CN105022040A - Array element error estimation method based on clutter data combined fitting - Google Patents

Abstract

The invention provides an array element error estimation method based on clutter data combined fitting. The method can raise array element error estimation precision and robustness. The method comprises the following steps: a model parameter of an airborne radar and a distribution parameter of clutter represented by clutter data received by the airborne radar are obtained; according to the model parameter of the airborne radar and the distribution parameter of the clutter data, a space-time guiding vector when the airborne radar receives the clutter data is calculated; an amplitude vector of reconstructing clutter data is calculated; the reconstructing clutter data is determined according to the amplitude vector of the reconstructing clutter data; F norm fitting of the clutter data received by the airborne radar and the reconstructing clutter data is carried out, and the array element error of the airborne radar is estimated.

Description

Based on the array element error estimation of clutter data associating matching

Technical field

The invention belongs to Radar Technology field, particularly relate to a kind of array element error estimation based on clutter data associating matching.

Background technology

Airborne radar under depending on the impact of ground clutter can be subject to during work.Due to the relative motion on carrier aircraft radar and ground, clutter doppler spectral can broadening, brings difficulty to moving object detection.Space-time adaptive process (space time adaptive processing, STAP) is a kind of two-dimensional filtering technique of combining spatial domain and time domain, and it can effective clutter reduction, improves radar to the detectability of moving target.

In the ideal case, STAP can obtain good performance, but in the engineer applied of reality, onboard radar system inevitably exists various error.In the present state-of-the technology, the precision of time dimension is usually higher, and its error is generally negligible; Space dimension is then different, and due to the restriction of manufacturing process, each magnitude-phase characteristics received between array element usually exists inconsistency.When there is this non-ideal factor of array element error in onboard radar system, will be greatly affected based on the moving target parameter estimation of STAP and positioning performance.

The correction of array element error mainly can be divided into active correction and self-correcting two class.Active correction utilizes outside accurately known auxiliary information source array element error to be carried out to the method for off-line correction, and the method can obtain good calibration result in theory, but has higher performance requirement to auxiliary information source and add the complexity of system.Self-correcting is that array element error correction is converted into a Parameter Estimation Problem, namely utilizes the echo data of reception to estimate array element error.For airborne radar, its echo received is mainly clutter component.Clutter data now can be utilized to estimate array element error.

The method of interfering based on adjacent array element is with an array element as a reference, utilizes reference array element and other array element to receive the relation of phase history between echo to estimate array element error.The method operand is low, but poor-performing, residence time lower in miscellaneous noise ratio is shorter.Method based on main-lobe clutter eigenvector is that the data of getting Doppler frequency corresponding to main-lobe clutter calculate spatial domain covariance matrix, then spatial domain covariance matrix feature decomposition is got the steering vector of eigenvalue of maximum characteristic of correspondence vector as reality.The method can obtain good effect when RADOP resolution is higher, but airborne radar is in order to realize the heavily visit rate higher to moving target, and its pulse number launched in single ripple position is less, now main-lobe clutter eigenvector method hydraulic performance decline.Method based on clutter subspace utilizes clutter pattern parameter and the real data structural theory clutter orthogonal complement space and actual clutter subspace respectively, and the orthogonality both then utilizing estimates array element error.The method, when the radar coherent accumulation time is shorter, can obtain good effect, but the factors such as interior clutter moition, Channel Mismatch can cause subspace to be leaked, and now subspace orthogonality declines, and declining appears in array element estimation of error performance.

Summary of the invention

For the deficiency of above-mentioned prior art, the object of the invention is to propose a kind of array element error estimation based on clutter data associating matching, estimated accuracy and the robustness of array element error can be improved, and all can obtain good Parameter Estimation Precision and robustness when low number of samples, low pulse number.

For achieving the above object, the present invention adopts following technical scheme to be achieved.

