CN112255625B - One-dimensional linear array direction finding method based on deep learning under two-dimensional angle dependent error - Google Patents

One-dimensional linear array direction finding method based on deep learning under two-dimensional angle dependent error Download PDF

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CN112255625B
CN112255625B CN202010903250.1A CN202010903250A CN112255625B CN 112255625 B CN112255625 B CN 112255625B CN 202010903250 A CN202010903250 A CN 202010903250A CN 112255625 B CN112255625 B CN 112255625B
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潘玉剑
姚敏
高晓欣
王�锋
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Hangzhou Dianzi University
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    • G—PHYSICS
    • 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
    • G01S13/00—Systems using the reflection or reradiation of radio waves, e.g. radar systems; Analogous systems using reflection or reradiation of waves whose nature or wavelength is irrelevant or unspecified
    • G01S13/02—Systems using reflection of radio waves, e.g. primary radar systems; Analogous systems
    • G01S13/50—Systems of measurement based on relative movement of target
    • G01S13/58—Velocity or trajectory determination systems; Sense-of-movement determination systems
    • G01S13/62—Sense-of-movement determination

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Abstract

The invention discloses a one-dimensional linear array direction finding method based on deep learning under two-dimensional angle dependent errors. The method solves the problem of two-dimensional angle dependent array error calibration through machine learning based on the characteristic that deep learning is good at approximating complex nonlinear functions. In order to be able to handle both azimuth dependence and pitch dependence of the array error, two-dimensional acquisition of data is performed, i.e. different azimuth array steering vectors are acquired at different pitch angles. The measurement data is expanded by adopting local array flow pattern interpolation so as to reduce the fitting risk of the deep learning model; deep learning is performed on the lowest signal-to-noise ratio data to adapt it to the noisy signal. The method is used for improving the one-dimensional linear array direction-finding precision of the two-dimensional angle-dependent array error, reducing the residual array error, correcting the dependence of the array error on the azimuth angle and the pitch angle, and enabling the direction-finding method to have good performance on different pitch angles.

Description

One-dimensional linear array direction finding method based on deep learning under two-dimensional angle dependent error
Technical Field
The invention belongs to the field of array direction finding, in particular to a direction finding method of a radar, communication, sonar, microphone and other receiver sensor arrays under array errors, and particularly relates to a one-dimensional linear array direction finding method based on deep learning and suitable for the existence of azimuth pitching two-dimensional angle dependent array errors.
Background
Sensor arrays are widely used in radar, communication, sonar, and microphone applications. A precondition for direction finding with sensor arrays is the response of the array, i.e. the array steering vector is precisely known. Under the ideal condition of no array error, the responses of the sensors are the same and independent, the positions of the sensors are precisely known, and the array steering vector has a precise analytical expression. But this is not the case in practical applications: the sensor array typically has three array errors, namely, an amplitude-phase error, a mutual coupling, and an array element position error. Additionally, array errors are further exacerbated by the limitations of the array boot material. Eventually resulting in array errors that vary with angle. For a one-dimensional linear array, although it cannot estimate the pitch angle of the target but only the azimuth angle, it cannot be guaranteed that all targets come from the same pitch angle. Therefore, the array error in the one-dimensional linear array direction measurement needs to consider not only the dependence on azimuth angle but also the dependence on pitch angle.
Aiming at the problem of angle-dependent errors, the common method is to perform off-line calibration, and the idea is that: firstly, array guiding vectors of the array at different angles are measured in a darkroom, and then array error calibration and direction finding are carried out according to the array guiding vectors. Currently, there are three main off-line calibration methods, namely an exhaustive search method, an amplitude-phase compensation method and a global array interpolation method (see literature: mats Viberg, maria Lanne, astrid Lundgren. Chapter 3:Calibration in Array Processing,Classical and Modern Direction-of-Arrival Estimation [ M ], academic Press,2009, pages 93-124). Of these three methods, only the exhaustive search and global array interpolation have the ability to correct angle dependent array errors. However, when there is a two-dimensional array error that depends on both azimuth and pitch, the global array interpolation method may introduce a large residual array error due to the limitation of the linear least squares fitting capability that is adopted. The exhaustive search rule needs to two-dimensionally traverse all the measured array guide vectors and needs interpolation processing for the off-grid point targets, so that the calculation complexity is high and the storage data volume is large.
