Multi-frequency diversity radar target distance and speed estimation method

Abstract

The invention belongs to the field of radars, and relates to a multi-frequency diversity radar target distance and speed estimation method. According to the method, distance and speed estimation of multi-frequency diversity radar echoes is realized based on a distance and speed dimension super-resolution orthogonal matching pursuit (SRC-OMP) sparse processing algorithm. The high-resolution distance and speed estimation of a multi-frequency diversity radar echo signal is generally realized by combining sparse representation and sparse processing, and a traditional OMP algorithm based on a matched inner product is easy to judge a plurality of targets as one target for estimation when the targets are close to each other due to the characteristics of a sinker function. A distance-velocity two-dimensional spectrum is constructed according to an observation vector and a dictionary matrix, atoms corresponding to peak values in the two-dimensional spectrum are estimated, the positions of the atoms are stored, a set of atomic position indexes and the atoms is updated, and then a residual vector is updated. And then calculating a sparse coefficient solution to obtain a high-resolution target distance and speed detection result. The method is beneficial to high-resolution estimation of the target distance and speed by the multi-frequency diversity radar.

Description

Technical Field

[0001] The invention belongs to the field of radar, and in particular relates to a method for estimating target distance and speed of a multi-frequency diversity radar. Technical Background

[0002] The carrier frequency of each pulse of the multi-frequency diversity waveform randomly jumps within a certain range at a certain frequency hopping interval, and the duration of a single frequency point is short, so that the enemy cannot obtain the radar's pulse carrier frequency and other information in a timely and accurate manner. Therefore, the multi-frequency diversity waveform has excellent low interception and anti-interference performance, and can effectively counter most deceptive interference. In addition, the waveform can cover a larger bandwidth and obtain high-resolution performance in distance. However, the phase of the multi-frequency diversity waveform echo signal changes with the position of the target and its carrier frequency. Therefore, the traditional multi-pulse processing method based on fast Fourier transform (FFT) fails and cannot accurately estimate the target's distance and speed. The sparse processing algorithm can overcome the problem that the traditional fast Fourier transform cannot process the multi-pulse signal of the multi-frequency diversity waveform, and is used to estimate the distance and speed of the multi-frequency diversity waveform echo signal. The OMP algorithm is one of the commonly used sparse reconstruction algorithms. However, the traditional OMP algorithm based on matching inner product is prone to misjudge two or more targets as one when the signal-to-noise ratio is low or the targets are close to each other, resulting in missed detection, and the probability of sparse reconstruction of the target is reduced. Summary of the invention

[0003] The present invention overcomes the shortcomings of the existing orthogonal matching pursuit algorithm based on matching inner product, and proposes a multi-frequency diversity radar target distance and speed estimation method based on a high-resolution orthogonal matching pursuit algorithm, which is used to solve the target parameter estimation problem of multi-frequency diversity waveforms. This method replaces the process of solving the matching inner product of the traditional OMP algorithm with the process of solving the two-dimensional spectrum of distance and speed. When the targets are close to each other, two or more targets can be distinguished more clearly. This method improves the super-resolution performance of the orthogonal matching pursuit algorithm, thereby improving the estimation accuracy of the target distance and speed.

[0004] In order to achieve the above object, the present invention adopts the following technical methods to achieve it.

[0005] A multi-frequency diversity radar target distance and speed estimation method mainly comprises the following steps:

[0006] Step 1: Establish a multi-frequency diversity radar transmission signal model s(t), and perform pulse compression processing on the obtained radar echo signal. The echo signal obtained after pulse compression is x(t).

[0007] Step 2, calculate the distance resolution unit and speed resolution unit of the radar echo signal. The distance resolution unit includes a coarse resolution distance unit and a high resolution distance unit; the speed resolution unit includes a coarse resolution speed unit and a high resolution speed unit. The high resolution distance grid is divided in the coarse resolution distance unit, and the high resolution speed grid is divided in the coarse resolution speed unit. Thus, a high resolution speed-distance dictionary matrix D is constructed.