Based on an array element error estimation for clutter data associating matching, comprise the steps:

Step 1, the distribution parameter of the clutter that the clutter data that the model parameter of acquisition airborne radar and described airborne radar receive characterizes, the described clutter data echo data that airborne radar receives represents;

Step 2, according to the model parameter of described airborne radar and the distribution parameter of described clutter data, steering vector when to calculate when described airborne radar receives described clutter data empty;

Step 3, calculates the amplitude vector of reconstruct clutter data;

Step 4, according to the amplitude vector of described reconstruct clutter data, determines described reconstruct clutter data;

Step 5, the clutter data received by airborne radar and described reconstruct clutter data carry out the matching of F norm, estimate the array element error of described airborne radar.

Feature of the present invention and being further improved to:

(1) in step 1, the model parameter of airborne radar is:

The carrier aircraft speed of airborne radar is v, carrier aircraft velocity reversal is along X-axis positive dirction, carrier aircraft height is h, the aerial array of airborne radar is the uniform line-array be made up of N number of array element, array element distance is d, aerial array is axially along X-direction, and airborne radar launches M pulse in a coherent processing inteval, and pulse repetition rate is f _r, radar operation wavelength is λ;

The distribution parameter of the clutter that the clutter data that described airborne radar receives characterizes is:

Clutter is φ relative to the position angle of airborne radar, and clutter is θ relative to the angle of pitch of airborne radar, and clutter relative to the normalization Doppler frequency of airborne radar is clutter relative to the normalization spatial frequency of airborne radar is

(2) during empty when airborne radar described in step 2 receives described clutter data, steering vector comprises time domain steering vector v _t(w _d) and spatial domain steering vector v _s(w _s):

$v_t\left(w_d\right)={\left[\begin{array}{cc}1& e^{j2{\mathrm{\πw}}_d}\mathrm{...}{e}^{j2\mathrm{\π}(M-1)w_d}\end{array}\right]}^T$

$v_s\left(w_s\right)={\left[\begin{array}{cc}1& e^{j2{\mathrm{\πw}}_s}\mathrm{...}{e}^{j2\mathrm{\π}(N-1)w_s}\end{array}\right]}^T$

(3) step 3 specifically comprises following sub-step:

(3a) to clutter data along orientation to sampling, obtaining one group of space-time two-dimensional frequency point set is

(3b) steering vector and described space-time two-dimensional frequency point set during empty when receiving described clutter data according to described airborne radar, when to obtain when described airborne radar receives described clutter data empty, guiding matrix V is $V=\left[\begin{array}{ccc}{v}_1(w_d^1,w_s^1)& \mathrm{...}& v_{N_c}(w_d^{N_c},w_s^{N_c})\end{array}\right];$

(3c) described reconstruct clutter data is expressed as

Wherein, for reconstruct clutter data matrix, for the complex magnitude matrix of reconstruct clutter matrix to be estimated, wherein k=1 ..., K, K are number of samples;

(3d) structure is about complex magnitude matrix optimization problem:

In formula || || _frepresent F norm, X=[x ₁..., x _k] the echo data matrix that receives for airborne radar;

(3e) solve described about complex magnitude matrix optimization problem, obtain estimate complex magnitude matrix thus obtain described reconstruct clutter data

Further, sub-step (3e) specifically comprises following sub-step:

(3e1) by described optimization problem expansion is expressed as thus described optimization problem is equivalent to K independently optimization problem $\underset{{\hat{a}}_k}{\min }\left|\right|x_k-V{\hat{a}}_k|{|}_2,k=1,\mathrm{...},K;$

(3e2) adopt the singular value decomposition method blocked to each optimization problem in described K independently optimization problem k=1 ..., K solves, thus the solution obtaining each optimization problem is: ${\hat{a}}_k=\underset{i=1}{\overset{r}{\Σ}}\frac{u_i^H{x}_k}{{\mathrm{\σ}}_i}{w}_i,$

Wherein, u _ifor the left singular vector of guiding matrix V during described sky, w _ifor the right singular vector of guiding matrix V during described sky, σ _ifor the singular value of guiding matrix V during described sky, the numerical value order of guiding matrix V when r is described sky.

