CN103777190A - Angle estimation method of bistatic MIMO (Multiple-Input Multiple-Output) radar high-speed and high-maneuvering target - Google Patents

Abstract

The invention discloses an angle estimation method of a bistatic MIMO (Multiple-Input Multiple-Output) radar high-speed and high-maneuvering target. The angle estimation method comprises the steps of receiving an echo signal of a high-speed and high-maneuvering target by a receiving array of a bistatic MIMO (Multiple-Input Multiple-Output) radar; performing conjugate multiplication on echo of the receiving array and sending signals in different distant units; performing Fourier transform on data after performing conjugate multiplication in a fast time domain and a slow time domain in sequence; estimating a target speed according to a peak value in the step 3; extracting target slow time frequency domain components of different separation channels in a fast time frequency domain along with a target Doppler frequency value; splicing target frequency domain data in different distance gates to form virtual array data crossing a plurality of distance gates; and estimating sending angles and receiving angles of the targets by using a super-resolution algorithm. Through the angle estimation method, the influence on separation of MIMO radar channels caused due to high-speed and high-maneuvering movement of the target can be avoided; an effective virtual array can be formed by crossing the plurality of distance gates; and the problem of target angle parameter estimation of the bistatic MIMO radar under the high-speed and high-maneuvering target can be solved.

Description

The angle estimating method of the high maneuvering target of a kind of bistatic MIMO radar high speed

Technical field

The present invention relates to the application of multi-input multi-output radar system, particularly the angle estimating method of the high maneuvering target of a kind of bistatic MIMO radar high speed.

Background technology

The bistatic radar of bistatic has stronger anti-antiradiation missile, anti-electronic interferences, anti-low-level penetration and anti-stealthy " four is anti-" ability, and by multiple-input and multiple-output (Multiple-Input Multiple-Output, MIMO) technology is applied in bistatic radar, can solve and in traditional bistatic radar, receive and dispatch the synchronous problem of spatial beams.Therefore bistatic MIMO radar has a wide range of applications, and its target detection and parameter estimation have become a study hotspot of field of radar.The emission array of bistatic MIMO radar is launched mutually orthogonal signal, and the receiving array of apart from each other can utilize the orthogonality transmitting to form virtual array by matched filtering method, then utilize traditional super-resolution angle estimation algorithm can from virtual array, estimate the emission angle of target (Direction Of Departure, and acceptance angle (Direction Of Arrival DOD), DOA), thus the multiple targets in implementation space without fuzzy cross bearing.

Modern radar is not only faced with the threat of high-speed flight guided missile and fighter plane in antiaircraft field, and in space industry, also needs real time monitoring sky unoccupied orbital target, and therefore the high maneuvering target of high speed is the new problem facing in modern radar target detection.Although the DOD of bistatic MIMO radar and DOA associating algorithm for estimating are widely studied, and emerge some effective algorithms, most of algorithm is not considered the impact that the high-speed motion of target is estimated angle on target.In bistatic MIMO radar, effective formation of virtual array and the Chief Signal Boatswain time integral of echo are the keys that angle on target is estimated.Because the large Doppler frequency that high-speed moving object produces can not be ignored the modulation transmitting within the matched filtering time, there is echoed signal serious distortion phenomenon, make the serious mismatch of matched filtering, thereby cause MIMO radar cannot effectively form virtual array, cause traditional super-resolution algorithm to be difficult to angle on target and estimate.Simultaneously, high-speed moving object can cross over multiple range units integration time at echo in angle estimation process, be that target energy is dispersed on multiple range units, therefore, when MIMO radar utilizes traditional super-resolution algorithm estimating target angle, must first target energy be focused on single range unit, otherwise can affect the angle estimation precision of target.R.P.Perry etc. are range correction technology conventional in a kind of radar in 188 pages of conversion of the Keystone to 200 pages of propositions of IEEE Transactions on Aerospace and Electronic Systems periodical the 35th the 1st phase of volume in 1999, it can align target echo envelope by the change of scale of slow time shaft within long echo integration time, owing to still can retain phase of echo relation in low signal-to-noise ratio situation, be therefore applicable to faint high-speed target and detect.But Keystone conversion can be lost efficacy in the time that doppler ambiguity appears in target, but target high-speed motion will inevitably cause doppler ambiguity under the low-repetition-frequency restriction of radar signal, and Keystone conversion also cannot be proofreaied and correct the range curvature being caused by the radial acceleration of the high maneuvering target of high speed, realize because change of scale generally needs interpolation arithmetic, therefore its operand is larger simultaneously.Qin Guodong is in 2763 pages to 2768 pages of electronic letters, vol periodical the 38th the 12nd phase of volume in 2010 multi-Dimensional parameters that cascade Keystone conversion are applied to multi-carrier frequency MIMO radar high-speed target are estimated, lost efficacy for fear of Keystone conversion, the method is first searched for estimation to the doppler ambiguity number of high-speed moving object, then poor correction of Doppler frequency of utilizing respectively Keystone transfer pair echo range walk and causing in each split tunnel because transmitting carrier frequency is different, thus the combine estimation of MIMO radar to high-speed moving object multi-Dimensional parameters solved.Cannot convert correction by Keystone but the Doppler frequency in different split tunnels being caused by the acceleration of high maneuvering target is poor, this can cause the virtual array of multi-carrier frequency MIMO radar effectively to form.Chen Jinli is electronics and information journal the 35th the 4th phase of volume in 2013 859 pages to the 864 pages a kind of methods that propose bistatic MIMO radar high-speed moving object DOD and DOA, for the echo signal that is dispersed in different distance unit is effectively added up, the method averages the sample covariance matrix that is dispersed in the object matching filtering output data on different distance unit, improves the estimated accuracy of angle on target by improving the estimated accuracy of covariance matrix.For fear of matched filter mismatch, the method expands its doppler tolerance by reducing matched filtering duration, but has sacrificed the channel separation performance of matched filter, makes the performance of the virtual array of MIMO radar formation can not reach optimum.

