CN102866388A - Iterative computation method for self-adaptive weight number in space time adaptive processing (STAP) - Google Patents

Abstract

The invention provides an iterative computation method for self-adaptive weight number in space time adaptive processing (STAP), aiming at solving the problem that the real-time requirement is hardly met by STAP technology due to the fact that great computation quantity and equipment quantity of a system are consumed as the STAP arithmetic self-adaptive weight value computation needs to directly inverse a space-time covariance matrix. The iterative computation method comprises the following steps of: firstly, obtaining an inverse matrix of a first impulse covariance matrix in a recursion way according to the Hermitian matrix properties, and obtaining the inversion of the final space-time covariance matrix step by step by means of nestification and recursion according to the impulse order, so that the computation quantity for computing the STAP self-adaptive weight value can be greatly reduced. According to the iterative computation method, the clutter suppression performance which is as same as that of the covariance matrix direct inversion STAP algorithm can be obtained, and the computation quantity for solving the self-adaptive weight value is only about 50% of the computation quantity of the covariance matrix direct inversion since the computation of the covariance matrix direct inversion is avoided, so that the engineering realization can be preferably carried out.

Description

Adaptive weight iterative calculation method during a kind of space-time adaptive is processed

Technical field

The invention belongs to airborne phased array radar Clutter Rejection Technique field, relate to the adaptive weight iterative calculation method in a kind of space-time adaptive processing.

Background technology

Airborne phased array radar can be realized the effective detection to ground moving object, will face the ground even more serious than ground radar/extra large clutter problem but be in the lower airborne phased array radar of looking duty.Ground/extra large clutter not only has a very wide distribution, intensity is large, and presents very strong coupled characteristic when empty.Space-time adaptive is processed (STAP) technology can take full advantage of spatial domain and time-domain information, when echo signal is carried out coherent accumulation, self-adapting airspace processed and adaptive Doppler is processed both advantages and combined, at the time domain combined self-adaptation filtering clutter of sky, can obtain better main-lobe clutter rejection, improve the at a slow speed detection of target; Can the little target that disturb by sidelobe clutter effectively be detected simultaneously.

The training sample that conventional full dimension STAP algorithm need to satisfy independent same distribution (I.I.D) condition in a large number estimates covariance matrix, and this condition especially is not being met in non-homogeneous clutter environment; And when degree of freedom in system is very high, entirely ties up the direct inversion operation of covariance matrix (SMI) and under existing calculated level, almost can't realize.Although dimensionality reduction and non-homogeneous STAP algorithm can reduce the operand of STAP adaptive weight calculating and improve STAP algorithm clutter rejection in the non-homogeneous clutter environment, but conventional dimensionality reduction STAP algorithm still is faced with the computing that covariance matrix is directly inverted when finding the solution adaptive weight, this will expend the very large operand of system and equipment amount, so that the STAP technology is difficult to satisfy the requirement of system real time.In addition, although need not to estimate sample covariance matrix based on the contrary SMI algorithm that upgrades of covariance matrix, the number of times of its iterative computation equals the number of training sample, but because there is not inverse matrix in null matrix, this algorithm will be difficult to arrange the self-adaptation weight vector that initial inverse matrix is come the SMI of finding the solution algorithm of equal value, the solution that can only obtain to be similar to.

Summary of the invention

Covariance matrix is directly inverted when the present invention is directed to conventional STAP algorithm adaptive weight calculating need to sky, expend system very macrooperation amount and equipment amount, so that the STAP technology is difficult to the problem of requirement of real time, be the characteristic of Hermitian matrix according to covariance matrix, utilize pulse data exponent number piecemeal recursion, propose the adaptive weight iterative calculation method in a kind of space-time adaptive processing.

Receive data model when step 1, foundation sky;

Suppose that the radar antenna array element number is N, the transponder pulse number is M, and array element distance is d, and the carrier aircraft flying speed is v, highly is h, and pulse repetition rate PRF is f _r, T _r=1/f _rBe pulse-recurrence time; If be R with oblique distance _cThe clutter rang ring at place is divided into N at orientation angles θ _cThe individual Δ θ=2 π/N that is spaced apart _cThe clutter scattering unit, θ and Position angle and the angle of pitch of clutter scattering unit,