(4) step 4 is specially: according to the solution of each optimization problem described k=1 ..., K, forms the complex magnitude matrix of described estimation thus obtain described reconstruct clutter data

(5) step 5 specifically comprises following sub-step:

(5a) described reconstruct clutter data is revised, obtain

Wherein, for taper vector, for array element error, diag () represents vector diagonalization;

(5b) clutter data received by airborne radar described in matching and revised reconstruct clutter data are estimated corresponding objective function is

(5c) described objective function is solved obtain array element error

The present invention compared with prior art has the following advantages: (1) technical solution of the present invention all can obtain higher Parameter Estimation Precision and robustness when low number of samples, low pulse number; (2) technical solution of the present invention has higher robustness when low number of samples, low pulse number; (3) technical solution of the present invention operand compared with additive method is low, fast operation.

Accompanying drawing explanation

In order to be illustrated more clearly in the embodiment of the present invention or technical scheme of the prior art, be briefly described to the accompanying drawing used required in embodiment or description of the prior art below, apparently, accompanying drawing in the following describes is only some embodiments of the present invention, for those of ordinary skill in the art, under the prerequisite not paying creative work, other accompanying drawing can also be obtained according to these accompanying drawings.

Fig. 1 is the schematic flow sheet of the array element error estimation that the embodiment of the present invention provides;

Fig. 2 is airborne radar platform geometry schematic diagram;

Fig. 3 is the curve synoptic diagram of range error RMSE with distance sample number of variations;

Fig. 4 is the curve synoptic diagram of phase error RMSE with distance sample number of variations;

Fig. 5 is that range error RMSE is with umber of pulse change curve schematic diagram;

Fig. 6 is that phase error RMSE is with pulse number change curve schematic diagram;

Fig. 7 is that array element error RMSE is with numerical value order threshold variation curve synoptic diagram.

Embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present invention, be clearly and completely described the technical scheme in the embodiment of the present invention, obviously, described embodiment is only the present invention's part embodiment, instead of whole embodiments.Based on the embodiment in the present invention, those of ordinary skill in the art, not making the every other embodiment obtained under creative work prerequisite, belong to the scope of protection of the invention.

F norm is expressed as: Α representing matrix, the line number of m representing matrix, the columns of n representing matrix, a _ijthe i-th row jth element of representing matrix Α.

As shown in Figure 1, implementation process of the present invention is as follows:

Step 1, the distribution parameter of the clutter that the clutter data that the model parameter of acquisition airborne radar and described airborne radar receive characterizes.

The described clutter data echo data that airborne radar receives represents.

Airborne Pulse Doppler Radar geometry as shown in Figure 2.

Carrier aircraft speed is v, and velocity reversal is along X-axis positive dirction, and carrier aircraft height is h.The aerial array of airborne radar is the uniform line-array be made up of N number of array element, and array element distance is d, and aerial array axially along the x-axis direction.Radar launches M pulse in a coherent processing inteval, and pulse repetition rate is f _r.Radar operation wavelength is λ.

Ground clutter is φ relative to the position angle of airborne radar, and ground clutter is θ relative to the angle of pitch of airborne radar.Airborne radar is sampled when receiving echo data to the echo data of each array element, is enrolled.

Ground clutter relative to the normalization Doppler frequency of radar is ground clutter is relative to the normalization spatial frequency of radar

Step 2, according to the model parameter of described airborne radar and the distribution parameter of described clutter data, steering vector when to calculate when described airborne radar receives described clutter data empty.

Time domain steering vector v corresponding when airborne radar receives described clutter data _t(w _d) and spatial domain steering vector v _s(w _s) can be expressed as:

$v_t\left(w_d\right)={\left[\begin{array}{cc}1& e^{j2{\mathrm{\πw}}_d}\mathrm{...}{e}^{j2\mathrm{\π}(M-1)w_d}\end{array}\right]}^T---\left(1\right)$

$v_s\left(w_s\right)={\left[\begin{array}{cc}1& e^{j2{\mathrm{\πw}}_s}\mathrm{...}{e}^{j2\mathrm{\π}(N-1)w_s}\end{array}\right]}^T---\left(2\right)$

Corresponding to single rang ring, the signal form of the clutter component that each array element receives is

In formula, ⊙ represents that Hadamard amasss, represent that Kronecker amasss, α is the receiver voltage amplitude of clutter corresponding to different orientations.T _sfor array element response vector, concrete form is:

$\begin{array}{cc}{t}_{s,i}=(1+{\mathrm{\γ}}_i)e^{{\mathrm{j\β}}_i}& j=1,\mathrm{...},N---\left(4\right)\end{array}$

γ in formula _ifor array element range error, β _ifor array element phase error.