Summary of the invention

For addressing the above problem, the invention discloses the angle estimating method of the high maneuvering target of a kind of bistatic MIMO radar high speed.

For achieving the above object, the method that the present invention adopts is: the angle estimating method of the high maneuvering target of a kind of bistatic MIMO radar high speed, comprises the steps:

(1), receive the echoed signal of the high maneuvering target of high speed by the receiving array of bistatic MIMO radar;

(2), receiving array echo be positioned at transmitting on different distance unit and carry out conjugate multiplication;

(3), data after conjugate multiplication are carried out to Fourier transform in fast time domain and slow time domain successively;

(4), go out target velocity according to the peak estimation in step 3 result;

(5), be extracted in the slow time frequency domain components of target in different split tunnels at fast temporal frequency domain along target Doppler frequency value;

(6), by the splicing of the target frequency domain data on different distance door, realize across multiple range gate and form virtual array data;

(7), utilize super-resolution algorithm to estimate each target emission angle and acceptance angle.

Beneficial effect:

The angle estimating method of the high maneuvering target of a kind of bistatic MIMO radar high speed disclosed by the invention, compared with prior art tool has the following advantages:

(1) the high motion of automobile of the high speed of target causes the serious mismatch of conventional matched-filter, therefore bistatic MIMO radar cannot effectively form virtual array, thereby make traditional ultra-resolution method be difficult to effective estimation of target emission angle and reception, the inventive method is by carrying out the Fourier transform processing of fast time domain and slow time domain to data after receiving array echo and the conjugate multiplication that transmits, then be extracted in the target frequency domain components in different split tunnels, impact with the high motion of automobile of high speed of having avoided target on MIMO radar channel separation, make virtual array be able to effective formation.

(2) the present invention is spliced again by the target frequency domain components to being dispersed in multiple range units, thereby in the time that estimating, angle on target can effectively accumulate the target energy on different distance unit, to improve the estimated accuracy of target DOD and DOA, and its operand is more much lower than existing Range Walk Correction method, is conducive to Project Realization.

Accompanying drawing explanation

Fig. 1 is realization flow figure of the present invention;

Fig. 2 is bistatic MIMO radar arrangement schematic diagram of the present invention;

Fig. 3 is that the present invention carries out two-dimension fourier transform result figure to the data that transmit after conjugate multiplication on receiving array echo and different distance unit;

Fig. 4 is for utilizing traditional algorithm (ESPRIT algorithm) to estimate the planisphere of high-speed target angle;

Fig. 5 utilizes algorithm of the present invention to estimate the planisphere of high-speed target angle;

Fig. 6 is the angle estimation RMSE of target 1 and the graph of a relation of signal to noise ratio snr.

Embodiment

Below in conjunction with the drawings and specific embodiments, further illustrate the present invention, should understand following embodiment and only be not used in and limit the scope of the invention for the present invention is described.It should be noted that, word 'fornt', 'back', " left side ", " right side ", "up" and "down" that use is described below refer to the direction in accompanying drawing, and word " interior " and " outward " refer to respectively the direction towards or away from specific features geometric center.

The angle estimating method of the high maneuvering target of a kind of bistatic MIMO radar high speed of the present invention comprises the following steps:

Step 1, the receiving array by bistatic MIMO radar receives the echoed signal of the high maneuvering target of high speed.

Suppose that bistatic MIMO radar emission array and receiving array all adopt equidistant even linear array, be made up of respectively M transmitting array element and N reception array element, its array element distance is respectively d _tand d _r, as shown in Figure 2.M transmitting array element is launched mutually orthogonal cycle baseband phase coded signal, can be expressed as

$S(\tilde{t},t_l)={[S_1(\tilde{t},t_l)S_2(\tilde{t},t_l)\·\·\·S_M(\tilde{t},t_l)]}^T---\left(1\right)$

In formula, [] ^trepresent vector transposition; t _l=lT is the slow time, the repetition period that wherein T is radar signal;

wherein t is the fast time, 0≤t < T; be transmitting of m transmitting array element.

Suppose on identical initial Range resolution unit, to have P the high maneuvering target of high speed, its emission angle (DOD) is expressed as θ _t1, θ _t2..., θ _tP, acceptance angle (DOA) is expressed as θ _r1, θ _r2..., θ _rP, (θ so _tp, θ _rp) can represent p (p=1,2 ..., P) locus of individual target.P target made uniformly accelrated rectilinear motion, makes v _p=v _tp+ v _rpand a _p=a _tp+ a _rpbe " radial velocity and " and " radial acceleration and " of p target, v _tpand v _rpbe the radial velocity of p target with respect to emission array and receiving array, a _tpand a _rpbe the radial acceleration of p target with respect to emission array and receiving array.The distance that high-speed target moves within echoed signal integration time is less than its distance from emission array and receiving array, and the subtle change that therefore target DOA and DOD occur within echo integration time is negligible.Receiving array base band echoed signal can be expressed as

$X(\tilde{t},t_l)=\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}{a}_r\left({\mathrm{\&theta;}}_{\mathrm{rp}}\right){\mathrm{\&rho;}}_p{a}_t^T\left({\mathrm{\&theta;}}_{\mathrm{tp}}\right)S(\tilde{t}-\frac{v_p\tilde{t}}{c}-\frac{a_{\mathrm{<figure-callout\; id="2"\; label="p\; t"\; filenames="140225173602.png"\; state="\{\{state\}\}">p</figure-callout>}}\stackrel{}{t^{}}\widetilde{{}^2}}{2c},t_l)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="140225173602.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}(f_{\mathrm{dp}}\tilde{t}+\frac{a_{\mathrm{<figure-callout\; id="2"\; label="p"\; filenames="140225173602.png"\; state="\{\{state\}\}">p</figure-callout>}}}{2\mathrm{\&lambda;}}\stackrel{~}{{\mathrm{<figure-callout\; id="2"\; label="t"\; filenames="140225173602.png"\; state="\{\{state\}\}">t</figure-callout>}}^2})}+\mathrm{\&omega;}(\tilde{t},t_l)---\left(2\right)$

