CN104678373A - Simple radar multi-target parameter extraction method - Google Patents

Abstract

The invention discloses a simple radar multi-target parameter extraction method. In the method, D is equal to three targets, when the number of targets is greater than 3, equations similar to equations (3) and (4) can be written in an imitating manner, but only the expression is relatively lengthy. The simple radar multi-target parameter extraction method specifically comprises the following steps: 1), estimating initial parameters of a signal direction, wherein when i ranges from 1 to D, D represents the sequence number of signals and is supposed to be equal to 3, if i is equal to 1, a formula shown in the description and another formula shown in the description are calculated so as to obtain an estimated target direction parameter initial value shown in the description, and i ranges from 1 to 3; 2), performing main iterative circulation, estimating a parameter shown in the description according to the initial parameters obtained in the step 1), thereby obtaining precise estimation on i, wherein i ranges from 1 to 3; 3), for the precise estimation on the value as shown in the description obtained in the step 2), calculating another two formulas shown in the description so as to obtain estimation on three target waveform parameters according to formula (4) and (8) shown in the specification, thereby providing parameter basis on target positioning and waveform identification, wherein i ranges from 1 to 3; when the number of the targets is greater than or equal to 3, writing a corresponding matrix shown in the description, Qi and expression of a projection matrix operator Pak,i according to existing expression such as P <A2-3> and matrix inversion iterative calculation relationship shown in the description. Therefore, the calculation complexity degree is substantially reduced, and the inversion errors can be avoided.

Description

A kind of easy Radar Multi Target parameter extracting method

Technical field

The invention belongs to Radar Multi Target parameter detecting and estimation technique field, particularly the easy Radar Multi Target parameter extracting method of one.

Background technology

Radar Multi Target parameter detecting and estimation technique are widely used in military and civilian field, and especially under same of current multiple warhead and many interference co-existences military technology background and extensive multiple-input and multiple-output civilian technology system, this technology seems particularly important.

Radar Multi Target parameter detecting and estimation technique be obtain multiple different target the parameter such as orientation, waveform to distinguish it separately, and then for identification they provide basis.Existing Radar Multi Target parameter detecting and estimation technique are roughly divided into data fitting and subspace fitting, the former will relate to matrix inversion when multiple goal realizes and the latter relates to matrix-eigenvector-decomposition computing, these computings are main causes of their complexity, and the application is mainly for data fitting.

Data fitting class technology is mostly by maximum likelihood multiple goal parameter detecting derives from technology, the greatest drawback of this technology is realizing will relating to inverting of corresponding matrix in multiple goal separation and identification process, the complexity that matrix inversion not only makes detection realize promotes, more crucially when multiple target is gathered among a small circle, its arithmetic eror will significantly increase, thus the difficulty that realizes not only promoting target detection identification also increases its detection and identification error rate.

Classical Radar Multi Target detection signal model is:

y(t)＝A(Θ)s(t)+n(t)，t＝1,2,…,N

Wherein y (t) is radar measured data, and A (Θ) is referred to as array manifold matrix, and it comprises target number, and information such as orientation (pitching), its structural form depends on the structure of radar.S (t) is target echo waveform, and n (t) is additive noise, and N is data sampling number or claims data time domain length (fast umber of beats).In the research of Radar Multi Target detection technique, the form structure of radar, target number (having special detection algorithm research to discuss) is all supposed known.If there will be a known D target and only pay close attention to its direction parameter, then Θ=(θ ₁, θ ₂..., θ _d)

A(Θ)＝[a(θ ₁),a(θ ₂),,…,a(θ _D)]

Wherein a (θ _d) be referred to as array manifold vector, for uniform linear array vector a (θ) common type with M array element be,

a(θ)＝[1,e ^{j2π(d/λ)sin(θ)},,…,e ^{j2π(M-1)(d/λ)sin(θ)}] ^T

Classical maximum likelihood target component Detection and estimation algorithm can be expressed as (data fitting) [1-3]

Target azimuth ${\min }_{({\mathrm{\&theta;}}_1,{\mathrm{\&theta;}}_2,...,{\mathrm{\&theta;}}_D)\&Element;\mathrm{\&Omega;}}\frac{1}{N}{\mathrm{\&Sigma;}}_{t=1}^N{\left|\right|y\left(t\right)-A\left(\mathrm{\&Theta;}\right)s\left(t\right)\left|\right|}^2;$

Target waveform s (t)=[A ^h(Θ) A (Θ)] ^-1a ^h(Θ) y (t)

Or be expressed as (data covariance matrix matching):

Target azimuth ${\min }_{\mathrm{\&Theta;}}\mathrm{tr}\left\{\right[I-A\left(\mathrm{\&Theta;}\right){\left(A^H\left(\mathrm{\&Theta;}\right)A\left(\mathrm{\&Theta;}\right)\right)}^{-1}{A}^H\left(\mathrm{\&Theta;}\right)\left]\hat{R}\right\}$

Target waveform s (t)=[A ^h(Θ) A (Θ)] ^-1a ^h(Θ) y (t)

Wherein tr{} is for asking mark computing, for the data covariance matrix of measurement data y (t).To be data fitting or data covariance matrix matching be all " multi-target non-linear " optimizes.

Document Superresolution frequency estimation by alternating notch period-gram[J.K.Hwang, Y.C.Chen, IEEE Trans SP-41, No.2,727-741, multi-objective nonlinear optimization is converted into the iteration form of a series of simple target nonlinear optimization by the alternating projection multiple goal parameter detecting estimation technique Feb., 1993] proposed, and the steps include:

The first step: initial parameter is estimated, for i=1 to D (supposing there be D target), calculates

${\widehat{\mathrm{\&theta;}}}_i^{\left(0\right)}={\arg \max }_{{\mathrm{\&theta;}}_i}\left\{b^H({\mathrm{\&theta;}}_i,{\mathrm{\&Theta;}}_i^{\left(0\right)})\hat{R}b({\mathrm{\&theta;}}_i,{\mathrm{\&Theta;}}_i^{\left(0\right)})\right\}$

Wherein $b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_i^{\left(0\right)})=P_{A\left({\mathrm{\&Theta;}}_i^{\left(0\right)}\right)}a\left(\mathrm{\&theta;}\right)/\left|\right|P_{A\left({\mathrm{\&Theta;}}_i^{\left(0\right)}\right)}a\left(\mathrm{\&theta;}\right)\left|\right|,A\left({\mathrm{\&Theta;}}_i^{\left(0\right)}\right)=(a\left({\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)}\right),a\left({\widehat{\mathrm{\&theta;}}}_2^{\left(0\right)}\right),...,a\left({\widehat{\mathrm{\&theta;}}}_{i-1}^{\left(0\right)}\right)),$

$P_{A\left({\mathrm{\&Theta;}}_i\right)}=A\left({\mathrm{\&Theta;}}_i\right){\left[A^H\left({\mathrm{\&Theta;}}_i\right)A\left({\mathrm{\&Theta;}}_i\right)\right]}^{-1}{A}^H\left({\mathrm{\&Theta;}}_i\right)---\left(1\right)$ Obtain initial parameter like this to estimate , i is from 1 to D.

