CN103792509A - Two dimensional direction of arrival angle estimation method of electromagnetic signal - Google Patents

Abstract

The invention discloses a two dimensional direction of arrival angle estimation method of an electromagnetic signal, the two dimensional direction of arrival angle estimation method mainly solves the problems of slow reaction rate and large estimation error of the target reconnaissance and passive location caused by huge computation task of the two dimensional direction of arrival angle estimation in the prior art. The two dimensional direction of arrival angle estimation method comprises the following steps that even planar arrays are formed by the adoption of antenna receivers, echo signals of all antenna receivers are calculated, noise subspaces of the echo signals of the antenna receivers are calculated, a direction vector of the included angle of a y axis is obtained by plugging the included angle of an x-axis, which is made to be a fixed value, into an angle solving function, multiple sets of values are obtained through multiple times of computations, an amplitude spectra is generated by the adoption of multiple sets of values, the included angle of the x axis is obtained by seeking peak points of the amplitude spectra, and the included angle of the y axis is obtained through the least square method. By means of the two dimensional direction of arrival angle estimation method, the two dimensional direction of arrival angle estimation process is simplified into a one dimensional direction of arrival angle estimation process, the computation tasks are greatly reduced, the reaction rates of the target reconnaissance and passive location are improved, the parameter estimation error caused by delayed information can be avoided, and the method can be used for the quick target reconnaissance and passive location.

Description

The 2-d direction finding angle method of estimation of electromagnetic signal

Technical field

The invention belongs to electromagnetic signal processing technology field, particularly a kind of 2-d direction finding angle method of estimation, can be used for target reconnaissance and passive location.

Background technology

Direction of arrival angle DOA estimates it is the electromagnetic signal of utilizing the signal source of the multiple different directions of aerial signal array received in space diverse location to send, use modern signal processing method to estimate fast and accurately the direction of signal source, there is significant application value in fields such as radar, sonar, radio communications.2-d direction finding angle estimates that general employing face battle array or vector sensor realize the estimation of two-dimensional parameter, most efficient 2-d direction of arrival angle algorithm for estimating belongs to one-dimensional wave and reaches the direct expansion of deflection algorithm for estimating, do not make full use of the multidimensional information of carrying in array received signal, often exist operand excessive or have shortcomings such as angle pairing.

Traditional 2-d direction finding angle method of estimation comprises two kinds: one is to utilize two dimension angular search to obtain two dimension angular simultaneously; Another kind is to ask for respectively wherein one dimension angle value, then carries out angle pairing.First method need to be used two-dimensional search, its operand be linear search square doubly, therefore operand is huge; Second method also needs use angle pairing algorithm completing respectively after one dimension angle estimation, this process still needs to spend certain operand, and therefore these two kinds of methods all have compared with macrooperation amount.In practical application, target reconnaissance and passive location all need to be carried out on the basis of angle estimation, if angle estimation operand senior general cause target reconnaissance and passive location reaction velocity slow, even cause the parameter estimating error causing due to information delay larger.

Summary of the invention

The object of the invention is to the deficiency for above-mentioned prior art, a kind of 2-d direction finding angle method of estimation of electromagnetic signal is proposed, with the operand that significantly reduces to estimate, improve target reconnaissance and passive location reaction velocity, avoid the parameter estimating error causing because of information delay.

For achieving the above object, performing step of the present invention comprises as follows:

1) adopt aerial receiver to form uniform planar battle array, wherein x direction of principal axis has N aerial receiver, and y direction of principal axis has M aerial receiver, and aerial receiver spacing is d, N >=2, and M >=2,0<d≤λ/2, λ is incident narrow band signal wavelength;

2) by Q incoherent narrow band signal s _q(t) with x axle clamp angle α _qwith y axle clamp angle β _qincide in antenna uniform planar battle array, wherein, q=1,2 ..., Q, 1≤Q<NM, α _qrepresent the incident direction of q narrow band signal to be asked and the angle of x axle, β _qrepresent the incident direction of q narrow band signal to be asked and the angle of y axle, and α _q∈ (0 °, 180 °], β _q∈ (0 °, 180 °];

3) the echoed signal Y of each aerial receiver in calculating antenna uniform planar battle array _n,m(t);