In formula, for the output echoed signal vector of receiving array; ρ _prepresent the scattering coefficient of p target; $a_r\left({\mathrm{\&theta;}}_{\mathrm{rp}}\right)={[1e^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;})d_r{\sin \mathrm{\&theta;}}_{\mathrm{rp}}}\&CenterDot;\&CenterDot;\&CenterDot;e^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;})(N-1)d_r{\sin \mathrm{\&theta;}}_{\mathrm{rp}}}]}^T$ Be the receiving array steering vector of size for N × 1 dimension, λ is carrier wavelength; $a_r\left({\mathrm{\&theta;}}_{\mathrm{rp}}\right)={[1e^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;})d_r{\sin \mathrm{\&theta;}}_{\mathrm{rp}}}\&CenterDot;\&CenterDot;\&CenterDot;e^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;})(N-1)d_r{\sin \mathrm{\&theta;}}_{\mathrm{rp}}}]}^T$ The emission array steering vector of size for M × 1 dimension; f _dp(t) be the Doppler frequency of p target, can be expressed as f _dp=(v _tp+ v _rp)/λ=v _p/ λ; λ is wavelength; for the noise vector of receiving array, obey zero-mean, variance is

multiple Gaussian distribution, wherein I _nfor the unit matrix of N × N.The envelope variation being caused by acceleration within whole echo integration time is much smaller than range resolution, and be also very small by target velocity caused envelope variation within the fast time, therefore by aimed acceleration within echo integration time and the envelope variation that causes within the fast time of target velocity can ignore.Therefore formula (2) can be reduced to

$X(\tilde{t},t_l)\&ap;\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}{a}_r\left({\mathrm{\&theta;}}_{\mathrm{rp}}\right){\mathrm{\&rho;}}_p{a}_t^T\left({\mathrm{\&theta;}}_{\mathrm{tp}}\right)S(\tilde{t}-\frac{v_p{t}_l}{c},t_l)e^{{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="140225173602.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}}_{\mathrm{dp}}t}\&CenterDot;e^{{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="140225173602.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}}_{\mathrm{dp}}{t}_l}{e}^{{-\mathrm{j\&pi;a}}_{\mathrm{<figure-callout\; id="2"\; label="p\; t\; l"\; filenames="140225173602.png"\; state="\{\{state\}\}">p</figure-callout>}}{{t_l}^{}}_{}{{{}_{}}^2}_{}/\mathrm{\&lambda;}}+\mathrm{\&omega;}(\tilde{t},t_l)---\left(3\right)$

From formula (3), within long echo integration time, the change of distance of high-speed moving object tends to be greater than the range resolution of radar, and the phenomenon of walking about can appear in target echo envelope within integration time; And the Doppler frequency variation range being caused by aimed acceleration can be greater than Doppler's resolution element, there are target Doppler diffusion phenomena, but because aimed acceleration causes that within the fast time it is very small that caused phase place changes, therefore in formula (3), in the 3rd exponential term, only consider that the phase place that aimed acceleration produces in slow time domain changes.The range walk of high-speed target and Doppler's diffusion phenomena cause target energy to be dispersed on multiple range units and Doppler unit.First exponential term in formula (3) represents that Doppler frequency can be to transmitting and modulate in the fast time, because the Doppler frequency of high-speed moving object is often greater than the half of radar signal repetition frequency,

doppler frequency caused phase place variation within the fast time be can not ignore, be that serious distortion can occur echoed signal, cause the serious mismatch of matched filter, thereby cannot effectively form virtual array, therefore bistatic MIMO radar is difficult to effectively estimate the high maneuvering target DOD of high speed and DOA.

Step 2, receiving array echo be positioned at transmitting on different distance unit and carry out conjugate multiplication.

The high maneuvering target of high speed produces large Doppler frequency and not only destroys the orthogonality between transmitting, and make the mismatch loss of matched filter serious, and the energy of the high maneuvering target of high speed is dispersed on different resolution elements, what this all can cause bistatic MIMO radar cannot form effective virtual array, and then affects the estimation of angle on target parameter.Make z _p(t _l) the range unit number crossed within the 1st cycle that transmits for p target, z _p(t _l) value is integer, the wherein distance between target and emission array and receiving array and corresponding Range resolution unit δ=c/B, B is transmitted signal bandwidth, so

In formula,

represent to be more than or equal to the smallest positive integral of b.Walk about and can ignore the impact of echo envelope due to the target range less than distance by radar resolution, therefore formula (3) can be reduced to

$X(\tilde{t},t_l)\&ap;\underset{p=1}{\overset{P}{\mathrm{\&Sigma;}}}{a}_r\left({\mathrm{\&theta;}}_{\mathrm{rp}}\right){\mathrm{\&rho;}}_p{a}_t^T\left({\mathrm{\&theta;}}_{\mathrm{tp}}\right)S(\tilde{t}-\frac{v_p{t}_l}{c},t_l)e^{{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="140225173602.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}}_{\mathrm{dp}}t}\&CenterDot;e^{{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="140225173602.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}}_{\mathrm{dp}}{t}_l}{e}^{{-\mathrm{j\&pi;a}}_{\mathrm{<figure-callout\; id="2"\; label="p\; t\; l"\; filenames="140225173602.png"\; state="\{\{state\}\}">p</figure-callout>}}{{t_l}^{}}_{}{{{}_{}}^2}_{}/\mathrm{\&lambda;}}+\mathrm{\&omega;}(\tilde{t},t_l)---\left(5\right)$

