CN103207380A - Broadband target direction finding method based on two-dimensional frequency domain sparse constraint - Google Patents

Abstract

The invention discloses a broadband target direction finding method based on two-dimensional frequency domain sparse constraint. The method mainly solves the problems of a low angle resolution ratio, the poor coherent signal source estimation accuracy and a large calculation amount of common algorithms of prior methods. The technical scheme includes that the method comprises the steps of fully using target space sparseness and priori knowledge of array element receiving signals in a two-dimensional domain, and performing two-dimensional domain projection conversion on the array element receiving signals to obtain a two-dimensional projection spectrum; performing angle division on the angle measuring range, and designing a sparse base of the two-dimensional projection spectrum; solving an optimization problem through an optimization solving algorithm to obtain a high-resolution angle spectrum; and performing peak value detection on the angle spectrum through a threshold comparison method to obtain a target angle value. The broadband target direction finding method has the advantages of being small in calculation amount, high in measuring accuracy and angle resolution ratio and applicable to target angle estimation of radars and sonars.

Description

Broadband target direction-finding method based on the sparse constraint of two-dimensional frequency

Technical field

The invention belongs to communication technical field, further relate to a kind of broadband target direction-finding method based on the sparse constraint of two-dimensional frequency in the Array Signal Processing field, the angle on target that can be used for radar, sonar is estimated.

Background technology

Phased array is to utilize electromagnetic relevant principle, by the phase place of computer control feedback toward each radiation array element electric current, thus the array antenna of change beam direction.Traditional adjust the method for beam position based on the mechanical scanning structure, because rotational frequency is lower, Data Update slowly can't adapt to the detecting real-time task of high maneuvering target.Phased array antenna adopts the electron scanning mode, can realize the real-time update of echo data, has therefore obtained to pay close attention to widely.Wherein utilizing the phased array angle measurement is the main aspect that phased array is used.

At present, the wideband phased array angle measurement technique mainly contains based on the disposal route ISM of noncoherent signal with based on two kinds of the disposal route CSM of coherent signal.

First kind, based on noncoherent signal disposal route ISM.These class methods are that wideband data is decomposed into different narrow band datas, then each narrow band signal are handled according to the narrow band signal disposal route, the final comprehensive angular spectrum that obtains.For example, Zhouning County, Guo Na paper " based on the ISM algorithm of svd " (" Xinxiang University's journal " 2009,26 (6)) is exactly a kind of noncoherent signal disposal route, the maximum deficiency of this method be calculated amount big, be unable to estimate the coherent signal source.

Second kind, based on the coherent signal disposal route.These class methods focus on the reference frequency point with the signal space of broadband signal different frequency composition, and then the method that adopts narrow band signal to handle is carried out the estimation of high-resolution angle.For example, in red flag, Liu Jian, Huang Zhitao, (" electronic countermeasure " 2007 No.5) is exactly a kind of coherent signal disposal route to space paper Monday " based on the wave beam territory Broadband DOA method of estimation of CSM ".The deficiency that this method exists is to need the structure focussing matrix and carry out the angle pre-estimation, and estimated accuracy is subjected to the influence of pre-estimation error easily.

Summary of the invention

The object of the invention is the deficiency at above-mentioned prior art, proposes a kind of broadband target direction-finding method based on the sparse constraint of two-dimensional frequency, to reduce the calculated amount that noncoherent signal is handled, avoid coherent signal handle in the angle pre-estimation to the influence of angle measurement accuracy.

The technical thought that realizes the object of the invention is by setting up sparse reconstruction model, and the iterative optimization problem obtains the high-resolution angular spectrum, detects the angle information that obtains target by angular spectrum being carried out peak value.Its concrete steps comprise as follows:

(1) broadband signal of establishing radar emission is s (t), and the signal that the distance between i target and m the array element causes is propagated relative time and postponed to be τ _Mi, make up the target echo model that m array element receives and be:

$x_m\left(t\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}s(t-{\mathrm{\τ}}_{\mathrm{mi}})+n_m\left(t\right),m=\mathrm{1,2},\·\·\·,M$

Wherein, x _m(t) be m the target echo that array element receives, t represents the time, and N is the target sum, and M is array element number, n _m(t) be m the noise that array element receives;