Formula (3) is suitably arranged, can obtain

In formula for steering vector during clutter sky, for taper vector, represent that array element is to the modulation of noise signal.

Airborne radar each range unit receive empty time fast beat of data (airborne radar echo data) be

x＝x _c+x _n(6)

X in formula _nrepresent white Gaussian noise component.

Step 3, calculates the amplitude vector of reconstruct clutter data.

(3a) to clutter data along orientation to sampling, obtaining one group of space-time two-dimensional frequency point set is

On the geometric locus that clutter is corresponding, along orientation discrete sampling N _cpoint (N _c>=MN), can obtain one group of space-time two-dimensional frequency point set is

(3b) steering vector and described space-time two-dimensional frequency point set during empty when receiving clutter data according to described airborne radar, when to obtain when described airborne radar receives clutter data empty, guiding matrix V is $V=\left[\begin{array}{ccc}{v}_1(w_d^1,w_s^1)& \mathrm{...}& v_{N_c}(w_d^{N_c},w_s^{N_c})\end{array}\right].$

This group two-dimensional frequency point set is substituted into formula (1) with formula (2), and when can to calculate when corresponding airborne radar receives clutter data empty, steering vector matrix is

$V=\left[\begin{array}{ccc}{v}_1(w_d^1,w_s^1)& \mathrm{...}& v_{N_c}(w_d^{N_c},w_s^{N_c})\end{array}\right]---\left(7\right)$

(3c) described reconstruct clutter data is expressed as

After angle Doppler domain is by clutter discrete sampling, the clutter data of reconstruct can be expressed as

${\hat{X}}_c=V\hat{A}---\left(8\right)$

In formula for the clutter data matrix of reconstruct, for the clutter complex magnitude matrix estimated, wherein (k=1 ..., K, K number of samples).For positive side battle array, the space-time two-dimensional spectral line that different clutter range unit is corresponding overlaps, then now can carry out the clutter data of linear spanning different distance unit with single basis matrix V.

(3d) structure is about complex magnitude matrix optimization problem:

Between the clutter data received to make airborne radar and the clutter data of reconstruct, square error is minimum, can obtain following optimization problem

$\begin{array}{cc}\underset{\hat{A}}{\min }& \left|\right|X-V\hat{A}|{|}_F^2---\left(9\right)\end{array}$

In formula || || _frepresent F norm, X=[x ₁..., x _k] data matrix (i.e. airborne radar receive echo data) for measuring, be mainly clutter data.

(3e) solve described about complex magnitude matrix optimization problem, obtain estimate complex magnitude matrix thus obtain described reconstruct clutter data

Formula (9) is launched expression can obtain

$\begin{array}{cc}\underset{{\hat{a}}_1,\mathrm{...},{\hat{a}}_K}{\min }& \left|\right|\begin{array}{ccc}{x}_1-V{\hat{a}}_1& \mathrm{...}& x_K-V{\hat{a}}_K\end{array}|{|}_F^2---\left(10\right)\end{array}$

Formula (10) can be equivalent to K independently optimization problem, namely

$\begin{array}{ccc}\underset{{\hat{a}}_k}{\min }& \left|\right|x_k-V{\hat{a}}_k|{|}_2& k=1,\mathrm{...},K---\left(11\right)\end{array}$

In formula || || ₂represent 2 norms.

