CN104199008A - Method for estimating parameters of aerial maneuvering target based on compressed sensing - Google Patents

Abstract

The invention discloses a method for estimating the parameters of an aerial maneuvering target based on compressed sensing. The method provides the method for estimating the parameters of the aerial maneuvering target based on the compressed sensing by taking full advantage of the sparse characteristics of a maneuvering target signals. The method comprises the steps of firstly, separating out a component containing acceleration information from an original echo signal by virtue of triple phase transformation, establishing a complete redundancy dictionary based on a maneuvering target echo signal and obtaining the estimated value of the acceleration by use of the compressed sensing technology, secondly, demodulating the original signal by use of the estimated value of the acceleration, and finally, estimating the initial velocity of the target by use of the compressed sensing method. By comparing the simulation result with the estimation result of sampling methods based on FRFT and based on reconstruction time, the method for estimating the parameters of the aerial maneuvering target based the compressed sensing has the advantage that the desired sampling frequency can be greatly reduced without losing parameter estimation accuracy; when few pules are emitted by an airborne radar CPI, the advantage of the method is more obvious and relatively high parameter estimation accuracy can be kept, and the effectiveness of the method is further verified.

Description

Air mobile target component method of estimation based on compressed sensing

Technical field

The invention belongs to Radar Signal Processing and moving-target and detect and parameter estimation techniques field, particularly relate to a kind of air mobile target component method of estimation based on compressed sensing.

Background technology

Modern war environment is very complicated, requires intelligence channel that abundanter information can be provided better, quickly, and the airborne radar of high-performance becomes one of indispensable technical equipment.Airborne radar is usingd aircraft as carrier, more traditional ground radar, and its coverage is larger, detection range is farther, viability and anti-electronic interferences ability is higher, maneuverability more, thereby has been subject to increasingly extensive attention.

When maneuvering target is done uniformly accelerated motion, target echo signal is linear frequency modulation (Linear Frequency Modulation, LFM) signal, so the detection of maneuvering target and estimation problem can be converted into the detection of linear FM signal and parameter estimation.In recent years, detection and the method for parameter estimation of the LFM signal based on various time frequency analyzing tool constantly occur, comprise Short Time Fourier Transform (Short Time Fourier Transform, STFT), wavelet transformation (Wavelet Transform, WT) and Fourier Transform of Fractional Order (Fractional Fourier Transform, FRFT) etc.STFT utilizes the sliding window function simple extension that conversion is carried out to Fourier, but the time frequency resolution of STFT can be subject to the impact of view window, thereby resolution is not high.Wavelet transformation need to be selected suitable female small echo, is difficult to find an optimum standard optimal base to adapt to varying environment, is all generally to choose based on experience, so process more complicated.FRFT is a kind of Fourier transformation method of broad sense, it by signal decomposition on the chirp base of one group of quadrature of fractional number order Fourier, and can realize fast by FFT (Fast Fourier Transform), in ground radar and synthetic-aperture radar (Synthetic Aperture Radar, SAR), application is more extensive.Yet concerning airborne radar, a relevant processing time (Coherent Processing Interval, CPI) interior umber of pulse is relatively limited; Under the certain condition of pulse repetition rate (Pulse Repetition Frequency, PRF), shortened the integration time of signal, just there will be the problems such as maneuvering target detectability variation and Parameter Estimation Precision reduction.For this problem, 2012, the people such as Wu Renbiao proposed a kind of maneuvering target based on reconstitution time sampling and have detected and method for parameter estimation, utilize reconstitution time sampling and FRFT to complete the detection of maneuvering target and estimation, can improve the precision of parameter estimation; But the operand that this method needs is large and have a problem of velocity ambiguity.These methods about LFM detection and estimation are all the sampled signals that requires based on nyquist sampling theorem above, exist the poor problem of Parameter Estimation Precision in the situation that sample frequency is higher and the interior transponder pulse number of airborne radar CPI is limited.

In recent years, the people such as Donoho, Candes and Tao have proposed a kind of new acquisition of information guiding theory, i.e. compressed sensing (Compressive Sensing, CS).The method can guarantee, the in the situation that of loss of information not, to use far below the frequency of nyquist sampling theorem requirement and signal is sampled and compress, and can realize again the reconstruct of signal.But not yet find compressed sensing technology for estimating the achievement in research of air mobile target component aspect at present.

Summary of the invention

In order to address the above problem, the object of the present invention is to provide a kind of air mobile target component method of estimation based on compressed sensing.

In order to achieve the above object, the air mobile target component method of estimation based on compressed sensing provided by the invention comprises the following step carrying out in order:

1) total echoed signal airborne radar being received is carried out clutter inhibition, obtains the signal after clutter suppresses;

2) signal after clutter inhibition is utilized to phase tranformation separate targets parameter three times, obtain only containing the signal of maneuvering target acceleration information;

3) discretize aimed acceleration space, and estimate required redundant dictionary according to the parametric configuration target component of discretize, to only containing the signal of maneuvering target acceleration information, utilize compression sensing method to carry out echo signal reconstruct, thereby obtain the acceleration estimation value of target;

4) utilize step 3) the former quadratic polynomial phase signal of acceleration estimation value demodulation that obtains, obtain the signal after demodulation; Discretize target initial velocity space, and estimate required redundant dictionary according to the parametric configuration target component of discretize, to the signal after demodulation, utilize compression sensing method to carry out the reconstruct of echo signal, thereby obtain the initial velocity estimated value of target.