(2) to target echo x _m(t) carry out discrete sampling, obtain discrete data x _m(n), again with discrete data x _m(n) capable as m, structure reception signal matrix X (m, n):

$X(m,n)=\left[\begin{array}{c}{x}_1\left(n\right)\\ \·\\ \·\\ \·\\ x_m\left(n\right)\\ \·\\ \·\\ \·\\ x_M\left(n\right)\end{array}\right];$

To received signal matrix X (m n) carries out pre-service, namely to received signal matrix X (m, n) data that m is capable multiply by (1) ^m, obtain pretreated data X'(m, n);

(3) to pretreated data X'(m, n) do the two-dimensional frequency projective transformation, obtain the frequency spectrum F of two-dimensional projection (ω, u), wherein ω represents the empty position frequently of projection, u represents discrete time-frequency sampled point;

(4) (ω u) follows and adds up, and obtains projection spectral line Y (ω) to the frequency spectrum F of two-dimensional projection;

(5) press following formula with the radar angle measurement range Theta _Min～θ _MaxEqual angles is divided into P angle:

${\mathrm{\θ}}_i={\mathrm{\θ}}_{\min }+\frac{i-1}{P-1}({\mathrm{\θ}}_{\max }-{\mathrm{\θ}}_{\min }),i=\mathrm{1,2},...,P,$

Wherein, θ _Min, θ _MaxBe respectively minimum value and the maximal value of angle measurement scope;

(6) calculating does not have under the situation of making an uproar respectively, and angle on target is θ ₁, θ ₂..., θ _PThe time corresponding projection spectral line Y ₁(ω), Y ₂(ω) ..., Y _P(ω);

(7) by projection spectral line Y ₁(ω), Y ₂(ω) ..., Y _P(ω) construct sparse base:

W=[Y ₁(ω),Y ₂(ω),...,Y _P(ω)]；

(8) utilize sparse basic W and projection spectral line Y (ω), by finding the solution following formula, obtain angular spectrum vector β:

$\underset{\mathrm{\β}}{\min }\{{\left|\right|Y\left(\mathrm{\ω}\right)-\mathrm{W\β}\left|\right|}_2+\mathrm{\λ}{\left|\right|\mathrm{\β}\left|\right|}_1\}$

Wherein,

The sign of operation that expression is minimized, λ are the regularization parameter by user's input, || || ₁, || || ₂1 norm and 2 norms of vector are asked in expression respectively;

(9) adopt the threshold value relative method, angular spectrum vector β is carried out peak value detect, obtain angular spectrum vector peak value element index value l;

(10) the angle value θ that determines target by following formula by peak value index value l is:

$\mathrm{\θ}={\mathrm{\θ}}_{\min }+\frac{l-1}{P-1}({\mathrm{\θ}}_{\max }-{\mathrm{\θ}}_{\min }).$

The present invention compared with prior art has following advantage:

The first, because the whole signal processing of the present invention all is that wideband echoes signal integral body is handled, taken full advantage of the information of broadband signal, can reach higher resolution.

The second, because the present invention is more outstanding to the angle detection effect of coherent signal by set up sparse base based on transmitting.

The 3rd, because the make of the sparse base of the present invention and angle on target value have nothing to do, avoided the step of angle pre-estimation in the coherent signal processing, therefore the angle to coherent signal detects more accurately, stablizes.

Description of drawings

Fig. 1 is process flow diagram of the present invention;

Fig. 2 is for obtaining the simulation result figure of angular spectrum vector with existing noncoherent signal disposal route;

Fig. 3 is for obtaining the simulation result figure of angular spectrum vector with existing coherent signal disposal route;

Fig. 4 is the simulation result figure that obtains the angular spectrum vector with the inventive method.

Embodiment

Below in conjunction with accompanying drawing the present invention is described in further detail.

With reference to Fig. 1, concrete implementation step of the present invention is as follows:

Step 1 is obtained the target echo that m array element receives.

If the broadband signal of radar emission is s (t), the signal that the distance between i target and m the array element causes is propagated relative time and is postponed to be τ _Mi, obtain the target echo that m array element receives and be:

$x_m\left(t\right)=\underset{i=1}{\overset{N}{\mathrm{\Σ}}}s(t-{\mathrm{\τ}}_{\mathrm{mi}})+n_m\left(t\right),m=\mathrm{1,2},\·\·\·,M$

Wherein, x _m(t) be m the target echo that array element receives, t represents the time, and N is the target sum, and M is array element number, n _m(t) be m the noise that array element receives.

