CN104076337B - Airborne radar clutter suppression method based on array element amplitude and phase error correction - Google Patents

Abstract

The invention belongs to radar clutter suppression technology field, particularly to airborne radar clutter suppression method based on array element amplitude and phase error correction.Should comprise the following steps by airborne radar clutter suppression method based on array element amplitude and phase error correction: step 1, pulse signal launched by the non-working side array antenna utilizing airborne radar, and receiving corresponding echo data, it is four-dimensional echo data that airborne radar receives the echo data of correspondence；According to described four-dimensional echo data, estimate the amplitude phase error vector of each row submatrix；Step 2, according to the amplitude phase error vector of m-th row submatrix, draws data after m-th row submatrix the l distance unit clutter recognition；Utilize m-th row submatrix the 1st distance unit clutter recognition after data to m-th row submatrix l-th distance unit clutter recognition after data composition m-th row submatrix clutter recognition after data；Utilize after the 1st row submatrix clutter recognition data to data after data composition airborne radar clutter suppression after m-th row submatrix clutter recognition.

Description

Airborne radar clutter suppression method based on array element amplitude-phase error correction

Technical Field

The invention belongs to the technical field of radar clutter suppression, and particularly relates to an airborne radar clutter suppression method based on array element amplitude-phase error correction, in particular to a method for filtering short-range clutter by utilizing a pitching degree of freedom. The method is mainly used for solving the problem of non-stationarity of short-range clutter of the airborne radar non-front side view array under the condition of array element amplitude-phase errors, and can effectively filter the short-range clutter, thereby enhancing the distance stationarity of the clutter and greatly improving the subsequent space-time two-dimensional self-adaptive processing performance.

Background

When the airborne radar looks down, to just looking side array antenna, clutter Doppler frequency hardly expands along with the change of distance, and the clutter satisfies the stationarity on the distance this moment. Therefore, enough training samples can be obtained from adjacent range units in the process of space-time adaptive processing for estimating a covariance matrix, and the clutter suppression method is widely applied in the field of radar signal processing. However, in order to realize omnidirectional scanning coverage of the radar on targets from all directions, multiple antennas are usually required to work in combination, and when an included angle between the axial direction of the placed antennas and the flight speed direction of the aircraft is not zero, the antennas are called as non-front side view array antennas. For non-positive side view array antennas, the range-doppler spectrum of the clutter appears curved, i.e., the doppler frequency of the clutter varies strongly with range. This distance dependence is mainly determined by the 0 th ambiguity distance, or short range clutter.

The short-range clutter of the non-front side array presents strong non-stationarity, and the degree of the non-stationarity is enhanced along with the increase of the included angle between the axis of the antenna and the speed direction of the carrier. In phased array antenna systems, however, the ultra-low side lobe antenna technique is difficult to implement with existing radar technology, and therefore the power level of the short-range clutter is usually very high. In this case, the number of distance units satisfying independent and same distribution for the short-range clutter region is very limited and no longer satisfies the requirement of Brennan criterion on the number of training samples, which results in degraded performance of sta (Space-Time Adaptive Processing) Processing of clutter, and thus the application of the sta technique is limited. In order to alleviate the distance non-stationary characteristic caused by the non-positive side array, the Doppler compensation firstly draws attention of radar workers, and the basic idea of the method is to carry out different Doppler compensation on clutter at different distances so that the center frequencies of main clutter at different distances tend to be consistent. The specific realization only needs to multiply the corresponding linear phase by the pulse time data of each distance, the processing structure is simple and effective, but the processing structure only compensates the main clutter center, the compensation of the side lobe clutter is not ideal, and the processing structure is only suitable for the condition without distance ambiguity. The subsequent angle Doppler compensation, registration compensation, integral updating method and the like have a certain mitigation effect on the non-stationarity of the short-range clutter to a certain extent, but the application of the methods is limited under the condition that the pulse repetition frequency of the radar is high to cause distance ambiguity.

The short-range clutter of the airborne non-front side-looking array radar is suppressed under the condition of distance ambiguity, and the pitching freedom of the array antenna can be utilized and combined with the azimuth and the time domain to form three-dimensional space-time adaptive processing. The method can effectively suppress the clutter, but inevitably causes the problem of overlarge calculation amount, and the number of required independent same-distribution samples is increased due to high degree of freedom of the system, which is often not satisfied in practice. The traditional space-time two-dimensional adaptive processing needs dimension reduction processing, and how to perform dimension reduction processing on the three-dimensional adaptive processing method is the key to whether the three-dimensional adaptive processing method can be applied or not. In order to solve the above problems, a method of pre-filtering pitch by using the pitch degree of freedom is proposed, which is called a pitch pre-filtering method. The pitching pre-filtering method can carry out weighting array subarray synthesis on the received three-dimensional clutter data without self-adaptive processing to convert the three-dimensional clutter data into two-dimensional data, and can suppress short-range clutter in the conversion process. The specific implementation process is as follows: and (3) adopting fixed constraint zero setting at a pitch angle corresponding to the short-range clutter, and simultaneously keeping the clutter gain in the main beam direction unchanged. The method is proposed under the condition of ideal clutter, namely, the method is only suitable for the condition that array element amplitude phase errors do not exist, namely, the method is not robust to the short-range clutter suppression method when radar system errors exist.

A reasonable error correction algorithm is provided to be the key for solving the robustness of the short-range clutter suppression algorithm, and the traditional array error correction method comprises an active correction method and a self-correction method. The direction of arrival of the auxiliary information source is required to be accurately known in active correction, and once the direction of the auxiliary information source is deviated, a large error is brought. In the invention, because the radar parameters are known a priori, the direction of arrival can be accurately known through calculation, and therefore, an active correction method is adopted for error correction.

Disclosure of Invention

The invention aims to provide an airborne radar clutter suppression method based on array element amplitude and phase error correction, aiming at the problem that the traditional space-time two-dimensional adaptive processing performance is reduced due to the non-stationarity of short-range clutter of a non-front side view array. According to the method, the array element amplitude-phase error is corrected, and then the corrected clutter data is subjected to pitching filtering processing, so that the clutter suppression performance of STAP processing is greatly improved.

