CN110471026B - Phase-enhanced meter-wave radar target low elevation DOA estimation method - Google Patents
Phase-enhanced meter-wave radar target low elevation DOA estimation method Download PDFInfo
- Publication number
- CN110471026B CN110471026B CN201910662647.3A CN201910662647A CN110471026B CN 110471026 B CN110471026 B CN 110471026B CN 201910662647 A CN201910662647 A CN 201910662647A CN 110471026 B CN110471026 B CN 110471026B
- Authority
- CN
- China
- Prior art keywords
- data set
- input data
- phase
- phase characteristics
- doa estimation
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 108
- 238000012360 testing method Methods 0.000 claims abstract description 72
- 238000003062 neural network model Methods 0.000 claims abstract description 38
- 239000011159 matrix material Substances 0.000 claims abstract description 35
- 238000012545 processing Methods 0.000 claims abstract description 25
- 238000010606 normalization Methods 0.000 claims abstract description 11
- 230000005540 biological transmission Effects 0.000 claims abstract description 5
- 230000002708 enhancing effect Effects 0.000 claims abstract description 5
- 230000006870 function Effects 0.000 claims description 18
- 238000012549 training Methods 0.000 claims description 16
- 239000013598 vector Substances 0.000 claims description 15
- 230000003044 adaptive effect Effects 0.000 claims description 3
- 238000005259 measurement Methods 0.000 description 31
- 238000010586 diagram Methods 0.000 description 23
- 238000013528 artificial neural network Methods 0.000 description 9
- 230000001427 coherent effect Effects 0.000 description 5
- 238000005070 sampling Methods 0.000 description 5
- 238000013135 deep learning Methods 0.000 description 4
- 230000008569 process Effects 0.000 description 4
- 230000004913 activation Effects 0.000 description 3
- 238000013459 approach Methods 0.000 description 3
- 238000007796 conventional method Methods 0.000 description 3
- 238000013461 design Methods 0.000 description 3
- 238000009499 grossing Methods 0.000 description 3
- 238000013507 mapping Methods 0.000 description 3
- 238000004088 simulation Methods 0.000 description 3
- 238000012512 characterization method Methods 0.000 description 2
- 238000010276 construction Methods 0.000 description 2
- 238000012856 packing Methods 0.000 description 2
- 229920006395 saturated elastomer Polymers 0.000 description 2
- ORILYTVJVMAKLC-UHFFFAOYSA-N Adamantane Natural products C1C(C2)CC3CC1CC2C3 ORILYTVJVMAKLC-UHFFFAOYSA-N 0.000 description 1
- 238000007476 Maximum Likelihood Methods 0.000 description 1
- 238000004458 analytical method Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000011156 evaluation Methods 0.000 description 1
- 238000002474 experimental method Methods 0.000 description 1
- 239000000284 extract Substances 0.000 description 1
- 238000000605 extraction Methods 0.000 description 1
- 238000005457 optimization Methods 0.000 description 1
- 238000004806 packaging method and process Methods 0.000 description 1
- 238000005192 partition Methods 0.000 description 1
- 230000004044 response Effects 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 238000012706 support-vector machine Methods 0.000 description 1
Images
Classifications
-
- 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
- G01S3/00—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received
- G01S3/02—Direction-finders for determining the direction from which infrasonic, sonic, ultrasonic, or electromagnetic waves, or particle emission, not having a directional significance, are being received using radio waves
- G01S3/14—Systems for determining direction or deviation from predetermined direction
-
- 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
- G01S7/00—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00
- G01S7/02—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00
- G01S7/41—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section
- G01S7/417—Details of systems according to groups G01S13/00, G01S15/00, G01S17/00 of systems according to group G01S13/00 using analysis of echo signal for target characterisation; Target signature; Target cross-section involving the use of neural networks
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Radar, Positioning & Navigation (AREA)
- Remote Sensing (AREA)
- Artificial Intelligence (AREA)
- Evolutionary Computation (AREA)
- Computer Networks & Wireless Communication (AREA)
- Radar Systems Or Details Thereof (AREA)
Abstract
The invention discloses a phase-enhanced meter-wave radar target low elevation DOA estimation method, which comprises the steps of carrying out normalization processing on an input data set; inputting the normalized input data set into a neural network model to obtain a network output data set; constructing an objective function according to the network output data set and the label data set, carrying out reverse transmission on the objective function, and updating a network parameter set of the neural network model; enhancing the test data set according to the network parameter set to obtain a new data covariance matrix, and obtaining a new test data set according to the new data covariance matrix; and carrying out DOA estimation on the new test data set to obtain the elevation angle of the target. According to the DOA estimation method provided by the invention, the neural network model is constructed according to an actual scene, so that the problem of mismatch between an actual signal model and an ideal far-field plane wave model in the DOA estimation of physical drive is effectively solved, and the DOA estimation precision is higher.
Description
Technical Field
The invention belongs to the technical field of radars, and particularly relates to a phase-enhanced method for estimating a low elevation angle DOA of a meter-wave radar target.
Background
At present, the DOA estimation problem of a low-elevation target is an important difficult problem to be solved urgently in the field of meter-wave radars, because the wave beam of the meter-wave radar is wide, when the low-elevation target is detected, the wave beam 'hits the ground', multipath signals reflected by the ground and direct signals reflected by the target are received by the radar from the main lobe direction, and therefore the direct signal characteristics do not meet the simple far-field plane wave model characteristics any more, but are far-field plane wave models with amplitude and phase distortion, and the amplitude and phase distortion is caused by the multipath signals.