Formula (11) is one and linearly owes to determine least square problem, and normal equations or QR decomposition method can be adopted in theory to solve.But because steering vector matrix V during sky is a super complete matrix, between its column vector, there is correlativity.In this case, conditional number k (V) numerical value of matrix V is excessive,

k(V)＝σ _max(V)/σ _min(V) (12)

The conditional number of k (V) representing matrix V in formula, σ _max, σ _minbe respectively the maximum of V and minimum singular value.

D () solves formula (11) by the svd of blocking (Truncated Singular Value Decomposition, TSVD) method.According to TSVD, the solution of formula (11) correspondence is

${\hat{a}}_k=\underset{i=1}{\overset{r}{\Σ}}\frac{u_i^H{x}_k}{{\mathrm{\σ}}_i}{w}_i---\left(13\right)$

U in formula _i, w _iwith σ _icorrespond respectively to the left singular vector of V, right singular vector and singular value.R is the numerical value order (or being called effective order) of V, can calculate, namely according to following criterion

$r=\arg \underset{q}{min}(\underset{i=1}{\overset{q}{\Σ}}{\mathrm{\σ}}_i>\mathrm{\η}\underset{i=1}{\overset{NM}{\Σ}}{\mathrm{\σ}}_i)---\left(14\right)$

In formula η be one close to 1 constant.Choose minimum q value that formula (14) the is set up numerical value order r as V.

Step 4, according to the amplitude vector of described reconstruct clutter data, determines described reconstruct clutter data.

Formula (14) is estimated the clutter amplitude vector obtained the clutter data matrix based on the reconstruct of clutter spectrum distributed architecture just can be obtained in substitution formula (8)

Step 5, the clutter data received by airborne radar and described reconstruct clutter data carry out the matching of F norm, estimate the array element error of described airborne radar.

Step 5 specifically comprises following sub-step:

(5a) described reconstruct clutter data is revised, obtain

In order to improve the accuracy of the clutter data of reconstruct, it is right to need do respective handling, to compensate the impact that array element error band comes.Taper vector on desirable clutter data dot product is shown as by the modulation of array element to clutter data of formula (5) known airborne radar.According to this model, the clutter data of reconstruct is modified to

${\tilde{X}}_c=\hat{T}{\hat{X}}_c---\left(15\right)$

In formula for taper vector to be estimated, diag () represents vector diagonalization.

(5b) clutter data received by airborne radar described in matching and revised reconstruct clutter data are estimated corresponding objective function is

By the metric data of matching reality (i.e. airborne radar receive echo data) with compensate after the clutter data of reconstruct estimate corresponding objective function is

$\begin{array}{cc}\underset{\hat{T}}{\min }& \left|\right|X-\hat{T}{\hat{X}}_c|{|}_F^2---\left(16\right)\end{array}$

(5c) described objective function is solved obtain array element error

According to the addition property of partitioned matrix, formula (16) can be launched to be expressed as

$\begin{array}{cc}\underset{{\hat{t}}_s}{\min }& \left|\right|\begin{array}{ccc}{x}_1-diag(1\⊗{\hat{t}}_s){\hat{x}}_{c,1}& \mathrm{...}& x_K-diag(1\⊗{\hat{t}}_s){\hat{x}}_{c,K}\end{array}|{|}_F^2---\left(17\right)\end{array}$

Formula (17) can equivalently representedly be

$\begin{array}{cc}\underset{{\hat{t}}_s}{\min }& \left|\right|\begin{array}{ccc}{x}_1-Y_1(1\⊗{\hat{t}}_s)& \mathrm{...}& x_K-Y_K(1\⊗{\hat{t}}_s)\end{array}|{|}_F^2---\left(18\right)\end{array}$

In formula $Y_k=diag\left({\hat{x}}_{c,k}\right).$

The character long-pending according to Kronecker can obtain

$(1\⊗{\hat{t}}_s)=(1\⊗I_N)(1\⊗{\hat{t}}_s)---\left(19\right)$

I in formula _nfor the unit matrix of N × N dimension.

