A multi-station frequency-agile radar anti-jamming and synergistic method

Abstract

The application provides a multi-station frequency agile radar anti-interference and synergistic method, through two short baseline pulse interval frequency agile radars receiving echo signals and carrying out mixing processing and pulse compression; interference pulses of an echo data matrix are removed and the remaining pulses are combined to obtain a new echo data matrix; a distance-speed two-dimensional redundant dictionary matrix corresponding to the new echo data matrix and matched with target information is constructed in combination with transmission parameters; then a compressed sensing model is constructed and a reconstruction result of an original signal is obtained by solving.The application selects two pulse interval frequency agile radars to work synergistically, which can effectively improve signal processing gain, has strong electronic countermeasure capability, good target detection capability and excellent electromagnetic compatibility; by utilizing the characteristic that only some pulses of echo of the pulse interval frequency agile radar may be interfered, the interfered pulses are directly removed in the echo data matrix, and complex matrix operation is not involved, so that the calculation complexity is low and the running speed is fast.

Description

Technical Field

[0001] This invention belongs to the field of radar signal processing technology, specifically relating to a method for anti-interference and synergistic enhancement of multi-station frequency-agile radar. Background Technology

[0002] With the continuous development of electronic countermeasures technology, the battlefield electromagnetic environment for radar is becoming increasingly complex. Active mainlobe jamming is currently the main threat to radar detection. Mainlobe deception and strong suppression jamming patterns can severely degrade radar detection performance: Suppression jamming transmits high-power noise interference, causing the radar receiver to receive a large amount of noise, reducing the signal-to-noise ratio and obscuring the target. Dense decoy jamming generates multiple false targets with characteristics similar to the real target, consuming radar system resources and saturating the radar data processing system. When the number of false targets is large and the spacing between them is small, the false targets distributed around the real target can affect the radar's detection of the real target.

[0003] Frequency-agile radar systems, with their carrier frequency agility, can actively avoid interference bands, effectively countering repeater-based deception jamming and narrowband targeting suppression jamming, and reducing the probability of radar signal interception. To suppress interference using frequency-agile radar systems, a whitening filter method can be employed to process the radar echo signal. This involves calculating the covariance matrix of the baseband echo matrix and performing eigenvalue decomposition. After setting an eigenvalue threshold, eigenvectors are extracted based on the threshold to form the whitening matrix of the baseband echo. Whitening filtering can suppress interference energy while preserving target energy. The drawbacks of this method are that constructing the whitening matrix involves eigenvalue decomposition of the covariance matrix of the baseband echo matrix, resulting in a large computational load; improper selection of the eigenvalue threshold can lead to residual interference energy or loss of target echo energy, easily affecting radar target detection results. Summary of the Invention

[0004] To address the aforementioned problems in the existing technology, this invention provides a method for anti-jamming and synergistic enhancement of multi-station frequency-agile radar.

[0005] This invention provides a method for anti-jamming and synergistic enhancement of multi-station frequency-agile radar, comprising:

[0006] S100 transmits orthogonal signals through two short-baseline pulse-agile frequency-speed radars and receives echo signals; the echo signals are then mixed and pulse-compressed sequentially to obtain a pulse-compressed echo data matrix.

[0007] S200 utilizes the power difference between the interference signal and the target echo signal to eliminate interference pulses in the echo data matrix and merges the remaining pulses to obtain a new echo data matrix;

[0008] S300, combined with the transmission parameters of short baseline inter-pulse frequency agile radar, constructs a range-velocity two-dimensional redundant dictionary matrix that corresponds to the new echo data matrix and matches the target information;

[0009] S400 constructs a two-dimensional high-resolution echo signal compressed sensing model based on the distance-velocity two-dimensional redundant dictionary matrix, and obtains the reconstruction result of the original signal by solving the optimal problem of the echo signal compressed sensing model.

[0010] Compared with the prior art, the present invention has the following advantages:

[0011] (1) The present invention uses pulse frequency agile radar, which has strong electronic countermeasures capability, good target detection capability and excellent electromagnetic compatibility compared with traditional pulse Doppler radar.

