CN115015923B - Sparse linear array SAR three-dimensional imaging method based on data rotation - Google Patents

Abstract

The invention discloses a sparse linear array SAR three-dimensional imaging method based on data rotation, which comprises the following steps: s1, initializing system parameters; s2, echo recording and demodulation; s3, carrying out correlation processing on the echo signal and the reference signal; s4, data rotation expansion transformation; s5, matrix filling is achieved by adopting a singular value threshold method; s6, performing rotary expansion inverse transformation on the result of the S5; s7, repeating the steps of S4-S6, and filling and recovering all distance section signals to obtain a final reconstructed three-dimensional signal; s8, realizing three-dimensional imaging of the target by adopting a back projection method. According to the method, the proportion of missing data and the position of specific data to be recovered are determined by gridding the sparse linear array echo according to the rule of half wavelength; by performing data rotation expansion transformation on the distance section signals, the problem that matrix filling cannot complement a row-column missing matrix is solved. The invention has the advantages of high imaging effect quality, wide applicability, simple data storage, low operation processing complexity and the like.

Description

Sparse linear array SAR three-dimensional imaging method based on data rotation

Technical Field

The invention belongs to the technical field of linear array synthetic Aperture Radar (LINEAR ARRAY SYNTHETIC Aperture Radar) imaging, and particularly relates to a sparse linear array SAR three-dimensional imaging method based on data rotation.

Background

In recent years, with the high-speed development of modern electronic technology, electronic countermeasure is increasingly strong, various interference patterns are layered, and the normal operation of a radar system is seriously hindered. For main lobe interference, the interference energy has absolute advantages, the main lobe interference is highly overlapped with a target in dimensions such as space time frequency, and the like, the effect of the existing interference suppression means is poor, and the main lobe interference is still one of the problems to be solved in the radar industry. The general main lobe interference resistance method comprises the following steps: signal processing and waveform design.

In terms of a signal processing main lobe interference resisting method, a common signal processing method includes: blind source separation and filtering. The blind source separation can separate the mixed signals without priori knowledge, and as in literature [G.Huang,L.Yang,G.Su.Blind source separation used for radar anti-jamming[C].2003International Conference on Neural Networks and Signal Processing,Nanjing,China,2003:1382-1385.], a blind source separation main lobe interference resisting algorithm based on matrix combination diagonalization feature vectors is provided, and the target signals and the interference signals are separated to realize interference suppression. However, after the mixed signal is separated, there is often a small amount of interference residual, and a single type of interference is aimed at. The filtering process mainly utilizes the difference of interference signals and target echoes in time, frequency, space, polarization and other domains to design filter parameters in different dimensions so as to achieve the effect of interference suppression, and as in document [S.Zhang,Y.Yang,G.Cui,et al.Range-velocity jamming suppression algorithm based on adaptive iterative filtering[C].2016IEEE Radar Conference,Philadelphia,PA,USA,2016:1-6.],, a mismatch filter is designed for each distance-Doppler unit so as to achieve the effect of distance-speed joint spoofing interference suppression. However, this method requires that the waveform of the interfering signal be precisely known and is only applicable to a certain interference type.

The method for resisting main lobe interference by waveform design is characterized by that the difference of target echo and interference signal in time, frequency, space and polarization domains is amplified by designing the information of phase and frequency of intra-pulse and inter-pulse waveforms so as to attain the goal of resisting interference, for example, the document [ Xu Leilei ] radar waveform design and several technical researches for resisting main lobe active interference [ D ] Xishan electronic science and technology university, 2019 ] ], and the interference signal is compressed by utilizing waveform optimization method based on the amplitude difference between angle domain waveform and interference signal so as to effectively resist DRFM forward interference. However, this method can only resist a single type of interference, and cannot effectively resist the composite interference where multiple interference types are superimposed.

Disclosure of Invention

The invention aims to overcome the defects of the prior art and provides a method for determining the proportion of missing data and the position of specific data to be recovered by gridding a sparse linear array echo according to a rule of half wavelength; by performing data rotation expansion transformation on the distance section signals, the data rotation-based sparse linear array SAR three-dimensional imaging method solves the problem that matrix filling cannot complement a row-column missing matrix.