And f _t=β f _sBe respectively normalization spatial frequency and Doppler frequency, β=2vT _r/ d represents the slope of clutter spectrum; The N of i clutter scattering unit * 1 dimension space steering vector c (f so _{S, i}) and M * 1 dimension time steering vector c (f _{T, i}) namely be expressed as

$\left\{\begin{array}{c}c\left(f_{s,i}\right)={[1,\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="DEST\_PATH\_HDA00002061939000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_{s,i}\right),...,\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="DEST\_PATH\_HDA00002061939000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}(N-1)f_{s,i}\right)]}^T\\ c\left(f_{t,i}\right)={[1,\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="DEST\_PATH\_HDA00002061939000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_{t,i}\right),...,\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="DEST\_PATH\_HDA00002061939000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}(M-1)f_{t,i}\right)]}^T\end{array}\right.---\left(5\right)$

Oblique distance R _cThe clutter echo at place is N _cIndividual spatially separate clutter scattering source response sum

$x_c={\mathrm{\&Sigma;}}_{i=1}^{N_c}{a}_{i}c(f_{s,i},f_{t,i})---\left(6\right)$

Wherein

Steering vector, wherein α when being i clutter scattering unit empty _i(θ) be the echoed signal complex magnitude of clutter scattering unit, wherein α _i(θ) not only depend on the emitting antenna directional diagram, also relevant with the clutter scattering properties, be modeled as generalized stationary random process

$E\left\{a_i{a}_j^{*}\right\}=0,\&ForAll;i,j:i\&NotEqual;j---\left(7\right)$

And the gain that the mean intensity of i clutter scattering unit is assumed to be with emitting antenna is directly proportional

E{|α _i| ²}＝G _i,for i＝1,...,N _c (8)

G wherein _iBe positive real constant, direct ratio and transmitter antenna gain (dBi), the vector form that receive data is expressed as during empty in l range gate so

x _k＝x _c，k+x _n，k

＝[x _1，k，x _2，k，...，x _M，k] ^T (9)

X wherein _{N, k}The white Gaussian noise of expression zero-mean, and x _{M, k}=[x _{1, m, k}, x _{2, m, k}..., x _{N, m, k}] ^TThe array data that represents the N of m reception of impulse * 1 dimension;

Step 2: estimate the STAP covariance matrix; Utilize the training sample data that NM * NM dimension covariance matrix is estimated

$\hat{R}=\frac{1}{L}{\mathrm{\&Sigma;}}_{l=1}^L{x}_l{x}_l^H---\left(6\right)$

Wherein L is the training sample number that satisfies the I.I.D condition; Covariance matrix

Be nonnegative definite Hermitian matrix, suppose to exist the I.I.D training sample of sufficient amount, then

Full rank is the Hermitian matrix of positive definite;

Step 3: set up based on the covariance matrix iteration of the pulse exponent number model of inverting;

The covariance matrix of range unit to be detected is expressed as

And

Decompose as follows according to the pulse exponent number

$R_l\left(M\right)=E\left(\left[\begin{array}{c}{x}_{1,l}\\ .\\ .\\ .\\ x_{m,l}\\ .\\ .\\ .\\ x_{M,l}\end{array}\right]{\left[\begin{array}{c}{x}_{1,l}\\ .\\ .\\ .\\ x_{m,l}\\ .\\ .\\ .\\ x_{M,l}\end{array}\right]}^H\right)=\left[\begin{array}{cc}{R}_l(M-1)& F_l(M-1)\\ F_l^H(M-1)& G_l\left(M\right)\end{array}\right]---\left(7\right)$

Matrix wherein

$R_l(M-1)=E\left(\left[\begin{array}{c}{x}_{1,l}\\ .\\ .\\ .\\ x_{m,l}\\ .\\ .\\ .\\ x_{M-1,l}\end{array}\right]\left[\begin{array}{ccccccccc}{x}_{1,l}^H& .& .& .& x_{m,l}^H& .& .& .& x_{M-1,l}^H\end{array}\right]\right)---\left(8\right)$

The covariance matrix of the N (M-1) of M-1 received pulse data formation before the expression * N (M-1) dimension,

$F_l(M-1)=E\left(\left[\begin{array}{c}{x}_{1,l}{x}_{M,l}^H\\ x_{2,l}{x}_{M,l}^H\\ .\\ .\\ .\\ x_{m,l}{x}_{M,l}^H\\ .\\ .\\ .\\ x_{M-1,l}{x}_{M,l}^H\end{array}\right]\right)---\left(9\right)$

