Bistatic radar high-speed target detection method based on space-time Doppler coherent accumulation

Abstract

The invention discloses a bistatic radar high-speed target detection method based on space-time Doppler coherent accumulation, and the method comprises the steps: building a bistatic array radar system signal echo model, and carrying out the pulse compression processing of radar echo data; based on the array receiving signal, the direction matrix of the receiving beam and the corresponding weight vector, performing simultaneous multi-beam forming processing on the signal after pulse compression to obtain a signal after beam forming; constructing a beam compensation function; performing transformation compensation on the signal after beam forming by using a beam compensation function to obtain a signal after beam walking correction; performing line demodulation processing on each beam of the signal after beam walking correction to obtain a two-dimensional signal of a distance-modulation frequency domain; and detecting to obtain a target detection result. According to the method, the effects of range migration, pitching beam migration, azimuth beam migration and Doppler frequency migration can be effectively eliminated, the detection performance of the high-speed moving target is improved, and accurate positioning and speed estimation of the high-speed moving target are realized.

Description

Technical Field

[0001] The present invention belongs to the technical field of radar target detection, and in particular relates to a bistatic radar high-speed target detection method based on space-time Doppler coherent integration. Background Art

[0002] With the continuous advancement of science and technology, the effective detection and parameter estimation of high-speed moving targets such as hypersonic vehicles, ballistic missiles, and high-speed cruise missiles have attracted widespread attention in the modern radar field. However, the radar cross-section of these high-speed moving targets is typically low, resulting in weak radar returns, making detection more difficult with single-base radars. GNSS (Global Navigation Satellite System)-based dual-base array radars, due to their unique dual-base configuration and dual-base angles generally greater than 135°, offer anti-stealth and anti-interference capabilities. Consequently, they have been increasingly used for high-speed moving target detection in recent years.

[0003] The main problem with GNSS-based bistatic array radar is that its power density near the Earth's surface is close to -135dBW / m 2 , which makes radar detection difficult. In order to cope with this limitation and achieve effective detection of airborne high-speed moving targets, the signal-to-noise ratio and detection performance can be improved by integrating the target echo during a long dwell time. However, during the long coherent integration time, the higher radial velocity of the high-speed moving target will cause the bistatic range difference to change continuously, thereby causing problems such as linear range drift, secondary range bending, and Doppler frequency shift. Correspondingly, the higher tangential velocity of the high-speed moving target causes the azimuth and pitch angles to change continuously, causing problems such as pitch beam mismatch and azimuth beam mismatch. In particular, when the receiver adopts a narrow receiving beam to meet the high angular resolution of the system, the beam mismatch problem will be more obvious, and may even cause pitch beam offset and azimuth beam offset problems.

[0004] For the former, the echo energy of a high-speed moving target within an accumulation period causes a spectral peak energy diffusion effect in the time-frequency domain. This means that the target's energy is dispersed across different range and Doppler bins, resulting in a reduction in the radar's pre-detection signal-to-noise ratio and post-detection probability. To address this issue, many researchers in the field are dedicated to researching range-Doppler motion compensation techniques to eliminate the problem of spectral peak energy leakage.

[0005] Radon-Fourier transform, maximum likelihood estimation, axis of rotation, Keystone transform, and coherent Radon transform are commonly used coherent detection algorithms. However, they do not consider second-order range walk and Doppler spread caused by the target's velocity variations. Later, some studies used the generalized Radon-Fourier transform to eliminate range walk, range curvature, and Doppler shift. However, without prior knowledge, the generalized Radon-Fourier transform suffers from blind velocity sidelobes and high computational complexity due to its wide and high-dimensional search characteristics. Because targets with extreme parameters are easily detected when the search space is not large enough, avoiding search operations can greatly reduce complexity and improve algorithm robustness. Some studies have proposed range symmetry transforms and detuning to correct for offsets, but this discards valuable range information. Fu proposed the RVDT method, which can address range walk while preserving range information, but does not consider the target's second-order terms.

[0006] For the latter, when the target's tangential velocity is high or the receiving beam is narrow, it crosses the radar beam's mainlobe during the beam dwell time. This phenomenon occurs when the target leaves the radar beam's mainlobe illumination area, causing a sharp drop in the target echo's signal-to-noise ratio. In other words, after the target crosses the radar beam, the radar beamforming filters out the target's energy in the spatial domain, rendering traditional time-frequency domain processing algorithms ineffective. To address the beamwalk problem, literature has proposed a three-dimensional signal model based on range-Doppler-beam and corresponding time-sharing multi-beam (TSMB) and spatially shared multi-beam (SSMB) coherent integration algorithms. However, these two methods only consider the phase difference between different beams, not the phase difference caused by the target's tangential velocity. Furthermore, these models approximate the nonlinear beam mismatch factor as a linear one, resulting in a decrease in algorithm accuracy. Later, based on the spatially shared multi-beam model, a multi-scale sliding window phase difference (MSWPD) method was proposed to achieve energy accumulation between multiple beams. However, this approach requires estimating the time when the target enters and leaves the beam, and sequentially mapping the two-dimensional time-frequency data in different beams to three-dimensional XYZ data for accumulation, which has high computational complexity. Furthermore, both of the above methods only consider the cross-beam problem in azimuth, without also considering the two-dimensional beam movement in azimuth and elevation. Summary of the Invention

[0007] To address the above-mentioned problems in the prior art, the present invention provides a high-speed target detection method for a bistatic radar based on space-time Doppler coherent integration. The technical problem to be solved by the present invention is achieved through the following technical solutions:

[0008] A high-speed target detection method for a bistatic radar based on space-time Doppler coherent integration, comprising:

[0009] Establish a signal echo model for a bistatic array radar system, perform pulse compression on the radar echo data, and obtain a pulse compressed signal.

