CN111323750A - Direct positioning method based on acoustic vector array network - Google Patents

Direct positioning method based on acoustic vector array network Download PDF

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CN111323750A
CN111323750A CN202010197246.8A CN202010197246A CN111323750A CN 111323750 A CN111323750 A CN 111323750A CN 202010197246 A CN202010197246 A CN 202010197246A CN 111323750 A CN111323750 A CN 111323750A
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时胜国
张旭
杨德森
方尔正
莫世奇
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Harbin Engineering University
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    • G01—MEASURING; TESTING
    • G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
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Abstract

The invention provides a direct positioning method based on an acoustic vector array network, and belongs to the field of passive target positioning. Firstly, carrying out segmented frequency domain transformation on sound pressure and vibration speed data received by each array node; then scanning point by point in the area to be measured, and calculating the guiding direction and time delay at the scanning point; weighting and summing the sound pressure and vibration velocity data to obtain weighted data matrixes of all the arrays; calculating equivalent array manifold by using a frequency domain positioning model; then, calculating the spatial spectrum on each frequency by using a spatial spectrum estimation algorithm, and accumulating to obtain the total spatial spectrum of all frequencies; and calculating the spatial spectrum of each point in the region to be measured according to the proper scanning step length, and searching the peak value of the spatial spectrum value to obtain the position of the target to be measured. The invention introduces the acoustic vector array into the multi-array target direct positioning method, obtains higher positioning precision and spatial resolution than a scalar array by utilizing the sound pressure and vibration velocity combined processing technology, and has better adaptability to target positioning under the condition of low signal-to-noise ratio.

Description

Direct positioning method based on acoustic vector array network
Technical Field
The invention relates to a direct positioning method based on an acoustic vector array network, belonging to the field of passive target positioning.
Background
The target passive positioning method utilizes the signal radiated or reflected by the target to position and track, has strong concealment and long action distance, and has wide application in the fields of regional warning, environmental monitoring and the like. The multi-station passive positioning system takes the sensor arrays as nodes to form a distributed array network, utilizes information provided by the arrays to carry out cooperative processing, obtains target position parameters, and has higher positioning precision compared with single-point positioning.
The passive positioning method of an object using an array network is generally classified into a two-step positioning method and a direct positioning method. The two-step positioning method firstly calculates intermediate positioning parameters such as the target direction of arrival (AOA), the time delay Difference (DTOA), the Doppler frequency shift or the signal intensity, and then calculates the target position by using the intermediate parameters. The method only needs to transmit the intermediate positioning parameters to the resolving center, and has low requirements on communication bandwidth and calculated amount. However, since the estimation of the parameters is completed by each node in isolation, part of information is inevitably lost, the precision is reduced, and meanwhile, the problem of multi-target parameter matching is also brought. Compared with the two-step positioning method, the direct positioning method (DPD) directly utilizes the original data output by the bottom layer array, estimates the position information through single-step calculation, avoids the defects of the two-step positioning method, and has better performance than the two-step positioning method under the condition of low signal-to-noise ratio.
The direct positioning method (DPD) was first proposed by Weiss a J in 2004. According to the method, the processing idea of non-coherent subspace decomposition in broadband spectrum estimation is used for reference, time delay information is separated from a frequency domain through segmented Discrete Fourier Transform (DFT), an equivalent array manifold matrix is defined, and a target position is solved by using a traditional spatial spectrum estimation method. Such as multi-target maximum likelihood direct localization algorithms for known waveforms (Amar A, Weiss A J. direct localization (DPD) of multiple known and unwwn radio-frequency signals [ C ]. 200412 th European Signal Processing Conference, Vienna,2004:1115-1118.), and MUSIC-based direct localization algorithms for unknown waveforms (Weiss AJ, Amar A. direct localization of multiple radio signals [ J ]. EURASIP Journal Advances in Signal Processing,2005, 37-49). In 2015, Tom Tirer and Anthony J.Weiss introduced the minimum variance distortion free response (MVDR) spatial spectrum estimation algorithm into the direct positioning method, (Tirer T, Weiss AJ.high resolution direct Position Determination of Radio Frequency Sources [ J ]. IEEE Signalprocessing Letters,2015,23(2): 192) which is more suitable for low signal-to-noise ratio environment and higher spatial resolution. However, most of the array nodes involved in the above direct localization algorithm are based on scalar sensors, and target localization is achieved only by using scalar information, and vector information in a physical field is not considered.
In fact, the physical quantities describing the sound field have a medium particle velocity vector in addition to the sound pressure. Due to the limitation of technical conditions, the traditional sonar only uses scalar sound pressure information and ignores vector vibration velocity information, and the sound vector sensor can synchronously pick up the sound pressure scalar and the vibration velocity vector of a sound field in a space concurrent mode, so that the description of the sound field is more accurate and comprehensive. Compared with an acoustic scalar array, the acoustic vector array has the advantages of high array gain, low detection domain, strong anti-noise interference capability and the like. In 1994, Arye Nehorai first proposed an acoustic vector sensor Signal Processing framework (Nehorai A, Paldi E. acoustic vector-sensor arraying [ J ]. IEEE Transactions on Signal Processing,1994,42(9):2481 and 2491.), and sound pressure and vibration velocity information were processed as independent array elements. The national scholars huijingi et al have set forth the concept and method of sound pressure and vibration velocity combined processing (huijingi. vector acoustic signal processing foundation [ M ]. national defense industry press, 2009.) and theoretically demonstrate the anti-noise advantage of the sound pressure and vibration velocity combined processing technology.
Disclosure of Invention
The invention provides a direct positioning method based on an acoustic vector array network. The invention combines the sound pressure and vibration velocity combined processing technology with the idea of a direct positioning method, and outputs a high-resolution space spectrogram of a target detection area by using a space spectrum estimation method.
The purpose of the invention is realized as follows: the node of the acoustic vector array network is a multi-array element acoustic vector sensor array, each array element can output the same-point sound pressure scalar and the same-point vibration velocity vector information, and the method comprises the following steps:
step 1, establishing a narrow-band signal array positioning model of the array network to obtain the ith arraySound pressure output P of nodel(t) sum velocity vector output Vxl(t),Vyl(t)；
Step 2, dividing the sound pressure and vibration velocity data into J sections, and respectively carrying out frequency domain transformation on each section of data to obtain Fourier transformation P of the jth section of observation signal of the ith array in the kth frequency componentl(k,j),Vxl(k,j),Vyl(k,j)；
Step 3, scanning point by point in the area to be measured, and calculating the guiding azimuth psi from the point to the I-th array reference point at the scanning point dl(d) And time delay taul(d)；
Step 4, using the guide orientation psil(d) Sound pressure P to the same segmentl(k, j) and the vibration velocity Vxl(k,j),Vyl(k, j) combined treatment to give Yl(k, j), summing Y for all L arraysl(k, j) obtaining a total data matrix Y (k, j);
step 5, defining and calculating equivalent array manifold by using the array positioning frequency domain signal model
Figure BDA0002418068600000021
Summing all L arrays
Figure BDA0002418068600000022
Obtaining the total equivalent array manifold matrix
Figure BDA0002418068600000023
Step 6, extracting the fourier transform Y (k, J) of the J-segment data under the k-th frequency component, wherein J is 1, … and J to form Y (k), and calculating the frequency f by using a spatial spectrum estimation algorithmkUpper spatial spectral values Q (k, d);
step 7, obtaining a total space spectrum Q (d) of accumulated K frequencies;
and 8, setting a proper scanning step length, repeating the steps 3 to 7, traversing the whole region to be detected, outputting a spatial spectrogram, and searching a spectral value peak value to obtain the position of the target to be detected.
The invention also includes such structural features:
1. step 4 utilizing psil(d) Sound pressure P to the same segmentl(k, j) and the vibration velocity Vxl(k,j),Vyl(k, j) summing to obtain the vibration velocity of the j-th section sound pressure and the Fourier transform Y of the k-th frequency componentl(k,j)：
Yl(k,j)＝Pl(k,j)+Vxl(k,j)cosψl(d)+Vyl(k,j)sinψl(d)
Summing Y of all L arraysl(k, j) obtaining a total array data matrix Y (k, j) ═ Y1(k,j)T,…,YL(k,j)T]T。
2. The step 5 specifically comprises the following steps:
step 5-1, outputting Y by the array l in the positioning networklThe frequency domain model of (k, j) is:
Figure BDA0002418068600000031
in the formula, S (k, j), Nl(k, j) are frequency domain representations of the source and noise, respectively;
step 5-2, defining and calculating the equivalent array manifold according to the following formula
Figure BDA0002418068600000032
Figure BDA0002418068600000033
Summing all L arrays
Figure BDA0002418068600000034
Is a total equivalent array manifold matrix
Figure BDA0002418068600000035
Step 5-3, order
Figure BDA0002418068600000036
Due to blFor unknown complex scalars, it is usual to set 1, b[b1,…,bL]TThen the array positioning frequency domain signal model can be expressed as:
Figure BDA0002418068600000037
the frequency domain signal model is in accordance with the conventional array signal model.
3. Step 6 relates to a spatial spectrum estimation method including but not limited to CBF, MVDR, MUSIC, etc., taking a MUSIC spatial spectrum estimation algorithm as an example, the method specifically includes the following steps:
step 6-1, extracting fourier transform Y (k, J), J being 1, …, J, constituting Y (k), Y (k) ═ Y (k,1), …, Y (k, J) of J-segment data in k-th frequency component]By the use of Rk＝Y(k)·YH(k) J calculating frequency fkUpper covariance matrix, RkLM × LM dimension covariance matrix;
step 6-2, to covariance matrix RkPerforming characteristic decomposition to obtain a signal subspace U consisting of characteristic vectors corresponding to larger D characteristic valuesS(k) And a noise subspace U consisting of eigenvectors corresponding to other smaller eigenvaluesN(k) Wherein D is the target number;
step 6-3, at frequency fkThe MUSIC spatial spectrum above is:
Figure BDA0002418068600000041
in the formula (I), the compound is shown in the specification,
Figure BDA0002418068600000042
ILis a L × L dimensional unit matrix, JMIs an M × 1 dimensional full 1 array,
Figure BDA0002418068600000043
representing the Kronecker product, the above formula is equivalent to:
Figure BDA0002418068600000044
order to
Figure BDA0002418068600000045
Since b is 1, G (k, d) is a quadratic form under the constraint, and its eigenvalue is the maximum value of G (k, d) eigenvalue, Q (k, d) is:
Q(k,d)＝max(λmax(G(k,d)))
4. step 7 sums all frequency-space spectra Q (k, d), the total space spectrum Q (d) being:
Figure BDA0002418068600000046
compared with the prior art, the invention has the beneficial effects that: the invention introduces an acoustic vector sensor into a target direct positioning method of a multi-array node, and provides a direct positioning method based on an acoustic vector array network. The method combines the superior performance of the acoustic vector array with the advantage of a direct positioning method, and obtains a high-resolution space spectrogram of a target detection area by using a space spectrum estimation method. The method has higher positioning precision and spatial resolution, and has better adaptability to target positioning under the condition of low signal-to-noise ratio.
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FIG. 1 is a schematic diagram of the distribution of a region to be measured;
FIGS. 2a-b are spatial spectrum pseudocolor maps for single source direct localization at a signal-to-noise ratio of-15 dB, and (a) scalar MUSIC-DPD algorithm; (b) vector MUSIC-DPD algorithm;
FIGS. 3a-b are three-dimensional plots of spatial spectra for direct localization by a single source at a signal-to-noise ratio of-15 dB, and (a) scalar MUSIC-DPD algorithm; (b) vector MUSIC-DPD algorithm;
FIGS. 4a-b are spatial spectrum pseudocolor maps for single source direct localization at-20 dB, and (a) scalar MUSIC-DPD algorithm; (b) vector MUSIC-DPD algorithm;
FIG. 5 is a three-dimensional plot of the spatial spectrum for direct localization by a single source at a signal-to-noise ratio of-20 dB, and (a) scalar MUSIC-DPD algorithm; (b) vector MUSIC-DPD algorithm;
FIGS. 6a-b are spatial spectrum pseudocolor maps for direct localization of dual sources at a signal-to-noise ratio of 0dB, and (a) scalar MUSIC-DPD algorithm; (b) vector MUSIC-DPD algorithm;
FIGS. 7a-b are spatial spectrum three-dimensional plots for 0dB, dual source direct localization, and (a) scalar MUSIC-DPD algorithm; (b) vector MUSIC-DPD algorithm
FIG. 8 is a graph showing the variation of the positioning error under different SNR conditions.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
The invention combines the sound pressure and vibration velocity combined processing technology with the idea of a direct positioning method, and outputs a high-resolution space spectrogram of a target detection area by using a space spectrum estimation method. The method has higher positioning precision and spatial resolution, and has better adaptability to target positioning under the condition of low signal-to-noise ratio.
The technical scheme adopted by the invention for solving the technical problem comprises the following steps: the node of the acoustic vector array network is a multi-array element acoustic vector sensor array, each array element can output the same-point sound pressure scalar and vibration velocity vector information,
step 1, establishing a narrow-band signal array positioning model of the array network, and obtaining sound pressure output P of the ith array nodel(t) sum velocity vector output Vxl(t),Vyl(t)；
Step 2, dividing the sound pressure and vibration velocity data into J sections, and respectively carrying out frequency domain transformation on each section of data to obtain Fourier transformation P of the jth section of observation signal of the ith array in the kth frequency componentl(k,j),Vxl(k,j),Vyl(k,j)；
Step 3, scanning point by point in the area to be measured, and calculating the guiding azimuth psi from the point to the I-th array reference point at the scanning point dl(d) And time delay taul(d)；
Step 4, using the guide orientation psil(d) Sound pressure P to the same segmentl(k, j) and the vibration velocity Vxl(k,j),Vyl(k, j) combined treatment to give Yl(k, j), summing Y for all L arraysl(k, j) obtaining a total data matrix Y (k, j);
step 5, defining and calculating equivalent array manifold by using the array positioning frequency domain signal model
Figure BDA0002418068600000051
Summing all L arrays
Figure BDA0002418068600000052
Obtaining the total equivalent array manifold matrix
Figure BDA0002418068600000053
Step 6, extracting the fourier transform Y (k, J) of the J-segment data under the k-th frequency component, wherein J is 1, … and J to form Y (k), and calculating the frequency f by using a spatial spectrum estimation algorithmkUpper spatial spectral values Q (k, d);
step 7, obtaining a total space spectrum Q (d) of accumulated K frequencies;
and 8, setting a proper scanning step length, repeating the steps 3 to 7, traversing the whole region to be detected, outputting a spatial spectrogram, and searching a spectral value peak value to obtain the position of the target to be detected.
Step 4 of the invention utilizes psil(d) Sound pressure P to the same segmentl(k, j) and the vibration velocity Vxl(k,j),Vyl(k, j) summing to obtain the vibration velocity of the j-th section sound pressure and the Fourier transform Y of the k-th frequency componentl(k,j)：
Yl(k,j)＝Pl(k,j)+Vxl(k,j)cosψl(d)+Vyl(k,j)sinψl(d)
Summing Y of all L arraysl(k, j) obtaining a total array data matrix Y (k, j) ═ Y1(k,j)T,…,YL(k,j)T]T。
The step 5 of the invention specifically comprises the following steps:
step 5-1, outputting Y by the array l in the positioning networklThe frequency domain model of (k, j) is:
Figure BDA0002418068600000061
in the formula, S (k, j), Nl(k, j) are frequency domain representations of the source and noise, respectively;
step 5-2, defining and calculating the equivalent array manifold according to the following formula
Figure BDA0002418068600000062
Figure BDA0002418068600000063
Summing all L arrays
Figure BDA0002418068600000064
Is a total equivalent array manifold matrix
Figure BDA0002418068600000065
Step 5-3, order
Figure BDA0002418068600000066
Due to blFor unknown complex scalars, it is usual to set 1, b | | | b | |, b1,…,bL]TThen the array positioning frequency domain signal model can be expressed as:
Figure BDA0002418068600000067
the frequency domain signal model is in accordance with the conventional array signal model.
The step 6 of the invention relates to a spatial spectrum estimation method which comprises, but is not limited to CBF, MVDR, MUSIC and the like, taking a MUSIC spatial spectrum estimation algorithm as an example, the method specifically comprises the following steps:
step 6-1, extracting fourier transform Y (k, J), J being 1, …, J, constituting Y (k), Y (k) ═ Y (k,1), …, Y (k, J) of J-segment data in k-th frequency component]By the use of Rk＝Y(k)·YH(k) J calculating frequency fkUpper covariance matrix, RkLM × LM dimension covariance matrix;
step 6-2, to covariance matrix RkPerforming characteristic decomposition to obtainSignal subspace U composed of eigenvectors corresponding to larger D eigenvaluesS(k) And a noise subspace U consisting of eigenvectors corresponding to other smaller eigenvaluesN(k) Wherein D is the target number;
step 6-3, calculating the frequency f by using the following formulakMUSIC spatial spectrum above:
Figure BDA0002418068600000071
in the formula (I), the compound is shown in the specification,
Figure BDA0002418068600000072
ILis a L × L dimensional unit matrix, JMIs an M × 1 dimensional full 1 array,
Figure BDA0002418068600000073
representing the Kronecker product, the above formula is equivalent to:
Figure BDA0002418068600000074
order to
Figure BDA0002418068600000075
Since | | | b | | | 1, G (k, d) is a quadratic form under the constraint, whose characteristic value is the maximum value of the characteristic value of G (k, d), Q (k, d) can be expressed as:
Q(k,d)＝max(λmax(G(k,d)))
step 7 of the present invention sums all frequency space spectra Q (k, d), and the total space spectrum Q (d) can be expressed as:
Figure BDA0002418068600000076
the invention is described in detail with reference to the accompanying drawings:
step 1, establishing a narrow-band signal array positioning model of an array network, considering that L available network nodes are distributed in a long distance in a region to be measured as shown in figure 1, wherein each node is an M-element vector sensor array and a node referenceThe point location is (x)l,yl) D narrow-band source targets exist, and the position coordinate of the target D is (x)d,yd) And the positions of the array elements are accurately known, and the attitude coordinate systems are consistent without amplitude and phase errors. The wave front of the signal incident from the information source to each array is a plane, the noise is white noise meeting Gaussian distribution, the noise among channels is uncorrelated, and the signal and the noise are uncorrelated.
Sound pressure data P outputted from the ith array nodel(t) and vector vibration velocity data Vxl(t),Vyl(t) can be represented by
Figure BDA0002418068600000077
In the formula, Pl(t),Vxl(t),Vyl(t) respectively representing sound pressure received by the ith array and vector vibration velocity signals in x and y directions, S (t) is an information source time domain snapshot matrix, Npl(t),Nxl(t),Nyl(t) receiving noise of sound pressure and x, y direction vibration velocity channels respectively; blTo be the attenuation coefficient, αl(d) For M × D dimensional array manifold, τl(d) The time delay from the source at the d position to the l array is obtained;
Figure BDA0002418068600000081
Figure BDA0002418068600000082
the d-th position source direction.
Step 2, sound pressure Pl(t) and the vibration velocity Vxl(t),Vyl(t) equally dividing the data into J sections, wherein the length of each section is TJ, and respectively performing Discrete Fourier Transform (DFT) on each section of data to obtain a frequency domain signal model P of the jth section of observation signal of the array l at the kth frequency componentl(k, j) and Vxl(k,j),Vyl(k,j)：
Figure BDA0002418068600000083
In the formula, S (k, j), Npl(k,j),Nxl(k,j),Nyl(k, j) are S (t), Npl(t),Nxl(t),Nyl(t) discrete fourier transform of the jth segment of data at the kth frequency;
step 3, scanning point by point in the area to be measured, and scanning the area in the coordinate (x)d,yd) At the scanning point d, the guiding orientation ψ from the scanning point d to the ith array reference point position is calculated by the following formulal(d) And time delay taul(d)：
Figure BDA0002418068600000084
In the formula (x)d,yd) For the scanning point position coordinates, (x)l,yl) Is the coordinate of the position of the datum point of the array l, and C is the sound velocity.
Step 4, using the guide orientation psil(d) For P of the same segmentl(k, j) and Vxl(k,j),Vyl(k, j) summing to obtain the vibration velocity of the j-th section sound pressure and the Fourier transform Y of the k-th frequency componentl(k,j)：
Yl(k,j)＝Pl(k,j)+Vxl(k,j)cosψl(d)+Vyl(k,j)sinψl(d) (4)
And Y isl(k, j) can also be expressed as:
Figure BDA0002418068600000085
in the formula, Nl(k, j) is Npl(k,j),Nxl(k,j),NylThe sum of (k, j);
summing Y of all L arraysl(k, j) obtaining a total array data matrix Y (k, j) ═ Y1(k,j)T,…,YL(k,j)T]T。
Step 5, defining and calculating equivalent array manifold
Figure BDA0002418068600000086
Summing all L arrays
Figure BDA0002418068600000087
Obtaining the total equivalent array manifold matrix
Figure BDA0002418068600000088
Order to
Figure BDA0002418068600000089
blFor unknown complex scalars, it is usual to set 1, b | | | b | |, b1,…,bL]TThen the array positioning frequency domain signal model can be expressed as:
Figure BDA0002418068600000091
the frequency domain signal model represented by equation (6) is consistent with the conventional array signal model form.
Step 6, extracting fourier transform Y (k, J), J being 1, …, J, of J-segment data in k-th frequency component, forming Y (k), Y (k) ([ Y (k,1), …, Y (k, J)]Using the formula Rk＝Y(k)·YH(k) J calculating frequency fkUpper covariance matrix, RkIs LM × LM dimension covariance matrix, and the pair covariance matrix RkPerforming characteristic decomposition to obtain a signal subspace U consisting of characteristic vectors corresponding to larger D characteristic valuesS(k) And a noise subspace U consisting of eigenvectors corresponding to other smaller eigenvaluesN(k)；
The frequency f is calculated using the following formulakMUSIC spatial spectrum above:
Figure BDA0002418068600000092
in the formula (I), the compound is shown in the specification,
Figure BDA0002418068600000093
ILis a L × L dimensional unit matrix, JMIs an M × 1 dimensional full 1 array,
Figure BDA0002418068600000094
representing the Kronecker product, the above formula is equivalent to:
Figure BDA0002418068600000095
order to
Figure BDA0002418068600000096
Since | | | b | | | 1, G (k, d) is a quadratic form under the constraint, whose characteristic value is the maximum value of the characteristic value of G (k, d), Q (k, d) can be expressed as:
Q(k,d)＝max(λmax(G(k,d))) (9)
step 7, the total spatial spectrum q (d) of all frequencies can be expressed as:
Figure BDA0002418068600000097
and 8, setting a proper scanning step length, repeating the steps 3 to 7, traversing the whole region to be detected, outputting a spatial spectrogram, and searching a spectral value peak value to obtain the position of the target to be detected.
The above description is directed to the embodiments of the present invention, and the following description is directed to the simulation examples.
Example one: single source processing effect analysis
The example parameters are set as follows, as shown in figure 1, 500m × 500m area to be measured, the narrowband information source to be measured is located at (200,300) m, the number of enabled array nodes is 2, the network nodes are respectively located at (0,0) m and (500,0) m positions, the network nodes are 8-element uniform linear arrays, the array element spacing of the arrays is half wavelength, the horizontal direction of the linear arrays is consistent with the set x direction, the environmental noise is stable narrowband Gaussian white noise, the sound speed is set to be 1500m/s, the system sampling rate is 2kHz, the fast beat number is 320, the received data are uniformly divided into 8 segments, each segment has 40 points, the whole area to be measured is traversed, and the scanning step size is 1 m.
And analyzing the positioning performance of the scalar MUSIC direct positioning algorithm and the vector MUSIC direct positioning algorithm on the single information source under the conditions of different signal-to-noise ratios. FIG. 2 and FIG. 3 show a spatial spectrum pseudo-color map and a three-dimensional map of single source positioning by two direct positioning algorithms when the signal-to-noise ratio is-15 dB, respectively; FIGS. 4 and 5 show the spatial spectrum pseudo-color map and three-dimensional map of single source positioning by two direct positioning algorithms when the signal-to-noise ratio is-20 dB, respectively;
comparing fig. 2-5, it can be seen that under the signal-to-noise ratio-15 dB condition, the scalar MUSIC direct positioning algorithm is affected by noise, and the background fluctuation is obvious, compared with the vector MUSIC direct positioning method, the space spectrum estimation background is smooth, the spectrum peak is more obvious and prominent, and the positioning accuracy is better; when the signal-to-noise ratio is-20 dB, the scalar MUSIC direct positioning algorithm basically fails, and the vector MUSIC direct positioning method using the vector array has stronger noise suppression capability, and can still effectively position the target with high precision under the condition of lower signal-to-noise ratio.
Example two: analysis of dual target resolution
The parameter setting is the same as in the first example, two narrowband source positions are set to be (250,245) m and (250,255) m, and the positioning performance and the resolution effect of the three direct positioning algorithms on two sources which are very close to each other are analyzed.
FIGS. 6 and 7 show the spatial spectrum pseudo-color and three-dimensional plots of the dual-signal-source resolution effect of the three direct positioning algorithms when the signal-to-noise ratio is 0dB, respectively;
through comparative analysis, when the two information sources are 10m apart, under the same condition, the space spectrum peaks corresponding to the two information sources are partially overlapped by the scalar MUSIC direct positioning algorithm, and the existence of the two targets is difficult to identify; the vector MUSIC direct positioning algorithm provided by the invention has higher spatial resolution, two adjacent targets are completely separated, and the positions of the two targets can be obviously distinguished in the pseudo-color image and the three-dimensional image.
Example three: performance analysis of different signal-to-noise ratio methods
The parameter setting is the same as that in the first example, the signal-to-noise ratio is increased from-30 dB to 20dB, 50 Monte Carlo experiments are carried out at each signal-to-noise ratio, and the positioning accuracy of the two direct positioning algorithms under different signal-to-noise ratios is analyzed and compared. Fig. 8 shows the positioning accuracy of two direct positioning algorithms as a function of the signal to noise ratio.
It can be clearly seen from the figure that when the signal-to-noise ratio is increased from-30 dB to 20dB, the positioning accuracy of the vector MUSIC direct positioning is better, the positioning error is lower, especially under the low signal-to-noise ratio condition below-10 dB, the positioning performance of the vector processing on the target is obviously improved compared with a scalar, that is, the vector MUSIC direct positioning algorithm has better adaptability to the target positioning under the low signal-to-noise ratio condition.
In summary, the invention discloses a direct positioning method based on an acoustic vector array network, and belongs to the field of target passive positioning. Firstly, carrying out segmented frequency domain transformation on sound pressure and vibration speed data received by each array node; then scanning point by point in the area to be measured, and calculating the guiding direction and time delay at the scanning point; weighting and summing the sound pressure and vibration velocity data to obtain weighted data matrixes of all the arrays; calculating equivalent array manifold by using a frequency domain positioning model; then, calculating the spatial spectrum on each frequency by using a spatial spectrum estimation algorithm, and accumulating to obtain the total spatial spectrum of all frequencies; and calculating the spatial spectrum of each point in the region to be measured according to the proper scanning step length, and searching the peak value of the spatial spectrum value to obtain the position of the target to be measured. The invention introduces the acoustic vector array into the multi-array target direct positioning method, obtains higher positioning precision and spatial resolution than a scalar array by utilizing the sound pressure and vibration velocity combined processing technology, and has better adaptability to target positioning under the condition of low signal-to-noise ratio.

Claims (5)

1. A direct positioning method based on an acoustic vector array network is characterized in that: the node of the acoustic vector array network is a multi-array element acoustic vector sensor array, each array element can output the same-point sound pressure scalar and the same-point vibration velocity vector information, and the method comprises the following steps:
step 1, establishing a narrow-band signal array positioning model of the array network, and obtaining sound pressure output P of the ith array nodel(t) sum velocity vector output Vxl(t),Vyl(t)；
Step 2, dividing the sound pressure and vibration velocity data into J sections, and respectively carrying out frequency domain transformation on each section of data to obtain Fourier transformation P of the jth section of observation signal of the ith array in the kth frequency componentl(k,j),Vxl(k,j),Vyl(k,j)；
Step 3, scanning point by point in the area to be measured, and calculating the guiding azimuth psi from the point to the I-th array reference point at the scanning point dl(d) And time delay taul(d)；
Step 4, using the guide orientation psil(d) Sound pressure P to the same segmentl(k, j) and the vibration velocity Vxl(k,j),Vyl(k, j) combined treatment to give Yl(k, j), summing Y for all L arraysl(k, j) obtaining a total data matrix Y (k, j);
step 5, defining and calculating equivalent array manifold by using the array positioning frequency domain signal model
Figure FDA0002418068590000011
Summing all L arrays
Figure FDA0002418068590000012
Obtaining the total equivalent array manifold matrix
Figure FDA0002418068590000013
Step 6, extracting the fourier transform Y (k, J) of the J-segment data under the k-th frequency component, wherein J is 1, … and J to form Y (k), and calculating the frequency f by using a spatial spectrum estimation algorithmkUpper spatial spectral values Q (k, d);
step 7, obtaining a total space spectrum Q (d) of accumulated K frequencies;
and 8, setting a proper scanning step length, repeating the steps 3 to 7, traversing the whole region to be detected, outputting a spatial spectrogram, and searching a spectral value peak value to obtain the position of the target to be detected.
2. The direct positioning method based on the acoustic vector array network as claimed in claim 1, wherein: step 4 utilizing psil(d) Sound pressure P to the same segmentl(k, j) and the vibration velocity Vxl(k,j),Vyl(k, j) summing to obtain the vibration velocity of the j-th section sound pressure and the Fourier transform Y of the k-th frequency componentl(k,j)：
Yl(k,j)＝Pl(k,j)+Vxl(k,j)cosψl(d)+Vyl(k,j)sinψl(d)
Summing Y of all L arraysl(k, j) obtaining a total array data matrix Y (k, j) ═ Y1(k,j)T,…,YL(k,j)T]T。
3. The direct positioning method based on the acoustic vector array network as claimed in claim 2, wherein: the step 5 specifically comprises the following steps:
step 5-1, outputting Y by the array l in the positioning networklThe frequency domain model of (k, j) is:
Figure FDA0002418068590000021
in the formula, S (k, j), Nl(k, j) are frequency domain representations of the source and noise, respectively;
step 5-2, defining and calculating the equivalent array manifold according to the following formula
Figure FDA0002418068590000022
Figure FDA0002418068590000023
Summing all L arrays
Figure FDA0002418068590000024
Is a total equivalent array manifold matrix
Figure FDA0002418068590000025
Step 5-3, order
Figure FDA0002418068590000026
Due to blFor unknown complex scalars, it is usual to set 1, b | | | b | |, b1,…,bL]TThen the array positioning frequency domain signal model can be expressed as:
Figure FDA0002418068590000027
the frequency domain signal model is in accordance with the conventional array signal model.
4. The direct positioning method based on the acoustic vector array network as claimed in claim 3, wherein: step 6 relates to a spatial spectrum estimation method including but not limited to CBF, MVDR, MUSIC, etc., taking a MUSIC spatial spectrum estimation algorithm as an example, the method specifically includes the following steps:
step 6-1, extracting fourier transform Y (k, J), J being 1, …, J, constituting Y (k), Y (k) ═ Y (k,1), …, Y (k, J) of J-segment data in k-th frequency component]By the use of Rk＝Y(k)·YH(k) Calculating frequency fkUpper covariance matrix, RkLM × LM dimension covariance matrix;
step 6-2, to covariance matrix RkPerforming characteristic decomposition to obtain a signal subspace U consisting of characteristic vectors corresponding to larger D characteristic valuesS(k) And a noise subspace U consisting of eigenvectors corresponding to other smaller eigenvaluesN(k) Wherein D is the target number;
step 6-3, at frequency fkThe MUSIC spatial spectrum above is:
Figure FDA0002418068590000028
in the formula (I), the compound is shown in the specification,
Figure FDA0002418068590000029
ILis a L × L dimensional unit matrix, JMIs an M × 1 dimensional full 1 array,
Figure FDA0002418068590000031
representing the Kronecker product, the above formula is equivalent to:
Figure FDA0002418068590000032
order to
Figure FDA0002418068590000033
Since | | | b | | | 1, G (k, d) is a quadratic form under the constraint, and its eigenvalue is the maximum value of the G (k, d) eigenvalue, Q (k, d) is:
Q(k,d)＝max(λmax(G(k,d))) 。
5. the direct positioning method based on the acoustic vector array network as claimed in claim 4, wherein: step 7 sums all frequency-space spectra Q (k, d), the total space spectrum Q (d) being:
Figure FDA0002418068590000034
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