The range unit number that hypothetical target is crossed within echo integration time is in [Z, Z], and wherein Z is integer.Be used in the reference signal on z (z ∈ [Z, Z]) range unit at receiving end so

to the echo of n reception array element carry out conjugate multiplication, can the conjugate multiplication on z range unit be output as

$\begin{array}{c}{Y}_{\mathrm{mn}}(t,t_l,z)=\underset{p\&Element;C_{\mathrm{zl}}}{\overset{P}{\underset{p=1}{\mathrm{\&Sigma;}}}}{\mathrm{\&beta;}}_p{\left(z\right)e}^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;})(n-1)d_r{\sin \mathrm{\&theta;}}_{\mathrm{rp}}}{\&CenterDot;e^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;})\left(\text{m-1}\right)d_t{\sin \mathrm{\&theta;}}_{\mathrm{tp}}}e}^{{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="140225173602.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}}_{\mathrm{dp}}\text{t}}\&CenterDot;e^{{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="140225173602.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}}_{\mathrm{dp}}{t}_l}{e}^{{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="140225173602.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}}_{\mathrm{<figure-callout\; id="2"\; label="dp\; t\; l"\; filenames="140225173602.png"\; state="\{\{state\}\}">dp</figure-callout>}}{{t_l}^{}}_{}{{{}_{}}^2}_{}/\mathrm{\&lambda;}}\\ +{\mathrm{\&phi;}}_{\mathrm{mn}}(t,t_l,z)+W_{\mathrm{mn}}(t,t_l,z)\end{array}---\left(6\right)$

Formula ⁱⁿ, C _zlfor p meets z _p(t _l)=z (p=1,2 ..., value p) ^collectionclose;

ψ (z) represents the initial phase of target p echo on z range unit;

in formula (6), Section 1 is owing to working as z _p(t _lwhen)=z

and form, in fast time domain, Section 1 has become sinusoidal signal, and wherein [] * represents to get complex conjugate; Section 2 φ in formula (6) _mn(t, t _l, z) can be expressed as

$\begin{array}{c}{\mathrm{\&phi;}}_{\mathrm{mn}}(\tilde{t},t_l,z)=\underset{p\&Element;C_{\mathrm{zl}}}{\overset{P}{\underset{p=1}{\mathrm{\&Sigma;}}}}{\mathrm{\&beta;}}_p{\left(z\right)e}^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;}){(n-1)d}_r{\sin \mathrm{\&theta;}}_{\mathrm{rp}}}\&CenterDot;\underset{i\&NotEqual;m}{\overset{M}{\underset{i=1}{\mathrm{\&Sigma;}}}}{e}^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;}){(i-1)d}_r{\sin \mathrm{\&theta;}}_{\mathrm{tp}}}{S}_i(t+t_l-\frac{\mathrm{z\&delta;}}{c},t_l)S_m^{*}(t+t_l-\frac{\mathrm{z\&delta;}}{c},t_l)\\ \&CenterDot;e^{{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="140225173602.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}}_{\mathrm{dp}}t}\&CenterDot;e^{{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="140225173602.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}}_{\mathrm{dp}}{t}_l}{e}^{{-\mathrm{j\&pi;a}}_p{t_l}^2/\mathrm{\&lambda;}}+\underset{p\&NotElement;C_{\mathrm{zl}}}{\overset{P}{\underset{p=1}{\mathrm{\&Sigma;}}}}{\mathrm{\&beta;}}_p{e}^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;}){(N-1)d}_r{\sin \mathrm{\&theta;}}_{\mathrm{rp}}}{a_t}^T\left({\mathrm{\&theta;}}_{\mathrm{tp}}\right)\\ \&CenterDot;S(t+t_l-\frac{z_p\left(t_l\right)\mathrm{\&delta;}}{c},t_l)S_m^{*}(t+t_l-\frac{\mathrm{z\&delta;}}{c},t_l)e^{{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="140225173602.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}}_{\mathrm{dp}}t}\&CenterDot;e^{{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="140225173602.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}}_{\mathrm{dp}}{t}_l}{e}^{{-\mathrm{j\&pi;a}}_p{t_l}^2/\mathrm{\&lambda;}}\end{array}---\left(7\right)$

Step 3, carries out Fourier transform in fast time domain and slow time domain successively to data after conjugate multiplication.

In fast time domain to Y _mn(t, t _l, z) carrying out Fourier transform, can obtain

$\begin{array}{c}{Y}_{\mathrm{mn}}(f,t_l,z)={\&Integral;}_0^T{Y}_{\mathrm{mn}}{(t,t_l)e}^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="140225173602.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;ft}}\mathrm{dt}\\ =\underset{p\&Element;C_{\mathrm{zl}}}{\overset{P}{\underset{p=1}{\mathrm{\&Sigma;}}}}{\mathrm{\&beta;}}_p{\left(z\right)e}^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;}){(n-1)d}_r{\sin \mathrm{\&theta;}}_{\mathrm{rp}}}\&CenterDot;e^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;}){(m-1)d}_t{\sin \mathrm{\&theta;}}_{\mathrm{tp}}}\&CenterDot;\frac{\sin \left[\mathrm{\&pi;}(f+f_{\mathrm{dp}})T\right]}{\mathrm{\&pi;}(f+f_{\mathrm{dp}})T}\\ \&CenterDot;e^{-\mathrm{j\&pi;}(f+f_{\mathrm{dp}})T}\&CenterDot;e^{{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="140225173602.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}}_{\mathrm{dp}}{t}_l}{e}^{{-\mathrm{j\&pi;a}}_{\mathrm{<figure-callout\; id="2"\; label="p\; t\; l"\; filenames="140225173602.png"\; state="\{\{state\}\}">p</figure-callout>}}{t_l}^{}{{}_{}}^2/\mathrm{\&lambda;}}+{\mathrm{\&phi;}}_{\mathrm{mn}}(f,t_l,z)+W_{\mathrm{mn}}(f,t_l,z)\end{array}----\left(8\right)$

