CN103116162B - High-resolution sonar location method based on sparsity of objective space - Google Patents

Abstract

The invention discloses a high-resolution sonar location method based on a sparsity of an objective space and mainly solves the problems that a limited array aperture causes insufficient spatial resolution and a signal source coherence causes an inaccurate estimation of an objective location and calculating work of subspace decomposition and data volume are considerable in the prior art. According to the method, a projection matrix which is from a spatial spectrum vector quantity to a ranks synthesis data vector is constructed. By taking advantage of the apriori information of the sparsity of the space target and obtaining data of large signal to noise ratio through a matched filtering, the spatial spectrum vector quantity is carried out with peak detection through an iterative computation to obtain the high-resolution spatial spectrum vector quantity. The objective location can be achieved by taking advantage of the received index value of a peak element through the calculation to gain an objective azimuth angle and an objective pitch angle. The location method has the advantages of being low in the needed data size and calculated amount in the iterative process, suitable for a hardware implementation, high in angular accuracy and improving markedly the spatial resolution.

Description

The high-resolution sonar localization method of based target spatial sparsity

Technical field

The invention belongs to communication technical field, further relate to the high-resolution sonar localization method of a kind of based target spatial sparsity in Array Signal Processing field.It is limited that the present invention can effectively solve sonar transducer array aperture, and the problem of the spatial resolution deficiency causing realizes high-resolution sonar target location.

Background technology

Due to the rising sharp-decay of the energy of frequency electromagnetic waves when the water transmission along with frequency, make the sound wave of low frequency become the effective carrier that underwater environment information is transmitted, so the application of sonar technology and research are paid close attention to widely.Wherein utilize sonar array to carry out the main aspect that target localization is the application of sonar technology.

At present, sonar target location technology mainly contains two kinds of multi-beam forming method sum of subspace methods.

The first, multi-beam forming method.For example, Cao Huiqiong, Wang Yingmin, Li Na paper " a kind of improved three wave beam direction-finding methods " (< < electroacoustic basis > > 2009, 33 (8): 42-44), disclose a kind of three wave beam direction-finding methods, the method is that the data of all passages to gathering are carried out multi-beam formation, utilize three larger wave beams to form output valve, by quadratic fit, obtain a quafric curve, peak value by finding this quafric curve is to target localization, although the method can accurately be carried out target localization, but the deficiency still existing is, the method cannot realize multiobject location simultaneously.

The second, subspace method.The patented claim that PLA Air Force equipment research institute's radar territory electronic countermeasure research institute proposes " be applicable to the direction-finding method of coherent under nonstationary noise background " (application number: 200610113172.5, publication number: disclose a kind of high resolution target direction-finding method based on Subspace Decomposition 101150345A).The method overcomes the coherence of signal source by Subarray Smoothing, by being carried out to feature decomposition, the covariance matrix obtaining comes picked up signal subspace and noise subspace, then at signal subspace, form spatial spectrum, by being carried out to spectrum peak search, comes goal orientation spatial spectrum, but the deficiency still existing is, the method has reduced array aperture, caused spatial resolution decline, while the method need to gather a large amount of data and carry out estimate covariance matrix, more greatly, and in the method, feature decomposition calculated amount is larger for the data volume needing.

Summary of the invention

The object of the invention is to overcome above-mentioned the deficiencies in the prior art, propose a kind of high-resolution sonar localization method of based target spatial sparsity.The present invention is to each channel peak smnr data of sonar array, synthetic according to the arrangement mode procession of basic matrix array element, build spatial spectrum vector to the projection matrix of ranks generated data vector, by cost function of iteration optimization, obtain high-resolution spatial spectrum vector, spatial spectrum vector is carried out to peak value and detect the azimuth pitch angle that obtains target, thereby realize the location to target.

