppler Migration" (Acta Armamentarii, 2009, 20(10)) uses the fractional Fourier transform to form a frequency sweep filter bank to realize the secondary phase compensation for each Doppler frequency detection unit. This method is based on the premise that the target does not have cross-range cell walk. For the case of cross-range cell walk, a good accumulation effect cannot be achieved; the literature "Research on the Detection Method of Long-Time Coherent Accumulation Targets for Wide-Swath Radar" (Journal of National University of Defense Technology, 2010, 32(6)) proposes a multi-target detection method that combines the Keystone transform and the Dechirping method for coherent accumulation. However, the Doppler dimension compensation of this method performs multi-channel acceleration search, but no quantitative calculation is given for the maximum search acceleration and the search step size, which is very easy to produce errors.

[0004] Therefore, only by effectively compensating for the target distance and Doppler walk can the general exploration characteristics of the general exploration radar be better reflected, and the detection ability of weak targets in a strong clutter background can be improved. Summary of the Invention

[0005] Aiming at the above deficiencies in the prior art, a method for correcting target range-Doppler walk based on a general exploration radar provided by the present invention solves the problems of cross-range cell and cross-Doppler cell caused by target movement during long-term accumulation.

[0006] In order to achieve the above invention purpose, the technical solution adopted by the present invention is: a method for correcting target range-Doppler walk based on a general exploration radar, including the following steps:

[0007] S1. Establish a geometric scene with the radar as the origin to obtain the instantaneous distance of the target;

[0008] S2. Pulse compress the instantaneous distance of the target to obtain a range compression result;

[0009] S3. Perform Fourier transform on the range compression result in the fast time domain;

[0010] S4. Perform slow time-fast time frequency decoupling on the range compression result after Fourier transform;

[0011] S5. Perform inverse Fourier transform on the frequency decoupling result in the fast time domain;

[0012] S6. Perform range-Doppler domain transformation on the decoupling result after inverse Fourier transform, and then perform phase walk compensation to obtain a relational expression between the target range-Doppler domain result and the phase walk amount to be estimated;

[0013] S7. Use the coordinate descent iterative method to solve the optimal solution of the relational expression between the target range-Doppler domain result and the phase walk amount to be estimated.

[0014] Further: The specific step S1 is as follows:

[0015] Establish a geometric scene with the radar as the origin. The initial distance between the target and the radar is R0, the initial angle with the Y-axis is θ0, the target moves along the Y-axis with a velocity v and an acceleration α in uniform acceleration, and the initial slant range of the target is At any time t, the instantaneous distance of the target is R(t), and the specific formula is:

[0016]

[0017] In the above formula, x is the abscissa of the target, and y is the ordinate of the target.

[0018] Further: The range compression result s in step S2 rc(τ,t) The specific formula is:

[0019]

[0020] In the above formula, ω az (t) is the azimuth envelope, sinc(·) is the range pulse compression response function, B is the transmit signal bandwidth, τ is the fast time in the range direction, t is the slow time in the azimuth direction, c is the electromagnetic propagation speed, λ is the carrier wavelength, and j is the imaginary symbol.

[0021] Furthermore: The specific formula for the Fourier transform in the fast time domain in step S3 is:

[0022] S rc (fτ,t) = Aw az (t)G 2B (f τ )

[0023]

[0024] In the above formula, S rc (fτ,t) is the range compression result after Fourier transform, A is a constant, G 2B is the range envelope, f τ is the fast time domain frequency, f c is the carrier frequency.

[0025] Furthermore: The specific formula for the slow time - fast time frequency decoupling in step S4 is:

[0026]

[0027] In the above formula, S rc' (f τ ,t m ) is the frequency decoupling result, t m is the variable substitution of the slow time, expressed as t m =(f c +f τ )t / f c , and K is the variable relation formula, expressed as

[0028] Furthermore: The specific formula for the inverse Fourier transform in the fast time domain in step S5 is:

[0029]

[0030] In the above formula, s rc' (τ,t m ) is the frequency decoupling result after inverse Fourier transform.

