CN103728606A - Doppler channel correlation two-stage dimension reduction method for onboard multiple input multiple output (MIMO) radar - Google Patents

Abstract

The invention discloses a Doppler channel correlation two-stage dimension reduction method for an onboard multiple input multiple output (MIMO) radar. The method includes constructing an onboard MIMO radar clutter signal model and a target space time two-dimensional guide vector; utilizing Doppler filtering to conduct time domain dimension reduction processing on the echo data; resolving weight vectors formed by a space domain transmitting-receiving two-dimensional wave beam into a Kronecker product of a receiving weight and a transmitting weight, building a dyadic and square cost function, utilizing alternative computation to calculate the optimal weight, utilizing the optimal weight to conduct receiving and transmitting two-dimensional self-adaptation wave beam forming and restraining clutter. By means of the method, the dimension of the obtained weight vectors is greatly reduced, optimum covariance matrix estimation can be obtained through less samples, and the clutter restraining performance is greatly improved under small samples. Meanwhile, high-dimensional sampling covariance matrix inversion is avoided, and the calculation quantity is greatly reduced. By means of clutter restraining, further target detection, target location and tracking and flight track forming are facilitated. The method is applied to various actual systems like navigation systems.

Description

The associated two-stage dimension reduction method of Doppler's passage of airborne MIMO radar

Technical field

The invention belongs to Radar Signal Processing Technology field, relate generally to the dimension-reduction treatment of Radar Clutter Signal, the associated two-stage dimension reduction method of a kind of Doppler's passage of airborne MIMO radar specifically, can reduce the dimension, operand of processor and to the requirement of number of reference object, for the clutter of airborne MIMO radar signal, suppress.

Background technology

In modern war, grasping control of the air is the important guarantee triumphantly of winning the war.Airborne early warn ing radar, owing to being erected on very high platform, much far away than ground radar to the visual range of low flyer, thereby in widespread attention.Airborne radar is done down while looking work, and not only scope is wide for ground clutter, intensity is large, and the clutter of different directions is all different with respect to the speed of carrier aircraft, thereby makes clutter spectrum broadening greatly, causes the target detection ability of radar to be had a strong impact on.Therefore, how effectively clutter reduction is the problem that airborne radar must solve.

Due to carrier aircraft motion, land clutter presents very strong coupling when empty, this has just determined that airborne radar clutter suppresses to belong to typical space-time two-dimensional filtering problem, and, it is processed real-time adaptive again and realizes, be that clutter reduction need to adopt space-time adaptive to process (STAP), typical STAP method has 1DT method and mDT method.1DT method refers to the clutter suppression method that the space domain self-adapted wave beam of cascade forms after first time domain doppler filtering, also referred to as factorization method (FA, Factored Approach), research shows, 1DT method is quasi-optimal in secondary lobe clutter district performance, and Dan main clutter district performance is to be improved.There is improving one's methods of 1DT for this reason---the mDT(spreading factor method (EFA that is otherwise known as, Extended Factored Approach)), associating m(m gets odd number 3,5 etc. conventionally near Ji main clutter district) individual Doppler's passage carries out self-adaptive processing, obviously improved the rejection of main clutter.

Centralized MIMO(multiple-input and multiple-output) radar is the development of phased-array radar, it utilizes a small amount of antenna can obtain more processing degree of freedom, receiving array aperture has been expanded in equivalence, thereby the clutter that effectively improves early warning radar suppresses ability and moving-target detects performance, have the incomparable advantage of phased-array radar, so MIMO-STAP becomes rapidly a study hotspot of international radar circle.But the same with phased-array radar, MIMO-STAP faces the estimation of higher-dimension covariance matrix and the problem of inverting equally.Although the dimension-reduction treatment method proposing for phased array STAP also can be alleviated the problem of MIMO-STAP, but the cause due to transmitted waveform diversity, MIMO-STAP expands to sky-time-code (waveform) three dimensions by traditional sky-time two-dimensional process, the sharply increase of data dimension causes the problems such as operand and covariance matrix to become more outstanding, applies mechanically simply the requirement that these methods are still difficult to meet real-time.Therefore, in the urgent need to studying more efficient dimensionality reduction STAP method for airborne MIMO radar.

Summary of the invention

When the present invention is directed to traditional mDT method and being applied to airborne MIMO radar clutter and suppressing, be subject to the restriction of the problems such as covariance matrix and operand are large, and the send-receive two dimension wave beam that is still faced with spatial domain after doppler filtering forms the large problem of weight vector computation complexity, a kind of operand is proposed little, computation complexity is low, and number of samples requires the associated two-stage dimension reduction method of Doppler's passage of little airborne MIMO radar.

The present invention is the associated two-stage dimension reduction method of a kind of Doppler's passage of airborne MIMO radar, it is characterized in that: the processing mode that adopts spatial domain after first time domain, first utilize doppler filtering to realize time domain fixed sturcture dimensionality reduction, rear cascade replaces iterative processing and alternately optimizes and transmit and receive wave beam and form weight vector and complete spatial domain secondary dimensionality reduction.The associated two-stage reduction process of Doppler's passage of the present invention comprises the steps:

Step 1. builds airborne MIMO radar clutter model, radar antenna receives the clutter of ground return, the present invention utilizes reference transmitted signal at a relevant echo data receiving in interval of processing, to carry out matched filtering to radar antenna, when setting radar antenna is launched K pulse within a relevant processing time interval, echo data to K pulse mates, and exports KMN * 1 dimension clutter plus noise data vector y after matched filtering is processed.

Step 2. establishing target space-time two-dimensional steering vector b, if testing distance unit has target to exist, the space-time two-dimensional steering vector of the echo signal after matched filtering is expressed as to the long-pending form of Kronecker of target Doppler steering vector, emission array steering vector and receiving array steering vector

$b(f_{s,0},f_{d,0})=a_d\left(f_{d,0}\right)\⊗a_t\left(f_{s,0}\right)\⊗a_r\left(f_{s,0}\right),$

Wherein b is the space-time two-dimensional steering vector of target after matched filtering, f _{s, 0}for the normalization spatial frequency of target, f _{d, 0}for target Doppler frequency, a _d(f _{d, 0}) be K * 1 dimension target Doppler steering vector, a _t(f _{s, 0}) for take the M * 1 emission array steering vector that the normalization spatial frequency of target is variable, a _r(f _{s, 0}) for take the N * 1 dimension receiving array steering vector that the normalization spatial frequency of target is variable,

represent that Kronecker is long-pending.

The echo data after coupling that step 3. utilizes doppler filtering to receive airborne MIMO radar antenna, echo data comprises clutter plus noise data and target data, target data is random, only has while there is target in to-be-measured cell, and target data just can record.Carry out the associated time domain dimension-reduction treatment of Doppler's passage, two-dimensional guide vector C while obtaining data vector z after dimensionality reduction and the target empty after dimensionality reduction; Data vector z is the clutter plus noise data after dimensionality reduction.

Step 4. is set up the cost function of spatial domain dimension-reduction treatment, and the data vector z after time domain dimensionality reduction is carried out to spatial processing, sets up the cost function that dimensionality reduction space-time adaptive is processed:

$\left\{\begin{array}{c}\underset{w}{\min }{w}^H{R}_{z}w\\ s.t.w^H[{\tilde{a}}_t\left(f_{s,0}\right)\⊗a_r\left(f_{s,0}\right)]=1\end{array}\right.,$

In formula, R _z=E{zz ^hbe clutter and the noise covariance matrix after dimensionality reduction, w is that spatial domain send-receive two dimension wave beam forms weight vector,

for the mM * 1 dimension equivalence transmitting steering vector after time domain dimensionality reduction, a _r(f _s) be N * 1 dimension receiving array steering vector.