In order to achieve the technical purpose, the invention is realized by adopting the following technical scheme.

The airborne radar clutter suppression method based on array element amplitude and phase error correction comprises the following steps: step 1, a non-positive side-looking array antenna is arranged on an airborne radar and consists of M array sub-arrays, each array sub-array is a uniform linear array consisting of N array elements, M and N are natural numbers, the array element interval of each array sub-array is d, and the interval between any two adjacent array sub-arrays is d;

transmitting a pulse signal by using a non-front side view array antenna of an airborne radar, and receiving corresponding echo data, wherein the corresponding echo data received by the airborne radar is four-dimensional echo data; estimating the amplitude-phase error vector of each array subarray according to the four-dimensional echo data;

step 2, obtaining data after the clutter suppression of the ith distance unit of the mth array subarray according to the amplitude-phase error vector of the mth array subarrayM is 1 to M, L is 1 to L, P is the number of pulses emitted by a non-positive side view array antenna of the airborne radar, and L represents the number of distance units of the airborne radar; forming data after clutter suppression of the mth array sub-array by using data after clutter suppression of the 1 st distance unit of the mth array sub-array to data after clutter suppression of the lth distance unit of the mth array sub-arrayData after clutter suppression by using 1 st array subarrayData after clutter suppression of array to MthForming airborne radar clutter suppressed data

The invention is characterized by further improvement:

the specific substeps of the step 1 are as follows:

(1.1) the distance fuzzy times of the clutter corresponding to the first distance unit is N_rlSecond, i1 th distance ambiguity clutterA pitch angle with respect to the non-frontal side view array antenna ofThenThe pitch steering vector of (a) is expressed as:

wherein T represents the transposition of a matrix or a vector, and lambda is the wavelength of the airborne radar transmitting signal;

by usingToPitching guide matrix B forming mth array subarray_m：

(1.2) Pitch steering matrix B to the m-th column subarray_mPerforming characteristic decomposition to obtain a pitching guide matrix B in the m-th column subarray_mSelecting K maximum eigenvalues from all eigenvalues of (1), K<N_rl(ii) a Forming an array manifold matrix A of the mth array sub-matrix by using the selected eigenvectors corresponding to the K maximum eigenvalues_m，

A_m＝[a_m1,a_m2,···,a_mK]；

Wherein, a_m1To a_mKRespectively representing the feature vectors corresponding to the selected K maximum feature values;

(1.3) the airborne radar receives a corresponding representation of the echo dataFor four-dimensional echo data X_N×M×P×LIn the four-dimensional echo data X_N×M×P×LExtracting two-dimensional data X corresponding to the ith distance unit of the mth array subarray_N×P(m, l) and then two-dimensional data X is obtained_N×P(m, l) Pitch covariance matrix R_ml：

R_ml＝(X_N×P(m,l)X^H _N×P(m,l))/P

Wherein H represents the conjugate transpose of the matrix;

(1.4) to R_mlPerforming characteristic decomposition on R_mlSelecting N-K minimum eigenvalues from all eigenvalues, and forming a noise subspace U by using eigenvectors corresponding to the selected N-K minimum eigenvalues_N；

Constructing a cost function J_mCost function J_mThe expression of (a) is:

$J_m=\underset{k^{\&prime;}=1}{\overset{K}{\mathrm{\&Sigma;}}}{\mathrm{\&delta;}}_m^H{\mathrm{\&alpha;}}_{{\mathrm{mk}}^{\&prime;}}^H{U}_N{U}_N^H{\mathrm{\&alpha;}}_{{\mathrm{mk}}^{\&prime;}}{\mathrm{\&delta;}}_m$

wherein H represents the conjugate transpose of the matrix, K 'is a natural number and K' is 1 to K, α_mk'＝diag(a_mk')，a_mk'The feature vector, diag (a), corresponding to the k' -th feature value selected in substep (1.3) is represented_mk') Is represented by a_mk'A diagonal matrix composed of each element of (1) as a main diagonal element;

order to ${\mathrm{\&Omega;}}_m=\underset{k^{\&prime;}=1}{\overset{K}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{{\mathrm{mk}}^{\&prime;}}^H{U}_N{U}_N^H{\mathrm{\&alpha;}}_{{\mathrm{mk}}^{\&prime;}},$ Then the cost function J_mExpressed as:

$J_m={\mathrm{\&delta;}}_m^H{\mathrm{\&Omega;}}_m{\mathrm{\&delta;}}_m$

then, establishing a quadratic constraint optimization problem as follows:

$\left\{\begin{array}{c}{\mathrm{\&delta;}}_m=\underset{{\mathrm{\&delta;}}_m}{\min }{\mathrm{\&delta;}}_m^H{\mathrm{\&Omega;}}_m{\mathrm{\&delta;}}_m\\ s.t.{\mathrm{\&delta;}}_m^{H}f=1\end{array}\right.$

wherein,_mf is a column vector with N × 1 dimension, the first element of f is 1, and the other elements are 0;

estimating the mth by solving the quadratic constraint optimization problemAmplitude-phase error vector of array subarray_m. In the substep (1.4), the quadratic constraint optimization problem is solved by using a Lagrange multiplier method, and the amplitude-phase error vector of the m-th column subarray is solved_mComprises the following steps:

${\mathrm{\&delta;}}_m=\frac{{\mathrm{\&Omega;}}_m^{-1}f}{f^T{\mathrm{\&Omega;}}_m^{-1}f}$

where T represents the transpose of the matrix or vector and the superscript-1 represents the inverse of the matrix.