Disclosure of Invention
Aiming at the defects of the prior art, the invention provides a one-dimensional linear array direction finding method under two-dimensional angle dependent errors based on deep learning, which aims to solve the problems of large residual array errors or high calculation complexity and large data storage quantity of a calibration method in the prior art.
The one-dimensional linear array direction finding method based on the two-dimensional angle dependence error of the deep learning comprises the following steps:
and step 1, placing the M-element one-dimensional linear array on a servo platform in a darkroom, fixing a radiation source in the far field of the array, and collecting two-dimensional calibration data. The system parameters are set so that the signal-to-noise ratio of the array output baseband signal is as close as possible to the maximum value within the dynamic range. Setting an azimuth grid point set omega= { theta in the azimuth view angle of the array 1 ,θ 2 ,...,θ L Setting a set of pitch grid points within a pitch field angleWherein L is azimuth grid point number, and I is pitch grid point number. Rotating the servo platform to enable the radar pitch angle to be +.>The azimuth angle scans the grid point set omega, and each grid point records M-dimensional array output baseband signals corresponding to each angle>Where θ e Ω, i=1, 2,...
Step 2, measuring the baseband signal of each darkroomZero-mean Gaussian white noise was added using the Monte Carlo method. For->Q Monte Carlo experiments are carried out, and the signal of the (I) is obtained by the (Q) th Monte Carlo experiment> For variance +.>Zero mean white gaussian noise +.>Representing the variance of the noise to be added by the ith pitch grid point data corresponding to the ith azimuth grid point. The noise power is such that +.>The minimum value of the target signal-to-noise ratio dynamic range is obtained in practical application. />The signal-to-noise ratio calculation formula is
Wherein the unit of SNR is dB,representation->Is a 2-norm of (c).
And 3, calculating an array guide vector. Directly calculating an array guiding vector for the azimuth grid points measured by each pitching angle darkroom, carrying out local array flow pattern interpolation processing for the azimuth grid points which are not measured by each pitching angle darkroom,and the angle corresponding to the azimuth grid point after the thinning is adopted.
(1) If it isNamely, the azimuth angle is in the grid point situation, and the steering vector calculation formula is as follows:
wherein the method comprises the steps ofIs->Is the first element of (a);
(2) if it isNamely, it is squareThe situation of bit angle from grid point, assume +.>The steering vector calculation formula is:
wherein the method comprises the steps ofFor ideal resolved steering vectors, T, which are related to array configuration and azimuth but not to pitch angle i A matrix is interpolated for the local array flow pattern.
T i Least squares estimation of (c)The calculation method of (1) is as follows: is provided with->To include theta l And theta l+1 An azimuth sub-grid set consisting of M' consecutive azimuth angle grid points, if θ l And theta l+1 Not at the edge of the grid set, Ω 'has M' -1 extraction methods. For each method, a least square method can be used to calculate an interpolation matrix, and the calculation formula is as follows:
wherein ( + Representing the pseudo-inverse of the matrix,and A + And (omega ') is an array flow pattern matrix formed by taking a guide vector obtained by calculation of measurement data and an ideal guide vector as columns on the azimuth sub grid point set omega'. Thus, P grids are thinned by interpolation between every two continuous darkroom measurement azimuth grid points, due to each thinned gridThe lattice can calculate (M '-1) guide vectors, and P (M' -1) guide vectors are interpolated between every two grids. Considering the Monte Carlo noise processing of step 2 and the edge effect of the grid set, the number of array steering vectors calculated by the darkroom measurement grid and the interpolation refinement grid is (L+ (L-M '+1) (M' -1) P) IQ.
And 4, extracting phase differences under corresponding complex modes for each array guide vector, and constructing the characteristics of the deep learning training set. The phase difference extraction method in the complex mode is as follows:
(1) calculating covariance matrix(·) H Representing performing conjugate transpose operation on vectors;
(2) extracting all elements below the diagonal but not including the diagonal in R to form an N-dimensional column vector β', n=m (M-1)/2;
(3) the phase difference calculation formula in the complex mode is beta=beta '/abs (beta'), wherein +/represents a dot division, namely, division by elements, and abs (·) represents an absolute value.