Second step: main iterative loop, for k=0 to a larger positive integer, i from 1 to D, double counting

${\widehat{\mathrm{\&theta;}}}_i^{\left(k\right)}={\arg \max }_{{\mathrm{\&theta;}}_i}\left\{b^H({\mathrm{\&theta;}}_i,{\mathrm{\&Theta;}}_i^{\left(k\right)})\hat{R}b({\mathrm{\&theta;}}_i,{\mathrm{\&Theta;}}_i^{\left(k\right)})\right\}$

Wherein $b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_i^{\left(k\right)})=P_{A\left({\mathrm{\&Theta;}}_i^{\left(k\right)}\right)}a\left(\mathrm{\&theta;}\right)/\left|\right|P_{A\left({\mathrm{\&Theta;}}_i^k\right)}a\left(\mathrm{\&theta;}\right)\left|\right|,P_{A\left({\mathrm{\&Theta;}}_i^{\left(k\right)}\right)}=A\left({\mathrm{\&Theta;}}_i^{\left(k\right)}\right){\left[A^H\left({\mathrm{\&Theta;}}_i^k\right)A\left({\mathrm{\&Theta;}}_i^{\left(k\right)}\right)\right]}^{-1}{A}^H\left({\mathrm{\&Theta;}}_i^{\left(k\right)}\right),$ $A_{\left(i\right)}=A\left({\mathrm{\&Theta;}}_i^{\left(k\right)}\right)=(a\left({\widehat{\mathrm{\&theta;}}}_1^{\left(k\right)}\right),...,a\left({\widehat{\mathrm{\&theta;}}}_{i=1}^{\left(k\right)}\right),a\left({\widehat{\mathrm{\&theta;}}}_{i+1}^{\left(k\right)}\right),...,a\left({\widehat{\mathrm{\&theta;}}}_D^{\left(k\right)}\right));$

Until for all i from 1 to D, ε is the threshold value preset.

3rd step: " precisely " that obtain is estimated i is from 1 to D.Utilize

$\hat{s}\left(t\right)={\left[A^H\left(\widehat{\mathrm{\&Theta;}}\right)A\left(\widehat{\mathrm{\&Theta;}}\right)\right]}^{-1}{A}^H\left(\widehat{\mathrm{\&Theta;}}\right)y\left(t\right)$

Obtain target echo to estimate.

So just for target localization and target identification provide foundation.No matter be wherein initial estimation or main iteration loop part, matrix inversion all inevitable.

In conjunction with ASAP algorithm [Shao court being alternately separated (AS) and alternating projection (AP) algorithm, collect Deng Chinese science E, 34 (4), 448-456, what 2004] propose is one and is similar to alternating projection multiple goal parameter detecting estimation technique, it is also a data covariance fitting detection technique, and their difference is embodied in following steps, the steps include:

The first step: initial parameter is estimated, for i from 1 to D, supposes there be D target, calculates,

${\widehat{\mathrm{\&theta;}}}_i^{\left(0\right)}={\arg \max }_{{\mathrm{\&theta;}}_i}\left\{b^H({\mathrm{\&theta;}}_i,{\mathrm{\&Theta;}}_i^{\left(0\right)})\hat{R}b({\mathrm{\&theta;}}_i,{\mathrm{\&Theta;}}_i^{\left(0\right)})\right\}$

Wherein q ₁=I, obtains and initially estimates parameter meter $({\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)},...,{\widehat{\mathrm{\&theta;}}}_i^{\left(0\right)},...,{\widehat{\mathrm{\&theta;}}}_D^{(k-1)});$

Second step: major loop iteration part, for k=0 to a larger positive integer, i from 1 to D, double counting,

${\widehat{\mathrm{\&theta;}}}_i^{\left(k\right)}={\arg \max }_{{\mathrm{\&theta;}}_i}\left\{b({\mathrm{\&theta;}}_i,{\mathrm{\&Theta;}}_i^{\left(k\right)})\hat{R}{b}^H({\mathrm{\&theta;}}_i,{\mathrm{\&Theta;}}_i^{\left(k\right)})\right\}$

Wherein matrix Q _istructural form be:

$Q_i=I-A_{\left(i\right)}(H_{\left(i\right)}^{-1}+{\mathrm{\&beta;}}_i{H}_{\left(i\right)}^{-1}{v}_i{v}_i^H{H}_{\left(i\right)}^{-1})A_{\left(i\right)}^H+{\mathrm{\&beta;}}_i{A}_{\left(i\right)}{H}_{\left(i\right)}^{-1}{v}_i{a}_i^H---\left(2\right)$

Wherein $A_{\left(i\right)}=(a\left({\widehat{\mathrm{\&theta;}}}_1^{\left(k\right)}\right),...,a\left({\widehat{\mathrm{\&theta;}}}_{i-1}^{\left(k\right)}\right),a\left({\widehat{\mathrm{\&theta;}}}_{i+1}^{(k-1)}\right),...,a\left({\widehat{\mathrm{\&theta;}}}_D^{(k-1)}\right));H_{\left(i\right)}^{-1}={\left(A_{\left(i\right)}^H{A}_{\left(i\right)}\right)}^{-1},v_i=A_{\left(i\right)}^{H}a\left({\widehat{\mathrm{\&theta;}}}_i^{(k+1)}\right),$ Projection matrix operator $P_{A_{\left(i\right)}}^{\&perp;}=P_{A\left({\mathrm{\&Theta;}}_i\right)}^{\&perp;}=I-P_{A\left({\mathrm{\&Theta;}}_i\right)},$ math><mrow><msub><mi>P</mi><mrow><mi>A</mi><mrow><mo>(</mo><msub><mi>&amp;Theta;</mi><mi>i</mi></msub><mo>)</mo></mrow></mrow></msub><mo>=</mo><mi>A</mi><mrow><mo>(</mo><msub><mi>&amp;Theta;</mi><mi>i</mi></msub><mo>)</mo></mrow><msup><mrow><mo>[</mo><msup><mi>A</mi><mi>H</mi></msup><mrow><mo>(</mo><msub><mi>&amp;Theta;</mi><mi>i</mi></msub><mo>)</mo></mrow><mi>A</mi><mrow><mo>(</mo><msub><mi>&amp;Theta;</mi><mi>i</mi></msub><mo>)</mo></mrow><mo>]</mo></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup><msup><mi>A</mi><mi>H</mi></msup><mrow><mo>(</mo><msub><mi>&amp;Theta;</mi><mi>i</mi></msub><mo>)</mo></mrow><mo>;</mo></mrow></math>