Specific embodiment of the invention step is as follows:

(1) gather the data that each passage of array receives, and store in Installed System Memory;

(2) matched filtering

2a) adopt matched filtering formula, the data of each passage gathering are carried out to matched filtering;

2b) data after each passage matched filtering are got to maximal value;

(3) ranks are synthetic

3a) by step 2b) in all data maximal values of obtaining according to the position of the corresponding array element of passage separately, at two dimensional surface, rearrange, obtain a data matrix as follows:

$\left[\begin{array}{ccc}0& M_5& 0\\ M_2& M_3& M_4\\ 0& M_1& 0\end{array}\right]$

Wherein, 0 represents null matrix, M ₁, M ₂, M ₃, M ₄and M ₅represent respectively five matrixes;

3b) extract successively matrix M ₂, M ₃and M ₄in column vector, the column vector extracting is rearranged and forms a matrix, all row vectors of this matrix are added and obtain row generated data vector R;

3c) extract successively matrix M ₁, M ₃and M ₅in row vector, the row vector extracting is rearranged and forms a matrix, all column vectors of this matrix are added and obtain row generated data vector C;

(4) build projection matrix

4a) computer azimuth dimension space is composed the projection matrix element that vector arrives row generated data vector according to the following formula:

$A(r,c)=e^{j\frac{2\mathrm{\&pi;}}{N}(r-1)(c-1)}$

Wherein, A (r, c) represents that azimuth dimension spatial spectrum vector is to the element of the capable c row of r in the projection matrix of row generated data vector, 0 < r < L, L represents step 3b) described in the dimension of row generated data vector n represents the dimension of azimuth dimension spatial spectrum vector, and j represents imaginary unit;

4b) by step 4a) element that obtains is according to ranks positional alignment, forms azimuth dimension spatial spectrum vector to the projection matrix of row generated data vector;

4c) calculate according to the following formula the projection matrix element that pitching dimension space spectrum vector arrives row generated data vector:

$B(h,l)=e^{j\frac{2\mathrm{\&pi;}}{K}(h-1)(l-1)}$

Wherein, B (h, l) represents that pitching dimension space spectrum vector is to the element of the capable l row of h in the projection matrix of row generated data vector, 0 < h < D, D represents step 3c) described in the dimension of row generated data vector k represents that pitching dimension space composes vectorial dimension, and j represents imaginary unit;

4d) by step 4c) the middle element obtaining is according to ranks positional alignment, and formation pitching dimension space spectrum vector arrives the projection matrix of row generated data vector;

(5) obtain spatial spectrum vector

5a) by solving following formula, obtain azimuth dimension spatial spectrum vector:

$\underset{\mathrm{\&alpha;}}{\min }\{{\left|\mathrm{\&alpha;}\right|}_p+\mathrm{\&zeta;}|R-\mathrm{A\&alpha;}\left|\right\}$

Wherein, α represents azimuth dimension spatial spectrum vector, || _prepresent to ask vectorial p norm, ζ represents the regularization parameter of being inputted by user, || represent to ask vectorial mould, R represents step 3b) the row generated data vector that obtains, A represents step 4a) the azimuth dimension spatial spectrum vector that obtains is to the projection matrix of row generated data vector represent the sign of operation of minimizing;

5b) by solving following formula, obtain pitching dimension space spectrum vector:

$\underset{\mathrm{\&beta;}}{\min }\{{\left|\mathrm{\&beta;}\right|}_p+\mathrm{\&zeta;}|C-\mathrm{B\&beta;}\left|\right\}$

Wherein, β represents pitching dimension space spectrum vector, || _prepresent to ask vectorial p norm, ζ represents the regularization parameter of being inputted by user, || represent to ask vectorial mould, C represents step 3c) the row generated data vector that obtains, B represents step 4b) the pitching dimension space spectrum vector that obtains is to the projection matrix of row generated data vector represent the sign of operation of minimizing;

(6) peak value detects

6a) adopting threshold value comparison method, to step 5b) the pitching dimension space spectrum vector that obtains carries out peak value detection, and obtain pitching dimension space and compose vectorial peak value element index value;

6b) adopting threshold value comparison method, to step 5a) the azimuth dimension spatial spectrum vector that obtains carries out peak value detection, obtains azimuth dimension spatial spectrum vector peak value element index value;

(7) target localization

7a) by step 6a) the pitching dimension space that obtains composes vectorial peak value element index value substitution following formula, calculates the picked up signal source angle of pitch:

Wherein, for the signal source angle of pitch, asin represents arcsin function, and λ represents system carrier wavelength, and K represents that pitching dimension space composes vectorial dimension, and d represents system array element distance, and u represents that pitching dimension space composes the index value of vectorial peak value element;

7b) by step 6b) the azimuth dimension spatial spectrum vector peak value element index value and the step 7a that obtain) the signal source angle of pitch substitution following formula that obtains, calculates picked up signal source side parallactic angle:

Wherein, θ is signal source position angle, and asin represents arcsin function, and λ represents system carrier wavelength, and N represents the dimension of azimuth dimension spatial spectrum vector, and d represents system array element distance, and v represents the index value of azimuth dimension spatial spectrum vector peak value element, expression step 6a) the signal source angle of pitch obtaining.