[0031] Furthermore: Step S6 is specifically:

[0032] Perform a discrete Fourier transform in the slow-time dimension on the frequency decoupling result after the inverse Fourier transform to obtain the range-Doppler domain result The specific formula is as follows:

[0033]

[0034] In the above formula, f is the frequency in the Doppler domain, is the sampling value of the fast time τ, is the slow time t m sampling value of, N r and N a are the sampling points in the fast-time dimension and the slow-time dimension respectively, N is the total number of sampling points in the slow-time dimension, and ω is the angular frequency;

[0035] Perform phase walk compensation on the range-Doppler domain result, and the range-Doppler result after Doppler walk compensation The specific formula is as follows:

[0036]

[0037] In the above formula, is the Doppler walk amount to be estimated.

[0038] Furthermore: The specific step S7 is as follows:

[0039] Denote as the nth phase walk correction amount in the i-th iteration, and the (i + 1)-th iteration is expressed as:

[0040]

[0041]

[0042] Among them,

[0043]

[0044] yy = (s rc' |q) exp(-jω(t m )) q )

[0045] In the above formula, yy is the q-th frequency point and its amplitude before correction, xx is the linear combination of all other frequency points except the q-th frequency point, s rc' refers to s rc' (τ, t m ), which is the frequency decoupling result after the inverse Fourier transform, is the phase estimation of the q-th frequency point, is the N aPhase estimation of a frequency point, (t m ) q is the q-th sampling point after variable substitution of slow time;

[0046] According to the obtained xx and yy, the intensity v at the l-th pixel point in the range-Doppler domain l is expressed as:

[0047]

[0048] In the above formula, refers to the of the l-th pixel point, which is the range-Doppler result after Doppler walk compensation, is the conjugate of xx l xx of the l-th pixel point, yy l is yy of the l-th pixel point, xx l * is the conjugate of xx l yy l * is the conjugate of yy l , is the real part symbol representation;

[0049] According to the intensity v l calculate The specific formula is:

[0050]

[0051] In the above formula, is the image sharpness expression, l ∈ [1~L], L is the number of all pixel points;

[0052] That is, under coordinate descent, the multi-dimensional optimization problem is reduced to a single-variable extreme value problem:

[0053]

[0054] Set the search phase error range [-π, π], search within this range, and obtain corresponding That is, the estimation of the phase error.

[0055] The beneficial effects of the present invention are as follows: The omnidirectional search radar can perform omnidirectional search detection on targets, thereby enabling long-time coherent integration and improving the detection probability of weak targets. However, long-time coherent integration will increase the range walk and Doppler walk of the targets. Only by effectively correcting the range and Doppler walks of the targets can the omnidirectional search characteristics of the omnidirectional search radar be better reflected. Therefore, the present invention proposes a method for correcting range walk and Doppler walk, which can simultaneously correct the range walk and Doppler walk of the targets without any prior information and is suitable for any target geometric scenario. BRIEF DESCRIPTION OF THE DRAWINGS

[0056] Figure 1 is a flowchart of the present invention;

[0057] Figure 2 is a geometric configuration diagram in an embodiment of the present invention;

[0058] Figure 3 is a diagram of the result before range-Doppler walk correction in an embodiment of the present invention;

[0059] Figure 4 is a diagram of the range walk correction result in an embodiment of the present invention;

[0060] Figure 5 is a diagram of the Doppler walk correction result in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0061] The following describes the specific embodiments of the present invention to facilitate those skilled in the art of the present technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art of the present technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions made using the inventive concept of the present invention are within the scope of protection.

[0062] In order to solve the range-Doppler domain walk problem caused by target movement in omnidirectional search radar detection and improve the detection ability of targets in omnidirectional search radar, the present invention proposes a method for correcting target range-Doppler walk based on omnidirectional search radar. This method is based on omnidirectional search radar, observes the target for a long time to obtain a high Doppler resolution of the target; in the range-Doppler domain, derives the relationship formula between target contrast and Doppler walk, establishes a corresponding optimization model according to the maximum contrast criterion, and uses the coordinate descent and univariate optimization solution methods to iteratively calculate the estimation of Doppler walk and correct it.