The Doppler frequency of high-speed moving object is often greater than the repetition frequency of radar signal, now there will be and owes the phenomenon of sampling.In this case, the true Doppler frequency of target p can be expressed as

f _dp＝f _dp0+n _p/T(9)

In formula, f _dp0for not fuzzy Doppler frequency; n _pfor doppler ambiguity number.By formula (9) substitution formula (8), can obtain

$\begin{array}{c}{Y}_{\mathrm{mn}}(f,t_l,z)=\underset{p\&Element;C_{\mathrm{zl}}}{\overset{P}{\underset{p=1}{\mathrm{\&Sigma;}}}}{\mathrm{\&beta;}}_p{\left(z\right)e}^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;}){(n-1)d}_r{\sin \mathrm{\&theta;}}_{\mathrm{rp}}}\&CenterDot;e^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;}){(m-1)d}_t{\sin \mathrm{\&theta;}}_{\mathrm{tp}}}\&CenterDot;\frac{\sin \left[\mathrm{\&pi;}(f+f_{\mathrm{dp}})T\right]}{\mathrm{\&pi;}\left(f{+f}_{\mathrm{dp}}\right)T}\\ \&CenterDot;e^{-\mathrm{j\&pi;}(f+f_{\mathrm{dp}})T}\&CenterDot;e^{{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="140225173602.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}}_{\mathrm{dp}0}{t}_l}\&CenterDot;e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="140225173602.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;}(n_p/T)t_l}\&CenterDot;e^{{-\mathrm{j\&pi;a}}_{\mathrm{<figure-callout\; id="2"\; label="p\; t\; l"\; filenames="140225173602.png"\; state="\{\{state\}\}">p</figure-callout>}}{t_l}^{}{{}_{}}^2/\mathrm{\&lambda;}}+{\mathrm{\&phi;}}_{\mathrm{mn}}(f,t_l,z)+W_{\mathrm{mn}}(f,f_l,z)\end{array}---\left(10\right)$

Due to 2 π (n in the 3rd exponential term in formula (10) the 2nd row _p/ T) t _lthe integral multiple of 2 π,

therefore formula (10) can be expressed as again

$\begin{array}{c}{Y}_{\mathrm{mn}}(f,t_l,z)=\underset{p\&Element;C_{\mathrm{zl}}}{\overset{P}{\underset{p=1}{\mathrm{\&Sigma;}}}}{\mathrm{\&beta;}}_p{\left(z\right)e}^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;}){(n-1)d}_r{\sin \mathrm{\&theta;}}_{\mathrm{rp}}}\&CenterDot;e^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;}){(m-1)d}_t{\sin \mathrm{\&theta;}}_{\mathrm{tp}}}\&CenterDot;\frac{\sin \left[\mathrm{\&pi;}(f+f_{\mathrm{dp}})T\right]}{\mathrm{\&pi;}\left(f{+f}_{\mathrm{dp}}\right)T}\\ \&CenterDot;e^{-\mathrm{j\&pi;}(f+f_{\mathrm{dp}})T}\&CenterDot;e^{{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="140225173602.png"\; state="\{\{state\}\}">j</figure-callout>}2\mathrm{\&pi;f}}_{\mathrm{dp}0}{t}_l}\&CenterDot;\&CenterDot;e^{{-\mathrm{j\&pi;a}}_{\mathrm{<figure-callout\; id="2"\; label="p\; t\; l"\; filenames="140225173602.png"\; state="\{\{state\}\}">p</figure-callout>}}{t_l}^{}{{}_{}}^2/\mathrm{\&lambda;}}+{\mathrm{\&phi;}}_{\mathrm{mn}}(f,t_l,z)+W_{\mathrm{mn}}(f,f_l,z)\end{array}---\left(11\right)$

Suppose that the signal energy of p target on z range unit appears at the repetition period and be numbered l=L _pmin, L _pmin+ 1 ..., L _pmaxmoment in, in slow time domain to formula (8) about t _lcarry out Fourier transform, can be obtained by the resident theorem of phase place,

$\begin{array}{c}{Y}_{\mathrm{mn}}(f,f_l,z)\&ap;\underset{p\&Element;C_{\mathrm{zl}}\&Element;}{\overset{P}{\underset{p=1}{\mathrm{\&Sigma;}}}}{\mathrm{\&beta;}}_p{\left(z\right)e}^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;}){(n-1)d}_r{\sin \mathrm{\&theta;}}_{\mathrm{rp}}}\&CenterDot;e^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;}){(m-1)d}_r{\sin \mathrm{\&theta;}}_{\mathrm{tp}}}\&CenterDot;\frac{\sin \left[\mathrm{\&pi;}(f+f_{\mathrm{dp}})T\right]}{\mathrm{\&pi;}(f+f_{\mathrm{dp}})T}{e}^{-\mathrm{j\&pi;}(f+f_{\mathrm{dp}})T}\\ \&CenterDot;\mathrm{rect}\left[\frac{f_l+f_{\mathrm{dp}0}}{(L_{\mathrm{pamx}}-L_{p\min })T\&CenterDot;a_p/\mathrm{\&lambda;}}\right]e^{\mathrm{j\&pi;}{(f_t+f_{\mathrm{dp}0})}^2/\left({a_p/\mathrm{\&lambda;}}_{}\right)}{e}^{-\mathrm{j\&pi;f}1(L_{\mathrm{pamx}}+L_{p\min })T}+{\mathrm{\&xi;}}_{\mathrm{mn}}(f,f_l,z)\end{array}---\left(12\right)$

In formula,

ζ _mn(f, fl, z)=φ _mn(f, f _l, z)+W _n(f, f _l, z).From formula (12), due to the existence of aimed acceleration, make the frequency spectrum of target in slow time domain there will be broadening phenomenon.

