CN103207380B - 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 Bearing method based on two-dimensional frequency sparse constraint

Technical field

The invention belongs to communication technical field, further relate to a kind of broadband Bearing method based on two-dimensional frequency sparse constraint in 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 computer control, presents the phase place toward each radiation array element electric current, thereby changes the array antenna of beam direction.Traditional method of adjusting beam position based on mechanical scanning structure, because rotational frequency is lower, Data Update slowly cannot adapt to the detecting real-time task of high maneuvering target.Phased array antenna adopts electron scanning mode, can realize the real-time update of echo data, has therefore obtained widely and has paid close attention to.Wherein utilizing phased array angle measurement is a main aspect of phased array application.

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

The first, 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 processed according to narrow band signal disposal route, the final comprehensive angular spectrum that obtains.For example, Zhouning County, Guo Na paper " the ISM algorithm based on svd " (the journal > > of < < Xinxiang University 2009,26 (6)) be exactly a kind of noncoherent signal disposal route, the maximum deficiency of the method be calculated amount large, be unable to estimate coherent signal source.

The second, based on coherent signal processing method.These class methods focus on reference frequency point by the signal space of broadband signal different frequency composition, and then the method that adopts narrow band signal to process is carried out high-resolution angle estimation.For example, in red flag, Liu Jian, Huang Zhitao, (< < electronic countermeasure > > 2007, No.5) is exactly a kind of related signal processing method to space paper Monday " the Beam Domain Broadband DOA Estimation method based on CSM ".The deficiency that the method exists is need to construct focussing matrix and carry out angle pre-estimation, and estimated accuracy is easily subject to the impact of pre-estimation error.

Summary of the invention

The object of the invention is the deficiency for above-mentioned prior art, proposes a kind of broadband Bearing method based on two-dimensional frequency sparse constraint, and the calculated amount of processing to reduce noncoherent signal, avoids the impact of angle pre-estimation on angle measurement accuracy in coherent signal processing.

The technical thought that realizes the object of the invention is by setting up sparse reconstruction model, and iterative optimization problem obtains high-resolution angular spectrum, by angular spectrum being carried out to peak value, detects the angle information that obtains target.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 array element causes is propagated relative time and postponed for τ _mi, build the target echo model 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 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), then with discrete data x _m(n) capable as m, structure receives signal matrix X (m, n):

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

Matrix X (m, n) carries out pre-service to received signal, and the capable data of matrix X (m, n) m are multiplied by (1) to received signal ^m, obtain pretreated data X'(m, n);

(3) to pretreated data X'(m, n) do 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) the frequency spectrum F of two-dimensional projection (ω, u) is followed cumulative, obtain projection spectral line Y (ω);

(5) press following formula by 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 measurable angle range;

(6) calculate without making an uproar in situation respectively, angle on target is θ ₁, θ ₂..., θ _ptime 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 base W and projection spectral line Y (ω), by solving 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, represent the sign of operation of minimizing, the regularization parameter of λ for being inputted by user, || || ₁, || || ₂represent to ask respectively 1 norm and 2 norms of vector;

(9) adopt threshold value comparison method, to angular spectrum vector, β carries out peak value detection, obtains angular spectrum vector peak value element index value l;

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

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

The present invention compared with prior art tool has the following advantages:

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

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

The 3rd, because make and the angle on target value of the sparse base of the present invention are irrelevant, avoided the step of angle pre-estimation in coherent signal processing, therefore the angle of coherent signal is detected more accurately, stablized.

Accompanying drawing explanation

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

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

Fig. 3 is for obtaining the simulation result figure of angular spectrum vector by existing coherent signal processing method;

Fig. 4 obtains the simulation result figure of angular spectrum vector by the inventive method.

Embodiment

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

With reference to Fig. 1, specific embodiment of the invention step is as follows:

Step 1, obtains 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 array element causes is propagated relative time and is postponed for 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 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), then with this discrete data x _m(n) capable as m, structure receives signal matrix X (m, n):

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

Matrix X (m, n) carries out pre-service to received signal, and the capable data of matrix X (m, n) m are multiplied by (1) to received signal ^m, obtain pretreated data X'(m, n).