After the phase difference is real-changed, the phase difference is used as a deep learning training set characteristic gamma, gamma= [ Re ] T (β)；Im T (β)] T Wherein Re (·), im (·) and (·) T And represent the real, imaginary and transpose parts, respectively.
And 5, deep learning network training. Training a deep learning neural network f (gamma) in a regression mode by using a counter propagation algorithm by taking a real phase difference vector gamma as an input characteristic and an incoming wave azimuth angle theta as an output, wherein the deep learning neural network f (gamma) is a fully connected neural network, the number of neurons of an input layer is 2N, the number of hidden layer J is more than or equal to 3, the number of neurons of an output layer is 1, the cost function of the training neural network selects a mean square error for minimizing a network output value, and a regularization term based on a 2 norm of a network weight is set for preventing overfitting to obtain the trained deep learning network
Step 6, utilizing the trained deep learning networkAnd (5) direction finding is carried out. Assuming that the baseband signal for testing output by the array is z, taking z as a guiding vector, and calculating according to the step 4 to obtain a phase difference vector beta in a complex mode z To be quantized into gamma z After-input trained deep learning network>The incoming wave azimuth angle theta corresponding to the test signal z can be obtained z 。
The invention has the following beneficial effects:
1. by utilizing the advantage of deep learning good at approximating a complex nonlinear function, machine learning is introduced to calibrate angle-dependent complex array errors, the problem that the angle-dependent array errors are difficult to calibrate in traditional array calibration is solved, the corrected residual array errors are smaller, and the direction finding precision is higher;
2. the data of different pitch angles are adopted in the training process of the deep learning model, and meanwhile, the dependence of the array error on the azimuth angle and the pitch angle is corrected, so that the direction finding method still has excellent performance when applied to different pitch angles.
3. The neural network has only one output, so that correction can be performed only for a single target. However, the multiple targets may be separated into multiple single targets in the frequency domain, the time domain, the doppler domain, or the like in advance, so the present invention is universal in most cases.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a graph showing the direction finding error at zero pitch angle compared with other methods under noiseless conditions;
FIG. 3 is a graph showing the root mean square error of azimuth direction finding at different pitch angles in the noise free condition compared with other methods of the present invention;
FIG. 4 is a graph showing the root mean square error of the azimuth direction finding under different signal to noise ratios compared with other methods.
Detailed Description
The invention is further explained below with reference to the drawings;
as shown in fig. 1, the present invention includes the steps of:
step 1, an M-element one-dimensional linear array is placed on a servo platform in a darkroom, a radiation source is fixed in the far field of the array, two-dimensional calibration data are collected, the influence of multipath interference can be reduced by collecting signals in the darkroom, and the obtained baseband signal is ensured to be in response to a single target. The system parameters are set to enable the signal-to-noise ratio of the output baseband signals of the array to be as close to the maximum value in the dynamic range as possible, the collected baseband signals can be ensured to be close to a noiseless state, and the Monte Carlo method plus noise in the step 2 can obtain the signal-to-noise ratio as accurate as possible. Setting an azimuth grid point set omega= { theta in the azimuth view angle of the array 1 ,θ 2 ,...,θ L Setting a set of pitch grid points within a pitch field angleWherein L is azimuth grid point number, and I is pitch grid point number. Rotating the servo platform to enable the radar pitch angle to be +.>The azimuth angle scans the grid point set omega, and each grid point records M-dimensional array output baseband signals corresponding to each angle>Where θ e Ω, i=1, 2,... And (3) scanning and sampling the azimuth angles on different pitch angles, so that the deep learning training data in the step (5) has array guide vectors with different pitch angles and different azimuth angles, thereby achieving the purposes of correcting azimuth angle dependent array errors and correcting pitch angle dependent array errors.
(1) If the array is an ideal one-dimensional linear array, i.e. there is no array error, then the azimuth angle θ pitch angleAcquisition Signal->The method comprises the following steps:
where a (θ) is the ideal array steering vector, it can be seen that the steering vector of the ideal linear array is independent of pitch angle. The analytical expression of a (theta) is a (theta) =exp (j 2 pi mu sin (theta)/lambda), mu is an array element position vector, lambda is a signal wavelength,
(2) if there is an error in the array, a (θ) needs to be changed toUnknown, there is no more analytical expression. At this time, a->The expression of (2) is:
it can be seen that the steering vector of the linear array with array errors is related to pitch angle.