In step 2) in, described signal after clutter is suppressed utilizes phase tranformation separate targets parameter three times, and the method that obtains only containing the signal of maneuvering target acceleration information is:

According to the ultimate principle of three phase tranformations, the maneuvering target echoed signal that radar is received at certain fixed time t0, carry out following bilinear transformation:

$\begin{array}{c}{s}_{t_0}\left(\mathrm{\τ}\right)=s(t_0+\mathrm{\τ})s(t_0-\mathrm{\τ})\\ =A^2{e}^{j(\frac{4\mathrm{\π}}{\mathrm{\λ}}{v}_0{t}_0+\frac{2\mathrm{\π}}{\mathrm{\λ}}{\mathrm{at}}_0^2)}{e}^{j2\left(\frac{2\mathrm{\π}}{\mathrm{\λ}}a\right){\mathrm{\τ}}^2}\\ ={\tilde{A}}^2{e}^{j{\mathrm{\Ω}}_0{\mathrm{\τ}}^2}\end{array}---\left(1\right)$

Wherein, the conversion delay of τ>=0 for introducing, v ₀represent respectively initial velocity and the acceleration of maneuvering target, amplitude with a and instantaneous frequency at fixed time t ₀for constant; Above formula shows, carries out the signal after bilinear transformation about variable τ, only has quadratic term coefficient based on this characteristic, its Cubic phase function is expressed as:

$\begin{array}{c}\mathrm{CPF}(t,\mathrm{\&Omega;})={\&Integral;}_0^{+\&infin;}s(t+\mathrm{\&tau;})s(t-\mathrm{\&tau;})e^{\mathrm{j\&Omega;}{\mathrm{\&tau;}}^2}\mathrm{d\&tau;}\\ =\left\{\begin{array}{c}{\tilde{A}}^2\sqrt{\frac{\mathrm{\&pi;}}{8|\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}a-\mathrm{\&Omega;}|}}(1+j),(\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}a>\mathrm{\&Omega;})\\ {\tilde{A}}^2\sqrt{\frac{\mathrm{\&pi;}}{8|\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}a-\mathrm{\&Omega;}|}}(1+j),(\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}a<\mathrm{\&Omega;})\end{array}\right.\end{array}---\left(2\right)$

Wherein, the instantaneous frequency of Ω representation signal; From above formula, the result of quadratic polynomial phase signal after above-mentioned conversion will be place forms maximal value; Parameter that can realize target through above-mentioned steps is separated, and the signal of note after three phase tranformations conversion is x _cpt:

$x_{\mathrm{cpt}}=\mathrm{CPF}(t,\mathrm{\&Omega;})={\&Integral;}_0^{+\&infin;}s(t+\mathrm{\&tau;})s(t-\mathrm{\&tau;})e^{-\mathrm{j\&Omega;}{\mathrm{\&tau;}}^2}\mathrm{d\&tau;}---\left(3\right).$

In step 3) in, described discretize aimed acceleration space, and estimate required redundant dictionary according to the parametric configuration target component of discretize, to only containing the signal of maneuvering target acceleration information, utilize compression sensing method to carry out the reconstruct of echo signal, thereby the method that obtains the acceleration estimation value of target is:

Maneuvering target acceleration spatial spreading is turned to N _aindividual grid, corresponding discretize target component space is structure is suc as formula the K * N shown in (4) _athe frequency domain redundant dictionary of dimension:

After clutter is suppressed, signal carries out three phase tranformations conversion, has realized parameter separated, and signal x after conversion _cptuse redundant dictionary D _abe expressed as:

x _cpt＝Φ ₁D _ag ₁+n ₁ (5)

Wherein, Φ ₁for the measurement matrix of M * K, M<K, n ₁for the noise contribution in observation signal, g ₁for sparse coefficient vector; g ₁can solve by following optimization method:

$\min \left({\left|\right|{\hat{g}}_1\left|\right|}_1\right),s.t.{\left|\right|x_{\mathrm{cpt}}-{\mathrm{\&Phi;}}_1{D}_a{\hat{g}}_1\left|\right|}_2\&le;\mathrm{\&epsiv;}---\left(6\right)$

Wherein, || || ₂represent l ₂norm, ε represents the error level that sparse recovery allows; Adopt conventional optimized algorithm to solve formula (6), obtain coefficient vector find peaked coordinate, and at redundant dictionary D _ain find the position of this coordinate, obtain thus the estimated value of maneuvering target acceleration

In step 4) in, the described step 3 of utilizing) the former quadratic polynomial phase signal of acceleration estimation value demodulation that obtains, obtain the signal after demodulation; Discretize target initial velocity space, and estimate required redundant dictionary according to the parametric configuration target component of discretize, utilizes compression sensing method to carry out echo signal reconstruct to the signal after demodulation, thereby the method that obtains the initial velocity estimated value of target is:

Utilize step 3) estimated value of the acceleration that obtains the former quadratic polynomial phase signal of demodulation, the signal that obtains only containing the simple signal of former target initial velocity information and defining after demodulation is x _dec; In order to construct D _vmaneuvering target initial velocity spatial spreading is turned to N _vindividual grid, corresponding discretize target component space is structure is suc as formula the K * N shown in (7) _vthe frequency domain redundant dictionary of dimension:

Signal x after demodulation _decuse redundant dictionary D _vbe expressed as:

x _dec＝Φ ₂D _vg ₂+n ₂ (8)