Step 3, to pretreated data X'(m, n) carry out two-dimensional frequency projective transformation, obtain two-dimensional projection's frequency spectrum.

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

$H(v,u)=\underset{m=0}{\overset{M-1}{\mathrm{\&Sigma;}}}\underset{n=0}{\overset{T-1}{\mathrm{\&Sigma;}}}{X}^{\&prime;}(m,n)e^{-j\frac{2\mathrm{\&pi;}}{M^{\&prime;}}\mathrm{mv}}{e}^{-j\frac{2\mathrm{\&pi;}}{T^{\&prime;}}\mathrm{nu}}$

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) data in 2-d spectrum H (v, u) are carried out to 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, by following formula, is obtained

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

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

(3.c) by step (3.a) and step (3.b), be comprehensively that a step realizes, obtain the frequency spectrum F of two-dimensional projection (ω, u) to be:

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

Step 4, coherent is cumulative.

The frequency spectrum F of two-dimensional projection (ω, u) is followed cumulative, obtains projection spectral line Y (ω) and be:

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

Step 5, constructs sparse base.

(5.a) press following formula by 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 measurable angle range;

(5.b) calculate without making an uproar in situation respectively, angle on target is θ ₁, θ ₂..., θ _ptime 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 angular spectrum vector.

Utilize sparse base W and projection spectral line Y (ω), can solve following formula by optimized 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, represent the sign of operation of minimizing, the regularization parameter of λ for being inputted by user, || || ₁, || || ₂represent to ask respectively 1 norm and 2 norms of vector.

Step 7, determines angle on target value.

(7.a) angular spectrum vector β is normalized, obtains normalization angle spectrum vector

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

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

Wherein, for normalization angle spectrum vector i element;

(7.d) the angle value θ that determines target by peak value index value l by following formula 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 E84003.00GHz, 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 carrier frequency	1GHz
Modulating bandwidth	400MHz
		Element number of array	16
System array element distance	0.125m
		Array aperture	2m
Time-sampling is counted	32
		Time-sampling frequency	2.4GHz
Signal to noise ratio (S/N ratio)	10dB
		Target number	2
Angle on target	0°,3.5°

2. emulation content and result

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

Emulation 2, obtains angular spectrum vector by existing coherent signal processing method, and simulation result as shown in Figure 3;

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

From Fig. 2 and Fig. 3, existing noncoherent signal disposal route and existing coherent signal processing method, in the situation that array aperture is limited, cannot be differentiated two little and relevant targets of angle intervals;

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

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 Bearing method based on two-dimensional frequency sparse constraint, comprises the steps:

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

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

Wherein, x _m(t) be m the target echo that array element receives, t represents the time, and N is 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), then with discrete data x _m(n) capable as m, structure receives signal matrix X (m, n):

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

Matrix X (m, n) carries out pre-service to received signal, and the capable data of matrix X (m, n) m are multiplied by (1) to received signal ^m, obtain pretreated data X'(m, n);

(3) to pretreated data X'(m, n) do 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) the frequency spectrum F of two-dimensional projection (ω, u) is followed cumulative, obtain projection spectral line Y (ω);

(5) press following formula by 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 measurable angle range;

(6) calculate without making an uproar in situation respectively, angle on target is θ ₁, θ ₂..., θ _ptime 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 base W and projection spectral line Y (ω), by Newton method or method of conjugate gradient and weighted iteration least square optimized algorithm, solve 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, represent the sign of operation of minimizing, the regularization parameter of λ for being inputted by user, || || ₁, || || ₂represent to ask respectively 1 norm and 2 norms of vector;

(9) adopt threshold value comparison method, to angular spectrum vector, β carries out peak value detection, obtains angular spectrum vector peak value element index value l;

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

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

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

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

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

3. the broadband Bearing method based on two-dimensional frequency sparse constraint according to claim 1, the described employing threshold value comparison method of step (9) wherein, to angular spectrum vector, β carries out peak value detection, obtains angular spectrum vector peak value element index value l, carries out as follows:

(9a) angular spectrum vector β is normalized, obtains normalization angle spectrum vector

(9b) threshold epsilon=0.1 is set, by following formula, obtains peak value index value l and be:

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

Wherein, for normalization angle spectrum vector i element.