[0063] A method for correcting target range-Doppler walk based on omnidirectional search radar, as Figure 1 shown, includes the following steps:

[0064] Step 1: Establish a geometric scene with the radar as the origin, as shown in Figure 2 . Here, 1 represents the target, with an initial distance of R0 from the radar and an initial angle of θ0 with the Y-axis. The target moves with a uniform acceleration of a and a velocity of v along the Y-axis (when approaching the radar, the target velocity is positive; when moving away from the radar, the target velocity is negative). The initial slant range of the target is At any time t, the instantaneous distance of the target is R(t), and the expression is as follows:

[0065]

[0066] Since R0 >> vt, perform a Taylor series expansion of Equation (1) around t = 0 and neglect terms of the third order and above to obtain:

[0067]

[0068] Step 2: Range compression

[0069] Assume that the echo signal under long-term accumulation is:

[0070]

[0071] The above four terms are respectively denoted as the range envelope, azimuth envelope, transmitted signal phase, and Doppler modulation term.

[0072] The range compression process is expressed as:

[0073] s rc (τ, t) = IFFT(s(fτ, t)H(fτ)) (4)

[0074] where H(f τ ) is the response function of the reference function, and s(f τ , t) is the Fourier transform of the echo s(τ, t) in the fast time domain. Substitute the Fourier transform of Equation (3) in the fast time domain into Equation (4) and neglect the envelope effect to obtain the result of range compression as:

[0075]

[0076] where, sinc(·) is the range pulse compression response function. It can be seen from Equation (5) that the envelope after pulse compression is related to t and produces a corresponding offset as it changes, that is, range migration.

[0077] Step 3: Fast time domain Fourier transform

[0078] Perform a fast time domain Fourier transform on Equation (5), and substitute Equation (2) into the result of (5) to obtain:

[0079]

[0080] Among them, A is a constant, and G 2B is the distance envelope.

[0081] Step 4: Slow-time - fast-time frequency decoupling

[0082] Let t m =(f c + f τ )t / f c , substitute it into Equation (6) for slow-time scale transformation to achieve slow-time - fast-time frequency decoupling, that is, the Keystone transform. After arrangement, it is approximately obtained that:

[0083]

[0084] Among them,

[0085] Step 5: Inverse Fourier transform in the fast-time domain

[0086] Perform the inverse Fourier transform on Equation (7) in the fast-time dimension. Ignoring the envelope effect, it can be obtained that:

[0087]

[0088] It can be seen from Equation (9) that the Keystone transform can approximately achieve the decoupling of slow-time - fast-time frequency, and there will be no range cell migration within the accumulation time. However, the Doppler migration still exists at this time, and corresponding compensation must be carried out, so further compensation is carried out.

[0089] Step 6: Range-Doppler domain transformation

[0090] The sampling value of the fast time τ is denoted as The sampling value of the slow time t m is denoted as Among them, N r and N a respectively represent the sampling points in the fast-time dimension and the slow-time dimension. There are N r ∈ [1, M], N a ∈ [1, N]. Perform the discrete Fourier transform on Equation (9) in the slow-time dimension to obtain the range-Doppler domain result, as shown in the following equation:

[0091]

[0092] f represents the Doppler domain frequency. According to Equation (10), the Doppler migration caused by the target movement is expressed in the form of phase migration, that is, there is phase migration at each movement moment of the target Modify (10) to (11), where:

[0093]

[0094]

[0095] is the pulse compression result with no Doppler walk for the target. Therefore, according to (12), the phase walk needs to be compensated, expressed as:

[0096]

[0097] represents the range-Doppler result after Doppler walk compensation, is the Doppler walk amount to be estimated.

[0098] Step Seven: Optimization Model Establishment

[0099] The relationship between the target range-Doppler domain result and the phase walk amount to be estimated is obtained in Step Six. Considering that there is no closed-form solution for error solving under this relationship, the present invention will use an iterative method of coordinate descent to solve the optimal solution.

[0100] In the coordinate descent algorithm, each iteration updates the phase variables in sequence while keeping other phase variables fixed. Denote as the nth phase walk correction amount in the i-th iteration. Then the (i + 1)-th iteration can be expressed as:

[0101]

[0102]

[0103] where

[0104]

[0105] yy = (s rc' |q) exp(-jω(t m )) q ))

[0106] where yy represents the q-th frequency point and its amplitude without correction, and xx represents the linear combination of all other frequency points except the q-th frequency point.

[0107] The intensity of the l-th pixel point in the range-Doppler domain can be expressed as:

[0108]

[0109]

[0110] where l ∈ [1~L], L is the number of all pixel points, and L = M * N.

