CN103926572B - A kind of clutter suppression method of battle array radar self adaptation subspace, airborne anon-normal side - Google Patents

Abstract

The invention belongs to the field of radar technology, and discloses a clutter suppression method for an airborne non-frontal array radar using an adaptive subspace, which firstly estimates by fitting the clutter power spectrum estimated by echo data and the theoretical clutter curve For the unknown configuration parameters of the two-dimensional distribution curve of clutter, the LTS method is used in the fitting process to improve the robustness of parameter estimation, and then the estimated configuration parameters are used to calculate the clutter subspace, and then the data is transferred to the corresponding clutter subspace Orthogonal complement space for projection to suppress clutter. The simulation experiment results show that the parameter estimation method of the present invention is robust and accurate, and the weight vector calculated by using the estimated parameters can obtain better clutter suppression effect.

Description

An adaptive subspace clutter suppression method for airborne non-frontal array radar

technical field

The invention belongs to the field of radar technology, and relates to a method for suppressing clutter in an adaptive subspace for an airborne non-frontal array radar. The clutter subspace of the distance unit, and then project the data to the orthogonal complement space corresponding to the clutter subspace to suppress the clutter.

Background technique

The airborne radar is mainly in the working state of looking down, and it is inevitable to observe a lot of ground clutter. At the same time, due to the movement of the aircraft, the clutter spectrum is greatly expanded, and the traditional pulse Doppler technology is no longer effective. Space-time adaptive processing (spacetime adaptive processing, STAP) technology can effectively suppress ground clutter and improve the detection performance of moving targets. STAP technology usually selects the adjacent distance unit of the distance unit to be detected as the training sample to calculate the adaptive weight. When the training sample satisfies the independent identically distributed (IID) condition, the performance of adaptive processing gradually increases with the number of samples. converges to the optimum. In practice, in order to realize all-round search, airborne radar usually sets up multiple array antennas on the fuselage at the same time, and each antenna is responsible for a certain azimuth scanning. corner, the array is placed on the non-positive side. The non-positive side array structure will cause the Doppler characteristics of the clutter angle to change with the distance, so that the training samples no longer meet the independent and identical distribution conditions, which seriously affects the estimation accuracy of the covariance matrix and reduces the performance of space-time adaptive processing.

For the non-stationary problem of clutter angle Doppler characteristics changing with distance (that is, clutter distance non-stationarity), domestic and foreign scholars have proposed a variety of solutions. Zatman proposed a derivative-based updating method (derivative-basedupdating, DBU), which assumes that the weight vector is a function of the distance, but when the clutter distance is very non-stationary, the above assumption is no longer valid. Melvin and Davis proposed an angle Doppler compensation method (angledoppler compensation, ADW), which compensates the center of the main lobe clutter, but the compensation for the side lobe clutter is not very ideal. Ries and Lapierre proposed a registration-based compensation method (registration-based compensation, RBC), which is based on the clutter distribution curve and performs registration processing on the clutter power spectra of different distance units to solve the problem of non-stationary range of clutter , but it is difficult to determine the mapping relationship of different distance unit curves during registration. Friedlander et al. proposed an algorithm based on the clutter subspace. This method directly uses the configuration parameters of the clutter two-dimensional distribution curve to calculate the clutter subspace of the range unit to be detected, and then transfers the echo data to the orthogonal complement space corresponding to the clutter subspace. Projection to suppress the clutter component. This method does not need to use training samples and avoids the non-stationary problem of samples changing with distance. However, the calculation of the clutter subspace needs to use the configuration parameters of the two-dimensional distribution curve of the clutter, and the configuration parameters of the two-dimensional distribution curve of the clutter are related to the parameters of the radar system and the movement parameters of the aircraft. Know.

Contents of the invention

Aiming at the problem that the clutter distance non-stationarity of airborne non-frontal array radar and the subspace method need to utilize the configuration parameters of the two-dimensional distribution curve of clutter, the purpose of the present invention is to provide an airborne non-frontal array radar. The adaptive subspace clutter suppression method does not need to use training samples and has excellent clutter suppression performance.

In order to achieve the above object, the present invention adopts the following technical solutions to achieve.

A kind of clutter suppressing method for airborne non-frontal array radar with self-adaptive subspace, it is characterized in that, comprises the following steps:

Step 1, establish the signal model of the airborne non-frontal array radar, where the operating wavelength of the radar is λ, M pulses are transmitted within the coherent processing interval, the pulse repetition frequency is f _r , and the antenna array is an equidistant line composed of N array elements The distance between array elements is d, the height of the carrier aircraft is H, the speed of the carrier aircraft is v, the angle between the direction of the carrier speed direction and the axis of the antenna array is ψ, and the pitch angle and azimuth angle of the ground clutter scatterer are θ and , the slant distance between the carrier aircraft and the ground clutter scatterer is R;

Its echo signal can be expressed as

$x=x_c+\mathrm{no}=\underset{l=1}{\overset{N_c}{\mathrm{\Σ}}}{\mathrm{\α}}_l{u}_l+\mathrm{no}$ l=1,2…N _c

where n is the noise component, x _c is the clutter component, N _c is the number of independent clutter blocks in the ground clutter ring with a slant distance of R, α _l is the amplitude of the lth clutter block in the clutter ring, and Different clutter blocks are independent of each other, u _l is the space-time steering vector of the lth clutter block in the clutter ring;

The clutter two-dimensional distribution curve of its clutter ring is

${<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&psi;</span>}}{\mathrm{<span\; class="notranslate">\; vd</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; cos</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}{\mathrm{<span\; class="notranslate">\; sin</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&psi;</span>}$

The simplified function expression of the above formula

C= _Γ (η(λ,d,fr ,v,ψ,θ))

In the formula, C is the clutter curve, Γ is the operator for calculating the two-dimensional distribution curve of clutter through the parameter vector, and η is the parameter vector of the two-dimensional distribution curve of clutter, where in the parameter vector η of the two-dimensional distribution curve of clutter, λ , d, f _r are known parameters of radar system, v, ψ, θ are unknown quantities;

Step 2, discretize the echo signal on the Angle Doppler plane, and then perform weighted two-dimensional Fourier transform in the space domain and time domain to obtain the Fourier spectrum P _b , and then take the square of the absolute value of the Fourier spectrum P _b to obtain the corresponding noise wave power spectrum;

Set the first threshold, filter out the grid cells outside the two-dimensional distribution curve of clutter, and use the grid cells on the two-dimensional distribution curve of clutter to construct a search submatrix According to the fact that the complex amplitude γ of the echo signal on the grid cell corresponding to the angle Doppler plane has sparse characteristics, the sparse algorithm $\begin{array}{c}\min {\left|\right|\mathrm{\&gamma;}\left|\right|}_1,\\ \mathrm{the\; s}.t.{\left|\right|x-\widetilde{\mathrm{\&Phi;\&gamma;}}\left|\right|}_2^2\&le;\mathrm{\&epsiv;}\end{array}$ Solve the complex amplitude γ of the grid unit on the two-dimensional distribution curve of clutter, where |||| _p represents the L _p norm, and ε represents the error limit of the sparse algorithm solution, which is the set value;

According to the complex amplitude γ of the grid unit on the two-dimensional distribution curve of clutter, set the second threshold, filter out the secondary grid units with smaller amplitude |γ _i | on the two-dimensional distribution curve of clutter, and obtain the power reflecting the clutter The spectral distribution is in a typical grid cell corresponding to the space-time two-dimensional plane distribution;

Step 3, the two-dimensional distribution curve of clutter for the clutter ring

${<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&psi;</span>}}{\mathrm{<span\; class="notranslate">\; vd</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; cos</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}{\mathrm{<span\; class="notranslate">\; sin</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&psi;</span>}$

Carry out transformation and arrangement, and write it in vector form as y=a ^T β, where β=[1/v ² cosψ/vsin ² ψcos ² θ]T, a=[(f _r λw _d /2) ² -λ ₂ f _r w _s w _d /d-1] ^T , Among them, β is related to the unknown parameters v, ψ, and θ in η, and a, y are related to the known parameters λ, d, f _r in η and the space-time two-dimensional frequency of clutter; T represents the transpose operation.