[0010] performing simultaneous multi-beamforming processing on the pulse compressed signal based on the array received signal, the direction matrix of the received beam, and the corresponding weight vector to obtain a beamformed signal;

[0011] constructing a beam compensation function based on the beamformed signal; performing transformation compensation on the beamformed signal using the beam compensation function to obtain a beam movement corrected signal;

[0012] Performing a de-modulation process on each beam of the beam movement corrected signal to obtain a two-dimensional signal in a range-modulation frequency domain;

[0013] The two-dimensional signal in the range-modulation frequency domain is detected to obtain a target detection result.

[0014] In one embodiment of the present invention, the signal echo model of the bistatic array radar system has the following settings:

[0015] The bistatic array radar system transmits signals via GEO satellites and receives them via ground-based receivers. The receiver uses a uniform rectangular array and is placed in the XY plane of a three-dimensional Cartesian coordinate system, with M antenna units in each column and N antenna units in each row. The spacing between adjacent antenna units is assumed to be d in both dimensions. The receiver uses simultaneous multi-beam technology to form multiple spatially connected narrow beams to receive reflected signals from the monitored airspace. The uniform rectangular array forms a reference beam pointing to the satellite to receive direct wave signals.

[0016] In one embodiment of the present invention, the signal after the pulse compression is expressed as:

[0017]

[0018] Among them, s r (t,t m ) represents the signal after the pulse pressure, t represents the fast time, t m represents the slow time, σ represents the complex reflectivity of the target, T a represents the entire integration time, rect(·) represents the window function, ρ(·) represents the cross-correlation function between the reflected signal and the reference signal, exp represents the exponential function, j represents the imaginary unit, c represents the speed of light, and λ represents the wavelength. represents the biradical distance, R0 represents the initial biradical distance, C1, C2, and C3 represent the equivalent first-order, second-order, and third-order derivatives of the initial biradical distance and the third-order Taylor expansion, respectively.

[0019] In one embodiment of the present invention, performing simultaneous multi-beamforming processing on the pulse compressed signal based on the array received signal, the direction matrix, and the weight vector to obtain the beamformed signal includes:

[0020] Determine the expression of the array received signal in the fast time and slow time two-dimensional domains, specifically:

[0021] x(t,t m )=As r (t,t m )+n(t,t m );

[0022] Among them, x(t,t m ) represents the array receiving signal, t represents the fast time, t m Indicates slow time; Contains the target's direction of arrival information, (·) T represents transpose, a u =[1,e ju ,…,e j(M-1)u ], a v =[1,e jv ,…,e j(N-1)v ],u=2πdcosθ(t m ) / λ represents the path difference along the Y axis, represents the path difference along the X axis, d = λ / 2 represents the spacing between antenna units, θ(t m )=θ0+ω θ t m represents the pitch angle, θ0 represents the initial pitch angle of the target, ω θ represents the target’s pitch-dimensional tangential angular velocity, represents the azimuth, represents the initial azimuth of the target, Indicates the azimuth tangential angular velocity of the target, s r (t,t m ) represents the signal after the pulse pressure, n(t,t m ) represents the noise matrix;

[0023] The expression for determining the direction matrix of the receiving beam is:

[0024]

[0025] Where, κ represents the direction matrix, θ l-1 =(l-1)θ Φ represents the beam pitch angle, represents the beam azimuth, represents the half-power point width of the azimuth main lobe, represents the half-power point width of the elevation main lobe, l represents the number of beams per row or column, M represents the number of antenna elements per column, and N represents the number of antenna elements per row;

[0026] The expression for the weight vector of the direction matrix of the receiving beam is determined as follows:

[0027]

[0028] Among them, H τ,η represents the weight vector, θ τ =θ Φ τ represents the angle of the light beam to the X axis, represents the angle of the beam to the Y axis, 0≤τ,η≤l-1 represents the beam row variable and column variable;

[0029] Based on the expressions of the array received signal in the fast time and slow time two-dimensional domains, the expression of the direction matrix and the expression of the weight vector, the simplified expression of the beamformed signal is determined as:

[0030]

[0031] Among them, s(t,t m ,τ,η) represents the signal after beamforming, represents the target complex reflectivity after beamforming.

[0032] In one embodiment of the present invention, constructing a beam compensation function based on the beamformed signal includes:

[0033] performing a three-dimensional fast Fourier transform on the beamformed signal at a fast time, an elevation beam time, and an azimuth beam time to obtain a frequency domain signal;

[0034] A time reversal operation is performed on the phase of the frequency domain signal along the slow time direction to obtain a beam compensation function; the beam compensation function is expressed as:

[0035]

[0036] in, represents the beam compensation function, f, f τ 、f η are the fast time frequency, elevation beam frequency and azimuth beam frequency, respectively, and f c Indicates the carrier frequency, T c Represents the coherent processing time.

[0037] In one embodiment of the present invention, constructing a beam compensation function based on the beamformed signal; and performing transformation compensation on the beamformed signal using the beam compensation function to obtain a beam walk corrected signal includes:

[0038] multiplying the frequency domain signal by the conjugate of its first pulse extension signal to obtain a transformed frequency domain signal;

[0039] multiplying the beam compensation function and the transformed frequency domain signal to obtain a beam correction frequency domain signal;

[0040] Performing a three-dimensional inverse fast Fourier transform of the fast time frequency, the pitch beam frequency, and the azimuth beam frequency on the beam correction frequency domain signal to obtain a beam correction time domain signal as a beam movement corrected signal;

[0041] The beam correction time domain signal is expressed as:

[0042]

[0043] Among them, s′(t,t m ,τ,η) represents the beam correction time domain signal, R end represents the terminal double base distance, θ end represents the terminal pitch angle of the target, Indicates the terminal bearing of the target.