[0111] That is, under coordinate descent, the multi-dimensional optimization problem is reduced to a single-variable extreme value problem:

[0112]

[0113] Step Eight: Solving the optimization model

[0114] Set the search phase error range to [-π, π], search within this range, and obtain The corresponding That is, the estimation of the phase error.

[0115] Example 1:

[0116] Step One: Establish a rectangular coordinate system with the radar platform as the origin as Figure 2 shown, set 1 moving target in the scene, and the detailed simulation parameters are shown in Table 1. The initial radial distance corresponding to the target is 1995m, and the initial azimuth angle (the angle offset from the Y-axis) θ 01 = 14°, and the target moves along the Y-axis with a uniform acceleration of 0.5m / s2 at an initial speed of 6m / s. Based on the Matlab platform, the echo s(τ, t) is obtained according to the parameters described in Table 1.

[0117] Table 1 Simulation parameter settings

[0118] Carrier frequency Bandwidth PRF Pulse width 10 GHZ 80 MHZ 1024 HZ 2 us Radial distance Initial velocity Acceleration Integration time 1995m 6 m / s <![CDATA[0.5m / s 2 > 1s

[0119] Step Three: Fast-time domain Fourier transform

[0120] Substitute s(τ, t) into Equation (4) for pulse compression to obtain the pulse compression result s rc (τ, t). The pulse compression result is as Figure 3 (a) shows. It can be seen that after pulse compression, the target distance dimension shows an inclination, that is, range migration.

[0121] Step Four: Slow-time - fast-time frequency decoupling

[0122] Perform a fast-time domain Fourier transform on s rc (τ, t) to obtain the result S rc (f τ , t). The fast-time domain Fourier transform result is as Figure 3 (b) shows, and the target Doppler frequency shows broadening, that is, Doppler migration.

[0123] Step Five: Set t

[0124] Set t m = (f c + f τ )t / f c Substitute into Src (f τ , t), to obtain S rc' (f τ , t m ).

[0125] Step Five: Inverse Fast Time - Domain Fourier Transform

[0126] Perform the inverse fast time - domain Fourier transform on S rc' (f τ , t m ) to obtain s rc' (τ, t m ). At this time, the processing result is as shown in Figure 4 (a). By comparing Figure 3 (a) and Figure 4 (a), it can be seen that the target range - dimension walk is compensated. s rc' (τ, t m ) is inverse - transformed to the range - Doppler domain. At this time, the Doppler spread still exists, and further compensation for the Doppler walk is required.

[0127] Step Six: Range - Doppler Domain Transformation

[0128] Starting from N a = 1, perform azimuth - direction discrete Fourier transform on s rc' (τ, t m ) according to Equation (10).

[0129] Step Seven: Optimization Model Establishment

[0130] Respectively obtain xx and yy according to the results in Step Six, and calculate

[0131] Step Eight: Model Solving

[0132] Traverse N a = 2 up to N a = N in sequence, and solve according to Step Six, Step Seven, and Step Eight. Finally, the estimation of the phase error is obtained.

[0133] By comparing Figure 5 (b) and Figure 4 (b), it can be seen that at this time, the Doppler broadening in the target Doppler dimension is corrected, the target is focused, and the targets can be distinguished from each other. At the same time, there is no velocity ambiguity for the target. The simulation results verify the feasibility of the proposed algorithm.

Claims

1. A method for target range-Doppler walk correction based on a general search radar, characterized in that, Including the following steps: S1. Establish a geometric scene with the radar as the origin to obtain the instantaneous distance of the target; S2. Perform pulse compression on the instantaneous distance of the target to obtain a distance compression result; S3. Perform Fourier transform in the fast time domain on the distance compression result; S4. Perform slow time-fast time frequency decoupling on the distance compression result after Fourier transform; S5. Perform inverse Fourier transform in the fast time domain on the result of frequency decoupling; S6. Perform distance-Doppler domain transformation on the decoupling result after inverse Fourier transform, and then perform phase walk compensation to obtain a relationship between the target distance-Doppler domain result and the phase walk amount to be estimated; S7. Use the iterative method of coordinate descent to solve the optimal solution of the relationship between the target distance-Doppler domain result and the phase walk amount to be estimated.