Step 4, goes out target velocity according to the peak estimation in step 2 result.

Owing to there being the echoed signal of each target on initial distance door z=0, therefore can utilize frequency domain data Y on initial distance door _mn(f, f _l, z=0) and (m=1,2, ..., M, n=1,2, ..., N) Doppler frequency of estimating target and fuzzy Doppler frequency, in order to improve the main secondary lobe of target peak than to be conducive to target detection, can combine the frequency domain data of all about different transmitting array element and reception array element and estimate, the Doppler frequency and the fuzzy Doppler frequency that are target p can be estimated by following formula

$(\widehat{f_{\mathrm{dp}}},\hat{f_{\mathrm{<figure-callout\; id="0"\; label="dp"\; filenames="140225173609.png,140225173617.png"\; state="\{\{state\}\}">dp</figure-callout>}0}})=\underset{f,f_l}{\arg \max }\underset{m=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{n-1}{\overset{N}{\mathrm{\&Sigma;}}}\left|Y_{\mathrm{mn}}(-f,{-f}_{l}z=0)\right|---\left(13\right)$

In engineering application, for reducing operand, Fourier transform is replaced by fast fourier transform.Due to estimated value

be the integral multiple of radar signal repetition frequency, therefore can not utilize estimated value with

separate target velocity fuzzy, therefore " radial velocity and " estimated value of target velocity target p only by

conversion obtains,

$\widehat{v_p}=\mathrm{\&lambda;}\&CenterDot;\widehat{f_{\mathrm{dp}}}---\left(14\right)$

Step 5, is extracted in the slow time frequency domain components of target in different split tunnels at fast temporal frequency domain along target Doppler frequency value.

In by fast temporal frequency domain, extract target at slow time frequency domain components along target Doppler frequency value, can be expressed as

$Y_{\mathrm{mn}}(-\stackrel{}{v_{\text{p}}}/\mathrm{\&lambda;},f_l,z)=e^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;}){(n-1)d}_r{\sin \mathrm{\&theta;}}_{\mathrm{rp}}}\&CenterDot;e^{-j(2\mathrm{\&pi;}/\mathrm{\&lambda;}){(m-1)d}_t{\sin \mathrm{\&theta;}}_{\mathrm{tp}}}\&CenterDot;H_p(-\widehat{v_p}/\mathrm{\&lambda;}{,f}_l,z)+{\mathrm{\&xi;}}_{\mathrm{mn}}(-\widehat{v_p}/\mathrm{\&lambda;},f_l,z),p\&Element;C_{\mathrm{zl}}---\left(15\right)$

In formula,

$H_p(-\widehat{v_p}/\mathrm{\&lambda;},f_l,z)={\mathrm{\&beta;}}_p{\left(z\right)e}^{-\mathrm{j\&pi;}(\widehat{v_p}/\mathrm{\&lambda;}+f_{\mathrm{dp}})T}\&CenterDot;\mathrm{rect}\left[\frac{f_l+f_{\mathrm{dp}0}}{(L_{p\max }-L_{p\min })T\&CenterDot;a_p/\mathrm{\&lambda;}}\right]\&CenterDot;e^{-\mathrm{j\&pi;}{\left(f_l{+f}_{\mathrm{dp}0}\right)}^2/(a_p/\mathrm{\&lambda;})}{e}^{-j\mathrm{\&pi;}{f}_t(L_{p\max }+L_{p\min })T}.$

mn the channel components that the target p echoed signal on z range unit of distribution forms through above-mentioned processing in fact, m=1,2 ..., M, n=1,2 ..., N.Can obtain and be distributed in the component of signal of target p echoed signal in other split tunnels on z range unit according to same method so, on z range unit, the signal of target p in all MN split tunnel can be expressed as

$(-\widehat{v_p},\mathrm{\&lambda;},f_l,z)=({\mathrm{\&theta;}}_{\mathrm{rp}},{\mathrm{\&theta;}}_{\mathrm{tp}})H_P(-\widehat{v_p}/\mathrm{\&lambda;},f_l,z)+\mathrm{\&xi;}(-\widehat{v_p}/\mathrm{\&lambda;},f_l,z),C_{\mathrm{zl}}---\left(16\right)$

In formula, $Y(-\widehat{v_p}/\mathrm{\&lambda;},f_l,z)={[Y_1(-\widehat{v_p}/\mathrm{\&lambda;},f_l,z),Y_2(-\widehat{v_p}/\mathrm{\&lambda;},f_l,z),...,Y_{\mathrm{MN}}(-\widehat{v_p}/\mathrm{\&lambda;},f_l,z)]}^T;$ A (θ _rp, θ _tp)=

for Kronecker amasss;

be to be MN × 1 n dimensional vector n, formed by the mutual distracter of the noise after channel separation and echo signal.

be exactly that target p is distributed in the virtual array output data that the echoed signal on z range unit forms after above-mentioned processing in fact.

Step 6, by the splicing of the target frequency domain data on different distance door, realizes across multiple range gate and forms virtual array data.