[0044] In one embodiment of the present invention, performing a de-modulation process on each beam of the beam walk corrected signal to obtain a two-dimensional signal in the range-modulation frequency domain includes:

[0045] Detecting different beams of the signal after beam movement correction to obtain fast and slow time signals of the beam where the target end moment is located;

[0046] Performing a fast Fourier transform on the fast and slow time signals along the fast time to obtain a fast time frequency domain-slow time domain signal;

[0047] According to the linear frequency modulation characteristics of the fast time frequency domain-slow time time domain signal, a Doppler compensation function is constructed by constructing a de-linear frequency modulation signal; wherein the Doppler compensation function is expressed as:

[0048]

[0049] in, represents the Doppler compensation function, P(f) represents power, Indicates C d There are many different estimates of C d =2C2+3C3T c ;

[0050] Performing a demodulation process on the fast-time frequency domain-slow-time time domain signal using the demodulated signal to obtain a demodulated time domain signal;

[0051] The demultiplexed line-modulated time domain signal is coherently integrated in a slow time to obtain a two-dimensional signal in a range-modulated frequency domain.

[0052] In one embodiment of the present invention, performing a demodulation process on the fast-time frequency domain-slow-time time domain signal using the demodulated signal to obtain a demodulated time domain signal includes:

[0053] Multiplying the de-modulated signal by the fast-time frequency domain-slow-time time domain signal to obtain a de-modulated frequency domain signal;

[0054] Perform inverse fast Fourier transform of the time-frequency dimension on the de-modulated frequency domain signal to obtain a de-modulated time domain signal, which is expressed as:

[0055]

[0056] in, represents the demodulated time domain signal.

[0057] In one embodiment of the present invention, the two-dimensional signal in the range-modulation frequency domain is expressed as:

[0058]

[0059] in, represents the range-modulated frequency domain two-dimensional signal, Indicates the demodulated time domain signal.

[0060] In one embodiment of the present invention, detecting the two-dimensional signal in the range-modulation frequency domain to obtain a target detection result includes:

[0061] CA-CFAR detection is performed on the two-dimensional signal in the range-frequency modulation domain to obtain a target detection result.

[0062] An embodiment of the present invention provides a bistatic radar high-speed target detection method based on space-time Doppler coherent integration. First, a signal echo model of a bistatic array radar system is established, and pulse compression processing is performed on radar echo data to obtain a pulse-compressed signal. Secondly, based on the array received signal, the direction matrix of the received beam, and the corresponding weight vector, simultaneous multi-beamforming processing is performed on the pulse-compressed signal to obtain a beamformed signal. Next, a beam compensation function is constructed based on the beamformed signal. The beamformed signal is transformed and compensated using the beam compensation function to obtain a beam movement corrected signal. Then, each beam of the beam movement corrected signal is demodulated to obtain a two-dimensional signal in the range-modulation frequency domain. Finally, the two-dimensional signal in the range-modulation frequency domain is detected to obtain a target detection result.

[0063] By establishing a signal echo model for a bistatic array radar system and performing a series of operations, including pulse compression, simultaneous multi-beam forming, beam compensation function construction, and line modulation processing, the present invention effectively eliminates range migration, elevation beam migration, azimuth beam migration, and Doppler frequency migration. This effectively focuses echo energy, eliminates spectrum peak leakage, and improves the detection signal-to-noise ratio. This enables precise positioning and velocity estimation of high-speed moving targets, enhancing detection performance and having significant implications for the detection of high-speed maneuvering targets. Therefore, the present invention has high practical value and broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 A schematic flow chart of a method for high-speed target detection using a bistatic radar based on space-time Doppler coherent integration provided by an embodiment of the present invention;

[0065] Figure 2 A schematic diagram of the overall structure of a bistatic array radar for high-speed moving target detection provided by the present invention;

[0066] Figure 3 This is a diagram showing the results of simultaneous multi-beamforming in a bistatic array radar system configuration provided by an embodiment of the present invention;

[0067] Figure 4 A result diagram of step 3 of a bistatic radar high-speed target detection method based on space-time Doppler coherent integration provided by an embodiment of the present invention;

[0068] Figure 5 The (33°, 33°) beam magnification diagram in step 3 of the result diagram of a bistatic radar high-speed target detection method based on space-time Doppler coherent integration provided by an embodiment of the present invention;

[0069] Figure 6A diagram showing the result of the demodulation processing in step 4 of a bistatic radar high-speed target detection method based on space-time Doppler coherent integration provided by an example of the present invention;

[0070] Figure 7 This is a result diagram of step 4 of a bistatic radar high-speed target detection method based on space-time Doppler coherent integration provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0071] The present invention will be further described in detail below with reference to specific examples, but the embodiments of the present invention are not limited thereto.

[0072] High-speed moving targets, such as hypersonic vehicles, have a low radar cross-section and weak echo energy, making single-base radar detection challenging. Long-term data accumulation is required to improve the signal-to-noise ratio (SNR). Due to the targets' high velocity and acceleration, the high radial velocity of high-speed moving targets during long-term data accumulation causes the bistatic range difference to continuously vary, leading to linear range drift, quadratic range curvature, and Doppler shift. This results in echo energy diffusion in the time-frequency domain, dispersing spectral peak energy across different range and Doppler bins, reducing both the pre-detection SNR and the post-detection probability.

[0073] Currently, commonly used coherent detection algorithms, such as the Radon-Fourier transform and maximum likelihood estimation, fail to account for second-order range walk and Doppler spread caused by target velocity variations. While the generalized Radon-Fourier transform can partially mitigate these issues, its search characteristics lead to blind velocity sidelobes and high computational complexity. Range symmetry transforms and detuning can discard valuable range information. The RVDT method fails to consider the target's second-order terms. The three-dimensional range-Doppler-beam signal model and related algorithms only consider the phase difference between different beams, ignoring the phase difference caused by the target's tangential velocity. They also approximate the nonlinear beam mismatch factor as a linear function, resulting in reduced algorithm accuracy. The multi-scale sliding window phase difference method has high computational complexity and only considers cross-beam issues in azimuth, ignoring two-dimensional beam walk in azimuth and elevation.