The cross-correlation matrix that N (M-1) * N ties up that represents a M reception of impulse data and front M-1 reception of impulse data reaches

$G_l\left(M\right)=E\left(x_{M,l}{x}_{M,l}^H\right)---\left(10\right)$

Represent that the N of M reception of impulse data * N ties up covariance matrix;

Covariance matrix represented when covariance matrix R was by front M-1 reception of impulse data formation empty during the M of range gate to be detected reception of impulse data formation empty, as long as namely obtain the array received data of the 1st pulse, covariance matrix is contrary when namely carrying out the recursive calculation sky according to the pulse exponent number, and then obtains the space-time adaptive weights; Utilize the characteristic of the Hermitian partitioning of matrix and pulse recursion, calculate the covariance matrix R of front m reception of impulse data _lThe covariance matrix R of contrary and front m-1 reception of impulse data (m) _l(m-1) iterative relation between contrary

$R^{-1}\left(m\right)={\left[\begin{array}{cc}R(m-1)& F(m-1)\\ F^H(m-1)& G\left(m\right)\end{array}\right]}^{-1}$ (11)

$=\left[\begin{array}{cc}{R}^{-1}(m-1)+B\left(m\right)P^{-1}\left(m\right)B^H\left(m\right)& B\left(m\right)P^{-1}\left(m\right)\\ P^{-1}\left(m\right)B^H\left(m\right)& P^{-1}\left(m\right)\end{array}\right]$

Wherein matrix B (m)=-R ^-1(m) F (m-1), matrix P (m)=G (m)-F ^H(m-1) R ^-1(m) F (m-1);

Carry out the contrary following methods that adopts of recursive calculation covariance matrix when empty according to the pulse exponent number described in the step 3:

When receiving the 1st pulse data, utilize apart from training sample and calculate covariance matrix R (1), because this matrix is the Hermitian matrix, utilize the order principal minor array iteration of Hermitian matrix to finish inverting of the 1st pulse covariance matrix; Then receiving the 2nd until during M pulse data, facility with above alternative manner calculate front 2 until front M reception of impulse data covariance matrix contrary; In the recursive process, intermediate variable matrix P (2) is until matrix P (M) contrary, equally according to the character of Hermitian matrix, utilizes the order principal minor array iteration of Hermitian matrix to finish the contrary calculating of matrix of variables of above-mentioned N * N dimension.

Step 4, calculating STAP self-adaptation weight vector; STAP processes the self-adaptation weight vector and obtains by following optimization problem with linear constraints

w＝R ^-1a(f _s0,f _t0) (12)

A (f wherein _S0, f _T0) steering vector when representing target empty, and the filtering of l range unit is output as

y _l＝w ^Hx _l (13)

Wherein H represents conjugate transpose computing, x _lRepresent range unit data to be detected; Since then, a kind of computing method of processing the adaptive weight iteration for space-time adaptive have just been finished.

A kind of computing method of processing the adaptive weight iteration for space-time adaptive that the present invention proposes, the contrast prior art, therefore the computing of having avoided covariance matrix directly to invert greatly reduces the operand that calculates the STAP adaptive weight, be more conducive to Project Realization, its effect is specific as follows:

1. the present invention has avoided the computing that covariance matrix is directly inverted, and can greatly reduce the operand that calculates the STAP adaptive weight;

2. among the present invention based on the method for pulse exponent number iterative computation, can select arbitrarily to carry out the reception of impulse data that STAP self-adaptation weight vector calculates, can on the basis of retention, further reduce computation complexity;

3. the present invention does not need to arrange the next self-adaptation weight vector of finding the solution of equal value of initial inverse matrix, therefore can obtain the exact solution of STAP self-adaptation weight vector.

Description of drawings

Fig. 1 is airborne phased array radar geometry schematic diagram;

Fig. 2 is that computation complexity compares;

Fig. 3 is that the space-time adaptive directional diagram compares;

Wherein figure (a) is direct matrix in verse, (b) is the Hermitian matrix inversion, (c) for to invert based on pulse exponent number iteration;

Fig. 4 compares for actual measurement MCARM data distance-Doppler Output rusults.

Wherein figure (a) is direct matrix in verse, (b) is the Hermitian matrix inversion, (c) for to invert based on pulse exponent number iteration.

Embodiment

Elaborate below in conjunction with the embodiment of accompanying drawing to the inventive method.