Step 2, structure receives signal matrix.

To target echo x _m(t) carry out discrete sampling, obtain discrete data x _m(n), again with this discrete data x _m(n) capable as m, structure reception signal matrix X (m, n):

$X(m,n)=\left[\begin{array}{c}{x}_1\left(n\right)\\ \·\\ \·\\ \·\\ x_m\left(n\right)\\ \·\\ \·\\ \·\\ x_M\left(n\right)\end{array}\right];$

To received signal matrix X (m n) carries out pre-service, namely to received signal matrix X (m, n) data that m is capable multiply by (1) ^m, obtain pretreated data X'(m, n).

Step 3 to pretreated data X'(m, n) is carried out the two-dimensional frequency projective transformation, obtains two-dimensional projection's frequency spectrum.

(3.a) with pretreated data X'(m, n) by as shown in the formula carrying out two-dimensional Fourier transform, obtain 2-d spectrum H (v, u):

$H(v,u)=\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{T-1}{\mathrm{\&Sigma;}}}{X}^{\&prime;}(m,n)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00002909505500021.png,HDA00002909505500031.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{M^{\&prime;}}\mathrm{mv}}{e}^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00002909505500021.png,HDA00002909505500031.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{T^{\&prime;}}\mathrm{nu}}$

Wherein, v represents discrete empty frequency sampling point, and u represents discrete time-frequency sampled point, and M' represents that discrete empty frequency sampling counts, and T' represents discrete time-frequency sampling number;

(3.b) to 2-d spectrum H (v, u) data in are carried out projection by following formula, obtain the frequency spectrum F of two-dimensional projection (ω, u):

F(ω,u)=H(v,u)

Wherein ω represents projected position, is obtained by following formula

$\mathrm{\&omega;}=\mathrm{round}(\frac{v-\frac{M^{\&prime;}}{2}}{u}{u}_p+\frac{M^{\&prime;}}{2})$

In the formula, u _pExpression projection time-frequency axle, round () represents rounding operation;

Comprehensively be to realize in a step step (3.a) and step (3.b) (3.c), obtain the frequency spectrum F of two-dimensional projection (ω u) is:

$F(\mathrm{\&omega;},u)=\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{T-1}{\mathrm{\&Sigma;}}}{X}^{\&prime;}(m,n)e^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00002909505500021.png,HDA00002909505500031.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{T^{\&prime;}}\mathrm{nu}}{e}^{-\mathrm{<figure-callout\; id="2"\; label="j"\; filenames="HDA00002909505500021.png,HDA00002909505500031.png"\; state="\{\{state\}\}">j</figure-callout>}\frac{2\mathrm{\&pi;}}{M^{\&prime;}}m[\frac{u}{u_p}(\mathrm{\&omega;}-\frac{M^{\&prime;}}{2})+\frac{M^{\&prime;}}{2}]},$

Step 4, coherent adds up.

To the frequency spectrum F of two-dimensional projection (ω u) follows and adds up, and obtains projection spectral line Y (ω) and is:

$Y\left(\mathrm{\&omega;}\right)=\underset{u=1}{\overset{T^{\&prime;}}{\mathrm{\&Sigma;}}}F(\mathrm{\&omega;},u)$

Step 5 is constructed sparse base.

(5.a) press following formula with the radar angle measurement range Theta _Min～θ _MaxEqual angles is divided into P angle:

${\mathrm{\&theta;}}_i={\mathrm{\&theta;}}_{\min }+\frac{i-1}{P-1}({\mathrm{\&theta;}}_{\max }-{\mathrm{\&theta;}}_{\min }),i=\mathrm{1,2},...,P,$

Wherein, θ _Min, θ _MaxBe respectively minimum value and the maximal value of angle measurement scope;

(5.b) calculating does not have under the situation of making an uproar respectively, and angle on target is θ ₁, θ ₂..., θ _PThe time corresponding projection spectral line Y ₁(ω), Y ₂(ω) ..., Y _P(ω);

(5.c) by projection spectral line Y ₁(ω), Y ₂(ω) ..., Y _P(ω) construct sparse base:

W=[Y ₁(ω),Y ₂(ω),...,Y _P(ω)]。

Step 6 obtains the angular spectrum vector.