$Y_{n,m}\left(t\right)=\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}[a_n\left({\mathrm{\&alpha;}}_q\right)\&CircleTimes;a_m\left({\mathrm{\&beta;}}_q\right)]\&CenterDot;s_q\left(t\right)+N\left(t\right)$

Wherein,

the computing of representing matrix multiplication cross, N (t) is noise signal vector, a _n(α _q) and a _m(β _q) represent respectively the x axle clamp angle α of the narrow band signal of q incident _qwith y axle clamp angle β _qcorresponding direction vector, expansion form is expressed as:

a _n(α _q)=(1,exp(j2πd·cosα _q/λ),...,exp[j2πd·(N-1)·cosα _q/λ]) ^T

a _m(β _q)=(1,exp(j2πd·cosβ _q/λ),...,exp[j2πd·(M-1)·cosβ _q/λ]) ^T

Wherein, j represents imaginary unit, () ^tthe computing of representing matrix transposition;

4) according to aerial receiver echoed signal Y _n,m(t), calculating noise subspace U _n;

5) structure angle solved function is: $\min \left(a_m^H\left({\mathrm{\&beta;}}_q\right)G\left({\mathrm{\&alpha;}}_q\right)a_m\left({\mathrm{\&beta;}}_q\right)\right),$

Wherein, $G\left({\mathrm{\&alpha;}}_q\right)={[a_n\left({\mathrm{\&alpha;}}_q\right)\&CircleTimes;I_M]}^H{U}_n{U}_n^H[a_n\left({\mathrm{\&alpha;}}_q\right)\&CircleTimes;I_M]$ For intermediate variable, min () represents to minimize computing, () ^hthe computing of representing matrix conjugate transpose, I _mrepresent the unit matrix of M × M dimension;

6) establish x axle clamp angle α _qfor (0 °, 180 °] fixed value in scope, by x axle clamp angle α _qsubstitution intermediate variable function G (α _q) obtain intermediate variable matrix G _q, then utilize following formula calculated direction vector a _m(β _q):

a _m(β _q)=P _min(G _q)，

Wherein, P _min() represents the corresponding proper vector of minimal eigenvalue of solution matrix;

7) get x axle clamp angle α _qfor (0 °, 180 °] other fixed value in scope, repeated execution of steps 6), obtain corresponding direction vector a _m(β _q);

8) by got multiple x axle clamp angle α _qwith the multiple directions vector a obtaining _m(β _q) substitution function:

in, obtain corresponding multiple functional value Z _q, then in plane with (0,0) for origin, with many groups of (α _q, Z _q) be x, y coordinate is drawn range value point, and each point is connected and obtains amplitude spectrogram;

9) from amplitude spectrogram, find according to order from high to low front Q the spectrum peak that amplitude is larger, using x axial coordinate the value corresponding peak point at these spectrum peaks as the x axle clamp angle α trying to achieve _qvalue;

10) according to each x axle clamp angle α trying to achieve _qvalue, finds corresponding direction vector a _m(β _q) value, recycling least square method is tried to achieve corresponding y axle clamp angle β _qvalue, the 2-d direction finding angle that completes electromagnetic signal is estimated.

The present invention is owing to becoming one-dimensional wave to reach orientation angle estimation procedure two dimensional angle estimation procedure abbreviation, only need one dimension angle searching can obtain two dimensional angle simultaneously, avoid two dimension angular search or angle pairing process, greatly reduced computational complexity.

Experimental result shows, the operand that the present invention calculates two dimensional angle angle is only

Ο { LM ²n ²+ M ³n ³+ n[(M ²n+M ²) (MN-Q)+M ³+ M ²], and the operand of traditional 2D-MUSIC method calculating two dimensional angle angle is

Ο { LM ²n ²+ M ³n ³+ n ²[MN (MN-Q)] }, wherein solve α _qwith β _qtime search point be n, n>=1, because x direction of principal axis receiver quantity N, y direction of principal axis receiver quantity M, narrow band signal quantity Q and fast umber of beats L are all much smaller than n, therefore the magnitude of operand of the present invention is n, and the magnitude of 2D-MUSIC method operand is n ², the operand of visible the inventive method, far below traditional 2D-MUSIC method, can improve reaction velocity and the parameter estimation accuracy of target reconnaissance and passive location, has avoided the parameter estimating error causing because of information delay.