Then, substituting the space-time two-dimensional frequencies and known configuration parameters of P2 typical grid cells exceeding the second threshold obtained in step 2 into a, y of y=a ^T β, the following equations can be obtained

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}$

In the formula, P2 grid cells correspond to the measured value of y $\widehat{\mathrm{the\; y}}={\left[\begin{array}{ccc}{\widehat{\mathrm{the\; y}}}_1& ...& {\widehat{\mathrm{the\; y}}}_P\end{array}\right]}^T$ is the P2×1-dimensional response vector, the measured value of a corresponding to P2 typical grid cells $\hat{A}={\left[\begin{array}{ccc}{\hat{a}}_1& ...& {\hat{a}}_{N_p}\end{array}\right]}^T$ is a measurement matrix of P2×3 dimension, ξ is an error vector of P2×1 dimension, and is a set value;

Step 4, using the least intercept squares method to solve the system of equations obtained in step 3 Get an estimate of β Then solve the estimated values corresponding to the configuration parameters v, ψ, and θ of the two-dimensional distribution curve of clutter

Step 5, using the configuration parameters of the estimated two-dimensional distribution curve of clutter With the known parameters λ, d, f _r , calculate the corresponding clutter space-time steering vector matrix of the clutter two-dimensional distribution curve Subspace Orthographic Projection Operator And filter weight vector W;

Step 6: Construct a corresponding space-time filter according to the filter weight vector W to suppress the clutter in the echo signal X, and obtain the final Doppler spectrum of the current clutter block after clutter suppression: Z=W ^H X.

Specifically, use the k-th Doppler channel filter weight vector W _k to construct a corresponding space-time filter to suppress the clutter in the echo signal X, and obtain the output of the current clutter block and the k-th Doppler channel for: k=1,2...K, K is the number of Doppler channels, H represents the conjugate transpose operation; get the final Doppler spectrum of the current clutter block after clutter suppression: Z=[Z ₁ ,Z ₂ ,… ,Z _K ] ^T , T represents the transpose operation.

The features and further improvements of the technical solution of the present invention are:

(1) The specific sub-steps of step 2 are:

2a) Discretize the angular Doppler plane, the number of grid cells corresponding to the Doppler frequency is N _d , and the number of grid cells corresponding to the spatial frequency is N _s ;

Establish a space-time steering vector search matrix Φ based on the grid cells in the clutter block, the specific form $\mathrm{\&Phi;}=[u(w_{d,1},w_{\mathrm{the\; s},1}),...,u(w_{d,i},w_{\mathrm{the\; s},j}),...u(w_{d,N_d},w_{\mathrm{the\; s},N_{\mathrm{the\; s}}})],$ where i=1,…N _d ; j=1,…N _s in u(w _d,i ,w _s,j ) represents the space-time two-dimensional frequency of the grid unit whose coordinates are (i,j), namely In the formula is the Kronecker product, where u _t (w _{d, i} ) and u _s (w _{s, j} ) are the time-domain steering vector and the spatial-domain steering vector of the grid cell with coordinates (i, j) in the clutter block, respectively;

Then the echo signal X is expressed as X=Φγ, is the complex amplitude of the echo signal on the grid cell corresponding to the angle Doppler plane, where T represents the transpose operation;

2b) Perform weighted two-dimensional Fourier transform in the spatial domain and time domain on the angular Doppler plane discretized echo signal, in the form of where P _b is the Fourier spectrum, t _w is the weighting coefficient in the space domain and time domain, is the Hadamard product to get the Fourier spectrum P _b ;

2c) Taking the square of the absolute value of the Fourier spectrum _Pb obtained after the two-dimensional Fourier transform in the weighted space domain and time domain to obtain the corresponding clutter power spectrum, and performing the first threshold detection on it, and detecting that the power exceeds the first threshold P1 grid cells with value TH1, the corresponding space-time two-dimensional frequency is $\left[\begin{array}{ccc}u(w_{d,1}^1,w_{\mathrm{the\; s},1}^1)& ...& u(w_{d,P1}^1,w_{\mathrm{the\; s},P1}^1)\end{array}\right]$ Superscript 1 means passing the first threshold TH1; and build a search submatrix $\widetilde{\mathrm{\&Phi;}}=\left[\begin{array}{ccc}u(w_{d,1}^1,w_{\mathrm{the\; s},1}^1)& ...& u(w_{d,P1}^1,w_{\mathrm{the\; s},P1}^1)\end{array}\right],$ It is a subset of the search matrix Φ;

2d) The complex amplitude γ of the echo signal on the grid cell corresponding to the angle Doppler plane has a sparse characteristic, and the sparse algorithm $\begin{array}{c}\min {\left|\right|\mathrm{\&gamma;}\left|\right|}_1,\\ \mathrm{the\; s}.t.{\left|\right|x-\widetilde{\mathrm{\&Phi;\&gamma;}}\left|\right|}_2^2\&le;\mathrm{\&epsiv;}\end{array}$ Solve the complex amplitude γ on the estimation unit, where |||| _p represents the L _p norm, and ε represents the error limit of the sparse algorithm solution, which is the set value;

2e) After estimating the amplitude of the complex amplitude γ on the grid unit, according to the amplitude |γ _i |≥TH2, i=1,...N _d N _s , where TH2 is the set second threshold value, Filter out the secondary grid units with smaller amplitude |γ _i | on the two-dimensional distribution curve of clutter, and obtain the typical grid unit reflecting the power spectrum distribution of clutter in the corresponding space-time two-dimensional plane distribution;

2f) The space-time two-dimensional frequency corresponding to the detected P2 typical grid units is

$\left[\begin{array}{ccc}u(w_{d,1}^2,w_{\mathrm{the\; s},1}^2)& ...& u(w_{d,P2}^2,w_{\mathrm{the\; s},P2}^2)\end{array}\right],$ Superscript 2 means passing through the second threshold TH2; the distribution of typical grid cells in the space-time two-dimensional plane reflects the power spectrum distribution of clutter.