Wherein, Φ ₂for the measurement matrix of M * K, M<K, n ₂for the noise contribution in signal after demodulation, g ₂for sparse coefficient vector; g ₂equation of constraint that can through type (9) solves:

$\min \left({\left|\right|{\hat{g}}_2\left|\right|}_1\right),s.t.{\left|\right|x_{\mathrm{dec}}-{\mathrm{\&Phi;}}_2{D}_v{\hat{g}}_2\left|\right|}_2\&le;\mathrm{\&epsiv;}---\left(9\right)$

Equally, by solving formula (9), obtain coefficient vector find peaked coordinate, and at sparse base dictionary D _vin find the position of this coordinate, just can acquire the estimated value of maneuvering target initial velocity

The present invention makes full use of maneuvering target signal in the sparse characteristic of empty time domain, has proposed a kind of air mobile target component method of estimation based on compressed sensing; First utilize three phase tranformations (Cubic Phase Transform, CPT) in separated former echoed signal, contain acceleration information part, according to maneuvering target echo features, set up complete redundant dictionary, and adopted compressed sensing technology to obtain the estimated value of acceleration; And then utilize acceleration estimation value demodulation original signal, finally by compression sensing method, estimate to obtain the initial velocity of target.By simulation result with based on FRFT and the estimated result based on the reconstitution time method of sampling, compare, this method is under the condition of loss parameter estimated accuracy not, required sample frequency can reduce greatly; When in airborne radar CPI, transponder pulse number is less, its superiority is more obvious, still can keep higher Parameter Estimation Precision, has further verified the validity of this method.

Accompanying drawing explanation

Fig. 1 is the maneuvering target method for parameter estimation process flow diagram based on compressed sensing provided by the invention.

Fig. 2 utilizes compression sensing method to estimate the sparse coefficient distribution plan obtaining.

Maneuvering target parameter root-mean-square error when Fig. 3 is umber of pulse K=64 is with signal to noise ratio (S/N ratio) variation diagram.

Maneuvering target parameter root-mean-square error when Fig. 4 is umber of pulse K=32 is with signal to noise ratio (S/N ratio) variation diagram.

Fig. 5 is that maneuvering target parameter parameter root-mean-square error is with sample frequency variation diagram.

Embodiment

Below in conjunction with the drawings and specific embodiments, the air mobile target component method of estimation based on compressed sensing provided by the invention is elaborated.

Set up maneuvering target echo data model:

If the maneuvering target echo that airborne radar receives is:

$s_r(\hat{t},t_m)=A\&CenterDot;p(\hat{t}-\mathrm{\&tau;})\&CenterDot;e^{j2\mathrm{\&pi;}{f}_c\mathrm{\&tau;}}=A\&CenterDot;p(\hat{t}-\mathrm{\&tau;})\&CenterDot;e^{j2\mathrm{\&pi;}{f}_c\frac{2R\left(t_m\right)}{c}}---\left(1\right)$

In formula, A is target echo amplitude, and p () is normalization echo envelope, for fast time, f _cfor carrier frequency, τ=2R (t _m)/c is echo delay, R (t _m) be that target is at slow time t _mthe moment is apart from the distance of airborne radar platform.For remote air mobile point target, its radial motion rule is:

$R\left(t_m\right)=R_0+v_0{t}_m+{\mathrm{at}}_m^2/2---\left(2\right)$

Wherein, R ₀for target at initial time the distance apart from airborne radar platform, v ₀for target initial velocity, a is its acceleration.When maneuvering target is done accelerated motion, ignore variation and the range migration impact of echo amplitude in the short time, its doppler changing rate is:

${\mathrm{\&Delta;f}}_d=\frac{2}{\mathrm{\&lambda;}}\frac{\mathrm{dR}\left(t\right)}{\mathrm{dt}}=\frac{{2v}_0}{\mathrm{\&lambda;}}+\frac{{2\mathrm{at}}_m}{\mathrm{\&lambda;}}---\left(3\right)$

λ is radar signal wavelength.From formula (3), the Doppler who causes for target initial velocity once, the Doppler's quadratic term causing for aimed acceleration, i.e. Doppler's item of walking about.Therefore, when the acceleration of maneuvering target is constant,

The variation of target Doppler frequency can be described with linear frequency modulation model.Suppose that its echo model is:

$s\left(t\right)=A\&CenterDot;e^{j(\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}{v}_{0}t+\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}{\mathrm{at}}^2)---\left(4\right)}$

Wherein, 0≤t≤T, T is pulse length integration time, A is target echo signal amplitude.

Provide the maneuvering target echo data form that airborne radar receives below.If airborne platform is placed N unit even linear array along course direction, array element distance is d, and d=λ/2; In a CPI, have K umber of pulse, during detected unit empty, snap can be write as:

x＝b _ta(ω _s,ω _t)+x _c+x _n (5)

Wherein, x, x _cand x _nbe the column vector of NK * 1, clutter component and noise component while representing respectively interior receive empty of a certain range unit in data and data.B _tthe complex magnitude that represents target echo, a (ω _s, ω _t) be the space-time two-dimensional steering vector of target:

$a({\mathrm{\&omega;}}_s,{\mathrm{\&omega;}}_t)=a\left({\mathrm{\&omega;}}_s\right)\&CircleTimes;a\left({\mathrm{\&omega;}}_t\right)---\left(6\right)$