If target p moves away from radar, known according to formula (13), its range unit of crossing within echo integration time is respectively z _p=0,1 ..., Z _p, the virtual array data that target p is distributed on all range units are spliced by formula (17),

$\widetilde{Y_{\mathrm{pl}}}=[Y(-\widehat{v_p}/\mathrm{\&lambda;},f_l,0)Y(-\widehat{v_p/\mathrm{\&lambda;},f_l,1}),...,Y(-\widehat{v_p}/\mathrm{\&lambda;},f_l,Z_p)]---\left(17\right)$

The output data of virtual array after splicing

covariance matrix be

$R_p=\frac{1}{Z_{p}L}\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}\widetilde{Y_{\mathrm{pl}}}\&CenterDot;\widetilde{Y_{\mathrm{pl}}^H}=\frac{1}{Z_p}\underset{z=0}{\overset{Z_p}{\mathrm{\&Sigma;}}}\frac{1}{L}\&CenterDot;\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}Y(-\widehat{v_p}/\mathrm{\&lambda;},f_l,z)Y^H(-\widehat{v_p}/\mathrm{\&lambda;},f_l,z)---\left(18\right)$

In formula, () ^hrepresent conjugate transpose; L is the fast umber of beats for estimate covariance matrix.After through formula (17), by target p, the virtual array data on all range units are spliced, its fast umber of beats has become Z _pl, therefore can improve the estimated accuracy of covariance matrix, thereby the emission angle of target p and the estimated accuracy of acceptance angle also can be improved thereupon.If target p moves towards radar, known according to formula (13), its range unit of crossing within echo integration time is respectively z _p=0 ,-1 ... ,-Z _p, the virtual array data that target p is distributed on all range units are carried out similar splicing,

$\widetilde{Y_{\mathrm{pl}}}=[Y(-\widehat{v_p}/\mathrm{\&lambda;},f_l,0)Y(-\widehat{v_p/\mathrm{\&lambda;},f_l,1}),...,Y(-\widehat{v_p}/\mathrm{\&lambda;},f_l,{-Z}_p)]---\left(19\right)$

The output data of virtual array after splicing

covariance matrix be

$R_p=\frac{1}{Z_{p}L}\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}\widetilde{Y_{\mathrm{pl}}}\&CenterDot;\widetilde{Y_{\mathrm{pl}}^H}=\frac{1}{Z_p}\underset{z=-\mathrm{<figure-callout\; id="0"\; label="Z"\; filenames="140225173609.png,140225173617.png"\; state="\{\{state\}\}">Z</figure-callout>}}{\overset{0}{\mathrm{\&Sigma;}}}\frac{1}{L}\&CenterDot;\underset{l=1}{\overset{L}{\mathrm{\&Sigma;}}}Y(-\widehat{v_p}/\mathrm{\&lambda;},f_l,z)Y^H(-\widehat{v_p}/\mathrm{\&lambda;},f_l,z)---\left(20\right)$

Step 7, utilizes super-resolution algorithm to estimate each target emission angle and acceptance angle.

To covariance matrix R _pcarrying out feature decomposition has

$R_p=U_s{\mathrm{\&Sigma;}}_S{U_s}^H+U_n{\mathrm{\&Sigma;}}_n{U_n}^H---\left(21\right)$

In formula, Σ _sfor scalar, the large eigenwert of corresponding target p, this is due to virtual array output data

in only there is target p; Σ _nfor diagonal matrix, diagonal element is made up of little eigenwert;

with

be respectively signal subspace and the noise subspace of virtual array.U _s=A (θ _rp, θ _tp) T, in the time there is single target, T is scalar.Order

a'(θ so _rp, θ _tp) can be by A (θ _rp, θ _tp) obtain through several times line translations, adopt so the identical line translation can be from U _sin can obtain U' _s, suppose U _s1and U _s2be respectively U _sbefore (N-1) M capable and rear (N-1) M capable; And U' _s1and U' _s2be respectively U' _sbefore (M-1) N capable and rear (M-1) N capable.Order

$r_{\mathrm{rp}}=\frac{1}{M(N-1)}\underset{i=1}{\overset{M(N-1)}{\mathrm{\&Sigma;}}}\frac{U_{s2}\left(i\right)}{U_{\mathrm{sl}}\left(i\right)}---\left(22\right)$

$r_{\mathrm{rp}}=\frac{1}{N(M-1)}\underset{i=1}{\overset{N(M-1)}{\mathrm{\&Sigma;}}}\frac{{U^{\&prime;}}_{s2}\left(i\right)}{{U^{\&prime;}}_{\mathrm{sl}}\left(i\right)}---\left(23\right)$

In formula, U _s1and U (i) _s2(i) be respectively U _s1and U _s2in i row element; U' _s1and U' (i) _s2(i) be respectively U' _s1and U' _s2in i row element.The DOA θ of target p so _rpwith DOD θ _tpestimated value is respectively

$\widehat{{\mathrm{\&theta;}}_{\mathrm{rp}}}=\arcsin (-\mathrm{\&lambda;}\&CenterDot;\frac{\mathrm{angle}\left(r_{\mathrm{rp}}\right)}{{2\mathrm{\&pi;d}}_r})---\left(24\right)$

$\widehat{{\mathrm{\&theta;}}_{\mathrm{rp}}}=\arcsin (-\mathrm{\&lambda;}\&CenterDot;\frac{\mathrm{angle}\left(r_{\mathrm{tp}}\right)}{{2\mathrm{\&pi;d}}_t})---\left(25\right)$

The acceptance angle of other targets and emission angle also can adopt same method to obtain.

Technique effect of the present invention can further illustrate by following simulation result.

Radar system parametric description: the carrier frequency of bistatic MIMO radar is f ₀=10GHz, transmitting array number M=6, receives array number N=8, transmits and receives array element distance d _t=d _r=1.5cm.The each array element of emission array is launched mutually orthogonal Gold coded signal, symbol width τ=0.1 _{μ s}, the phase encoding length within the cycle is 1023, radar signal cycle T=102.3 _{μ s}within echo integration time, the signal repetition period is counted L=128.

Emulation content 1: the Fourier transform results of data in fast time domain and slow time domain after conjugate multiplication.