[0012] (2) This invention utilizes the characteristic that only some pulses of the inter-pulse frequency agile radar echo may be interfered with, and directly removes the interfered pulses from the echo data matrix. It does not involve complex matrix operations, so the computational complexity is low and the running speed is fast.

[0013] (3) Considering the large amount of interference in complex electromagnetic space and the low energy of the target echo after interference suppression, the present invention can effectively improve the signal processing gain by working in concert with two radars to fuse their echoes.

[0014] The present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating the implementation of a multi-station frequency-agile radar anti-jamming and synergistic enhancement method according to the present invention.

[0016] Figure 2(a) is a schematic diagram of the echo signal matrix after pulse compression processing of radar 1 echo;

[0017] Figure 2(b) is a schematic diagram of the echo signal matrix after pulse compression processing of radar 2 echo;

[0018] Figure 3(a) is a schematic diagram of the echo data matrix after interference removal from the radar 1 echo;

[0019] Figure 3(b) is a schematic diagram of the echo data matrix after interference removal from the radar 2 echo;

[0020] Figure 4 This is a schematic diagram of the echo data matrix after echo fusion of two radar stations in the simulation experiment of this invention;

[0021] Figure 5 This is a diagram showing the target parameter estimation results of the fused waveform in the simulation experiment of this invention;

[0022] Figure 6 This is a schematic diagram of the distance parameter estimation of the target in the simulation experiment of this invention;

[0023] Figure 7 This is a schematic diagram illustrating the estimation of the target's velocity parameters in the simulation experiment of this invention;

[0024] Figure 8 This is a graph showing the amplitude-normalized target parameter estimation results of the bistatic radar composite echo;

[0025] Figure 9 This is a graph showing the amplitude normalized target parameter estimation results of a single-station radar echo. Detailed Implementation

[0026] The present invention will be further described in detail below with reference to specific embodiments, but the implementation of the present invention is not limited thereto.

[0027] refer to Figure 1 This invention provides a method for anti-jamming and synergistic enhancement of multi-station frequency-agile radar, comprising:

[0028] S100 transmits orthogonal signals through two short-baseline pulse-agile frequency-speed radars and receives echo signals; the echo signals are then mixed and pulse-compressed sequentially to obtain a pulse-compressed echo data matrix.

[0029] Relative to the location of a distant target, the short-baseline radars can be considered to be approximately located at the same position. Both radar stations simultaneously transmit orthogonal signals in the same direction. S100 of this invention includes:

[0030] S110 transmits orthogonal signals in the same direction at the same time through two short-baseline inter-pulse frequency-agile radars located at the same position.

[0031] Two short-baseline pulse-agile frequency-agile radars are configured to transmit Q narrowband pulse signals within a coherent processing interval. Each pulse has a signal bandwidth of B and a pulse width of T. p The linear modulation frequency is γ = B / T p A linear frequency modulated signal with a pulse repetition time of T. r The center frequencies of the q-th pulse signals transmitted by the two short-baseline pulse-agile frequency-speed radars are f1 and f2, respectively. q f2 q It satisfies: taking M≥Q, using the original signal carrier frequency f0 as the starting frequency, and the frequency hopping interval as Δf, a frequency hopping sequence vector f containing P elements is generated. P =[f0,…,f0+(p-1)Δf,…,f0+(P-1)Δf] T It is easy to obtain that the total frequency hopping bandwidth is P·Δf, from the vector f P The vector f is obtained by randomly selecting the first Q elements.Q =[f 1 ,…,f q ,…,f Q ] T ;

[0032] The transmitted signals from two short-baseline pulse-agile frequency-skimming radars are orthogonal, ensuring |f1 when generating frequency-hopping sequences. q -f2 q If |>B, then the q-th pulse signal is as follows:

[0033]

[0034]

[0035] Where t is the fast time, rect(·) is the rectangular window function, and rect(·) is effective when |t|≤T. p The value within / 2 is 1, j represents the imaginary unit, and t q =T r ·(q-1) represents slow time;

[0036] S120, both short-baseline pulse-agile frequency-speed radars receive echo signals;

[0037] The echo signal includes the target echo signal, interference signal, and noise;

[0038] Suppose a radar observation scenario includes one target and one self-defense jammer, with the jammer employing a dense decoy jamming pattern. The signals received by the radar system include the target echo signal, the jamming signal, and the receiver thermal noise, which can be expressed as:

[0039]

[0040] in, These are the target echo signals from two multi-station frequency-agile radars, respectively. J(t) is the interference signal, and n(t) is the receiver thermal noise.