In order to describe more easily content of the present invention, at first the order principal minor array that utilizes the Hermitian matrix is carried out the contrary description below of doing of iterative computation covariance matrix:

Hypothesis matrix R is the Hermitian matrix of D * D dimension, and matrix R _D+1D+1 rank order principal minor array, the i.e. R of expression R _D+1=R (1:d+1,1:d+1).According to piecemeal Hermitian Matrix Properties, matrix R _D+1Contrary can utilize R _dContrary calculating.Because matrix R _D+1Inverse matrix Q _D+1Also be the Hermitian matrix, then

$Q_{d+1}=\left[\begin{array}{cc}{Q}_d& q_{d+1}\\ q_{d+1}^H& q_{d+1}\end{array}\right]---\left(1\right)$

Q wherein _D+1Expression Q _D+1D+1 diagonal element, i.e. q _D+1=Q _D+1(d+1, d+1); q _D+1Representing matrix Q _D+1D+1 be listed as the column vector that front d element forms, i.e. q _D+1=Q _D+1(1:d, d+1); Q _dQ _D+1D rank orders principal minor array, i.e. Q _d=Q _D+1(1:d, 1:d).Be that unit matrix can get according to inverse matrix product each other

$R_{d+1}{Q}_{d+1}=\left[\begin{array}{cc}{R}_d& r_{d+1}\\ r_{d+1}^H& {\mathrm{\&rho;}}_{d+1}^b\end{array}\right]\left[\begin{array}{cc}{Q}_d& q_{d+1}\\ q_{d+1}^H& q_{d+1}\end{array}\right]=\left[\begin{array}{cc}{I}_d& 0_{d+1}\\ 0_{d+1}^H& 1\end{array}\right]---\left(2\right)$

Wherein 0 _D+1It is the null vector of d * 1 dimension.By calculating, can obtain following iterative formula

$R_{d+1}^{-1}={\left[\begin{array}{cc}{R}_d& r_{d+1}\\ r_{d+1}^H& {\mathrm{\&rho;}}_{d+1}\end{array}\right]}^{-1}=\left[\begin{array}{cc}{R}_d^{-1}& 0_{d+1}\\ 0_{d+1}^{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="DEST\_PATH\_HDA00002061939000012.png,DEST\_PATH\_HDA00002159896500021.png"\; state="\{\{state\}\}">H</figure-callout>}}& 0\end{array}\right]+\frac{1}{{\mathrm{\&alpha;}}_{d+1}}\left[\begin{array}{cc}{b}_{d+1}{b}_{d+1}^H& b_{d+1}\\ b_{d+1}^H& 1\end{array}\right]---\left(3\right)$

Vectorial b wherein _D+1And factor alpha _D+1Be defined as follows

$b_{d+1}=-R_d^{-1}{r}_{d+1}$ (4)

${\mathrm{\&alpha;}}_{d+1}={\mathrm{\&rho;}}_{d+1}-r_{d+1}^H{R}_d^{-1}{r}_{d+1}={\mathrm{\&rho;}}_{d+1}+r_{d+1}^H{\mathrm{<figure-callout\; id="1"\; label="b\; d\; +"\; filenames="DEST\_PATH\_HDA00002061939000012.png,DEST\_PATH\_HDA00002159896500021.png"\; state="\{\{state\}\}">b</figure-callout>}}_{d+}$

ρ wherein _D+1=R _D+1(d+1, d+1) and r _D+1=R _D+1(1:d, d+1).

Utilize the contrary concrete steps of the order principal minor array iterative computation covariance matrix of Hermitian matrix as follows:

* explanation: Re () is for getting real-part operator.The impact that can effectively avoid the error of calculation to cause algorithm to lose efficacy by getting the real part computing obtains sane recursion computation process.

A kind of computing method of processing the adaptive weight iteration for space-time adaptive, the process that the method realizes is as follows:

Clutter data model when step 1, reception sky

Receive data modeling when 1. empty

According to airborne phased array radar geometry as shown in Figure 1, suppose that the radar antenna array element number is N, the transponder pulse number is M, array element distance is d.The carrier aircraft flying speed is v, highly is h.Pulse repetition rate (PRF) is f _r, T _r=1/f _rBe pulse-recurrence time.If be R with oblique distance _cThe clutter rang ring at place is divided into N at orientation angles θ _cThe individual Δ θ=2 π/N that is spaced apart _cThe clutter scattering unit.θ and

Position angle and the angle of pitch of clutter scattering unit.