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

The first, because the present invention detects to locate by high-resolution spatial spectrum vector is carried out to peak value, can realize multiobject location simultaneously.

The second, because the present invention is by building spatial spectrum vector to the projection matrix of ranks generated data vector, in the situation that not reducing array aperture, has overcome the correlativity in echo signal source, and only needed single snapshot data, reduced required data volume.

The 3rd, because adopting iterative process, the present invention obtains spatial spectrum vector, and be applicable to hardware and realize, calculated amount is little.

Accompanying drawing explanation

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

Fig. 2 is emulation schematic diagram of the present invention.

Embodiment

Below in conjunction with accompanying drawing, the present invention will be further described.

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

Step 1. gathers the data that each passage of array receives, and stores in Installed System Memory.

The baseband receiving signals of sonar array array element respective channel is carried out to AD sampling, be converted to digital signal, the digital signal being converted to is utilized to memory device, stores.

Step 2. matched filtering.

2a) adopt matched filtering formula, data to each passage gathering are carried out matched filtering, in order to obtain the Y-PSNR data of each passage, each channel data gathering is carried out respectively to matched filtering, calculate according to the following formula data after m passage matched filtering:

x _m(t)＝FT ^-1[e _m·s ^*]

Wherein, x _m(t) represent the data after m passage matched filtering, t represents time-domain sampling point, FT ^-1represent inverse Fourier transform, e _mthe frequency spectrum that represents m channel data, s represents known reference signal frequency spectrum, * represents to get conjugation, represents multiplication of vectors.

2b) data after each passage matched filtering are got to maximal value.

Step 3. ranks are synthetic.

3a) by step 2b) in all data maximal values of obtaining according to the position of the corresponding array element of passage separately, at two dimensional surface, rearrange, obtain a data matrix as follows:

$\left[\begin{array}{ccc}0& M_5& 0\\ M_2& M_3& M_4\\ 0& M_1& 0\end{array}\right]$

Wherein, 0 represents null matrix, M ₁, M ₂, M ₃, M ₄and M ₅represent respectively five matrixes.

3b) extract successively matrix M ₂, M ₃and M ₄in column vector, the column vector extracting is rearranged and forms a matrix, all row vectors of this matrix are added and obtain row generated data vector R.

3c) extract successively matrix M ₁, M ₃and M ₅in row vector, the row vector extracting is rearranged and forms a matrix, all column vectors of this matrix are added and obtain row generated data vector C.

3a) all data maximal values that obtain in step 2 are rearranged in the position of two dimensional surface according to each passage array element shown in Fig. 3, obtain a data matrix.

Step 4. builds projection matrix.

According to the requirement of spatial resolution, N and K angle-unit will be marked off respectively within the scope of the azimuth coverage in space, signal source place and the angle of pitch, owing to there is consistance in Space domain sampling and time-domain sampling, the projection matrix according to discrete Fourier kernel function conformational space spectrum vector to ranks generated data vector.

4a) computer azimuth dimension space is composed the projection matrix element that vector arrives row generated data vector according to the following formula:

$A(r,c)=e^{j\frac{2\mathrm{\&pi;}}{N}(r-1)(c-1)}$

Wherein, A (r, c) represents that azimuth dimension spatial spectrum vector is to the element of the capable c row of r in the projection matrix of row generated data vector, 0 < r < L, L represents step 3b) described in the dimension of row generated data vector n represents the dimension of azimuth dimension spatial spectrum vector, and j represents imaginary unit.

4b) by step 4a) element that obtains is according to ranks positional alignment, forms azimuth dimension spatial spectrum vector to the projection matrix of row generated data vector.

