CN107402380A - A kind of quick self-adapted alternative manner for realizing Doppler beam sharpened imaging - Google Patents

Abstract

The invention discloses a fast iterative self-adaptive method for realizing Doppler beam sharpening imaging, which mainly utilizes the fast calculation of the covariance matrix and the fast inversion of the covariance matrix to realize multi-angle super-resolution in the front squint area of aircraft, missiles and the like. Puller beam sharpening imaging solves the problem of high complexity in calculating the covariance matrix and the inversion of the covariance matrix in the traditional direct iterative adaptive method. Its characteristic is to solve the problem of covariance matrix calculation and matrix inversion in iterative self-adaptation, using the properties of its Toeplitz matrix and Hermitian matrix to quickly obtain the matrix by solving a column of elements, and using Gohberg Semencul (GS) The type decomposition method realizes the fast solution of the inverse matrix of the covariance matrix, which makes the Doppler beam sharpening imaging method using the iterative adaptive method occupy less computing resources in engineering applications and is more efficient.

Description

A Fast Adaptive Iterative Method for Realizing Doppler Beam Sharpening Imaging

technical field

The invention relates to the field of radar detection and imaging, and is especially suitable for scanning radar Doppler beam sharpening imaging.

Background technique

In the existing pulse Doppler radar system, the Doppler beam sharpening imaging method is usually used to realize the imaging observation of the forward squint area in the forward squint direction of the carrier aircraft. In this method, the Doppler phase change law produced by the mutual motion between the carrier aircraft and the target is used, and the azimuth imaging resolution of the radar's oblique forward squint area is improved through a signal processing method. In the traditional Doppler beam sharpening imaging method, the fast Fourier transform (FFT) method is used to estimate the Doppler phase change caused by the relative motion of the platform and the target, but due to the influence of the radar azimuth echo due to the antenna pattern The resulting low-pass filtering effect results in a lower spectral resolution achieved by the FFT method. Therefore, using the method of super-resolution spectrum estimation to realize Doppler beam sharpening imaging will help improve the imaging resolution and imaging quality.

In order to improve the imaging quality of Doppler beam sharpening, in the literature "Qi L, Zheng M, Yu W, et al. Super-resolution Doppler beam sharpening imaging based on an iterative adaptive approach [J]. Remote Sensing Letters, 2016, 7( 3):259-268.", a method based on iterative adaptive super-resolution spectrum estimation is adopted, which is applied to Doppler beam sharpening imaging, compared with the traditional Fast Fourier Transform (FFT) method , this method improves the imaging resolution, but it has the disadvantages of high computational complexity, which is not conducive to engineering implementation. In the paper "Yongchao Zhang, Wenchao Li, Yin Zhang. A Fast Iterative Adaptive Approach for Scanning Radar Angular Superresolution, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.", the author proposes a fast iterative approach based on fast matrix inversion Adaptive (F-IAA) method, the operation matrix of this method must have specific requirements, and is not suitable for the operation matrix constructed during Doppler beam sharpening imaging.

Based on the above background technology, the inventor proposes a Fast Iterative Adaptive (F-IAA) method for realizing Doppler beam sharpening imaging in a radar forward squint area. First of all, this method utilizes the Toeplitz and Hermitian matrix characteristics of the covariance matrix to quickly obtain the covariance matrix by solving a column of elements. Secondly, the Gohberg Semencul (GS) decomposition method is used to accelerate the calculation of The inverse matrix of the matrix R solves the problem of high computational complexity and time-consuming in the process of calculating the covariance matrix and the inversion of the covariance matrix in the original direct iterative adaptive (brute force IAA) method. Finally, through fast iteration The spectrum estimation result obtained by the adaptive algorithm is used to obtain the beam sharpening imaging result of the forward squint area of the radar moving platform.

Contents of the invention

In order to solve the above-mentioned technical problems, the present invention proposes a fast self-adaptive iterative method for Doppler beam sharpening imaging, adopts the iterative self-adaptive method, and adopts the rapid calculation of the echo covariance matrix and the inverse of the covariance matrix The fast solution of the matrix realizes fast and high-performance beam sharpening imaging in the forward squint area of the scanning radar.