(2) The specific sub-steps of step 4 are:

4a) Solve the optimization problem using the least intercept squares method

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; min</span>}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; P</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; .</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; Q</span>}\\ {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; 0,1</span>}<span\; class="notranslate">\; \}</span>\end{array}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

In the formula, z _i represents the flag bit, z _i =1 indicates that the data is a normal point, z _i =0 indicates that the data is an interference point, e represents a vector of all 1s, Q is the number of non-zero elements in z, and Q<P;

4b) Solve the above optimization problem to get the estimated value of β Then calculate the estimated values corresponding to v, ψ, and θ respectively Its calculation formula is as follows

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\sqrt{{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; LTS</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}$

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arccos</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; LTS</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\sqrt{{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; LTS</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>$

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arccos</span>}\sqrt{{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; LTS</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; LTS</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\sqrt{{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; LTS</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}$

(3) The specific sub-steps of step 5 are:

5a) The estimated configuration parameters that will be obtained and the known parameters λ, d, f _r , substitute into the normalized Doppler frequency and the normalized spatial frequency , get the estimated time-domain steering vector corresponding to the lth clutter block $u_t\left({\hat{w}}_{d,l}\right)={\left[\begin{array}{cc}1& e^{j2\mathrm{\&pi;}{\hat{w}}_{d,l}}...e^{j2\mathrm{\&pi;}(m-1){\hat{w}}_{d,l}}\end{array}\right]}^T$ and the airspace steering vector $u_{\mathrm{the\; s}}\left({\hat{w}}_{\mathrm{the\; s},l}\right)={\left[\begin{array}{cc}1& e^{j2\mathrm{\&pi;}{\hat{w}}_{\mathrm{the\; s},l}}...e^{j2\mathrm{\&pi;}(N-1){\hat{w}}_{\mathrm{the\; s},l}}\end{array}\right]}^T,$ Then the estimated space-time steering vector corresponding to the lth clutter block is ${\hat{V}}_{c,l}=u_t\left({\hat{w}}_{d,l}\right)\&CircleTimes;u_{\mathrm{the\; s}}\left({\hat{w}}_{\mathrm{the\; s},l}\right),$ Estimated clutter space-time steering vector matrix ${\hat{V}}_c=[{\hat{V}}_{c,1},...{\hat{V}}_{c,l,}...{\hat{V}}_{c,N_c}],$ l=1,2,…N _c , where Product for Kronecker;

5b) Calculate the projection operator orthogonal to the clutter subspace according to the following formula

${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; \&perp;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{<span\; class="notranslate">\; (</span>{{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&mu;I</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}$

where μ is a positive number to ensure that the matrix Reversible; ⊥ means orthogonal projection operator, Η means conjugate transpose operation, () ^-1 means matrix inversion, I means identity matrix;

5c) Utilize the target space-time steering vector That is, s=[s ₁ ,s ₂ ,…,s _k ,…s _K ] and the projection operator estimated in step 5b is orthogonal to the clutter subspace Calculate the filter weight vector of the space-time filter of the kth Doppler channel k=1,2...K, K is the number of Doppler channels. filter weight vector

in $u_{\mathrm{tar}}\left(w_d\right)={\left[\begin{array}{cc}1& e^{j2\mathrm{\&pi;}{w}_d}...e^{j2\mathrm{\&pi;}(m-1)w_d}\end{array}\right]}^T$ is the time-domain steering vector of the target, $u_{\mathrm{tar}}\left(w_{\mathrm{the\; s}}\right)={\left[\begin{array}{cc}1& e^{j2\mathrm{\&pi;}{w}_{\mathrm{the\; s}}}...e^{j2\mathrm{\&pi;}(N-1)w_{\mathrm{the\; s}}}\end{array}\right]}^T$ is the airspace steering vector of the target, where the normalized Doppler frequency normalized spatial frequency v represents the speed of the target; θ ₀ represents the pitch angle of the main beam, Indicates the azimuth angle of the main beam, and ψ indicates the angle between the velocity direction of the carrier aircraft and the axis of the antenna array.

The clutter suppression method for airborne non-frontal array radar with self-adaptive subspace first estimates the unknown structure of the clutter two-dimensional distribution curve by fitting the clutter power spectrum estimated from the echo data and the theoretical clutter curve In the fitting process, the LTS method is used to improve the robustness of parameter estimation, and then the estimated configuration parameters are used to calculate the clutter subspace, and then the data is projected to the orthogonal complement space corresponding to the clutter subspace to suppress the clutter. Wave. The simulation experiment results show that the parameter estimation method of the present invention is robust and accurate, and the weight vector calculated by using the estimated parameters can obtain better clutter suppression effect.

In practice, due to the accuracy of inertial navigation and the lack of terrain elevation knowledge, the configuration parameters of the two-dimensional distribution curve of clutter will be inaccurate. At this time, it is necessary to use the received echo data to estimate these unknown configuration parameters. Since the trajectory of the power spectrum of the clutter on the angular Doppler plane is determined by the two-dimensional distribution curve of the clutter, the present invention estimates the corresponding configuration parameters by fitting the power spectrum of the clutter and the two-dimensional distribution curve of the clutter.

In order to reduce the spread of the power spectrum of the clutter, the present invention utilizes the sparsity of the clutter in the angle Doppler plane, and uses a sparse algorithm to estimate the power spectrum of the echo data. In fact, there are not only clutter signals in radar echo data, but also target signals (main lobe target or side lobe target). When the signal-to-noise ratio of the target signal is large, the grid cells corresponding to the angular Doppler plane of the target will also pass the threshold detection after being solved by the sparse algorithm. These target points are interference points, which will seriously affect the parameter estimation accuracy of the least squares (LS) method; in order to solve this problem, the present invention uses the least trimmed squares (LTS) method instead of the LS method to solve the problem.

In the present invention, the unknown configuration parameters of the two-dimensional distribution curve of the clutter are estimated by fitting the power spectrum estimated by the echo data and the theoretical clutter curve, and the LTS method is used in the fitting process to improve the accuracy of parameter estimation and robustness.

In the present invention, the configuration parameters are directly used to calculate the clutter subspace of the unit to be detected, and then the data is projected to the orthogonal complement space corresponding to the clutter subspace to suppress the clutter component. This method does not need to use training samples and avoids the problem of non-stationary samples.

Description of drawings

The present invention will be described in further detail below in conjunction with the accompanying drawings and specific embodiments.

Fig. 1 is a flow chart of airborne non-frontal array radar clutter suppression in the present invention.

Fig. 2 is a geometric structure diagram of the airborne radar of the present invention.

Figure 3a is a schematic diagram of the fitting results of the real clutter curve and the least squares (LS) and least truncated squares (LTS) of the present invention when there is no interference point; the abscissa indicates the normalized Doppler frequency, and the ordinate indicates the normalized the spatial frequency.

Figure 3b is a schematic diagram of the fitting results of the real clutter curve and least squares (LS) and least truncated squares (LTS) in the presence of interference points in the present invention; the abscissa represents the normalized Doppler frequency, and the ordinate represents normalization the spatial frequency.