In step 2, obtaining the data of the mth array subarray after the clutter suppression of the mth distance unitComprises the following substeps:

firstly, obtaining the short-range clutter guiding vector a corresponding to the ith distance unit of the mth array subarray_1mlThe path clutter guide vector a corresponding to the ith distance unit of the mth array subarray_2ml；

Wherein T represents the transpose of a matrix or vector, and lambda is the wavelength of the airborne radar transmission signal,indicating 0 th distance fuzzy correspondencesA pitch angle of the blade is set,representing the main beam direction when the airborne radar transmits signals;

then, according to the following formula, obtaining the short-range clutter guiding vector with error compensation corresponding to the ith distance unit of the mth array subarrayRemote clutter guide vector with error compensation corresponding to ith distance unit of mth array subarray

Wherein,representing a Hadamard product;_mthe amplitude and phase error vector of the mth array subarray;

constructing a pitching filtering weight vector corresponding to the ith distance unit of the mth array subarray according to the following formula

$\left\{\begin{array}{c}{\tilde{w}}_{\mathrm{ml}}^H{\tilde{a}}_{1\mathrm{ml}}=0\\ {\tilde{w}}_{\mathrm{ml}}^H{\tilde{a}}_{2\mathrm{ml}}=1\end{array}\right.$

Wherein H represents the conjugate transpose of the matrix;

in the four-dimensional echo data X_N×M×P×LExtracting two-dimensional data X corresponding to the ith distance unit of the mth array subarray_N×P(m, l) according to the pitch filtering weight vector corresponding to the ith distance unit of the mth array subarrayObtaining data after clutter suppression of the ith distance unit of the mth array subarray ${\tilde{X}}_{N\&times;P}(m,l)$ Comprises the following steps: ${\tilde{X}}_{N\&times;P}(m,l)={\tilde{w}}_{\mathrm{ml}}^H{X}_{N\&times;P}(m,l).$

the invention has the beneficial effects that:

1) aiming at the problem of non-stationarity of the distance of short-range clutter of the airborne radar non-front side view array, the pitching filtering processing is carried out by fully utilizing the pitching degree of freedom, a notch is formed at the short-range clutter which changes rapidly along with the distance for each distance unit by a fixed pitching weight, and meanwhile, the gain of the long-range clutter is kept unchanged, so that the short-range clutter is well suppressed, and meanwhile, the main beam clutter has large surplus;

2) for the situation that array element amplitude phase errors exist, notches formed by the pitching filtering weights deviate from the position of the short-range clutter, and the short-range clutter is greatly remained after pitching filtering. The invention compensates the traditional pitching filtering weight vector by using the estimated column subarray amplitude-phase error vector, and then performs matched filtering on clutter data corresponding to the column subarray in a pitching dimension by using the weight vector. Experiments show that the short-range clutter is basically and effectively suppressed by adopting the array element amplitude-phase error correction algorithm provided by the invention to correct and then carrying out pitching filtering processing, and the radar parameter prior information is fully utilized, so that the calculated amount is small, and the engineering application is facilitated.

Drawings

FIG. 1 is a flow chart of an airborne radar clutter suppression method based on array element amplitude-phase error correction according to the present invention;

FIG. 2a is a graph comparing the estimated amplitude error of each array element of the 5 th array subarray with the actual amplitude error of each array element of the 5 th array subarray in a simulation experiment according to the present invention;

FIG. 2b is a graph comparing the estimated phase error of each array element of the 5 th sub-array with the actual phase error of each array element of the 5 th sub-array according to the present invention in a simulation experiment;

FIG. 2c is a schematic diagram of the root-mean-square-error-of-amplitude curves for each array element of the 5 th array subarray estimated according to the present invention in a simulation experiment;

FIG. 2d is a schematic diagram of root-mean-square-error curves of phase of each array element of the 5 th array subarray estimated according to the present invention in a simulation experiment;

fig. 3a is a pitch directional diagram of the 5 th array subarray in the simulation experiment before array amplitude and phase error correction, a pitch directional diagram after array amplitude and phase error correction, a static pitch directional diagram, and a short-range clutter pitch directional diagram;

FIG. 3b is an enlarged partial schematic view of FIG. 3 a;

FIG. 4 is a range-Doppler plot of raw echo data with array element amplitude-phase errors in a simulation experiment;

FIG. 5a is a range-Doppler plot of echo data after pitch filtering without correction of array amplitude-phase errors in a simulation experiment;

FIG. 5b is a range-Doppler plot of echo data after pitch filtering and EFA processing without array amplitude-phase error correction in a simulation experiment;

FIG. 6a is a range-Doppler plot of echo data after pitch filtering under the condition of array magnitude-phase error correction in a simulation experiment;

fig. 6b is a range-doppler plot of echo data after pitch filtering and EFA processing under the condition of array amplitude-phase error correction in a simulation experiment.

Detailed Description

The invention will be further described with reference to the accompanying drawings in which:

referring to fig. 1, a flowchart of an airborne radar clutter suppression method based on array element amplitude-phase error correction according to the present invention is shown. The airborne radar is provided with a non-positive side-looking array antenna, the non-positive side-looking array antenna is an N multiplied by M-dimensional rectangular area array antenna, N and M are natural numbers, N represents the array element row number (azimuth array element number) of the non-positive side-looking array antenna, and M represents the array element column number (pitching array element number) of the non-positive side-looking array antenna. That is to say, the non-front side view array antenna is composed of M array sub-arrays, each array sub-array is a uniform linear array composed of N array elements, the array element interval of each array sub-array is d, and the interval between any two adjacent array sub-arrays is d, that is, the non-front side view array antenna azimuth array element interval and the non-front side view array antenna pitch array element interval are both d.

Firstly, the relation between the Doppler frequency of the clutter and the slant distance of the clutter to the carrier is analyzed, and the clutter is ignoredInfluence of spherical curvature on the result of the calculation, clutter Doppler frequency f_dComprises the following steps:

$f_d=\frac{2V}{\mathrm{\&lambda;}}(\cos \mathrm{\&psi;}\cos \mathrm{\&alpha;}-\sqrt{1-{\left(\frac{H^{\&prime;}}{R_l}\right)}^2-{\cos }^2\mathrm{\&psi;}}\sin \mathrm{\&alpha;})$

where V is the flight speed of the aircraft, λ is the wavelength of the signal emitted by the aircraft radar, H' and R_lRepresenting the height of the aircraft and the skew of the clutter to the aircraft, α is the yaw angle (antenna axis and flight direction), α is constant since the non-positive side view array antenna is mounted on the aircraft radar, psi represents the cone angle at the same wave position (angle between the main beam pointing direction and the axial direction of the antenna) corresponding to the clutter, phi is a constant value_dIs R_lAs a function of (c). When H'/R_lWhen the size is larger, the slant distance from the clutter to the antenna array surface is smaller, and the pitch angle is smaller(clutter to antenna) is large, when f_dFollowing slope distance R_lThe change is severe; otherwise, f_dFollowing slope distance R_lThe change is relatively gradual. This characteristic of clutter is most pronounced in the case of non-orthoscopic arrays, which in embodiments of the present invention are forward looking arrays.