The technical scheme adopted in the present invention is: a fast adaptive iterative method for realizing Doppler beam sharpening imaging, comprising:

S1. Initialize the parameters of the radar system, specifically: the aircraft advances along the Y axis at a constant speed V at a height H above the ground, and the azimuth of the target point relative to the aircraft’s advancing direction is θ( _xi , y _i ). The angle between the direction of the target line and the forward direction of the aircraft is α, and the pitch angle of the target relative to the aircraft is The distance between the aircraft and the target at the initial moment is R ₀ , the scanning radar scans the imaging area at a constant angular velocity ω, and the position of the target is assumed to be ( _xi , y _i );

S2. Echo signal generation, specifically: obtaining a transmission signal according to the radar system parameters in step S1, performing discretization processing on the transmission signal, and obtaining a discretized echo signal;

S3. Echo signal preprocessing, specifically: constructing a beam scanning range-to-pulse compression frequency-domain matching function; performing fast Fourier transform on the echo signal received by beam scanning along the distance direction, and performing a distance-frequency domain-azimuth The time domain signal is multiplied by the matching function, and then the two-dimensional signal with high resolution in the distance direction is obtained through the inverse fast Fourier transform (IFFT); the phase compensation factor is corrected by multiplying the two-dimensional pulse pressure signal in the frequency domain by the distance walk; obtaining a preprocessed echo signal;

S4. For the echo signal obtained in step S3, the autocorrelation matrix R of the echo signal is obtained by quickly solving the covariance matrix;

S5, rapid implementation of covariance matrix inversion; the autocorrelation matrix obtained in step S4 is inverted to obtain R ^-1 ;

S6, Doppler beam sharpening imaging; according to R ^-1 of step S5, the imaging result of a single range direction is obtained; in the echo distance-Doppler domain, along the Doppler frequency direction, according to the number of echoes in the target imaging area Doppler distribution range, intercept the beam sharpening imaging results within the imaging range, and then obtain the Doppler beam sharpening imaging results of the imaging scene.

Further, the step S2 is specifically:

Assuming that the transmitted signal is a chirp signal:

Among them, rect( ) represents a rectangular signal, and τ is the distance fast time variable, T represents the duration of the transmitted pulse, c is the speed of light, λ represents the wavelength, K _r is the frequency modulation slope; j represents an imaginary number;

When the antenna sweeps the front squint area Ω, the discretized echo signal expression is obtained:

Among them, Ω represents the area where the radar beam scans, σ( _xi , y _j ) represents the scattering coefficient of the point target ( _xi , y _j ), θ _β represents the 3dB width of the antenna beam, θ( _xi , y _j ) Indicates the angle between the point (x _i , y _j ) in the scene and the line connecting the airborne platform and the flight direction, is the window function in the slow time domain, which represents the modulation of the antenna pattern function in the azimuth direction, and R( _xi , y _i ; t) represents the distance between the target point and the airborne platform.

Further, the step S4 is specifically:

Expressing the echo signal obtained in step S3 as a discrete form,

Among them, m=1,2,...,M; n=1,2,...,N, K represents the number of sampling points of the signal in the frequency domain, k represents the sampling point, k=0,1,2,... ,K-1, Indicates the normalized Doppler frequency, σ _k (m) indicates the scattering coefficient of the normalized Doppler frequency k within the mth distance unit in the azimuth direction of the region, and e(m,n) indicates the added noise;

For the echo signal S=[s(m,1),...,e(m,N)] ^T in the distance direction located in the mth distance unit, T represents the transpose operation; define the operation matrix A=[a ₁ ,a ₂ ,...,a _k ,...,a _K ], a _k =[e ^j2πk/K ,e ^j2π2k/K ,...,e ^j2πNk/K ]; noise vector e=[e (m,1),e(m,2),...,e(m,N)] ^T ; Based on the idea of weighted least squares, define the cost function:

Among them, * represents the conjugate operation, Q _k = Rp _k a _k (a _k ) ^* is the echo covariance matrix, is the echo autocorrelation matrix, P=diag(p), p=(p ₀ ,p ₁ ,p ₂ ,...,p _k ,...,p _K-1 ) ^T , Indicates the estimated value of the power at the frequency grid point 2πk/K, v indicates the number of iterations, and the optimal estimated value of σ _k can be expressed as:

According to the relationship between matrix Q and matrix R: Q _k ＝Rp _k a _k (a _k ) ^H ; then according to the matrix inversion lemma, the optimal estimated value of σ _k can be transformed into:

remember The autocorrelation matrix of the echo signal can be expressed as,

in,

Calculated according to p _k to get r _n , so as to get the autocorrelation matrix R.

Further, the step S5 is specifically:

First, according to the Toeplitz structure of the autocorrelation matrix R, the matrix R can be expressed as,

Then its inverse matrix can be expressed as,

in, H represents the conjugate transpose operation;

At the same time, the autocorrelation matrix R can also be expressed as,

At this point, its inverse matrix can be expressed as,

in, J _N-1 J _N-1 = I _N-1 , I _N-1 is an N-order identity matrix;

remember with According to the Gohberg-Semencul decomposition algorithm, R ^-1 can be expressed as the following form,

Among them, L(u,D)=(u,Du,D ² u,...,D ^N-1 u), D represents the transfer matrix.

Furthermore, the specific form of the matrix D is,

Beneficial effects of the present invention: a fast iterative adaptive method for realizing Doppler beam sharpening imaging of the present invention; utilizing the mathematical characteristics of Toeplitz and Hermitian matrix of the autocorrelation matrix to realize For the fast solution of the autocorrelation matrix, the Gohberg Semencul (GS) type decomposition of the autocorrelation matrix is used to realize the fast solution of the inverse matrix of the autocorrelation matrix, so as to reduce the complexity of the algorithm operation and improve the operation efficiency.

Description of drawings

Fig. 1 is a flow chart of the method of the present invention;

Fig. 2 is a schematic diagram of the working geometric model of the airborne scanning radar provided by the embodiment of the present invention;

FIG. 3 is a target scene distribution diagram provided by an embodiment of the present invention;

Fig. 4 provides real beam imaging results under the condition of 10db signal-to-noise ratio according to the embodiment of the present invention;

Fig. 5 is the imaging result using the present invention under the condition of 10db signal-to-noise ratio provided by the embodiment of the present invention;

Fig. 6 is a comparison of the imaging sections of the target at the position R=4980m provided by the embodiment of the present invention.

detailed description

In order to facilitate those skilled in the art to understand the technical content of the present invention, the content of the present invention will be further explained below in conjunction with the accompanying drawings.

For the convenience of describing the content of the present invention, the following terms are explained herein.

Term 1: Toeplitz matrix

Toeplitz matrix (diagonal-constant matrix) means that the elements on each diagonal line from upper left to lower right in the matrix are the same.

Term 2: Hermitian Matrix

The Hermitian Matrix means that the symmetric units of the complex matrix A are conjugate to each other, that is, the conjugate transpose matrix of A is equal to itself.

The present invention proposes a fast iterative adaptive method for realizing Doppler beam sharpening imaging, using the Toeplitz (Toeplitz) and Hermitian (Hermitian matrix) characteristics of the covariance matrix to quickly solve the covariance matrix; Gohberg Semencul (GS) decomposition method quickly solves the inverse matrix of matrix R; uses fast iterative adaptive algorithm to realize beam sharpening. Specific steps are as follows:

S1. Initialize radar system parameters

The Doppler beam sharpening technology utilizes the Doppler phase change law generated by the relative motion between the airborne platform and the target to achieve high resolution in azimuth. The system parameters of the radar platform used in this embodiment are shown in Table 1.