2. The method for target range-Doppler walk correction based on a general search radar according to claim 1, characterized in that The specific content of step S1 is as follows: A geometric scene is established with the radar as the origin. The initial distance between the target and the radar is R0, and the initial angle with the Y-axis is θ0. The target moves with a uniform acceleration of α and a velocity of v along the Y-axis. The initial slant range of the target is At any time t, the instantaneous distance of the target is R(t), and the specific formula is: In the above formula, x is the abscissa of the target, and y is the ordinate of the target.

3. The method for target range-Doppler walk correction based on a wide-swath radar according to claim 2, characterized in that, The distance compression result s in the step S2 rc (τ,t) has the following specific formula: In the above formula, ω az (t) is the azimuth envelope, sinc(·) is the range pulse compression response function, B is the transmit signal bandwidth, τ is the fast time in the range direction, t is the slow time in the azimuth direction, c is the electromagnetic propagation speed, λ is the carrier wavelength, and j is the imaginary symbol.

4. The method for target range-Doppler walk correction based on a general search radar according to claim 3, wherein The specific formula for the Fourier transform in the fast time domain in step S3 is: S rc (f τ ,t) = Aw az (t)G 2B (f τ ) In the above formula, S rc (f τ , t) is the result of range compression after Fourier transform, A is a constant, G 2B is the range envelope, f τ is the fast-time domain frequency, f c is the carrier frequency.

5. According to the method for correcting target distance-Doppler walk based on a pan-exploration radar described in claim 4, the specific formula for slow time-fast time frequency decoupling in step S4 is: In the above formula, S rc' (f τ , t m ) is the frequency decoupling result, and t m is the variable substitution of the slow time, expressed as t m =(f c +f τ )t / f c , and K is the variable relation expression, expressed as 6. The method for target range-Doppler walk correction based on a wide-swath radar according to claim 5, wherein The specific formula for the inverse Fourier transform in the fast time domain in step S5 is: In the above formula, s rc' (τ, t m ) is the frequency decoupling result after the inverse Fourier transform.

7. The method for target range-Doppler walk correction based on a fan-shaped radar according to claim 6, wherein The specific content of step S6 is as follows: Perform a discrete Fourier transform in the slow time dimension on the frequency decoupling result after the inverse Fourier transform to obtain the range-Doppler domain result The specific formula is as follows: In the above formula, f is the Doppler-domain frequency, is the sampling value of the fast time τ, is the sampling value of the slow time t m , N r and N a are the sampling points of the fast time dimension and the slow time dimension respectively, N is the total number of sampling points of the slow time dimension, and ω is the angular frequency; Perform phase walk compensation on the range-Doppler domain results, and the range-Doppler results after Doppler walk compensation The specific formula is as follows: In the above formula, is the Doppler shift amount to be estimated.

8. The method for target range-Doppler walk correction based on a general exploration radar according to claim 7, wherein The specific content of step S7 is as follows: Record is the nth phase walk correction amount for the i-th iteration, and the (i + 1)-th iteration is expressed as: Wherein, yy = (s rc' |q)exp(-jω(t m ) q ) In the above formula, yy is the q-th frequency point and its amplitude before correction, xx is the linear combination of all other frequency points except the q-th frequency point, s rc' denotes s rc' (τ, t m ), is the frequency decoupling result after the inverse Fourier transform, is the phase estimation of the q-th frequency point, is the phase estimation of the N a -th frequency point, (t m ) q is the q-th sampling point after the variable substitution of the slow time; According to the obtained xx and yy, the intensity v of the l-th pixel in the range-Doppler domain is expressed as: l expressed as: In the above formula, referring to the l-th pixel point, is the conjugate of xx, l xx of the l-th pixel point, l is yy of the l-th pixel point, l * is xx, l the conjugate of yy, l * is yy, l the conjugate of, is the real part symbol representation; According to intensity v l Calculate The specific formula is as follows: In the above formula, is the clarity expression of the image, where l ∈ [1 to L], and L is the number of all pixel points; That is, under coordinate descent, the multi-dimensional optimization solution is transformed into a single-variable extreme value problem: Set the search phase error range to [-π, π], and search within this range to obtain the corresponding i.e., the estimation of the phase error.

Images