Step 5. is decomposed two-dimentional wave beam and is formed weight vector, spatial domain send-receive two dimension wave beam formation weight vector w is expressed as to Launch Right v long-pending with the Kronecker that receives power u,

and foundation is about the dihydric phenol cost function of these two weights.

Step 6. utilizes alternately alternative manner to calculate optimal transmit weights vector v and the optimum weight vector u that receives.

The optimal transmit weights vector v that step 7. utilization is tried to achieve and the optimum weight vector u that receives, radar data after dimensionality reduction is received, sending out two-dimensional adaptive wave beam forms, the optimal transmit weights vector v that step 6 is solved and the optimum weight vector u substitution two dimension wave beam that receives form in weight vector w formula, while utilizing two-dimentional wave beam to form weight vector w to the testing distance unit after time domain dimensionality reduction empty, data vector is weighted summation, make array output power minimum, specific direction formation main beam in target is used for receiving useful wanted signal, and inhibition is from the undesired signal of other directions, utilize the optimum weight vector of obtaining to receive, sending out two-dimensional adaptive wave beam forms, thereby complete spatial domain secondary dimensionality reduction, clutter is inhibited, further detect target, target is positioned, follow the tracks of, and form flight path, be applied in various real systems, as navigational system.

The present invention proposes the associated two-stage dimension reduction method (dimensionality reduction mDT method) of a kind of airborne MIMO RADOP passage on the basis of mDT method.By the two-stage dimension-reduction treatment in spatial domain after first time domain, the spatial domain two dimension wave beam formation problem that the method faces mDT method is separated into two one dimension wave beams and forms problem, finally utilize a kind of alternative manner that can Fast Convergent alternately to optimize two low-dimensional weight vectors, thereby greatly reduce operand and to the requirement of independent same distribution number of reference object.

Realization of the present invention is also: build airborne MIMO radar clutter model, radar antenna receives the clutter of ground return, the present invention utilizes reference transmitted signal at a relevant echo data receiving in interval of processing, to carry out matched filtering to radar antenna, when setting radar antenna is launched K pulse within a relevant processing time interval, echo data to K pulse mates, after matched filtering is processed, export KMN * 1 dimension clutter plus noise data vector y, particular content is as follows:

Build airborne MIMO Radar Clutter Signal model; Be set in relevant a processing in interval (CPI), airborne MIMO radar is respectively launched the train of impulses waveform that array element radiation is simultaneously comprised of K pulse, and M transmitted waveform is mutually orthogonal, at each, receive array element place, utilize respectively M reference transmitted signal to carry out matched filtering to the echo data of K recurrence interval, the output of all matched filters is arranged in following MNK * 1 dimension clutter and noise vector

$y={\∫}_0^{\mathrm{\π}}\mathrm{\ρ}\left(\mathrm{\θ}\right)b(f_s,f_d)\mathrm{d\θ}+y_w,$

In formula,

it is the clutter scattering coefficient of obeying the multiple Gaussian distribution of zero-mean;

represent normalization clutter Doppler frequency, wherein T _rfor the pulse repetition time, λ is carrier wavelength, θ and represent respectively position angle and the angle of pitch on observation ground;

represent normalization clutter spatial frequency;

the space-time two-dimensional steering vector that is called clutter, wherein

represent that Kronecker is long-pending, a _t(f _s)=[1 exp (j2 π f _sα) ... exp (j2 π f _sα (M-1))] ^tfor M * 1 dimension emission array steering vector, [] ^trepresent vector transposition, α=d _t/ d _r, M is transmitting array number, and N is for receiving array number, and K is transponder pulse number, d _tfor transmitting array element distance, d _rfor receiving array element distance; a _r(f _s)=[1 exp (j2 π f _s) ... exp (j2 π f _s(N-1))] ^tfor N * 1 dimension receiving array steering vector, a _d(f _dexp)=[1 (j2 π fd) ... exp (j2 π f _d(K-1))] ^tfor K * 1 dimension Doppler steering vector;

be to obey 0 average, variance is

mNK * 1 dimension white Gaussian noise vector, I _mNKrepresent MNK * MNK unit matrix,

represent input clutter power,

represent noise power.

Realization of the present invention is also: if testing distance unit has target to exist, the space-time two-dimensional steering vector of the echo signal after matched filtering is expressed as to the long-pending form of Kronecker of target Doppler steering vector, emission array steering vector and receiving array steering vector

$b(f_{s,0},f_{d,0})=a_d\left(f_{d,0}\right)\⊗a_t\left(f_{s,0}\right)\⊗a_r\left(f_{s,0}\right),$

Wherein b is the two dimension of target after matched filtering steering vector when empty, f _{s, 0}for the normalization spatial frequency of target, f _{d, 0}for target Doppler frequency, a _d(f _{d, 0}) be K * 1 dimension target Doppler steering vector, a _t(f _{s, 0}) for take the M * 1 emission array steering vector that the normalization spatial frequency of target is variable, a _r(f _{s, 0}) for take the N * 1 dimension receiving array steering vector that the normalization spatial frequency of target is variable,

represent that Kronecker is long-pending;

Realization of the present invention is also: the echo data after coupling that utilizes doppler filtering to receive airborne MIMO radar antenna, echo data comprises clutter plus noise data and target data, target data is random, only has while there is target in to-be-measured cell, and target data just can record.Carry out the associated time domain dimension-reduction treatment of Doppler's passage, two-dimensional guide vector C while obtaining data vector z after dimensionality reduction and the target empty after dimensionality reduction; Data vector z is the clutter plus noise data after dimensionality reduction.Comprise the steps:

3.1 adopt mDT method to carry out dimensionality reduction, and time domain dimensionality reduction matrix B is expressed as

$B=F\⊗I_{\mathrm{MN}},$

In formula, I _mNrepresent MN * MN unit matrix, F=[a _d(f _{d ,-1}), a _d(f _{d, 0}), a _d(f _{d, 1})] be the bank of filters being formed by Doppler's steering vector, wherein f _{d, 0}for the Doppler frequency of destination channel, f _{d ,-1}and f _{d, 1}the adjacent Doppler's passage in difference corresponding destination channel left and right, m represents Doppler's port number;

When the data vector z after 3.2 dimensionality reductions and the target empty after dimensionality reduction, two-dimensional guide vector C is expressed as

$\left\{\begin{array}{c}z=B^{H}y\∈C^{\mathrm{mMN}\×1}\\ c=B^{H}b(f_{s,0},f_{d,0})=\widetilde{a_t}\left(f_{s,0}\right)\⊗a_r\left(f_{s,0}\right)\end{array}\right.,$

F wherein _{s, 0}represent target normalization spatial frequency,

for the mM * 1 dimension equivalence transmitting steering vector after dimensionality reduction; () ^hthe complex-conjugate transpose of representing matrix or vector.

Realization of the present invention is also: the data vector z after time domain dimensionality reduction is carried out to spatial processing, set up the cost function that dimensionality reduction space-time adaptive is processed:

$\left\{\begin{array}{c}\underset{w}{\min }{w}^H{R}_{z}w\\ s.t.w^H[{\tilde{a}}_t\left(f_{s,0}\right)\⊗a_r\left(f_{s,0}\right)]=1\end{array}\right.,$

In formula, R _z=E{zz ^hbe clutter and the noise covariance matrix after dimensionality reduction, w is that spatial domain send-receive two dimension wave beam forms weight vector,

for the mM * 1 dimension equivalence transmitting steering vector after time domain dimensionality reduction, a _r(f _s) be N * 1 dimension receiving array steering vector.