[0074] On the other hand, the target's high tangential velocity can cause changes in pitch and azimuth angles, leading to pitch and azimuth beam mismatch, and even beam crossing. When a target crosses the radar beam's main lobe, the echo signal-to-noise ratio plummets, rendering traditional time-frequency domain processing algorithms ineffective. Existing algorithms for addressing beam walk, such as the range-Doppler-beam three-dimensional signal model and related algorithms, suffer from issues such as not accounting for phase differences caused by the target's tangential velocity, approximating the nonlinear beam mismatch factor as a linear factor, resulting in reduced accuracy, and high computational complexity.

[0075] To address these issues, the present invention specifically studies the accumulation, compensation, and detection of high-speed maneuvering target echo signals. It aims to provide a bistatic radar high-speed target detection method based on space-time Doppler coherent integration. By establishing a bistatic array radar system signal echo model and performing a series of operations, including pulse compression, simultaneous multi-beamforming, beam compensation function construction, and line modulation processing, the method effectively eliminates the effects of range migration, elevation beam migration, azimuth beam migration, and Doppler frequency migration, thereby improving the detection performance of high-speed moving targets and achieving precise positioning and velocity estimation of high-speed moving targets.

[0076] For details, see Figure 1 The embodiment of the present invention provides a bistatic radar high-speed target detection method based on space-time Doppler coherent integration, which may include the following steps:

[0077] S1, establish a signal echo model of the bistatic array radar system, perform pulse compression processing on the radar echo data, and obtain the pulse compressed signal;

[0078] The present invention primarily designs and researches a target enhancement and detection method based on the transmission of GEO navigation satellites as external radiation sources and reception by ground-based array radars. First, using GEO navigation satellite signals as external radiation sources, the ground-based array radar receives the echo signals of high-speed moving targets. A mathematical model for speed and range measurement based on the geometric configuration of a bistatic array radar is derived, and a corresponding mathematical model for the received signal is established.

[0079] Specifically, see Figure 2 , Figure 2 This is the overall structure of the bistatic array radar for high-speed moving target detection provided by the present invention. The signal echo model of the bistatic array radar system has the following settings:

[0080] The dual-base array radar system is connected to the GEO satellite T x The signal is transmitted through the ground receiver R x Receive signals; the receiver uses a uniform rectangular array and is placed in the XY plane of a three-dimensional Cartesian coordinate system, with M antenna units in each column and N antenna units in each row; the spacing between adjacent antenna units is assumed to be d in both dimensions; the receiver uses simultaneous multi-beam technology to form multiple spatially connected narrow beams to receive reflected signals from the monitored airspace; in order to subsequently perform distance compression, the uniform rectangular array forms a reference beam pointing to the satellite to receive direct wave signals.

[0081] Assume that there is a high-speed moving target in the monitoring area, R T and R R are the distance vectors between the target and the satellite and the receiver, R bis the distance from the satellite to the receiver, R(t m )=||R T ||+||R R ||-||R b || is the bistatic distance, θ(t m )and are the angles of the target about the Y-axis and X-axis in the rectangular coordinate domain, which are defined as the pitch angle and azimuth angle of the target in this invention. The speed of the target can be decomposed into the angles parallel to R R High radial velocity in the direction and perpendicular to R R The high tangential angular velocity in the direction of m ), pitch angle θ(t m ) and azimuth Changes over time. Figure 2 The geometric relationship shown is based on Taylor series expansion, R(t m ) can be expanded into a second-order term, and θ(t m )and It can be expanded into first-order terms, namely:

[0082]

[0083] Among them, t m represents the slow time variable, θ0 represents the initial pitch angle of the target, represents the initial azimuth of the target, ω θ represents the target's pitch angle and tangential angular velocity, represents the azimuth tangential angular velocity of the target, R0 is the initial bistatic distance, C1, C2, and C3 represent the equivalent first-order, second-order, and third-order derivatives of the third-order Taylor expansion of the initial bistatic distance, respectively.

[0084] The signal transmitted by the satellite is continuous, in which the ranging code and navigation message are modulated on the carrier. The ranging code is pseudo-random and periodic. The period of the ranging code is regarded as an equivalent pulse repetition interval T r , the received continuous direct wave and reflected signal are converted into fast time t and slow time t m The delay, Doppler, and phase values are extracted from the direct wave to obtain the reference signal for the corresponding matched filter.

[0085] After pulse compression, the target echo signal received by the receiving antenna of each unit in the uniform array radar can be modeled in the fast time and slow time domains. Therefore, the pulse compressed signal can be expressed as:

[0086]

[0087] Among them, s r (t,t m) represents the signal after the pulse pressure, t represents the fast time, t m represents the slow time, σ represents the complex reflectivity of the target, T a represents the entire integration time, rect(·) represents the window function, ρ(·) represents the cross-correlation function between the reflected signal and the reference signal, exp represents the exponential function, j represents the imaginary unit, c represents the speed of light, and λ represents the wavelength. represents the biradical distance, R0 represents the initial biradical distance, C1, C2, and C3 represent the equivalent first-order, second-order, and third-order derivatives of the initial biradical distance and the third-order Taylor expansion, respectively.

[0088] S2, performing simultaneous multi-beamforming processing on the pulse compressed signal based on the array received signal, the direction matrix of the received beam, and the corresponding weight vector to obtain a beamformed signal;

[0089] The path difference between the received signal at the antenna unit (m, n), 1≤m≤M, 1≤n≤N and the reference antenna can be expressed as:

[0090] β m,n =(m-1)u+(n-1)v;

[0091] Where u = 2πdcosθ(t m ) / λ is the path difference along the Y axis, is the path difference along the X-axis, and the spacing between antenna units (i.e., antenna spacing) d=λ / 2.

[0092] Substituting the antenna spacing formula into the path difference formula, we can know that β m,n Independent of wavelength.