Obtaining a clutter space-time snapshot vector c under an ideal condition, wherein the clutter space-time snapshot vector c under the ideal condition is as follows:

wherein N is_rNumber of distance ambiguities, N_cNumber of independent clutter sources being a range ring_ipFor the ith distance to blur the clutter complex amplitude of the p independent clutter source, i is 1 to N_rP is 1 to N_c，The clutter airspace pitch steering vector of the ith distance ambiguity,is the space domain azimuth guiding vector of the p independent clutter source blurred by the ith distance,and V is the flight speed of the carrier.

Andare respectively:

wherein,blurring the pitch angle, θ, of each independent clutter source relative to the non-frontal side view array antenna for the ith distance_ipThe azimuth angle of the p independent clutter source relative to the non-front side view array antenna is blurred by the ith distance, α is an included angle between the axial direction of the non-front side view array antenna (in a mode of being perpendicular to the array surface of the non-front side view array antenna) and the flight direction of the aircraft, d is the array element spacing of each array sub-array, d is the spacing between any two adjacent array sub-arrays, lambda is the wavelength of an emitted signal of the aircraft radar, f is the spacing between any two adjacent array sub-arrays_rThe number of the array element rows of the non-front side view array antenna is the pulse repetition frequency, N represents the number of the array element rows of the non-front side view array antenna, M represents the array element rows of the non-front side view array antenna, and P is the number of pulses transmitted by the non-front side view array antenna of the airborne radar.

And establishing an array element amplitude and phase error matrix of the non-front side view array antenna, and obtaining an echo data model of the non-front side view array antenna according to the array element amplitude and phase error matrix of the non-front side view array antenna and an expression of a clutter space-time snapshot vector c.

Specifically, firstly, an array element amplitude phase error matrix of the non-front side array antenna is established, and the array element amplitude phase error matrix of the non-front side array antenna is expressed as follows:

where ρ is_nmThe amplitude error phi of the array element of the nth row and the mth column of the non-front side-view array antenna is shown_nmAnd the phase error of the array element of the nth row and the mth column of the non-front side-view array antenna is shown, wherein N is 1 to N, and M is 1 to M. Order toThat is, in the above array element amplitude-phase error model, the first array element is usually used as a reference array element,_mrepresenting the magnitude-phase error vector of the mth column subarray,_mis in the form of:

${\mathrm{\&delta;}}_m={[{\mathrm{\&rho;}}_{1m}{e}^{{\mathrm{j\&phi;}}_{1m}},{\mathrm{\&rho;}}_{2m}{e}^{{\mathrm{j\&phi;}}_{2m}},...,{\mathrm{\&rho;}}_{\mathrm{Nm}}{e}^{{\mathrm{j\&phi;}}_{\mathrm{Nm}}}]}^T.$

obtaining clutter space-time snap-shot vector when array element amplitude-phase error existsClutter space-time snapshot vector when array element amplitude-phase error existsComprises the following steps:

wherein N is_rNumber of distance ambiguities, N_cNumber of independent clutter sources being a range ring_ipFor the ith distance to blur the clutter complex amplitude of the p independent clutter source, i is 1 to N_rP is 1 to N_c；A＝[11…1]^TA is a column vector of dimension P × 1, the elements in A are all 1, and T represents the transpose of matrix or vector.Representing the Kronecker product (outer product),representing a Hadamard product (inner product).

Then the echo data model of the non-front side view array antenna is:

$\tilde{x}=\tilde{c}+n$

wherein n is a Gaussian white noise vector with NMP dimension, the obedient mean value is zero, and the variance is sigma²I_NMPGaussian distribution of (I)_NMPAn identity matrix representing the NMP dimension.

The airborne radar clutter suppression method based on array element amplitude-phase error correction comprises the following steps:

step 1, transmitting a pulse signal by using a non-front side view array antenna of an airborne radar, and receiving corresponding echo data, wherein the corresponding echo data received by the airborne radar is four-dimensional echo data; and estimating the amplitude-phase error vector of each array subarray according to the four-dimensional echo data.

The method comprises the following specific substeps:

since the M different column sub-arrays of the non-front side view array antenna are independent from each other, the estimation problem of the array element amplitude-phase error matrix of the non-front side view array antenna can be decomposed into the estimation problem of the amplitude-phase error vectors of the M independent column sub-arrays.

Estimating the amplitude-phase error vector of the 1 st array₁Amplitude-phase error vector to Mth array subarray_M. Estimating the amplitude-phase error vector of the mth array subarray_mComprises the following substeps:

(1.1) the distance fuzzy times of the clutter corresponding to the first distance unit is N_rlThen, the i1 th range ambiguity clutter (each independent clutter source) has a pitch angle with respect to the non-positive side view array antenna i1 from 1 to N_rlH 'represents the aircraft height, R'_i1The slope distance for the i1 th distance blur,thenThe pitch steering vector of (a) is expressed as:

wherein T represents the transposition of a matrix or a vector, d is the array element interval of each column subarray, d is the interval between any two adjacent column subarrays, lambda is the wavelength of an airborne radar transmitting signal, and N represents the array element row number of the non-front side view array antenna.