Realization of the present invention is also: decompose two-dimentional wave beam and form weight vector, the Kronecker that spatial domain send-receive two dimension wave beam formation weight vector w is expressed as to Launch Right v and reception power u is long-pending,

and foundation is about the dihydric phenol cost function of these two weights.Comprise the steps:

5.1 form weight vector w by two-dimentional wave beam is expressed as the cascade that launching beam forms weight vector and received beam formation weight vector,

$w=v\⊗u,$

In formula, u represents that N * 1 dimension received beam forms weight vector, and v represents that mM * 1 dimension launching beam forms weight vector;

5.2 will

and a _r(f _{s, 0}) respectively brief note be

and a _r, introduce a common-used formula

by in its substitution cost function, obtain new cost function

Be called the dihydric phenol cost function 1 about vector u and v, in formula

it is N * N matrix;

5.3 in like manner will

substitution cost function equivalence obtains

Be called the dihydric phenol cost function 2 about vector u and v, in formula it is mM * mM matrix;

5.4 are taken as conventional launching beam by v forms weight vector

and in substitution dihydric phenol cost function 1, obtain the optimum weight vector that receives and be

5.5 are taken as conventional received beam by u forms weight vector a _r/ (a _r ^ha _r), in substitution dihydric phenol cost function 2, obtain optimal transmit weights vector and be

Realization of the present invention is also: in step 6, utilize alternately alternative manner to calculate optimal transmit weights vector v and the optimum weight vector u that receives, comprise the steps:

The initial value of 6.1 given u and v, the initial value of getting u is: u ₍₀₎=a _r/ (a _r ^ha _r), a wherein _rfor the steering vector of target with respect to receiving array; The initial value of getting v is:

wherein

for the steering vector of target with respect to emission array;

6.2 use Launch Right vector initial value v ₍₀₎structure dimensionality reduction matrix

and calculate dimensionality reduction covariance matrix

by v ₍₀₎with

the optimum reception in weight vector formula of substitution upgraded and received weight vector u ₍₁₎

6.3 use receive weight vector initial value u ₍₀₎structure dimensionality reduction matrix

and calculate dimensionality reduction covariance matrix

by u ₍₁₎with in substitution optimal transmit weights vector expression, upgrade Launch Right vector v ₍₁₎

6.4 judgement inequality || u ₍₁₎-u ₍₀₎|| < ε or || v ₍₁₎-v ₀₎|| whether < ε sets up, and wherein ε is greater than 0 and be not more than 1 thresholding, completes output optimal transmit weights vector v=v if inequality is set up interative computation ₍₁₎receive weight vector u=u with optimum ₍₁₎;

If 6.5 inequality are false, by v ₍₁₎as initial value repeated execution of steps 6.2-step 6.3, obtain u ₍₂₎and v ₍₂₎, judgement inequality || u ₍₁₎-u ₍₀₎|| < ε or || v ₍₁₎-v ₀₎|| whether < ε sets up, and completes output optimal transmit weights vector v=v if set up interative computation ₍₂₎receive weight vector u=u with optimum ₍₂₎;

If 6.6 are still false, repeat above step 6.2,6.3, until inequality || u _(i)-u _(i-1)|| < ε or || v _(i)-v _(i-1)|| < ε finally obtains optimal transmit weights vector v=v till setting up _(i)receive weight vector u=u with optimum _(i).

The present invention forms the optimal transmit weights vector v solving and the optimum weight vector u substitution two dimension wave beam that receives in weight vector w formula, while utilizing two-dimentional wave beam to form weight vector w to the testing distance unit after time domain dimensionality reduction empty, data vector is weighted summation, make array output power minimum, thereby at specific direction, form main beam and be used for receiving useful wanted signal, and inhibition is from the undesired signal of other directions, utilizing the optimum weight vector of obtaining to carry out sending and receiving two-dimensional adaptive wave beam forms, thereby complete spatial domain secondary dimensionality reduction, clutter is inhibited.Further detect target, target is positioned, followed the tracks of, and form flight path, be applied in various real systems, as navigational system.

The present invention compared with prior art has following characteristics:

1, operand of the present invention is little, and computation complexity is low, has further reduced the dimension of processor, and the operand of classic method is large.If transmitting array number and reception array number are respectively M and N, Doppler's port number is m, and traditional dimension reduction method requires the independent same distribution reference unit of method for supporting should be no less than 2mMN, and this is conventionally difficult to meet in radar actual working environment.In addition covariance matrix R, _zthe operand of inverting is O (m ³m ³n ³), realize invert in real time very difficult.And dimensionality reduction mDT method of the present invention only need be to N * N matrix at each iteration cycle

and mM * mM matrix estimate and invert, therefore sample demand is down to 2max (mM, N), and the calculated amount of single iteration cycle is O[(N ³+ m ³m ³)].Processor dimension of the present invention is max (mM, N), and the processor dimension of existing mDT method is up to mMN, can find out, the inventive method greatly reduces processor dimension, and sample demand of the present invention is significantly smaller than mDT method of the prior art, has reduced computation complexity, has improved the efficiency of data processing.As shown in Figure 4, Fig. 4 is that dimensionality reduction mDT method of the present invention is detecting Doppler frequency f _{d, 0}=0.25 o'clock iteration convergence curve, can find out that the inventive method can approach convergence in 10 iteration cycles, and therefore total calculated amount is about O[10 (N ³+ m ³m ³)], the calculated amount of mDT method is (mMN) ³.With M=5, N=10, m=3 is example, the calculated amount of mDT method is approximately 77 times of dimensionality reduction mDT method of the present invention.

2, the required sample number of mDT method that dimensionality reduction mDT method of the present invention is relatively traditional is little.For 1DT and 3DT method, original samples number is made as respectively 50 and 150 to guarantee the covariance matrix R after doppler filtering _zthereby full rank is reversible.The original samples number of dimensionality reduction 1DT and dimensionality reduction 3DT method is made as respectively 10 and 15.By relatively finding, dimensionality reduction 1DT and dimensionality reduction 3DT have utilized respectively 20 and 30 samples just substantially to obtain the performance of 3dB, and its speed of convergence is obviously faster than 1DT and 3DT method.As can be seen here, be difficult to obtain in the true clutter environment of a large amount of independent same distribution reference units, dimensionality reduction mDT method has greater advantage.

3, more traditional mDT method, dimensionality reduction mDT method of the present invention has better robustness under condition of small sample, and clutter rejection is better.At target Doppler frequency f _{d, 0}under=0.25 condition, independently carry out 5 tests, every kind of method is all exported 5 spatial domain response curves, as shown in Figure 7, Fig. 7 is the spatial domain directional diagram of five independent experiments of four kinds of methods, although can find out that several method can form directional diagram recess adaptively at clutter place, but the big rise and fall of the directional diagram of 1DT and 3DT method between each test, and minor level higher than main lobe level to such an extent as to principal subsidiary lobe be difficult to distinguish.By contrast, the directional diagram of dimensionality reduction 1DT and dimensionality reduction 3DT method has obvious main lobe and lower secondary lobe, and directional diagram recess is darker.Above result absolutely proves that dimensionality reduction mDT method has better robustness under condition of small sample.

Accompanying drawing explanation

Fig. 1 is airborne MIMO radar system model schematic diagram;

Fig. 2 is flow chart of data processing figure of the present invention;

Fig. 3 is the alternately alternative manner process flow diagram adopting in the present invention;

Fig. 4 is that dimensionality reduction mDT method of the present invention is detecting Doppler frequency f _{d, 0}the iteration convergence curve map of=0.25 o'clock;

Fig. 5 is that mDT method and the present invention are with the convergence curve comparison diagram of number of training;

Fig. 6 is that the improvement factor of four kinds of methods is with the change curve of normalization Doppler frequency;

Fig. 7 is the spatial domain directional diagram of five independent experiments of four kinds of methods, and wherein Fig. 7 (a) is the spatial domain directional diagram of dimensionality reduction 1DT; The spatial domain directional diagram that Fig. 7 (b) is 1DT; Fig. 7 (c) is the spatial domain directional diagram of dimensionality reduction 3DT method; Fig. 7 (d) is the spatial domain directional diagram of 3DT method.

Embodiment

Method implementation process of the present invention is described with reference to the accompanying drawings.