A (ω _s) and a (ω _t) be respectively spatial domain steering vector and the time domain steering vector of target, represent that Kronecker is long-pending.The spatial domain of target and time domain steering vector are defined as respectively:

$a\left({\mathrm{\&omega;}}_s\right)={\left[\begin{array}{ccccc}1& e^{{\mathrm{j\&omega;}}_s}& e^{j{2\mathrm{\&omega;}}_s}& ...& e^{j(N-1){\mathrm{\&omega;}}_s}\end{array}\right]}^T---\left(7\right)$

$a\left({\mathrm{\&omega;}}_t\right)={\left[\begin{array}{ccccc}1& e^{{\mathrm{j\&omega;}}_t}& e^{j{2\mathrm{\&omega;}}_t}& ...& e^{j(N-1){\mathrm{\&omega;}}_t}\end{array}\right]}^T---\left(8\right)$

While only having a target in to-be-measured cell, in azimuth angle theta _smaneuvering target normalization Space Angle frequency be:

${\mathrm{\&omega;}}_s=\frac{2\mathrm{\&pi;}d\cos {\mathrm{\&theta;}}_s}{\mathrm{\&lambda;}}---\left(9\right)$

The spatial domain steering vector of target can be expressed as:

$\begin{array}{c}a\left({\mathrm{\&omega;}}_s\right)={\left[\begin{array}{ccccc}1& e^{j{\mathrm{\&omega;}}_s}& e^{j{2\mathrm{\&omega;}}_s}& ...& e^{j(N-1)}\end{array}\right]}^T\\ ={\left[\begin{array}{ccccc}1& e^{j2\mathrm{\&pi;}d\cos {\mathrm{\&theta;}}_s/\mathrm{\&lambda;}}& e^{j2\&CenterDot;2\mathrm{\&pi;}d\cos {\mathrm{\&theta;}}_s/\mathrm{\&lambda;}}& ...& e^{j2\&CenterDot;(N-1)\mathrm{\&pi;}d\cos {\mathrm{\&theta;}}_s/\mathrm{\&lambda;}}\end{array}\right]}^T\end{array}---\left(10\right)$

Normalization time-angle frequency is:

${\mathrm{\&omega;}}_{t_m}={2\mathrm{\&pi;f}}_{t_m}/f_r=2\mathrm{\&pi;}\frac{\frac{2v}{\mathrm{\&lambda;}}+\frac{2a{t}_m}{\mathrm{\&lambda;}}}{f_r}=\frac{4\mathrm{\&pi;v}}{{\mathrm{\&pi;f}}_r}+\frac{4\mathrm{\&pi;}{\mathrm{at}}_m}{{\mathrm{\&lambda;f}}_r}---\left(11\right)$

Wherein, f _rfor pulse repetition rate; And time domain steering vector is

$\begin{array}{c}a\left({\mathrm{\&omega;}}_{t_m}\right)={\left[\begin{array}{ccccc}1& e^{j{\mathrm{\&omega;}}_{t_m}}& e^{j2{\mathrm{\&omega;}}_{t_m}}& ...& e^{j(N-1){\mathrm{\&omega;}}_{t_m}}\end{array}\right]}^T\\ ={\left[\begin{array}{ccccc}1& e^{j(\frac{4\mathrm{\&pi;v}}{{\mathrm{\&lambda;f}}_r}+\frac{4\mathrm{\&pi;a}{t}_m{}_{}}{{\mathrm{\&lambda;f}}_r})}& e^{j2(\frac{4\mathrm{\&pi;v}}{{\mathrm{\&lambda;f}}_r}+\frac{{4\mathrm{\&pi;at}}_m}{{\mathrm{\&lambda;f}}_r})}& ...& e^{j(K-1)(\frac{4\mathrm{\&pi;v}}{{\mathrm{\&lambda;f}}_r}+\frac{4\mathrm{\&pi;a}{t}_n}{{\mathrm{\&lambda;f}}_r})}\end{array}\right]}^T\end{array}---\left(12\right)$

When utilizing existing LFM to detect, with method for parameter estimation, motor-driven range estimation is carried out to parameter estimation, exist the poor problem of Parameter Estimation Precision in the situation that sample frequency is higher and the interior transponder pulse number of airborne radar CPI is limited, the present invention proposes a kind of air mobile target component method of estimation based on compressed sensing.

First, adopt three phase tranformations that the two-dimensional search process of estimating about air mobile target echo signal is converted into two linear search processes, thereby the operand of parameter estimation is reduced greatly.Then according to radar, receive echoed signal in the sparse characteristic of time-frequency domain, constructed complete redundant dictionary, recycling compression sensing method is estimated respectively the parameter of maneuvering target.

As shown in Figure 1, the air mobile target component method of estimation based on compressed sensing provided by the invention comprises the following step carrying out in order:

1) total echoed signal airborne radar being received is carried out clutter inhibition, obtains the signal after clutter suppresses;

First utilize the echo data of adjacency door to estimate to obtain the clutter covariance matrix of range gate to be detected, the contrary clutter covariance matrix of estimating range gate to be detected that then utilizes adjacency door clutter covariance matrix contrary; By space-time adaptive processing method, complete effective inhibition for the treatment of clutter in detecting unit again, and then obtain the signal after clutter suppresses:

$x_{\mathrm{proj}}={\hat{R}}^{-1}x---\left(13\right)$

2) signal after clutter inhibition is utilized to phase tranformation separate targets parameter three times, obtain only containing the signal of maneuvering target acceleration information;