As detection technique above.Compare with detection technique above, matching vector herein essential distinction is had with matching vector above.But matrix Q _iexpression formula in matrix inversion inevitable.Matrix inversion operation be not only computational complexity defect, more crucially when target azimuth parameter (i is from 1 to D), when difference is less conditional number very littlely to cause the error of calculation is very large, makes detection algorithm easily be absorbed in local extremum and then whole detection technique was lost efficacy.

Summary of the invention

In order to overcome above-mentioned the deficiencies in the prior art, the object of the invention is to propose a kind of easy Radar Multi Target parameter extracting method, can matrix be evaded inversion operation and can equivalent realize above the method for same detection technique, the present invention is also by matrix inversion be expressed as the algebraic sum form of signal stream shape vector apposition according to target number and make corresponding form, fundamentally reduce its computational complexity and evade time error of inverting, no matter that hardware implementing or software and hardware combining realize bringing great convenience to above-mentioned detection technique, as target number D=3, formula (1) and (2) correspondingly can be reduced to formula (3) and formula (4):

$P_{A_{\mathrm{2,3}}}=\mathrm{\&alpha;}(a_2{a}_2^H+a_3{a}_3^H)-\mathrm{\&alpha;}\left(a_3^H{a}_2\right)a_3{a}_2^H-\mathrm{\&alpha;}\left(a_2^H{a}_3\right)a_2{a}_3^H---\left(3\right)$

Wherein constant coefficient $\mathrm{\&alpha;}={(1-a_3^H{a}_2{a}_2^H{a}_3)}^{-1};$

$Q_1=I-P_{A_{\mathrm{2,3}}}-\mathrm{\&beta;}{P}_{A_{\mathrm{2,3}}}{a}_1{a}_1^H[P_{A_{\mathrm{2,3}}}-I]---\left(4\right)$

Wherein constant coefficient: $\mathrm{\&beta;}={(1-{\mathrm{\&alpha;}}_1(a_1^H{a}_2{a}_2^H{a}_1+a_1^H{a}_3{a}_3^H{a}_1-a_3^H{a}_2{a}_2^H{a}_1{a}_1^H{a}_3-a_1^H{a}_2{a}_2^H{a}_3{a}_3^H{a}_1))}^{-1}.$

For achieving the above object, the technical solution used in the present invention is: a kind of easy Radar Multi Target parameter extracting method, D=3 target, when number of targets is more than 3, (3) can be copied, formula that the derivation principle of (4) formula writes out similar (3) and (4), just expression formula is more tediously long, specifically comprises the following steps:

Step 1), estimated signal orientation initial parameter, i, from 1 to D, D representation signal ordinal number, supposes D=3, for i=1, calculates $P_{a\left({\mathrm{\&theta;}}_1^{\left(0\right)}\right)}=I,b(\mathrm{\&theta;},{\mathrm{\&theta;}}_0^{\left(0\right)})=a\left(\mathrm{\&theta;}\right),$ Utilize formula:

${\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&theta;}}_0^{\left(0\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&theta;}}_0^{\left(0\right)})\right\}---\left(5\right)$

? for i=2, order $A\left({\mathrm{\&Theta;}}_1^{\left(0\right)}\right)=a\left({\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)}\right),P_{A\left({\mathrm{\&Theta;}}_1\right)}=a\left({\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)}\right)a^H\left({\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)}\right),$ $b(\mathrm{\&theta;},{\mathrm{\&theta;}}_1^{\left(0\right)})=P_{A\left({\mathrm{\&Theta;}}_1\right)}a\left(\mathrm{\&theta;}\right)/\left|\right|P_{A\left({\mathrm{\&Theta;}}_1\right)}a\left(\mathrm{\&theta;}\right)\left|\right|;$

Utilize formula

${\widehat{\mathrm{\&theta;}}}_2^{\left(0\right)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&theta;}}_1^{\left(0\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&theta;}}_1^{\left(0\right)})\right\}---\left(6\right)$

? for i=3, order $a_1=a\left({\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)}\right),a_2=a\left({\widehat{\mathrm{\&theta;}}}_2^{\left(0\right)}\right),b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(0\right)})=P_{A\left({\mathrm{\&Theta;}}_2\right)}a\left(\mathrm{\&theta;}\right)/\left|\right|P_{A\left({\mathrm{\&Theta;}}_2\right)}a\left(\mathrm{\&theta;}\right)\left|\right|,$ In original signal direction parameter searching method formula (3) is adopted to calculate; Constant utilize formula:

${\widehat{\mathrm{\&theta;}}}_3^{\left(0\right)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(0\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(0\right)})\right\}---\left(7\right)$

? obtain estimating target direction parameter initial value i is from 1 to 3;

Step 2), main iterative loop, according to step 1) initial parameter that obtains estimates from 1 to 3; For obtaining their accurate estimation, specific practice is, utilizes following formula to carry out the conversion of ring shift assignment and obtains new target azimuth parameter from 1 to 3; Circulate until for all i from 1 to 3, in formula: ε is the threshold value preset, and k is iterations;

For i=1, order in original signal direction parameter searching method calculate with formula (3), $b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_1^{\left(k\right)})=P_{A\left({\mathrm{\&Theta;}}_1^{\left(k\right)}\right)}a\left(\mathrm{\&theta;}\right)/\left|\right|P_{A\left({\mathrm{\&Theta;}}_1^{\left(k\right)}\right)}a\left(\mathrm{\&theta;}\right)\left|\right|,$ Utilize formula

${\widehat{\mathrm{\&theta;}}}_1^{(k+1)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&Theta;}}_1^{\left(k\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_1^{\left(k\right)})\right\}---\left(5\right)$