[0008] Step 3: Construct a distance-velocity two-dimensional spectrum based on the observation vector and dictionary matrix to find the atom corresponding to the peak in the distance-velocity two-dimensional spectrum, store the position of the atom, update the atom position index and the set of atoms, and then update the residual vector. The initial residual vector is the observation data vector. Finally, the sparse coefficient solution is calculated to obtain the result of high-resolution target distance and velocity detection.

[0009] Compared with the prior art, the present invention has the following beneficial effects:

[0010] Aiming at the problem that the traditional orthogonal matching pursuit method based on matching inner product cannot separate targets when they are close to each other, an orthogonal matching pursuit method based on super-resolution criterion is proposed. It can effectively solve the reconstruction probability of targets when target parameters are relatively similar, improve the accuracy of target parameter estimation, and improve detection performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] The present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0013] Figure 1 This is a flow chart of using the SRC-OMP algorithm to achieve multi-frequency diversity radar target range and speed estimation.

[0014] Figure 2 It is a program processing flow chart of the SRC-OMP method.

[0015] Figure 3 (a) is the distance-velocity two-dimensional spectrum of the SRC-OMP algorithm simulated on the Matlab platform. Figure 3 (b) Its detail diagram.

[0016] Figure 4 This is a comparison chart of the traditional orthogonal matching pursuit algorithm OMP method under the same parameter conditions simulated on the Matlab platform.

[0017] Figure 5 It is a plane diagram of distance and speed detection results based on SRC-OMP algorithm simulated on Matlab platform. DETAILED DESCRIPTION

[0018] The present invention will be further described below in conjunction with the accompanying drawings. The following embodiments are only used to more clearly illustrate the technical solution of the present invention, and cannot be used to limit the protection scope of the present invention.

[0019] like Figure 1 The flowchart of realizing multi-frequency diversity radar target range and speed estimation based on SRC-OMP algorithm is shown, which includes the following steps:

[0020] A multi-frequency diversity radar transmission signal model s(t) is established, and the radar echo signal obtained is subjected to pulse compression processing. The echo signal obtained after pulse compression is x(t).

[0021] Specifically, step 1 includes the following sub-steps:

[0022] Sub-step 1.1, assume that the radar transmits a total of P pulses, the carrier frequencies of the P pulses randomly jump within a certain synthetic bandwidth, and a frequency diversity waveform is used in a single pulse, including multiple sub-pulses transmitted simultaneously. Assume that its initial carrier frequency is f0, the inter-pulse frequency hopping interval is Δf, and the minimum frequency interval of the frequency diversity sub-pulses within a pulse is equal to the minimum inter-pulse frequency hopping interval. Then the carrier frequency of the signal transmitted by the qth array element of the pth pulse is f p，q =f0+k p Δf+k q Δf, where k p is the code of the pth pulse, k p ∈{0, 1, 2, ..., I-1}, I is the number of carrier frequency jumps; k q is the frequency hopping variable of the qth array element signal in the pth pulse, k q ∈{-k p , -k p +1, ..., I-1-k p}, where q = 1, 2, ..., Q p , Q p is the number of sub-pulses in the p-th pulse. Then the q-th sub-pulse emission signal of the p-th pulse can be expressed as:

[0023] s p，q (t) = s(t-pT)exp(j2πf p，q t) (1)

[0024] Wherein, j is the imaginary unit, t is the fast time, T is the pulse repetition period, and s(t) is the radar transmitting pulse baseband signal waveform.

