CN102866388B - 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 in a kind of space-time adaptive processing

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, but under will face the ground even more serious than ground radar/extra large clutter problem depending on the airborne phased array radar of 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 processing (STAP) technology can make full use of spatial domain and time-domain information, when echo signal is carried out to coherent accumulation, self-adapting airspace is 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 detection of target at a slow speed; Can effectively detect the little target that disturbed by sidelobe clutter simultaneously.

The training sample that conventional full dimension STAP algorithm need to meet independent same distribution (I.I.D) condition in a large number estimates covariance matrix, and in non-homogeneous clutter environment, this condition is especially not being met; And in the time that degree of freedom in system is very high, entirely ties up the direct inversion operation of covariance matrix (SMI) and almost cannot realize under existing calculated level.Although dimensionality reduction and non-homogeneous STAP algorithm can reduce the operand of STAP adaptive weight calculating and improve STAP algorithm clutter rejection in non-homogeneous clutter environment, but conventional dimensionality reduction STAP algorithm is still faced with the computing that covariance matrix is directly inverted in the time solving adaptive weight, this will expend operand and the equipment amount that system is very large, makes STAP technology be difficult to meet the requirement of system real time.In addition, although the SMI algorithm based on the contrary renewal of covariance matrix is without estimating sample 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, by being difficult to arrange the self-adaptation weight vector of the next SMI of the solving algorithm of equal value of initial inverse matrix, can only obtain approximate solution.

Summary of the invention

The present invention is directed to conventional STAP algorithm adaptive weight calculates covariance matrix need be to sky time and directly inverts, expend very macrooperation amount and equipment amount of system, make STAP technology be difficult to the problem of requirement of real time, it is 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.

Step 1, foundation receive data model when empty;

Suppose that radar antenna array element number is N, transponder pulse number is M, and array element distance is d, and carrier aircraft flying speed is v, is highly h, and pulse repetition rate PRF is f _r, T _r=1/f _rfor pulse-recurrence time; If be R by oblique distance _cthe clutter rang ring at place is divided into N on orientation angles θ _cthe individual Δ θ=2 π/N that is spaced apart _cclutter 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; N × 1 dimension space steering vector c (the f of i clutter scattering unit so _s,i) and M × 1 dimension time steering vector c (f _t,i) be expressed as

$\left\{\begin{array}{c}c\left(f_{s,i}\right)={[1,\exp \left({\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00002159896500012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}}_{s,i}\right),...,\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00002159896500012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}(N-1)f_{s,i}\right)]}^T\\ c\left(f_{t,i}\right)={[1,\exp \left({\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00002159896500012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}}_{t,i}\right),...,\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00002159896500012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}(M-1)f_{t,i}\right)]}^T\end{array}\right.---\left(5\right)$

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 a while being i clutter scattering unit empty _i(θ) be the echoed signal complex magnitude of clutter scattering unit, wherein a _i(θ) not only depend on emitting antenna directional diagram, also relevant with 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 mean intensity of i clutter scattering unit is assumed to be with the gain of emitting antenna and is directly proportional

E{|a _i| ²}＝G _i,for i＝1,...,N _c (8)

Wherein G _ifor positive real constant, direct ratio and transmitter antenna gain (dBi), receive data when empty in l range gate so and be expressed as following vector form

x _k＝x _c,k+x _n,k

＝[x _1，k，x _2，k，...，x _M，k] ^T (9)

Wherein x _n,krepresent the white Gaussian noise of zero-mean, and x _m,k=[x _{1, m, k}, x _{2, m, k}..., x _{n, m, k}] ^trepresent the array data of N × 1 dimension of m reception of impulse;

Step 2: estimate STAP covariance matrix; Utilize training sample data to estimate NM × NM dimension covariance matrix

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

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

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

full rank is the Hermitian matrix of positive definite;

Step 3: set up covariance matrix iteration based on 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 pulse exponent number