The orientation obtaining target 1 is more accurately estimated

For i=2, order $A\left({\mathrm{\&Theta;}}_2^{\left(k\right)}\right)=[a\left({\widehat{\mathrm{\&theta;}}}_1^{(k+1)}\right),a\left({\widehat{\mathrm{\&theta;}}}_3^{\left(k\right)}\right)],P_{A\left({\mathrm{\&Theta;}}_2^{\left(k\right)}\right)}=P_{A_{\mathrm{2,3}}},$ Even $a_2=a\left({\widehat{\mathrm{\&theta;}}}_1^{(k+1)}\right),a_3=a\left({\widehat{\mathrm{\&theta;}}}_3^{\left(k\right)}\right)$ Substitute into formula (3), $b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(k\right)})=P_{A\left({\mathrm{\&Theta;}}_2^{\left(k\right)}\right)}a\left(\mathrm{\&theta;}\right)/\left|\right|P_{A\left({\mathrm{\&Theta;}}_2^{\left(k\right)}\right)}a\left(\mathrm{\&theta;}\right)\left|\right|,$ Utilize formula

${\widehat{\mathrm{\&theta;}}}_2^{(k+1)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(k\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(k\right)})\right\}---\left(6\right)$

The orientation obtaining target 2 is more accurately estimated

For i=3, order $A\left({\mathrm{\&Theta;}}_3^{\left(k\right)}\right)=[a\left({\widehat{\mathrm{\&theta;}}}_1^{(k+1)}\right),a\left({\widehat{\mathrm{\&theta;}}}_2^{(k+1)}\right)],P_{A\left({\mathrm{\&Theta;}}_3^{\left(k\right)}\right)}=P_{A_{\mathrm{2,3}}},$ Even substitute into formula (3), $b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_3^{\left(k\right)})=P_{A\left({\mathrm{\&Theta;}}_3^{\left(k\right)}\right)}a\left(\mathrm{\&theta;}\right)/\left|\right|P_{A\left({\mathrm{\&Theta;}}_3^{\left(k\right)}\right)}a\left(\mathrm{\&theta;}\right)\left|\right|,$ Utilize formula

${\widehat{\mathrm{\&theta;}}}_3^{(k+1)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&Theta;}}_3^{\left(k\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_3^{\left(k\right)})\right\}---\left(7\right)$

The orientation obtaining target 3 is more accurately estimated

Step 3), for step 2) the accurate estimation that obtains i, from 1 to 3, utilizes formula (4) and formula (8) to calculate with $\hat{s}\left(t\right)={\left[A^H\left(\widehat{\mathrm{\&Theta;}}\right)A\left(\widehat{\mathrm{\&Theta;}}\right)\right]}^{-1}{A}^H\left(\widehat{\mathrm{\&Theta;}}\right)y\left(t\right),$ Obtain 3 target waveform parameter estimation, for target localization, waveform identification provide parameter foundation;

When target number D>=3, by means of existing expression formula as matrix inversion interative computation relation below $(H_{\left(D\right)}^{-1}={\left[A^H({\mathrm{\&theta;}}_1,{\mathrm{\&theta;}}_2,...,{\mathrm{\&theta;}}_D)A({\mathrm{\&theta;}}_1,{\mathrm{\&theta;}}_2,...,{\mathrm{\&theta;}}_D)\right]}^{-1}),$

$H_{\left(D\right)}^{-1}{A}_D^H=\left[\begin{array}{c}{H}_{(D-1)}^{-1}{A}_{D-1}^H+{\mathrm{\&beta;}}_D{H}_{(D-1)}^{-1}{A}_{D-1}^H{a}_D{a}_D^H{A}_{D-1}{H}_{(D-1)}^{-1}{A}_{D-1}^H-{\mathrm{\&beta;}}_D{H}_{(D-1)}^{-1}{A}_{D-1}^H{a}_D{a}_D^H\\ -{\mathrm{\&beta;}}_D{a}_D^H{A}_{D-1}{H}_{(D-1)}^{-1}{A}_{D-1}^H+{\mathrm{\&beta;}}_D{a}_D^H\end{array}\right]---\left(8\right)$

Just can intactly write out corresponding matrix q _iand projection matrix operator expression formula.

The invention has the beneficial effects as follows:

Suppose there is the uniform linear array radar system be made up of 10 array elements, array element distance equals 1/2nd of signal wavelength; There are three targets in spatial domain relative to array radar normal, and their position angle is-2 ° respectively, 0 ° and+2 °, and target side potential difference at this moment approximates 1/5th half power lobe width, is more common for this situation super-resolution radar.Suppose that having identical signal to noise ratio (S/N ratio) in each target of big-sample data situation relative to neighbourhood noise is 20 (dB).

Compared with the conventional method, in original signal direction parameter searching method formula (1) is adopted to calculate; And the present invention uses following very succinct formula:

$P_{A\left({\mathrm{\&Theta;}}_2\right)}=P_{A_{\mathrm{1,2}}}=\mathrm{\&alpha;}(a_1{a}_1^H+a_2{a}_2^H)-\mathrm{\&alpha;}\left(a_1^H{a}_2\right)a_1{a}_2^H-\mathrm{\&alpha;}\left(a_2^H{a}_1\right)a_2{a}_1^H$

Formula that it is (3); Advantage of the present invention is fairly obvious.Realize bringing significantly improving by the software and hardware of these class methods.

The present invention is applied to several more classical Radar Multi Target parameter detecting involved by current document and method of estimation: the maximum likelihood Radar Multi Target parameter detecting realized as monodimensional iterative and estimation technique Maximumlikelihood localization of multiple sources by alternating projection[Ziskind and M.Wax, IEEE Trans.Acoust., Speech, Signal Process., vol.36, no.10, pp.1553 – 1560, Oct.1988], characterization of the IterativeMulti-Parameter (IMP) algorithm[J.L.Mather, proceedings of the Institute of Acoustics, vol-11, part-8, 189-197, 1989], Superresolution frequency estimation by alternating notch period-gram and multiple goal replace separation parameter Detection and estimation technology.

Accompanying drawing explanation

When Fig. 1 is for directly utilizing former alternative projection algorithm to detect echo signal, system is because of the warning screenshot capture of matrix inversion error.

Fig. 2 is the search procedure figure of the alternative projection algorithm Direction-of-Arrival [-2 °, 0 ° ,+2 °] utilizing the present invention to realize.

Fig. 3 is the search procedure figure of the alternately separation detection technique Direction-of-Arrival [-2 °, 0 ° ,+2 °] utilizing the present invention to realize.

Embodiment

Below in conjunction with the drawings and specific embodiments, the present invention is described in further detail.

Of the present inventionly provide two groups of embodiments, one is the detection algorithm directly adopting former maximum likelihood alternating projection to realize, and two is that the detection method that realizes of the maximum likelihood alternating projection adopting the present invention to simplify and the present invention replace separate targets signal detecting method.