Step 2, measuring the baseband signal of each darkroomZero-mean Gaussian white noise was added using the Monte Carlo method. For->Q Monte Carlo experiments are carried out, and the signal of the (I) is obtained by the (Q) th Monte Carlo experiment> For variance +.>Zero mean white gaussian noise +.>Representing the variance of the noise to be added by the ith pitch grid point data corresponding to the ith azimuth grid point. The noise power is such that +.>The minimum value of the target signal-to-noise ratio dynamic range is obtained in practical application. />The signal-to-noise ratio calculation formula is
Wherein the unit of SNR is dB,representation->Is a 2-norm of (c).
The signal-to-noise ratio after noise addition is taken as the minimum value in the dynamic range of the target signal-to-noise ratio in practical application, so that the generalization performance of the deep learning neural network on noisy signals can be improved.
For baseband signals with errorsDifferent noises are added to respectively obtain a low signal-to-noise ratio signal and a high signal-to-noise ratio signal y Lo 、y Hi ：
Wherein the subscript (·) Lo 、(·) Hi Representing low and high signal-to-noise modes, respectively. Due to epsilon Lo And epsilon Hi All conform to the gaussian distribution if as much epsilon as possible is generated by the monte carlo method Lo The generated low signal-to-noise ratio signals cover the distribution of the high signal-to-noise ratio signals, so that the neural network trained in the low signal-to-noise ratio has good generalization performance on the high signal-to-noise ratio signals.
And 3, calculating an array guide vector. Directly calculating an array guiding vector for the azimuth grid points measured by each pitching angle darkroom, carrying out local array flow pattern interpolation processing for the azimuth grid points which are not measured by each pitching angle darkroom,and the angle corresponding to the azimuth grid point after the thinning is adopted.
(1) If it isNamely, the azimuth angle is in the grid point situation, and the steering vector calculation formula is as follows:
wherein the method comprises the steps ofIs->Is the first element of (a);
(2) if it isI.e. azimuth off-grid point situationLet->The steering vector calculation formula is:
wherein the method comprises the steps ofFor ideal resolved steering vectors, T, which are related to array configuration and azimuth but not to pitch angle i A matrix is interpolated for the local array flow pattern.
T i Least squares estimation of (c)The calculation method of (1) is as follows: is provided with->To include theta l And theta l+1 An azimuth sub-grid set consisting of M' consecutive azimuth angle grid points, if θ l And theta l+1 Not at the edge of the grid set, Ω 'has M' -1 extraction methods. For each method, a least square method can be used to calculate an interpolation matrix, and the calculation formula is as follows:
wherein ( + Representing the pseudo-inverse of the matrix,and A + And (omega ') is an array flow pattern matrix formed by taking a guide vector obtained by calculation of measurement data and an ideal guide vector as columns on the azimuth sub grid point set omega'. Therefore, P grids are thinned by interpolation between every two continuous darkroom measurement azimuth grid points, and (M' -1) can be calculated due to each thinned gridThe guide vectors are interpolated by P (M' -1) guide vectors between every two grids. Considering the Monte Carlo noise processing of step 2 and the edge effect of the grid set, the number of array steering vectors calculated by the darkroom measurement grid and the interpolation refinement grid is (L+ (L-M '+1) (M' -1) P) IQ.
And 4, extracting phase differences under corresponding complex modes for each array guide vector, and constructing the characteristics of the deep learning training set. The phase difference extraction method in the complex mode is as follows:
(1) calculating covariance matrix(·) H Representing performing conjugate transpose operation on vectors;
(2) extracting all elements below the diagonal but not including the diagonal in R to form an N-dimensional column vector β', n=m (M-1)/2;
(3) the phase difference phi of the array element pair is close to + -pi, and the phase jump phenomenon can occur. This problem can be avoided by converting the phase into a complex mode, in which:
β＝exp(jφ)＝exp(j2πdsin(θ)/λ)
where d is the baseline length between array element pairs. The complex phase difference is obtained and then the amplitude is normalized. Elements below the diagonal but not containing the diagonal in R correspond to phase differences and amplitude differences between different array elements, and the amplitude normalization is performed by the following formula:
β＝β′./abs(β′)
wherein/represents dot division, i.e., division by element, abs (·) represents taking absolute value.