The aim of the invention is realized by the following technical scheme: a sparse linear array SAR three-dimensional imaging method based on data rotation comprises the following steps:

s1, initializing system parameters, wherein the initialized parameters comprise a transmitting signal carrier frequency f ₀, an azimuth sampling frequency PRF, a distance sampling point number N _r, target irradiation time T _s, an azimuth sampling point number M, a linear array element number N', and a sparse linear array element interval d _i;

S2, echo recording and demodulation, wherein the specific process is as follows:

S21, initializing a sparse three-dimensional echo matrix Wherein N represents the number of array elements when the linear array spacing meets the Nyquist theorem, and O is a zero matrix;

S22, recording and demodulating the echo received by each array element at each azimuth moment to a baseband, and filling the baseband into S _echo according to the spatial position of each array element to obtain a three-dimensional LASAR echo signal S _echo (t, m, n);

S3, performing correlation processing on the echo signal S _echo (t, m, n) and the reference signal S _ref (t) to obtain a distance pulse compressed result S _r (t, m, n):

Where χ _R (·) is the distance pulse pressure blur function, χ _R (·) =sinc (·) in this example;

S4, data rotation expansion transformation: for each distance cut of S _r (t, m, n)

S _r ⁱ(m,n),i∈[1,N_r, m E [1, M ], n E [1, N ] are subjected to data rotation expansion processing, and an expansion matrix is initialized to beThe information of the original matrix S _r ⁱ is in one-to-one correspondence with the expanded matrix S ₂, and the rule is as follows:

Transformed There are known elements in each row and each column;

s5, filling a matrix of the result obtained in the step S4, and realizing matrix filling by adopting a singular value threshold method;

s6, performing rotary expansion inverse transformation on the result of the S5;

S7, repeating the steps of S4-S6, and filling and recovering all distance section signals to obtain a final reconstructed three-dimensional signal

S8, realizing three-dimensional imaging of the target by adopting a back projection method.

Further, the specific process of step S5 is as follows:

S51, initializing parameters, setting maximum iteration times MAX, initializing iteration times k=1, iteration step delta, projection matrix P _Ω and matrix to be recovered S ₀ =0;

S52, singular value decomposition: Wherein U _k-1 and V _k-1 are orthogonal matrices, Σ _k-1＝diag({σ_j }1 is less than or equal to j is less than or equal to r), r is the rank of Y _k-1, and sigma _j is a singular value;

S53, calculating a singular value contraction operator: x _k＝D_τ(Y_k-1)＝U_k-1D_τ(Σ_k-1)V_k-1 ^T, wherein D _τ (·) is a soft threshold operation, the non-negative portion represented by D _τ(Σ_k-1)＝diag({σ_j-τ}₊),t₊, i.e., t ₊ =max (0, t);

s54, updating: wherein P _Ω is a projection matrix;

s55, matrix filling iteration termination judgment based on singular value threshold, if k=MAX, the maximum iteration number is reached, the iteration is terminated, Otherwise, k=k+1, returning to S52, and continuing the k+1st iteration.

Further, the specific steps of the step S8 are as follows:

s81, initializing a backward projection imaging space, and carrying out grid division on the imaging space into P pixel units, wherein in order to enable two adjacent point targets to be distinguished, the grid interval is slightly smaller than the resolution requirement;

S82, calculating the distance histories of each grid pixel point and the receiving array element at different azimuth moments, and calculating corresponding time delays according to the distance histories, wherein the time delay of the nth array element at the mth azimuth moment from the pixel point P _p(x_p,y_p,z_p) is tau _m,n,p:

s83, extracting echo data on corresponding delay migration tracks of each grid pixel point P _p(x_p,y_p,z_p in an imaging scene, and carrying out phase compensation on the extracted data along the tracks by utilizing the delay obtained in S82, wherein the phase compensation factors are as follows:

S84, performing coherent superposition, namely performing coherent superposition on the echo data after phase compensation, and multiplying and accumulating the echo obtained in the S7 and the compensation phase obtained in the S83:

and obtaining a final three-dimensional imaging result.

The beneficial effects of the invention are as follows: the invention provides a sparse linear array SAR three-dimensional imaging method based on data rotation according to signal characteristics of sparse linear array SAR echoes and precondition characteristics of matrix filling. The proportion of missing data and the position of specific data to be recovered are determined by gridding the sparse linear array echo according to the rule of half wavelength; the problem that matrix filling cannot complement a row-column missing matrix is solved by performing data rotation expansion transformation on the distance tangent plane signals, and the related characteristics of the original matrix are not destroyed, so that the matrix filling can be applied to a sparse linear array scene. After the data is restored, the invention adopts matrix expansion inverse transformation, reduces the size of the data and is convenient for subsequent rapid imaging. The invention has the advantages of high imaging effect quality, wide applicability, simple data storage, low operation processing complexity and the like.