Based on three phase tranformations, quadratic polynomial phase signal (linear FM signal) is carried out to parameter separation below.From upper surface analysis, when the acceleration of maneuvering target is constant, the maneuvering target echoed signal that airborne radar receives can be expressed as:

$s\left(t\right)=A\&CenterDot;e^{j(\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}{v}_{0}t+\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}{\mathrm{at}}^2)}---\left(14\right)$

By signal at certain fixed time t ₀carry out following bilinear transformation:

$\begin{array}{c}{s}_{t_0}\left(\mathrm{\&tau;}\right)=s(t_0+\mathrm{\&tau;})s(t_0-\mathrm{\&tau;})\\ =A^2{e}^{j(\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}{v}_0{t}_0+\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}{\mathrm{at}}_0^2)}{e}^{j2\left(\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}a\right){\mathrm{\&tau;}}^2}\\ ={\tilde{A}}^2{e}^{j{\mathrm{\&Omega;}}_0{\mathrm{\&tau;}}^2}\end{array}---\left(15\right)$

Wherein, the conversion delay of τ>=0 for introducing, with at fixed time t ₀for constant.Above formula shows, carries out the signal after bilinear transformation about variable τ, only has quadratic term coefficient based on this characteristic, Peter O ' Shea has defined following Cubic phase function:

$\begin{array}{c}\mathrm{CPF}(t,\mathrm{\&Omega;})={\&Integral;}_0^{+\&infin;}s(t+\mathrm{\&tau;})s(t-\mathrm{\&tau;})e^{\mathrm{j\&Omega;}{\mathrm{\&tau;}}^2}\mathrm{d\&tau;}\\ =\left\{\begin{array}{c}{\tilde{A}}^2\sqrt{\frac{\mathrm{\&pi;}}{8|\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}a-\mathrm{\&Omega;}|}}(1+j),(\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}a>\mathrm{\&Omega;})\\ {\tilde{A}}^2\sqrt{\frac{\mathrm{\&pi;}}{8|\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}a-\mathrm{\&Omega;}|}}(1+j),(\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}a<\mathrm{\&Omega;})\end{array}\right.\end{array}---\left(16\right)$

Wherein, the instantaneous frequency of Ω representation signal.From above formula, after the conversion of quadratic polynomial phase signal, result will be place forms maximal value.Parameter that just can realize target through above-mentioned steps is separated, and the signal of note after three phase tranformations convert is x _cpt:

$x_{\mathrm{cpt}}=\mathrm{CPF}(t,\mathrm{\&Omega;})={\&Integral;}_0^{+\&infin;}s(t+\mathrm{\&tau;})s(t-\mathrm{\&tau;})e^{-\mathrm{j\&Omega;}{\mathrm{\&tau;}}^2}\mathrm{d\&tau;}---\left(17\right)$

3) discretize aimed acceleration space, and estimate required redundant dictionary according to the parametric configuration target component of discretize, to only containing the signal of maneuvering target acceleration information, utilize compression sensing method to carry out the reconstruct of echo signal, thereby obtain the acceleration estimation value of target;

Utilize compressed sensing technology to carry out parameter estimation to target and echo signal is reconstructed, and from formula (6), steering vector when echo signal reconstruct can be converted into reconstruct target empty; And then adopt the base methods such as (Basis-Pursuit, BP) of following the trail of that target component estimation problem is converted into a dictionary selection problem.Quadratic polynomial phase signal radar being received in previous step carries out after three phase tranformations, is equivalent to maneuvering target to accelerate the second order Doppler information separated cause out, here first aimed acceleration is estimated.According to maneuvering target echo, in the sparse characteristic of empty time domain, consider to build acceleration redundant dictionary D _a.In order to construct D _a, maneuvering target acceleration spatial spreading is turned to N _aindividual grid, corresponding discretize target component space is structure is suc as formula the K * N shown in (18) _athe frequency domain redundant dictionary of dimension:

After clutter is suppressed, signal carries out three phase tranformations conversion, has realized parameter separated, and signal x after conversion _cptavailable redundancy dictionary D _abe expressed as:

x _cpt＝Φ ₁D _ag ₁+n ₁ (19)

Wherein, Φ ₁for the measurement matrix of M * K, M<K, Φ ₁with redundant dictionary D _ameet incoherent condition; n ₁for the noise contribution in observation signal, g ₁for sparse coefficient vector, and g ₁most elements be all 0 or be approximately 0 to only have the value of oligo-element larger.G ₁can solve by following optimization method:

$\min \left({\left|\right|{\hat{g}}_1\left|\right|}_1\right),s.t.{\left|\right|x_{\mathrm{cpt}}-{\mathrm{\&Phi;}}_1{D}_a{\hat{g}}_1\left|\right|}_2\&le;\mathrm{\&epsiv;}---\left(20\right)$

Wherein, || || ₂represent l ₂norm, ε represents the error level that sparse recovery allows.L ₁norm constraint object is to make restoring signal sparse as far as possible, and l ₂the constraint of norm makes remaining composition as far as possible little.In fact, in formula (20), the cost function of definition remains a protruding optimization problem, can adopt conventional optimized algorithm as the realization of BP scheduling algorithm.By solving formula (20), obtain coefficient vector find peaked coordinate, and at redundant dictionary D _ain find the position of this coordinate, just can acquire the estimated value of maneuvering target acceleration

4) utilize step 3) the former quadratic polynomial phase signal of acceleration estimation value demodulation that obtains, obtain the signal after demodulation; Discretize target initial velocity space, and estimate required redundant dictionary according to the parametric configuration target component of discretize, to the signal after demodulation, utilize compression sensing method to carry out the reconstruct of echo signal, thereby obtain the initial velocity estimated value of target.