[0041] S130: Each short-baseline pulse-agile frequency-agile radar uses its own transmit carrier frequency to mix the echo signal it receives, so that the echo frequency of the orthogonal signal it transmits is shifted to zero frequency.

[0042] The two radar stations each perform digital down-conversion processing on the received signals, that is, they use their respective transmit carrier frequencies to mix the received signals, so that the echo frequency of the signals transmitted by each radar substation is shifted to zero frequency, while the remaining components of the received signals are not at zero frequency. Therefore, the echo signals after mixing by the two short-baseline pulse-agile frequency-agile radars are:

[0043]

[0044]

[0045] S140, each short-baseline pulse-agile frequency-speed radar performs pulse compression processing on the mixed echo signal.

[0046] The two radar stations continue pulse compression processing to construct a matched filter h(t):

[0047]

[0048] The echo signal after pulse compression is:

[0049]

[0050]

[0051] in, Indicates conjugate processing. Indicates Fourier transform;

[0052] Because of the pulse-agile radar system, some radar pulses operate at frequencies outside the jammer's operating band, making it impossible for the jammer to interfere with these pulses. The dense decoy jamming pattern stores radar pulses and continuously relays them. During subsequent radar signal pulse repetition cycles, the relayed jamming pulses have a different carrier frequency than the radar signal pulses, and are directly filtered out after down-conversion and pulse compression. The signals received by the radar stations are processed to retain only the echoes of the corresponding transmitted signals. Therefore, the signals received by the two radar stations can be divided into pulses without interference:

[0053]

[0054]

[0055] And interfering pulses:

[0056]

[0057]

[0058] Where J1′(t), J2′(t), n′1(t), and n′2(t) represent the results of the interference signal and noise after down-conversion and pulse compression processing at the two radar stations, respectively. Let q represent the echo delay of the target corresponding to the q-th pulse, and r and v represent the initial radial distance and radial velocity of the target relative to the radar, respectively. Since the two radars are arranged with a short baseline, it can be approximately assumed that the target's distance, velocity, and echo delay to the two radars are equal.

[0059] S150: According to the sequence of received radar echo signals, the pulse-compressed echo signals within a coherent processing interval are arranged sequentially to obtain the pulse-compressed echo data matrix.

[0060] The echo data matrix after pulse compression in S150 is as follows:

[0061]

[0062]

[0063] S200 utilizes the power difference between the interference signal and the target echo signal to eliminate interference pulses in the echo data matrix and merges the remaining pulses to obtain a new echo data matrix;

[0064] S200 includes:

[0065] S210, by utilizing the power difference between the interference signal and the target echo signal, the interfered pulses in the echo data matrix are removed to obtain the signal matrix after interference removal;

[0066] After pulse compression, only a portion of the echo data matrix contains interference signals, and there is a significant difference in power between the pulses with and without interference. By using a threshold to remove the interference-containing pulses, the pulse compression result after interference removal is obtained, and the target signal is revealed.

[0067] The signal matrix after interference removal in S210 is represented as follows:

[0068]

[0069]

[0070] S220 merges the remaining pulse signals after removing the two short-baseline pulse-agile frequency radars into a new complete echo signal, resulting in a new echo data matrix.