Drawings

FIG. 1 is a flow chart of a sparse linear array SAR three-dimensional imaging method based on data rotation;

FIG. 2 is a sparse linear array SAR imaging geometry applicable to the present invention;

FIG. 3 is a diagram of data rotation expansion;

FIG. 4 is a graph of a matrix fill effect based on data rotation expansion;

Fig. 5 is a three-dimensional imaging diagram of sparse linear array SAR at a sparsity of 20%.

Detailed Description

The method solves the problem that imaging defocusing is caused by the fact that the Nyquist theorem is not satisfied by the sparse linear array SAR signal. The invention utilizes the characteristic that the matrix filling can carry out the complement restoration on the matrix, the reconstruction of the sparse linear array echo is regarded as the restoration process of missing data, the three-dimensional echo signal is firstly subjected to distance compression, and then the low-rank characteristic of the sparse linear array SAR on the distance section after the distance compression is utilized to realize the signal restoration by adopting the matrix filling, but the traditional matrix filling method can not solve the restoration problem of the row deletion due to the row deletion of the matrix; then, matrix rotation expansion inversion conversion is carried out to restore the matrix to the original size, so that the subsequent calculated amount is reduced; and finally, realizing high-precision three-dimensional imaging by adopting an imaging algorithm. The technical scheme of the invention is further described below with reference to the accompanying drawings.

As shown in fig. 1, the sparse linear array SAR three-dimensional imaging method based on data rotation of the invention comprises the following steps:

S1, initializing system parameters, wherein the initialized parameters comprise a transmitting signal carrier frequency f ₀, an azimuth sampling frequency PRF, a distance sampling point number N _r, a target irradiation time T _s, an azimuth sampling point number M, a linear array element number N', a sparse linear array element interval d _i, N ⁺ is a positive integer, i.e. the array element spacing is half wavelengthIs a multiple of (2); the geometry of this embodiment is shown in fig. 2, assuming that sampling of the radar system in the azimuth direction is at intervals of half wavelength or less, the nyquist sampling rate is satisfied. The array element spacing is non-uniform and sparse, and the spacing is integer times of half wavelength, and the basic parameters are shown in table 1. In this embodiment, it is assumed that there are five point targets in the scene, and the distribution thereof is shown in table 2, where target 1 is the center position of the scene.

TABLE 1

Platform speed (v)	0.375m/s
		Center time platform position (R 0)	(0,0,0.4)
Carrier frequency (f 0)/wavelength (lambda)	100GHz/3mm
		Transmitting signal bandwidth (B r)	5GHz
Pulse width of transmitting signal (T r)	0.5μs
		Distance oversampling coefficient (gamma r)	1.20
Distance direction sampling point number (N r)	118
		Target irradiation time (T s)	0.4s
Pulse Repetition Frequency (PRF)	2500Hz
		Direction sampling point number (M)	100
Number of linear array elements (N')	20
		Sum of array element distance at two ends of linear array (d sum)	0.15m

Setting the sampling rate of the system as

F_s＝γ_rB_r＝6GHz

Setting the number of array elements required when the linear array meets the Nyquist theorem:

setting data sparsity:

I＝N′/N＝20％

TABLE 2

S2, echo recording and demodulation, wherein the specific process is as follows:

S21, initializing a sparse three-dimensional echo matrix Wherein N represents the number of array elements when the linear array spacing satisfies the Nyquist theorem, namely S _echo＝O_{100×100×118}, and O is a zero matrix;

S22, recording and demodulating the echo received by each array element at each azimuth moment to a baseband, wherein the expression is as follows:

Wherein L is the total number of scattering points of the target; w _r (·) represents the distance-to-window function, which in this embodiment takes a simple rectangular window; k _r is the signal modulation frequency, c is the speed of light, t is the distance-to-time variable, and m is the azimuth time variable; the distance history R (m, n; l) is:

(x _l,y_l,z_l) is the coordinates of the first target point; the range of azimuth time variable m is:

m＝[-M/2:M/2]/PRF

＝[-0.02:0.02]s

The range of the fast time variable t is:

t＝[-N_r/2:N_r/2]/F_s

＝[-9.83e^-9:9.83e^-9]s

n is the height position number of the constructed sparse array element, n=1,..100; s _echo (t, m, n) =0 when no array element at the n position receives an echo; filling the space positions of the array elements into S _echo to obtain a three-dimensional LASAR echo signal S _echo (t, m, n);

S3, performing correlation processing on the echo signal S _echo (t, m, n) and the reference signal S _ref (t) to obtain a distance pulse compressed result S _r (t, m, n):

Where χ _R (·) is the distance pulse pressure blur function, χ _R (·) =sinc (·) in this example;

s4, data rotation expansion transformation: as shown in FIG. 3, for each distance cut of S _r (t, m, n)

S _r ⁱ(m,n),i∈[1,N_r, m E [1, M ], n E [1, N ] are subjected to data rotation expansion processing, and an expansion matrix is initialized to beThe information of the original matrix S _r ⁱ is in one-to-one correspondence with the expanded matrix S ₂, and the rule is as follows:

Transformed There are known elements in each row and each column;

s5, filling a matrix of the result obtained in the step S4, and realizing matrix filling by adopting a singular value threshold method; the specific process is as follows:

S51, initializing parameters, setting maximum iteration times MAX, initializing iteration times k=1, iteration step delta, projection matrix P _Ω and matrix to be recovered S ₀ =0;

S52, singular value decomposition: Wherein U _k-1 and V _k-1 are orthogonal matrices, Σ _k-1＝diag({σ_j}1≤j≤r),_r is the rank of Y _k-1, σ _j is the singular value;

S53, calculating a singular value contraction operator: x _k＝D_τ(Y_k-1)＝U_k-1D_τ(Σ_k-1)V_k-1 ^T, wherein D _τ (·) is a soft threshold operation, the non-negative portion represented by D _τ(Σ_k-1)＝diag({σ_j-τ}₊),t₊, i.e., t ₊ =max (0, t);

s54, updating: wherein P _Ω is a projection matrix;

s55, matrix filling iteration termination judgment based on singular value threshold, if k=MAX, the maximum iteration number is reached, the iteration is terminated, Otherwise, k=k+1, returning to S52, and continuing the k+1st iteration.

S6, performing rotation expansion inverse transformation on the result of the S5:

After inverse transformation Is the original size;

S7, circularly reconstructing echo from the distance to the tangential plane: repeating the steps S4-S6, and filling and recovering all distance section signals to obtain a final reconstructed three-dimensional signal

S8, realizing three-dimensional imaging of the target by adopting a back projection method; the method comprises the following specific steps:

s81, initializing a backward projection imaging space, and carrying out grid division on the imaging space into P pixel units, wherein in order to enable two adjacent point targets to be distinguished, the grid interval is slightly smaller than the resolution requirement;

S82, calculating the distance histories of each grid pixel point and the receiving array element at different azimuth moments, and calculating corresponding time delays according to the distance histories, wherein the time delay of the nth array element at the mth azimuth moment from the pixel point P _p(x_p,y_p,z_p) is tau _m,n,p:

s83, extracting echo data on corresponding delay migration tracks of each grid pixel point P _p(x_p,y_p,z_p in an imaging scene, and carrying out phase compensation on the extracted data along the tracks by utilizing the delay obtained in S82, wherein the phase compensation factors are as follows:

S84, performing coherent superposition, namely performing coherent superposition on the echo data after phase compensation, and multiplying and accumulating the echo obtained in the S7 and the compensation phase obtained in the S83:

and obtaining a final three-dimensional imaging result.

The simulation results of this embodiment are shown in fig. 4 and 5. FIG. 4 (a) is a graph of the filling effect after rotational expansion transformation of sparse matrix data; (b) Filling an effect diagram for a matrix after the data rotation expansion transformation; (c) a filling effect diagram after the data rotation expansion inverse transformation; as can be seen from fig. 4, after matrix expansion, the new matrix has known elements in each row and each column, so that the matrix filling can be realized by the data which cannot be recovered originally. FIG. 5 (a) is a direct sparse three-dimensional imaging; (b) The method is used for three-dimensional imaging of the sparse linear array SAR based on data rotation matrix filling. As can be seen from fig. 5, direct sparse imaging without matrix filling can cause grating lobes to generate, influence imaging results, and high-precision three-dimensional imaging can be obtained after matrix filling, so that the invention can realize high-resolution three-dimensional imaging of sparse linear array SAR.