And f _t=β f _sBe respectively normalization spatial frequency and Doppler frequency, β=2vT _r/ d represents the slope of clutter spectrum.The N of i clutter scattering unit * 1 dimension space steering vector c (f so _{S, i}) and M * 1 dimension time steering vector c (f _{T, i}) can be expressed as

$\left\{\begin{array}{c}c\left(f_{s,i}\right)={[1,\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="DEST\_PATH\_HDA00002061939000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_{s,i}\right),...,\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="DEST\_PATH\_HDA00002061939000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}(N-1)f_{s,i}\right)]}^T\\ c\left(f_{t,i}\right)={[1,\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="DEST\_PATH\_HDA00002061939000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_{t,i}\right),...,\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="DEST\_PATH\_HDA00002061939000012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}(M-1)f_{t,i}\right)]}^T\end{array}\right.---\left(14\right)$

Oblique distance R _cThe clutter echo at place is N _cIndividual spatially separate clutter scattering source response sum

$x_c={\mathrm{\&Sigma;}}_{i=1}^{N_c}{a}_{i}c(f_{s,i},f_{t,i})---\left(15\right)$

Wherein

Steering vector, wherein α when being i clutter scattering unit empty _i(θ) be the echoed signal complex magnitude of clutter scattering unit.The vector form that receive data can be expressed as during empty in l range gate so

x _k＝x _c,k+x _n,k

(16)

＝[x _1,k,x _2,k,...,x _M,k] ^T

X wherein _{N, k}The white Gaussian noise of expression zero-mean, and x _{M, k}=[x _{1, m, k}, x _{2, m, k}..., x _{N, m, k}] ^TThe array data that represents the N of m reception of impulse * 1 dimension.

2. STAP covariance matrix

During STAP processed, the noise performance of range gate to be detected was unknown, need to utilize the training sample data that NM * NM dimension covariance matrix is estimated

$\hat{R}=\frac{1}{L}{\mathrm{\&Sigma;}}_{l=1}^L{x}_l{x}_l^H---\left(17\right)$

Wherein L is the training sample number that satisfies the I.I.D condition.Obviously, covariance matrix

Be nonnegative definite Hermitian matrix.Suppose to exist the I.I.D training sample of sufficient amount, then

Full rank is the Hermitian matrix of positive definite.

Step 2, based on the STAP adaptive weight iterative computation of pulse exponent number

1. based on the covariance matrix iteration of the pulse exponent number model of inverting

Can be found out by formula (7), covariance matrix represented when covariance matrix R can be by front M-1 reception of impulse data formation empty during the M of range gate to be detected reception of impulse data formation empty, as long as namely obtain the array received data of the 1st pulse, covariance matrix is contrary in the time of just can constantly carrying out the recursive calculation sky according to the pulse exponent number, and then obtains the space-time adaptive weights.By utilizing the characteristic of the Hermitian partitioning of matrix and pulse recursion, can calculate the covariance matrix R of front m reception of impulse data _lThe covariance matrix R of contrary and front m-1 reception of impulse data (m) _l(m-1) iterative relation between contrary

$R^{-1}\left(m\right)={\left[\begin{array}{cc}R(m-1)& F(m-1)\\ F^H(m-1)& G\left(m\right)\end{array}\right]}^{-1}$ (18)

$=\left[\begin{array}{cc}{R}^{-1}(m-1)+B\left(m\right)P^{-1}\left(m\right)B^H\left(m\right)& B\left(m\right)P^{-1}\left(m\right)\\ P^{-1}\left(m\right)B^H\left(m\right)& P^{-1}\left(m\right)\end{array}\right]$

Wherein matrix B (m)=-R ^-1(m) F (m-1), matrix P (m)=(G (m)-F ^H(m-1) R ^-1(m) F (m-1)).

2. based on the covariance matrix iteration of the pulse exponent number concrete steps of inverting

Can be found out by formula (11), the method that the present invention proposes is when receiving the 1st pulse data, utilization is calculated covariance matrix R (1) apart from training sample, because this matrix is the Hermitian matrix, can utilize the order principal minor array iteration of Hermitian matrix to finish inverting of the 1st pulse covariance matrix.Then, receiving the 2nd until during M pulse data, just can utilize above alternative manner calculate front 2 until front M reception of impulse data covariance matrix contrary.But in recursion, need to ask intermediate variable matrix P (2) until matrix P (M) contrary, but equally according to the character of Hermitian matrix, can utilize the order principal minor array iteration of Hermitian matrix to finish the contrary calculating of matrix of variables that above-mentioned N * N ties up.