[0071] Removing interfering pulses can filter out interference in the echo signal, but it also results in a loss of some echo signal energy. When both radar stations are affected by a large number of interfering pulses, or for distant, weakly scattering targets, performing subsequent target parameter estimation on the signal matrix after interference removal will reduce the signal processing gain, thus affecting subsequent target detection processing. To improve the signal processing gain, the uninterrupted pulses from the two radars are spliced ​​into a new complete echo signal, i.e., the pulses are shifted in the data matrix. S220 includes:

[0072] S221, count the number K of missing pulses in the signal matrix after removing interference from the two short baseline pulse-to-pulse frequency-agile radars, and count the number Q' of pulse position indices {q1,q2,q3,...} that still have data;

[0073] Among them, the number of pulses N corresponding to the new echo data matrix is ​​N = 2Q' = 2(QK);

[0074] S222, determine the relationship between the number of pulses N in the new echo data matrix and the number of pulses Q transmitted by a single short baseline inter-pulse agile frequency-agile radar.

[0075] S223, If N > Q, then determine that the first Q pulses of the new echo data matrix are the same as the signal matrix after the first short baseline inter-pulse frequency agile radar interference is removed, and that the data of the (Q+1) to Nth pulses are zero. Count the pulse position indices that are set to zero in the new echo data matrix, and denote them as {k1,k2,k3,...}.

[0076] S224, If N < Q, then determine that the first N pulses of the new echo data matrix are the same as the first N pulses of the signal matrix after the interference of the first short baseline pulse-to-pulse agile radar is eliminated, and count the pulse position indices that are set to zero in the new echo data matrix, denoted as {k1,k2,k3,...};

[0077] S225 transforms the {q1,q2,q3,...} pulses in the signal matrix after the second short baseline inter-pulse agile radar interference is removed to the positions of the corresponding {k1,k2,k3,...} pulses, thus obtaining a new echo data matrix.

[0078] The transformation principle is as follows:

[0079] Comparing the pulse-compressed radar echo data from the two radar sites reveals that, under the same pulse, the only difference lies in the signal carrier frequency, while f1... q and It utilizes the same original signal carrier frequency f0 and frequency hopping interval Δf, and generates frequencies in the frequency hopping sequence through the same strategy, thus enabling radar echoes to meet the conditions for inter-pulse fusion.

[0080] If N > Q, use radar 2 data to fill the pulses with zero data in the new echo data matrix; if N < Q, then in addition to radar 2 data, the pulses located later in radar 1 data also need to be filled into the new echo data matrix.

[0081] It is important to note that if the q-th pulse of the original matrix changes to the k-th pulse of the new data matrix, the carrier frequency of the k-th pulse remains unchanged. That is, the new data matrix corresponds to a new frequency hopping sequence. During the transformation, the original pulse position index q = [q′1,…,q′] of each pulse in the new data matrix is ​​recorded. k ,…,q′ K ] T The corresponding pulse position index in the new data matrix is ​​k = [1, 2, ..., K]. T And record the new frequency hopping sequence fK =[f 1 ,…,f k ,…,f K ] T .

[0082] After data fusion from the two radar stations, the new echo data matrix in S225 is as follows:

[0083] Φ=[s 1 (t),…,s k (t),…,s K (t)] T (13);

[0084] in,

[0085]

[0086]

[0087] t k =T r ·(k-1)=T r ·(q′ k -1) (16).

[0088] S300, combined with the transmission parameters of short baseline inter-pulse frequency agile radar, constructs a range-velocity two-dimensional redundant dictionary matrix that corresponds to the new echo data matrix and matches the target information;

[0089] The S300 includes:

[0090] S310 divides the unambiguous range element Δr and unambiguous velocity element Δv of the short baseline inter-pulse frequency agile radar into M×L grids.

[0091] Each unambiguous distance cell is divided into M independent distance grids, denoted as Δr. M =Δr / M, whose index is m∈{1,2,...,M}, r m =m·Δr M The distance is the m-th distance grid cell; each unambiguous velocity cell is divided into L independent distance grid cells, denoted as Δv. L =Δv / L, with indices l∈{1,2,...,L}, v l =l·Δv is the velocity of the l-th velocity grid;

[0092] S320, define variables based on the fused echo signal:

[0093]

[0094] Where, γ m,lLet d(k) be the original signal to be recovered, and d(k) be the frequency hopping code of the synthesized echo data matrix, which satisfies: f k =f0+d(k)Δf,Γ m (k) is the range phase term, Ψ l (k) is the velocity phase term, when r m =r,v l When = v, Γ m (k) contains unambiguous distance information of the target, Ψ l If (k) contains unambiguous velocity information of the target, then the echo can be represented as:

[0095] s m,l (T k )=γ m,l Ψ l (k)Γ m (k)+n(T k (18);

[0096] Where n(T) k ) represents the noise sampling vector;

[0097] S330, based on the echo signal representation in S320, constructs a range-velocity two-dimensional redundant dictionary matrix Ω:

[0098]

[0099]

[0100] Among them, Ω contains all possible distance and velocity information of the target. m,l It is a K×1 column vector, and ⊙ represents the Hadamard product.

[0101] S400 constructs a two-dimensional high-resolution echo signal compressed sensing model based on the distance-velocity two-dimensional redundant dictionary matrix, and obtains the original signal reconstruction result by solving the optimization problem of the echo signal compressed sensing model.

[0102] The S400 includes:

[0103] S410, constructs a two-dimensional high-resolution compressed sensing model for echo signals based on a two-dimensional redundant dictionary matrix of range-velocity:

[0104] s=Ωθ+δ (21);

[0105] Where δ is the noise vector and θ is the unknown target range-velocity parameter;

[0106] S420, the original signal is reconstructed by solving the l1 norm optimization problem in the compressed sensing model of the echo signal, and the reconstructed signal result is obtained:

[0107]

[0108] This enables high resolution of the target velocity and high resolution of the target unit distance coherent accumulation.

[0109] The effects of this invention can be further illustrated by the following simulations:

[0110] 1. Simulation Scenarios and Parameters

[0111] Assume a moving target exists in the scenario, with a radial distance of 4001.54 m and a radial velocity of 80.3 m / s. A self-defense dense decoy jammer exists, employing a full-pulse cyclic forwarding strategy. The distance corresponding to the jamming forwarding delay is random within the range of 100.5–130 m. Two short-baseline radars are approximately located at the same position, transmitting inter-pulse frequency agile intra-pulse linear frequency modulated signals. The only difference between the two transmitted signals is the frequency hopping code. Relevant radar parameters are shown in Table 1.

[0112] Table 1 Radar Simulation Parameters

[0113] parameter numerical values parameter numerical values Pulse count 64 Signal bandwidth (MHz) 10 Total frequency hopping 128 Frequency hopping interval (MHz) 9 Pulse width (μs) 4 Initial carrier frequency (GHz) 14 Pulse repetition frequency (kHz) 25 Sampling rate (MHz) 50

[0114] Both radars simultaneously transmit radar signals in the same direction, with inter-pulse carrier frequency variations ranging from 14 to 15.14 GHz, resulting in a total synthesized bandwidth of 1.14 GHz. A jammer receives the synthesized radar signals from both radars and interferes with signals within its jamming bandwidth. The radar receives the synthesized target echoes and jamming signals from both radars, achieving a signal-to-noise ratio of -5 dB.

[0115] 2. Simulation Content

[0116] The simulation results of the combined target echo and interference signals received by the radar from two radars, after mixing and pulse compression, are shown in Figure 2; the results after removing interference are shown in Figure 3; the combined radar echo is shown in Figure 4. Figure 4 As shown. High-resolution distance and velocity were obtained as follows. Figure 5 As shown, Figure 6 , Figure 7 These figures represent distance and velocity estimation, respectively. As can be seen from the figure, the peak value indicating the target is clearly visible, and interference has been successfully suppressed. The method estimated the target distance to be 4001.56 km and the velocity to be 78.78 m / s, with a distance estimation error of 0.0005% and a velocity estimation error of 1.89%. Within a certain error range, the method of this invention can effectively estimate the target's motion parameters.

[0117] With the radar observation scenario, transmission parameters, and signal processing methods kept the same, the target parameter estimation results of dual-station radar signal collaborative processing and single-station radar signal processing are compared. Figure 8 , Figure 9The amplitude-normalized target parameter estimation results of the bistatic radar synthesized echo and the monostatic radar echo after 30 iterations of OMP algorithm reconstruction are shown. It can be clearly seen that the signal-to-noise ratio of the monostatic radar processing result is low, while the signal-to-noise ratio of the bistatic radar synthesized echo is significantly higher than that of the monostatic radar processing result. It can be concluded that the fused signal significantly improves the signal processing gain.