Utilize the estimated value of the acceleration that previous step obtains the former quadratic polynomial phase signal of demodulation, the signal that obtains only containing the simple signal of former target initial velocity information and defining after demodulation is x _dec.Consider structure initial velocity redundant dictionary D _v, the same initial velocity v that estimates maneuvering target with compression sensing method.In like manner, in order to construct D _vfirst maneuvering target initial velocity spatial spreading is turned to N _vindividual grid, corresponding discretize target component space is structure is suc as formula the K * N shown in (21) _vthe frequency domain redundant dictionary of dimension.

Signal x after demodulation _deccan utilize redundant dictionary D _vbe expressed as:

x _dec＝Φ ₂D _vg ₂+n ₂ (22)

Wherein, Φ ₂for the measurement matrix of M * K, M<K, Φ ₂with redundant dictionary D _vmeet incoherent condition; n ₂for the noise contribution in the signal after demodulation, g ₂for sparse coefficient vector.G ₂equation of constraint that can through type (22) solves:

$\min \left({\left|\right|{\hat{g}}_2\left|\right|}_1\right),s.t.{\left|\right|x_{\mathrm{dec}}-{\mathrm{\&Phi;}}_2{D}_v{\hat{g}}_2\left|\right|}_2\&le;\mathrm{\&epsiv;}---\left(23\right)$

Equally, by solving formula (23), obtain coefficient vector find peaked coordinate, and at sparse base dictionary D _vin find the position of this coordinate, just can acquire the estimated value of maneuvering target initial velocity for the enough reconstruction precision of sparse and signal of the sparse coefficient that guarantees to solve, can improve by increasing redundant dictionary Atom number the redundancy of transformation system, and then strengthen the dirigibility of Signal approximation and improve the rarefaction representation ability of signal.

Simulation result and analysis:

The effect of the air mobile target component method of estimation based on compressed sensing that the present invention proposes can further illustrate by following emulation experiment.Simulation parameter arranges: antenna is the even linear array of array number N=16, array element interval d=0.5 λ.Carrier aircraft speed v _p=120m/s, airborne radar operation wavelength λ=0.32m, podium level H=10km, the range resolution △ R=20m of airborne radar, pulse repetition rate f _r=1500Hz, input signal-to-noise ratio SNR=0dB, miscellaneous noise ratio CNR=50dB.Air mobile target is in detecting unit, in azimuth angle theta _slocate for=90 °, initial velocity is v=24.01m/s, and acceleration is a=99.9m/s ², Monte Carlo experiment number of times M=300.

1, sparse coefficient distributes

Fig. 2 utilizes compression sensing method to estimate the sparse coefficient distribution plan obtain, the sparse coefficient distribution plan that Fig. 2 (a) obtains when estimating initial velocity, the sparse coefficient distribution plan that Fig. 2 (b) obtains during for estimated acceleration.Can find out, the most elements of the sparse coefficient obtaining through compression sensing method is all 0 or is approximately 0, only have the value of a small amount of sparse coefficient larger, the atom that these large coefficients are corresponding has mated the feature of each parameter in signal, make original signal concentration of energy on several best atoms, on only a few atom, reach maximum coupling.And the position at maximal value place is easy to just distinguish, consistent with theoretical analysis result above, and the atom in the corresponding redundant dictionary in the position at maximizing place, just can obtain the estimated result of target component.

2, the parameter estimation Performance Ratio under different signal to noise ratio (S/N ratio) conditions

Fig. 3 and Fig. 4 have provided respectively the relation of target component estimated performance and signal to noise ratio (S/N ratio), and provide corresponding CRB (Cramer-Rao Bound) theoretical curve.The root-mean-square error of parameter estimation in experiment (Root Mean Square Error, RMSE) is defined as: wherein, for the estimated value of solve for parameter x, M is Monte Carlo experiment number of times.

When Fig. 3 is umber of pulse K=64, distinct methods estimates that the target component root-mean-square error obtaining is with signal to noise ratio (S/N ratio) change curve, wherein Fig. 3 (a) is the comparison diagram that initial velocity root-mean-square error changes with signal to noise ratio (S/N ratio), the comparison diagram that Fig. 3 (b) changes with signal to noise ratio (S/N ratio) for acceleration-root-mean square error.The reconstitution time method of sampling is the method that the people such as Wu Ren young tiger in 2012 propose, and CRB is the theory lower-bound of maneuvering target parameter estimation result.As can be seen from Figure 3, the inventive method is significantly improved compared with the parameter estimation performance of FRFT method, can obtain the parameter estimation performance suitable with the reconstitution time method of sampling; But the method does not need the two-dimensional search in the reconstitution time method of sampling to complete estimated parameter, only need two linear searches can complete the parameter estimation of target; When two-dimensional parameter is estimated, the operand of parameter search is O (N _vn _a), and the operand of parameter search is O (N during two one dimension parameter estimation _v+ N _a), operand obviously reduces.