[0025] If the radar transmit pulse baseband signal is a linear frequency modulation signal, s(t) can be expressed as

[0026]

[0027] In formula (2), B p is the transmit signal bandwidth, T p is the transmission signal time width. rect(·) is the rectangular window function. If μ=B p / T p is the frequency modulation slope of the linear frequency modulation signal, then equation (1) can be simplified to

[0028]

[0029] Assume that there are M target scattering points in the target observation scene, and the initial distance of the mth (m=1, 2, ..., M) target scattering point is R m0 , the speed is v m , then the distance of the mth target scattering point at time t can be expressed as r m (t) = R m0 +v m t (4)

[0030] The time from the radar transmitting the pulse signal to receiving the target echo signal is called the echo delay. Let the echo delay of the mth target scattering point be τ m If the time when the radar receives the echo signal is t, then the time when the radar transmits the signal is t-τ m , the time when the radar signal reaches the target is t-τ m / 2. From the time the radar transmits the pulse signal to the time the radar receives the target echo signal, the distance the electromagnetic wave travels is cτ m , where c represents the speed of light. From equation (4), the distance between the mth target scattering point and the target can be expressed as r m (t-τ m / 2), the following relationship holds:

[0031] cτ m =2r m (t-τ m / 2)=2[R m0 +v m (t-τ m / 2)] (5)

[0032] That is, the distance the electromagnetic wave travels is twice the distance between the radar and the target scattering point. Then the echo delay τ of the mth target m It can be expressed as:

[0033]

[0034] In actual application scenarios, there are v m <<c holds true, then formula (6) can be simplified to

[0035]

[0036] It is known that the echo signal received by the radar is the superposition of the echo signals of all target scattering points in the observation scene, and for a single pulse echo, it is the superposition of the echoes of all sub-pulses in the pulse, so the echo signal of the pth pulse can be expressed as:

[0037]

[0038] Among them, ξ m is the scattering coefficient of the mth target scattering point, and it can be obtained from formula (3):

[0039]

[0040] Substituting equation (9) into equation (8), we can obtain

[0041]

[0042] Sub-step 1.2, the above formula is for the initial radar echo signal that has not been processed by the receiver. The received radar echo signal is down-converted and pulse compressed, and the radar echo signal expression after pulse compression is obtained as follows:

[0043]

[0044] It is known that a coarse resolution range unit of the radar is ΔR = c / 2B p , B p is the transmission signal bandwidth. In order to make the distance between each adjacent sampling point equal to a coarse resolution distance unit, the sampling rate f s Equal to the transmitted signal bandwidth, that is, f s =B p Assuming there are N sampling points, the time corresponding to the nth (n=1, 2, ..., N)th sampling point of the pth pulse is t n =pT+n / f s , T is the pulse repetition period. The distance unit corresponding to the nth sampling point is

[0045] r(n)=nΔR=nc / 2B p =nc / 2f s (12)

[0046] From equation (12), we can get that the distance between adjacent sampling points is exactly one coarse resolution distance unit. Therefore, the echo signal of the nth sampling point of the pth pulse is:

[0047]

[0048] From the properties of the sinc function, we know that when n / f s-τ m =0, that is, n = τ m f s When the pulse compression result of the echo signal reaches the maximum value. In a coarse resolution distance unit, the fast time parameter n / f in the exponential term s Can be ignored. Formula (13) can be simplified as:

[0049]

[0050] In practical applications, the radar receiver system will contain a certain amount of noise σ(t n ), so the expression of the echo signal actually received by the radar is:

[0051] In formula (15), the first exponential term is a constant term, which is independent of the speed and distance of the target; the second exponential term is the distance phase term, which changes with the pulse code k. p and the sub-pulse code k q The third exponential term is the velocity phase term, 1+(k p +k q )Δf / f0 represents the change of the qth sub-pulse signal of the pth pulse relative to the initial carrier frequency, which contains the speed information of the target, referred to as the speed term.

[0052] Step 2, calculate the distance resolution unit and speed resolution unit of the radar echo signal. The distance resolution unit includes a coarse resolution distance unit and a high resolution distance unit; the speed resolution unit includes a coarse resolution speed unit and a high resolution speed unit. The high resolution distance grid is divided in the coarse resolution distance unit, and the high resolution speed grid is divided in the coarse resolution speed unit. Thus, a high resolution speed-distance dictionary matrix D is constructed.