By usingToPitching guide matrix B forming mth array subarray_m：

(1.2) due toWhen i1 takes from 2 to N_rlWhen the temperature of the water is higher than the set temperature,for long-range clutterThe angle of elevation,toVery close to each other, so the pitch steering vectorToThere is a strong correlation. Thus, the pitch steering matrix B for the m-th column sub-array_mPerforming characteristic decomposition to obtain a pitching guide matrix B in the m-th column subarray_mSelecting K maximum eigenvalues (larger than noise eigenvalues) from all eigenvalues of (A), K<N_rlAnd the value of K is determined according to the characteristic value of a Gaussian white noise vector n of NMP dimension, and each selected maximum characteristic value is ensured to be larger than all the characteristic values of n.

Forming an array manifold matrix A of the mth array sub-matrix by using the selected eigenvectors corresponding to the K maximum eigenvalues_m，

A_m＝[a_m1,a_m2,···,a_mK]。

Wherein, a_m1To a_mKRespectively representing the feature vectors corresponding to the selected K maximum feature values.

(1.3) transmitting pulse signals by using a non-side view array antenna of the airborne radar and receiving corresponding echo data, wherein the corresponding echo data received by the airborne radar is four-dimensional echo data X_N×M×P×LThe number of the array element rows of the non-front side array antenna is represented by N, the number of the array element columns of the non-front side array antenna is represented by M, the number of the pulses transmitted by the non-front side array antenna of the airborne radar is represented by P, and the number of the distance units of the airborne radar is represented by L.

In four-dimensional echo data X_N×M×P×LIn the middle, the first one of the m-th array subarray is extractedTwo-dimensional data X corresponding to distance unit_N×P(m, l) and then two-dimensional data X is obtained_N×P(m, l) Pitch covariance matrix R_ml：

R_ml＝(X_N×P(m,l)X^H _N×P(m,l))/P

Where H represents the conjugate transpose of the matrix.

(1.4) because the amplitude-phase errors of different distance units in the same subarray of the non-positive side-view array antenna are the same, the amplitude-phase error vector corresponding to the ith distance unit of the mth subarray can be used as the error amplitude-phase vector of the mth subarray. The amplitude-phase error vector of the mth array can be estimated according to the following steps_m：

To R_mlPerforming characteristic decomposition on R_mlSelecting N-K minimum eigenvalues from all eigenvalues, and forming a noise subspace U by using eigenvectors corresponding to the selected N-K minimum eigenvalues_N。

Constructing a cost function J_mCost function J_mThe expression of (a) is:

$J_m=\underset{k^{\&prime;}=1}{\overset{K}{\mathrm{\&Sigma;}}}{\mathrm{\&delta;}}_m^H{\mathrm{\&alpha;}}_{{\mathrm{mk}}^{\&prime;}}^H{U}_N{U}_N^H{\mathrm{\&alpha;}}_{{\mathrm{mk}}^{\&prime;}}{\mathrm{\&delta;}}_m$

wherein H represents the conjugate transpose of the matrix, K 'is a natural number and K' is 1 to K, α_mk'＝diag(a_mk')，a_mk'Indicates the selection in substep (1.3)The feature vector corresponding to the k' th feature value is obtained, diag (a) represents the diagonal matrix, diag (a)_mk') Is represented by a_mk'A diagonal matrix (a) in which each element of (a) is constituted as a main diagonal element_mk'Is arranged at α in the order of its elements_mkOn the main diagonal line).

Order to ${\mathrm{\&Omega;}}_m=\underset{k^{\&prime;}=1}{\overset{K}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_{{\mathrm{mk}}^{\&prime;}}^H{U}_N{U}_N^H{\mathrm{\&alpha;}}_{{\mathrm{mk}}^{\&prime;}},$ Then the cost function J_mExpressed as:

$J_m={\mathrm{\&delta;}}_m^H{\mathrm{\&Omega;}}_m{\mathrm{\&delta;}}_m$

then, establishing a quadratic constraint optimization problem as follows:

$\left\{\begin{array}{c}{\mathrm{\&delta;}}_m=\underset{{\mathrm{\&delta;}}_m}{\min }{\mathrm{\&delta;}}_m^H{\mathrm{\&Omega;}}_m{\mathrm{\&delta;}}_m\\ s.t.{\mathrm{\&delta;}}_m^{H}f=1\end{array}\right.$

wherein,for constraint, H represents the conjugate transpose of the matrix, f ═ 1,0, ·,0]^TF is a column vector of N × 1 dimension, the first element of f is 1, the other elements are 0, when the 1 st distance ambiguity wave has a pitch angle relative to the non-positive side view array antennaTo Nth_rThe secondary range ambiguity clutter has a pitch angle with respect to the non-positive side view array antenna ofWhen the error vector is known accurately, the amplitude-phase error vector of the m-th array subarray is solved by using the Lagrange multiplier method_m，_mComprises the following steps:

${\mathrm{\&delta;}}_m=\frac{{\mathrm{\&Omega;}}_m^{-1}f}{f^T{\mathrm{\&Omega;}}_m^{-1}f}$

where T represents the transpose of the matrix or vector and the superscript-1 represents the inverse of the matrix.

And 2, performing matched filtering on the echo data of the corresponding array subarrays in a pitching dimension according to the amplitude-phase error vector of each array subarray to obtain data after clutter suppression of the corresponding array subarrays. Forming airborne radar clutter suppressed data by using data after clutter suppression of the 1 st array subarray to data after clutter suppression of the Mth array subarrayThe data after the mth array clutter suppression is expressed asM is 1 to M, and the airborne radar clutter is suppressedComprises the following steps: ${\tilde{X}}_{N\&times;M\&times;P\&times;L}=[{\tilde{X}}_{N\&times;P\&times;L}\left(1\right),...,{\tilde{X}}_{N\&times;P\&times;L}\left(M\right)].$

data after m-th array sub-array clutter suppressionThe data after clutter suppression of the 1 st distance unit of the mth array subarray to the data after clutter suppression of the L th distance unit of the mth array subarray are formed, namely ${\tilde{X}}_{N\&times;P\&times;L}\left(m\right)$ Comprises the following steps:

${\tilde{X}}_{N\&times;P\&times;L}\left(m\right)={[\tilde{X}}_{N\&times;P}(m,1),...,{\tilde{X}}_{N\&times;P}(m,l),...,{\tilde{X}}_{N\&times;P}(m,L)].$

wherein,and (4) representing data after clutter suppression of the ith distance unit of the mth array subarray, wherein L is 1-L.