In response to this problem, a number of researchers in recent years have explored some effective physically-driven DOA estimation methods. In the early days, a far-field plane wave model with amplitude-phase distortion was modeled as a two-point coherent source model, i.e., a direct signal and a multipath signal were modeled as a pair of strongly coherent point source signals. In 1985, shann et al published a Spatial smoothing-based decorrelated multiple signal classification (SSMUSIC) method in volume 3, pages 806 to 811, 34 of the IEEE Transactions on Antennas and Propagation journal, which first achieves decorrelation processing of coherent sources by a subarray smoothing method, and finally performs super-resolution estimation. In 1998, Ziskind et al disclose a maximum likelihood estimation method based on alternative projection on pages 10 to 1560 of the journal of IEEE Transaction on Acoustics Speech, and Signal Processing under the condition that the noise distribution characteristics are known a priori, i.e., the noise distribution is consistent with Gaussian white noise, and realize DOA estimation of coherent sources through the optimization process of the alternative projection. In recent years, with the rapid development of deep learning techniques, deep learning techniques are being applied not only to the field of image processing and the like but also to the field of signal processing. In 1997, Zooghby et al proposed a DOA estimation method using radial-basis-function network (RBFN) in IEEE Transactions on Antennas and Propagation journal, volume 45, phase 11, pages 1611 to 1617, simplifying the DOA estimation problem into a complex mapping relationship of covariance matrix data and output, and learning the relationship between data covariance matrix data and DOA information by training RBFN to realize DOA estimation of coherent sources and incoherent sources. In 1 month 2019, Xiang et al published a DOA estimation method based on unsupervised learning in IET radio Sonar and Navigation journal volume 13, volume 1, and further invert DOA information by learning spatial domain data characteristics of received data. In 4 months of 2019, Wang et al propose a Support Vector Regression (SVR) -based DOA estimation method in volume 26, 642 pages to 646 of IEEE Signal Processing Letters journal, and learn a complex mapping relationship between real and imaginary data of received data and DOA information by using a Support Vector machine, thereby realizing DOA estimation.
Although the above several super-resolution DOA estimation methods based on physical driving are currently more DOA estimation methods, in an actual array environment, multipath signal distribution is more complex, for example, the number of multipath signals may be multiple, and the multipath signals received by the array may not satisfy a far-field plane wave model, so that DOA estimation accuracy is not high; the DOA estimation methods based on deep learning can be regarded as end-to-end learning methods, namely, complex mapping relations between some characteristics of received data and DOA are directly learned, and DOA estimation is further achieved.
Disclosure of Invention
In order to solve the above problems in the prior art, the present invention provides a phase-enhanced method for estimating a low elevation angle DOA of a meter-wave radar target, including:
acquiring phase characteristics of an input data set and phase characteristics of a tag data set;
normalizing the phase characteristics of the input data set to obtain the phase characteristics of the normalized input data set;
inputting the phase characteristics of the normalized input data set into a neural network model to obtain the phase characteristics of a network output data set;
constructing an objective function according to the phase characteristics of the network output data set and the label data set, performing reverse transmission processing on the objective function by using a first preset method, and updating a network parameter set of the neural network model by using a second preset method;
according to the network parameter set, carrying out enhancement processing on a test data set to obtain a new data covariance matrix, and according to the new data covariance matrix, obtaining a new test data set;
and carrying out DOA estimation on the new test data set by using a preset DOA estimation model to obtain the elevation angle of the meter wave radar target.
In one embodiment of the invention, acquiring phase characteristics of an input data set and phase characteristics of a tag data set comprises:
constructing a receiving array, and obtaining an array receiving signal and an array guide vector according to the receiving array;
respectively obtaining an input data set and a tag data set according to the array receiving signals and the array steering vectors;
dividing the input data set and the label data set respectively to obtain a divided input data set and a divided label data set;
and respectively extracting the phase characteristics of the upper triangular elements of the divided input data set and the divided label data set to obtain the phase characteristics of the input data set and the phase characteristics of the label data set.
In an embodiment of the present invention, the dividing the input data set and the tag data set to obtain a divided input data set and a divided tag data set respectively includes:
acquiring input data of a current frame and the data division number m, wherein m is a positive odd number;
respectively and continuously extracting (m-1)/2 frames of input data from the input data set forwards and backwards by taking the current frame of input data as a central frame to obtain forward input data and backward input data;
obtaining the divided input data set according to the current frame input data, the forward input data and the backward input data;
and obtaining the divided label data set according to the current frame input data.
In an embodiment of the present invention, normalizing the phase characteristics of the input data set to obtain the phase characteristics of the normalized input data set includes:
obtaining a mean and a standard deviation of phase characteristics of the input data set;
and carrying out Gaussian normalization processing on the phase characteristics of the input data set according to the mean value and the standard deviation to obtain the phase characteristics of the normalized input data set.
In an embodiment of the present invention, training a neural network model according to the phase characteristics of the normalized input data set to obtain the phase characteristics of a network output data set includes:
constructing a four-layer deep neural network model;
and inputting the phase characteristics of the normalized input data set into the four-layer deep neural network model, and training to obtain the phase characteristics of the network output data set.
In one embodiment of the present invention, the objective function is constructed by:
wherein,
representing the phase characteristics of the network output data set,
representing the phase characteristics of the tag data set.
In one embodiment of the invention, the first predetermined method comprises a back propagation method and the second predetermined method comprises an adaptive moment estimation method.
In one embodiment of the invention, the set of network parameters of the neural network model comprises a network weight value W and a network bias value b, wherein,
the network weight W is:
the network bias value b is:
where α represents a learning rate, ∈ represents a fixed constant,
respectively, are intermediate variables of the network weight W,
respectively, intermediate variables of the network bias value b.
In an embodiment of the present invention, the enhancing the test data set according to the network parameter set to obtain a new data covariance matrix, and obtaining a new test data set according to the new data covariance matrix includes:
acquiring a test data set;
dividing the test data set to obtain a divided test data set;
extracting the phase characteristics of the upper triangular elements of the divided test data set to obtain the phase characteristics of the test data set;
inputting the phase characteristics of the test data set subjected to normalization processing into the four-layer deep neural network model to obtain the phase characteristics of the enhanced test data set;
obtaining the new data covariance matrix according to the phase characteristics of the enhanced test data set;
and obtaining a new test data set according to the new data covariance matrix.
In an embodiment of the present invention, the preset DOA estimation model is:
wherein R'iRepresents a new data covariance matrix, a (θ), in a new test data seti) Representing array steering vectors, aH(θi) Denotes a (theta)i) The conjugate transpose of (a) is performed,
representing the estimated elevation angle of the meter-wave radar target.