Table 1 System parameters of the radar platform

First, the working model of the scanning radar system is established, as shown in Figure 2, and the target scene distribution is shown in Figure 3, the horizontal axis Azimuth dimension (degree) represents the azimuth dimension; the vertical axis represents the distance dimension. The aircraft is at a height H above the ground, and is moving forward at a constant speed V along the Y axis. The azimuth angle of the target point relative to the aircraft's advancing direction is θ( _xi , y _i ). The angle is α, and the pitch angle of the target relative to the aircraft is The distance between the aircraft and the target at the initial moment is R ₀ , the scanning radar scans the imaging area at a constant angular velocity ω, assuming that the position of the target is ( _xi , y _i ),

Establish the echo model according to the initialized radar system parameters; specifically:

The distance history R(x _i , y _i ; t) between the airborne platform and the target at time t is:

The expression of the distance history is carried out by Taylor expansion, and the higher-order terms above the second order have very little influence on the imaging of the front squint area, and the expression of the distance history can be obtained after ignoring it:

in, The symbol represents approximately equal to, R( _xi , y _i ) the distance from the radar to the target ( _xi , y _i ) in the scene.

S2, echo signal generation; specifically:

In the Doppler beam sharpening imaging process, the linear frequency modulation (LFM) signal with a large time-width bandwidth product can be transmitted through the antenna and the reference signal can be matched and filtered to achieve high resolution in the range direction. Assuming that the transmitted signal is a chirp signal:

Among them, rect( ) represents a rectangular signal, which is defined as: Among them, τ is the fast time variable in the distance direction, T represents the duration of the transmitted pulse, c is the speed of light, λ represents the wavelength, and K _r is the frequency modulation slope. When the antenna sweeps the front squint area Ω, the discretized echo analytical expression can be obtained:

Among them, Ω represents the area where the radar beam scans, σ( _xi , y _j ) represents the scattering coefficient of the point target ( _xi , y _j ), θ _β represents the 3dB width of the antenna beam, θ( _xi , y _j ) Indicates the angle between the point (x _i , y _j ) in the scene and the line connecting the airborne platform and the flight direction, is the window function in the slow time domain, which represents the modulation of the antenna pattern function in the azimuth direction, and R( _xi , y _i ; t) represents the distance between the target point and the airborne platform.

S3. Echo signal preprocessing, specifically:

Constructing beam-scanning range-to-pulse compression frequency-domain matching function Perform fast Fourier transform on the echo signal received by beam scanning along the distance direction, and match the obtained distance frequency domain-azimuth time domain signal with the matching function Multiply, and then through the inverse fast Fourier transform (IFFT) to obtain a two-dimensional signal with high resolution in the distance direction:

Among them, B represents the bandwidth of transmitting chirp signal. Subsequently, the phase compensation factor is corrected by multiplying the two-dimensional pulse pressure signal by the distance walking in the frequency domain: t represents the time that the scanning radar beam passes through a certain target. Therefore, the signal expression of the echo signal obtained by multi-beam scanning target scene can be obtained as:

Among them, sinc[·] is the distance pulse pressure response function.

S4, fast solution of covariance matrix;

Based on the derivation result of step S3, in order to realize high-resolution azimuth processing, the two-dimensional high-resolution echo signal in the range direction is expressed in a discrete form, for a target point located at m in the range direction and n in the azimuth direction. Its echo can be expressed as:

Among them, m=1,2,...,M; n=1,2,...,N, K represents the number of sampling points of the signal in the frequency domain, Indicates the normalized Doppler frequency, σ _k (m) indicates the scattering coefficient of the normalized Doppler frequency k within the mth distance unit in the azimuth direction of the region, and e(m,n) indicates the added noise. For the echo signal S=[s(m,1),...,e(m,N)] ^T in the distance direction located in the mth distance unit, where T represents the transpose operation, in order to accurately estimate the signal S Spectrum distribution of , define operation matrix A=[a ₁ ,a ₂ ,...,a _k ,...,a _K ], where a _k =[e ^j2πk/K ,e ^j2π2k/K ,..., e ^j2πNk/K ]. Then define the noise vector e=[e(m,1),e(m,2),...,e(m,N)] ^T , based on the model established by formula (6), based on the weighted least squares The idea of multiplication defines the cost function:

Among them, * represents the conjugate operation, Q _k = Rp _k a _k (a _k ) ^* is the echo covariance matrix, is the echo autocorrelation matrix, P=diag(p), p=(p ₀ ,p ₁ ,p ₂ ,...,p _k ,...,p _K-1 ) ^T , Indicates the estimated value of the power at the frequency grid point 2πk/K, v indicates the number of iterations, the range of v is 10-20, and the optimal estimated value of σ _k can be expressed as:

According to the relationship between matrix Q and matrix R: Q _k ＝Rp _k a _k (a _k ) ^H , and then according to the matrix inversion lemma, the optimal estimated value of σ _k can be transformed into: In this formula, the score is The denominator is numerator in the formula denominator In the calculation process of , the echo autocorrelation matrix can be expressed as,

in, Observing the basic form of the matrix R, we can see that the autocorrelation matrix R has the Toeplitz matrix structure and the properties of the Hermitian matrix, so the calculation result of the entire matrix can be obtained through the calculation of one row of elements. Then according to the calculation formula It can be obtained that the calculation of the elements in the first row of the matrix R can be obtained by the FFT method. Therefore, in the calculation of the autocorrelation matrix, the value of the elements in the first row of the autocorrelation matrix is obtained through the FFT operation, and then the value of R is obtained according to the properties of the autocorrelation matrix. value.

In the calculation process of the autocorrelation matrix R, if the calculation formula in the traditional direct iterative adaptive (brute force IAA) method is used To calculate the autocorrelation matrix, as the number of observation points N and the number of sampling points K in the frequency domain increase, the computational complexity is O(N ² K). In the fast iterative adaptive (F-IAA) method, the element values of the first row of the matrix R are obtained by the FFT method, and the entire matrix element values are obtained according to the properties of the autocorrelation matrix. The computational complexity of this method is O(K log 2K ₎ .

S5. Fast implementation of covariance matrix inversion;

In order to calculate the inverse R ^-1 of the autocorrelation matrix, first, according to the Toeplitz structure of the autocorrelation matrix R, the matrix R is divided by rows and columns, which can be expressed as,

Then its inverse matrix can be expressed as,

in, H represents the conjugate transpose operation.

At the same time, the autocorrelation matrix R can also be expressed as,

At this point, its inverse matrix can be expressed as,

in, J _N-1 J _N-1 = I _N-1 , where I _N-1 is an N-order identity matrix.

In the above formula (11) and formula (13), record with According to the Gohberg-Semencul (GS) decomposition algorithm, R ^-1 can be expressed as the following form,

Among them, L(u,D)=(u,Du,D ² u,...,D ^N-1 u), D represents the transfer matrix. The GS decomposition algorithm is a commonly used algorithm in this field, and will not be described in detail here.

The specific form of the matrix D is,

vector u and It can be obtained by using the Levinson-Durbin algorithm for R.

In the process of solving the matrix R ^-1 , if the matrix inversion operation in the traditional direct iterative adaptive (brute force IAA) method is used, the computational complexity is O(N ² K). In the fast iterative adaptive (F-IAA) method, the inverse matrix of the matrix R is obtained by the Levinson-Durbin algorithm, and the computational complexity of this method is O(N ² ).

S6, Doppler beam sharpening imaging;

According to the calculation of step S4 and step S5, in order to solve According to the operation relationship of the matrix, the numerator in the formula will be solved with denominator The calculations are solved using the transform relationship between the time domain and the frequency domain. upcoming formula The solution of , converted to Φ _N ＝F ^-1 (R ^-1 S) _K , the formula The solution of , converted to Φ _D ＝F ^-1 (R ^-1 ) _K , where, F ^-1 (·) _K represents the inverse Fourier transform of K point, obtained The calculation result in the echo range-Doppler domain, so far, the imaging result of a single range direction can be obtained. Take the data of each distance in the real beam echo and substitute it into step S4 and step S5 for calculation. Finally, in the echo range-Doppler domain, along the Doppler frequency direction, according to the echo Doppler distribution range of the target imaging area , intercepting the beam-sharpening imaging result within the imaging range, the Doppler beam-sharpening imaging result of the imaging scene can be obtained, as shown in Fig. 5 . At the position of R=4980m, the comparison results of the imaging sections are shown in Figure 6.