The concrete steps of inverting based on the covariance matrix iteration of pulse exponent number are as follows:

Step 3, calculating STAP self-adaptation weight vector

STAP processes the self-adaptation weight vector and can obtain by following optimization problem with linear constraints

w＝R ^-1a(f _s0,f _t0) (19)

A (f wherein _S0, f _T0) steering vector when representing target empty, and the filtering of l range unit is output as

y _l＝w ^Hx _l (20)

Since then, a kind of computing method of processing the adaptive weight iteration for space-time adaptive have just been finished.The computing that the method that the present invention proposes has avoided covariance matrix directly to invert can reduce the operand that calculates the STAP adaptive weight greatly, therefore is more conducive to Project Realization.

In order to verify the performance of the STAP adaptive weight iterative calculation method that the present invention provides, carried out following simulating, verifying.At first relatively secondly the computation complexity of put forward the methods of the present invention and conventional STAP algorithm utilizes respectively emulated data and actual measurement MCARM data that its performance is compared analysis.

Experiment one, computation complexity are relatively

Suppose the STAP algorithm process be N * M * K dimension empty the time data cube, wherein N represents array element number, M represents the pulse number in the CPI, and K represents unambiguous range gate number, and the training sample number of covariance matrix was K0 when directly covariance matrix was inverted SMI algorithm estimation sky.In full dimension STAP algorithm,, estimate that the operand that NM * covariance matrix of NM dimension needs is K ₀(NM) ², the operand that filtering operation needs is KNM.The operand that direct covariance matrix is inverted is maximum, is (NM) ³, secondly be that the direct iteration of Hermitian covariance matrix is inverted, the operand that needs is approximately 2 (NM) ³The covariance matrix operand that needs of inverting is approximately (NM) in the adaptive weight iterative calculation method that/3+NM/3, the present invention propose ³/ 3+K ₀(NM) ²/ 2+K ₀N ²+ 2N ³/ 3.The operand of above-mentioned three kinds of algorithms is summarized as follows shown in the table.

For the operand of more intuitive more above-mentioned algorithm, suppose that array element number is N=14, the pulse number in the CPI is M=12, the training number that is used for covariance matrix is K ₀=2NM, so directly covariance matrix invert SMI algorithm, Hermitian covariance matrix invert the SMI algorithm and based on pulse exponent number iteration covariance matrix invert the SMI algorithm operand more as shown in Figure 2.

Can obviously be observed out by figure, directly the invert operand of SMI algorithm of covariance matrix is maximum, the operand of SMI algorithm is only second to direct matrix in verse and the Hermitian covariance matrix is inverted, and utilizes the direct iterative computation of Hermitian Matrix Properties not reduce how many operands.Comparatively speaking, the adaptive weight iterative calculation method that the present invention proposes is all low more than front two kinds of algorithms, the pulse exponent number of recurrence is fewer, operand is lower, even but all umber of pulses are all utilized, operand also is direct covariance matrix 50% of the SMI algorithm of inverting, and this is very favourable for practical engineering application.

Experiment two, emulated data Performance Ratio are

This experiment is to airborne phased array radar clutter echo simulation, and the parameter of emulation is as shown in the table.

Use respectively direct covariance matrix the invert SMI algorithm and the clutter data of above-mentioned generation are carried out STAP process based on the pulse exponent number iteration covariance matrix SMI algorithm of inverting of SMI algorithm, Hermitian covariance matrix of inverting, the space-time adaptive directional diagram result that various algorithms obtain as shown in Figure 3.

Can obviously be observed out by figure, the space-time adaptive directional diagram of several covariance matrix inversion algorithms all forms dark recess in the clutter direction, therefore can detect echo signal by the establishment clutter.In addition, because these algorithms can both obtain identical self-adaptation weight vector, so the space-time adaptive directional diagram is all mutually the same.Therefore the adaptive weight iterative calculation method of the present invention's proposition can further reduce the operand that covariance matrix is inverted in retention, has good practical meaning in engineering.

Experiment three, actual measurement MCARM data performance are relatively

Below above-mentioned three kinds of covariance matrix inversion algorithms actual measurement MCARM data carried out STAP process, the distance-Doppler Output rusults that obtains is as shown in Figure 4.