Compared with the prior art, the invention has the beneficial effects that:
according to the phase-enhanced meter-wave radar target low elevation DOA estimation method, the neural network model is constructed according to the actual scene, so that the problem of mismatch between the actual signal model and the ideal far-field plane wave model in the physical driving DOA estimation is effectively solved, and the meter-wave radar target DOA estimation precision is higher.
The present invention will be described in further detail with reference to the accompanying drawings and examples.
Drawings
FIG. 1 is a schematic flowchart of a method for estimating a low elevation DOA of a phase-enhanced meter-wave radar target according to an embodiment of the present invention;
FIG. 2 is a schematic structural diagram of a four-layer deep neural network in a phase-enhanced meter-wave radar target low elevation DOA estimation method provided by an embodiment of the present invention;
FIG. 3 is a schematic diagram illustrating a comparison result of angle measurement errors of a phase-enhanced meter-wave radar target low elevation DOA estimation method under different signal-to-noise ratios according to an embodiment of the present invention;
FIG. 4 is a schematic diagram illustrating a comparison result of goodness of fit of features of a phase-enhanced meter-wave radar target low elevation DOA estimation method under different signal-to-noise ratios according to an embodiment of the present invention;
FIG. 5 is a schematic diagram showing a comparison result of an angle measurement error of a phase-enhanced meter-wave radar target low elevation DOA estimation method under a mismatch condition of a signal-to-noise ratio according to an embodiment of the present invention;
FIG. 6 is a schematic diagram showing comparison results of goodness of fit of features of a phase-enhanced meter-wave radar target low elevation DOA estimation method under a mismatch condition of signal-to-noise ratio according to an embodiment of the present invention;
FIG. 7 is a diagram illustrating comparison results of angle measurement errors under different phase errors of a phase-enhanced meter-wave radar target low elevation DOA estimation method provided by an embodiment of the present invention;
FIG. 8 is a diagram illustrating comparison results of goodness of fit of features of a phase-enhanced meter-wave radar target low elevation DOA estimation method under different phase errors according to an embodiment of the present invention;
FIG. 9 is a schematic diagram illustrating a comparison result of an angle measurement error under a phase error condition mismatch by a phase-enhanced meter-wave radar target low elevation DOA estimation method according to an embodiment of the present invention;
FIG. 10 is a diagram illustrating a comparison result of goodness of fit of features of a phase-enhanced meter-wave radar target low elevation DOA estimation method under a phase error condition mismatch according to an embodiment of the present invention;
fig. 11 is a schematic diagram of a measured data track in a phase-enhanced meter-wave radar target low elevation DOA estimation method according to an embodiment of the present invention;
FIG. 12 is a schematic diagram of angle measurement error of measured data processed by two conventional methods according to an embodiment of the present invention;
fig. 13 is a schematic view of an angle measurement error of processing measured data by the phase-enhanced meter-wave radar target low elevation DOA estimation method according to the embodiment of the present invention.
Detailed Description
The present invention will be described in further detail with reference to specific examples, but the embodiments of the present invention are not limited thereto.
Example one
Currently, radar DOA estimation methods include a physically-driven super-resolution DOA estimation method and a DOA estimation method based on deep learning. The physically-driven super-resolution DOA estimation method enables multi-path signals received by the array to possibly not meet a far-field plane wave model along with the complexity of multi-path signal distribution in an actual array environment, so that DOA estimation accuracy is low; due to the fact that an existing network model is simple and effective features and redundant features of DOA estimation analysis data are not available, redundant features are used as input of a network, complexity of network training is brought on one hand, and DOA estimation accuracy is low on the other hand.
To solve the above problems, please refer to fig. 1, where fig. 1 is a flowchart illustrating a phase-enhanced low elevation DOA estimation method for a meter-wave radar target according to an embodiment of the present invention. The embodiment provides a phase-enhanced meter-wave radar target low elevation angle DOA estimation method, which comprises the following steps:
and 6, carrying out DOA estimation on the new test data set by using a preset DOA estimation model to obtain the elevation angle of the meter-wave radar target.
Specifically, in this embodiment, a neural network model suitable for the scene is obtained according to the phase characteristics of the input data set, an objective function is constructed through training of the phase characteristics of the network output data set of the neural network model and the phase characteristics of the tag data set, the phase characteristics of the network output data set are made to approach the phase characteristics of the tag data set through back propagation processing of the objective function, at this time, an optimal network parameter set corresponding to the neural network model is obtained at the same time, then, any test data set is trained through the set neural network model with the optimal network parameters, an enhanced new test data set is obtained, and accordingly, an accurate elevation angle of the metric wave radar target is obtained from the enhanced new test data set.
According to the phase-enhanced meter-wave radar target low elevation DOA estimation method, the neural network model is built according to an actual scene, the problem that an actual signal model is mismatched with an ideal far-field plane wave model in the physical driving DOA estimation is effectively solved, and therefore the meter-wave radar target DOA estimation accuracy is higher.
Further, step 1 acquires the phase characteristics of the input data set and the phase characteristics of the tag data set, and includes step 1.1, step 1.2, step 1.3, and step 1.4:
step 1.1, a receiving array is constructed, and array receiving signals and array guide vectors are obtained according to the receiving array.
Specifically, the receiving array constructed in the actual scene of this embodiment is a uniform linear array of K array elements, and the fast beat number (sampling number) is L, then the array steering vector of this embodiment is designed as:
wherein d represents the array element spacing, lambda represents the signal wavelength, and theta represents the elevation angle of the meter-wave radar target.
The multipath signals in the scenario of this embodiment can be simplified to amplitude-phase disturbance superimposed on the direct signal, and if the amplitude-phase disturbance is τ, the received signal of the array of this embodiment is designed as:
x(t)＝τ⊙a(θ)s(t)+n(t),t＝1,…,L (2)
wherein n (t) ═ n1(t),n2(t),…,nK(t)]TRepresenting a noisy data vector, s (t) representing signal source data, a (θ) representing the array steering vector, a indicates a dot product.
And 1.2, respectively obtaining an input data set and a tag data set according to the array receiving signals and the array guide vectors.