[0053] Specifically, step 2 includes the following sub-steps:

[0054] Sub-step 2.1: Calculate the range resolution unit and speed resolution unit of the radar echo signal. The range resolution unit includes a coarse resolution range unit and a high resolution range unit; the speed resolution unit includes a coarse resolution speed unit and a high resolution speed unit. Divide the high resolution range grid points in the coarse resolution range unit, and divide the high resolution speed grid points in the coarse resolution speed unit.

[0055] The high-resolution distance unit refers to the distance resolution obtained by the radar receiver after coherent processing of the echo signal. Its size depends on the synthetic bandwidth of the echo signal. If there is no frequency overlap between the pulses, the pulse frequency hopping interval Δf can be made equal to the transmission signal bandwidth B. p If the frequency hopping number of the multi-frequency diversity waveform is known to be I, the synthetic bandwidth can be expressed as:

[0056] B=B p +(I-1)Δf=IΔf (16)

[0057] Then the high-resolution distance unit can be expressed as:

[0058]

[0059] It is known that a coarse resolution distance unit is ΔR = c / 2B p , then the number of high-resolution distance units contained in a coarse-resolution distance unit is

[0060]

[0061] The velocity unambiguity range, i.e. the size of a coarse resolution velocity unit, is

[0062]

[0063] The high-resolution speed resolution of the radar depends on the working wavelength λ and the signal width. A high-resolution speed unit can be expressed as

[0064]

[0065] Then the number of high-resolution velocity units contained in a coarse-resolution velocity unit is:

[0066]

[0067] Sub-step 2.2, according to the above theory, divide the coarse resolution distance unit into Φ high resolution distance units and divide the coarse resolution velocity unit into Ψ velocity units, so as to construct the dictionary matrix D. That is, the number of grid points in the velocity dimension of the dictionary matrix is ​​Φ, and the number of grid points in the velocity dimension is Ψ. Define the distance corresponding to the φth grid point in the distance dimension of the dictionary matrix as r φ , where φ=1,2,...,Φ, the velocity dimension The velocity corresponding to each grid point is in Define the following variables:

[0068]

[0069] When the target distance R m0 =r φ , Target speed hour, It can be expressed as

[0070]

[0071] ζ(p) can be expressed as:

[0072]

[0073] θ is expressed as Then the echo signal of the pth pulse can be expressed as:

[0074]

[0075] The dictionary matrix constructed in this way can be expressed as:

[0076]

[0077] Then the sparse model of the target echo signal received by the radar can be expressed as: X=θD+σ (27)

[0078] Among them, θ is the scattering coefficient, D is the dictionary matrix, and σ is the noise.

[0079] Step 3: Construct a distance-velocity two-dimensional spectrum based on the observation vector and dictionary matrix to find the atom corresponding to the peak in the distance-velocity two-dimensional spectrum, store the position of the atom, update the atom position index and the set of atoms, and then update the residual vector. The initial residual vector is the observation data vector. Finally, the sparse coefficient solution is calculated to obtain the result of high-resolution target distance and velocity detection.

[0080] Specifically, step 3 includes the following sub-steps:

[0081] Sub-step 3.1: Take the coarse resolution range gate data of the target as the observation vector X, input the observation vector X and the dictionary matrix D, and determine the number of iterations L according to the target sparsity; initialize the atom set and residual vector: atom index set Residual vector r (0) =X, initialize the number of iterations l = 1. Initialize the atomic set in represents the empty set symbol, the superscript “(0)” represents initialization, and the superscript “(l)” represents the lth iteration.