Utilize sparse basic W and projection spectral line Y (ω), can find the solution following formula by optimization algorithms such as Newton method or method of conjugate gradient and weighted iteration least squares, acquisition angular spectrum vector β is:

$\underset{\mathrm{\&beta;}}{\min }\{{\left|\right|Y\left(\mathrm{\&omega;}\right)-\mathrm{W\&beta;}\left|\right|}_2+\mathrm{\&lambda;}{\left|\right|\mathrm{\&beta;}\left|\right|}_1\}$

Wherein,

The sign of operation that expression is minimized, λ are the regularization parameter by user's input, || || ₁, || || ₂1 norm and 2 norms of vector are asked in expression respectively.

Step 7 is determined the angle on target value.

(7.a) angular spectrum vector β is carried out normalized, obtain normalization angle spectrum vector

(7.b) threshold epsilon=0.1 is set, obtains peak value index value l by following formula and be:

$l=\left\{i\right|{\stackrel{\&OverBar;}{\mathrm{\&beta;}}}_i>\mathrm{\&epsiv;},i=\mathrm{1,2},...,P\}$

Wherein,

Be normalization angle spectrum vector

I element;

(7.d) the angle value θ that determines target by following formula by peak value index value l is:

$\mathrm{\&theta;}={\mathrm{\&theta;}}_{\min }+\frac{l-1}{P-1}({\mathrm{\&theta;}}_{\max }-{\mathrm{\&theta;}}_{\min }).$

Effect of the present invention can be illustrated by following emulation experiment:

1. simulated conditions

Operational system is Intel (R) Core (TM) Duo CPU [email protected], 32-bit Windows operating system, and simulation software adopts MATLAB R (2011b), and simulation parameter arranges as shown in the table.

Parameter	Parameter value
		System's carrier frequency	1GHz
Modulating bandwidth	400MHz
		Element number of array	16
System's array element distance	0.125m
		Array aperture	2m
Time-sampling is counted	32
		The time-sampling frequency	2.4GHz
Signal to noise ratio (S/N ratio)	10dB
		The target number	2
Angle on target	0°,3.5°

2. emulation content and result

Emulation 1 obtains the angular spectrum vector with existing noncoherent signal disposal route, and simulation result as shown in Figure 2;

Emulation 2 obtains the angular spectrum vector with existing coherent signal disposal route, and simulation result as shown in Figure 3;

Emulation 3 obtains the angular spectrum vector with the inventive method, and simulation result as shown in Figure 4.

By Fig. 2 and Fig. 3 as can be known, existing noncoherent signal disposal route and existing coherent signal disposal route can't be differentiated two little and relevant targets of angle intervals under the array aperture condition of limited;

As shown in Figure 4, the inventive method is successfully told two little and relevant targets of angle intervals.Angle such as the table 1 at two target places:

Table 1 angle on target value result of calculation

Extraterrestrial target	Target 1	Target 2
			Angle	0.2°	3.5°

As shown in Table 1, the angle value of two targets has all obtained high-precision calculating.

Claims (3)

1. the broadband target direction-finding method based on the sparse constraint of two-dimensional frequency comprises the steps:

(1) broadband signal of establishing radar emission is s (t), and the signal that the distance between i target and m the array element causes is propagated relative time and postponed to be τ _Mi, obtain the target echo that m array element receives and be:

$x_m\left(t\right)=\underset{i=1}{\overset{N}{\mathrm{\&Sigma;}}}s(t-{\mathrm{\&tau;}}_{\mathrm{mi}})+n_m\left(t\right),m=\mathrm{1,2},\&CenterDot;\&CenterDot;\&CenterDot;,M$

Wherein, x _m(t) be m the target echo that array element receives, t represents the time, and N is the target sum, and M is array element number, n _m(t) be m the noise that array element receives;

(2) to target echo x _m(t) carry out discrete sampling, obtain discrete data x _m(n), again with discrete data x _m(n) capable as m, structure reception signal matrix X (m, n):

$X(m,n)=\left[\begin{array}{c}{x}_1\left(n\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ x_m\left(n\right)\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ x_M\left(n\right)\end{array}\right];$