Specifically, for a meter-wave radar target in a flight state, the true elevation angle of the target is in a continuous change state, the meter-wave radar target is continuously detected for N times in the embodiment, where N is an integer greater than 0, and an input data set { R is obtained1,R2,…,RNAnd label data set
RiRepresenting the covariance matrix of the incoming data received by the multipath array,
representing a covariance matrix of data of a multipath array receiving tag, an input data covariance matrix RiLabel data covariance matrix
Each comprising an amplitude characteristic and a phase characteristic, wherein,
input data covariance matrix R in each input data setiThe design is as follows:
tag data covariance matrix in each tag data set
The design is as follows:
and 1.3, dividing the input data set and the label data set respectively to obtain a divided input data set and a divided label data set.
Specifically, in this embodiment, to obtain a more accurate DOA estimation, step 1.3 specifically includes step 1.3.1, step 1.3.2, step 1.3.3, and step 1.3.4:
step 1.3.1, obtaining input data of a current frame and the data division number m, wherein m is a positive odd number.
Specifically, the present embodiment derives from the input data set { R }1,R2,…,RNGet the current frame input data, for example, the current frame input data may be R1May also be R2(ii) a From a tag data set
Obtain the current frame tag data, for example, the previous frame tag data may be
Can also be
Meanwhile, the data division number m is confirmed, which determines how many frame phase enhancements are performed, and the data division number m in this embodiment takes the value of positive odd number, that is, m takes the values of 1, 3, 5, and … ….
And step 1.3.2, taking the current frame input data as a central frame, and respectively and continuously extracting (m-1)/2 frames of input data from the input data set forwards and backwards to obtain forward input data and backward input data.
Specifically, the present embodiment takes the number of data divisions m as an example, and the current frame input data as a center frame, and continues forward from the input data set { R }1,R2,…,RNExtracting (m-1)/2 frames of input data as forward input data, and successively backward extracting from the input data set { R }1,R2,…,RNExtracting (m-1)/2 frames of input data as backward input data, ensuring that the divided input data are m frames, and thus, the whole input data set { R }1,R2,…,RNDivide. Specifically, for example, the number of data divisions m is 3, and in the input data set { R }1,R2,…,RNIn with R2For the current frame input data, 1 frame input data is continuously extracted forward, i.e. the input data extracted forward is R1R is to be1As forward input data, then extracting 1 frame of input data continuously backward, i.e. extracting the input data backward as R3R is to be3As backward input data, for example, the number of data divisions m is 5, in the input data set { R }1,R2,…,RNIn with R3For the current frame input data, 2 frames of input data are continuously extracted forward, i.e. the input data extracted forward is R1And R2R is to be1And R2Extracting 2 frames of input data continuously backward as forward input data, i.e. extracting the input data backward as R4And R5R is to be4And R5As backward input data.
And step 1.3.3, obtaining a divided input data set according to the current frame input data, the forward input data and the backward input data.
Specifically, the present embodimentPacking the current frame input data, the forward input data and the backward input data obtained in the step 1.3.2 to obtain divided input data, and integrating the input data set { R }1,R2,…,RNDividing to obtain a divided input data set (phi)1,Φ2,…,ΦMWhere phi isiThe method comprises the steps of packaging certain current frame input data, forward input data and backward input data to obtain divided input data. Specifically, the number of data divisions m is 3, and R is2For the current frame input data, the forward input data obtained is R1And backward input data is R3From the current frame input data R2Forward input data R1Backward input data R3Packing to obtain divided input data phi1Specific diameter of1＝{R1,R2,R3For example, the number of data partitions m is 5, in the input data set { R }1,R2,…,RNIn with R3For the current frame input data, the resulting forward input data is { R }1,R2The backward input data is { R }4,R5R from the current frame3Forward input data { R1,R2R, backward input data { R }4,R5Packing to obtain divided input data phi2Specific diameter of2＝{R1，R2，R3，R4，R5}. Wherein M is less than or equal to N.
Note that Φ obtained when the data division number m is 3 or 5 in the present embodiment1Or phi2By way of example only, specific Φ1Or phi2Determined by the actual input data set.
And step 1.3.4, obtaining a divided frame label data set according to the current frame input data.
Specifically, in the present embodiment, the tag data corresponding to the central frame is taken as the divided tag data, and the entire tag data set is subjected to tag data division
Is divided intoObtaining a partitioned label data set
Specifically, the number of data divisions m is 3, and R is2For the current frame input data, the current frame input data R2The corresponding tag data is
Tag data
As divided tag data
Further, for example, the number of data divisions m is 5, in R3For the current frame input data, the current frame input data R2The corresponding tag data is
Tag data
As divided tag data
Wherein M is less than or equal to N.
Note that, this embodiment obtains when the data division number m is 3 or 5
Or
By way of example only, and in particular
Or
Determined by the actual tag data set.
And step 1.4, respectively extracting the phase characteristics of the upper triangular elements of the divided input data set and the divided label data set to obtain the phase characteristics of the input data set and the label data set.
Specifically, the present embodiment extracts the divided input data set { Φ1,Φ2,…,ΦMThe phase characteristics of the upper triangular element of the input data set, resulting in the phase characteristics of the input data set, { phi }1,φ2,…,φM}; similarly, extracting the divided label data set
The phase characteristics of the upper triangular element to obtain the phase characteristics of the tag data set
The phase characteristics of the input data set obtained in this embodiment not only utilize the characteristics of the input data of the current frame, but also fully utilize the characteristics of the correlation between multiple frames of input data, so that the DOA estimation accuracy is higher.
Further, the step 2 of normalizing the phase characteristics of the input data set to obtain the phase characteristics of the normalized input data set includes:
acquiring a mean value and a standard deviation of phase characteristics of an input data set;
and performing Gaussian normalization processing on the phase characteristics of the input data set according to the mean value and the standard deviation to obtain the phase characteristics of the normalized input data set.
Specifically, to ensure non-linearity during subsequent neural network training and preserve the distribution characteristics of the input data set, the present embodiment applies the phase characteristics { φ + to the input data set1,φ2,…,φMPerforming Gaussian normalization processing on the feature dimension, and counting the mean value of the feature dimension of the input data set to be u1Standard deviation of σ1Then the normalized phase signature corresponding to the input data set is designed to be:
phase characteristics for input data set phi1,φ2,…,φMNormalizing the phase characteristics of each input data to obtain the phase characteristics of a normalized input data set
Further, step 3, training the neural network model according to the phase characteristics of the normalized input data set to obtain the phase characteristics of the network output data set.