Can obviously be observed out by figure, after above-mentioned three kinds of covariance matrix inversion algorithms are processed the MCARM data, target peak and the Background Noise Power of distance-Doppler output are all basically identical, and can both be-0.15 in the normalization Doppler frequency, range gate be that No. 299 position detects echo signal.But the adaptive weight iterative calculation method that the present invention proposes can reduce computation complexity on the basis that keeps target detection performance, only has about 50% of direct matrix in verse algorithm, therefore is more conducive to Project Realization.

Claims (2)

1. the adaptive weight iterative calculation method during a space-time adaptive is processed is characterized in that, may further comprise the steps:

Receive data model when step 1, foundation sky;

Suppose that the radar antenna array element number is N, the transponder pulse number is M, and array element distance is d, and the carrier aircraft flying speed is v, highly is h, and pulse repetition rate PRF is f _r, T _r=1/f _rBe pulse-recurrence time; If be R with oblique distance _cThe clutter rang ring at place is divided into N at orientation angles θ _cThe individual Δ θ=2 π/N that is spaced apart _cThe clutter scattering unit, θ and

Position angle and the angle of pitch of clutter scattering unit,

And f _t=β f _sBe respectively normalization spatial frequency and Doppler frequency, β=2vT _r/ d represents the slope of clutter spectrum; The N of i clutter scattering unit * 1 dimension space steering vector c (f so _{S, i}) and M * 1 dimension time steering vector c (f _{T, i}) namely be expressed as

$\left\{\begin{array}{c}c\left(f_{s,i}\right)={[1,\exp \left(j2\mathrm{\&pi;}{f}_{s,i}\right),...,\exp \left(j2\mathrm{\&pi;}(N-1)f_{s,i}\right)]}^T\\ c\left(f_{t,i}\right)={[1,\exp \left(j2\mathrm{\&pi;}{f}_{t,i}\right),...,\exp \left(j2\mathrm{\&pi;}(M-1)f_{t,i}\right)]}^T\end{array}\right.---\left(5\right)$

Oblique distance R _cThe clutter echo at place is N _cIndividual spatially separate clutter scattering source response sum

$x_c={\mathrm{\&Sigma;}}_{i=1}^{N_c}{a}_{i}c(f_{s,i},f_{t,i})---\left(6\right)$

Wherein

Steering vector, wherein α when being i clutter scattering unit empty _i(θ) be the echoed signal complex magnitude of clutter scattering unit, wherein α _i(θ) not only depend on the emitting antenna directional diagram, also relevant with the clutter scattering properties, be modeled as generalized stationary random process

$E\left\{a_i{a}_j^{*}\right\}=0,\&ForAll;i,j:i\&NotEqual;j---\left(7\right)$

And the gain that the mean intensity of i clutter scattering unit is assumed to be with emitting antenna is directly proportional

E{|α _i| ²}＝G _i,for i＝1,...,N _c (8)

G wherein _iBe positive real constant, direct ratio and transmitter antenna gain (dBi), the vector form that receive data is expressed as during empty in l range gate so

x _k＝x _c，k+x _n，k

＝[x _1，k，x _2，k，...，x _M，k] ^T (9)

X wherein _{N, k}The white Gaussian noise of expression zero-mean, and x _{M, k}=[x _{1, m, k}, x _{2, m, k}..., x _{N, m, k}] ^TThe array data that represents the N of m reception of impulse * 1 dimension;

Step 2: estimate the STAP covariance matrix; Utilize the training sample data that NM * NM dimension covariance matrix is estimated

$\hat{R}=\frac{1}{L}{\mathrm{\&Sigma;}}_{l=1}^L{x}_l{x}_l^H---\left(6\right)$

Wherein L is the training sample number that satisfies the I.I.D condition; Covariance matrix

Be nonnegative definite Hermitian matrix, suppose to exist the I.I.D training sample of sufficient amount, then Full rank is the Hermitian matrix of positive definite;

Step 3: set up based on the covariance matrix iteration of the pulse exponent number model of inverting;