[0118] Furthermore, the terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Thus, a feature defined as "first" or "second" may explicitly or implicitly include one or more of that feature. In the description of this invention, "a plurality of" means two or more, unless otherwise explicitly specified.

[0119] Although this application has been described herein in conjunction with various embodiments, those skilled in the art will understand and implement other variations of the disclosed embodiments by reviewing the accompanying drawings, the disclosure, and the appended claims in carrying out the claimed application. In the claims, the word "comprising" does not exclude other components or steps, and "a" or "an" does not exclude a plurality.

[0120] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various simple deductions or substitutions can be made without departing from the concept of the present invention, and all such modifications and substitutions should be considered within the scope of protection of the present invention.

Claims

1. A method for anti-interference and synergistic enhancement of multi-station frequency-agile radar, characterized in that, include: The S100 transmits orthogonal signals and receives echo signals through two short-baseline inter-pulse frequency-agile radars. The echo signal is sequentially mixed and pulse compressed to obtain a pulse-compressed echo data matrix. S200 utilizes the power difference between the interference signal and the target echo signal to eliminate interference pulses in the echo data matrix and merges the remaining pulses to obtain a new echo data matrix; S300, combined with the transmission parameters of short baseline inter-pulse frequency agile radar, constructs a range-velocity two-dimensional redundant dictionary matrix that corresponds to the new echo data matrix and matches the target information; S400: Construct a two-dimensional high-resolution compressed sensing model for echo signals based on a range-velocity two-dimensional redundant dictionary matrix, and obtain the reconstructed result of the original signal by solving an optimization problem on the compressed sensing model for echo signals; S200 includes: S210, by utilizing the power difference between the interference signal and the target echo signal, the interfered pulses in the echo data matrix are removed to obtain the signal matrix after interference removal; S220 combines the remaining pulse signals after removing the interfered pulses from the two short-baseline pulse-agile frequency-agile radar echoes into a new complete echo signal, resulting in a new echo data matrix. S220 includes: S221, count the number of missing pulses in the signal matrix after the short baseline pulse-to-pulse frequency agile radar interference is removed , and count the pulse position index of the pulses that still have data , number ; The new echo data matrix corresponds to the number of pulses , ; S222, determine the number of new echo data matrix pulses The number of transmitted pulses of the single short baseline inter-pulse frequency agile radar Size relationship; S223, if , determine the new echo data matrix before The first short baseline pulse-to-pulse change frequency radar interference signal matrix is the same, and the The first pulse data is zero, and the pulse position index of the new echo data matrix is recorded as ; S224, if , it is determined that the new echo data matrix is the same as the first short baseline pulse-to-pulse variant frequency radar interference removed signal matrix , the pulse position index of the zero in the new echo data matrix is counted, and is recorded as ; S225, in the signal matrix after removing interference from the second short-baseline inter-pulse frequency-agile radar. Pulse transformation to corresponding A new echo data matrix is ​​obtained at the position of the pulse.

2. The multi-station frequency-agile radar anti-interference and synergistic enhancement method according to claim 1, characterized in that, S100 includes: S110 transmits orthogonal signals in the same direction at the same time through two short-baseline inter-pulse frequency-agile radars located at the same position. S120, both short-baseline pulse-agile frequency-speed radars receive echo signals; The echo signal includes the target echo signal, interference signal, and noise; S130: Each short-baseline pulse-agile frequency-agile radar uses its own transmit carrier frequency to mix the echo signal it receives, so that the echo frequency of the orthogonal signal it transmits is shifted to zero frequency. S140, each short-baseline pulse-agile frequency-speed radar performs pulse compression processing on the mixed echo signal. S150: According to the sequence of received radar echo signals, the pulse-compressed echo signals within a coherent processing interval are arranged sequentially to obtain the pulse-compressed echo data matrix.