Obtaining data after clutter suppression of the ith distance unit of the mth array subarrayComprises the following substeps:

firstly, obtaining the short-range clutter guiding vector a corresponding to the ith distance unit of the mth array subarray_1mlThe range clutter guide vector (main beam guide vector) a corresponding to the ith range unit of the mth array subarray_2ml. Sine value of pitch angle corresponding to fuzzy division of 0 th distanceBesides, the air conditioner is provided with a fan,toAre in close proximity to each other and,toAre all very close to 0. Therefore, the invention uses the sine value of the pitch angle corresponding to the main beam when the airborne radar transmits signalsSubstitutionTo

Then, the short-range clutter guiding vector a corresponding to the ith distance unit of the mth array subarray_1mlA remote clutter guide vector (main beam guide vector) a corresponding to the ith distance unit of the mth array subarray_2mlRespectively as follows:

wherein T represents the transposition of a matrix or a vector, d is the array element interval of each array subarray, d is the interval between any two adjacent array subarrays, lambda is the wavelength of a signal transmitted by an airborne radar, N represents the array element row number of the non-front side view array antenna,representing the pitch angle to which the 0 th distance ambiguity corresponds,representing the main beam pointing direction when the airborne radar transmits signals.

Then, according to the following formula, obtaining the short-range clutter guiding vector with error compensation corresponding to the ith distance unit of the mth array subarrayRemote clutter guide vector with error compensation corresponding to ith distance unit of mth array subarray

Constructing a pitching filtering weight vector corresponding to the ith distance unit of the mth array subarray according to the following formula

$\left\{\begin{array}{c}{\tilde{w}}_{\mathrm{ml}}^H{\tilde{a}}_{1\mathrm{ml}}=0\\ {\tilde{w}}_{\mathrm{ml}}^H{\tilde{a}}_{2\mathrm{ml}}=1\end{array}\right.$

Where H represents the conjugate transpose of the matrix, representing a generalized inverse operation.

Obtaining a pitching filtering weight vector corresponding to the ith distance unit of the mth array subarrayThen, in the four-dimensional echo data X_N×M×P×LExtracting two-dimensional data X corresponding to the ith distance unit of the mth array subarray_N×P(m, l) using the pitch filtering weight vector corresponding to the ith distance unit of the mth array subarrayFor the extracted two-dimensional data X_N×P(m, l) performing matched filtering in the pitching dimension to obtain data after clutter suppression of the ith distance unit of the mth array subarrayComprises the following steps:

${\tilde{X}}_{N\&times;P}(m,l)={\tilde{w}}_{\mathrm{ml}}^H{X}_{N\&times;P}(m,l)$

the pitch filtering method with error correction is actually a column subarray weighting synthesis process, namely, the pitch filtering weight vector is compensated by using the column subarray amplitude-phase error vector estimated by the method, and then matched filtering is performed on clutter data corresponding to the column subarray in a pitch dimension by using the compensated weight vector. Compared with the pitching filtering processing algorithm without amplitude-phase error correction, the algorithm can enable the formed notch to be more accurately aligned to the short-range clutter through error correction, so that the short-range clutter is effectively suppressed, and meanwhile, the gain of the long-range clutter is kept unchanged through the constraint weight vector, so that the main beam clutter has large residue. The clutter stationarity of adjacent distance units is enhanced, namely enough independent identically distributed sample estimation covariance matrixes can be obtained from the adjacent distance units when the distance units to be processed are subjected to subsequent EFA (extended factor estimated Algorithm), simulation experiments prove that the algorithm can achieve a good short-range clutter suppression effect, and long-range clutter is well suppressed after EFA processing.

The effect of the invention can be further illustrated by the following simulation experiment:

1. simulation data acquisition and experimental conditions

1) In this experiment, the simulation parameters are shown in table 1:

table 1 simulation experiment parameter list

Parameter name	Numerical value	Parameter name value
			Antenna array N × M	16×8	Radius of the earth Re/km6378
Number of pulses P	64	Speed v/(m.s) of the carrier-1)125
			Angle between main beam and array surface	90	Height H/m7000 of carrier
Angle between the front and the speed α/(°)	-90	Speed of light C/(m.s)-1)3×108
			Distance sampling frequency fs/MHz	1	Pulse repetition frequency 4000
Noise to noise ratio CNR/(dB)	80	Wavelength lambda/m 0.25

2) The airborne radar adopts a 16 x 8-dimensional rectangular area array antenna, compares an actual amplitude-phase error vector of a sub-array with an estimated amplitude-phase error vector of the sub-array by taking a 5 th sub-array of an array surface as an example, and compares a pitch directional diagram of the 5 th sub-array (the pitch directional diagram of the 5 th sub-array obtained by a traditional space-time two-dimensional adaptive processing method) which is not subjected to array element amplitude-phase error correction, a pitch directional diagram of the 5 th sub-array (obtained by the method) which is subjected to array element amplitude-phase error correction and a static pitch directional diagram of the 5 th sub-array.

3) The method comprises the steps of performing pitching filtering processing (a traditional space-time two-dimensional self-adaptive processing method) on original echo data with array element amplitude-phase errors, then performing EFA processing, and comparing a range-Doppler image of the original echo data with a range-Doppler image of the original echo data.

4) The method of the invention is firstly used for correcting the original echo data with array element amplitude phase errors by using the error correction method provided by the invention, and then the echo data after the pitching filtering processing is subjected to EFA processing, and the range Doppler image is compared with the range Doppler image of the original echo data.