When Fig. 4 is umber of pulse K=32, distinct methods estimates that the target component root-mean-square error obtaining is with signal to noise ratio (S/N ratio) change curve, the parameter estimation performance of known the inventive method is better than FRFT method and the reconstitution time method of sampling, more approaches the CRB that target component is estimated.This is because when PRF is constant, and umber of pulse reduces and means that the signal integration time shortens, and causes time domain data to reduce, frequency domain energy accumulation deficiency.And FRFT and the reconstitution time method of sampling be all based on on signal energy accumulation basis, the estimated accuracy of these two kinds of methods declines more in this case.And the impact that the inventive method is changed by umber of pulse is less, when reducing to K=32, umber of pulse still can keep higher estimated accuracy, and it is more obvious that its superiority embodies, and further verified the validity of the inventive method.

3, the parameter estimation Performance Ratio under different sample frequency conditions

In order to verify the inventive method, can use lower than FRFT and the required sample frequency f of the reconstitution time method of sampling _sestimate motor-driven parameter, suppose that signal integration duration is certain, the variation range of sample frequency is f _s∈ [100,1500] Hz, the minimum Nyquist sampling frequency of easily knowing maneuvering target echoed signal is f _n=375Hz.Fig. 5 is under above-mentioned sample frequency condition, and distinct methods is estimated the target component root-mean-square error curve map obtaining.Known, work as f _sduring >375Hz, the Parameter Estimation Precision of the inventive method is a little more than the estimated accuracy of FRFT and the reconstitution time method of sampling; Work as f _sduring <375Hz, the Parameter Estimation Precision based on FRFT and the reconstitution time method of sampling is variation sharply, and the estimated accuracy of the inventive method is far above above-mentioned two kinds of methods, more approaches the CRB that target component is estimated.When sample frequency is lower, the parameter estimation root-mean-square error of the inventive method is more less than other two kinds of methods, and its superiority is more obvious.This is because under the lower condition of sample frequency, based on FRFT method and the reconstitution time method of sampling, be subject to the restriction of that Qwest's sampling thheorem, can there is aliasing and cannot try to achieve correct target component result in echoed signal frequency spectrum, cause estimated accuracy to be difficult to guarantee; And compressed sensing technology is not subject to the restriction of sampling thheorem, as long as guarantee that the sparse property of signal projection in redundant dictionary and the incoherence of measurement matrix and redundant dictionary just can obtain accurate parameter estimation result.Because the projection sparse property of signal in redundant dictionary is directly proportional to the size of former word bank, the atomicity in former word bank is more, and the signal that projection obtains is just more sparse.Therefore under the condition allowing at computation complexity, by increasing atom number, improve as far as possible the rarefaction representation ability of echoed signal, and then improve the precision of maneuvering target parameter estimation.

First air mobile target component method of estimation based on compressed sensing provided by the invention utilizes three phase tranformations that the two-dimensional search process of estimating about air mobile target echo signal is converted into two linear search processes, thereby can make operand greatly reduce; And then according to the Its Sparse Decomposition characteristic that receives echoed signal, adopt compressed sensing technology to estimate target component, and simulation result is compared respectively with based on FRFT and the estimated result based on the reconstitution time method of sampling; Result shows: the in the situation that in airborne radar CPI, transponder pulse being counted, the method still can obtain parameter estimation result accurately, and parameter estimating error more approaches CRB circle.In addition, this method can be under guaranteeing compared with the condition of high parameter estimated accuracy, utilizing random measurement matrix to use much smaller than the sampling rate of traditional sampling theorem regulation samples to echoed signal and compresses, and the less advantage of sampling rate is more obvious, and can estimate exactly maneuvering target parameter.

Claims (4)

1. the air mobile target component method of estimation based on compressed sensing, is characterized in that: it comprises the following step carrying out in order:

1) total echoed signal airborne radar being received is carried out clutter inhibition, obtains the signal after clutter suppresses;

2) signal after clutter inhibition is utilized to phase tranformation separate targets parameter three times, obtain only containing the signal of maneuvering target acceleration information;

3) discretize aimed acceleration space, and estimate required redundant dictionary according to the parametric configuration target component of discretize, to only containing the signal of maneuvering target acceleration information, utilize compression sensing method to carry out echo signal reconstruct, thereby obtain the acceleration estimation value of target;

4) utilize step 3) the former quadratic polynomial phase signal of acceleration estimation value demodulation that obtains, obtain the signal after demodulation; Discretize target initial velocity space, and estimate required redundant dictionary according to the parametric configuration target component of discretize, to the signal after demodulation, utilize compression sensing method to carry out the reconstruct of echo signal, thereby obtain the initial velocity estimated value of target.

2. the air mobile target component method of estimation based on compressed sensing according to claim 1, it is characterized in that: in step 2) in, described signal after clutter is suppressed utilizes phase tranformation separate targets parameter three times, and the method that obtains only containing the signal of maneuvering target acceleration information is:

According to the ultimate principle of three phase tranformations, the maneuvering target echoed signal that radar is received at certain fixed time t ₀carry out following bilinear transformation:

$\begin{array}{c}{s}_{t_0}\left(\mathrm{\&tau;}\right)=s(t_0+\mathrm{\&tau;})s(t_0-\mathrm{\&tau;})\\ =A^2{e}^{j(\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}{v}_0{t}_0+\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}{\mathrm{at}}_0^2)}{e}^{j2\left(\frac{2\mathrm{\&pi;}}{\mathrm{\&lambda;}}a\right){\mathrm{\&tau;}}^2}\\ ={\tilde{A}}^2{e}^{j{\mathrm{\&Omega;}}_0{\mathrm{\&tau;}}^2}\end{array}---\left(1\right)$