Embodiment 1:

When the present invention is directed to traditional mDT method and being applied to airborne MIMO radar clutter and suppressing, be subject to the restriction of the problems such as covariance matrix and operand, and the send-receive two dimension wave beam that is still faced with spatial domain after doppler filtering forms problem, processor dimension is still very high, make the practical application of mDT method the situation such as be restricted, innovation and research have been carried out, a kind of associated two-stage dimension reduction method of Doppler's passage of airborne MIMO radar is proposed, further reduce the dimension of processor, reduce calculated amount.Referring to Fig. 2, the associated two-stage dimension reduction method of Doppler's passage of airborne MIMO radar of the present invention flow process is as follows:

Step 1. builds model, radar antenna receives the clutter of ground return, the present invention utilizes reference transmitted signal at a relevant echo data receiving in interval of processing, to carry out matched filtering to radar antenna, when setting radar antenna is launched K pulse within a relevant processing time interval, echo data to K pulse mates, and exports KMN * 1 dimension clutter plus noise data vector y after matched filtering is processed.The building process of airborne MIMO radar clutter model comprises the steps:

1.1 airborne MIMO radar system models are referring to Fig. 1, and carrier aircraft is along the unaccelerated flight of x direction of principal axis, and flying height is h, and speed is v.The emission array of MIMO radar and receiving array are and are parallel to the even linear array that carrier aircraft fuselage is placed, and transmitting array number is M, and reception array number is N, and transmitting array element distance is d _t, reception array element distance is d _r.Relevant a processing in interval, each launches the train of impulses waveform that array element radiation is simultaneously comprised of K pulse, and M transmitted waveform is mutually orthogonal.Make M * N _sthe row vector of dimension matrix S represents respectively transmit sequence, wherein N _srepresent the code length that transmits, S meets

$\frac{1}{N}{\mathrm{SS}}^H=I_M---\left(1\right)$

In formula, () ^hrepresent complex-conjugate transpose, I _mrepresent M * M unit matrix.Make θ represent to observe the position angle on ground,

the angle of pitch that represents observation ground, corresponding M * 1 dimension emission array steering vector and N * 1 dimension receiving array steering vector are respectively

a _t(f _s)＝[1 exp(j2πf _sα)...exp(j2πf _sα(M-1))] ^T (2)

A _r(f _s)=[1 exp (j2 π f _s) ... exp (j2 π f _s(N-1))] ^t(3) in formula, transmitting array element distance and the ratio cc=d that receives array element distance _t/ d _r,

represent normalization clutter spatial frequency, λ is carrier wavelength.

1.2 at k(k=1 ..., K) the individual recurrence interval, the noise signal of a certain detection range unit is expressed as:

$X\left(k\right)={\&Integral;}_0^{\mathrm{\&pi;}}\mathrm{\&rho;}\left(\mathrm{\&theta;}\right){\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HDA0000457842080000041.png"\; state="\{\{state\}\}">e</figure-callout>}}^j{a}_r{a_t}^T\left(f_s\right)\mathrm{Sd\&theta;}+X_w\left(k\right),k=,...,K---\left(4\right)$ In formula, ρ (θ) obeys zero-mean, and variance is

the random noise scattering coefficient of multiple Gaussian distribution, N ^crepresent multiple Gaussian distribution, scattering coefficient ρ (θ) is random generation, works as variance

value determine after, scattering coefficient ρ (θ) just can determine at random.

represent normalization clutter Doppler frequency, wherein T _rfor the pulse repetition time;

represent zero-mean Gaussian noise matrix.

1.3 utilize each reference transmitted signal to carry out matched filtering to echo data, and matched filter banks is output as

$\tilde{X}\left(k\right)=\frac{1}{N}X\left(k\right)S^H={\&Integral;}_0^{\mathrm{\&pi;}}\mathrm{\&rho;}\left(\mathrm{\&theta;}\right){\mathrm{<figure-callout\; id="2"\; label="e\; j"\; filenames="HDA0000457842080000041.png"\; state="\{\{state\}\}">e</figure-callout>}}^j{a}_r\left(f_s\right){a_t}^T\left(f_s\right)\mathrm{d\&theta;}+\widetilde{X_w}\left(k\right),k=1,...,K---\left(5\right)$

Wherein

definition K * 1 dimension Doppler steering vector

$\begin{array}{cccc}{a}_d\left(f_d\right)=[1& \exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000457842080000041.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_d\right)& ...& \exp {\left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000457842080000041.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_d(K-1)\right)]}^T\\ =[1& \exp \left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000457842080000041.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_s\mathrm{\&beta;}\right)& ...& \exp {\left(\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA0000457842080000041.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}{f}_s\mathrm{\&beta;}(K-1)\right)]}^T\end{array}---\left(6\right)$

β=f wherein _d/ f _s=2vT _r/ d _r.By the data of K recurrence interval

each leu is piled up, data vector while obtaining following MNK * 1 dimension sky

$y=\mathrm{vec}\left(Y\right)={\&Integral;}_0^{\mathrm{\&pi;}}\mathrm{\&rho;}\left(\mathrm{\&theta;}\right)b(f_s,f_d)\mathrm{d\&theta;}+y_w---\left(7\right)$

In formula,

$b(f_s,f_d)=a_d\left(f_d\right)\&CircleTimes;a_t\left(f_s\right)\&CircleTimes;a_r\left(f_s\right)---\left(8\right)$

The space-time two-dimensional steering vector that is called clutter,

Step 2. establishing target space-time two-dimensional steering vector b, if testing distance unit has target to exist, the space-time two-dimensional steering vector of the echo signal after matched filtering is expressed as to the long-pending form of Kronecker of target Doppler steering vector, emission array steering vector and receiving array steering vector

$b(f_{s,0},f_{d,0})=a_d\left(f_{d,0}\right)\&CircleTimes;a_t\left(f_{s,0}\right)\&CircleTimes;a_r\left(f_{s,0}\right),$

Wherein b is the space-time two-dimensional steering vector of target after matched filtering, f _{s, 0}for the normalization spatial frequency of target, f _{d, 0}for target Doppler frequency, a _d(f _{d, 0}) be K * 1 dimension target Doppler steering vector, a _t(f _{s, 0}) for take the M * 1 emission array steering vector that the normalization spatial frequency of target is variable, a _r(f _{s, 0}) for take the N * 1 dimension receiving array steering vector that the normalization spatial frequency of target is variable,

represent that Kronecker is long-pending.Particular content is as follows:

If testing distance unit has target to exist, and normalization spatial frequency and the Doppler frequency of target are respectively f _{s, 0}and f _{d, 0}, echo signal is expressed as

Y _t=ρ ₀b(f _{s, 0}, f _{d, 0}) in (9) formula, the space-time two-dimensional steering vector of target

$b(f_{s,0},f_{d,0})=a_d\left(f_{d,0}\right)\&CircleTimes;a_t\left(f_{s,0}\right)\&CircleTimes;a_r\left(f_{s,0}\right)---\left(10\right)$

For target Doppler steering vector a _d(f _{d, 0}), emission array steering vector a _t(f _{s, 0}) and receiving array steering vector a _r(f _{s, 0}) Kronecker long-pending; ρ ₀it is target echo amplitude.System input letter miscellaneous noise ratio (SCNR, Signal-to-Clutter-plus-Noise Ratio) is expressed as

${\mathrm{SCNR}}_i=\frac{{\left|{\mathrm{\&rho;}}_0\right|}^2}{{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="c"\; filenames="HDA0000457842080000041.png"\; state="\{\{state\}\}">c</figure-callout>}}^2+{\mathrm{\&sigma;}}_{\mathrm{<figure-callout\; id="2"\; label="w"\; filenames="HDA0000457842080000041.png"\; state="\{\{state\}\}">w</figure-callout>}}^2}=\frac{{\left|{\mathrm{\&rho;}}_0\right|}^2}{({\mathrm{CNR}}_i+1){\mathrm{\&sigma;}}_w^2}---\left(11\right)$

In formula,

represent input clutter power,

represent input noise power, CNR _ifor input miscellaneous noise ratio.