2. Simulation data processing results and analysis

In the simulation experiment, 10% of random amplitude error and 6-degree random phase error are added to the antenna array surface. Since the situation of the array surface 8 array subarrays is similar, the estimation result of the amplitude and phase errors of the array elements is only described by taking the 5 th array subarray as an example. Referring to fig. 2a, a graph comparing the amplitude error of each array element of the 5 th array subarray estimated according to the present invention in a simulation experiment with the actual amplitude error of each array element of the 5 th array subarray is shown. In fig. 2a, the horizontal axis represents the array element number of the 5 th sub-array, and the vertical axis represents the amplitude error of each array element of the 5 th sub-array, and the unit is dB. Referring to fig. 2b, a graph comparing the phase error of each array element of the 5 th array subarray estimated according to the present invention in a simulation experiment with the actual phase error of each array element of the 5 th array subarray is shown. In fig. 2b, the horizontal axis represents the number of elements in the 5 th sub-array, and the vertical axis represents the phase error of each element in the 5 th sub-array, in degrees. As can be seen from fig. 2a and 2b, the amplitude-phase error curve of each array element of the 5 th array subarray estimated by the present invention substantially matches the actual amplitude-phase error curve of each array element of the 5 th array subarray.

In order to eliminate the influence of the single experiment accidental situation on the amplitude-phase error estimation accuracy of the array elements, a Monte-Carlo experiment is additionally performed for 100 times in the simulation experiment, referring to fig. 2c, which is a graph illustrating the amplitude mean square error root curve of each array element of the 5 th array subarray estimated according to the invention in the simulation experiment, in fig. 2c, the horizontal axis represents the array element number of the 5 th array subarray, and the vertical axis represents the amplitude mean square error root of each array element of the 5 th array subarray, and the unit is dB. Referring to fig. 2d, a graph of the root mean square error of the phase of each array element of the 5 th array subarray estimated according to the present invention in a simulation experiment is schematically shown, in fig. 2c, the horizontal axis represents the serial number of the array element of the 5 th array subarray, and the vertical axis represents the root mean square error of the phase of each array element of the 5 th array subarray, and the unit is degree. As shown in fig. 2c and fig. 2d, the root mean square error of the amplitude and phase of each array element of the 5 th array subarray estimated according to the present invention is relatively small in the simulation experiment, which further proves the accuracy of the amplitude and phase error estimation method of the present invention.

In a simulation experiment, the estimated amplitude-phase error of each array element of the 5 th array subarray is used for carrying out array amplitude-phase error correction on the 5 th array subarray. Referring to fig. 3a, a comparison graph of a pitch directional diagram (corresponding to "array element amplitude and phase error" in fig. 3 a) before the 5 th column subarray in the simulation experiment is subjected to array amplitude and phase error correction, a pitch directional diagram (corresponding to "array element amplitude and phase error correction" in fig. 3 a) after the array amplitude and phase error correction, a static pitch directional diagram (corresponding to "static" in fig. 3 a), and a short-range clutter pitch directional diagram (corresponding to "clutter pitch angle" in fig. 3 a) is shown. Referring to fig. 3b, a partial enlarged view of fig. 3a is shown. In fig. 3a and 3b, the proximity clutter pitch angle is represented by vertical lines, the horizontal axis represents pitch angle in degrees, and the vertical axis represents the pitch pattern in dB. As can be seen from fig. 3a and 3b, the pitch pattern notch deviates from the short-range clutter position before the array amplitude and phase error correction is performed, and the notch position and the short-range clutter position are well registered after the array amplitude and phase error correction is performed, which illustrates the effectiveness of the error correction method proposed by the present invention.

In order to verify the benefits of pitch filtering after error correction, a simulation experiment shows a range-doppler plot of original echo data with array element amplitude-phase errors, a range-doppler plot of echo data subjected to pitch filtering (by a traditional space-time two-dimensional adaptive processing method) without array amplitude-phase error correction, a range-doppler plot of echo data subjected to pitch filtering and EFA processing without array amplitude-phase error correction, a range-doppler plot of echo data subjected to pitch filtering (by the space-time two-dimensional adaptive processing method of the present invention) with array amplitude-phase error correction, and a range-doppler plot of echo data subjected to pitch filtering and EFA processing with array amplitude-phase error correction. Fig. 4 is a range-doppler plot of raw echo data with array element amplitude-phase errors in a simulation experiment, fig. 5a is a range-doppler plot of echo data subjected to pitch filtering when the array amplitude-phase errors are not corrected in the simulation experiment, fig. 5b is a range-doppler plot of echo data subjected to pitch filtering and EFA processing when the array amplitude-phase errors are not corrected in the simulation experiment, fig. 6a is a range-doppler plot of echo data subjected to pitch filtering when the array amplitude-phase errors are corrected in the simulation experiment, and fig. 6b is a range-doppler plot of echo data subjected to pitch filtering and EFA processing when the array amplitude-phase errors are corrected in the simulation experiment. In fig. 4, 5a, 5b, 6a, and 6b, the horizontal axis represents the doppler cell number, the vertical axis represents the distance cell, the gray-scale value of the pixel represents the amplitude of the echo data, and the whiter the pixel point, the larger the amplitude value of the corresponding echo data.

As can be seen from fig. 5a, 5b, 6a and 6b, compared with the pitch-up filtered range-doppler plot under the condition that the conventional space-time two-dimensional adaptive processing method does not perform array amplitude-phase error correction, the short-range clutter of the range-doppler plot obtained after the pitch filtering is performed by the method of the present invention is well suppressed, and the clutter distance stationarity is enhanced.

It will be apparent to those skilled in the art that various changes and modifications may be made in the present invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.