4c) calculate according to the following formula the projection matrix element that pitching dimension space spectrum vector arrives row generated data vector:

$B(h,l)=e^{j\frac{2\mathrm{\&pi;}}{K}(h-1)(l-1)}$

Wherein, B (h, l) represents that pitching dimension space spectrum vector is to the element of the capable l row of h in the projection matrix of row generated data vector, 0 < h < D, D represents step 3c) described in the dimension of row generated data vector k represents that pitching dimension space composes vectorial dimension, and j represents imaginary unit.

4d) by step 4c) the middle element obtaining is according to ranks positional alignment, and formation pitching dimension space spectrum vector arrives the projection matrix of row generated data vector.

Step 5. obtains spatial spectrum vector.

By the spatial spectrum vector in step 4, to the projection matrix of ranks generated data matrix, can set up two following equations:

$\left\{\begin{array}{c}R=\mathrm{A\&alpha;}+n\\ C=\mathrm{B\&beta;}+n\end{array}\right.$

Wherein, α represents azimuth dimension spatial spectrum vector, R represents step 3b) the row generated data vector that obtains, A represents step 4a) the azimuth dimension spatial spectrum vector that obtains is to the projection matrix of row generated data vector, β represents pitching dimension space spectrum vector, C represents step 3c) the row generated data vector that obtains, B represents step 4b) the pitching dimension space spectrum vector that obtains is to the projection matrix of row generated data vector, n represents the noise vector of system.

Solve above-mentioned two equations and can obtain spatial spectrum vector, according to maximum a posteriori probability estimation theory, above-mentioned two equations can adopt following method to solve.

5a) by solving following formula, obtain azimuth dimension spatial spectrum vector:

$\underset{\mathrm{\&alpha;}}{\min }\{{\left|\mathrm{\&alpha;}\right|}_p+\mathrm{\&zeta;}|R-\mathrm{A\&alpha;}\left|\right\}$

Wherein, α represents azimuth dimension spatial spectrum vector, || _prepresent to ask vectorial p norm, ζ represents the regularization parameter of being inputted by user, || represent to ask vectorial mould, R represents step 3b) the row generated data vector that obtains, A represents step 4a) the azimuth dimension spatial spectrum vector that obtains is to the projection matrix of row generated data vector represent the sign of operation of minimizing.

5b) by solving following formula, obtain pitching dimension space spectrum vector:

$\underset{\mathrm{\&beta;}}{\min }\{{\left|\mathrm{\&beta;}\right|}_p+\mathrm{\&zeta;}|C-\mathrm{B\&beta;}\left|\right\}$

Wherein, β represents pitching dimension space spectrum vector, || _prepresent to ask vectorial p norm, ζ represents the regularization parameter of being inputted by user, || represent to ask vectorial mould, C represents step 3c) the row generated data vector that obtains, B represents step 4b) the pitching dimension space spectrum vector that obtains is to the projection matrix of row generated data vector represent the sign of operation of minimizing.

Step 5a) and step 5b) in solving of two formulas can be undertaken by iterative process as shown in Figure 4.

Step 6. peak value detects.

Adopt threshold value comparison method to carry out peak detection process to spatial spectrum vector simple, and peak value accuracy in detection is higher, the basic process of threshold value comparison method is as follows:

To spatial spectrum vector, ask first order difference to obtain difference vector; Find the zero crossing of difference vector and record zero crossing index value; Half of spatial spectrum vector maximum element value is set to threshold value; The element that the element intermediate value at spatial spectrum vector zero crossing index value place is greater than threshold value is peak value element, and the index value that peak value element is corresponding is the peak value element index value of spatial spectrum vector.

6a) adopting threshold value comparison method, to step 5b) the pitching dimension space spectrum vector that obtains carries out peak value detection, and obtain pitching dimension space and compose vectorial peak value element index value.

6b) adopting threshold value comparison method, to step 5a) the azimuth dimension spatial spectrum vector that obtains carries out peak value detection, obtains azimuth dimension spatial spectrum vector peak value element index value.

Step 7. target localization.