Those of ordinary skill in the art will recognize that the embodiments described herein are for the purpose of aiding the reader in understanding the principles of the present invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific modifications and combinations from the teachings of the present disclosure without departing from the spirit thereof, and such modifications and combinations remain within the scope of the present disclosure.

Claims (3)

1. The sparse linear array SAR three-dimensional imaging method based on data rotation is characterized by comprising the following steps of:

s1, initializing system parameters, wherein the initialized parameters comprise a transmitting signal carrier frequency f ₀, an azimuth sampling frequency PRF, a distance sampling point number N _r, target irradiation time T _s, an azimuth sampling point number M, a linear array element number N', and a sparse linear array element interval d _i;

S2, echo recording and demodulation, wherein the specific process is as follows:

S21, initializing a sparse three-dimensional echo matrix Wherein N represents the number of array elements when the linear array spacing meets the Nyquist theorem, and O is a zero matrix;

S22, recording and demodulating the echo received by each array element at each azimuth moment to a baseband, and filling the baseband into S _echo according to the spatial position of each array element to obtain a three-dimensional LASAR echo signal S _echo (t, m, n);

S3, performing correlation processing on the echo signal S _echo (t, m, n) and the reference signal S _ref (t) to obtain a distance pulse compressed result S _r (t, m, n);

S4, data rotation expansion transformation: performing data rotation expansion processing on each distance section S _r ⁱ(m,n),i∈[1,N_r of S _r (t, m, n), m epsilon [1, M ], n epsilon [1, N ], and initializing an expansion matrix as The information of the original matrix S _r ⁱ is in one-to-one correspondence with the expanded matrix S ₂, and the rule is as follows:

Transformed There are known elements in each row and each column;

s5, filling a matrix of the result obtained in the step S4, and realizing matrix filling by adopting a singular value threshold method;

s6, performing rotary expansion inverse transformation on the result of the S5;

S7, repeating the steps of S4-S6, and filling and recovering all distance section signals to obtain a final reconstructed three-dimensional signal

S8, realizing three-dimensional imaging of the target by adopting a back projection method.

2. The three-dimensional imaging method of sparse linear array SAR based on data rotation of claim 1, wherein the specific process of step S5 is as follows:

S51, initializing parameters, setting maximum iteration times MAX, initializing iteration times k=1, iteration step delta, projection matrix P _Ω and matrix to be recovered S ₀ =0;

S52, singular value decomposition: Wherein U _k-1 and V _k-1 are orthogonal matrices, Σ _k-1＝diag({σ_j }1 is less than or equal to j is less than or equal to r), r is the rank of Y _k-1, and sigma _j is a singular value;

S53, calculating a singular value contraction operator: x _k＝D_τ(Y_k-1)＝U_k-1D_τ(Σ_k-1)V_k-1 ^T, wherein D _τ (·) is a soft threshold operation, the non-negative portion represented by D _τ(Σ_k-1)＝diag({σ_j-τ}₊),t₊, i.e., t ₊ =max (0, t);

s54, updating:

s55, matrix filling iteration termination judgment based on singular value threshold, if k=MAX, the maximum iteration number is reached, the iteration is terminated, Otherwise, k=k+1, returning to S52, and continuing the k+1st iteration.

3. The three-dimensional imaging method of sparse linear array SAR based on data rotation of claim 1, wherein the specific steps of step S8 are as follows:

s81, initializing a backward projection imaging space, and carrying out grid division on the imaging space into P pixel units, wherein in order to enable two adjacent point targets to be distinguished, the grid interval is slightly smaller than the resolution requirement;

S82, calculating the distance histories of each grid pixel point and the receiving array element at different azimuth moments, and calculating corresponding time delays according to the distance histories, wherein the time delay of the nth array element at the mth azimuth moment from the pixel point P _p(x_p,y_p,z_p) is tau _m,n,p:

s83, extracting echo data on corresponding delay migration tracks of each grid pixel point P _p(x_p,y_p,z_p in an imaging scene, and carrying out phase compensation on the extracted data along the tracks by utilizing the delay obtained in S82, wherein the phase compensation factors are as follows:

S84, performing coherent superposition, namely performing coherent superposition on the echo data after phase compensation, and multiplying and accumulating the echo obtained in the S7 and the compensation phase obtained in the S83:

and obtaining a final three-dimensional imaging result.