Simulated conditions: suppose to have 3 high-speed targets on same initial Range resolution unit, their emission angle and acceptance angle are respectively (θ _t1, θ _r130 ° of)=(, 60 °), (θ _t2, θ _r25 ° of)=(, 40 °), (θ _t3, θ _r325 ° of)=(, 10 °), the radial velocity of 3 targets and be respectively 7500m/s, 9000m/s, 6500m/s, radial acceleration and be respectively 400m/s ², 500m/s ², 450m/s ², the signal to noise ratio snr=-30dB of three high-speed targets.In emulation by receiving array echoed signal respectively be positioned at transmitting on different distance unit and carry out conjugate multiplication, then carry out fast Fourier transform (FFT) processing in fast time domain and slow time domain, result as shown in Figure 3.As can be seen from Figure 3, in radar detection area, there are 3 high-speed targets, the signal energy of one of them target is dispersed in z=0, on 1,2 range unit, 3 range units have been crossed at echo internal object integration time, and the signal energy of two objects is dispersed in z=0,1,2 in addition, on 3 range units, 4 range units are crossed at echo internal object integration time; Target echo signal energy conversion can be represented in fast time speed-slow time Speed Two Dimensions region by the processing of this paper method, can be without the speed of 3 of a blur estimation high-speed target according to fast time speed territory, wherein the fast time velocity estimation value of 3 targets is respectively 7625.8m/s, 9092.3m/s, 6452.6m/s, but because the lower speed estimation error that causes of speed resolution is larger, relative error is respectively 1.7%, 1.03%, 0.73%.But in slow time domain, carrying out FFT processes estimated target velocity and has fuzzy problem.

Emulation content 2: bistatic MIMO radar utilizes traditional algorithm and algorithm of the present invention to estimate the planisphere of high-speed target angle.

Simulated conditions: target component arranges same emulation content 1.Bistatic MIMO radar utilizes respectively DOD and the DOA of traditional algorithm and algorithm estimating target of the present invention, and traditional algorithm adopts Chen Duofang the 770th page of ESPRIT algorithm to the bistatic MIMO radar of being applied to of 771 pages of propositions of the 44th phase the 12nd volume in 2008 at Electronics Letters periodical.Fig. 4 and Fig. 5 are respectively the parameter planisphere that bistatic MIMO radar utilizes traditional algorithm and the inventive method to estimate, in figure, "+" represents the actual position of target, carry out 150 Monte Carlo experiments.From Figure 4 and 5, traditional algorithm has been difficult to the parameter estimation of high-speed moving object under the impacts such as range migration and matched filter mismatch; Algorithm of the present invention can effectively form virtual array, and can accumulate echo signal energy across range gate, therefore can the DOD of the high maneuvering target of high speed and DOA effectively be estimated and accurately be matched, can the high maneuvering target of the multiple high speeds of effective location.

Emulation content 3: the relation of high-speed target angle estimation RMSE and signal to noise ratio snr.

Simulated conditions: the signal to noise ratio snr of supposing three high-speed targets changes between-30dB～0dB, and other simulation parameters are with emulation content 1.The root-mean-square error of objective definition angle estimation is

wherein θ _rwith θ _tbe respectively estimated value and the actual value of target acceptance angle DOA and emission angle DOD.Independently carry out 200 Monte-Carlo experiments, when the bistatic MIMO radar of Fig. 6 utilizes the inventive method and classic method, the variation relation of target 1 angle estimation root-mean-square error and target signal to noise ratio as shown.There is acceleration, target without acceleration and only do not utilize initial distance door to form in virtual array data estimation angle on target situation across range gate estimating target angle and carry out emulation respectively in the inventive method in target, and classic method respectively target at a high speed and have acceleration (target component arranges same emulation content 1) and target low speed and without acceleration situation under carry out emulation, when wherein target low speed is without acceleration situation, 3 target velocities are set to respectively 55m/s, 0m/s, 100m/s, other parameters are with emulation content 1.As can be seen from Figure 6, the inventive method can effectively be estimated emission angle and the acceptance angle parameter of the high maneuvering target of high speed, its angle estimation precision close to classic method in target low speed situation without the angle estimation precision in the situations such as range walk and matched filter mismatch, but classic method can lose efficacy in the time existing target range to walk about with matched filter mismatch, is unable to estimate the angle parameter of the high maneuvering target of high speed; It is less that the angle estimation performance of the inventive method is affected by aimed acceleration; The inventive method is carried out data splicing by target frequency domain components target being dispersed in multiple range gate, realize across multiple range gate and form virtual array data, therefore its angle estimation precision is apparently higher than only utilizing target frequency domain data in single range gate to carry out the precision of angle estimation.

The disclosed technological means of the present invention program is not limited only to the disclosed technological means of above-mentioned technological means, also comprises the technical scheme being made up of above technical characterictic combination in any.The above is the specific embodiment of the present invention; it should be pointed out that for those skilled in the art, under the premise without departing from the principles of the invention; can also make some improvements and modifications, these improvements and modifications are also considered as protection scope of the present invention.

Claims (1)

1. an angle estimating method for the high maneuvering target of bistatic MIMO radar high speed, is characterized in that: comprise the steps:

(1), receive the echoed signal of the high maneuvering target of high speed by the receiving array of bistatic MIMO radar;

(2), receiving array echo be positioned at transmitting on different distance unit and carry out conjugate multiplication;

(3), data after conjugate multiplication are carried out to Fourier transform in fast time domain and slow time domain successively;

(4), go out target velocity according to the peak estimation in step 3 result;

(5), be extracted in the slow time frequency domain components of target in different split tunnels at fast temporal frequency domain along target Doppler frequency value; (6), by the splicing of the target frequency domain data on different distance door, realize across multiple range gate and form virtual array data;

(7), utilize super-resolution algorithm to estimate each target emission angle and acceptance angle.

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