Embodiment 1

The monodimensional iterative of classical Maximum Likelihood Detection technology realizes---the implementation method of alternating projection detection technique.

The structure of array radar system is completely known, thus the popular vector form of its array is completely known, i.e. vector a (θ _i)=a _iform be completely known.For the fast beat of data that radar exports, we can calculate its covariance matrix R.

This technology is in the acquisition initial estimation stage, just need by method designed by this technology if relate to more than 3 targets, (3) algebraic expression of what formula provided is two Target situation projection operators, when two target components are known to estimate the 3rd target component time, just utilize this formula.More multiple goal situation is used (expansion) Inversion Formula to iterate again and is asked it.Its concrete implementation step is:

Estimated signal orientation initial value, for 3 targets

The first step: initial parameter is estimated, for i from 1 to 3,

1. calculate: $P_{a\left({\mathrm{\&theta;}}_1^{\left(0\right)}\right)}=I,b(\mathrm{\&theta;},{\mathrm{\&theta;}}_0^{\left(0\right)})=a\left(\mathrm{\&theta;}\right),$ Utilize formula:

${\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&theta;}}_0^{\left(0\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&theta;}}_0^{\left(0\right)})\right\}$

Obtain " first " target initial parameter to estimate

2. make $A\left({\mathrm{\&Theta;}}_1^{\left(0\right)}\right)=a\left({\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)}\right),P_{A\left({\mathrm{\&Theta;}}_1\right)}=a\left({\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)}\right)a^H\left({\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)}\right),b(\mathrm{\&theta;},{\mathrm{\&theta;}}_1^{\left(0\right)})=P_{A\left({\mathrm{\&Theta;}}_1\right)}a\left(\mathrm{\&theta;}\right)/\left|\right|P_{A\left({\mathrm{\&Theta;}}_1\right)}a\left(\mathrm{\&theta;}\right)\left|\right|;$ Utilize formula:

${\widehat{\mathrm{\&theta;}}}_2^{\left(0\right)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&theta;}}_1^{\left(0\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&theta;}}_1^{\left(0\right)})\right\}$

Obtain second target initial parameter to estimate

3. make $a_1=a\left({\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)}\right),a_2=a\left({\widehat{\mathrm{\&theta;}}}_2^{\left(0\right)}\right),b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(0\right)})=P_{A\left({\mathrm{\&Theta;}}_2\right)}a\left(\mathrm{\&theta;}\right)/\left|\right|P_{A\left({\mathrm{\&Theta;}}_2\right)}a\left(\mathrm{\&theta;}\right)\left|\right|,$ Wherein $P_{A\left({\mathrm{\&Theta;}}_2\right)}=P_{A_{\mathrm{1,2}}}=\mathrm{\&alpha;}(a_1{a}_1^H+a_2{a}_2^H)-\mathrm{\&alpha;}\left(a_1^H{a}_2\right)a_1{a}_2^H-\mathrm{\&alpha;}\left(a_2^H{a}_1\right)a_2{a}_1^H$ I.e. (3) formula above, constant $\mathrm{\&alpha;}={(1-a_1^H{a}_2{a}_2^H{a}_1)}^{-1},$ Utilize formula:

${\widehat{\mathrm{\&theta;}}}_3^{\left(0\right)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(0\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(0\right)})\right\}$

Obtain " the 3rd " target initial parameter to estimate obtain initial parameter like this to estimate from 1 to 3;

Second step: main iterative loop, for k=50 or 100, a larger positive integer, in actual applications might the just convergence of little several iteration! Here only for its acquisition track clearly can be shown, if obtained target azimuth parameter from 1 to 3; Obtain further below accurate estimation, provide herein be ring shift assignment conversion, also can adopt other displacement assignment conversion;

1. make $a_1=a\left({\widehat{\mathrm{\&theta;}}}_1^{\left(k\right)}\right),a_2=a\left({\widehat{\mathrm{\&theta;}}}_2^{\left(k\right)}\right),b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(k\right)})=P_{A\left({\mathrm{\&Theta;}}_3\right)}a\left(\mathrm{\&theta;}\right)/\left|\right|P_{A\left({\mathrm{\&Theta;}}_3\right)}a\left(\mathrm{\&theta;}\right)\left|\right|,$ $\mathrm{\&alpha;}={(1-a_1^H{a}_2{a}_2^H{a}_1)}^{-1},P_{A\left({\mathrm{\&Theta;}}_2\right)}=\mathrm{\&alpha;}(a_1{a}_1^H+a_2{a}_2^H)-\mathrm{\&alpha;}\left(a_1^H{a}_2\right)a_1{a}_2^H-\mathrm{\&alpha;}\left(a_2^H{a}_1\right)a_2{a}_1^H,$ Utilize following formula

${\widehat{\mathrm{\&theta;}}}_3^{(k+1)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(k\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(k\right)})\right\}$

Obtain the further fine estimation of the 3rd target azimuth parameter

2. make $a_1=a\left({\widehat{\mathrm{\&theta;}}}_1^{\left(k\right)}\right),a_2=a\left({\widehat{\mathrm{\&theta;}}}_3^{\left(k\right)}\right),b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(k\right)})=P_{A\left({\mathrm{\&Theta;}}_2\right)}a\left(\mathrm{\&theta;}\right)/\left|\right|P_{A\left({\mathrm{\&Theta;}}_2\right)}a\left(\mathrm{\&theta;}\right)\left|\right|,$ $\mathrm{\&alpha;}={(1-a_1^H{a}_2{a}_2^H{a}_1)}^{-1},P_{A\left({\mathrm{\&Theta;}}_2\right)}=\mathrm{\&alpha;}(a_1{a}_1^H+a_2{a}_2^H)-\mathrm{\&alpha;}\left(a_1^H{a}_2\right)a_1{a}_2^H-\mathrm{\&alpha;}\left(a_2^H{a}_1\right)a_2{a}_1^H,$

${\widehat{\mathrm{\&theta;}}}_2^{(k+1)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(k\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(k\right)})\right\}$

Obtain the further fine estimation of second target direction parameter

3. make $a_1=a\left({\widehat{\mathrm{\&theta;}}}_2^{(k+1)}\right),a_2=a\left({\widehat{\mathrm{\&theta;}}}_3^{(k+1)}\right),b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_1^{\left(k\right)})=P_{A\left({\mathrm{\&Theta;}}_1\right)}a\left(\mathrm{\&theta;}\right)/\left|\right|P_{A\left({\mathrm{\&Theta;}}_1\right)}a\left(\mathrm{\&theta;}\right)\left|\right|,$ $\mathrm{\&alpha;}={(1-a_1^H{a}_2{a}_2^H{a}_1)}^{-1},P_{A\left({\mathrm{\&Theta;}}_1\right)}=\mathrm{\&alpha;}(a_1{a}_1^H+a_2{a}_2^H)-\mathrm{\&alpha;}\left(a_1^H{a}_2\right)a_1{a}_2^H-\mathrm{\&alpha;}\left(a_2^H{a}_1\right)a_2{a}_1^H$