The echo data after coupling that step 3. utilizes doppler filtering to receive airborne MIMO radar antenna, echo data comprises clutter plus noise data and target data, target data is random, only has while there is target in to-be-measured cell, and target data just can record.Carry out the associated time domain dimension-reduction treatment of Doppler's passage, two-dimensional guide vector C while obtaining data vector z after dimensionality reduction and the target empty after dimensionality reduction, data vector z is the clutter plus noise data after dimensionality reduction.

The echo data after coupling that utilizes doppler filtering to receive airborne MIMO radar antenna, the process of echo data being carried out to dimensionality reduction includes:

3.1 ideally clutter spectrum in space-time two-dimensional plane, along diagonal line, distribute, therefore adopt doppler filtering will be distributed in the clutter localization in whole spatial domain, reduce the degree of freedom of clutter, then dimensionality reduction self-adaptive processing is carried out in the output that just can combine adjacent m Doppler's passage, and this is the basic thought of mDT method just.Take m=3 as example, and dimensionality reduction matrix B can be expressed as

$B=F\&CircleTimes;I_{\mathrm{MN}}---\left(12\right)$

In formula, I _mNrepresent MN * MN unit matrix, F=[a _d(f _{d ,-1}), a _d(f _{d, 0}), a _d(f _{d, 1})] be the bank of filters being formed by Doppler's steering vector, wherein f _{d, 0}the Doppler frequency of destination channel, f _{d ,-1}and f _{d, 1}distinguish the adjacent Doppler's passage in corresponding destination channel left and right.In this example, be m=3, have the association of 3 Doppler's passages jointly to carry out time domain dimensionality reduction self-adaptive processing.

If 3.2 make f _{s, 0}represent target normalization spatial frequency, two-dimensional guide vector is expressed as when the data vector after dimensionality reduction and target empty

$\left\{\begin{array}{c}z=B^{H}y\&Element;C^{\mathrm{mMN}\&times;1}\\ c=B^{H}b(f_{s,0},f_{d,0})={\tilde{a}}_t\left(f_{s,0}\right)\&CircleTimes;a_r\left(f_{s,0}\right)\end{array}\right.---\left(13\right)$

Wherein

it is the mM * 1 dimension equivalence transmitting steering vector after dimensionality reduction.

Step 4. is set up the cost function of spatial domain dimension-reduction treatment, and the data vector z after time domain dimensionality reduction is carried out to spatial processing, sets up the cost function that dimensionality reduction space-time adaptive is processed:

$\left\{\begin{array}{c}\underset{w}{\min }{w}^H{R}_{z}w\\ s.t.w^H[{\tilde{a}}_t\left(f_{s,0}\right)\&CircleTimes;a_r\left(f_{s,0}\right)]=1\end{array}\right.,$

In formula, R _z=E{zz ^hbe clutter and the noise covariance matrix after dimensionality reduction, w is that spatial domain send-receive two dimension wave beam forms weight vector,

for the mM * 1 dimension equivalence transmitting steering vector after time domain dimensionality reduction, a _r(f _s) be N * 1 dimension receiving array steering vector.

Set up the cost function that dimensionality reduction space-time adaptive is processed:

$\left\{\begin{array}{c}\underset{w}{\min }{w}^H{R}_{z}w\\ s.t.w^H[{\tilde{a}}_t\left(f_{s,0}\right)\&CircleTimes;a_r\left(f_{s,0}\right)]=1\end{array}\right.---\left(14\right)$

In formula, R _z=E{zz ^hbe clutter and the noise covariance matrix after dimensionality reduction, w is that spatial domain send-receive two dimension wave beam forms weight vector,

for the mM * 1 dimension equivalence transmitting steering vector after dimensionality reduction, a _r(f _s) be N * 1 dimension receiving array steering vector;

The solution of formula (14) is

$w={\mathrm{\&mu;R}}_z^{-1}[{\tilde{a}}_t\left(f_{s,0}\right)\&CircleTimes;a_r\left(f_{s,}\right)]---\left(15\right)$

Wherein μ is the non-zero constant that does not affect output letter miscellaneous noise ratio, [] ^-1expression is to matrix inversion.

What formula (14) was described is that a send-receive two dimension wave beam forms problem, although processor dimension with complete when empty STAP compare and decrease, but still up to mMN.This just requires the independent same distribution reference unit of method for supporting should be no less than 2mMN, and this is conventionally difficult to meet in radar actual working environment.In addition matrix R, _zthe operand of inverting is O (m ³m ³n ³), realize invert in real time very difficult.Therefore, must after doppler filtering, do the dimension-reduction treatment of further spatial domain.And the present invention changes into two one dimension wave beams formation problems by send-receive two dimension wave beam formation problem, the calculated amount of processor is reduced greatly.

Step 5. is decomposed two-dimentional wave beam and is formed weight vector, spatial domain send-receive two dimension wave beam formation weight vector w is expressed as to Launch Right v long-pending with the Kronecker that receives power u,

and foundation is about the dihydric phenol cost function of these two weights.

Foundation comprises about the process of the dihydric phenol cost function of these two weights:

5.1 traditional cascades and space-time two-dimensional power is separated into spatial domain power to space-time cascade STAP method and time domain is weighed two parts when empty.Use for reference this thought, the two-dimentional wave beam of formula (14) is formed to weight vector w and be expressed as the cascade that launching beam forms weight vector and received beam formation weight vector,

$w=v\&CircleTimes;u---\left(16\right)$

In formula, u represents that N * 1 dimension received beam forms weight vector, and v represents that mM * 1 dimension launching beam forms weight vector.

5.2 describe for convenience of method, will

and a _r(f _{s, 0}) respectively brief note be and a _r.Introduce a common-used formula

by its substitution formula (13), obtain the dihydric phenol cost function 1 about vector u and v:

In formula

it is N * N matrix.

5.3 in like manner, will

substitution formula (14), equivalence obtains the dihydric phenol cost function 2 about vector u and v:

In formula

it is mM * mM matrix.

Formula (17) and (18) are of equal value and be all the Binary quadratic functions about vector u and v, therefore cannot obtain the analytic solution of u and v simultaneously.But fixedly in u and v any one, the analytic solution of another weight vector are all easy to try to achieve.

5.4 are taken as conventional launching beam by v forms weight vector

formula (17) is simplified to a N * 1 dimension received beam and forms problem, by v substitution formula (17), obtains the optimum weight vector that receives and is expressed as

5.5 in like manner, u is taken as to conventional received beam and forms weight vector a _r/ (a _r ^ha _r), formula (18) is reduced to mM * 1 dimension launching beam and forms problem, by u substitution formula (18), obtains optimal transmit weights vector and is

Step 6. utilizes alternately alternative manner to calculate optimal transmit weights vector v and the optimum weight vector u that receives.First select initial value u ₍₀₎=a _r/ (a _r ^ha _r) and each iteration cycle is divided into two steps, minimizes cost function respectively about u and v.I the iteration cycle of take provides method flow as example:

Step I: structure dimensionality reduction matrix

and calculate dimensionality reduction covariance matrix

the optimum reception in weight vector formula of substitution upgraded u _(i)

Step II: structure dimensionality reduction matrix

and calculate dimensionality reduction covariance matrix

in substitution optimal transmit weights vector expression, upgrade v _(i)

The step that hockets I and Step II, until || u _(i)-u _(i-1)|| or || v _(i)-v _(i-1)|| being less than thresholding ε (0 < ε < < 1) time stops, and finally makes u=u _(i), v=v _(i).