Specifically, in this embodiment, the neural network model is trained according to the phase feature set of the normalized input data set obtained in step 2, and step 3 specifically includes step 3.1 and step 3.2:
and 3.1, constructing a four-layer deep neural network model.
Specifically, please refer to fig. 2, fig. 2 is a schematic structural diagram of a four-layer deep neural network in a phase-enhanced meter-wave radar target low elevation DOA estimation method according to an embodiment of the present invention. In this embodiment, a four-layer deep neural network model is adopted, a specific structure of the network model is shown in fig. 2, the number of hidden layer nodes in the network is 1024, and an activation function in the network adopts a ReLU activation function, where a specific ReLU activation function is denoted as f (x) ═ max (x, 0).
And 3.2, inputting the phase characteristics of the normalized input data set into a four-layer deep neural network model, and training to obtain the phase characteristics of a network output data set.
Specifically, in this embodiment, the phase characteristics of the normalized input data set are input to the four-layer deep neural network model constructed in step 3.1, and the network is obtained through trainingPhase characterization of output data set
In order to make the network output the phase characteristics of the data set during the training process
And phase characteristics of the tag data set
In this embodiment, the last layer of the four-layer deep neural network model is mapped linearly.
Further, step 4, an objective function is constructed according to the phase characteristics of the network output data set and the phase characteristics of the label data set, reverse transmission processing is carried out on the objective function by using a first preset method, and the network parameter set of the neural network model is updated by using a second preset method.
Specifically, the objective function constructed in this embodiment is:
wherein,
representing the phase characteristics of the network output data set,
representing the phase characteristics of the tag data set.
In this embodiment, the target function of formula (6) is reversely transmitted by using a first preset method, so that the network outputs the data set
Phase characterization of tag data sets
Matching while usingAnd updating the network parameter set of the four-layer deep neural network model by using a second preset method.
The network parameter set of the four-layer deep neural network model of the present embodiment includes a network weight W and a network bias value b, wherein,
the network weight W is designed as:
the network bias value b is designed as:
where α represents a learning rate, ∈ represents a fixed constant,
representing intermediate variables in the solution of sets of network parameters, e.g. in the form of intermediate variables
The design of (2) is as follows:
wherein, beta1Is the exponential decay rate, beta, of the first moment of the network weight W and the network bias value2Exponential decay rate, v, of the second moment being the network weight W and the network bias valuedWFirst moment, s, representing the network weight WdWSecond moment, v, representing the network weight WdbFirst moment, s, representing network bias value bdbSecond moment, v, representing network bias value bdW,vdb,sdW,sdbAll initial values of (2) are 0.
And repeatedly training the four-layer deep neural network until the Loss of the target function is converged, and correspondingly training to obtain the network parameter set as the optimal network parameter of the four-layer deep neural network.
Preferably, the first predetermined method is a Back Propagation (BP) method, and the second predetermined method is an Adaptive moment estimation (Adam) method.
And further, step 5, enhancing the test data set according to the network parameter set to obtain a new data covariance matrix, and obtaining a new test data set according to the new data covariance matrix.
Specifically, step 5 of this embodiment includes step 5.1, step 5.2, step 5.3, step 5.4, step 5.5, and step 5.6:
and 5.1, acquiring a test data set.
Specifically, the present embodiment obtains a test data set from an actual scene, and the construction of the test data set is as that of the input data set in formula (3).
And 5.2, dividing the test data set to obtain a divided test data set.
Specifically, in this embodiment, the test data set is divided according to the dividing manner of the input data set in step 1.3, so as to obtain the divided test data set.
And 5.3, extracting the phase characteristics of the upper triangular elements of the divided test data set to obtain the phase characteristics of the test data set.
Specifically, in this embodiment, according to the extraction manner of the input data set and the label data set divided in step 1.3, the phase feature of the upper triangular element of the divided test data set is extracted to obtain the phase feature of the test data set.
And 5.4, inputting the phase characteristics of the test data set subjected to the normalization processing into a four-layer deep neural network model, and training to obtain the phase characteristics of the enhanced test data set.
Specifically, in this embodiment, before inputting the phase characteristics of the test data set into the four-layer deep neural network model, the phase characteristics of the test data set are normalized, and the normalization specific manner is as described above for the normalization processing manner of the input data set, so that the normalized phase characteristics of the test data set are designed as follows:
wherein,
phase characteristics, u, of the test data set obtained in step 5.32Means, σ, representing the phase characteristic through the statistical label data set2Representing the standard deviation of the phase signature through the statistical tag data set.
And 5.5, obtaining a new data covariance matrix according to the phase characteristics of the enhanced test data set.
In particular, the example obtained in step 5.4
As the input of the four-layer deep neural network, the enhanced phase characteristic phi of the test data set is obtained after the four-layer deep neural network trainingi', amplitude information rho in the original test data setiDiagonal element gammaiAnd enhanced phase feature phi'iRecombining to obtain a new data covariance matrix R'i。
And 5.6, obtaining a new test data set according to the new data covariance matrix.
Specifically, in this embodiment, the phase features of the normalized test data set are respectively subjected to the training process in step 5.5, so as to obtain a new data covariance matrix R 'corresponding to each test data set'iFrom these new data covariance matrices R'iConstruction to obtain a new test data set { R'1,R′2,...,R′N}。
Further, step 6, the preset DOA estimation model is used for carrying out DOA estimation on the new test data set to obtain the elevation angle of the meter-wave radar target.
Specifically, in the present embodiment, DOA estimation is performed on each new data covariance matrix in a new test data set, specifically, DOA estimation is performed on each new data covariance matrix by using a preset DOA estimation model, where the preset DOA estimation model is designed as:
wherein R'iRepresents a new data covariance matrix, a (θ), in a new test data seti) Representing array steering vectors, aH(theta) represents a (theta)i) The conjugate transpose of (c).