Fig. 4 is optimal processing, sampling covariance, SNR loss curve schematic diagram of the inventive method (adaptive subspace); Abscissa represents normalized Doppler frequency, and ordinate represents SNR loss (dB ).

detailed description

With reference to Fig. 1, illustrate that airborne non-positive side array radar of the present invention uses the clutter suppressing method of adaptive subspace, its concrete steps are as follows:

Step 1. Establish the airborne non-frontal array radar signal model, and the two-dimensional clutter distribution curve of its clutter ring

${<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&psi;</span>}}{\mathrm{<span\; class="notranslate">\; vd</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; cos</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}{\mathrm{<span\; class="notranslate">\; sin</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&psi;</span>}$

The simplified function expression of the above formula

C= _Γ (η(λ,d,fr ,v,ψ,θ))

In the formula, C is the clutter curve, Γ is the operator for calculating the two-dimensional distribution curve of clutter through the parameter vector, and η is the parameter vector of the two-dimensional distribution curve of clutter, where in the parameter vector η of the two-dimensional distribution curve of clutter, λ , d, f _r are known parameters of the radar system, v, ψ, θ are unknown quantities.

The specific example is as follows: Among them, the structure of the airborne non-frontal array radar is shown in Figure 2, the radar operating wavelength is λ, M pulses are transmitted in the coherent processing interval, the pulse repetition frequency is f _r , and the antenna array is N arrays An equidistant linear array composed of elements, the distance between the array elements is d, the height of the aircraft is H, the speed of the aircraft is v, the angle between the speed direction of the aircraft and the axis of the antenna array is ψ, the pitch angle of the ground clutter scatterer and The azimuth angles are θ and The slant distance between the carrier aircraft and the ground clutter scatterer is R. According to the above signal model, the echo signal can be expressed as

$x=x_c+\mathrm{no}=\underset{l=1}{\overset{N_c}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_l{u}_l+\mathrm{no}$ l=1,2…N _c

where n is the noise component, x _c is the clutter component, N _c is the number of independent clutter blocks in the ground clutter ring with a slant distance of R, α _l is the amplitude of the lth clutter block in the clutter ring, and Different clutter blocks are independent of each other, u _l is the space-time steering vector of the lth clutter block in the clutter ring.

Without loss of generality, the space-time steering vector of a clutter block can be expressed as

$\mathrm{<span\; class="notranslate">\; u</span>}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; ,</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; \&CircleTimes;</span>{\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span>$

In the formula is the Kronecker product, u _t (w _d ) and u _s (w _s ) are the time-domain steering vector and the spatial-domain steering vector of the clutter block, respectively;

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; t</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}& {\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}}\end{array}\right]}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

${\mathrm{<span\; class="notranslate">\; u</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; (</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; =</span>{\left[\begin{array}{cc}\mathrm{<span\; class="notranslate">\; 1</span>}& {\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}<span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span><span\; class="notranslate">\; .</span>{\mathrm{<span\; class="notranslate">\; e</span>}}^{\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; \&pi;</span>}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}}\end{array}\right]}^{\mathrm{<span\; class="notranslate">\; T</span>}}$

In the formula is the normalized Doppler frequency, To normalize the spatial frequency, T represents the transpose operation.

The two-dimensional distribution curve of the clutter ring in the angle Doppler domain can be obtained by transforming the relationship between w _d and w _s :

${<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&psi;</span>}}{\mathrm{<span\; class="notranslate">\; vd</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; cos</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}{\mathrm{<span\; class="notranslate">\; sin</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&psi;</span>}$

At this time, the two-dimensional clutter distribution curve of any clutter ring can be expressed as

C= _Γ (η(λ,d,fr ,v,ψ,θ))

In the formula, C is the clutter curve, Γ is the operator for calculating the two-dimensional distribution curve of clutter through the parameter vector, and η is the parameter vector of the two-dimensional distribution curve of clutter, where in the parameter vector η of the two-dimensional distribution curve of clutter, λ , d, f _r are known parameters of the radar system, v, ψ, θ are unknown quantities.

Step 2, discretize the echo signal on the Angle Doppler plane, and then perform weighted two-dimensional Fourier transform in the space domain and time domain to obtain the Fourier spectrum P _b , and then take the square of the absolute value of the Fourier spectrum P _b to obtain the corresponding noise wave power spectrum;

Set the first threshold, filter out the grid cells outside the two-dimensional distribution curve of clutter, and use the grid cells on the two-dimensional distribution curve of clutter to construct a search submatrix According to the fact that the complex amplitude γ of the echo signal on the grid cell corresponding to the angle Doppler plane has sparse characteristics, the sparse algorithm $\begin{array}{c}\min {\left|\right|\mathrm{\&gamma;}\left|\right|}_1,\\ \mathrm{the\; s}.t.{\left|\right|x-\widetilde{\mathrm{\&Phi;\&gamma;}}\left|\right|}_2^2\&le;\mathrm{\&epsiv;}\end{array}$ Solve the complex amplitude γ of the grid unit on the two-dimensional distribution curve of clutter, where |||| _p represents the L _p norm, and ε represents the error limit of the sparse algorithm solution, which is the set value;

According to the complex amplitude γ of the grid unit on the two-dimensional distribution curve of clutter, set the second threshold, filter out the secondary grid units with smaller amplitude |γ _i | on the two-dimensional distribution curve of clutter, and obtain the power reflecting the clutter The spectral distribution is in a typical grid cell corresponding to a space-time two-dimensional planar distribution.

The specific sub-steps are described as follows:

2a) The angular Doppler plane is discretized, the number of grid cells corresponding to the Doppler frequency is N _d , and the number of grid cells corresponding to the spatial frequency is N _s .

Establish a space-time steering vector search matrix Φ based on the grid cells in the clutter block, the specific form $\mathrm{\&Phi;}=[u(w_{d,1},w_{\mathrm{the\; s},1}),...,u(w_{d,i},w_{\mathrm{the\; s},j}),...u(w_{d,N_d},w_{\mathrm{the\; s},N_{\mathrm{the\; s}}})],$ where i=1,…N _d ; j=1,…N _s in u(w _d,i ,w _s,j ) represents the space-time two-dimensional frequency of the grid unit whose coordinates are (i,j), namely In the formula is the Kronecker product, where u _t (w _{d, i} ) and u _s (w _{s, j} ) are the time-domain steering vector and the spatial-domain steering vector of the grid cell with coordinates (i, j) in the clutter block, respectively.

Then the echo signal X can be expressed as X=Φγ, is the complex amplitude of the echo signal on the grid cell corresponding to the angular Doppler plane, where T represents the transpose.

2b) Perform weighted two-dimensional Fourier transform in the spatial domain and time domain on the angular Doppler plane discretized echo signal, in the form of where P _b is the Fourier spectrum, t _w is the weighting coefficient in the space domain and time domain, For the Hadamard product, the Fourier spectrum P _b is obtained.

2c) Take the square of the absolute value of the Fourier spectrum _Pb obtained after the two-dimensional Fourier transform in the space domain and time domain to obtain the corresponding clutter power spectrum, and perform the first threshold detection on it, assuming that there are a total of P1 grid units detected The power exceeds the first threshold value TH1, TH1 is the set first threshold value, generally set to 5-10dB. Take 8dB in the simulation experiment.