Claims (3)

1. The clutter suppression method of the airborne radar based on array element amplitude-phase error correction is characterized in that a non-positive side-looking array antenna is arranged on the airborne radar, the non-positive side-looking array antenna is composed of M array sub-arrays, each array sub-array is a uniform linear array composed of N array elements, M and N are natural numbers, the array element interval of each array sub-array is d, and the interval between any two adjacent array sub-arrays is d;

the airborne radar clutter suppression method based on array element amplitude and phase error correction comprises the following steps:

step 1, transmitting a pulse signal by using a non-front side view array antenna of an airborne radar, and receiving corresponding echo data, wherein the corresponding echo data received by the airborne radar is four-dimensional echo data; estimating the amplitude-phase error vector of each array subarray according to the four-dimensional echo data;

step 2, obtaining data after the clutter suppression of the ith distance unit of the mth array subarray according to the amplitude-phase error vector of the mth array subarrayM is 1 to M, L is 1 to L, P is the number of pulses emitted by a non-positive side view array antenna of the airborne radar, and L represents the number of distance units of the airborne radar; forming data after clutter suppression of the mth array sub-array by using data after clutter suppression of the 1 st distance unit of the mth array sub-array to data after clutter suppression of the lth distance unit of the mth array sub-arrayData after clutter suppression by using 1 st array subarrayData after clutter suppression of array to MthForming airborne radar clutter suppressed data

In step 2, obtaining the data of the mth array subarray after the clutter suppression of the mth distance unitComprises the following substeps:

firstly, obtaining the short-range clutter guiding vector a corresponding to the ith distance unit of the mth array subarray_1mlThe remote clutter guide vector a corresponding to the ith distance unit of the mth array subarray_2ml；

Wherein T represents the transpose of a matrix or vector, and lambda is the wavelength of the airborne radar transmission signal,representing the pitch angle to which the 0 th distance ambiguity corresponds,representing the main beam direction when the airborne radar transmits signals;

then, according to the following formula, obtaining the short-range clutter guiding vector with error compensation corresponding to the ith distance unit of the mth array subarrayRemote clutter guide vector with error compensation corresponding to ith distance unit of mth array subarray

Wherein ⊙ represents a Hadamard product;_mthe amplitude and phase error vector of the mth array subarray;

constructing a pitching filtering weight vector corresponding to the ith distance unit of the mth array subarray according to the following formula

$\left\{\begin{array}{c}{\tilde{w}}_{ml}^H{\tilde{a}}_{1ml}=0\\ {\tilde{w}}_{ml}^H{\tilde{a}}_{2ml}=1\end{array}\right.$

Wherein H represents the conjugate transpose of the matrix;

in the four-dimensional echo data X_N×M×P×LExtracting two-dimensional data X corresponding to the ith distance unit of the mth array subarray_N×P(m, l) according to the pitch filtering weight vector corresponding to the ith distance unit of the mth array subarrayObtaining data after clutter suppression of the ith distance unit of the mth array subarrayComprises the following steps:

2. the method for suppressing airborne radar clutter based on array element amplitude-phase error correction as claimed in claim 1, wherein the detailed sub-steps of the step 1 are:

(1.1) the distance fuzzy times of the clutter corresponding to the first distance unit is N_rlThen, the i1 th distance ambiguity wave has a pitch angle with respect to the non-positive side view array antennaThenThe pitch steering vector of (a) is expressed as:

wherein T represents the transposition of a matrix or a vector, and lambda is the wavelength of the airborne radar transmitting signal;

by usingToPitching guide matrix B forming mth array subarray_m：

(1.2) Pitch steering matrix B to the m-th column subarray_mPerforming characteristic decomposition to obtain a pitching guide matrix B in the m-th column subarray_mSelecting K maximum eigenvalues from all eigenvalues, K being less than N_rl(ii) a Forming an array manifold matrix A of the mth array sub-matrix by using the selected eigenvectors corresponding to the K maximum eigenvalues_m，

A_m＝[a_m1，a_m2，…，a_mK]；

Wherein, a_m1To a_mKRespectively representing the feature vectors corresponding to the selected K maximum feature values;

(1.3) the corresponding echo data received by the airborne radar is expressed as four-dimensional echo data X_N×M×P×LIn the four-dimensional echo data X_N×M×P×LExtracting two-dimensional data X corresponding to the ith distance unit of the mth array subarray_N×P(m, l) and then two-dimensional data X is obtained_N×P(m, l) Pitch covariance matrix R_ml：

R_ml＝(X_N×P(m，l)X^H _N×P(m，l))/P

Wherein H represents the conjugate transpose of the matrix;

(1.4) to R_mlPerforming characteristic decomposition on R_mlSelecting N-K minimum eigenvalues from all eigenvalues, and forming a noise subspace U by using eigenvectors corresponding to the selected N-K minimum eigenvalues_N；

Constructing a cost function J_mCost function J_mThe expression of (a) is:

$J_m=\underset{k=1}{\overset{K}{\&Sigma;}}{\mathrm{\&delta;}}_m^H{\mathrm{\&alpha;}}_{{\mathrm{mk}}^{\&prime;}}^H{U}_N{U}_N^H{\mathrm{\&alpha;}}_{{\mathrm{mk}}^{\&prime;}}{\mathrm{\&delta;}}_m$

wherein H represents the conjugate transpose of the matrix, K 'is a natural number and K' is 1 to K, α_mk′＝diag(a_mk′)，a_mk′The feature vector, diag (a), corresponding to the k' -th feature value selected in substep (1.3) is represented_mk′) Is represented by a_mk′A diagonal matrix composed of each element of (1) as a main diagonal element;

order toThen the cost function J_mExpressed as:

$J_m={\mathrm{\&delta;}}_m^H{\mathrm{\&Omega;}}_m{\mathrm{\&delta;}}_m$

then, establishing a quadratic constraint optimization problem as follows:

$\left\{\begin{array}{c}\underset{{\mathrm{\&delta;}}_m}{min}{\mathrm{\&delta;}}_m^H{\mathrm{\&Omega;}}_m{\mathrm{\&delta;}}_m\\ s.t.{\mathrm{\&delta;}}_m^{H}f=1\end{array}\right.$

wherein,_mf is a column vector with N × 1 dimension, the first element of f is 1, and the other elements are 0;

estimating the amplitude-phase error vector of the mth array subarray by solving the quadratic constraint optimization problem_m。

3. The method for suppressing airborne radar clutter based on array element amplitude-phase error correction according to claim 2, wherein in sub-step (1.4), the quadratic constraint optimization problem is solved by using lagrange multiplier method, and the amplitude-phase error vector of the m-th column subarray is solved_mComprises the following steps:

${\mathrm{\&delta;}}_m=\frac{{\mathrm{\&Omega;}}_m^{-1}f}{f^T{\mathrm{\&Omega;}}_m^{-1}f}$

where T represents the transpose of the matrix or vector and the superscript-1 represents the inverse of the matrix.