In the embodiment, the elevation angle of each meter-wave radar target in the test data set is solved through the formula (12)
In summary, compared with the DOA estimation method driven by physics, the DOA estimation method provided by the embodiment effectively solves the mismatch problem between the actual signal model and the ideal far-field plane wave model, so that the DOA estimation precision is higher; compared with the existing data-driven DOA estimation method (such as the DOA estimation method based on SVR), the DOA estimation method provided by the embodiment not only utilizes the characteristics of the input data of the current frame, but also fully utilizes the characteristics of the correlation among the input data of multiple frames, so that the DOA estimation precision is higher.
In order to verify the effectiveness of the phase-enhanced meter-wave radar target low elevation DOA estimation method provided by the present application, the present embodiment is further described by the following simulation experiments:
simulation environment
Data generation and processing of the experiment was done on MATLAB2017a, and four-layer deep neural network model training was done on python 3.5. The effectiveness of the method is verified through four simulation scenes.
In a scene, the array structure is a uniform linear array of 21 array elements, the wavelength lambda is 1 meter, the array element spacing d is half wavelength, the fast beat number is 42, the signal-to-noise ratio range is-10 dB to-2 dB, the signal-to-noise ratio sampling interval is 2dB, the range of a target elevation angle is 1-5 degrees, and the phase error in the array is 20 degrees. Please refer to fig. 3 and 4, fig. 3 is a schematic diagram of a comparison result of angle measurement errors under different signal-to-noise ratios of a phase-enhanced meter-wave radar target low elevation DOA estimation method provided by an embodiment of the present invention, fig. 4 is a schematic diagram of a comparison result of feature fitting goodness under different signal-to-noise ratios of a phase-enhanced meter-wave radar target low elevation DOA estimation method provided by an embodiment of the present invention, an abscissa of fig. 3 represents a signal-to-noise ratio, an ordinate represents an angle measurement error, an abscissa of fig. 4 represents a signal-to-noise ratio, an ordinate represents a feature fitting goodness, and the angle measurement error of this embodiment is a root-mean-square error, as can be seen from fig. 3 and 4, the higher the signal-to-noise ratio, the larger the number of frames (data division number), the better the feature fitting goodness, and the smaller angle measurement error.
The array structure in the scene is a uniform linear array of 21 array elements, the wavelength lambda is 1 meter, the array element spacing d is half wavelength, the fast beat number is 42, the signal-to-noise ratio range of the label data set is-10 dB-0 dB, the signal-to-noise ratio range of the test data set is-11 dB-1 dB, the signal-to-noise ratio sampling intervals are 2dB, the target elevation angle range is 1-5 degrees, and the phase error existing in the array is 20 degrees. Referring to fig. 5 and 6, fig. 5 is a schematic diagram of a comparison result of an angle measurement error under a condition mismatch of a signal-to-noise ratio in a phase-enhanced meter-wave radar target low elevation angle DOA estimation method provided by an embodiment of the present invention, fig. 6 is a schematic diagram of a comparison result of a feature fitting goodness under a condition mismatch of a signal-to-noise ratio in a phase-enhanced meter-wave radar target low elevation angle DOA estimation method provided by an embodiment of the present invention, an abscissa of fig. 5 represents a signal-to-noise ratio, an ordinate represents an angle measurement error, an abscissa of fig. 6 represents a signal-to-noise ratio, and an ordinate represents a feature fitting goodness, the angle measurement error in this embodiment is a root-mean-square error, and it can be seen from fig. 5 and 6 that the higher the signal-to-. Meanwhile, as can be seen from fig. 6, when the number of frames is increased to a certain degree, the correlation between the frames is reduced, so that the network characteristic fitting performance approaches to a saturated state, and it can be seen that the method has a strong generalization capability for the signal-to-noise ratio.
In a scene, the array structure is a uniform linear array of 21 array elements, the wavelength lambda is 1 meter, the array element spacing d is half wavelength, the fast beat number is 42, the signal-to-noise ratio is 0dB, the target elevation angle range is 1-5 degrees, the range of phase errors existing in the array is 5-20%, and the error sampling interval is 5%. Referring to fig. 7 and 8, fig. 7 is a schematic diagram of a comparison result of angle measurement errors under different phase errors of a phase-enhanced meter-wave radar target low elevation DOA estimation method provided by an embodiment of the present invention, fig. 8 is a schematic diagram of a comparison result of feature fitting goodness under different phase errors of a phase-enhanced meter-wave radar target low elevation DOA estimation method provided by an embodiment of the present invention, an abscissa of fig. 7 represents a phase error, an ordinate represents an angle measurement error, an abscissa of fig. 8 represents a phase error, an ordinate represents a feature fitting goodness, the angle measurement error of this embodiment is a root mean square error, as can be seen from fig. 7, the larger the number of frames is, the smaller the angle measurement error is, compared with the existing method, the angle measurement accuracy of the present application is effectively improved, as can be seen from fig. 8, the larger the number of frames is, the better the feature fitting goodness is, compared with the existing method, the network characteristic fitting performance of the method is superior to that of the existing method.
The array structure in the scene is a uniform linear array of 21 array elements, the wavelength lambda is 1 meter, the array element spacing d is half wavelength, the fast beat number is 42, the signal-to-noise ratio is 0dB, the phase error range of the tag data set is 5% -20%, the phase error range of the test data set is 3% -23%, the phase error sampling intervals are 5%, and the target elevation angle range is 1-5 degrees. Fig. 9 is a schematic diagram of a comparison result of angle measurement errors under a phase error condition mismatch of a phase-enhanced meter wave radar target low elevation DOA estimation method provided by an embodiment of the present invention, fig. 10 is a schematic diagram of a comparison result of feature fitting goodness under a phase error condition mismatch of a phase-enhanced meter wave radar target low elevation DOA estimation method provided by an embodiment of the present invention, an abscissa of fig. 9 represents a phase error, an ordinate represents an angle measurement error, an abscissa of fig. 10 represents a phase error, and an ordinate represents a feature fitting goodness, an angle measurement error in this embodiment is a root mean square error, as can be seen from fig. 9, a larger frame number is, a smaller angle measurement error is, as compared with the existing method, the angle measurement accuracy of the present application is effectively improved, as can be seen from fig. 10, a larger frame number is, a better is, as compared with the existing method, the network feature fitting performance of the present application is superior to the existing method, meanwhile, as can be seen from fig. 10, when the number of frames is increased to a certain degree, the correlation between the frames is reduced, so that the network fitting performance approaches to a saturated state, and it can be seen that the present application also has a higher generalization performance on phase errors.