3. The multi-station frequency-agile radar anti-interference and synergistic enhancement method according to claim 2, characterized in that, In the S110, both short-baseline inter-pulse frequency-agile radars transmit within a coherent processing interval. A narrowband pulse signal, each pulse having a signal bandwidth of [missing information]. Pulse width is The linear modulation frequency is A linear frequency modulated signal with a pulse repetition time of 1 / 2. The first transmissions from two short-baseline pulse-agile frequency-speed radars The center frequencies of the pulse signals are respectively , It satisfies: Take Using the original signal carrier frequency The frequency starting point is [frequency value], and the frequency hopping interval is [frequency value]. , generate containing Frequency hopping sequence vector of elements The total bandwidth of frequency hopping is easily obtained as follows: From vector Random selection before The elements yield a vector. ;in, Represents frequency hopping sequence vector Center front The first frequency hopping frequency Frequency hopping; Represents frequency hopping sequence vector The element index in the text; The transmitted signals from the two short-baseline pulse-agile frequency-skimming radars are orthogonal, ensuring that the frequency-hopping sequence is generated correctly. Then the first The pulse signals are as follows: （1）； （2）； in, To save time, For rectangular window functions, exist Take 1 from the inside. Represents the imaginary unit. Slow time; The echo signal in S120 is represented as follows: （3）； in, , These are target echo signals from two multi-station frequency-agile radars. This is an interference signal. For receiver thermal noise; The echo signal after mixing between the two short-baseline inter-pulse frequency-agile radars in the S130 is: （4）； （5）； The matched filter used in pulse compression processing in S140 for: （6）； The echo signal after pulse compression is: （7）； （8）； in, This indicates that conjugation is performed first, followed by Fourier transform. Indicates Fourier transform; The echo data matrix after pulse compression in S150 is as follows: （9）； （10）。 4. The multi-station frequency-agile radar anti-interference and synergistic enhancement method according to claim 3, characterized in that, The signal matrix after interference removal in S210 is represented as follows: （11）； （12）； The new echo data matrix in S225 is as follows: （13）； （14）； in, The intermediate parameter is represented as: （15）； Indicates the new frequency hopping sequence The kth new frequency hopping in This represents the initial radial distance of the target relative to the radar. This represents the initial radial velocity of the target relative to the radar. This represents intermediate parameters, expressed as （16）； in, This indicates the k-th original pulse position in the original pulse position index q.

5. The multi-station frequency-agile radar anti-interference and synergistic enhancement method according to claim 4, characterized in that, The S300 includes: S310 will integrate the unambiguous range unit of short-baseline inter-pulse frequency-agile radar. and unambiguous velocity unit Divided into equal parts One grid; Each unambiguous distance unit is divided into There are three independent distance grids, denoted as distance grid . Its index is , For the first The distance of each distance grid; each unambiguous velocity unit is divided into... Each independent distance grid is denoted as the velocity grid. Its index is , For the first The speed of each speed grid; S320, define variables based on the fused echo signal: （17）； in, The original signal to be restored. This represents intermediate parameters, expressed as , It is the frequency hopping code of the synthesized echo data matrix, which satisfies: , It is the range phase term. It is the velocity phase term, when , hour, Includes unambiguous distance information of the target. If the echo contains unambiguous velocity information of the target, then the echo can be represented as: （18）； in This is the noise sampling vector; S330, based on the echo signal representation in S320, constructs a range-velocity two-dimensional redundant dictionary matrix. : （19）； （20）； in, Includes all possible distance and speed information of the target. for Column vectors This represents Hadamard product, and q indicates the original pulse position index.

6. The multi-station frequency-agile radar anti-interference and synergistic enhancement method according to claim 5, characterized in that, The S400 includes: S410, constructs a two-dimensional high-resolution compressed sensing model for echo signals based on a two-dimensional redundant dictionary matrix of range-velocity: （21）； in, For noise vectors, For unknown target distance-velocity parameters; S420, the compressed sensing model for echo signals is solved by... The norm optimality problem is used to reconstruct the original signal, and the reconstructed signal is obtained: ,subject to (22)。

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