Formula (19) is substituted in formula (18), with season can obtain

$\begin{array}{cc}\underset{{\hat{t}}_s}{\min }& \left|\right|\begin{array}{ccc}{x}_1-Y_{1}P{\hat{t}}_s& \mathrm{...}& x_K-Y_{K}P{\hat{t}}_s\end{array}|{|}_F^2---\left(20\right)\end{array}$

According to the character of matrix F norm, can obtain

||A|| _F＝||vec(A)|| ₂(21)

In formula, vec () is matrix vector operator, to represent matrix by rearrangement to be a column vector.Formula (20) can equivalently representedly be

$\begin{array}{cc}\underset{{\hat{t}}_s}{\min }& \left|\right|\begin{array}{c}{x}_1-Z_1{\hat{t}}_s\\ .\\ .\\ .\\ x_K-Z_K{\hat{t}}_s\end{array}|{|}_2^2---\left(22\right)\end{array}$

Z in formula _k=Y _kp.

According to partitioned matrix multiplicative property, formula (22) is done and is suitably arranged and can obtain

$\begin{array}{cc}\underset{{\hat{t}}_s}{\min }& \left|\right|\left[\begin{array}{c}{x}_1\\ .\\ .\\ .\\ x_K\end{array}\right]-\left[\begin{array}{c}{Z}_1\\ .\\ .\\ .\\ Z_k\end{array}\right]{\hat{t}}_s|{|}_2^2---\left(23\right)\end{array}$

Formula (23) be one without constrained least-squares problem, corresponding solution is

${\hat{t}}_s={\left({\left[\begin{array}{c}{Z}_1\\ .\\ .\\ .\\ Z_k\end{array}\right]}^H\left[\begin{array}{c}{Z}_1\\ .\\ .\\ .\\ Z_k\end{array}\right]\right)}^{-1}{\left[\begin{array}{c}{Z}_1\\ .\\ .\\ .\\ Z_k\end{array}\right]}^H\left[\begin{array}{c}{x}_1\\ .\\ .\\ .\\ x_k\end{array}\right]---\left(24\right)$

Wherein the array element error will estimated exactly.

Advantage of the present invention further illustrates by emulated data experiment:

Emulation experiment parameter: radar carrier frequency is 1200MHz, pulse repetition rate is 2000Hz.Bay number is 10, and array element distance is 0.125m.Carrier aircraft height is 5km, and speed is 100m/s.Miscellaneous noise ratio is 50dB.In array element error, range error is 5%, and phase error is 5 °.Thresholding during evaluation order is set to 0.99.

Experiment content and interpretation of result: consider without decorrelation effect during emulation and have situations both decorrelation effect (non-ideal factor such as interior clutter moition, passage fluctuating causes), the mathematical model that the form of wherein clutter decorrelation proposes for Guerci and Bergin.In Fig. 3-Fig. 7, the figure (a) of its correspondence is the schematic diagram without decorrelation effect, and figure (b) is for there being the schematic diagram of decorrelation effect.Clutter data F norm fitting process invention technical scheme proposed in experiment and adjacent array element interferometric method, main-lobe clutter eigenvector method and clutter Orthogonal Subspaces method are analyzed.In literary composition with root-mean-square error (Root Mean Square Error, RMSE) for criterion weighs each method performance, corresponding form is

$RMSE={\[\frac{1}{L}\frac{1}{N}\underset{l=1}{\overset{L}{\Σ}}\underset{i=1}{\overset{N}{\Σ}}{({\widehat{\mathrm{\ρ}}}_i^l-{\mathrm{\ρ}}_i^l)}^2\]}^{1/2}---\left(25\right)$

In formula, L is Monte Carlo experiment number of times, and N is array element number, with be respectively the l time experiment, the amplitude of i-th array element or the estimated value of phase error and actual value.