7a) by step 6a) the pitching dimension space that obtains composes vectorial peak value element index value substitution following formula, calculates the picked up signal source angle of pitch:

Wherein, for the signal source angle of pitch, asin represents arcsin function, and λ represents system carrier wavelength, and K represents that pitching dimension space composes vectorial dimension, and d represents system array element distance, and u represents that pitching dimension space composes the index value of vectorial peak value element;

7b) by step 6b) the azimuth dimension spatial spectrum vector peak value element index value and the step 7a that obtain) the signal source angle of pitch substitution following formula that obtains, calculates picked up signal source side parallactic angle:

Wherein, θ is signal source position angle, and asin represents arcsin function, and λ represents system carrier wavelength, and N represents the dimension of azimuth dimension spatial spectrum vector, and d represents system array element distance, and v represents the index value of azimuth dimension spatial spectrum vector peak value element, expression step 6a) the signal source angle of pitch obtaining.

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

1. simulated conditions

Operational system is Intel (R) Core (TM) i5CPU6503.20GHz, 32-bit Windows operating system, and simulation software adopts MATLAB R (2011a), and simulation parameter arranges as shown in the table.

Parameter	Parameter value
		System carrier frequency	25kHz
System array element distance	0.03m
		Pulse repetition time	2s
Duration of pulse	85ms
		Modulating bandwidth	1kHz
Basic matrix aperture	0.36m
		Signal to noise ratio (S/N ratio)	25dB
Target number	3
		Azimuth of target	-3.5°，0°，3.5°
The target angle of pitch	-3.5°，0°，3.5°

2. simulation result

Fig. 2 (a) represents that wave beam forms the spatial spectrum vector and the peak value that obtain and detects the peak value element obtaining, and in Fig. 2 (a), " zero " represents peak value element.Fig. 2 (b) represents that spatial spectrum vector and peak value that Subspace Decomposition obtains detect the peak value element obtaining, and in Fig. 2 (b), " zero " represents peak value element.Fig. 2 (c) represents that spatial spectrum vector and peak value that the present invention obtains detect the peak value element obtaining, and in Fig. 2 (c), " zero " represents peak value element.Beam-forming schemes is in the situation that array aperture is limited as shown in Figure 2, cannot differentiate the close a plurality of targets in locus, and Subspace Decomposition method is relevant in spacing wave source in the situation that, still cannot differentiate the close a plurality of targets in locus, the inventive method is successfully told three close and relevant targets of locus.The azimuth pitch angle that following table illustrates three targets all obtains high-precision calculating.

Extraterrestrial target	Position angle	The angle of pitch
			Target 1	-3.44°	-3.47°
Target 2	0.01°	0.03°
			Target 3	3.55°	3.51°

Claims (3)

1. a high-resolution sonar localization method for based target spatial sparsity, comprises the steps:

(1) gather the data that each passage of array receives, and store in Installed System Memory;

(2) matched filtering

2a) adopt matched filtering formula, the data of each passage gathering are carried out to matched filtering;

2b) data after each passage matched filtering are got to maximal value;

(3) ranks are synthetic

3a) by step 2b) in all data maximal values of obtaining according to the position of the corresponding array element of passage separately, at two dimensional surface, rearrange, obtain a data matrix as follows:

$\left[\begin{array}{ccc}0& M_5& 0\\ M_2& M_3& M_4\\ 0& M_1& 0\end{array}\right]$

Wherein, 0 represents null matrix, M ₁, M ₂, M ₃, M ₄and M ₅represent respectively five matrixes;

3b) extract successively matrix M ₂, M ₃and M ₄in column vector, the column vector extracting is rearranged and forms a matrix, all row vectors of this matrix are added and obtain row generated data vector R;

3c) extract successively matrix M ₁, M ₃and M ₅in row vector, the row vector extracting is rearranged and forms a matrix, all column vectors of this matrix are added and obtain row generated data vector C;

(4) build projection matrix

4a) computer azimuth dimension space is composed the projection matrix element that vector arrives row generated data vector according to the following formula:

$A(r,c)=e^{j\frac{2\mathrm{\&pi;}}{N}(r-1)(c-1)}$

Wherein, A (r, c) represents that azimuth dimension spatial spectrum vector is to the element of the capable c row of r in the projection matrix of row generated data vector, 0 < r < L, L represents step 3b) described in the dimension of row generated data vector n represents the dimension of azimuth dimension spatial spectrum vector, and j represents imaginary unit;

4b) by step 4a) element that obtains is according to ranks positional alignment, forms azimuth dimension spatial spectrum vector to the projection matrix of row generated data vector;

4c) calculate according to the following formula the projection matrix element that pitching dimension space spectrum vector arrives row generated data vector:

$B(h,l)=e^{j\frac{2\mathrm{\&pi;}}{K}(h-1)(l-1)}$

Wherein, B (h, l) represents that pitching dimension space spectrum vector is to the element of the capable l row of h in the projection matrix of row generated data vector, 0 < h < D, D represents step 3c) described in the dimension of row generated data vector k represents that pitching dimension space composes vectorial dimension, and j represents imaginary unit;

4d) by step 4c) the middle element obtaining is according to ranks positional alignment, and formation pitching dimension space spectrum vector arrives the projection matrix of row generated data vector;

(5) obtain spatial spectrum vector

5a) by solving following formula, obtain azimuth dimension spatial spectrum vector:

$\underset{\mathrm{\&alpha;}}{\min }\{{\left|\mathrm{\&alpha;}\right|}_p+\mathrm{\&zeta;}|R-\mathrm{A\&alpha;}\left|\right\}$

Wherein, α represents azimuth dimension spatial spectrum vector, || _prepresent to ask vectorial p norm, ζ represents the regularization parameter of being inputted by user, || represent to ask vectorial mould, R represents step 3b) the row generated data vector that obtains, A represents step 4a) the azimuth dimension spatial spectrum vector that obtains is to the projection matrix of row generated data vector represent the sign of operation of minimizing;

5b) by solving following formula, obtain pitching dimension space spectrum vector:

$\underset{\mathrm{\&beta;}}{\min }\{{\left|\mathrm{\&beta;}\right|}_p+\mathrm{\&zeta;}|C-\mathrm{B\&beta;}\left|\right\}$

Wherein, β represents pitching dimension space spectrum vector, || _prepresent to ask vectorial p norm, ζ represents the regularization parameter of being inputted by user, || represent to ask vectorial mould, C represents step 3c) the row generated data vector that obtains, B represents step 4b) the pitching dimension space spectrum vector that obtains is to the projection matrix of row generated data vector represent the sign of operation of minimizing;

(6) peak value detects

6a) adopting threshold value comparison method, to step 5b) the pitching dimension space spectrum vector that obtains carries out peak value detection, and obtain pitching dimension space and compose vectorial peak value element index value;

6b) adopting threshold value comparison method, to step 5a) the azimuth dimension spatial spectrum vector that obtains carries out peak value detection, obtains azimuth dimension spatial spectrum vector peak value element index value;

(7) target localization

7a) by step 6a) the pitching dimension space that obtains composes vectorial peak value element index value substitution following formula, calculates the picked up signal source angle of pitch:

Wherein, for the signal source angle of pitch, asin represents arcsin function, and λ represents system carrier wavelength, and K represents that pitching dimension space composes vectorial dimension, and d represents system array element distance, and u represents that pitching dimension space composes the index value of vectorial peak value element;

7b) by step 6b) the azimuth dimension spatial spectrum vector peak value element index value and the step 7a that obtain) the signal source angle of pitch substitution following formula that obtains, calculates picked up signal source side parallactic angle:

Wherein, θ is signal source position angle, and asin represents arcsin function, and λ represents system carrier wavelength, and N represents the dimension of azimuth dimension spatial spectrum vector, and d represents system array element distance, and v represents the index value of azimuth dimension spatial spectrum vector peak value element, expression step 6a) the signal source angle of pitch obtaining.

2. the high-resolution sonar localization method of based target spatial sparsity according to claim 1, is characterized in that: the matched filtering formula step 2a) is as follows:

x _m(t)＝FT ^-1[e _m·s*]

Wherein, x _m(t) represent the data after m passage matched filtering, t represents time-domain sampling point, FT ^-1represent inverse Fourier transform, e _mthe frequency spectrum that represents m channel data, s represents known reference signal frequency spectrum, * represents to get conjugation, represents multiplication of vectors.

3. the high-resolution sonar localization method of based target spatial sparsity according to claim 1, is characterized in that: the threshold value comparison method described in step (6) is: to spatial spectrum vector, ask first order difference to obtain difference vector; Find the zero crossing of difference vector and record zero crossing index value; Half of spatial spectrum vector maximum element value is set to threshold value; The element that the element intermediate value at spatial spectrum vector zero crossing index value place is greater than threshold value is peak value element, and the index value that peak value element is corresponding is the peak value element index value of spatial spectrum vector.