${\widehat{\mathrm{\&theta;}}}_1^{(k+1)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&Theta;}}_1^{\left(k\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_1^{\left(k\right)})\right\}$

Obtain further " accurately " estimated value of " first aim " direction parameter so just obtain new target azimuth parameter i is from 1 to 3;

Circulate until for all i from 1 to 3, ε is the threshold value preset;

3rd step: " precisely " that obtain is estimated i, from 1 to 3, utilizes (8) to calculate with $\hat{s}\left(t\right)={\left[A^H\left(\widehat{\mathrm{\&Theta;}}\right)A\left(\widehat{\mathrm{\&Theta;}}\right)\right]}^{-1}{A}^H\left(\widehat{\mathrm{\&Theta;}}\right)y\left(t\right)$ Obtain three target echo (waveform) parameter estimation simultaneously.

Embodiment 2

The alternately implementation method of separation detection technique.

The initial detection stage of target component only need use formula repeatedly any number of target component initial estimation can be obtained.

In main iteration loop, what (4) formula provided is that hypothetical target 2 and 3 is known, and target 1 obtains initial estimation, but will obtain its operator relatively accurately estimating to adopt further.Because target label is completely artificially specified.So the direction parameter that iterative cycles utilizes (4) formula can obtain target 1,2 and 3 is accurately estimated.More multiple goal situation Resolving probiems strategy is similar completely, just writes out corresponding (4) formula.

Estimated signal orientation initial value (for 3 targets)

The first step: initial parameter is estimated, for i from 1 to 3,

1. calculate: Q ₁=I, utilize following formula

${\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&theta;}}_0^{\left(0\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&theta;}}_0^{\left(0\right)})\right\}$

Obtain first aim direction parameter initial estimation

2. make q ₂=I-P _a1q ₁, utilize following formula

${\widehat{\mathrm{\&theta;}}}_2^{\left(0\right)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&theta;}}_2^{\left(0\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&theta;}}_2^{\left(0\right)})\right\}$

Obtain second target direction parameter initial estimation

3. make $a_1=a\left({\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)}\right),a_2=a\left({\widehat{\mathrm{\&theta;}}}_2^{\left(0\right)}\right),Q_3=I-P_{a_1}{Q}_1-P_{a_2}{Q}_2,b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_3^{\left(0\right)})=Q_{3}a\left(\mathrm{\&theta;}\right),$ Utilize following formula

${\widehat{\mathrm{\&theta;}}}_3^{\left(0\right)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&Theta;}}_3^{\left(0\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_3^{\left(0\right)})\right\}$

Obtain " the 3rd target " direction parameter initial estimation obtain initial parameter like this to estimate i is from 1 to 3.

Second step: main iterative loop, for k=50 or 100, a larger positive integer, if we have obtained target azimuth parameter i is from 1 to 3; Obtain its " accurately " estimation below further, what provide is the conversion of ring shift assignment herein, also can adopt other displacement assignment conversion;

1. make $a_1=a\left({\widehat{\mathrm{\&theta;}}}_1^{\left(k\right)}\right),a_2=a\left({\widehat{\mathrm{\&theta;}}}_2^{\left(k\right)}\right),a_3=a\left({\widehat{\mathrm{\&theta;}}}_3^{\left(k\right)}\right)$ (order 1-2-3), $\mathrm{\&alpha;}={(1-a_3^H{a}_2{a}_2^H{a}_3)}^{-1},$ Put again

$P_{A_{\mathrm{2,3}}}=\mathrm{\&alpha;}(a_2{a}_2^H+a_3{a}_3^H)-\mathrm{\&alpha;}\left(a_3^H{a}_2\right)a_3{a}_2^H-\mathrm{\&alpha;}\left(a_2^H{a}_3\right)a_2{a}_3^H;$

$Q_1=I-P_{A_{\mathrm{2,3}}}-\mathrm{\&beta;}{P}_{A_{\mathrm{2,3}}}{a}_1{a}_1^H[P_{A_{\mathrm{2,3}}}-I];$

$\mathrm{\&beta;}={(1-{\mathrm{\&alpha;}}_1(a_1^H{a}_2{a}_2^H{a}_1+a_1^H{a}_3{a}_3^H{a}_1-a_3^H{a}_2{a}_2^H{a}_1{a}_1^H{a}_3-a_1^H{a}_2{a}_2^H{a}_3{a}_3^H{a}_1))}^{-1}\text{;}$

$b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_1^{\left(k\right)})=\mathrm{Qa}\left(\mathrm{\&theta;}\right),$ Utilize following formula,

${\widehat{\mathrm{\&theta;}}}_1^{(k+1)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&Theta;}}_1^{\left(k\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_1^{\left(k\right)})\right\}$

Obtain " first aim " direction parameter " accurately " to estimate

2. make $a_1=a\left({\widehat{\mathrm{\&theta;}}}_2^{\left(k\right)}\right),a_2=a\left({\widehat{\mathrm{\&theta;}}}_3^{\left(k\right)}\right),a_3=a\left({\widehat{\mathrm{\&theta;}}}_1^{\left(k\right)}\right),$ Order 2-3-1, $\mathrm{\&alpha;}={(1-a_3^H{a}_2{a}_2^H{a}_3)}^{-1},$ Put again

$P_{A_{\mathrm{2,3}}}=\mathrm{\&alpha;}(a_2{a}_2^H+a_3{a}_3^H)-\mathrm{\&alpha;}\left(a_3^H{a}_2\right)a_3{a}_2^H-\mathrm{\&alpha;}\left(a_2^H{a}_3\right)a_2{a}_3^H;$

$Q_1=I-P_{A_{\mathrm{2,3}}}-\mathrm{\&beta;}{P}_{A_{\mathrm{2,3}}}{a}_1{a}_1^H[P_{A_{\mathrm{2,3}}}-I];$

$\mathrm{\&beta;}={(1-{\mathrm{\&alpha;}}_1(a_1^H{a}_2{a}_2^H{a}_1+a_1^H{a}_3{a}_3^H{a}_1-a_3^H{a}_2{a}_2^H{a}_1{a}_1^H{a}_3-a_1^H{a}_2{a}_2^H{a}_3{a}_3^H{a}_1))}^{-1}\text{;}$