To received signal matrix X (m n) carries out pre-service, namely to received signal matrix X (m, n) data that m is capable multiply by (1) ^m, obtain pretreated data X'(m, n);

(3) to pretreated data X'(m, n) do the two-dimensional frequency projective transformation, obtain the frequency spectrum F of two-dimensional projection (ω, u), wherein ω represents the empty position frequently of projection, u represents discrete time-frequency sampled point;

(4) (ω u) follows and adds up, and obtains projection spectral line Y (ω) to the frequency spectrum F of two-dimensional projection;

(5) press following formula with the radar angle measurement range Theta _Min～θ _MaxEqual angles is divided into P angle:

${\mathrm{\&theta;}}_i={\mathrm{\&theta;}}_{\min }+\frac{i-1}{P-1}({\mathrm{\&theta;}}_{\max }-{\mathrm{\&theta;}}_{\min }),i=\mathrm{1,2},...,P,$

Wherein, θ _Min, θ _MaxBe respectively minimum value and the maximal value of angle measurement scope;

(6) calculating does not have under the situation of making an uproar respectively, and angle on target is θ ₁, θ ₂..., θ _PThe time corresponding projection spectral line Y ₁(ω), Y ₂(ω) ..., Y _P(ω);

(7) by projection spectral line Y ₁(ω), Y ₂(ω) ..., Y _P(ω) construct sparse base:

W=[Y ₁(ω),Y ₂(ω),...,Y _P(ω)]；

(8) utilize sparse basic W and projection spectral line Y (ω), by finding the solution following formula, obtain angular spectrum vector β:

$\underset{\mathrm{\&beta;}}{\min }\{{\left|\right|Y\left(\mathrm{\&omega;}\right)-\mathrm{W\&beta;}\left|\right|}_2+\mathrm{\&lambda;}{\left|\right|\mathrm{\&beta;}\left|\right|}_1\}$

Wherein,

The sign of operation that expression is minimized, λ are the regularization parameter by user's input, || || ₁, || || ₂1 norm and 2 norms of vector are asked in expression respectively;

(9) adopt the threshold value relative method, angular spectrum vector β is carried out peak value detect, obtain angular spectrum vector peak value element index value l;

(10) the angle value θ that determines target by following formula by peak value index value l is:

$\mathrm{\&theta;}={\mathrm{\&theta;}}_{\min }+\frac{l-1}{P-1}({\mathrm{\&theta;}}_{\max }-{\mathrm{\&theta;}}_{\min }).$

2. the broadband target direction-finding method based on the sparse constraint of two-dimensional frequency according to claim 1, wherein step (3) is described to pretreated data X'(m, n) does the two-dimensional frequency projective transformation, is undertaken by following formula:

$F(\mathrm{\&omega;},u)=\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{T-1}{\mathrm{\&Sigma;}}}{X}^{\&prime;}(m,n)e^{-j\frac{2\mathrm{\&pi;}}{T^{\&prime;}}\mathrm{nu}}{e}^{-j\frac{2\mathrm{\&pi;}}{M^{\&prime;}}m[\frac{1}{u_p-\frac{T^{\&prime;}}{2}}(u-\frac{T^{\&prime;}}{2})(\mathrm{\&omega;}-\frac{M^{\&prime;}}{2})+\frac{M^{\&prime;}}{2}]}$

Wherein, (ω u) is two-dimensional projection's frequency spectrum after the two-dimensional frequency projective transformation to F, and T represents that time-sampling counts, and T' represents discrete time-frequency sampling number, and M' represents that discrete empty frequency sampling counts.

3. the broadband target direction-finding method based on the sparse constraint of two-dimensional frequency according to claim 1, the described employing threshold value of step (9) relative method wherein, angular spectrum vector β is carried out peak value detects, obtain angular spectrum vector peak value element index value l, carry out as follows:

(4a) angular spectrum vector β is carried out normalized, obtain normalization angle spectrum vector

(4b) threshold epsilon=0.1 is set, obtains peak value index value l by following formula and be:

$l=\left\{i\right|{\stackrel{\&OverBar;}{\mathrm{\&beta;}}}_i>\mathrm{\&epsiv;},i=\mathrm{1,2},...,P\}$

Wherein,

Be normalization angle spectrum vector

I element.

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