Accompanying drawing explanation

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

Fig. 2 is the operand comparison diagram of the present invention and existing 2D-MUSIC algorithm;

Fig. 3 is the x axle angle estimation root-mean-square error comparison diagram of the present invention and existing 2D-MUSIC algorithm;

Fig. 4 is the y axle angle estimation root-mean-square error comparison diagram of the present invention and existing 2D-MUSIC algorithm.

Embodiment

With reference to Fig. 1, the two dimensional angle estimation of electromagnetic signal of the present invention, implementation step is as follows:

Step 1: utilize aerial receiver to form uniform planar battle array.

Place 1 aerial receiver at x direction of principal axis every spacing d, place altogether N, be referred to as 1 row aerial receiver; Place 1 row aerial receiver at y direction of principal axis every spacing d, place altogether M capable, form the antenna uniform planar battle array that the total number of aerial receiver is NM, wherein N >=2, M >=2,0<d≤λ/2, λ is incident narrow band signal wavelength.

Step 2: narrow band signal is incided in antenna uniform planar battle array.

If the narrow band signal inciding in antenna uniform planar battle array is Q, and uncorrelated between signal, signal form s _q(t) represent;

Described narrow band signal meets following condition:

B·ΔT _max<<1，

Wherein B represents signal bandwidth, Δ T _maxrepresent that signal arrives the maximal value of the delay inequality of any two aerial receivers;

Described narrow band signal is from space any direction directive antenna uniform planar battle array, and this incident direction can be counted as a ray, and the angle that this ray and antenna uniform planar battle array place plane form is called 2-d direction finding angle, with x axle clamp angle α _qwith y axle clamp angle β _qrepresent, wherein, q=1,2 ..., Q, 1≤Q<NM, α _qrepresent the incident direction of q incident narrow band signal and the angle of x axle, β _qrepresent the incident direction of q incident narrow band signal and the angle of y axle, and α _q∈ (0 °, 180 °], β _q∈ (0 °, 180 °].

In this example, requiring narrow band signal number Q is known value, α _qand β _qit is value to be estimated.

Step 3: the echoed signal Y that calculates each aerial receiver in antenna uniform planar battle array _n,m(t):

$Y_{n,m}\left(t\right)=\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}[a_n\left({\mathrm{\&alpha;}}_q\right)\&CircleTimes;a_m\left({\mathrm{\&beta;}}_q\right)]\&CenterDot;s_q\left(t\right)+N\left(t\right)$

Wherein,

the computing of representing matrix multiplication cross, N (t) is noise signal vector, this vector is a random vector, at the echoed signal Y of each aerial receiver _n, _m(t) different in, signal to noise ratio (S/N ratio) is less, larger to the evaluated error of direction of arrival angle;

A _n(α _q) represent the x axle clamp angle α of narrow band signal of q incident _qdirection vector, a _m(β _q) represent the y axle clamp angle β of narrow band signal of q incident _qdirection vector, expansion form is expressed as:

a _n(α _q)=(1,exp(j2πd·cosα _q/λ),...,exp[j2πd·(N-1)·cosα _q/λ]) ^T

am(β _q)=(1,exp(j2πd·cosβ _q/λ),...,exp[j2πd·(M-1)·cosβ _q/λ]) ^T

Wherein, j represents imaginary unit, () ^tthe computing of representing matrix transposition.

Step 4: calculate aerial receiver echoed signal Y _n,m(t) noise subspace U _n.

In prior art, obtain aerial receiver echoed signal noise subspace U _nmethod have a lot, for example feature decomposition method, singular value decomposition method, multi-Stage Wiener Filter method, double iterative method, power iteration methods etc., have been used the comparatively general feature decomposition method of application in this example, concrete grammar is as follows:

4a) the covariance matrix of calculating aerial receiver signal: R=E[Y _n,m(t) Y _n,m(t) ^h],

Wherein E[] represent to ask mathematical expectation, () ^hthe computing of representing matrix conjugate transpose;

4b) covariance matrix R is carried out to feature decomposition, that is:

R=U·Λ·U ^H，

Wherein, Λ is the eigenvalue matrix of covariance matrix R, and the diagonal element of this matrix is eigenwert, and element except diagonal element is that 0, U is the corresponding eigenvectors matrix of eigenwert entirely;

4c) eigenwert in eigenvalue matrix Λ is pressed to sequence from big to small, after getting, (NM-Q) individual less eigenwert characteristic of correspondence vector matrix is as noise subspace U _n.