[0093] Therefore, S2 may include the following steps:

[0094] Determine the expression of the array received signal in the fast time and slow time two-dimensional domains, specifically:

[0095] x(t,t m )=As r (t,t m )+n(t,t m );

[0096] Among them, x(t,t m ) represents the array receiving signal, t represents the fast time, t m Indicates slow time; Contains the target's direction of arrival information, (·) T represents transpose, a u =[1,e ju ,…,e j(M-1)u ], a v =[1,e jv,…,e j(N-1)v ],u=2πdcosθ(t m ) / λ represents the path difference along the Y axis, represents the path difference along the X axis, d = λ / 2 represents the spacing between antenna units, θ(t m )=θ0+ω θ t m represents the pitch angle, θ0 represents the initial pitch angle of the target, ω θ represents the target’s pitch-dimensional tangential angular velocity, represents the azimuth, represents the initial azimuth of the target, Indicates the azimuth tangential angular velocity of the target, s r (t,t m ) represents the signal after the pulse pressure, n(t,t m ) represents the noise matrix;

[0097] In order to achieve ubiquitous reception of target echo signals and obtain good pitch and azimuth angle measurement accuracy, the bistatic array radar simultaneously forms adjacent narrow receiving beams covering the entire surveillance airspace. The number of beams is l 2 The main lobes of these beams are spatially connected to each other, l 2 The beams are simultaneously directed to l 2 The directional matrix of these beams can be determined by using different azimuth and elevation angles.

[0098] The expression for determining the direction matrix of the receiving beam is:

[0099]

[0100] Where, κ represents the direction matrix, θ l-1 =(l-1)θ Φ represents the beam pitch angle, represents the beam azimuth, represents the half-power point width of the azimuth main lobe, represents the half-power point width of the elevation main lobe, l represents the number of beams per row or column, M represents the number of antenna elements per column, and N represents the number of antenna elements per row;

[0101] Therefore, when the array forms a beam pattern, the direction matrices of different beams correspond to different weight vectors, and the expression of the weight vector can be determined.

[0102] The expression for the weight vector of the direction matrix of the receiving beam is determined as follows:

[0103]

[0104] Among them, H τ,ηrepresents the weight vector, θ τ =θ Φ τ represents the angle of the light beam to the X axis, represents the angle of the beam to the Y axis, 0≤τ,η≤l-1 represents the beam row variable and column variable;

[0105] Therefore, after simultaneous multi-beamforming, the beamformed signal received by the uniform rectangular array corresponding to the direction matrix κ(τ,η) can be expressed as:

[0106]

[0107] Among them, s(t,t m ,τ,η) represents the signal after beamforming, and represent the azimuth beam matching factor and elevation beam matching factor respectively.

[0108] Since the receiving beam of the system is a narrow beam, the above formula can be simplified to:

[0109]

[0110] Within a coherent integration time, the tangential Doppler value is unlikely to cross the zero Doppler channel, which means that the impact of the tangential Doppler on the target echo can be ignored. Therefore, the above formula can be further simplified. Specifically:

[0111] Based on the expressions of the array received signal in the fast time and slow time two-dimensional domains, the expression of the direction matrix and the expression of the weight vector, the simplified expression of the beamformed signal is determined as:

[0112]

[0113] Among them, s(t,t m ,τ,η) represents the signal after beamforming, represents the target complex reflectivity after beamforming.

[0114] S3, constructing a beam compensation function based on the beamformed signal; performing transformation compensation on the beamformed signal using the beam compensation function to obtain a beam movement corrected signal;

[0115] Constructing a beam compensation function based on the beamformed signal may include the following steps:

[0116] performing a three-dimensional fast Fourier transform on the beamformed signal at a fast time, an elevation beam time, and an azimuth beam time to obtain a frequency domain signal;

[0117] Specifically, in this step, since the target echo is located in the beam, the following conditions are satisfied:

[0118]

[0119] Within the error tolerance, τ and η can be respectively (θ0+ω θ t m ) / θ Φ and Perform a first-order Taylor expansion:

[0120]

[0121] Therefore, according to the stationary phase principle, the target echo signal received by the uniform rectangular linear array can be expressed in the pitch and azimuth beam frequency domains as follows:

[0122]

[0123] Among them, S(f,f τ ,f η ,t m ) represents the frequency domain signal, f, f τ , f η are the fast time frequency, elevation beam frequency and azimuth beam frequency, respectively, and f c Indicates the carrier frequency.

[0124] A time reversal operation is performed on the phase of the frequency domain signal along the slow time direction to obtain a beam compensation function; the beam compensation function is expressed as:

[0125]

[0126] in, represents the beam compensation function, f, f τ 、f η are the fast time frequency, elevation beam frequency and azimuth beam frequency, respectively, and f c Indicates the carrier frequency, T c Represents the coherent processing time.

[0127] Next, in S3, constructing a beam compensation function based on the beamformed signal; performing transformation compensation on the beamformed signal using the beam compensation function to obtain a beam movement corrected signal may include:

[0128] multiplying the frequency domain signal by the conjugate of its first pulse extension signal to obtain a transformed frequency domain signal;

[0129] The specific step is, first, select S(f,f τ ,f η ,t m) of S(f,f τ ,f η ,0) data and expand it to the original matrix size, and then combine the conjugate of the expanded matrix with S(f,f τ ,f η ,t m ) multiplied by the phase constant term to cancel out the phase constant term, and the transformed expression of the frequency domain signal can be obtained, that is, the transformed frequency domain signal is expressed as:

[0130]

[0131] Among them, S′(f,f τ ,f η ,t m ) represents the transformed frequency domain signal.

[0132] Next, multiplying the beam compensation function and the transformed frequency domain signal to obtain a beam correction frequency domain signal;

[0133] The specific step is to convert S′(f,f τ ,f η ,t m )and Multiplying and simplifying gives:

[0134]

[0135] Among them, Y(f,f τ ,f η ,t m ) represents the beam correction frequency domain signal, R end =R(t m =T c )=R0+C1T c +C2T c 2 +C3T c 3 represents the distance of the target at the end of coherent processing, θ end =θ(t m =T c )=θ0+ω θ T c represents the pitch angle of the target at the end of coherent processing, represents the azimuth of the target at the end of coherent processing.