Arranging pulse number in experiment one is 128, and analyze the relation of each method performance and distance sample number, acquired results as shown in Figure 3, Figure 4.Can find out when number of samples is less by Fig. 3, Fig. 4, clutter Orthogonal Subspaces method and F norm fitting process are better than adjacent array element interferometric method and main-lobe clutter eigenvector method.This is because adjacent array element interferometric method and main-lobe clutter eigenvector method are subject to noise bounce disturbance impact when number of samples is less is larger.It can also be seen that when there is decorrelation effect by Fig. 3, Fig. 4, F norm fitting process is better than clutter Orthogonal Subspaces method, this is because decorrelation effect can cause clutter subspace to be spread, thus clutter subspace is leaked to noise subspace, orthogonality between the two weakens, clutter Orthogonal Subspaces method hydraulic performance decline, and F norm fitting process is a kind of Parameterization estimate method based on norm matching, it utilizes data matrix itself instead of corresponding subspace to estimate array element error, makes its antithetical phrase spatial leaks problem have robustness.

Arranging distance sample number in experiment two is 100, and analyze the relation of each algorithm performance and transponder pulse number, acquired results as shown in Figure 5, Figure 6.Can find out that clutter Orthogonal Subspaces method and F norm fitting process are better than adjacent array element interferometric method and main-lobe clutter eigenvector method when pulse number is less by Fig. 5, Fig. 6.This is because when pulse number is less, DOPPLER RESOLUTION is lower, the doppler bandwidth that antenna main lobe is corresponding is larger.The main-lobe clutter that this and adjacent array element interferometric method and main-lobe clutter eigenvector are supposed is similar to this unmatched models of simple signal, and F norm fitting process is a kind of method based on original spatial-temporal data matching, have nothing to do with the quality of DOPPLER RESOLUTION, as long as clutter spectral line is accurate, it just can obtain good Parameter Estimation Precision.

Arranging pulse number in experiment three is 32, and distance sample number is 20, and the relation of thresholding η when analysis context of methods performance and evaluation order, acquired results as shown in Figure 7.As seen from Figure 7 when η changes between 0.99 ~ 0.998, algorithm performance change is little.This is because the singular value obtained after steering vector matrix V svd during sky is divided into principal singular value and time singular value two parts.Secondary singular value is the factor causing linear system numerical solution unsane.And the numerical value of secondary singular value is minimum, its proportion accounting for total singular value energy is less.η is set to the 0.99 or 0.998 numerical value order r calculated and changes little, therefore parameter estimation performance also relative held stationary.

The above; be only the specific embodiment of the present invention, but protection scope of the present invention is not limited thereto, is anyly familiar with those skilled in the art in the technical scope that the present invention discloses; change can be expected easily or replace, all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of described claim.

Claims (7)

1. based on an array element error estimation for clutter data associating matching, it is characterized in that, described method comprises the steps:

Step 1, the distribution parameter of the clutter that the clutter data that the model parameter of acquisition airborne radar and described airborne radar receive characterizes;

Step 2, according to the model parameter of described airborne radar and the distribution parameter of described clutter data, steering vector when to calculate when described airborne radar receives described clutter data empty;

Step 3, calculates the amplitude vector of reconstruct clutter data;

Step 4, according to the amplitude vector of described reconstruct clutter data, determines described reconstruct clutter data;

Step 5, the clutter data received by airborne radar and described reconstruct clutter data carry out the matching of F norm, estimate the array element error of described airborne radar.

2. the array element error estimation based on clutter data associating matching according to claim 1, is characterized in that, in step 1, the model parameter of airborne radar is:

The carrier aircraft speed of airborne radar is v, carrier aircraft velocity reversal is along X-axis positive dirction, carrier aircraft height is h, the aerial array of airborne radar is the uniform line-array be made up of N number of array element, array element distance is d, aerial array is axially along X-direction, and airborne radar launches M pulse in a coherent processing inteval, and pulse repetition rate is f _r, radar operation wavelength is λ;

The distribution parameter of the clutter that the clutter data that described airborne radar receives characterizes is:

Clutter is φ relative to the position angle of airborne radar, and clutter is θ relative to the angle of pitch of airborne radar, and clutter relative to the normalization Doppler frequency of airborne radar is clutter relative to the normalization spatial frequency of airborne radar is