[0082] Sub-step 3.2, start iterative operation. Each iteration includes the following steps:

[0083] Step 1: Calculate the covariance matrix of the residual vector It can be expressed as:

[0084]

[0085] In the above formula, (·) H represents the conjugate transpose. (l-1) Expressed as in represents the p-th pulse data of the residual vector of the l-th iteration, and P represents the total number of pulses. Then the covariance matrix It can be expressed as:

[0086]

[0087] In the above formula, (·) * represents the conjugate operation. The characteristic decomposition of the covariance matrix is:

[0088]

[0089] Among them, (U (l) ) H U (l) =I, I represents the unit matrix. In the above formula, in express The eigenvalue of , D represents the number of eigenvalues, which is equal to the number of pulses P.

[0090] Assume that the eigenvectors corresponding to the above eigenvalues ​​are The eigenvector corresponding to the smaller eigenvalue of the noise subspace As a column vector, it constitutes the noise subspace but It can be expressed as:

[0091]

[0092] Where M represents the number of targets.

[0093] Step 2: According to the dictionary matrix D and matrix Calculate the distance velocity two-dimensional spectrum as P (l) , the dictionary matrix D contains the target information, P (l) It can be expressed as:

[0094]

[0095] Step 3: When the noise subspace is orthogonal to the signal subspace, it appears as a peak in the distance-velocity two-dimensional spectrum. Find the distance-velocity two-dimensional spectrum P (l) The peaks corresponding to the atoms Store the position of the atom ω (l) ;

[0096] Step 4: Update the atomic index set:

[0097] Ω (l) =Ω (l-1) ∪ω (l) (33)

[0098] Update an atomic collection:

[0099]

[0100] Step 5: Update the residual vector:

[0101] r (l) =(I-β (k) )r (l-1) (35)

[0102] where β (k) For A (l) Column space orthogonal projection operator, β (k) It can be expressed as:

[0103] β (k) =A (l) [(A (l) ) T A (l) ] -1 (A (l) ) T (36)

[0104] Step 6: Calculate the sparse coefficient solution

[0105]

[0106] Step 7: If the number of iterations l reaches the preset value L, stop the iteration operation. Otherwise, increase the number of iterations by 1 and jump to the first step to repeat the above steps;

[0107] Step 8: Output the sparse coefficient solution vector θ.

[0108] Table 1 Simulation parameter settings

[0109]

[0110] According to the parameters in Table 1, it can be calculated that the synthesis bandwidth of the multi-frequency diversity waveform is B = 600MHz. The size of a coarse resolution range unit is c / 2B p =15m, the high-resolution distance unit size is c / 2B=0.25m. Then the number of high-resolution distance units that can be divided in a coarse-resolution distance unit is 60. The size of a coarse-resolution velocity unit is c / 2f0T=50m / s, the size of the high-resolution distance unit is c / 2f0PT=0.833m / s, then the number of high-resolution velocity grid points divided in a coarse-resolution velocity unit is 60. The simulation sets the number of pulses to 60, and the dimension of the constructed dictionary matrix is ​​60×3600.

[0111] There are two target scattering points in the radar observation scene, and the simulation data of their target speed and distance parameters are shown in Table 2.

[0112] Table 2 Target parameter settings

[0113]

[0114] In order to verify the super-resolution performance of the SRC-OMP method, the grid points of the dictionary matrix are divided more finely, which is doubled based on the original high-resolution distance unit, that is, the number of distance points divided in a coarse-resolution distance unit is 120. Figure 3 and Figure 4 The two-dimensional spectrum of distance-velocity using the super-resolution orthogonal matching pursuit method and the traditional orthogonal matching pursuit method based on matching inner product under the same parameters. Figure 3 and Figure 4 It can be seen that the SRC-OMP method has higher resolution performance than the traditional OMP method. Due to the characteristics of the sinc function, the OMP algorithm cannot separate the two targets when the distance between the two target scattering points is close, resulting in false detection and missed detection. Therefore, the sparse reconstruction probability is reduced.