[0136] Then, performing a three-dimensional inverse fast Fourier transform of the fast time frequency, the pitch beam frequency, and the azimuth beam frequency on the beam correction frequency domain signal to obtain a beam correction time domain signal as a beam movement corrected signal;

[0137] The beam correction time domain signal is expressed as:

[0138]

[0139] Among them, s′(t,t m ,τ,η) represents the beam correction time domain signal, R end represents the terminal double base distance, θ end represents the terminal pitch angle of the target, Indicates the terminal bearing of the target.

[0140] It can be seen that τ-t m and η-t m The coupling term is eliminated, which means that the beam walk problem is solved and the echo energy is concentrated in the beam where the target is located at the end moment.

[0141] S4, performing a de-modulation process on each beam of the beam walk corrected signal to obtain a two-dimensional signal in a range-modulation frequency domain;

[0142] The aforementioned processing solves the beam walk problem in multibeam data received simultaneously by a uniform rectangular array. However, the range walk and Doppler shift effects caused by C2 and C3 still exist in the target echo. Therefore, a frequency-domain demodulation algorithm is used to eliminate the range walk and Doppler shift effects of the echo. This algorithm removes the frequency modulation slope at fast time frequencies, then performs an FFT to integrate the range-modulation frequency domain. Finally, the target's azimuth, elevation, bistatic range, and modulation frequency are detected and obtained.

[0143] As can be seen from the above formula, the target's echo energy is embedded in the terminal pitch and azimuth beams. However, the echo is generally buried by noise, and the beam information is unknown. Therefore, the signals from different beams must be extracted sequentially for detection. Therefore, step S4 can specifically include the following steps:

[0144] S41, detecting different beams of the signal after beam movement correction to obtain the fast and slow time signals of the beam where the target end moment is located; specifically expressed as:

[0145]

[0146] It can be observed that the envelope and phase of the signal have a similar chirp structure. Moreover, the starting frequency of the chirp signal is T times the modulation frequency. c times, and T c is a known quantity, so the starting frequency and modulation frequency of the signal can be removed at the same time, significantly reducing the computational complexity of the demodulation algorithm.

[0147] S42, performing a fast Fourier transform on the fast-time and slow-time signals along the fast time to obtain a fast-time frequency domain-slow-time time domain signal;

[0148] Specifically, the fast Fourier transform is performed on the fast and slow time signals along the fast time, and the chirp signals in the envelope and phase are aggregated, which are expressed as follows:

[0149]

[0150] Among them, S(f,t m ) represents the fast time frequency domain-slow time domain signal, C d =2C2+3C3T c .

[0151] S43, constructing a Doppler compensation function by constructing a de-linear modulation signal according to the linear frequency modulation characteristics of the fast time frequency domain-slow time time domain signal; wherein the Doppler compensation function is expressed as:

[0152]

[0153] Since we don’t actually know the true C d , so different C d The demodulated signal of the value is shown in the above formula. Among them, represents the Doppler compensation function, P(f) represents power, Indicates C d There are many different estimates of C d =2C2+3C3T c ;

[0154] S44, performing a demodulation process on the fast-time frequency domain-slow-time time domain signal using the demodulated signal to obtain a demodulated time domain signal;

[0155] This step specifically includes:

[0156] S441, multiplying the de-modulated signal by the fast-time frequency domain-slow-time time domain signal to obtain a de-modulated frequency domain signal;

[0157] This step completes the frequency modulation processing by multiplying the demodulated signal with the fast time frequency domain-slow time time domain signal. The demodulated signal is the demodulated frequency domain signal, which is expressed as:

[0158]

[0159] S442, performing an inverse fast Fourier transform of the time-frequency dimension on the demultiplexed frequency-domain signal to obtain a demultiplexed time-domain signal, which is expressed as:

[0160]

[0161] in, represents the demodulated time domain signal.

[0162] S45 , performing coherent integration on the demultiplexed line-modulated time domain signal in a slow time domain to obtain a two-dimensional signal in a range-modulated frequency domain.

[0163] After demodulation, a fast Fourier transform is performed on the slow time to achieve coherent integration. According to the stationary phase principle, the coherent integration result is:

[0164]

[0165] Among them, f m is the Doppler frequency. It is not difficult to see from the phase of the above formula that it does not contain the first-order slow time frequency term f m , the phase shift is only related to the second-order slow frequency term About, when When , there is no phase change. Obviously, this peak must appear at zero Doppler, which means that there is no need to use a full FFT search. Only the signal at zero Doppler needs to be accumulated, which significantly reduces the computational complexity. Coherent accumulation can be simplified to summing the Doppler to zero. Therefore, after simplifying the above formula, the two-dimensional signal in the range-modulated frequency domain can be expressed as:

[0166]

[0167] in, represents the range-modulated frequency domain two-dimensional signal, Indicates the demodulated time domain signal.

[0168] Therefore, after the long integration, each extracted signal is integrated into the two-dimensional range-modulation frequency domain. After the above integration process is performed on each beam, it is obvious that the coordinates of the target spectrum peak in the 4-dimensional space are

[0169] S5, detecting the two-dimensional signal in the range-frequency modulation domain to obtain a target detection result.

[0170] Specifically, this step is to perform CA-CFAR detection on the two-dimensional signal in the range-modulation frequency domain to obtain a target detection result.

[0171] To address the cross-beam motion problem of high-speed target echoes, focus echo energy, eliminate spectral peak leakage, and improve the detection signal-to-noise ratio, an embodiment of the present invention provides a bistatic radar high-speed target detection method based on space-time Doppler coherent integration. First, a signal echo model of a bistatic array radar system is established, and pulse compression processing is performed on the radar echo data to obtain a pulse-compressed signal. Second, based on the array received signal, the direction matrix of the received beam, and the corresponding weight vector, simultaneous multi-beamforming processing is performed on the pulse-compressed signal to obtain a beamformed signal. Next, a beam compensation function is constructed based on the beamformed signal. The beamformed signal is transformed and compensated using the beam compensation function to obtain a beam motion-corrected signal. Then, each beam of the beam motion-corrected signal is demodulated to obtain a two-dimensional signal in the range-modulation frequency domain. Finally, the two-dimensional signal in the range-modulation frequency domain is detected to obtain a target detection result.