3. the array element error estimation based on clutter data associating matching according to claim 1, is characterized in that, during empty when airborne radar described in step 2 receives described clutter data, steering vector comprises time domain steering vector v _t(w _d) and spatial domain steering vector v _s(w _s):

$v_t\left(w_d\right)={\left[\begin{array}{cc}1& e^{j2{\mathrm{\πw}}_d}...e^{j2\mathrm{\π}(M-1)w_d}\end{array}\right]}^T$

$v_s\left(w_s\right)={\left[\begin{array}{cc}1& e^{j2{\mathrm{\πw}}_s}...e^{j2\mathrm{\π}(M-1)w_s}\end{array}\right]}^T$

4. the array element error estimation based on clutter data associating matching according to claim 1, it is characterized in that, step 3 specifically comprises following sub-step:

(3a) to clutter data along orientation to sampling, obtaining one group of space-time two-dimensional frequency point set is $\left[\begin{array}{ccc}(w_d^1,w_s^1)& ...& (w_d^{N_c},w_s^{N_c})\end{array}\right];$

(3b) steering vector and described space-time two-dimensional frequency point set during empty when receiving described clutter data according to described airborne radar, when to obtain when described airborne radar receives described clutter data empty, guiding matrix V is $V=\left[\begin{array}{ccc}{v}_1(w_d^1,w_s^1)& ...& v_{N_c}(w_d^{N_c},w_s^{N_c})\end{array}\right];$

(3c) described reconstruct clutter data is expressed as

Wherein, for reconstruct clutter data matrix, for the complex magnitude matrix of reconstruct clutter matrix to be estimated, wherein k=1 ..., K, K are number of samples;

(3d) structure is about complex magnitude matrix optimization problem:

In formula || || _frepresent F norm, X=[x ₁..., x _k] the echo data matrix that receives for airborne radar;

(3e) solve described about complex magnitude matrix optimization problem, obtain estimate complex magnitude matrix thus obtain described reconstruct clutter data

5. the array element error estimation based on clutter data associating matching according to claim 4, is characterized in that, sub-step (3e) specifically comprises following sub-step:

(3e1) by described optimization problem expansion is expressed as $\begin{array}{cc}\underset{{\hat{a}}_1,...,{\hat{a}}_K}{min}& \begin{array}{ccc}\left|\right|x_1-V{\hat{a}}_1& ...& x_K-V{\hat{a}}_K|{|}_F^2,\end{array}\end{array}$ Thus described optimization problem is equivalent to K independently optimization problem $\begin{array}{cc}\underset{{\hat{a}}_k}{min}& \left|\right|x_k-V{\hat{a}}_k|{|}_2,k=1,...,K\end{array};$

(3e2) adopt the singular value decomposition method blocked to each optimization problem in described K independently optimization problem $\begin{array}{cc}\underset{{\hat{a}}_k}{min}& \left|\right|x_k-V{\hat{a}}_k|{|}_2,k=1,...,K\end{array}$ Solve, thus the solution obtaining each optimization problem is: ${\hat{a}}_k=\underset{i=1}{\overset{r}{\Σ}}\frac{u_i^H{x}_k}{{\mathrm{\σ}}_i}{w}_i,$

Wherein, u _ifor the left singular vector of guiding matrix V during described sky, w _ifor the right singular vector of guiding matrix V during described sky, σ _ifor the singular value of guiding matrix V during described sky, the numerical value order of guiding matrix V when r is described sky.

6. the array element error estimation based on clutter data associating matching according to claim 1, it is characterized in that, step 4 is specially:

According to the solution of each optimization problem described k=1 ..., K, the complex magnitude matrix that composition is estimated thus obtain described reconstruct clutter data

7. the array element error estimation based on clutter data associating matching according to claim 1, it is characterized in that, step 5 specifically comprises following sub-step:

(5a) described reconstruct clutter data is revised, obtain

Wherein, for taper vector, for array element error, diag () represents vector diagonalization;

(5b) clutter data received by airborne radar described in matching and revised reconstruct clutter data are estimated corresponding objective function is

(5c) described objective function is solved obtain array element error