[0115] Figure 5 The detection plane is shown as the result of multi-frequency diversity radar target range and velocity estimation using super-resolution orthogonal matching pursuit algorithm. Figure 5 It can be observed that the use of the SRC-OMP algorithm can more accurately distinguish targets with close distance and speed parameters. Therefore, the algorithm greatly improves the target reconstruction probability and is beneficial to the detection of targets by multi-frequency diversity radar.

[0116] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the technical principles of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. A multi-frequency diversity radar target distance and speed estimation method, characterized in that: The following steps are involved: Step 1: Establish a multi-frequency diversity radar transmission signal model s(t), and perform pulse compression processing on the obtained radar echo signal. The echo signal obtained after pulse compression is x(t). Step 2, calculate the distance resolution unit and speed resolution unit of the radar echo signal. The distance resolution unit includes a coarse resolution distance unit and a high resolution distance unit; the speed resolution unit includes a coarse resolution speed unit and a high resolution speed unit. The high resolution distance grid is divided in the coarse resolution distance unit, and the high resolution speed grid is divided in the coarse resolution speed unit. Thus, a high resolution speed-distance dictionary matrix D is constructed. Step 3, call the super-resolution orthogonal matching pursuit algorithm (SRC-OMP), construct the distance-velocity two-dimensional spectrum according to the observation vector and the dictionary matrix, find the atom corresponding to the peak in the distance-velocity two-dimensional spectrum, store the position of the atom and update the atom position index and the set of atoms, and then update the residual vector. The initial residual vector is the observation data vector. Finally, the sparse coefficient solution is calculated to obtain the results of high-resolution target distance and velocity detection.