The space-time two-dimensional frequencies corresponding to these grid cells are $\left[\begin{array}{ccc}u(w_{d,1}^1,w_{\mathrm{the\; s},1}^1)& ...& u(w_{d,P1}^1,w_{\mathrm{the\; s},P1}^1)\end{array}\right],$ A superscript 1 indicates passing the first threshold TH1.

Build a new search submatrix from these grid cells $\widetilde{\mathrm{\&Phi;}}=\left[\begin{array}{ccc}u(w_{d,1}^1,w_{\mathrm{the\; s},1}^1)& ...& u(w_{d,P1}^1,w_{\mathrm{the\; s},P1}^1)\end{array}\right],$ It is a subset of the search matrix Φ.

2d) Since the power spectrum of the clutter is distributed along the two-dimensional distribution curve of the clutter, and the clutter component occupies the main component in the echo signal relative to the noise component. This means that the estimated power spectrum only has large amplitudes on a few grid cells near the clutter two-dimensional distribution curve, while the amplitudes on other grid cells are small and close to zero.

That is, the complex amplitude γ of the echo signal on the grid unit corresponding to the angle Doppler plane has a sparse characteristic, so it can be obtained through the sparse algorithm $\begin{array}{c}\min {\left|\right|\mathrm{\&gamma;}\left|\right|}_1,\\ \mathrm{the\; s}.t.{\left|\right|x-\mathrm{\&Phi;\&gamma;}\left|\right|}_2^2\&le;\mathrm{\&epsiv;}\end{array}$ Solve the complex amplitude γ on the grid unit, where |||| _p represents the L _p norm, and ε represents the error limit of the sparse algorithm solution, which is the set value.

In order to reduce the amount of computation, the search sub-matrix obtained in 2c) is used Instead of Φ in the sparse algorithm, the improved sparse algorithm is $\begin{array}{c}\min {\left|\right|\mathrm{\&gamma;}\left|\right|}_1,\\ \mathrm{the\; s}.t.{\left|\right|x-\widetilde{\mathrm{\&Phi;\&gamma;}}\left|\right|}_2^2\&le;\mathrm{\&epsiv;}\end{array}.$

2e) After estimating the amplitude of the complex amplitude γ on the grid unit, extract the large amplitude component |γ _i |≥TH2 according to the threshold criterion, i=1,...N _d N _s , where TH2 is set The second threshold value is generally 10-20dB, and the simulation experiment takes 16dB.

In this way, we filter out the minor grid units with smaller amplitude |γ _i | on the two-dimensional distribution curve of clutter, and obtain typical grid units that reflect the power spectrum distribution of clutter in the corresponding space-time two-dimensional plane distribution.

2f) Assuming that the amplitude |γ _i | of P2 typical grid units is detected to exceed the second threshold value TH2, the space-time two-dimensional frequency corresponding to these typical grid units is $\left[\begin{array}{ccc}u(w_{d,1}^2,w_{\mathrm{the\; s},1}^2)& ...& u(w_{d,P2}^2,w_{\mathrm{the\; s},P2}^2)\end{array}\right],$ The superscript 2 indicates passing the second threshold TH2. The distribution of these typical grid units in the space-time two-dimensional plane reflects the power spectrum distribution of clutter.

Step 3, the two-dimensional distribution curve of clutter for the clutter ring

${<span\; class="notranslate">\; (</span>\frac{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{<span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}{\mathrm{<span\; class="notranslate">\; 2</span>}\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&lambda;</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; r</span>}}\mathrm{<span\; class="notranslate">\; cos</span>}\mathrm{<span\; class="notranslate">\; \&psi;</span>}}{\mathrm{<span\; class="notranslate">\; vd</span>}}<span\; class="notranslate">\; )</span>{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}{\mathrm{<span\; class="notranslate">\; w</span>}}_{\mathrm{<span\; class="notranslate">\; d</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; cos</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&theta;</span>}{\mathrm{<span\; class="notranslate">\; sin</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\mathrm{<span\; class="notranslate">\; \&psi;</span>}$

Carry out transformation and arrangement, and write it in vector form as y=a ^T β, where β=[1/v ² cosψ/vsin ² ψcos ² θ] ^T , a=[(f _r λw _d /2) ² -λ ² f _r w _s w _d /d-1] ^T , Among them, β is related to the unknown parameters v, ψ, and θ in η, and a, y are related to the known parameters λ, d, f _r in η and the space-time two-dimensional frequency of clutter;

Then, substituting the space-time two-dimensional frequencies and known configuration parameters of P2 typical grid cells exceeding the second threshold obtained in step 2 into a, y of y=a ^T β, the following equations can be obtained

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; A</span>}}\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&xi;</span>}$

In the formula, P2 grid cells correspond to the measured value of y $\widehat{\mathrm{the\; y}}={\left[\begin{array}{ccc}{\widehat{\mathrm{the\; y}}}_1& ...& {\widehat{\mathrm{the\; y}}}_P\end{array}\right]}^T$ is the P2×1-dimensional response vector, the measured value of a corresponding to P2 typical grid cells $\hat{A}={\left[\begin{array}{ccc}{\hat{a}}_1& ...& {\hat{a}}_{N_p}\end{array}\right]}^T$ is a P2×3-dimensional measurement matrix, ξ is a P2×1-dimensional error vector, and is a set value.

Step 4, using the least intercept squares method to solve the system of equations obtained in step 3 Get an estimate of β Then solve the estimated values corresponding to the configuration parameters v, ψ, and θ of the two-dimensional distribution curve of clutter value.

The specific sub-steps are described as follows:

4a) LTS is a robust regression method that can be formulated as the following optimization problem

$\begin{array}{c}\mathrm{<span\; class="notranslate">\; min</span>}\underset{\mathrm{<span\; class="notranslate">\; i</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{\overset{\mathrm{<span\; class="notranslate">\; P</span>}}{\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}}}{\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}{<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; the\; y</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; a</span>}}}_{\mathrm{<span\; class="notranslate">\; i</span>}}\mathrm{<span\; class="notranslate">\; \&beta;</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}\\ \mathrm{<span\; class="notranslate">\; the\; s</span>}<span\; class="notranslate">\; .</span>\mathrm{<span\; class="notranslate">\; t</span>}<span\; class="notranslate">\; .</span>{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; T</span>}}\mathrm{<span\; class="notranslate">\; e</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; Q</span>}\\ {\mathrm{<span\; class="notranslate">\; z</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; \&Element;</span><span\; class="notranslate">\; \{</span>\mathrm{<span\; class="notranslate">\; 0,1</span>}<span\; class="notranslate">\; \}</span>\end{array}$

In the formula, z _i represents the flag bit, z _i =1 indicates that the data is a normal point, z _i =0 indicates that the data is an interference point, e represents a vector of all 1s, Q represents the number of non-zero elements in z, and Q< p.