Since deep learning can only receive real numbers as inputs, the phase difference is real-ized and then used as the feature gamma of the deep learning training set, gamma= [ Re ] T (β)；Im T (β)] T Wherein Re (·), im (·) and (·) T And represent the real, imaginary and transpose parts, respectively.
The reason for choosing the bit difference as the training set feature is:
1. according to the interferometer principle, the phase difference phi of the array element pair and the incoming wave angle theta have the following relation:
φ＝2πdsin(θ)/λ
from the formula, the wave angle is related to the phase difference only and not to the amplitude information.
2. The phase difference calculated based on the array steering vector and the baseband signal output based on the array is the same, so that the method is more flexible in practical application.
And 5, deep learning network training. The real phase difference vector gamma is taken as an input feature, which is a matrix of size 2Nx (L+ (L-M '+1) (M' -1) P) IQ, wherein the rows of the matrix represent feature dimensions and the columns of the matrix represent data sample dimensions. Training a deep learning neural network f (gamma) in a regression mode by using a back propagation algorithm, wherein the deep learning neural network f (gamma) is a fully connected neural network, the number of neurons of an input layer is 2N, the number of hidden layer J is more than or equal to 3, the number of neurons of an output layer is 1, the cost function of the training neural network selects a mean square error for minimizing a network output value, and a regularization term based on 2 norms of network weights is set for preventing overfitting to obtain a trained deep learning network
Step 6, utilizing the trained deep learning networkAnd (5) direction finding is carried out. Assuming that the baseband signal for testing output by the array is z, taking z as a guiding vector, and calculating according to the step 4 to obtain a phase difference vector beta in a complex mode z To be quantized into gamma z After-input trained deep learning network>The incoming wave azimuth angle theta corresponding to the test signal z can be obtained z 。
Example 1
And step 1, placing an 8-array element linear array with an antenna housing in a microwave darkroom, placing a radiation source at the far-field position of the array, and setting the test signal-to-noise ratio to be 60dB. Scanning is performed on the uniform azimuth angle grids within the range of-40 DEG, 40 DEG at intervals of 0.5 DEG on the depression angles of-3 DEG, -2 DEG, …,3 DEG respectively, and the array output baseband signals are acquired. The measurement data of the integral azimuth grids corresponding to all pitch angles, namely [ -40 °, -39 °, …,40 ° ], are used for constructing training data, and the decimal azimuth grids corresponding to all pitch angles, namely [ -39.5 °, -38.5 °, …,39.5 ° ], are used for testing calibration performance.
And 2, adding zero-mean Gaussian white noise by using a Monte Carlo method to generate a noise sample. And carrying out 100 Monte Carlo experiments on the acquired array output baseband signals, and setting the signal-to-noise ratio of the noise samples to be 15dB.
And 3, in the process of constructing training data by refining azimuth grids through local array flow pattern interpolation processing, taking L=81 and P=9, namely uniformly interpolating 9 refined grids among integer grids, wherein M=8 and M' =4. The number of final training samples was (l+ (L-M '+1) (M' -1) P) iq= 1530900.
And 4, extracting phase differences under corresponding complex modes for each array guide vector, extracting N=M (M-1)/2=28 phase differences in total, and obtaining 56 characteristic gamma after real realization.
And 5, training a deep learning network, namely setting the hidden layers of the neural network as 5 layers, setting each hidden layer neuron as 32, selecting ReLU as an activation function, selecting Adam as an optimizer, setting the maximum epoch number as 1000, setting the batch size as 14336, setting the initial learning rate as 0.001,2 norm regularization term coefficient as 0.0001.
And 6, utilizing the trained deep learning network to conduct direction finding.
The simulation results of the method based on the invention and the simulation results of the deep learning method, the pitching error compensation method and the global array interpolation method which only use pitching zero-degree training data are compared. The comparison index under the noise-free condition is the direction finding error and the root mean square error of the direction finding result on the decimal azimuth angle grid data, and the comparison index under the noise condition is the root mean square error of the direction finding result on the decimal azimuth angle grid data on a plurality of pitch angles. Wherein the amplitude phase compensation method and the global array interpolation method all adopt a beam forming method for angle measurement.
(1) The comparison results under the condition of no noise are shown in fig. 2 and 3, the test data in fig. 2 are different azimuth angle data on pitching zero degrees, and the test data in fig. 3 are different azimuth angle data on [ -3 degrees, -2 degrees, …,3 degrees ] pitch angles. If the deep learning model is trained with only array steering vectors at zero degrees of pitch, it will have the best performance at zero degrees of pitch, but the worst performance at other large pitch angles. The training data of the method adopts the array guide vectors corresponding to a plurality of pitch angles, so that the method has good performance on all pitch angles, and can well correct two-dimensional angle dependent errors. The performance of the global array interpolation method is slightly better than that of the amplitude-phase compensation method, but compared with the method, the performance of the method is better, and the direction finding error is smaller than 0.1 degrees.
(2) The results of the comparison in the noisy situation are shown in fig. 4, where the angular results were all averaged over 500 experiments. In the figure, the horizontal axis represents the signal-to-noise ratio from 15dB to 50dB, and the vertical axis represents the root mean square error of the angle measurement. The root mean square error of the global array interpolation method is slightly better than that of the amplitude-phase compensation method. In addition, the direction finding accuracy of the deep learning model trained with multiple pitch angle data is superior to the deep learning model trained with only pitch zero degrees at all signal to noise ratios, and to the other two signal processing based methods.
The foregoing description is only exemplary of the invention and is not intended to limit the invention to the particular embodiments disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the invention.

Claims (2)

1. The one-dimensional linear array direction finding method based on the two-dimensional angle dependence error of the deep learning is characterized by comprising the following steps of: the method specifically comprises the following steps:
step 1, an M-element one-dimensional linear array is placed on a servo platform in a darkroom, a radiation source is fixed in the far field of the array, and two-dimensional calibration data are acquired; setting system parameters to enable the signal-to-noise ratio of the array output baseband signal to be the maximum value in the dynamic range; in an array ofSetting azimuth grid point set omega= { theta in azimuth view angle 1 ,θ 2 ,...,θ L Setting a set of pitch grid points within a pitch field angleWherein L is azimuth grid point number, and I is pitch grid point number; rotating the servo platform to enable the radar pitch angle to be +.>The azimuth angle scans the grid point set omega, and each grid point records M-dimensional array output baseband signals corresponding to each angle>Where θ e Ω, i=1, 2,;
step 2, measuring the baseband signal of each darkroomAdding zero-mean Gaussian white noise by using a Monte Carlo method; for a pair ofQ Monte Carlo experiments are carried out, and the signal of the (I) is obtained by the (Q) th Monte Carlo experiment> For variance +.>Zero mean white gaussian noise +.>Representing noise to be added to the ith pitch grid point data corresponding to the ith azimuth grid pointIs a variance of (2); the noise power is such that +.>The minimum value of the target signal-to-noise ratio dynamic range is obtained in the practical application; />The signal-to-noise ratio calculation formula is
Wherein the unit of SNR is dB,representation->2 norms of (2);
step 3, calculating an array guide vector; directly calculating an array guiding vector for the azimuth grid points measured by each pitching angle darkroom, carrying out local array flow pattern interpolation processing for the azimuth grid points which are not measured by each pitching angle darkroom,the angle corresponding to the azimuth grid point after the thinning is adopted;
(1) if it isNamely, the azimuth angle is in the grid point situation, and the steering vector calculation formula is as follows:
wherein the method comprises the steps ofIs->Is the first element of (a);
(2) if it isI.e. azimuth off grid point case, assume +.>The steering vector calculation formula is:
wherein the method comprises the steps ofFor ideal resolved steering vectors, T, which are related to array configuration and azimuth but not to pitch angle i Interpolation matrix for local array flow pattern;
T i least squares estimation of (c)The calculation method of (1) is as follows: is provided with->To include theta l And theta l+1 An azimuth sub-grid set consisting of M' consecutive azimuth angle grid points, if θ l And theta l+1 M '-1 extraction methods are not arranged at the edge of the grid set, and omega' is provided; for each extraction method, a least square method is used for calculating an interpolation matrix, and the calculation formula is as follows:
wherein ( + Representing the pseudo-inverse of the matrix,and A + (Ω ') is an array flow pattern matrix composed of guide vectors and ideal guide vectors, which are respectively calculated by measurement data, on the azimuth sub-grid point set Ω'; therefore, P grids are thinned through interpolation between every two continuous darkroom measurement azimuth grid points, and P (M '-1) guide vectors are interpolated between every two grids because each thinned grid calculates (M' -1) guide vectors; considering the Monte Carlo noise processing and the edge effect of the grid set in the step 2, the number of the array guide vectors calculated by the darkroom measurement grid and the interpolation refinement grid is (L+ (L-M '+1) (M' -1) P) IQ;
step 4, extracting phase differences under corresponding complex modes for each array guide vector, and constructing features of a deep learning training set; the phase difference extraction method in the complex mode is as follows:
(1) calculating covariance matrix(·) H Representing performing conjugate transpose operation on vectors;
(2) extracting all elements below the diagonal but not including the diagonal in R to form an N-dimensional column vector β', n=m (M-1)/2;
(3) the phase difference calculation formula under the complex mode is beta=beta '/abs (beta'), wherein, the/represents point division, namely, the division is performed according to elements, and abs(s) represents absolute value;
after the phase difference is real-changed, the phase difference is used as a deep learning training set characteristic gamma, gamma= [ Re ] T (β)；Im T (β)] T Wherein Re (·), im (·) and (·) T And respectively representing the real part, the imaginary part and the transposition;
step 5, training a deep learning network; training regression by using the deep learning training set feature gamma as input feature and the incoming wave azimuth angle theta as output and using the counter propagation algorithmThe deep learning neural network f (gamma) in the mode is a fully-connected neural network, the number of neurons of an input layer is 2N, the number of hidden layer layers J is more than or equal to 3, the number of neurons of an output layer is 1, the cost function of the training neural network selects the mean square error of the minimum network output value, and a regularization term based on 2 norms of network weights is set for preventing overfitting, so that the trained deep learning network is obtained
Step 6, utilizing the trained deep learning networkDirection finding is carried out; assuming that the baseband signal for testing output by the array is z, taking z as a guiding vector, and calculating according to the step 4 to obtain a phase difference vector beta in a complex mode z To be quantized into gamma z After-input trained deep learning network>Obtaining the incoming wave azimuth angle theta corresponding to the baseband signal z for test z 。
2. The two-dimensional angle-dependent error one-dimensional linear array direction finding method based on deep learning as claimed in claim 1, wherein the method comprises the following steps: in step 5, the number of hidden layers of the deep learning network is 5, and the coefficient of the 2-norm regularization term is 0.0001.
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Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104535971A (en) * 2014-12-08 2015-04-22 广西大学 Clutter suppression method and device based on space-time interpolation
CN105044688A (en) * 2015-08-24 2015-11-11 西安电子科技大学 Radar robust space-time adaption processing method based on iterative subspace tracking algorithm
CN109212526A (en) * 2018-10-17 2019-01-15 哈尔滨工业大学 Distributive array target angle measurement method for high-frequency ground wave radar
CN111487478A (en) * 2020-03-27 2020-08-04 杭州电子科技大学 Angle-dependent complex array error calibration method based on deep neural network

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
FR2917180B1 (en) * 2007-06-08 2010-05-14 Thales Sa METHOD FOR ESTIMATING COMBINED SOURCE ARRIVAL ANGLES BY A SPATIAL LAUNDING TECHNIQUE ON AN ANY SENSOR ARRAY

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104535971A (en) * 2014-12-08 2015-04-22 广西大学 Clutter suppression method and device based on space-time interpolation
CN105044688A (en) * 2015-08-24 2015-11-11 西安电子科技大学 Radar robust space-time adaption processing method based on iterative subspace tracking algorithm
CN109212526A (en) * 2018-10-17 2019-01-15 哈尔滨工业大学 Distributive array target angle measurement method for high-frequency ground wave radar
CN111487478A (en) * 2020-03-27 2020-08-04 杭州电子科技大学 Angle-dependent complex array error calibration method based on deep neural network

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
基于空域稀疏性的方位依赖阵列误差校正算法;李存勖 等;《电子与信息学报》;第2219-2224页 *

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