2. The super-resolution orthogonal matching pursuit algorithm (SRC-OMP) according to claim 1, characterized in that: Step 1 contains the following steps: Sub-step 1.1: Assume that the radar transmits a total of P pulses, the carrier frequencies of the P pulses randomly jump within a certain synthetic bandwidth, and a frequency diversity waveform is used in a single pulse, including multiple sub-pulses transmitted simultaneously. Assume that its initial carrier frequency is f0, the inter-pulse frequency hopping interval is Δf, and the minimum frequency interval of the frequency diversity sub-pulses within a pulse is equal to the minimum inter-pulse frequency hopping interval. Then the carrier frequency of the signal transmitted by the qth array element of the pth pulse is f p，q =f0+k p Δf+k q Δf, where k p is the code of the pth pulse, k p ∈{0, 1, 2, ..., I-1}, I is the number of carrier frequency jumps; k q is the frequency hopping variable of the qth array element signal in the pth pulse, k q ∈{-k p , -k p +1,…,I-1-k p }, where q = 1, 2, ..., Q p , Q p is the number of sub-pulses in the p-th pulse. Then the q-th sub-pulse emission signal of the p-th pulse can be expressed as: s p，q (t)=s(t-pT)exp(j2πf p，q t) (1) Wherein, j is the imaginary unit, t is the fast time, T is the pulse repetition period, and s(t) is the radar transmitting pulse baseband signal waveform. If the radar transmit pulse baseband signal is a linear frequency modulation signal, s(t) can be expressed as In formula (2), B p is the transmit signal bandwidth, T p is the transmission signal time width. rect(·) is the rectangular window function. If μ=B p / T p is the frequency modulation slope of the linear frequency modulation signal, then equation (1) can be simplified to Assume that there are M target scattering points in the target observation scene, and the initial distance of the mth (m = 1, 2, ..., M) target scattering point is R m0 , the speed is v m , then the distance of the mth target scattering point at time t can be expressed as r m (t)=R m0 +v m t (4) The time from the radar transmitting the pulse signal to receiving the target echo signal is called the echo delay. Let the echo delay of the mth target scattering point be τ m If the time when the radar receives the echo signal is t, then the time when the radar transmits the signal is t-τ m , the time when the radar signal reaches the target is t-τ m / 2. From the time the radar transmits the pulse signal to the time the radar receives the target echo signal, the distance the electromagnetic wave travels is cτ m , where c represents the speed of light. From equation (4), the distance between the mth target scattering point and the target can be expressed as r m (t-τ m / 2), then the following relationship holds: c m =2r m (t-t m / 2)=2[R m0 +v m (t-t m / 2)] (5) That is, the distance the electromagnetic wave travels is twice the distance between the radar and the target scattering point. Then the echo delay τ of the mth target m It can be expressed as: In actual application scenarios, there are v m <<c holds true, then formula (6) can be simplified to It is known that the echo signal received by the radar is the superposition of the echo signals of all target scattering points in the observation scene, and for a single pulse echo, it is the superposition of the echoes of all sub-pulses in the pulse, so the echo signal of the pth pulse can be expressed as: Among them, ξ m is the scattering coefficient of the mth target scattering point, and it can be obtained from formula (3): Substituting formula (9) into formula (8) yields: Sub-step 1.2, the above formula is for the initial radar echo signal that has not been processed by the receiver. The received radar echo signal is down-converted and pulse compressed, and the radar echo signal expression after pulse compression is obtained as follows: It is known that a coarse resolution range unit of the radar is ΔR = c / 2B p , B p is the transmission signal bandwidth. In order to make the distance between each adjacent sampling point equal to a coarse resolution distance unit, the sampling rate f s Equal to the transmitted signal bandwidth, that is, f s =B p Assuming there are N sampling points, the time corresponding to the nth (n=1, 2, ..., N)th sampling point of the pth pulse is t n =pT+n / f s , T is the pulse repetition period. The distance unit corresponding to the nth sampling point is: <h2 style=";text-align:left;direction:ltr">r(n) = nΔR = nc / 2B<h2 style=";text-align:left;direction:ltr"> p <h2 style=";text-align:left;direction:ltr"> =nc / 2f<h2 style=";text-align:left;direction:ltr"> s <h2 style=";text-align:left;direction:ltr"> (12) From equation (12), we can get that the distance between adjacent sampling points is exactly one coarse resolution distance unit. Therefore, the echo signal of the nth sampling point of the pth pulse is: From the properties of the sinc function, we know that when n / f s -τ m =0, that is, n = τ m f s When the pulse compression result of the echo signal reaches the maximum value. In a coarse resolution distance unit, the fast time parameter n / f in the exponential term s Can be ignored. Formula (14) can be simplified as: In practical applications, the radar receiver system will contain a certain amount of noise σ(t n ), so the expression of the echo signal actually received by the radar is: In formula (15), the first exponential term is a constant term, which is independent of the speed and distance of the target; the second exponential term is the distance phase term, which changes with the pulse code k. p and the sub-pulse code k q It changes with the change of , which contains the distance information of the target, referred to as the distance term; the third exponential term is the velocity phase term, It represents the change of the qth sub-pulse signal of the pth pulse relative to the initial carrier frequency, which contains the speed information of the target and is referred to as the speed term.