Utilize alternately alternative manner alternately to optimize and receive weight vector and Launch Right vector, obtained optimal transmit weights vector v and the optimum weight vector u that receives.The present invention can find out by alternative manner alternately, only need be to N * N matrix at each iteration cycle

and mM * mM matrix

estimate and invert, therefore sample demand is down to 2max (mM, N), and the calculated amount of single iteration cycle is O[(N ³+ m ³m ³)], processor dimension of the present invention is max (mM, N), and the processor dimension of existing mDT method is up to mMN, can find out, the inventive method greatly reduces processor dimension, and sample demand of the present invention is significantly smaller than mDT method of the prior art, reduce computation complexity, improved the efficiency of data processing.

The optimal transmit weights vector v that step 7. utilization is tried to achieve and the optimum weight vector u that receives, radar data after dimensionality reduction is received, sending out two-dimensional adaptive wave beam forms, the optimal transmit weights vector v that step 6 is solved and the optimum weight vector u substitution two dimension wave beam that receives form in weight vector w formula, while utilizing two-dimentional wave beam to form weight vector w to the testing distance unit after time domain dimensionality reduction empty, data vector is weighted summation, make array output power minimum, specific direction formation main beam in target is used for receiving useful wanted signal, and inhibition is from the undesired signal of other directions, utilize the optimum weight vector of obtaining to receive, sending out two-dimensional adaptive wave beam forms, thereby complete spatial domain secondary dimensionality reduction, clutter is inhibited, further detect target, target is positioned, follow the tracks of, and form flight path, be applied in various real systems, as navigational system.

Fig. 7 is the spatial domain directional diagram of five independent experiments of four kinds of methods, the big rise and fall of the directional diagram of 1DT method and 3DT method between each test, and minor level higher than main lobe level to such an extent as to principal subsidiary lobe be difficult to distinguish.By contrast, the directional diagram of dimensionality reduction 1DT and dimensionality reduction 3DT method has obvious main lobe and lower secondary lobe, and directional diagram recess is darker.Above result absolutely proves that dimensionality reduction mDT method of the present invention has better robustness under condition of small sample and good clutter suppresses ability.

First the present invention builds airborne MIMO Radar Clutter Signal model, utilize doppler filtering first to realize time domain fixed sturcture dimensionality reduction, rear cascade spatial domain dimension-reduction treatment, in the dimension-reduction treatment of spatial domain, spatial domain send-receive two dimension wave beam is formed to weight vector and be converted into two one dimension wave beams formation weight vectors, thereby then utilize alternately alternative manner alternately to optimize to transmit and receive wave beam to form weight vector and complete spatial domain secondary dimensionality reduction, the optimum weight vector that utilization is obtained carries out sending and receiving two-dimensional adaptive wave beam and forms, clutter reduction.Thereby greatly reduce operand and to the requirement of number of reference object.

Embodiment 2:

The associated two-stage dimension reduction method of Doppler's passage of airborne MIMO radar is with embodiment 1, and wherein step 6 utilizes alternately alternative manner alternately to optimize two low-dimensional weight vectors, calculates optimal transmit weights vector v and the optimum weight vector u that receives, and as Fig. 3, its detailed process is as follows:

The initial value of 6.1 given u and v, the initial value of getting u at this is: u ₍₀₎=a _r/ (a _r ^ha _r), a wherein _rfor the steering vector of target with respect to receiving array; The initial value of getting v is:

wherein

for the steering vector of target with respect to emission array;

6.2 use Launch Right vector initial value v ₍₀₎structure dimensionality reduction matrix

and calculate dimensionality reduction covariance matrix by v ₍₀₎with the optimum reception in weight vector formula of substitution upgraded and received weight vector u ₍₁₎

6.3 use receive weight vector initial value u ₍₀₎structure dimensionality reduction matrix

and calculate dimensionality reduction covariance matrix

by u ₍₁₎with in substitution optimal transmit weights vector expression, upgrade Launch Right vector v ₍₁₎

The initial value structure dimensionality reduction matrix that receives any one in weight vector and Launch Right vector for the present invention, and by initial value and dimensionality reduction matrix computations, obtain the renewal value of another, realize alternately iteration.

6.4 judgement inequality || u ₍₁₎-u ₍₀₎|| < ε or || v ₍₁₎-v ₀₎|| whether < ε (0 < ε≤1) sets up, and completes output optimal transmit weights vector v=v if inequality is set up interative computation ₍₁₎receive weight vector u=u with optimum ₍₁₎;

If 6.5 inequality are false, by v ₍₁₎as initial value, carry out step 6.2-step 6.3 and obtain u ₍₂₎and v ₍₂₎, judgement inequality || u ₍₁₎-u ₍₀₎|| < ε or || v ₍₁₎-v ₀₎|| whether < ε (0 < ε≤1) sets up, and completes output optimal transmit weights vector v=v if inequality is set up interative computation ₍₂₎receive weight vector u=u with optimum ₍₂₎;

If 6.6 inequality are still false, repeat above step 6.2-step 6.3, until inequality || u _(i)-u _(i-1)|| < ε or || v _(i)-v _(i-1)|| < ε (0 < ε≤1) finally obtains optimal transmit weights vector v=v till setting up _(i)receive weight vector u=u with optimum _(i).

In order to transmit and receive wave beam, form and can both self-adaptation realize, thus filtering clutter more effectively.Therefore, the associated dimension reduction method of a kind of Doppler's passage that the present invention provides, also can be called dimensionality reduction mDT method, can realize sending and receiving two-dimensional adaptive wave beam simultaneously and form.

The convergence of this alternative manner as shown in Figure 4.

From formula (21) and formula (22), can find out, dimensionality reduction mDT method of the present invention only need be to N * N matrix at each iteration cycle

and mM * mM matrix estimate and invert, therefore sample demand is down to 2max (mM, N), and the calculated amount of single iteration cycle is O[(N ³+ m ³m ³)].Fig. 4 is that dimensionality reduction mDT method of the present invention is detecting Doppler frequency f _{d, 0}the iteration convergence curve map of=0.25 o'clock; Fig. 4 shows that the inventive method can approach convergence in 10 iteration cycles, and therefore total calculated amount is about O[10 (N ³+ m ³m ³)], the calculated amount of mDT method is (mMN) ³.With M=5, N=10, m=3 is example, the calculated amount of mDT method is approximately 77 times of dimensionality reduction mDT method of the present invention.

Embodiment 3:

The associated two-stage dimension reduction method of Doppler's passage of airborne MIMO radar is with embodiment 1-2, in order to further illustrate the superiority of the associated more existing method of time domain spatial domain two-stage dimension reduction method of Doppler's passage (as 1DT, 3DT) of airborne MIMO radar of the present invention, below by emulation, the present invention is explained again given following simulated conditions:

By numerical simulation, compare in m=1 and two kinds of situations of m=3 the performance of mDT and dimensionality reduction mDT method of the present invention.For m=1(1DT) situation, time domain doppler filtering employing-70dB Chebyshev weighting is to force down secondary lobe.Experiment parameter is set to: carrier aircraft speed v=150m/s, height h=9km, wavelength X=0.3m, umber of pulse K=32, pulse repetition time T _r=5 * 10 ^-4s, transmitting array number M=5, receives array number N=10, array element distance d _t=d _r=0.15m.Utilize quadrature that 5 code lengths of genetic method optimization are 512 four mutually code sequences as radar emission signal.During emulation, think that each range unit clutter is separate, noise power unit miscellaneous noise ratio is 60dB.In test, hypothetical target is all the time in the positive side-looking direction of radar, i.e. normalization spatial frequency f _{s, 0}=0.

Referring to Fig. 4, Fig. 4 is that dimensionality reduction mDT method of the present invention is detecting Doppler frequency f _{d, 0}=0.25 o'clock iteration convergence curve, as seen from Figure 4, after 5～6 step iteration, improvement factor just substantially reaches maximal value and tends towards stability, and illustrates that the inventive method has speed of convergence faster.