Step 5: structure angle solved function $\min \left(a_m^H\left({\mathrm{\&beta;}}_q\right)G\left({\mathrm{\&alpha;}}_q\right)a_m\left({\mathrm{\&beta;}}_q\right)\right).$

5a) according to Multiple Signal Classification feature decomposition MUSIC algorithm, construct angle solved function and be:

wherein, function V (α _q, β _q) be:

$V({\mathrm{\&alpha;}}_q,{\mathrm{\&beta;}}_q)={[a_n\left({\mathrm{\&alpha;}}_q\right)\&CircleTimes;a_m\left({\mathrm{\&beta;}}_q\right)]}^H{U}_n{U}_n^H[a_n\left({\mathrm{\&alpha;}}_q\right)\&CircleTimes;a_m\left({\mathrm{\&beta;}}_q\right)],$

Wherein, min () represents to minimize computing;

5b) by above-mentioned steps 5a) in equation be deformed into:

$V({\mathrm{\&alpha;}}_q,{\mathrm{\&beta;}}_q)=a_m^H\left({\mathrm{\&beta;}}_q\right){[a_n\left({\mathrm{\&alpha;}}_q\right)\&CircleTimes;I_M]}^H{U}_n{U}_n^H[a_n\left({\mathrm{\&alpha;}}_q\right)\&CircleTimes;I_M]a_m\left({\mathrm{\&beta;}}_q\right),$

Wherein, I _mrepresent the unit matrix of M × M dimension;

5c) make intermediate variable $G\left({\mathrm{\&alpha;}}_q\right)={[a_n\left({\mathrm{\&alpha;}}_q\right)\&CircleTimes;I_M]}^H{U}_n{U}_n^H[a_n\left({\mathrm{\&alpha;}}_q\right)\&CircleTimes;I_M],$ By above-mentioned steps 5b)

In equation be reduced to:

$V({\mathrm{\&alpha;}}_q,{\mathrm{\&beta;}}_q)=a_m^H\left({\mathrm{\&beta;}}_q\right)G\left({\mathrm{\&alpha;}}_q\right)a_m\left({\mathrm{\&beta;}}_q\right);$

5d) according to step 5c) in equation V (α _q, β _q), finally construct angle solved function and be:

$\min \left(a_m^H\left({\mathrm{\&beta;}}_q\right)G\left({\mathrm{\&alpha;}}_q\right)a_m\left({\mathrm{\&beta;}}_q\right)\right).$

Step 6: establish x axle clamp angle α _qfor (0 °, 180 °] fixed value in scope, calculated direction vector a _m(β _q).

6a) by x axle clamp angle α _qsubstitution formula: $G\left({\mathrm{\&alpha;}}_q\right)={[a_n\left({\mathrm{\&alpha;}}_q\right)\&CircleTimes;I_M]}^H{U}_n{U}_n^H[a_n\left({\mathrm{\&alpha;}}_q\right)\&CircleTimes;I_M]$ In, obtain intermediate variable matrix G _q;

6b) to middle matrix of variables G _qcarry out feature decomposition:

$G_q=U_q\&CenterDot;{\mathrm{\&Lambda;}}_q\&CenterDot;U_q^H$

Wherein, Λ _qfor intermediate variable matrix G _qeigenvalue matrix, U _qfor intermediate variable matrix G _qthe corresponding eigenvectors matrix of eigenwert;

6c) find intermediate variable matrix G _qthe eigenwert Λ of middle minimum _qmincharacteristic of correspondence vector U _qmin, by this proper vector U _qminas the direction vector a trying to achieve _m(β _q).