4b) Solve the above optimization problem to get the estimated value of β In turn, the estimated values corresponding to v, ψ, and θ can be calculated separately Its calculation formula is as follows

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; v</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; /</span>\sqrt{{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; LTS</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}$

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&psi;</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arccos</span>}<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; LTS</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\sqrt{{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; LTS</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>$

$\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&theta;</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; arccos</span>}\sqrt{{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; LTS</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; -</span>{<span\; class="notranslate">\; (</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; LTS</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 2</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span>\sqrt{{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; \&beta;</span>}}}_{\mathrm{<span\; class="notranslate">\; LTS</span>}}<span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 1</span>}<span\; class="notranslate">\; )</span>}<span\; class="notranslate">\; )</span>}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; )</span>}$

Step 5, using the configuration parameters of the estimated two-dimensional distribution curve of clutter With the known parameters λ, d, f _r , calculate the corresponding clutter space-time steering vector matrix of the clutter two-dimensional distribution curve Subspace Orthographic Projection Operator And filter weight vector W.

The specific sub-steps are described as follows:

5a) The estimated configuration parameters that will be obtained and the known parameters λ, d, f _r , substitute into the normalized Doppler frequency and the normalized spatial frequency , get the estimated time-domain steering vector corresponding to the lth clutter block $u_t\left({\hat{w}}_{d,l}\right)={\left[\begin{array}{cc}1& e^{j2\mathrm{\&pi;}{\hat{w}}_{d,l}}...e^{j2\mathrm{\&pi;}(m-1){\hat{w}}_{d,l}}\end{array}\right]}^T$ and the airspace steering vector $u_{\mathrm{the\; s}}\left({\hat{w}}_{\mathrm{the\; s},l}\right)={\left[\begin{array}{cc}1& e^{j2\mathrm{\&pi;}{\hat{w}}_{\mathrm{the\; s},l}}...e^{j2\mathrm{\&pi;}(N-1){\hat{w}}_{\mathrm{the\; s},l}}\end{array}\right]}^T,$ Then the estimated space-time steering vector corresponding to the lth clutter block is ${\hat{V}}_{c,l}=u_t\left({\hat{w}}_{d,l}\right)\&CircleTimes;u_{\mathrm{the\; s}}\left({\hat{w}}_{\mathrm{the\; s},l}\right),$ Estimated clutter space-time steering vector matrix ${\hat{V}}_c=[{\hat{V}}_{c,1},...{\hat{V}}_{c,l,}...{\hat{V}}_{c,N_c}],$ l=1,2,…N _c , where Product for Kronecker;

5b) Calculate the projection operator orthogonal to the clutter subspace according to the following formula

${\mathrm{<span\; class="notranslate">\; P</span>}}_{\mathrm{<span\; class="notranslate">\; c</span>}}^{<span\; class="notranslate">\; \&perp;</span>}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; I</span>}<span\; class="notranslate">\; -</span>{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}{<span\; class="notranslate">\; (</span>{{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&mu;I</span>}<span\; class="notranslate">\; )</span>}^{<span\; class="notranslate">\; -</span>\mathrm{<span\; class="notranslate">\; 1</span>}}{{\stackrel{<span\; class="notranslate">\; ^</span>}{\mathrm{<span\; class="notranslate">\; V</span>}}}_{\mathrm{<span\; class="notranslate">\; c</span>}}}^{\mathrm{<span\; class="notranslate">\; h</span>}}$

where μ is a positive number to ensure that the matrix Reversible; ⊥ means orthogonal projection operator, Η means conjugate transpose operation, () ^-1 means matrix inversion, I means identity matrix;

5c) Utilize the target space-time steering vector That is, s=[s ₁ ,s ₂ ,…,s _k ,…s _K ] and the projection operator estimated in step 5b is orthogonal to the clutter subspace Calculate the filter weight vector of the space-time filter of the kth Doppler channel k=1,2...K, K is the number of Doppler channels. filter weight vector

in $u_{\mathrm{tar}}\left(w_d\right)={\left[\begin{array}{cc}1& e^{j2\mathrm{\&pi;}{w}_d}...e^{j2\mathrm{\&pi;}(m-1)w_d}\end{array}\right]}^T$ is the time-domain steering vector of the target, $u_{\mathrm{tar}}\left(w_{\mathrm{the\; s}}\right)={\left[\begin{array}{cc}1& e^{j2\mathrm{\&pi;}{w}_{\mathrm{the\; s}}}...e^{j2\mathrm{\&pi;}(N-1)w_{\mathrm{the\; s}}}\end{array}\right]}^T$ is the airspace steering vector of the target, where the normalized Doppler frequency normalized spatial frequency v represents the speed of the target; θ ₀ represents the pitch angle of the main beam, Indicates the azimuth angle of the main beam, and ψ indicates the angle between the velocity direction of the carrier aircraft and the axis of the antenna array.

Step 6: Construct a corresponding space-time filter according to the filter weight vector W to suppress the clutter in the echo signal X, and obtain the final Doppler spectrum of the current clutter block after clutter suppression: Z=W ^H X.

Specifically, use the k-th Doppler channel filter weight vector W _k to construct a corresponding space-time filter to suppress the clutter in the echo signal X, and obtain the output of the current clutter block and the k-th Doppler channel for: k=1,2...K, K is the number of Doppler channels, H represents the conjugate transpose operation; get the final Doppler spectrum of the current clutter block after clutter suppression: Z=[Z ₁ ,Z ₂ ,… ,Z _K ] ^T , T represents the transpose operation.

The performance of the clutter suppression method of the present invention will be described in detail below through simulation experiments.

(1) Simulation experiment 1 verifies the robustness of the parameter estimation of the present invention

(1.1) Simulation parameters

The simulation parameters are shown in Table 1. The slant distance of the unit to be detected is 7km, and the noise-to-noise ratio is 50dB. Two interference points are added to represent the main lobe target and the side lobe target respectively. The corresponding space-time two-dimensional frequency is (-0.40. 0), (0.2-0.25), the signal-to-noise ratio is 20dB.

Table 1 Airborne Radar System Parameters

(1.2) Simulation data processing results and analysis

Figures 3a and 3b show the clutter curve fitting results of the least square (LS) and LTS methods when there are no interference points and interference points, respectively. In the figure, '○' corresponds to the clutter trace, and '*' corresponds to the target trace. It can be seen from Figure 3a that the clutter curves estimated by the two methods basically coincide with the real clutter curve when there are no interference points, which shows that both methods can achieve high parameter estimation accuracy when there are no interference points. It can be seen from Figure 3b that the clutter curve estimated by LS deviates significantly from the real clutter curve when there are interference points. This is because the LS method solves the coefficient vector by minimizing the residual error square of all data, without considering the influence of interference points. The clutter curve estimated by LTS still basically coincides with the real clutter curve. This is because LTS assumes that there are interference points in the data and selects normal data for calculation through optimization, so better parameter estimation results can be obtained.

(2) Simulation experiment 2 verifies the robustness of the parameter estimation of the present invention

(2.1) Simulation parameters

The simulation parameters are the same as the simulation experiment 1, and the Monte Carlo experiment is repeated 100 times, and the root mean square error (root mean square error, RMSE) of the parameter estimation of the LTS method is obtained as shown in Table 2.