Embodiment 4:

The associated two-stage dimension reduction method of Doppler's passage of airborne MIMO radar is with embodiment 1-3, in order to further illustrate the superiority of the associated more existing method of two-stage dimension reduction method of Doppler's passage (as 1DT, 3DT) of airborne MIMO radar of the present invention, below given simulated conditions with embodiment 3, by emulation, the present invention is explained again

Referring to Fig. 5, Fig. 5 be mDT and dimensionality reduction mDT method of the present invention with the convergence curve of number of training, be the average result of 200 Monte Carlo experiments.For 1DT and 3DT method, original samples number is made as respectively 50 and 150 to guarantee the covariance matrix R after doppler filtering _zthereby full rank is reversible.The original samples number of dimensionality reduction 1DT and dimensionality reduction 3DT method is made as respectively 10 and 15.By relatively finding, dimensionality reduction 1DT and dimensionality reduction 3DT have utilized respectively 20 and 30 samples just substantially to obtain the performance of 3dB, and its speed of convergence is obviously faster than 1DT and 3DT method.As can be seen here, be difficult to obtain in the true clutter environment of a large amount of independent same distribution reference units, the required sample of the inventive method is less, and under condition of small sample, the detection performance of target has greater advantage.

Embodiment 5:

The associated two-stage dimension reduction method of Doppler's passage of airborne MIMO radar is with embodiment 1-4, for the associated two-stage dimension reduction method of Doppler's passage (dimensionality reduction mDT) that the absolutely proves airborne MIMO radar of the present invention superiority under condition of small sample, given simulated conditions is with embodiment 3, in addition the sample number of 1DT method is made as to 50, the sample number of 3DT method is made as 150, just guarantees covariance matrix R _zfull rank.Do following experiment:

Referring to Fig. 6, Fig. 6 is that four kinds of methods are that the improvement factor of 1DT, dimensionality reduction 1DT, 3DT and dimensionality reduction 3DT method is with the change curve of normalization Doppler frequency.Improvement factor is the ratio of output signal to noise ratio with input signal to noise ratio, and its size can reflect the quality of method performance, and as can be seen from Figure 6, in m=1 and 3 two kinds of situations, the performance of dimensionality reduction mDT method of the present invention is all significantly better than mDT method.

Embodiment 6:

The associated two-stage dimension reduction method of Doppler's passage of airborne MIMO radar is with embodiment 1-5, for the associated two-stage dimension reduction method of Doppler's passage (dimensionality reduction mDT) that the absolutely proves airborne MIMO radar of the present invention superiority under condition of small sample, given simulated conditions, with embodiment 5, is done following experiment:

Referring to Fig. 7, Fig. 7 is at target Doppler frequency f _{d, 0}under=0.25 condition, independently carry out 5 tests, every kind of method is all exported 5 spatial domain response curves.Although several method can be adaptively forms directional diagram recess at clutter place, the big rise and fall of the directional diagram of 1DT and 3DT method between each test, and minor level higher than main lobe level to such an extent as to principal subsidiary lobe be difficult to distinguish.By contrast, the directional diagram of dimensionality reduction 1DT and dimensionality reduction 3DT method has obvious main lobe and lower secondary lobe, and directional diagram recess is darker.Above result absolutely proves that dimensionality reduction mDT method has better robustness under condition of small sample.

In brief, the invention discloses a kind of associated two-stage dimension reduction method of Doppler's passage of airborne MIMO radar, two-dimensional guide vector while first building airborne MIMO Radar Clutter Signal model and target empty; Utilize doppler filtering to carry out time domain dimension-reduction treatment to noise signal; During then to the data vector after dimensionality reduction and target empty, two-dimensional guide vector carries out spatial domain secondary dimensionality reduction, the Kronecker that spatial domain send-receive two dimension wave beam formation weight vector is resolved into reception weight vector and Launch Right vector is long-pending, and sets up the dihydric phenol cost function that forms weight vector about these two one dimension wave beams; Then utilize alternately alternative manner alternately to optimize two low-dimensional weights; Finally utilize the optimum weight vector of obtaining to carry out sending and receiving two-dimensional adaptive wave beam and form, clutter reduction.Because the dimension of required weight vector reduces greatly, under same case, with less reference unit, can obtain the preferably estimation of covariance matrix, the clutter rejection of two-stage dimensionality reduction clutter suppression method of the present invention under small sample significantly improved.Meanwhile, avoided high dimension sample covariance matrix to invert, calculated amount significantly reduces.After suppressing with clutter of the present invention, be beneficial to further detection target, target localization, tracking, and form flight path.The present invention is applied to as in the various real systems of navigational system etc.

Claims (5)

1. the associated two-stage dimension reduction method of Doppler's passage of airborne MIMO radar, is characterized in that: the associated two-stage reduction process of Doppler's passage of airborne MIMO radar comprises the steps:

Step 1. builds airborne MIMO radar clutter model, radar antenna receives the clutter of ground return, when setting radar antenna is launched K pulse within a relevant processing time interval, echo data to K pulse mates, and exports KMN * 1 dimension clutter plus noise data vector y after matched filtering is processed;

Step 2. establishing target space-time two-dimensional steering vector b, if testing distance unit has target to exist, the space-time two-dimensional steering vector of the echo signal after matched filtering is expressed as to the long-pending form of Kronecker of target Doppler steering vector, emission array steering vector and receiving array steering vector

$b(f_{s,0},f_{d,0})=a_d\left(f_{d,0}\right)\&CircleTimes;a_t\left(f_{s,0}\right)\&CircleTimes;a_r\left(f_{s,0}\right),$

Wherein b is the space-time two-dimensional steering vector of target after matched filtering, f _{s, 0}for the normalization spatial frequency of target, f _{d, 0}for target Doppler frequency, a _d(f _{d, 0}) be K * 1 dimension target Doppler steering vector, a _t(f _{s, 0}) for take the M * 1 emission array steering vector that the normalization spatial frequency of target is variable, a _r(f _{s, 0}) for take the N * 1 dimension receiving array steering vector that the normalization spatial frequency of target is variable,

represent that Kronecker is long-pending;

Step 3. utilizes the echo data after coupling that doppler filtering receives airborne MIMO radar antenna to carry out the associated time domain dimension-reduction treatment of Doppler's passage, two-dimensional guide vector C while obtaining data vector z after dimensionality reduction and the target empty after dimensionality reduction;

Step 4. is set up the cost function of spatial domain dimension-reduction treatment, and the data vector z after time domain dimensionality reduction is carried out to spatial processing, sets up the cost function that dimensionality reduction space-time adaptive is processed:

$\left\{\begin{array}{c}\underset{w}{\min }{w}^H{R}_{z}w\\ s.t.w^H[{\tilde{a}}_t\left(f_{s,0}\right)\&CircleTimes;a_r\left(f_{s,0}\right)]=1\end{array}\right.,$

In formula, R _z=E{zz ^hbe clutter and the noise covariance matrix after dimensionality reduction, w is that spatial domain send-receive two dimension wave beam forms weight vector, for the mM * 1 dimension equivalence transmitting steering vector after time domain dimensionality reduction, a _r(f _s) be N * 1 dimension receiving array steering vector;

Step 5. is decomposed two-dimentional wave beam and is formed weight vector, spatial domain send-receive two dimension wave beam formation weight vector w is expressed as to Launch Right v long-pending with the Kronecker that receives power u,

and foundation is about the dihydric phenol cost function of these two weights;

Step 6. utilizes alternately alternative manner to calculate optimal transmit weights vector v and the optimum weight vector u that receives;

The optimal transmit weights vector v that step 7. utilization is tried to achieve and the optimum weight vector u that receives, radar data after dimensionality reduction is received, sending out two-dimensional adaptive wave beam forms, the optimal transmit weights vector v that step 6 is solved and the optimum weight vector u substitution two dimension wave beam that receives form in weight vector w formula, while utilizing two-dimentional wave beam to form weight vector w to the testing distance unit after time domain dimensionality reduction empty, data vector is weighted summation, make array output power minimum, the optimum weight vector that utilization is obtained is received, sending out two-dimensional adaptive wave beam forms, complete spatial domain secondary dimensionality reduction, clutter is inhibited.