Step 7: get x axle clamp angle α _qfor (0 °, 180 °] other fixed value in scope, repeated execution of steps 6, obtains corresponding a _m(β _q) value; α _qin span, according to order from small to large, carry out value with fixed angle interval; The angle estimation precision that value interval reaches according to expectation is set, and value interval is less, and angle estimation precision is higher.

Step 8: draw amplitude spectrogram.

Above-mentioned got multiple x axle clamp angle α _qwith the multiple directions vector a obtaining _m(β _q) in, only have the angle of meeting solved function

q group α _qand β _qangle value is only required two dimension angular value, and concrete methods of realizing is by got multiple x axle clamp angle α _qwith the multiple directions vector a obtaining _m(β _q) difference substitution function

in, find α corresponding to minimum point _qand β _qangle value.

People's general custom is found maximum point in amplitude spectrogram, rather than minimum point, in order to meet people's observation custom, by got multiple x axle clamp angle α _qwith the multiple directions vector a obtaining _m(β _q) difference substitution function

in, with finding α corresponding to maximum point _qand β _qthe method of angle value replaces said method.

Concrete steps are:

8a) by got multiple angle [alpha] _qwith the multiple directions vector a obtaining _m(β _q) substitution function: $Z_q({\mathrm{\&alpha;}}_q,a_m\left({\mathrm{\&beta;}}_q\right))=1/\left[a_m^H\left({\mathrm{\&beta;}}_q\right)G\left({\mathrm{\&alpha;}}_q\right)a_m\left({\mathrm{\&beta;}}_q\right)\right]$ In, obtain corresponding multiple functional value Z _q;

8b) in plane with (0,0) for origin, with many groups of (α _q, Z _q) be x, y coordinate, draws range value point;

8c) each range value point is connected, obtains amplitude spectrogram.

Step 9: complete x axle clamp angle α _qestimation.

From amplitude spectrogram, find according to order from high to low front Q the spectrum peak that amplitude is larger, this example is got Q=3; Using x the coordinate figure corresponding peak point at these spectrum peaks as the x axle clamp angle α trying to achieve _qvalue.

Step 10: according to each x axle clamp angle α trying to achieve _qvalue, finds corresponding direction vector a _m(β _q) value, recycling least square method is tried to achieve corresponding y axle clamp angle β _qvalue, utilizes said method to solve y axle clamp angle β _qnumber of times be Q time, this example is got Q=3.

Solve y axle clamp angle β _qstep be:

10a) according to direction vector a _m(β _q) utilize following formula to ask angle vector g:

g=-angle(a _m(β _q))，

Wherein, angle () represents each element in vector to get phase angle;

10b) order matrix $P=\left(\begin{array}{cc}1& 0\\ 1& 1\\ .& .\\ .& .\\ .& .\\ 1& M-1\end{array}\right),$ Calculate following formula:

[c ₀,c ₁]=(P ^TP) ^-1P ^Tg，

Wherein, c ₀and c ₁represent two elements of required vector, () ^-1represent finding the inverse matrix computing;

10c) try to achieve y axle clamp angle β _qvalue:

${\mathrm{\&beta;}}_q=\arccos \left(\frac{c_1\mathrm{\&lambda;}}{2\mathrm{\&pi;d}}\right).$

Effect of the present invention can illustrate by following emulation:

1. simulated conditions and method:

Adopt aerial receiver to form uniform planar battle array, wherein x direction of principal axis has 8 aerial receivers, and y direction of principal axis has 8 aerial receivers, and aerial receiver spacing d equals λ/2.There are three narrow band signals to incide uniform planar battle array, wherein the angle α of narrow band signal incident direction and x axle _qangle β with narrow band signal incident direction and y axle _qvalue be respectively (60 °, 50 °), (90 °, 100 °) and (145 °, 75 °).Signal to noise ratio snr is 0dB, and fast umber of beats L equals 64, and angle searching value is spaced apart 0.01 degree.