Wherein, the conversion delay of τ>=0 for introducing, v ₀represent respectively initial velocity and the acceleration of maneuvering target, amplitude with a and instantaneous frequency at fixed time t ₀for constant; Above formula shows, carries out the signal after bilinear transformation about variable τ, only has quadratic term coefficient based on this characteristic, its Cubic phase function is expressed as:

$\begin{array}{c}\mathrm{CPF}(t,\mathrm{\&Omega;})={\&Integral;}_0^{+\&infin;}s(t+\mathrm{\&tau;})s(t-\mathrm{\&tau;})e^{\mathrm{j\&Omega;}{\mathrm{\&tau;}}^2}\mathrm{d\&tau;}\\ =\left\{\begin{array}{c}{\tilde{A}}^2\sqrt{\frac{\mathrm{\&pi;}}{8|\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}a-\mathrm{\&Omega;}|}}(1+j),(\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}a>\mathrm{\&Omega;})\\ {\tilde{A}}^2\sqrt{\frac{\mathrm{\&pi;}}{8|\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}a-\mathrm{\&Omega;}|}}(1+j),(\frac{4\mathrm{\&pi;}}{\mathrm{\&lambda;}}a<\mathrm{\&Omega;})\end{array}\right.\end{array}---\left(2\right)$

Wherein, the instantaneous frequency of Ω representation signal; From above formula, the result of quadratic polynomial phase signal after above-mentioned conversion will be place forms maximal value; Parameter that can realize target through above-mentioned steps is separated, and the signal of note after three phase tranformations conversion is x _cpt:

$x_{\mathrm{cpt}}=\mathrm{CPF}(t,\mathrm{\&Omega;})={\&Integral;}_0^{+\&infin;}s(t+\mathrm{\&tau;})s(t-\mathrm{\&tau;})e^{-\mathrm{j\&Omega;}{\mathrm{\&tau;}}^2}\mathrm{d\&tau;}---\left(3\right).$

3. the air mobile target component method of estimation based on compressed sensing according to claim 1, it is characterized in that: in step 3) in, described discretize aimed acceleration space, and estimate required redundant dictionary according to the parametric configuration target component of discretize, to only containing the signal of maneuvering target acceleration information, utilize compression sensing method to carry out the reconstruct of echo signal, thereby the method that obtains the acceleration estimation value of target is:

Maneuvering target acceleration spatial spreading is turned to N _aindividual grid, corresponding discretize target component space is structure is suc as formula the K * N shown in (4) _athe frequency domain redundant dictionary of dimension:

After clutter is suppressed, signal carries out three phase tranformations conversion, has realized parameter separated, and signal x after conversion _cptuse redundant dictionary D _abe expressed as:

x _cpt＝Φ ₁D _ag ₁+n ₁ (5)

Wherein, Φ ₁for the measurement matrix of M * K, M<K, n ₁for the noise contribution in observation signal, g ₁for sparse coefficient vector; g ₁can solve by following optimization method:

$\min \left({\left|\right|{\hat{g}}_1\left|\right|}_1\right),s.t.{\left|\right|x_{\mathrm{cpt}}-{\mathrm{\&Phi;}}_1{D}_a{\hat{g}}_1\left|\right|}_2\&le;\mathrm{\&epsiv;}---\left(6\right)$

Wherein, || || ₂represent l ₂norm, ε represents the error level that sparse recovery allows; Adopt conventional optimized algorithm to solve formula (6), obtain coefficient vector find peaked coordinate, and at redundant dictionary D _ain find the position of this coordinate, obtain thus the estimated value of maneuvering target acceleration

4. the air mobile target component method of estimation based on compressed sensing according to claim 1, it is characterized in that: in step 4) in, the described step 3 of utilizing) the former quadratic polynomial phase signal of acceleration estimation value demodulation obtaining, obtains the signal after demodulation; Discretize target initial velocity space, and estimate required redundant dictionary according to the parametric configuration target component of discretize, utilizes compression sensing method to carry out echo signal reconstruct to the signal after demodulation, thereby the method that obtains the initial velocity estimated value of target is:

Utilize step 3) estimated value of the acceleration that obtains the former quadratic polynomial phase signal of demodulation, the signal that obtains only containing the simple signal of former target initial velocity information and defining after demodulation is x _dec; In order to construct D _vmaneuvering target initial velocity spatial spreading is turned to N _vindividual grid, corresponding discretize target component space is structure is suc as formula the K * N shown in (7) _vthe frequency domain redundant dictionary of dimension:

Signal x after demodulation _decuse redundant dictionary D _vbe expressed as:

x _dec＝Φ ₂D _vg ₂+n ₂ (8)

Wherein, Φ ₂for the measurement matrix of M * K, M<K, n ₂for the noise contribution in signal after demodulation, g ₂for sparse coefficient vector; g ₂equation of constraint that can through type (9) solves:

$\min \left({\left|\right|{\hat{g}}_2\left|\right|}_1\right),s.t.{\left|\right|x_{\mathrm{dec}}-{\mathrm{\&Phi;}}_2{D}_v{\hat{g}}_2\left|\right|}_2\&le;\mathrm{\&epsiv;}---\left(9\right)$

Equally, by solving formula (9), obtain coefficient vector find peaked coordinate, and at sparse base dictionary D _vin find the position of this coordinate, just can acquire the estimated value of maneuvering target initial velocity