$b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_1^{\left(k\right)})=\mathrm{Qa}\left(\mathrm{\&theta;}\right),$ Utilize following formula,

${\widehat{\mathrm{\&theta;}}}_2^{(k+1)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(k\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(k\right)})\right\}$

Obtain " second target " direction parameter " accurately " to estimate

3. make $a_1=a\left({\widehat{\mathrm{\&theta;}}}_3^{\left(k\right)}\right),a_2=a\left({\widehat{\mathrm{\&theta;}}}_1^{(k+1)}\right),a_3=a\left({\widehat{\mathrm{\&theta;}}}_2^{(k+1)}\right),$ Order 3-1-2, $\mathrm{\&alpha;}={(1-a_3^H{a}_2{a}_2^H{a}_3)}^{-1},$ Put again

$P_{A_{\mathrm{2,3}}}=\mathrm{\&alpha;}(a_2{a}_2^H+a_3{a}_3^H)-\mathrm{\&alpha;}\left(a_3^H{a}_2\right)a_3{a}_2^H-\mathrm{\&alpha;}\left(a_2^H{a}_3\right)a_2{a}_3^H;$

$Q_1=I-P_{A_{\mathrm{2,3}}}-\mathrm{\&beta;}{P}_{A_{\mathrm{2,3}}}{a}_1{a}_1^H[P_{A_{\mathrm{2,3}}}-I];$

$\mathrm{\&beta;}={(1-{\mathrm{\&alpha;}}_1(a_1^H{a}_2{a}_2^H{a}_1+a_1^H{a}_3{a}_3^H{a}_1-a_3^H{a}_2{a}_2^H{a}_1{a}_1^H{a}_3-a_1^H{a}_2{a}_2^H{a}_3{a}_3^H{a}_1))}^{-1}\text{;}$

$b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_1^{\left(k\right)})=\mathrm{Qa}\left(\mathrm{\&theta;}\right),$ Utilize following formula,

${\widehat{\mathrm{\&theta;}}}_3^{(k+1)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(k\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(k\right)})\right\}$

Obtain " the 3rd target " direction parameter " accurately " to estimate so just obtain the target azimuth parameter of " newly " i=1,2,3; Circulate until for all i from 1 to 3, ε is the threshold value preset;

3rd step: " precisely " that obtain is estimated i, from 1 to 3, utilizes (4) and (8) to calculate with

$\hat{s}\left(t\right)={\left[A^H\left(\widehat{\mathrm{\&Theta;}}\right)A\left(\widehat{\mathrm{\&Theta;}}\right)\right]}^{-1}{A}^H\left(\widehat{\mathrm{\&Theta;}}\right)y\left(t\right)$

Obtain target echo to estimate.

For the uniform linear array radar system having 10 array elements to form, array element distance equals 1/2nd of signal wavelength, and this system half power lobe width approximates 10 °; Suppose that there are three targets in spatial domain, their position angle is-2 ° respectively relative to radar normal, 0 ° and+2 ° (target azimuth angle difference approximates 1/5th lobe widths, target must be distinguished) with super resolution technology, if it is 500 that system exports sampled data, it is 20 (dB) that each target has identical signal to noise ratio (S/N ratio) relative to neighbourhood noise.Iterative step in the specific implementation method adopting the present invention to provide, the Search Results of acquisition as shown in Figures 2 and 3.Two methods all obtain comparatively promising result.

Fig. 1 is when directly utilizing maximum likelihood alternating projection to realize detecting Multiple Target Signals, system makes detection method sink into the warning of objective function local extremum because of matrix inversion error, terminates until detect, and also fails the situation of constraint of breakaway function local extremum.Illustrate that at this moment former method is lost efficacy.

Fig. 2 and Fig. 3 be the detection method that realizes of the maximum likelihood alternating projection of the simplification adopting us to set up and the multiple goal of simplification replace method for separating and detecting realize as much target detection result.Although two methods of the trace specification in figure are all larger at beginning time error, along with iterations increases, method all converges to the actual value of target azimuth parameter.Namely illustrate that the method for inventing is effective.

Claims (1)

1. an easy Radar Multi Target parameter extracting method, D=3 target, when number of targets is more than 3, (3) can be copied, formula that the derivation principle of (4) formula writes out similar (3) and (4), just expression formula is more tediously long, specifically comprises the following steps:

Step 1), estimated signal orientation initial parameter, i, from 1 to D, D representation signal ordinal number, supposes D=3, for i=1, calculates $P_{a\left({\mathrm{\&theta;}}_1^{\left(0\right)}\right)}=I,b=(\mathrm{\&theta;},{\mathrm{\&theta;}}_0^{\left(0\right)})=a\left(\mathrm{\&theta;}\right),$ Utilize formula:

${\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)}=\arg {\max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&theta;}}_0^{\left(0\right)}\hat{R}b(\mathrm{\&theta;},{\mathrm{\&theta;}}_0^{\left(0\right)}))\right\}---\left(5\right)$ ? for i=2, order $A\left({\mathrm{\&Theta;}}_1^{\left(0\right)}\right)=a\left({\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)}\right),P_{A\left({\mathrm{\&Theta;}}_1\right)}=a\left({\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)}\right)a^H\left({\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)}\right),$ $b(\mathrm{\&theta;},{\mathrm{\&theta;}}_1^{\left(0\right)})=P_{A\left({\mathrm{\&Theta;}}_1\right)}a\left(\mathrm{\&theta;}\right)/\left|\right|P_{A\left({\mathrm{\&Theta;}}_1\right)}a\left(\mathrm{\&theta;}\right)\left|\right|;$

Utilize formula

${\widehat{\mathrm{\&theta;}}}_2^{\left(0\right)}=\arg {\max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&theta;}}_1^{\left(0\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&theta;}}_1^{\left(0\right)})\right\}---\left(6\right)$

? for i=3, order $a_1=a\left({\widehat{\mathrm{\&theta;}}}_1^{\left(0\right)}\right),a_2=a\left({\widehat{\mathrm{\&theta;}}}_2^{\left(0\right)}\right),b=(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(0\right)})=P_{A\left({\mathrm{\&Theta;}}_2\right)}a\left(\mathrm{\&theta;}\right)/\left|\right|P_{A\left({\mathrm{\&Theta;}}_2\right)}a\left(\mathrm{\&theta;}\right)\left|\right|,$ In original signal direction parameter searching method formula (3) is adopted to calculate; Constant utilize formula:

${\widehat{\mathrm{\&theta;}}}_3^{\left(0\right)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(0\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(0\right)})\right\}---\left(7\right)$

? obtain estimating target direction parameter initial value i is from 1 to 3;

Step 2), main iterative loop, according to step 1) initial parameter that obtains estimates i is from 1 to 3; For obtaining their accurate estimation, specific practice is, utilizes following formula to carry out the conversion of ring shift assignment and obtains new target azimuth parameter i is from 1 to 3; Circulate until for all i from 1 to 3, in formula: ε is the threshold value preset, and k is iterations;

For i=1, order $A\left({\mathrm{\&Theta;}}_1^{\left(k\right)}\right)=[a\left({\widehat{\mathrm{\&theta;}}}_2^{\left(k\right)}\right),a\left({\widehat{\mathrm{\&theta;}}}_3^{\left(k\right)}\right)],P_{A\left({\mathrm{\&Theta;}}_1^{\left(k\right)}\right)}=P_{A_{\mathrm{2,3}}},$ In original signal direction parameter searching method calculate with formula (3), $b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_1^{\left(k\right)})=P_{A\left({\mathrm{\&Theta;}}_1^{\left(k\right)}\right)}a\left(\mathrm{\&theta;}\right)/\left|\right|P_{A\left({\mathrm{\&Theta;}}_1^{\left(k\right)}\right)}a\left(\mathrm{\&theta;}\right)\left|\right|,$ Utilize formula

${\widehat{\mathrm{\&theta;}}}_1^{(k+1)}=\arg {\max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&Theta;}}_1^{\left(k\right)}\hat{R}b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_1^{\left(k\right)}))\right\}---\left(5\right)$

The orientation obtaining target 1 is more accurately estimated

For i=2, order $A\left({\mathrm{\&Theta;}}_2^{\left(k\right)}\right)=[a\left({\widehat{\mathrm{\&theta;}}}_1^{(k+1)}\right),a\left({\widehat{\mathrm{\&theta;}}}_3^{\left(k\right)}\right)],P_{A\left({\mathrm{\&Theta;}}_2^{\left(k\right)}\right)}=P_{A_{\mathrm{2,3}}},$ Even $a_2=a\left({\widehat{\mathrm{\&theta;}}}_1^{(k+1)}\right),a_3=a\left({\widehat{\mathrm{\&theta;}}}_3^{\left(k\right)}\right)$ Substitute into formula (3), $b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(k\right)})=P_{A\left({\mathrm{\&Theta;}}_2^{\left(k\right)}\right)}a\left(\mathrm{\&theta;}\right)/\left|\right|P_{A\left({\mathrm{\&Theta;}}_2^{\left(k\right)}\right)}a\left(\mathrm{\&theta;}\right)\left|\right|,$ Utilize formula

${\widehat{\mathrm{\&theta;}}}_2^{(k+1)}={\arg \max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(k\right)}\hat{R}b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_2^{\left(k\right)}))\right\}---\left(6\right)$

The orientation obtaining target 2 is more accurately estimated

For i=3, order $A\left({\mathrm{\&Theta;}}_3^{\left(k\right)}\right)=[a\left({\widehat{\mathrm{\&theta;}}}_1^{(k+1)}\right),a\left({\widehat{\mathrm{\&theta;}}}_2^{(k+1)}\right)],P_{A\left({\mathrm{\&Theta;}}_3^{\left(k\right)}\right)}=P_{A_{\mathrm{2,3}}},$ Even $a_2=a\left({\widehat{\mathrm{\&theta;}}}_2^{(k+1)}\right),$ $a_3=a\left({\widehat{\mathrm{\&theta;}}}_1^{(k+1)}\right)$ Substitute into formula (3), $b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_3^{\left(k\right)})=P_{A\left({\mathrm{\&Theta;}}_3^{\left(k\right)}\right)}a\left(\mathrm{\&theta;}\right)/\left|\right|P_{A\left({\mathrm{\&Theta;}}_3^{\left(k\right)}\right)}a\left(\mathrm{\&theta;}\right)\left|\right|,$ Utilize formula

${\widehat{\mathrm{\&theta;}}}_3^{(k+1)}=\arg {\max }_{\mathrm{\&theta;}}\left\{b^H(\mathrm{\&theta;},{\mathrm{\&Theta;}}_3^{\left(k\right)})\hat{R}b(\mathrm{\&theta;},{\mathrm{\&Theta;}}_3^{\left(k\right)})\right\}---\left(7\right)$

The orientation obtaining target 3 is more accurately estimated

Step 3), for step 2) the accurate estimation that obtains i, from 1 to 3, utilizes formula (4) and formula (8) to calculate ${\left[A^H\left(\widehat{\mathrm{\&Theta;}}\right)A\right]\left(\widehat{\mathrm{\&Theta;}}\right)}^{-1}{A}^H\left(\widehat{\mathrm{\&Theta;}}\right),$ With $\hat{s}\left(t\right)={\left[A^H\left(\widehat{\mathrm{\&Theta;}}\right)A\left(\widehat{\mathrm{\&Theta;}}\right)\right]}^{-1}{A}^H\left(\widehat{\mathrm{\&Theta;}}\right)y\left(t\right),$ Obtain 3 target waveform parameter estimation, for target localization, waveform identification provide parameter foundation;

When target number D>=3, by means of existing expression formula as matrix inversion interative computation relation below $(H_{\left(D\right)}^{-1}=[A^H({\mathrm{\&theta;}}_1,{\mathrm{\&theta;}}_2,...,{\mathrm{\&theta;}}_D)A({\mathrm{\&theta;}}_1,{\mathrm{\&theta;}}_2,...,{\mathrm{\&theta;}}_D){]}^{-1}),$

$H_{\left(D\right)}^{-1}{A}_D^H=\left[\begin{array}{c}{D}_{(D-1)}^{-1}{A}_{D-1}^H+{\mathrm{\&beta;}}_D{H}_{(D-1)}^{-1}{A}_{D-1}^H{A}_D{a}_H^D{A}_{D-1}{A}_{(D-1)}^{-1}{A}_{D-1}^H-{\mathrm{\&beta;}}_D{H}_{(D-1)}^{-1}{A}_{D-1}^H{a}_D{a}_H^D\\ {-\mathrm{\&beta;}}_D{a}_D^H{A}_{D-1}{H}_{(D-1)}^H{A}_{D-1}^H+{\mathrm{\&beta;}}_D{a}_D^H\end{array}\right]---\left(8\right)$ Just can intactly write out corresponding matrix q _iand projection matrix operator expression formula.