Table 2 parameter estimation RMSE

(2.2) Simulation data processing results and analysis

It can be seen from Table 2 that the root mean square error estimated by the LTS method is small, and the estimated parameters are close to the true value. This is because the position of the clutter spectrum estimated by the sparse spectrum is relatively accurate. It can be seen from Fig. 3a and Fig. 3b that the clutter trace is basically located near the real clutter spectral line, and the LTS method suppresses the influence of the interference point by weighting.

(3) Simulation experiment 3 verifies the clutter suppression performance of the present invention

(3.1) Experimental method

The performance of the algorithm is verified by using the SNR loss as the criterion, and the SNR loss is defined as

${\mathrm{<span\; class="notranslate">\; SINR</span>}}_{\mathrm{<span\; class="notranslate">\; L</span>}}<span\; class="notranslate">\; =</span>\frac{\mathrm{<span\; class="notranslate">\; SINR</span>}}{\mathrm{<span\; class="notranslate">\; SNR</span>}}<span\; class="notranslate">\; =</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; w</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}{\mathrm{<span\; class="notranslate">\; R</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}\mathrm{<span\; class="notranslate">\; w</span>}}{{\mathrm{<span\; class="notranslate">\; w</span>}}^{\mathrm{<span\; class="notranslate">\; h</span>}}\mathrm{<span\; class="notranslate">\; Rw</span>}}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; /</span><span\; class="notranslate">\; (</span>\frac{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; s</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}{{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; no</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}}\mathrm{<span\; class="notranslate">\; N\; M</span>}<span\; class="notranslate">\; )</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 18</span>}<span\; class="notranslate">\; )</span>$

In the formula Respectively represent the target power and noise power of a single pulse of a single array element, is the target correlation matrix, and R is the theoretical clutter plus noise covariance matrix.

(3.2) Simulation data processing results and analysis

Figure 4 shows the SNR loss curves of optimal processing, sampling covariance, and the method in this paper (adaptive subspace). It can be seen from Figure 4 that the sampling covariance is significantly lower than the optimal processing performance. This is because the sampling covariance uses the covariance matrix estimate R _avg obtained from the average distance sample to be a biased estimate of R. The performance of the self-adaptive subspace method of the present invention is obviously better than that of the sampling covariance method, because the subspace method directly uses configuration parameters to calculate the clutter subspace projection operator, avoiding the problem of non-stationary samples.

Claims (4)

1. the clutter suppression method of battle array radar self adaptation subspace, an airborne anon-normal side, it is characterised in that comprise the following steps:

Step 1, sets up airborne anon-normal side battle array radar signal model, and wherein, radar operation wavelength is λ, launches M pulse in coherent processing inteval, and pulse recurrence frequency is f_r, aerial array is the uniform line-array of N number of array element composition, and array element distance is d, and carrier aircraft height is H, and carrier aircraft speed is v, and the axial angle of carrier aircraft velocity attitude and aerial array is Ψ, the angle of pitch of ground clutter scattering object and azimuth respectively θ andThe oblique distance of carrier aircraft and ground clutter scattering object is R；

Its echo-signal can be expressed as

$X=x_c+n=\underset{l=1}{\overset{N_c}{\&Sigma;}}{\mathrm{\&alpha;}}_l{u}_l+n,l=1,2...N_c$

In formula, n is noise component(s), x_cFor clutter component, N_cFor clutter block number independent in ground clutter ring that oblique distance is R, α_lFor the amplitude of clutter the l clutter block of ring, and separate between different clutter block, u_lSteering vector during for clutter the l clutter block of ring empty；

The clutter Two dimensional Distribution curve of its clutter ring is

${\left(\frac{\mathrm{\&lambda;}}{d}\right)}^2{w}_s^2+{\left(\frac{f_r\mathrm{\&lambda;}}{2v}\right)}^2{w}_d^2-\left(\frac{{\mathrm{\&lambda;}}^2{f}_{r}cos\mathrm{\&psi;}}{vd}\right)w_s{w}_d={\cos }^2{\mathrm{\&theta;sin}}^2\mathrm{\&psi;}$

The simplified function expression formula of above formula

C=Г (η (λ, d, f_r, v, Ψ, θ))

In formula, C is clutter curve, and Г is the operator being calculated clutter Two dimensional Distribution curve by parameter vector, and η is the parameter vector of clutter Two dimensional Distribution curve, wherein in the parameter vector η of clutter Two dimensional Distribution curve, and λ, d, f_rFor radar system known parameters, v, Ψ, θ are unknown quantity, w_dFor normalization Doppler frequency, w_sFor normalization spatial frequency；

Step 2, carries out angle Doppler's plane discretization to echo-signal, then does weighting two-dimension fourier transform spatially and temporally and obtain fourier spectra P_b, then to fourier spectra P_bTake absolute value square, obtain correspondence clutter power spectrum；

First thresholding, the grid cell of filtering clutter Two dimensional Distribution extra curvature are set, utilize the grid cell structure search submatrix on the clutter Two dimensional Distribution curve obtainedAccording to echo-signal complex magnitude γ on angle Doppler's plane correspondence grid cell, there is sparse characteristic, pass through Corresponding Sparse AlgorithmSolve the complex magnitude γ of grid cell on clutter Two dimensional Distribution curve, in formula | | | |_pRepresent L_pNorm, ε represents the limits of error that Corresponding Sparse Algorithm solves, for setting value；

According to the complex magnitude γ of grid cell on clutter Two dimensional Distribution curve, the second thresholding is set, relatively small magnitude on filtering clutter Two dimensional Distribution curve | γ_i| secondary grid cell, obtain the Power Spectrum Distribution typical grid unit in corresponding space-time two-dimensional plane distribution of reflection clutter；

Step 3, the clutter Two dimensional Distribution curve to clutter ring

${\left(\frac{\mathrm{\&lambda;}}{d}\right)}^2{w}_s^2+{\left(\frac{f_r\mathrm{\&lambda;}}{2v}\right)}^2{w}_d^2-\left(\frac{{\mathrm{\&lambda;}}^2{f}_{r}cos\mathrm{\&psi;}}{vd}\right)w_s{w}_d={\cos }^2{\mathrm{\&theta;sin}}^2\mathrm{\&psi;}$

Carrying out conversion to arrange, being write as vector form is y=a^Tβ, β=[1/v in formula²cosΨ/vsin²Ψcos²θ]^T, a=[(f_rλw_d/2)²-λ²f_rw_sw_d/d-1]^T,Wherein in β and η, unknown parameter v, Ψ, θ are relevant, a, known parameters λ, d, f in y and η_rAnd the space-time two-dimensional frequency of clutter is relevant；T represents that transposition operates；

The space-time two-dimensional frequency of P2 the typical grid unit more than the second thresholding then step 2 obtained and configuration known parameter substitute into y=a^TIn a, the y of β, it is possible to obtain below equation group

$\hat{y}=\hat{A}\mathrm{\&beta;}+\mathrm{\&xi;}$

The measured value of P2 grid cell correspondence y in formulaFor the response vector of P2 × 1 dimension, the measured value of a that P2 typical grid unit is correspondingFor the measurement matrix of P2 × 3 dimension, ξ is the error vector of P2 × 1 dimension, for setting value；