In order further to evaluate performance of the present invention, to repeatedly independently experimental result carried out on average, and the root-mean-square error that adopts two dimension angular is as evaluation index:

$\left\{\begin{array}{c}{\mathrm{RMSE}}_{\mathrm{\&alpha;}}=\frac{1}{Q}\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}\sqrt{\frac{1}{\mathrm{Num}}\underset{\mathrm{num}=1}{\overset{\mathrm{Mum}}{\mathrm{\&Sigma;}}}{({\widehat{\mathrm{\&alpha;}}}_q-{\mathrm{\&alpha;}}_q)}^2}\\ {\mathrm{RMSE}}_{\mathrm{\&beta;}}=\frac{1}{Q}\underset{q=1}{\overset{Q}{\mathrm{\&Sigma;}}}\sqrt{\frac{1}{\mathrm{Mum}}\underset{\mathrm{num}=1}{\overset{\mathrm{Num}}{\mathrm{\&Sigma;}}}{({\widehat{\mathrm{\&beta;}}}_q-{\mathrm{\&beta;}}_q)}^2}\end{array}\right.,$

Wherein RMSE _αand RMSE _βrepresent respectively α _qand β _qestimation root-mean-square error, Num is experiment number, α _qbe the actual value of q angle,

represent the estimated value of q angle.This emulation adopts respectively the present invention and existing 2D-MUSIC algorithm to carry out.

2. emulation content and result

Emulation 1, utilizes the present invention and existing 2D-MUSIC algorithm to carry out respectively two dimensional angle estimation, and statistical calculation amount, and its result as shown in Figure 2.In Fig. 2, horizontal ordinate represents angle searching number of times, and ordinate represents operand.

As can be seen from Figure 2, the present invention, compared with existing 2D-MUSIC algorithm, has significantly reduced the operand of angle estimation, and along with the increase of angle searching number of times, it is larger that operand reduces amplitude.

Emulation 2, utilizes the present invention and existing 2D-MUSIC algorithm to carry out respectively 100 independently two dimensional angle estimation experiments, calculates respectively the root-mean-square error at x axle clamp angle and the root-mean-square error at y axle clamp angle, and its result as shown in Figure 3 and Figure 4.Wherein Fig. 3 is the root-mean-square error of calculating x axle clamp angle, and Fig. 4 is the root-mean-square error of calculating y axle clamp angle; In Fig. 3 and Fig. 4, horizontal ordinate represents signal to noise ratio (S/N ratio), and ordinate represents root-mean-square error, and signal to noise ratio (S/N ratio) variation range is-4dB～8dB.

Can find out from Fig. 3 and Fig. 4, the present invention is substantially suitable with existing 2D-MUSIC algorithm angle estimation precision.

To sum up, the present invention, in guaranteeing angle estimation precision, has significantly reduced operand, has guaranteed the rapid reaction of target reconnaissance and passive location, has avoided the parameter estimating error causing because of information delay.

Claims (4)

1. a 2-d direction finding angle method of estimation for electromagnetic signal, comprises the following steps:

1) adopt aerial receiver to form uniform planar battle array, wherein x direction of principal axis has N aerial receiver, _ydirection of principal axis has M aerial receiver, and aerial receiver spacing is d, N>=2, and M>=2,0<d≤λ/2, λ is incident narrow band signal wavelength;

2) by Q incoherent narrow band signal s _q(t) with x axle clamp angle α _qwith y axle clamp angle β _qincide in antenna uniform planar battle array, wherein, q=1,2 ..., Q, 1≤Q<NM, α _qrepresent the incident direction of q narrow band signal to be asked and the angle of x axle, β _qrepresent the incident direction of q narrow band signal to be asked and the angle of y axle, and α _q∈ (0 °, 180 °], β _q∈ (0 °, 180 °];

3) the echoed signal Y of each aerial receiver in calculating antenna uniform planar battle array _n,m(t);

Wherein, the computing of representing matrix multiplication cross, N (t) is noise signal vector, a _n(α _q) and a _m(β _q) represent respectively the x axle clamp angle α of the narrow band signal of q incident _qwith y axle clamp angle β _qcorresponding direction vector, expansion form is expressed as:

a _n(α _q)=(1,exp(j2πd·cosα _q/λ),...,exp[j2πd·(N-1)·cosα _q/λ]) ^T

a _m(β _q)=(1,exp(j2πd·cosβ _q/λ),...,exp[j2πd·(M-1)·cosβ _q/λ]) ^T

Wherein, j represents imaginary unit, () ^tthe computing of representing matrix transposition;