[0172] By establishing a signal echo model for a bistatic array radar system and performing a series of operations, including pulse compression, simultaneous multi-beam forming, beam compensation function construction, and line modulation processing, the present invention effectively eliminates range migration, elevation beam migration, azimuth beam migration, and Doppler frequency migration. This effectively focuses echo energy, eliminates spectrum peak leakage, and improves the detection signal-to-noise ratio. This enables precise positioning and velocity estimation of high-speed moving targets, enhancing detection performance and having significant implications for the detection of high-speed maneuvering targets. Therefore, the present invention has high practical value and broad application prospects.

[0173] In order to verify the effectiveness of the method provided by the embodiment of the present invention, the embodiment of the present invention conducted a simulation experiment. The embodiment of the present invention constructs echo data based on the signal model and then performs target enhancement and detection on it. Figure 3 、 Figure 4 、 Figure 5 、 Figure 6 and Figure 7 shown.

[0174] Figure 3 This is a diagram showing the results of simultaneous multi-beam forming under the dual-base array radar system configuration provided by an embodiment of the present invention. Figure 3 As can be seen in the figure, echo data for beam mainlobe and elevation pointing from (30°, 30°) to (33°, 33°) are arranged sequentially from the lower left to the upper right. It can be seen that within a single coherent integration time, the target appears in echoes with beam mainlobe pointing at (30°, 30°), (31°, 31°), (32°, 32°), and (33°, 33°). This indicates that the target exhibits significant azimuth and elevation beam movement, as well as range and Doppler movement within a single beam.

[0175] Figure 4The result diagram of step 3 of a bistatic radar high-speed target detection method based on space-time Doppler coherent integration provided in an embodiment of the present invention shows that the echo energy dispersed in different azimuth beams, different pitch beams, and different range beams is better corrected to the beam where the target end is located.

[0176] Figure 5 The (33°, 33°) beam magnification diagram in step 3 of the result diagram of a bistatic radar high-speed target detection method based on space-time Doppler coherent integration provided by an embodiment of the present invention is obtained from Figure 5 As can be seen in the figure, the fast and slow time trajectories of the target echo are corrected to be symmetrical about the central axis, and the initial range unit is corrected to be the same as the range unit of the final distance. Thus, the beam walk and third-order range walk problems are well solved, but the first-order and second-order range walks and their corresponding Doppler walks still exist.

[0177] Figure 6 The demodulation processing result diagram in step 4 of a bistatic radar high-speed target detection method based on space-time Doppler coherent integration provided by the example of the present invention shows that the echo trajectory is well corrected to the range unit where the target is located, and the range movement problem and the corresponding Doppler movement problem are solved.

[0178] Figure 7 The result diagram of step 4 of the bistatic radar high-speed target detection method based on space-time Doppler coherent integration provided by the embodiment of the present invention is obtained by Figure 6 The results of coherent accumulation of the same distance units of different pulses along the slow time domain are subsequently subjected to CA-CFAR detection to obtain accurate target position and velocity information, thereby achieving precise positioning and velocity estimation of high-speed moving targets.

[0179] In the description of this specification, the reference terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" mean that the specific features, structures, materials, or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representations of the above terms do not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials, or characteristics described can be combined in any appropriate manner in any one or more embodiments or examples. In addition, those skilled in the art can combine and combine different embodiments or examples described in this specification.

[0180] The above description is only a preferred embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention are included in the scope of protection of the present invention.

Claims

1. A bistatic radar high-speed target detection method based on space-time Doppler coherent integration, characterized in that: include: Establish a signal echo model for a bistatic array radar system, perform pulse compression on the radar echo data, and obtain a pulse compressed signal. performing simultaneous multi-beamforming processing on the pulse compressed signal based on the array received signal, the direction matrix of the received beam, and the corresponding weight vector to obtain a beamformed signal; constructing a beam compensation function based on the beamformed signal; performing transformation compensation on the beamformed signal using the beam compensation function to obtain a beam movement corrected signal; Performing a de-modulation process on each beam of the beam movement corrected signal to obtain a two-dimensional signal in a range-modulation frequency domain; The two-dimensional signal in the range-modulation frequency domain is detected to obtain a target detection result.

2. The method for high-speed target detection using a bistatic radar based on space-time Doppler coherent integration according to claim 1, wherein: The signal echo model of the bistatic array radar system has the following settings: The bistatic array radar system transmits signals via GEO satellites and receives them via ground-based receivers. The receiver uses a uniform rectangular array and is placed in the XY plane of a three-dimensional Cartesian coordinate system, with M antenna units in each column and N antenna units in each row. The spacing between adjacent antenna units is assumed to be d in both dimensions. The receiver uses simultaneous multi-beam technology to form multiple spatially connected narrow beams to receive reflected signals from the monitored airspace. The uniform rectangular array forms a reference beam pointing to the satellite to receive direct wave signals.

3. The method for high-speed target detection using a bistatic radar based on space-time Doppler coherent integration according to claim 2, wherein: The signal after the pulse pressure is expressed as: Among them, s r (t,t m ) represents the signal after the pulse pressure, t represents the fast time, t m represents the slow time, σ represents the complex reflectivity of the target, T a represents the entire integration time, rect(·) represents the window function, ρ(·) represents the cross-correlation function between the reflected signal and the reference signal, exp represents the exponential function, j represents the imaginary unit, c represents the speed of light, and λ represents the wavelength. represents the biradical distance, R0 represents the initial biradical distance, C1, C2, and C3 represent the equivalent first-order, second-order, and third-order derivatives of the initial biradical distance and the third-order Taylor expansion, respectively.