As shown in Figure 4, under the condition of 10db signal-to-noise ratio, it is the real beam imaging result of the system. Compared with Figure 6, it can be found that when the radar real aperture imaging is performed, the target in the scene cannot be resolved.

In order to verify that the method proposed in the present invention improves the operation speed of the traditional iterative adaptive Doppler beam sharpening algorithm, under the hardware simulation environment of Table 2, under different matrix dimensions, Table 3 provides Comparing the operation time of the adaptive algorithm and the fast iterative adaptive algorithm.

Table 2 Experimental simulation hardware and software platform conditions

Hardware and Software Platform parameter CPU Inter(R)Core(TM)i7-6700CPU 3.4GHz CPU memory size 8G run the software Matlab 2015B

Table 3 Comparison of operation time between traditional iterative adaptive algorithm and fast iterative adaptive algorithm

Those skilled in the art will appreciate that the embodiments described here are to help readers understand the principles of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Various modifications and variations of the present invention will occur to those skilled in the art. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principles of the present invention shall be included within the scope of the claims of the present invention.

Claims (5)

1. A fast adaptive iterative method for realizing Doppler beam sharpening imaging is characterized by comprising the following steps:

s1, initializing radar system parameters, specifically: the airplane advances at a constant speed V along the Y axis at a ground clearance H, and the azimuth angle of a target point relative to the advancing direction of the airplane is theta (x)_i,y_i) The included angle between the connecting line direction of the airplane and the target and the advancing direction of the airplane is α, and the pitch angle of the target relative to the airplane isThe distance between the initial moment of the aircraft and the target is R₀The scanning radar scans an imaging area with a constant angular velocity of omega, and the position where the target is assumed is (x)_i,y_i)；

S2, echo signal generation, specifically: obtaining a transmitting signal according to the radar system parameters in the step S1, and performing discretization processing on the transmitting signal to obtain a discretized echo signal;

s3, echo signal preprocessing, specifically: constructing a pulse compression frequency domain matching function of the beam scanning distance direction; fast Fourier transform is carried out on echo signals received by beam scanning along the distance direction, the obtained distance frequency domain-azimuth time domain signals are multiplied by the matching function, and then two-dimensional signals with high resolution in the distance direction are obtained through fast Fourier inverse transform (IFFT); multiplying the two-dimensional pulse pressure signal by a distance walking correction phase compensation factor in a frequency domain; obtaining a preprocessed echo signal;

s4, rapidly solving the echo signal obtained in the step S3 through a covariance matrix to obtain an autocorrelation matrix R of the echo signal;

s5, quickly realizing the inverse of the covariance matrix; inverting the autocorrelation matrix obtained in step S4 to obtain R^-1；

S6, Doppler beam sharpening imaging; r according to step S5^-1Obtaining an imaging result of a single distance direction; in the echo distance-Doppler domain, along the Doppler frequency direction, according to the echo Doppler distribution range of the target imaging region, a beam sharpening imaging result in the imaging range is intercepted, and then the Doppler beam sharpening imaging result of the imaging scene can be obtained.

2. The fast adaptive iterative method for implementing doppler beam sharpening imaging according to claim 1, wherein the step S2 specifically comprises:

assuming the transmitted signal is a chirp signal:

<mrow> <mi>s</mi> <mrow> <mo>(</mo> <mi>&amp;tau;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>r</mi> <mi>e</mi> <mi>c</mi> <mi>t</mi> <mo>&amp;lsqb;</mo> <mfrac> <mi>&amp;tau;</mi> <mi>T</mi> </mfrac> <mo>&amp;rsqb;</mo> <mo>&amp;CenterDot;</mo> <mi>exp</mi> <mrow> <mo>(</mo> <mi>j</mi> <mfrac> <mrow> <mn>2</mn> <mi>&amp;pi;</mi> <mi>c</mi> </mrow> <mi>&amp;lambda;</mi> </mfrac> <mi>&amp;tau;</mi> <mo>+</mo> <mi>j</mi> <mn>2</mn> <msub> <mi>&amp;pi;K</mi> <mi>r</mi> </msub> <msup> <mi>&amp;tau;</mi> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow>

wherein rect (-) represents a rectangular signal, andτ is the distance fast time variable, T represents the emission pulse duration, c is the speed of light, λ represents the wavelength, K_rIs the frequency modulation slope; j represents an imaginary number;

when the antenna sweeps a front squint area omega, obtaining a discretized echo signal expression:

where Ω denotes the region of action of the radar beam sweep, σ (x)_i,y_j) Indicating point object (x)_i,y_j) Scattering coefficient of (a), theta_βRepresents the antenna beam 3dB width, theta (x)_i,y_j) Representing a point (x) in a scene_i,y_j) The included angle between the connecting line of the aircraft-mounted platform and the flight direction,is a window function in the slow time domain, representing the modulation of the antenna pattern function in the azimuth direction, R (x)_i,y_i(ii) a t) represents the distance between the target point and the airborne platform.

3. The fast adaptive iterative method for implementing doppler beam sharpening imaging according to claim 1, wherein the step S4 specifically comprises:

the echo signals obtained in step S3 are represented in discrete form,

<mrow> <mi>s</mi> <mrow> <mo>(</mo> <mi>m</mi> <mo>,</mo> <mi>n</mi> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mi>&amp;Sigma;</mi> <mrow> <mi>k</mi> <mo>=</mo> <mn>0</mn> </mrow> <mrow> <mi>K</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>&amp;sigma;</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>m</mi> <mo>)</mo> </mrow> <mi>exp</mi> <mrow> <mo>(</mo> <msub> <mi>jnf</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>+</mo> <mi>e</mi> <mrow> <mo>(</mo> <mi>m</mi> <mo>,</mo> <mi>n</mi> <mo>)</mo> </mrow> </mrow>

wherein, M is 1, 2.. times.m; n, K represents the number of sampling points of the signal in the frequency domain, K represents the sampling points, K is 0,1,2, …, K-1,representing normalized Doppler frequency, σ_k(m) represents the scattering coefficient with normalized doppler frequency k located in the mth range bin of the azimuth in the region, and e (m, n) represents the added noise;

for an echo signal S located in the mth range bin, S ═ S (m,1),.., e (m, N)]^TT represents a transposition operation; define operation matrix a ═ a₁,a₂,...,a_k,...,a_K]，a_k＝[e^j2πk/K,e^j2π2k/K,...,e^j2πNk/K](ii) a Noise vector e ═ e (m,1), e (m,2),.., e (m, N)]^T(ii) a Based on the idea of the weighted least squares method, a cost function is defined:

<mrow> <msup> <mrow> <mo>(</mo> <mi>S</mi> <mo>-</mo> <msub> <mi>a</mi> <mi>k</mi> </msub> <msub> <mi>&amp;sigma;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mo>*</mo> </msup> <msubsup> <mi>Q</mi> <mi>k</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>S</mi> <mo>-</mo> <msub> <mi>a</mi> <mi>k</mi> </msub> <msub> <mi>&amp;sigma;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> </mrow>

wherein, represents a conjugate operation, Q_k＝R-p_ka_k(a_k)^*In order to be the echo covariance matrix,for the echo autocorrelation matrix, P ═ diag (P), P ═ P₀,p₁,p₂,...,p_k,...,p_K-1)^T，Denotes the power estimate at frequency grid point 2 π K/K, v denotes the number of iterations, σ_kThe optimized estimate of (c) can be expressed as:

<mrow> <msubsup> <mover> <mi>&amp;sigma;</mi> <mo>~</mo> </mover> <mi>k</mi> <mrow> <mo>(</mo> <mi>v</mi> <mo>+</mo> <mn>1</mn> <mo>)</mo> </mrow> </msubsup> <mo>=</mo> <mfrac> <mrow> <msubsup> <mi>a</mi> <mi>k</mi> <mo>*</mo> </msubsup> <msubsup> <mi>Q</mi> <mi>k</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mi>S</mi> </mrow> <mrow> <msubsup> <mi>a</mi> <mi>k</mi> <mo>*</mo> </msubsup> <msubsup> <mi>Q</mi> <mi>k</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <msub> <mi>a</mi> <mi>k</mi> </msub> </mrow> </mfrac> </mrow>

according to the relationship between matrix Q and matrix R: q_k＝R-p_ka_k(a_k)^H(ii) a Then, according to the matrix inversion theorem, sigma_kThe optimized estimate of (c) can be converted into:

note the bookThe autocorrelation matrix of the echo signal may be expressed as,

wherein,

according to p_kCalculated to obtain r_nThereby obtaining the autocorrelation matrix R.

4. The fast adaptive iterative method for implementing doppler beam sharpening imaging according to claim 1, wherein the step S5 specifically comprises:

first, the matrix R is divided into rows and columns according to the toeplitz structure of the autocorrelation matrix R, which can be expressed as,

<mrow> <msub> <mi>R</mi> <mi>N</mi> </msub> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <msub> <mi>r</mi> <mn>0</mn> </msub> </mtd> <mtd> <msubsup> <mi>r</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>H</mi> </msubsup> </mtd> </mtr> <mtr> <mtd> <msub> <mi>r</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>R</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> </mrow>

the inverse matrix thereof can be expressed as,

<mrow> <msubsup> <mi>R</mi> <mi>N</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <msubsup> <mi>R</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msubsup> </mtd> </mtr> </mtable> </mfenced> <mo>+</mo> <mfrac> <mn>1</mn> <msub> <mi>&amp;alpha;</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mfrac> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <msub> <mi>w</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> </msub> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "[" close = "]"> <mtable> <mtr> <mtd> <mrow> <mn>1</mn> <mo>,</mo> </mrow> </mtd> <mtd> <msubsup> <mi>w</mi> <mrow> <mi>N</mi> <mo>-</mo> <mn>1</mn> </mrow> <mi>H</mi> </msubsup> </mtd> </mtr> </mtable> </mfenced> </mrow>

wherein,h represents a conjugate transpose operation;

meanwhile, the autocorrelation matrix R can also be expressed as,

at this time, the inverse matrix thereof can be expressed as,

wherein,J_N-1J_N-1＝I_N-1,I_N-1is an N-order identity matrix;

note the bookAndaccording to the Gohberg-Semencult decomposition algorithm, R^-1Can be expressed in the form of,

<mrow> <msup> <mi>R</mi> <mrow> <mo>-</mo> <mn>1</mn> </mrow> </msup> <mo>=</mo> <mi>L</mi> <mrow> <mo>(</mo> <mi>u</mi> <mo>,</mo> <mi>D</mi> <mo>)</mo> </mrow> <msup> <mi>L</mi> <mi>H</mi> </msup> <mrow> <mo>(</mo> <mi>u</mi> <mo>,</mo> <mi>D</mi> <mo>)</mo> </mrow> <mo>-</mo> <mi>L</mi> <mrow> <mo>(</mo> <mover> <mi>u</mi> <mo>~</mo> </mover> <mo>,</mo> <mi>D</mi> <mo>)</mo> </mrow> <msup> <mi>L</mi> <mi>H</mi> </msup> <mrow> <mo>(</mo> <mover> <mi>u</mi> <mo>~</mo> </mover> <mo>,</mo> <mi>D</mi> <mo>)</mo> </mrow> </mrow>

wherein L (u, D) ═ u, Du, D²u,...,D^N-1u)，D denotes a transition matrix.

5. The fast adaptive iterative method for realizing Doppler beam sharpening imaging according to claim 4, wherein the matrix D is in the form of,