3. The super-resolution orthogonal matching pursuit algorithm (SRC-OMP) according to claim 2, characterized in that: Step 2 contains the following sub-steps: Sub-step 2.1: Calculate the range resolution unit and speed resolution unit of the radar echo signal. The range resolution unit includes a coarse resolution range unit and a high resolution range unit; the speed resolution unit includes a coarse resolution speed unit and a high resolution speed unit. Divide the high resolution range grid points in the coarse resolution range unit, and divide the high resolution speed grid points in the coarse resolution speed unit. The high-resolution distance unit refers to the distance resolution obtained by the radar receiver after coherent processing of the echo signal. Its size depends on the synthetic bandwidth of the echo signal. If there is no frequency overlap between the pulses, the pulse frequency hopping interval Δf can be made equal to the transmission signal bandwidth B. p If the frequency hopping number of the frequency diversity waveform is known to be I, the synthetic bandwidth can be expressed as: B=B p +(I-1)Δf=IΔf (16) Then the high-resolution distance unit can be expressed as: It is known that a coarse resolution distance unit is ΔR = c / 2B p , then the number of high-resolution distance units contained in a coarse-resolution distance unit is The velocity unambiguity range, i.e. the size of a coarse resolution velocity unit, is The high-resolution speed resolution of the radar depends on the working wavelength λ and the signal width. A high-resolution speed unit can be expressed as Then the number of high-resolution velocity units contained in a coarse-resolution velocity unit is: Sub-step 2.2, according to the above theory, divide the coarse resolution distance unit into Φ high resolution distance units and divide the coarse resolution velocity unit into Ψ velocity units, so as to construct the dictionary matrix D. That is, the number of grid points in the velocity dimension of the dictionary matrix is ​​Φ, and the number of grid points in the velocity dimension is Ψ. Define the distance corresponding to the φth grid point in the distance dimension of the dictionary matrix as r φ , where φ=1,2,…,Φ, the velocity dimension The velocity corresponding to each grid point is in Define the following variables: When the target distance R m0 =r φ , Target speed hour, It can be expressed as ζ(p) can be expressed as: θ is expressed as Then the echo signal of the pth pulse can be expressed as: The dictionary matrix constructed in this way can be expressed as: Then the sparse model of the target echo signal received by the radar can be expressed as: X=θD+σ (27) Among them, θ is the scattering coefficient, D is the dictionary matrix, and σ is the noise.

4. The super-resolution orthogonal matching pursuit algorithm (SRC-OMP) according to claim 3, characterized in that: Step 3 contains the following sub-steps: Sub-step 3.1: Input the observation vector X and dictionary matrix D, determine the number of iterations L according to the target sparsity; initialize the atom set and residual vector: atom index set Residual vector r (0) =X, initialize the number of iterations l = 1. Initialize the atomic set in represents the empty set symbol, the superscript "(0)" represents initialization, and the superscript "(l)" represents the lth iteration. Sub-step 3.2, start iterative operation. Each iteration includes the following steps: Step 1: Calculate the covariance matrix of the residual vector It can be expressed as: In the above formula, (·) H represents the conjugate transpose. (l-1) Expressed as in represents the p-th pulse data of the residual vector of the l-th iteration, and P represents the total number of pulses. Then the covariance matrix It can be expressed as: In the above formula, (·) * represents the conjugate operation. The characteristic decomposition of the covariance matrix is: Among them, (U (l) ) H U (l) =I, I represents the unit matrix. In the above formula, in express The eigenvalue of , D represents the number of eigenvalues, which is equal to the number of pulses P. Assume that the eigenvectors corresponding to the above eigenvalues ​​are The eigenvector corresponding to the smaller eigenvalue of the noise subspace As a column vector, it constitutes the noise subspace but It can be expressed as: Where M represents the number of targets. Step 2: According to the dictionary matrix D and matrix Calculate the distance velocity two-dimensional spectrum as P (l) , the dictionary matrix D contains the target information, P (l) It can be expressed as: Step 3: When the noise subspace is orthogonal to the signal subspace, it appears as a peak in the distance-velocity two-dimensional spectrum. Find the distance-velocity two-dimensional spectrum P (l) The peaks corresponding to the atoms Store the position of the atom ω (l) ; Step 4: Update the atomic index set: Oh (l) =Oh (l-1) ∪ω (l) (32) Update an atomic collection: Step 5: Update the residual vector: r (l) ＝(I-β (k) )r (l-1) (34) where β (k) For A (l) Column space orthogonal projection operator, β (k) It can be expressed as: β (k) =A (l) [(A (l) ) T A (l) ] -1 (A (l) ) T (35) Step 6: Calculate the sparse coefficient solution Step 7: If the number of iterations l reaches the preset value L, stop the iteration operation. Otherwise, increase the number of iterations by 1 and jump to the first step to repeat the above steps; Step 8: Output the sparse coefficient solution vector θ.

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