The covariance matrix of range unit to be detected is expressed as

And

Decompose as follows according to the pulse exponent number

$R_l\left(M\right)=E\left(\left[\begin{array}{c}{x}_{1,l}\\ .\\ .\\ .\\ x_{m,l}\\ .\\ .\\ .\\ x_{M,l}\end{array}\right]{\left[\begin{array}{c}{x}_{1,l}\\ .\\ .\\ .\\ x_{m,l}\\ .\\ .\\ .\\ x_{M,l}\end{array}\right]}^H\right)=\left[\begin{array}{cc}{R}_l(M-1)& F_l(M-1)\\ F_l^H(M-1)& G_l\left(M\right)\end{array}\right]---\left(7\right)$

Matrix wherein

$R_l(M-1)=E\left(\left[\begin{array}{c}{x}_{1,l}\\ .\\ .\\ .\\ x_{m,l}\\ .\\ .\\ .\\ x_{M-1,l}\end{array}\right]\left[\begin{array}{ccccccccc}{x}_{1,l}^H& .& .& .& x_{m,l}^H& .& .& .& x_{M-1,l}^H\end{array}\right]\right)---\left(8\right)$

The covariance matrix of the N (M-1) of M-1 received pulse data formation before the expression * N (M-1) dimension,

$F_l(M-1)=E\left(\left[\begin{array}{c}{x}_{1,l}{x}_{M,l}^H\\ x_{2,l}{x}_{M,l}^H\\ .\\ .\\ .\\ x_{m,l}{x}_{M,l}^H\\ .\\ .\\ .\\ x_{M-1,l}{x}_{M,l}^H\end{array}\right]\right)---\left(9\right)$

The cross-correlation matrix that N (M-1) * N ties up that represents a M reception of impulse data and front M-1 reception of impulse data reaches

$G_l\left(M\right)=E\left(x_{M,l}{x}_{M,l}^H\right)---\left(10\right)$

Represent that the N of M reception of impulse data * N ties up covariance matrix;

Covariance matrix represented when covariance matrix R was by front M-1 reception of impulse data formation empty during the M of range gate to be detected reception of impulse data formation empty, as long as namely obtain the array received data of the 1st pulse, covariance matrix is contrary when namely carrying out the recursive calculation sky according to the pulse exponent number, and then obtains the space-time adaptive weights; Utilize the characteristic of the Hermitian partitioning of matrix and pulse recursion, calculate the covariance matrix R of front m reception of impulse data _lThe covariance matrix R of contrary and front m-1 reception of impulse data (m) _l(m-1) iterative relation between contrary

$R^{-1}\left(m\right)={\left[\begin{array}{cc}R(m-1)& F(m-1)\\ F^H(m-1)& G\left(m\right)\end{array}\right]}^{-1}$ (11)

$=\left[\begin{array}{cc}{R}^{-1}(m-1)+B\left(m\right)P^{-1}\left(m\right)B^H\left(m\right)& B\left(m\right)P^{-1}\left(m\right)\\ P^{-1}\left(m\right)B^H\left(m\right)& P^{-1}\left(m\right)\end{array}\right]$

Wherein matrix B (m)=-R ^-1(m) F (m-1), matrix P (m)=G (m)-F ^H(m-1) R ^-1(m) F (m-1);

Step 4, calculating STAP self-adaptation weight vector; STAP processes the self-adaptation weight vector and obtains by following optimization problem with linear constraints

w＝R ^-1a(f _s0,f _t0) (12)

A (f wherein _S0, f _T0) steering vector when representing target empty, and the filtering of l range unit is output as

y _l＝w ^Hx _l (13)

Wherein H represents conjugate transpose computing, x _lRepresent range unit data to be detected; Since then, a kind of computing method of processing the adaptive weight iteration for space-time adaptive have just been finished.

2. the adaptive weight iterative calculation method during a kind of space-time adaptive as claimed in claim 1 is processed is characterized in that, carries out the contrary following methods that adopts of recursive calculation covariance matrix when empty according to the pulse exponent number described in the step 3:

When receiving the 1st pulse data, utilize apart from training sample and calculate covariance matrix R (1), because this matrix is the Hermitian matrix, utilize the order principal minor array iteration of Hermitian matrix to finish inverting of the 1st pulse covariance matrix; Then receiving the 2nd until during M pulse data, facility with above alternative manner calculate front 2 until front M reception of impulse data covariance matrix contrary; In the recursive process, intermediate variable matrix P (2) is until matrix P (M) contrary, equally according to the character of Hermitian matrix, utilizes the order principal minor array iteration of Hermitian matrix to finish the contrary calculating of matrix of variables of above-mentioned N * N dimension.

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