4. The method for high-speed target detection using a bistatic radar based on space-time Doppler coherent integration according to claim 3, wherein: The performing simultaneous multi-beamforming processing on the pulse compressed signal based on the array received signal, the direction matrix and the weight vector to obtain the beamformed signal includes: Determine the expression of the array received signal in the fast time and slow time two-dimensional domains, specifically: x(t,t m )=As r (t,t m )+n(t,t m ): Among them, x(t,t m ) represents the array receiving signal, t represents the fast time, t m Indicates slow time; Contains the target's direction of arrival information, (·) T represents transpose, a u =[1,e ju ,…,e j(M-1)u ], a v =[1,e jv ,…,e j(N-1)v ],u=2πdcosθ(t m ) / λ represents the path difference along the Y axis, represents the path difference along the X axis, d = λ / 2 represents the spacing between antenna units, θ(t m )=θ0+ω θ t m represents the pitch angle, θ0 represents the initial pitch angle of the target, ω θ represents the target’s pitch-dimensional tangential angular velocity, represents the azimuth, represents the initial azimuth of the target, Indicates the azimuth tangential angular velocity of the target, s r (t,t m ) represents the signal after the pulse pressure, n(t,t m ) represents the noise matrix; The expression for determining the direction matrix of the receiving beam is: Where, κ represents the direction matrix, θ l-1 =(l-1)θ Φ represents the beam pitch angle, represents the beam azimuth, represents the half-power point width of the azimuth main lobe, represents the half-power point width of the elevation main lobe, l represents the number of beams per row or column, M represents the number of antenna elements per column, and N represents the number of antenna elements per row; The expression for the weight vector of the direction matrix of the receiving beam is determined as follows: Among them, H τ,η represents the weight vector, θ τ =θ Φ τ represents the angle of the light beam to the X axis, represents the angle of the beam to the Y axis, 0≤τ,η≤l-1 represents the beam row variable and column variable; Based on the expressions of the array received signal in the fast time and slow time two-dimensional domains, the expression of the direction matrix and the expression of the weight vector, the simplified expression of the beamformed signal is determined as: Among them, s(t,t m ,τ,η) represents the signal after beamforming, represents the target complex reflectivity after beamforming.

5. The method for high-speed target detection by bistatic radar based on space-time Doppler coherent integration according to claim 4, characterized in that: Constructing a beam compensation function based on the beamformed signal, including: performing a three-dimensional fast Fourier transform on the beamformed signal at a fast time, an elevation beam time, and an azimuth beam time to obtain a frequency domain signal; A time reversal operation is performed on the phase of the frequency domain signal along the slow time direction to obtain a beam compensation function; the beam compensation function is expressed as: in, represents the beam compensation function, f, f τ 、f η are the fast time frequency, elevation beam frequency and azimuth beam frequency, respectively, and f c Indicates the carrier frequency, T c Represents the coherent processing time.

6. The method for high-speed target detection using a bistatic radar based on space-time Doppler coherent integration according to claim 5, wherein: Constructing a beam compensation function based on the beamformed signal; and performing transformation compensation on the beamformed signal using the beam compensation function to obtain a beam movement corrected signal, including: multiplying the frequency domain signal by the conjugate of its first pulse extension signal to obtain a transformed frequency domain signal; multiplying the beam compensation function and the transformed frequency domain signal to obtain a beam correction frequency domain signal; Performing a three-dimensional inverse fast Fourier transform of the fast time frequency, the pitch beam frequency, and the azimuth beam frequency on the beam correction frequency domain signal to obtain a beam correction time domain signal as a beam movement corrected signal; The beam correction time domain signal is expressed as: Among them, s′(t,t m ,τ,η) represents the beam correction time domain signal, R end represents the terminal double base distance, θ end represents the terminal pitch angle of the target, Indicates the terminal bearing of the target.

7. The method for high-speed target detection using a bistatic radar based on space-time Doppler coherent integration according to claim 6, wherein: Performing a de-modulation process on each beam of the beam movement corrected signal to obtain a two-dimensional signal in the range-modulation frequency domain, including: Detecting different beams of the signal after beam movement correction to obtain fast and slow time signals of the beam where the target end moment is located; Performing a fast Fourier transform on the fast and slow time signals along the fast time to obtain a fast time frequency domain-slow time domain signal; According to the linear frequency modulation characteristics of the fast time frequency domain-slow time time domain signal, a Doppler compensation function is constructed by constructing a de-linear frequency modulation signal; wherein the Doppler compensation function is expressed as: in, represents the Doppler compensation function, P(f) represents power, Indicates C d There are many different estimates of C d =2C2+3C3T c ; Performing a demodulation process on the fast-time frequency domain-slow-time time domain signal using the demodulated signal to obtain a demodulated time domain signal; The demultiplexed line-modulated time domain signal is coherently integrated in a slow time to obtain a two-dimensional signal in a range-modulated frequency domain.

8. The method for high-speed target detection using a bistatic radar based on space-time Doppler coherent integration according to claim 7, wherein: Performing a demodulation process on the fast-time frequency domain-slow-time time domain signal using the demodulated signal to obtain a demodulated time domain signal, including: Multiplying the de-modulated signal by the fast-time frequency domain-slow-time time domain signal to obtain a de-modulated frequency domain signal; Perform inverse fast Fourier transform of the time-frequency dimension on the de-modulated frequency domain signal to obtain a de-modulated time domain signal, which is expressed as: in, represents the demodulated time domain signal.

9. The method for high-speed target detection using a bistatic radar based on space-time Doppler coherent integration according to claim 8, wherein: The two-dimensional signal in the range-modulation frequency domain is expressed as: in, represents the range-modulated frequency domain two-dimensional signal, Indicates the demodulated time domain signal.

10. The method for high-speed target detection using a bistatic radar based on space-time Doppler coherent integration according to claim 8, wherein: Detecting the two-dimensional signal in the range-modulation frequency domain to obtain a target detection result includes: CA-CFAR detection is performed on the two-dimensional signal in the range-frequency modulation domain to obtain a target detection result.

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