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

Wherein matrix

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

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

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

Represent the N (M-1) of a M reception of impulse data and front M-1 reception of impulse data × N dimension cross-correlation matrix and

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

N × the N that represents M reception of impulse data ties up covariance matrix;

When the M of range gate to be detected reception of impulse data formation empty, covariance matrix R is by front M-1 reception of impulse data formation empty, covariance matrix represents, as long as obtain the array received data of the 1st pulse, while carrying out recursive calculation sky according to pulse exponent number, covariance matrix is contrary, and then obtains 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 _l(m) the covariance matrix R of contrary and front m-1 reception of impulse data _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);

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

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

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

w＝R ^-1a(f _s0,f _t0) (12)

Wherein a (f _s0, f _t0) represent steering vector when 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 adaptive weight iteration for space-time adaptive have just been completed.

A kind of computing method of processing adaptive weight iteration for space-time adaptive that the present invention proposes, contrast prior art, the computing of having avoided covariance matrix directly to invert, therefore greatly reduces the operand that calculates 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 STAP adaptive weight;

2. the method based on pulse exponent number iterative computation in the present invention, can select arbitrarily to carry out the reception of impulse data that STAP self-adaptation weight vector calculates, and 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 that solves of equal value of initial inverse matrix, therefore can obtain the exact solution of STAP self-adaptation weight vector.

Accompanying drawing explanation

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

Fig. 2 is computation complexity comparison;

Fig. 3 is the comparison of space-time adaptive directional diagram;

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

Fig. 4 is the comparison of actual measurement MCARM data distance-Doppler Output rusults.

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

Embodiment

Below in conjunction with accompanying drawing, the embodiment of the inventive method is elaborated.

In order to describe more easily content of the present invention, first to utilizing the order principal minor array of Hermitian matrix to carry 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+1represent d+1 rank order principal minor array, the i.e. R of 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.Due to matrix R _d+1inverse matrix Q _d+1also be Hermitian matrix,

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

Wherein q _d+1represent 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 of front d element composition, 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 obtain 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

$R_{d+1}^{-1}={\left[\begin{array}{cc}{R}_d& r_{d+1}\\ r_{d+1}^H& {\mathrm{\&rho;}}_{d+1}\end{array}\right]}^{-1}=\left[\begin{array}{cc}{R}_d^{-1}& 0_{d+1}\\ 0_{d+1}^{\mathrm{<figure-callout\; id="0"\; label="H"\; filenames="HDA00002159896500011.png,HDA00002159896500012.png"\; state="\{\{state\}\}">H</figure-callout>}}& 0\end{array}\right]+\frac{1}{{\mathrm{\&alpha;}}_{d+1}}\left[\begin{array}{cc}{b}_{d+1}{b}_{d+1}^H& b_{d+1}\\ b_{d+1}^H& 1\end{array}\right]---\left(\text{3}\right)$

Wherein vectorial b _d+1and factor alpha _d+1be defined as follows

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

(4)

${\mathrm{\&alpha;}}_{d+1}={\mathrm{\&rho;}}_{d+1}-r_{d+1}^H{R}_d^{-1}{r}_{d+1}={\mathrm{\&rho;}}_{d+1}+r_{d+1}^H{\mathrm{<figure-callout\; id="1"\; label="b\; d\; +"\; filenames="HDA00002159896500012.png"\; state="\{\{state\}\}">b</figure-callout>}}_{d+}$

Wherein ρ _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 real part computing, obtains sane recursion computation process.

Process computing method for adaptive weight iteration for space-time adaptive, the process that the method realizes is as follows:

Clutter data model when step 1, reception sky

1. when empty, receive data modeling

According to airborne phased array radar geometry as shown in Figure 1, suppose that radar antenna array element number is N, transponder pulse number is M, array element distance is d.Carrier aircraft flying speed is v, is highly h.Pulse repetition rate (PRF) is f _r, T _r=1/f _rfor pulse-recurrence time.If be R by oblique distance _cthe clutter rang ring at place is divided into N on orientation angles θ _cthe individual Δ θ=2 π/N that is spaced apart _cclutter 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.N × 1 dimension space steering vector c (the f of i clutter scattering unit so _s,i) and M × 1 dimension time steering vector c (f _t,i) can be expressed as

$\left\{\begin{array}{c}c\left(f_{s,i}\right)={[1,\exp \left({\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00002159896500012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}}_{s,i}\right),...,\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00002159896500012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}(N-1)f_{s,i}\right)]}^T\\ c\left(f_{t,i}\right)={[1,\exp \left({\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00002159896500012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}}_{t,i}\right),...,\exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00002159896500012.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}(M-1)f_{t,i}\right)]}^T\end{array}\right.---\left(14\right)$

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 a while being i clutter scattering unit empty _i(θ) be the echoed signal complex magnitude of clutter scattering unit.Receive so the vector form that data can be expressed as when empty in l range gate

x _k＝x _c,k+x _n,k

＝[x _1,k,x _2,k,...,x _M,k] ^T (16)

Wherein x _n,krepresent the white Gaussian noise of zero-mean, and x _m,k=[x _{1, m, k}, x _{2, m, k}..., x _{n, m, k}] ^trepresent the array data of N × 1 dimension of m reception of impulse.

2. STAP covariance matrix

During STAP processes, the noise performance of range gate to be detected is unknown, need to utilize training sample data to estimate NM × NM dimension covariance matrix

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

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

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

full rank is the Hermitian matrix of positive definite.

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

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

Can be found out by formula (7), when when the M of range gate to be detected reception of impulse data formation empty, covariance matrix R can be by front M-1 reception of impulse data formation empty, covariance matrix represents, as long as obtain the array received data of the 1st pulse, just can constantly carry out recursive calculation sky according to pulse exponent number time, covariance matrix is contrary, and then obtains 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 _l(m) the covariance matrix R of contrary and front m-1 reception of impulse data _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. the concrete steps of inverting of the covariance matrix iteration based on pulse exponent number

Can be found out by formula (11), the method that the present invention proposes is in the time receiving the 1st pulse data, utilize apart from training sample and calculate covariance matrix R (1), because this matrix is Hermitian matrix, can utilize the order principal minor array iteration of Hermitian matrix to complete inverting of the 1st pulse covariance matrix.Then, receiving the 2nd until when 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 same according to the character of Hermitian matrix, can utilize the order principal minor array iteration of Hermitian matrix to complete the contrary calculating of matrix of variables of above-mentioned N × N dimension.

The concrete steps that covariance matrix iteration based on pulse exponent number is inverted are as follows:

Step 3, calculating STAP self-adaptation weight vector

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

w＝R ^-1a(f _s0,f _t0)(19)

Wherein a (f _s0, f _t0) represent steering vector when 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 adaptive weight iteration for space-time adaptive have just been completed.The computing that the method that the present invention proposes has avoided covariance matrix directly to invert, can reduce the operand that calculates STAP adaptive weight greatly, is therefore more conducive to Project Realization.

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

Experiment one, computation complexity comparison

Suppose STAP algorithm process be N × M × K dimension empty time data cube, wherein N represents array element number, M represents the pulse number in CPI, and K represents unambiguous range gate number, and when directly covariance matrix is inverted SMI algorithm estimation sky, the training sample number of covariance matrix is K ₀.In full dimension STAP algorithm,, the operand that the covariance matrix of estimation NM × NM dimension needs is K ₀(NM) ², the operand that filtering operation needs is KNM.The operand that directly covariance matrix is inverted is maximum, is (NM) ³, be secondly that the direct iteration of Hermitian covariance matrix is inverted, the operand needing is approximately 2 (NM) ³/ 3+NM/3, the present invention propose adaptive weight iterative calculation method in covariance matrix invert need operand be approximately (NM) 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 table.

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

Can obviously be observed out by figure, the directly covariance matrix operand maximum of SMI algorithm of inverting, and Hermitian covariance matrix is inverted, the operand of SMI algorithm is only second to direct matrix in verse, 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 first two algorithm, the pulse exponent number of recurrence is fewer, operand is lower, even if but all umber of pulses are all utilized, operand is also 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 to STAP processing 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 clutter direction, and therefore effectively clutter reduction detects echo signal.In addition, because these algorithms can obtain identical self-adaptation weight vector, therefore space-time adaptive directional diagram is all mutually the same.Therefore the adaptive weight iterative calculation method that the present invention proposes can further reduce the operand that covariance matrix is inverted in retention, has good practical meaning in engineering.

Experiment three, the comparison of actual measurement MCARM data performance

Above-mentioned three kinds of covariance matrix inversion algorithms are carried out STAP processing to actual measurement MCARM data below, and the distance-Doppler Output rusults obtaining as shown in Figure 4.

Can obviously be observed out by figure, after above-mentioned three kinds of covariance matrix inversion algorithms are processed MCARM data, target peak and the Background Noise Power of distance-Doppler output are all basically identical, and can be-0.15 in normalization Doppler frequency, range gate be that the position of No. 299 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 50% left and right of direct matrix in verse algorithm, is therefore more conducive to Project Realization.

Claims (2)

1. the adaptive weight iterative calculation method in space-time adaptive processing, is characterized in that, comprises the following steps:

Step 1, foundation receive data model when empty;

Suppose that radar antenna array element number is N, transponder pulse number is M, and array element distance is d, and carrier aircraft flying speed is v, is highly h, and pulse repetition rate PRF is f _r, T _r=1/f _rfor pulse-recurrence time; If be R by oblique distance _cthe clutter rang ring at place is divided into N on orientation angles θ _cthe individual Δ θ=2 π/N that is spaced apart _cclutter 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; N × 1 dimension space steering vector c (the f of i clutter scattering unit so _s,i) and M × 1 dimension time steering vector c (f _t,i) 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 while 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 emitting antenna directional diagram, also relevant with 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 mean intensity of i clutter scattering unit is assumed to be with the gain of emitting antenna and is directly proportional

E{|α _i| ²}＝G _i,for i＝1,...,N _c (8)

Wherein G _ifor positive real constant, direct ratio and transmitter antenna gain (dBi), receive data when empty in l range gate so and be expressed as following vector form

x _k＝x _c，k+x _n，k

＝[x _1，k，x _2，k，...，x _M，k] ^T (9)

Wherein x _{n, k}represent the white Gaussian noise of zero-mean, and x _m,k=[x _{1, m, k}, x _{2, m, k}..., x _{n, m, k}] ^trepresent the array data of N × 1 dimension of m reception of impulse;

Step 2: estimate STAP covariance matrix; Utilize training sample data to estimate NM × NM dimension covariance matrix

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

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

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

Step 3: set up covariance matrix iteration based on 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 pulse exponent number

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

Wherein matrix

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

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

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

Represent the N (M-1) of a M reception of impulse data and front M-1 reception of impulse data × N dimension cross-correlation matrix and

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

N × the N that represents M reception of impulse data ties up covariance matrix;

When the M of range gate to be detected reception of impulse data formation empty, covariance matrix R is by front M-1 reception of impulse data formation empty, covariance matrix represents, as long as obtain the array received data of the 1st pulse, while carrying out recursive calculation sky according to pulse exponent number, covariance matrix is contrary, and then obtains 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 _l(m) the covariance matrix R of contrary and front m-1 reception of impulse data _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 self-adaptation weight vector and obtains by following optimization problem with linear constraints

w＝R ^-1a(f _s0,f _t0) (12)

Wherein a (f _s0, f _t0) represent steering vector when 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 adaptive weight iteration for space-time adaptive have just been completed.

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

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

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