2. the associated two-stage dimension reduction method of Doppler's passage of airborne MIMO radar according to claim 1, is characterized in that: the echo that utilizes reference transmitted signal to receive radar antenna described in step 1 carries out matched filtering, output clutter plus noise vector data y; Detailed process is as follows:

Be set in relevant a processing in interval (CPI), airborne MIMO radar is respectively launched the train of impulses waveform that array element radiation is simultaneously comprised of K pulse, and M transmitted waveform is mutually orthogonal, at each, receive array element place, utilize respectively M reference transmitted signal to carry out matched filtering to the echo data of K recurrence interval, the output of all matched filters is arranged in following MNK * 1 dimension clutter plus noise vector

$y={\&Integral;}_0^{\mathrm{\&pi;}}\mathrm{\&rho;}\left(\mathrm{\&theta;}\right)b(f_s,f_d)\mathrm{d\&theta;}+y_w,$

In formula,

it is the clutter scattering coefficient of obeying the multiple Gaussian distribution of zero-mean;

represent normalization clutter Doppler frequency, wherein T _rfor the pulse repetition time, λ is carrier wavelength, and v is carrier aircraft speed, θ and

represent respectively position angle and the angle of pitch on observation ground;

represent normalization clutter spatial frequency; $b(f_s,f_d)=a_d\left(f_d\right)\&CircleTimes;a_t\left(f_s\right)\&CircleTimes;a_r\left(f_s\right)$ The space-time two-dimensional steering vector that is called clutter, wherein represent that Kronecker is long-pending, a _t(f _s)=[1 exp (j2 π f _sα) ... exp (j2 π f _sα (M-1))] ^tfor M * 1 dimension emission array steering vector, [] ^trepresent vectorial transposition, α=d _t/ d _r, M is transmitting array number, and N is for receiving array number, and K is transponder pulse number, d _tfor transmitting array element distance, d _rfor receiving array element distance; a _r(f _s)=[1 exp (j2 π f _s) ... exp (j2 π f _s(N-1))] ^tfor N * 1 dimension receiving array steering vector, a _d(f _d)=[1 exp (j2 π f _d) ... exp (j2 π f _d(K-1))] ^tfor K * 1 dimension Doppler steering vector; be to obey 0 average, variance is

mNK * 1 dimension white Gaussian noise vector, I _mNKrepresent MNK * MNK unit matrix, represent input clutter power,

represent noise power.

3. the associated two-stage dimension reduction method of Doppler's passage of airborne MIMO radar according to claim 2, it is characterized in that: the echoed signal of utilizing doppler filtering to receive airborne MIMO radar antenna described in step 3 is carried out time domain dimension-reduction treatment, while obtaining data vector z after dimensionality reduction and target empty, two-dimensional guide vector C, comprises the steps:

3.1 adopt mDT method to carry out dimensionality reduction, and time domain dimensionality reduction matrix B is expressed as

$B=F\&CircleTimes;I_{\mathrm{MN}},$

In formula, I _mNrepresent MN * MN unit matrix, F=[a _d(f _{d ,-1}), a _d(f _{d, 0}), a _d(f _{d, 1})] be the bank of filters being formed by Doppler's steering vector, wherein f _{d, 0}for the Doppler frequency of destination channel, f _{d ,-1}and f _{d, 1}the adjacent Doppler's passage in difference corresponding destination channel left and right;

When the data vector z after 3.2 dimensionality reductions and target empty, two-dimensional guide vector C is expressed as

$\left\{\begin{array}{c}z=B^{H}y\&Element;C^{\mathrm{mMN}\&times;1}\\ c=B^{H}b(f_{s,0},f_{d,0})=\widetilde{a_t}\left(f_{s,0}\right)\&CircleTimes;a_r\left(f_{s,0}\right)\end{array}\right.,$

F wherein _{s, 0}represent target normalization spatial frequency,

for the mM * 1 dimension equivalence transmitting steering vector after dimensionality reduction, m represents Doppler's port number, () ^hthe complex-conjugate transpose of representing matrix or vector.

4. the associated two-stage dimension reduction method of Doppler's passage of airborne MIMO radar according to claim 3, it is characterized in that: the Kronecker that spatial domain send-receive two dimension wave beam formation weight vector w is expressed as to Launch Right vector v and reception weight vector u described in step 5 is long-pending, and sets up the dihydric phenol cost function about these two weights; Include following steps:

5.1 form weight vector w by two-dimentional wave beam is expressed as the cascade that launching beam forms weight vector and received beam formation weight vector,

$w=v\&CircleTimes;u,$

In formula, u represents that N * 1 dimension received beam forms weight vector, and v represents that mM * 1 dimension launching beam forms weight vector;

5.2 will

and a _r(f _{s, 0}) respectively brief note be

and a _r, introduce a common-used formula

by in its substitution cost function, obtain the dihydric phenol cost function 1 about vector u and v:

In formula

it is N * N matrix;

5.3 in like manner will

substitution cost function equivalence obtains the dihydric phenol cost function 2 about vector u and v:

In formula

it is mM * mM matrix;

5.4 are taken as conventional launching beam by v forms weight vector

and in substitution dihydric phenol cost function 1, obtain the optimum weight vector that receives and be

5.5 are taken as conventional received beam by u forms weight vector a _r/ (a _r ^ha _r), in substitution dihydric phenol cost function 2, obtain optimal transmit weights vector and be

5. the associated two-stage dimension reduction method of Doppler's passage of airborne MIMO radar according to claim 4, is characterized in that: the utilization described in step 6 replaces alternative manner and calculates optimal transmit weights vector v and the optimum weight vector u that receives, and comprises the steps:

The initial value of 6.1 given u and v, the initial value of getting u is: u ₍₀₎=a _r/ (a _r ^ha _r), a wherein _rfor the steering vector of target with respect to receiving array; The initial value of getting v is:

wherein

for the steering vector of target with respect to emission array;

6.2 use Launch Right vector initial value v ₍₀₎structure dimensionality reduction matrix

and calculate dimensionality reduction covariance matrix

by v ₍₀₎with

the optimum reception in weight vector formula of substitution upgraded and received weight vector u ₍₁₎

6.3 use receive weight vector initial value u ₍₀₎structure dimensionality reduction matrix

and calculate dimensionality reduction covariance matrix

by u ₍₁₎with

in substitution optimal transmit weights vector expression, upgrade Launch Right vector v ₍₁₎

6.4 judgement inequality || u ₍₁₎-u ₍₀₎|| < ε or || v ₍₁₎-v ₀₎|| whether < ε sets up, and wherein ε is greater than 0 and be not more than 1 thresholding, completes output optimal transmit weights vector v=v if inequality is set up interative computation ₍₁₎receive weight vector u=u with optimum ₍₁₎;

If 6.5 inequality are false, by v ₍₁₎as initial value repeated execution of steps 6.2-step 6.3, obtain u ₍₂₎and v ₍₂₎, judgement inequality || u ₍₁₎-u ₍₀₎|| < ε or || v ₍₁₎-v ₀₎|| whether < ε sets up, and completes output optimal transmit weights vector v=v if set up interative computation ₍₂₎receive weight vector u=u with optimum ₍₂₎;

If 6.6 are still false, repeat above step 6.2,6.3, until inequality || u _(i)-u _(i-1)|| < ε or || v _(i)-v _(i-1)|| < ε finally obtains optimal transmit weights vector v=v till setting up _(i)receive weight vector u=u with optimum _(i).

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