4) according to aerial receiver echoed signal Y _n,m(t), calculating noise subspace U _n;

5) structure angle solved function is:

Wherein,

for intermediate variable, min () represents to minimize computing, () ^hthe computing of representing matrix conjugate transpose, I _mrepresent the unit matrix of M × M dimension;

6) establish x axle clamp angle α _qfor (0 °, 180 °] fixed value in scope, by x axle clamp angle α _qsubstitution intermediate variable function G (α _q) obtain intermediate variable matrix G _q, then utilize following formula calculated direction vector a _m(β _q):

a _m(β _q)=P _min(G _q)，

Wherein, P _min() represents the corresponding proper vector of minimal eigenvalue of solution matrix;

7) get x axle clamp angle α _qfor (0 °, 180 °] other fixed value in scope, repeated execution of steps 6), obtain corresponding direction vector a _m(β _q);

8) by got multiple x axle clamp angle α _qwith the multiple directions vector a obtaining _m(β _q) substitution function:

in, obtain corresponding multiple functional value Z _q, then in plane with (0,0) for origin, with many groups of (α _q, Z _q) be x, y coordinate is drawn range value point, and each point is connected and obtains amplitude spectrogram;

9) from amplitude spectrogram, find according to order from high to low front Q the spectrum peak that amplitude is larger, using x axial coordinate the value corresponding peak point at these spectrum peaks as the x axle clamp angle α trying to achieve _qvalue;

10) according to each x axle clamp angle α trying to achieve _qvalue, finds corresponding direction vector a _m(β _q) value, recycling least square method is tried to achieve corresponding y axle clamp angle β _qvalue, the 2-d direction finding angle that completes electromagnetic signal is estimated.

2. the 2-d direction finding angle method of estimation of electromagnetic signal according to claim 1, wherein, the calculating aerial receiver echoed signal Y described in step 4) _n,m(t) noise subspace U _n, carry out as follows:

4a) the covariance matrix R=E[Y of calculating aerial receiver signal _n,m(t) Y _n,m(t) ^h], wherein E[] represent to ask mathematical expectation, () ^hthe computing of representing matrix conjugate transpose;

4b) covariance matrix R is carried out to following feature decomposition:

R=U·Λ·U ^H，

Wherein, Λ is the eigenvalue matrix of covariance matrix R, and U is the corresponding eigenvectors matrix of eigenwert;

4c) eigenwert in eigenvalue matrix Λ is pressed to sequence from big to small, after getting, (NM-Q) individual less eigenwert characteristic of correspondence vector matrix is as noise subspace U _n.

3. the 2-d direction finding angle method of estimation of electromagnetic signal according to claim 1, calculates intermediate variable matrix G in wherein said step 6) _qthe corresponding proper vector of minimal eigenvalue, try to achieve direction vector a _m(β _q), carry out as follows:

6a) to middle matrix of variables G _qcarry out feature decomposition:

Wherein, Λ _qfor intermediate variable matrix G _qeigenvalue matrix, U _qfor intermediate variable matrix G _qthe corresponding eigenvectors matrix of eigenwert, () ^hthe computing of representing matrix conjugate transpose;

6b) find intermediate variable matrix G _qthe eigenwert Λ of middle minimum _qmincharacteristic of correspondence vector U _qmin, by this proper vector U _qminas the direction vector a trying to achieve _m(β _q).

4. the 2-d direction finding angle method of estimation of electromagnetic signal according to claim 1, wherein described in step 10) according to direction vector a _m(β _q), utilize least square method to try to achieve y axle clamp angle β _qvalue, carry out as follows:

10a) according to direction vector a _m(β _q), utilize following formula to calculate angle vector g:

g=-angle(a _m(β _q))

Wherein, angle () represents each element in vector to get respectively phase angle;

10b) order matrix

calculate following formula:

[c ₀,c ₁] ^T=(P ^TP) ^-1P ^Tg，

Wherein, c ₀and c ₁represent respectively two elements of required vector, () ^-1represent finding the inverse matrix computing, () ^tthe computing of representing matrix transposition;

10c) try to achieve y axle clamp angle β _qvalue:

。

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