In order to verify the practicability of the DOA estimation method provided by the present application, the present embodiment processes the measured data of a certain array of meter-wave radar. In an actual scene, the radar 3dB beam width is about 5 °, the target is in a very harsh location environment, and there are many objects such as trees and hills, please refer to fig. 11, and fig. 11 is a schematic diagram of an actual data track measured in the phase-enhanced meter-wave radar target low elevation DOA estimation method provided in the embodiment of the present invention.
Referring to fig. 12 and 13, fig. 12 is a schematic diagram of angle measurement results of actual measurement data processed by two conventional methods according to an embodiment of the present invention, fig. 13 is a schematic diagram of angle measurement errors of actual measurement data processed by a phase-enhanced meter-wave radar target low elevation DOA estimation method according to an embodiment of the present invention, and as for the two conventional methods in fig. 12, a DBF method and an SSMUSIC method are used to process certain route data in an offline manner, as can be seen from fig. 12, both the DBF method and the SSMUSIC method fail because after the two methods are subjected to smoothing processing, all feature vectors are added to original data as noise vectors and multipath signals, so that a test data set and a tag data set are not matched, and further, the angle measurement errors are large. For the application, after the phase characteristics are enhanced through the four-layer deep neural network, as can be seen from fig. 13, the angle measurement errors are almost uniformly distributed within the range of +/-0.5 degrees, and the measurement performance is obviously improved. The angle measurement error is 0.3 degrees and is taken as an evaluation standard of the effective point trace, the effective point trace enhanced by the four-layer deep neural network is improved to 95.6 percent, and the performance is very obvious. The method and the device have high reliability.
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.
Claims (8)
1. A phase-enhanced meter-wave radar target low elevation DOA estimation method is characterized by comprising the following steps:
acquiring phase characteristics of an input data set and phase characteristics of a tag data set;
normalizing the phase characteristics of the input data set to obtain the phase characteristics of the normalized input data set;
inputting the phase characteristics of the normalized input data set into a neural network model to obtain the phase characteristics of a network output data set;
constructing an objective function according to the phase characteristics of the network output data set and the label data set, performing reverse transmission processing on the objective function by using a first preset method, and updating a network parameter set of the neural network model by using a second preset method;
according to the network parameter set, carrying out enhancement processing on a test data set to obtain a new data covariance matrix, and according to the new data covariance matrix, obtaining a new test data set;
performing DOA estimation on the new test data set by using a preset DOA estimation model to obtain an elevation angle of the meter-wave radar target;
wherein obtaining phase characteristics of the input data set and the tag data set comprises:
constructing a receiving array, and obtaining an array receiving signal and an array guide vector according to the receiving array;
respectively obtaining an input data set and a tag data set according to the array receiving signals and the array steering vectors;
dividing the input data set and the label data set respectively to obtain a divided input data set and a divided label data set;
respectively extracting the phase characteristics of the upper triangular elements of the divided input data set and the divided label data set to obtain the phase characteristics of the input data set and the phase characteristics of the label data set;
wherein, divide said input data set and label data set separately and get the input data set after dividing, label data set after dividing, including:
acquiring input data of a current frame and the data division number m, wherein m is a positive odd number;
respectively and continuously extracting (m-1)/2 frames of input data from the input data set forwards and backwards by taking the current frame of input data as a central frame to obtain forward input data and backward input data;
obtaining the divided input data set according to the current frame input data, the forward input data and the backward input data;
and obtaining the divided label data set according to the current frame input data.
2. The method of phase-enhanced meter wave radar target low elevation DOA estimation according to claim 1, wherein normalizing the phase signature of the input data set to obtain a normalized phase signature of the input data set comprises:
obtaining a mean and a standard deviation of phase characteristics of the input data set;
and carrying out Gaussian normalization processing on the phase characteristics of the input data set according to the mean value and the standard deviation to obtain the phase characteristics of the normalized input data set.
3. The phase-enhanced meter wave radar target low elevation DOA estimation method according to claim 1, wherein inputting the phase characteristics of the normalized input data set to a neural network model to obtain the phase characteristics of a network output data set comprises:
constructing a four-layer deep neural network model;
and inputting the phase characteristics of the normalized input data set into the four-layer deep neural network model, and training to obtain the phase characteristics of the network output data set.
4. The phase-enhanced meter-wave radar target low elevation DOA estimation method according to claim 1, wherein the constructed objective function is:
wherein,
representing the phase characteristics of the network output data set,
representing the phase characteristics of the tag data set.
5. The phase-enhanced meter-wave radar target low elevation DOA estimation method according to claim 1, wherein the first preset method comprises a back propagation method and the second preset method comprises an adaptive moment estimation method.
6. The phase-enhanced meter-wave radar target low elevation DOA estimation method according to claim 1, wherein the set of network parameters of the neural network model includes a network weight W and a network bias value b, wherein,
the network weight W is:
the network bias value b is:
where α represents a learning rate, ∈ represents a fixed constant,
respectively, are intermediate variables of the network weight W,
respectively, intermediate variables of the network bias value b.
7. The method of phase-enhanced metric wave radar target low elevation DOA estimation according to claim 3, wherein the enhancing the test dataset according to the network parameter set to obtain a new data covariance matrix, and the obtaining the new test dataset according to the new data covariance matrix comprises:
acquiring a test data set;
dividing the test data set to obtain a divided test data set;
extracting the phase characteristics of the upper triangular elements of the divided test data set to obtain the phase characteristics of the test data set;
inputting the phase characteristics of the test data set subjected to normalization processing into the four-layer deep neural network model to obtain the phase characteristics of the enhanced test data set;
obtaining the new data covariance matrix according to the phase characteristics of the enhanced test data set;
and obtaining a new test data set according to the new data covariance matrix.