Step 4, adopts the equation group that minimum intercepting least square method solution procedure 3 obtainsObtain the estimated value of βAnd then solve obtain the structure parameters v of clutter Two dimensional Distribution curve, estimated value that Ψ, θ are corresponding

Step 5, utilizes the structure parameters of the clutter Two dimensional Distribution curve estimatedWith known parameters λ, d, f_r, calculate steering vector matrix during the corresponding clutter sky of clutter Two dimensional Distribution curveOrthogonal Subspaces projection operatorWith filter weights vector W；

Step 6, constructs corresponding space-time filtering device according to filter weights vector W, it is suppressed that the clutter in echo-signal X, obtains the final doppler spectral after current clutter block clutter recognition: Z=W^HX；

Specifically, kth Doppler channel filtering weight vector W is utilized_kConstruct corresponding space-time filtering device, it is suppressed that the clutter in echo-signal X, obtain current clutter block, kth Doppler's passage is output as:K is Doppler's port number, and H represents conjugate transposition operation；Obtain the final doppler spectral after current clutter block clutter recognition: Z=[Z₁, Z₂..., Z_K]^T, T represents that transposition operates.

2. the clutter suppression method of battle array radar self adaptation subspace, airborne anon-normal side according to claim 1, it is characterised in that the concrete sub-step of step 2 is:

2a) by angle Doppler's plane discretization, grid cell number corresponding to Doppler frequency is N_d, grid cell number corresponding to spatial domain frequency is N_s；

Steering vector searching matrix Ф when setting up empty based on the grid cell in clutter block, concrete formWherein u (w_{D, i}, w_{S, j}) in i=1 ... N_d；J=1 ... N_sDenotation coordination be (i, the space-time two-dimensional frequency of grid cell j), namelyIn formulaAmass for Kronecker, wherein u_t(w_{D, i}) and u_s(w_{S, j}) respectively coordinate is (i, the time domain steering vector of grid cell j) and spatial domain steering vector in clutter block；

Then echo-signal X is expressed as X=Φ γ,For echo-signal complex magnitude on angle Doppler's plane correspondence grid cell, wherein T represents that transposition operates；

2b) angle Doppler's plane discretization echo-signal being done weighting two-dimension fourier transform spatially and temporally, its form is P_b=| Φ^H(x⊙t_w) |, P in formula_bFor fourier spectra, t_wFor weight coefficient spatially and temporally, ⊙ is that Hadamard amasss, and obtains fourier spectra P_b, x is angle Doppler's plane discretization echo-signal；

2c) to the fourier spectra P obtained after weighting spatially and temporally two-dimension fourier transform_bTake absolute value square, obtain the clutter power spectrum of correspondence, and it carried out the first Threshold detection, detect power P1 the grid cell more than the first threshold T H1, the space-time two-dimensional frequency of its correspondence isSubscript 1 represents by the first thresholding TH1；And build a search submatrix It is a subset of searching matrix Ф；

2d) echo-signal complex magnitude γ on angle Doppler's plane correspondence grid cell has sparse characteristic, passes through Corresponding Sparse AlgorithmSolve the complex magnitude γ on estimation unit, in formula | | | |_pRepresent L_pNorm, ε represents the limits of error that Corresponding Sparse Algorithm solves, for setting value；

After 2e) estimating the amplitude of complex magnitude γ on grid cell, according to amplitude | γ_i| >=TH2, i=1 ... N_dN_s, in formula, TH2 is the second threshold value set, relatively small magnitude on filtering clutter Two dimensional Distribution curve | γ_i| secondary grid cell, obtain the Power Spectrum Distribution typical grid unit in corresponding space-time two-dimensional plane distribution of reflection clutter；

The space-time two-dimensional frequency that P2 typical grid unit 2f) detecting is corresponding is

Subscript 2 represents by the second thresholding TH2；Typical grid unit, in the distribution of space-time two-dimensional plane, reflects the Power Spectrum Distribution of clutter.

3. the clutter suppression method of battle array radar self adaptation subspace, airborne anon-normal side according to claim 1, it is characterised in that the concrete sub-step of step 4 is:

4a) adopt minimum intercepting least square method solving-optimizing problem

$\min \underset{i=1}{\overset{P}{\&Sigma;}}{z}_i{({\hat{y}}_i-{\hat{a}}_i\mathrm{\&beta;})}^2$

s.t.z^TE=Q

z_i∈ { 0,1}

Z in formula_iRepresent flag bit, z_i=1 represents that these data are normal point, z_i=0 represents that these data are noise spot, and e represents complete 1 vector, and Q represents the number of nonzero element in z and Q < P；

4b) optimization problem above is obtained the estimated value of β And then calculating obtains estimated value corresponding to v, Ψ, θ respectively Its computing formula is as follows

$\hat{v}=1/\sqrt{{\widehat{\mathrm{\&beta;}}}_{LTS}\left(1\right)}$

$\widehat{\mathrm{\&psi;}}=\arccos \left({\widehat{\mathrm{\&beta;}}}_{LTS}\right(2)/\sqrt{{\widehat{\mathrm{\&beta;}}}_{LTS}\left(1\right)})$

$\widehat{\mathrm{\&theta;}}=\arccos \sqrt{{\widehat{\mathrm{\&beta;}}}_{LTS}\left(3\right)/(1-{\left({\widehat{\mathrm{\&beta;}}}_{LTS}\left(2\right)/\sqrt{{\widehat{\mathrm{\&beta;}}}_{LTS}\left(1\right)}\right)}^2)}.$

4. the clutter suppression method of battle array radar self adaptation subspace, airborne anon-normal side according to claim 1, it is characterised in that the concrete sub-step of step 5 is:

5a) the estimation structure parameters that will obtainWith known parameters λ, d, f_r, substitute into normalization Doppler frequencyWith normalization spatial frequencyIn, obtain the time domain steering vector of the l estimation corresponding to clutter blockWith spatial domain steering vectorDuring the estimation that then the l clutter block now is corresponding empty, steering vector isSteering vector matrix during the clutter sky estimatedIn formulaAmass for Kronecker；

5b) it is calculated as follows the projection operator being orthogonal to clutter subspace

$P_c^{\&perp;}=I-{\hat{V}}_c{({\hat{V}}_c^H{\hat{V}}_c+\mathrm{\&mu;}I)}^{-1}{\hat{V}}_c^H$

In formula, μ is positive number, to ensure matrixReversible；⊥ represents orthogonal project operator, and H represents conjugate transposition operation, ()^-1Representing matrix is inverted, I representation unit battle array；

Steering vector when 5c) utilizing target emptyI.e. s=[s₁, s₂..., s_k... s_K] and the projection operator being orthogonal to clutter subspace that estimates of step 5bCalculate the filter weights vector of the space-time filtering device obtaining kth Doppler's passageK is Doppler's port number, filter weights vector

WhereinFor the time domain steering vector of target,For the spatial domain steering vector of target, wherein normalization Doppler frequencyNormalization spatial frequencyWhat v represented is the speed of target；θ₀What represent is the angle of pitch of main beam,What represent is the azimuth of main beam, the angle that what Ψ represented is carrier aircraft velocity attitude is axial with aerial array.