8. The phase-enhanced meter-wave radar target low elevation angle DOA estimation method according to claim 1, wherein the preset DOA estimation model is:
wherein R'iRepresents a new data covariance matrix, a (θ), in a new test data seti) Representing array steering vectors, aH(θi) Denotes a (theta)i) The conjugate transpose of (a) is performed,
representing the estimated elevation angle, theta, of a meter-wave radar targetiRepresenting the true elevation angle of the meter-wave radar target.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910662647.3A CN110471026B (en) | 2019-07-22 | 2019-07-22 | Phase-enhanced meter-wave radar target low elevation DOA estimation method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910662647.3A CN110471026B (en) | 2019-07-22 | 2019-07-22 | Phase-enhanced meter-wave radar target low elevation DOA estimation method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110471026A CN110471026A (en) | 2019-11-19 |
| CN110471026B true CN110471026B (en) | 2021-08-24 |
Family
ID=68508174
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910662647.3A Active CN110471026B (en) | 2019-07-22 | 2019-07-22 | Phase-enhanced meter-wave radar target low elevation DOA estimation method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110471026B (en) |
Families Citing this family (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114791583B (en) * | 2022-03-08 | 2024-08-02 | 西安电子科技大学 | Low elevation angle target DOA estimation method based on sum/difference mode of deep neural network |
| CN116125421B (en) * | 2023-02-07 | 2023-10-20 | 中国电子科技集团公司第五十四研究所 | Array radar multi-echo signal target detection method based on deep learning |
Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104220896A (en) * | 2012-04-13 | 2014-12-17 | 高通股份有限公司 | Systems, methods, and apparatus for estimating direction of arrival |
| CN109725285A (en) * | 2018-12-28 | 2019-05-07 | 西安云脉智能技术有限公司 | A kind of DOA estimation method based on the adaptive phase angle conversion of MVDR covariance matrix element |
Family Cites Families (8)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102012505B (en) * | 2010-10-15 | 2012-12-05 | 西安电子科技大学 | Method for estimating direction of arrival of radar low-elevation target |
| CN102288944B (en) * | 2011-05-12 | 2013-09-25 | 西安电子科技大学 | Super-resolution height measuring method based on topographic matching for digital array meter wave radar |
| CN103353595B (en) * | 2013-06-18 | 2015-01-07 | 西安电子科技大学 | Meter wave radar height measurement method based on array interpolation compression perception |
| TW201734404A (en) * | 2016-03-30 | 2017-10-01 | 啟碁科技股份有限公司 | Angle estimating method and radar system |
| CN108535698B (en) * | 2018-04-04 | 2021-07-20 | 西安电子科技大学 | Meter-wave radar low elevation angle estimation method based on beam space |
| CN109597048B (en) * | 2018-11-29 | 2023-08-11 | 西安电子科技大学 | Meter wave radar DOA estimation method based on two-dimensional convolutional neural network |
| CN109597046B (en) * | 2018-11-29 | 2022-11-18 | 西安电子科技大学 | Metric wave radar DOA estimation method based on one-dimensional convolutional neural network |
| CN109597047B (en) * | 2018-11-29 | 2022-11-18 | 西安电子科技大学 | Meter wave radar DOA estimation method based on supervised deep neural network |
-
2019
- 2019-07-22 CN CN201910662647.3A patent/CN110471026B/en active Active
Patent Citations (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN104220896A (en) * | 2012-04-13 | 2014-12-17 | 高通股份有限公司 | Systems, methods, and apparatus for estimating direction of arrival |
| CN109725285A (en) * | 2018-12-28 | 2019-05-07 | 西安云脉智能技术有限公司 | A kind of DOA estimation method based on the adaptive phase angle conversion of MVDR covariance matrix element |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110471026A (en) | 2019-11-19 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| Xiang et al. | Improved de-multipath neural network models with self-paced feature-to-feature learning for DOA estimation in multipath environment | |
| CN109597046B (en) | Metric wave radar DOA estimation method based on one-dimensional convolutional neural network | |
| Randazzo et al. | Direction of arrival estimation based on support vector regression: Experimental validation and comparison with MUSIC | |
| CN107390197B (en) | Radar self-adaption sum-difference beam angle measurement method based on feature space | |
| WO2020083918A1 (en) | Method and system for adaptive beamforming of ultrasound signals | |
| EP3712651A1 (en) | Method and system for adaptive beamforming of ultrasound signals | |
| CN110471026B (en) | Phase-enhanced meter-wave radar target low elevation DOA estimation method | |
| CN114745237B (en) | Channel estimation method of intelligent super-surface auxiliary multi-user wireless communication system | |
| CN109597048B (en) | Meter wave radar DOA estimation method based on two-dimensional convolutional neural network | |
| CN109932717B (en) | ISAR high-resolution imaging method based on environmental statistics modeling | |
| CN111257845A (en) | Approximate message transfer-based non-grid target angle estimation method | |
| CN114791583B (en) | Low elevation angle target DOA estimation method based on sum/difference mode of deep neural network | |
| CN105699950A (en) | Radar clutter suppression method based on self-adaptive iteration forward and background smooth conjugate gradient | |
| CN106680779B (en) | Beam-forming method and device under impulsive noise | |
| CN115236584A (en) | Meter-wave radar low elevation angle estimation method based on deep learning | |
| Xu et al. | Acoustic localization in ocean reverberation via matrix completion with sensor failure | |
| Du et al. | Bayesian robust tensor factorization for angle estimation in bistatic MIMO radar with unknown spatially colored noise | |
| CN113111304B (en) | Coherent distribution source direction finding method based on quantum ray mechanism under strong impact noise | |
| CN108614235B (en) | Single-snapshot direction finding method for information interaction of multiple pigeon groups | |
| CN111352075A (en) | Underwater multi-sound-source positioning method and system based on deep learning | |
| CN117471457A (en) | Sparse SAR learning imaging method, device and medium based on deep expansion complex network | |
| US20230161021A1 (en) | Method and apparatus for determination of direction of arrival angle | |
| Zheng et al. | Antenna Failure Resilience: Deep Learning-Enabled Robust DOA Estimation with Single Snapshot Sparse Arrays | |
| CN111896929A (en) | DOD/DOA estimation algorithm of non-uniform MIMO radar | |
| Zeng et al. | DOA estimation for low angle targets using time reversal in frequency domain model |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |