CN109270509B - DOA estimation method and system based on matrix filling under data loss condition - Google Patents
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Abstract
The invention discloses a DOA estimation method and a DOA estimation system based on matrix filling under the condition of data loss, wherein the method comprises the following steps: when data is lost, constructing a recombined data matrix by using a space smoothing scheme, and disturbing the positions of damaged elements; performing data recovery on the recombined data matrix by using a matrix filling technology, and performing feature decomposition on covariance of the recombined data matrix; and obtaining a spatial spectrum based on the signal subspace and the noise subspace obtained by the feature decomposition, and searching the peak of the spatial spectrum to obtain the DOA direction. The method solves the problem that in the prior art, data cannot be recovered under the condition of partial data loss, so that DOA direction cannot be estimated; the method and the device can recover the damaged data even if only one group of available data exists, are beneficial to accurately estimating the DOA direction in the radar signal processing field, and reduce errors.
Description
Technical Field
The invention relates to the technical field of radar signal processing, in particular to a DOA estimation method and system based on matrix filling under the condition of data loss.
Background
The direction of arrival (DOA, direction of arrival) estimation of signals is an important research content in array signal processing, and is widely applied to the fields of radar, wireless communication, electromagnetic fields, sonar, seismic exploration, medical imaging and the like. The main purpose of DOA estimation is to resolve two objects that are very close in azimuth in noisy environments. There are two general classes of DOA estimation methods, namely: a non-parametric estimation method and a parametric estimation method. As non-parametric estimation methods, there are mainly beamforming methods, multiple signal classification methods based on subspace methods (MUSIC, multiple signal classification), and high-resolution spectrum estimation methods based on minimum variance without distortion, and the like.
In the prior art, in the DOA estimation method in the radar signal processing technical field, if part of elements in random positions of a low-rank matrix are lost, a matrix filling technology can be utilized to recover the matrix, so that estimation of the DOA direction is realized. However, when elements in the whole row (even several rows) are destroyed or lost, the data cannot be recovered directly by using the matrix filling technology, so that a large error is easily generated in the DOA estimation, and accurate estimation of the DOA direction cannot be realized.
Accordingly, the prior art is still in need of improvement and development.
Disclosure of Invention
The invention aims to solve the technical problems that aiming at the defects in the prior art, a DOA estimation method and a DOA estimation system based on matrix filling under the condition of data loss are provided, and aims to solve the problems that in the DOA estimation method in the technical field of radar signal processing in the prior art, when elements in the whole row (even a plurality of rows) are destroyed or lost, larger errors are easy to generate in DOA estimation, and the accurate estimation of the DOA direction cannot be realized.
The technical scheme adopted for solving the technical problems is as follows:
a matrix-filler based DOA estimation method in the event of data loss, wherein the method comprises:
when data is lost, constructing a recombined data matrix by using a space smoothing scheme, and disturbing the positions of damaged elements;
performing data recovery on the recombined data matrix by using a matrix filling technology, and performing feature decomposition on covariance of the recombined data matrix;
and obtaining a spatial spectrum based on the signal subspace and the noise subspace obtained by the feature decomposition, and searching the peak of the spatial spectrum to obtain the DOA direction.
The DOA estimation method based on matrix filling under the condition of data loss, wherein when the data is lost, a space smoothing scheme is utilized to construct a recombined data matrix, and the step of disturbing the positions of damaged elements specifically comprises the following steps:
when one or more lines of data in the damaged matrix are entirely missing, the damaged matrix is reorganized by using a space smoothing scheme;
a reorganized data matrix is obtained, wherein the lost elements in the reorganized data matrix are not redistributed in an entire row.
The DOA estimation method based on matrix filling under the condition of data loss, wherein the step of recombining the damaged matrix by using a space smoothing scheme specifically comprises the following steps:
dividing the damaged matrix into p subarrays, wherein the number of array elements of each subarray is m, and the data matrix is expressed as:
X f (t)＝[x 1 (t)，x 2 (t)，…，x p (t)]
＝[A 1 s(t)，A 2 s(t)，…，A p s(t)]
+[n 1 (t)，n 2 (t)，…，n p (t)]
wherein the guide matrix of the ith subarray is A i ＝[a i (θ 1 )，a i (θ 2 )，…，a i (θ L )]S (t) is a signal vector, n (t) is a gaussian distributed noise vector, { θ 1 ，θ 2 ，…，θ L And is the signal incidence angle of the received L narrowband signals.
The DOA estimation method based on matrix filling under the condition of data loss is characterized in that the step of reorganizing the damaged matrix by using a space smoothing scheme further comprises the following steps:
according to the displacement invariance of the uniform linear array, A is obtained i+1 ＝A i Φ，i＝1，…，p-1，
Rewriting the reorganized data matrix to X f (t)＝A 1 S f (t)+N f (t)，
wherein ,
the DOA estimation method based on matrix filling under the condition of data loss is characterized in that the step of reorganizing the damaged matrix by using a space smoothing scheme further comprises the following steps:
x is to be f (t) stacking the data generated on all snapshots to generate a reorganized data matrix, expressed as:
wherein ,
the DOA estimation method based on matrix filling under the condition of data loss is characterized by comprising the steps of carrying out data recovery on a recombined data matrix by using a matrix filling technology and carrying out characteristic decomposition on covariance of the recombined data matrix, and specifically comprising the following steps:
based on the formula
Solving->
wherein ,/>
Is the position coordinates of the loss element in the recombination data matrix Y, eta is a parameter related to the noise level,/->
Calculation of
Is the autocorrelation function of ∈K, get ∈K->
Covariance of the reconstructed data matrix;
for covariance matrix
And performing characteristic decomposition.
The DOA estimation method based on matrix filling under the condition of data loss is characterized in that the method comprises the steps of obtaining a space spectrum based on a signal subspace and a noise subspace obtained by feature decomposition, searching a peak of the space spectrum to obtain a DOA direction, and specifically comprises the following steps:
for covariance matrix
Performing feature decomposition to obtain two parts including signal subspace formed by signal feature vectors and noise subspace formed by noise feature vectors, which are expressed as +.>
Obtain corresponding spatial frequency spectrum
And searching the peak of the spatial frequency spectrum to obtain the DOA direction, wherein the DOA direction is the angle direction corresponding to the peak of the spatial frequency spectrum.
The DOA estimation method based on matrix filling under the condition of data loss, wherein the method further comprises the following steps:
and carrying out statistical performance test to verify the DOA estimation method.
The DOA estimation method based on matrix filling under the condition of data loss, wherein the step of carrying out statistical performance test specifically comprises the following steps:
estimating root mean square error at different signal-to-noise ratio levels, the root mean square error being expressed as
Wherein the number of monte carlo times k=100
As the signal-to-noise ratio increases, the root mean square error gradually decreases.
A matrix-filler based DOA estimation system based on any of the above claims in the event of a data loss, wherein the system comprises:
the data matrix reorganization module is used for constructing a reorganized data matrix by utilizing a space smoothing scheme when data are lost, and disturbing the positions of damaged elements;
the data recovery module is used for carrying out data recovery on the reconstructed data matrix by utilizing a matrix filling technology and carrying out characteristic decomposition on covariance of the reconstructed data matrix;
and the DOA direction estimation module is used for obtaining a spatial frequency spectrum based on the signal subspace and the noise subspace obtained by the feature decomposition and searching the peak of the spatial frequency spectrum to obtain the DOA direction.
The invention has the beneficial effects that: the method solves the problem that in the prior art, data cannot be recovered under the condition of partial data loss, so that DOA direction cannot be estimated; the method and the device can recover the damaged data even if only one group of available data exists, are beneficial to accurately estimating the DOA direction in the radar signal processing field, and reduce errors.
Drawings
FIG. 1 is a flow chart of a preferred embodiment of a matrix-filler based DOA estimation method in the event of data loss according to the present invention.
Fig. 2 is a schematic diagram of a spatial smoothing scheme in a matrix-filling-based DOA estimation method in the case of data loss according to the present invention.
Fig. 3 is a graph showing the spatial spectrum contrast obtained by the DOA estimation method of the present invention and the conventional MUSIC algorithm.
Fig. 4 is a root mean square error plot of the inventive DOA estimation method and the existing MUSIC algorithm at different signal-to-noise levels.
Fig. 5 is a functional block diagram of a matrix-filler based DOA estimation system with data loss according to the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more clear and clear, the present invention will be further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. The following description of at least one exemplary embodiment is merely exemplary in nature and is in no way intended to limit the invention, its application, or uses. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
The present embodiment provides a matrix filling-based DOA estimation method under the condition of data loss, as shown in fig. 1, including:
s100, when data are lost, constructing a recombined data matrix by using a space smoothing scheme, and disturbing the positions of damaged elements;
step S200, performing data recovery on the recombined data matrix by utilizing a matrix filling technology, and performing feature decomposition on covariance of the recombined data matrix;
and step S300, obtaining a spatial spectrum based on the signal subspace and the noise subspace obtained by the feature decomposition, and searching the peak of the spatial spectrum to obtain the DOA direction.
The DOA estimation method in the prior art adopts a common MUSIC method, and is specifically as follows:
assuming a uniform linear array with M array elements, L narrowband signals are received, and the incidence angle of the signals is { theta } 1 ，θ 2 ，…，θ L Observation data can be modeled as:
Assuming that there are N snapshots of data, the receiving matrix may be rewritten as:
X＝[x(1)，x(2)，…，x(N)]＝AS+N。
and further obtaining a covariance matrix of the data matrix as
Performing feature decomposition on covariance matrix to obtain two parts +.>
A signal subspace spanned by signal feature vectors, and a noise subspace spanned by noise feature vectors.
Thus, a spatial spectrum can be obtained
The peaks of the spatial spectrum can then yield the estimated DOA direction.
If there is a partial data loss in the data matrix, the accuracy of the MUSIC algorithm in estimating the direction of the DOA will be affected. It is therefore necessary to introduce matrix filling techniques to recover the corrupted data. The damage matrix considers the following 2 cases. First, the damaged elements are randomly distributed in the data matrix. In this case, the matrix filling technology can be directly adopted to recover the damaged data, and then the MUSIC algorithm is utilized to realize DOA direction estimation. However, if an entire row (or rows) of data is missing, the matrix fill technique cannot be directly utilized to recover the data. The present invention therefore requires the construction of an extended data matrix for the damaged matrix using a spatial smoothing scheme, which is mainly embodied on a uniform linear array structure, as shown in fig. 2 in particular, to thereby disturb the positions of the damaged elements, while also preserving the low rank nature of the data matrix.
Specifically, in this embodiment, the array is divided into p subarrays, and the number of array elements of each subarray is m. Each snapshot, the data matrix may be represented as:
wherein the guide matrix of the ith subarray is A i ＝[a i (θ 1 )，a i (θ 2 )，…，a i (θ L )]Specifically, there are
s (t) is a signal vector, n (t) is a noise vector of gaussian distribution, { θ 1 ，θ 2 ，…，θ L And is the signal incidence angle of the received L narrowband signals.
Further, according to the displacement invariance of the uniform linear array, the method obtains
A i+1 ＝A i Φ，i＝1，…，p-1，
The reorganized data matrix can be rewritten as X f (t)＝A 1 S f (t)+N f (t) in the general form of a data matrix received by a uniform linear array, which is rewritten to a uniform form in the present embodiment, the relevant DOA estimation method can be applied, for example, to a MUSIC algorithm.
Further, the method comprises, among other things,
x is to be f (t) stacking the data generated on all snapshots to generate a reorganized data matrix, expressed as:
wherein ,
when N is p When the temperature is more than or equal to L,
thus, a +.>
Is shown in neglecting noise
Is used for the recombination of data matrix->
Is of low rank. Most importantly, the lost element positions in the reorganized data matrix Y are no longer distributed throughout the rows, so that a matrix filling technique can be used to recover the reorganized data matrix Y.
Preferably, the algorithm formula of the matrix filling technique in this embodiment is as follows
wherein ,
is the position coordinates of the loss element in the recombined data matrix Y, η is a parameter related to the noise level.
Solving from the algorithmic formula of matrix filling techniques
It is->
Estimate of (i.e.)>
Calculate->
Is->
Covariance of the reconstructed data matrix, then +.>
And performing characteristic decomposition.
Preferably, due to
Is a column-full rank matrix, and can therefore be determined by +_for the covariance matrix>
And performing feature decomposition, and obtaining an estimated DOA direction by adopting a MUSIC algorithm. In this embodiment, by +_for covariance matrix>
Performing feature decomposition to obtain two parts including signal subspace formed by signal feature vectors andnoise subspace formed by the noise feature vector, denoted +.>
Then the corresponding spatial spectrum +.>
And searching the peak of the spatial frequency spectrum to obtain DOA, wherein the DOA direction is the angle direction corresponding to the peak of the spatial frequency spectrum.
Further, the embodiment also provides a DOA estimation method and a spatial spectrum contrast diagram of the existing MUSIC algorithm, as shown in FIG. 3. As can be seen from fig. 3, the angles corresponding to the spectral peaks of each spatial spectrum are estimated DOAs, and the damaged data matrix x is recovered by directly adopting a MUSIC square algorithm, so that the performance of the algorithm is greatly reduced; in contrast, the DOA estimation method provided by the invention has obvious peak at the position of the incident angle, so that DOA can be obtained more accurately.
Furthermore, the embodiment also carries out statistical performance test on the DOA estimation method provided by the invention, thereby verifying the DOA estimation method. As shown in fig. 4, the root mean square error is mainly estimated at different signal-to-noise ratio levels in the present embodiment, and is expressed as
Wherein the monte carlo number k=100. As is apparent from fig. 4, the RMSE (root mean square error) of the DOA estimation method of the present invention gradually decreases as the signal-to-noise ratio (SNR) increases. However, estimating DOA directly with MUSCI algorithm or directly based on X matrix filling method for data matrix containing corrupted data, it was found that satisfactory results could not be obtained even at high SNR because corrupted data was not processed correctly. In contrast, in the DOA estimation method provided by the invention, a better result can be obtained under a high SNR, namely, the error is smaller, so that the obtained DOA is more accurate.
Further, in this embodiment, there is also provided an analysis of the success probability of the DOA estimation method of the present invention within an allowable error range, where the success probability is defined as Ns=K, where Ns is the number of successful experiments, and one successful experiment means that the DOA estimation error does not exceed 0.5 °. The DOA estimation method provided by the invention can basically and accurately estimate DOA when the SNR reaches more than 5 dB.
Based on the above embodiment, the present invention further provides a matrix-filling based DOA estimation system in the case of data loss, as shown in FIG. 5, the system comprising:
the data matrix reorganization module 510 is configured to reorganize a data matrix by using a spatial smoothing scheme when data is lost, and scramble positions of damaged elements;
the data recovery module 520 is configured to perform data recovery on the reconstructed data matrix by using a matrix filling technique, and perform feature decomposition on covariance of the reconstructed data matrix;
the DOA direction estimation module 530 is configured to obtain a spatial spectrum based on the signal subspace and the noise subspace obtained by the feature decomposition, and search for a peak of the spatial spectrum to obtain the DOA direction.
In the DOA estimation system provided in this embodiment, the principle of each functional module and the effects produced by the same have been discussed in the above method embodiments, and will not be described here. Even though the DOA estimation system of the embodiment has only one group of available data, the damaged data can be recovered, and the DOA direction can be accurately found, so that the DOA direction can be accurately estimated in the radar signal processing field.
In summary, the present invention provides a DOA estimation method and system based on matrix filling under the condition of data loss, and the method includes: when data is lost, constructing a recombined data matrix by using a space smoothing scheme, and disturbing the positions of damaged elements; performing data recovery on the recombined data matrix by using a matrix filling technology, and performing feature decomposition on covariance of the recombined data matrix; and obtaining a spatial spectrum based on the signal subspace and the noise subspace obtained by the feature decomposition, and searching the peak of the spatial spectrum to obtain the DOA direction. The method solves the problem that in the prior art, data cannot be recovered under the condition of partial data loss, so that DOA direction cannot be estimated; the method and the device can recover the damaged data even if only one group of available data exists, are beneficial to accurately estimating the DOA direction in the radar signal processing field, and reduce errors.
It is to be understood that the invention is not limited in its application to the examples described above, but is capable of modification and variation in light of the above teachings by those skilled in the art, and that all such modifications and variations are intended to be included within the scope of the appended claims.
Claims (7)
1. A matrix-filler based DOA estimation method in the event of data loss, the method comprising:
when data is lost, constructing a recombined data matrix by using a space smoothing scheme, and disturbing the positions of damaged elements;
performing data recovery on the recombined data matrix by using a matrix filling technology, and performing feature decomposition on covariance of the recombined data matrix;
obtaining a spatial spectrum based on a signal subspace and a noise subspace obtained by feature decomposition, and searching peaks of the spatial spectrum to obtain a DOA direction;
when the data is lost, constructing a recombined data matrix by using a space smoothing scheme, and disturbing the positions of damaged elements, wherein the method specifically comprises the following steps of:
when one or more lines of data in the damaged matrix are entirely missing, the damaged matrix is reorganized by using a space smoothing scheme;
obtaining a reorganized data matrix, wherein lost elements in the reorganized data matrix are not distributed in the whole row;
the step of reorganizing the damaged matrix by using the spatial smoothing scheme specifically includes:
dividing the damaged matrix into p subarrays, wherein the number of array elements of each subarray is m, and the data matrix is expressed as:
wherein the guide matrix of the ith subarray is
，/>
Is the signal vector which is used to determine the signal,
is a gaussian distributed noise vector, +.>
Signal incidence angles for the L narrowband signals received;
the step of reorganizing the damaged matrix using a spatial smoothing scheme further includes:
according to the displacement invariance of the uniform linear array, the method obtains
，
，
Rewriting of a reorganized data matrix into
，
wherein ,
，
2. the matrix-filler based DOA estimation method for data loss as recited in claim 1, wherein the step of reorganizing the impairment matrices using a spatial smoothing scheme further comprises:
will be
The data generated on all snapshots are stacked to generate a reorganized data matrix, denoted:
wherein ,
，/>
。
3. the matrix-padding-based DOA estimation method as recited in claim 2, wherein the step of performing data recovery on the reconstructed data matrix using a matrix padding technique and performing feature decomposition on covariance of the reconstructed data matrix, specifically comprises:
based on the formula
Solving->
； wherein ,/>
Is the loss element in the recombination data matrix +.>
Position coordinates of>
Is a parameter related to noise level +.>
for covariance matrix
And performing characteristic decomposition.
4. A DOA estimation method based on matrix filling in the case of data loss as claimed in claim 3, wherein the step of obtaining a spatial spectrum based on a signal subspace and a noise subspace obtained by feature decomposition and searching for a peak of the spatial spectrum to obtain a DOA direction specifically comprises:
for covariance matrix
Performing feature decomposition to obtain two parts including signal subspace formed by signal feature vectors and noise subspace formed by noise feature vectors, which are expressed as +.>
；
Obtain corresponding spatial frequency spectrum
Searching the peak of the spatial spectrum to obtain a DOA direction, wherein the DOA direction is an angle direction corresponding to the peak of the spatial spectrum, and the DOA direction is a +.>
Indicating an angle of +>
Is provided.
5. The matrix-filler based DOA estimation method for data loss as recited in claim 4, further comprising:
and carrying out statistical performance test to verify the DOA estimation method.
6. The matrix-filler based DOA estimation method of claim 5, wherein the step of performing a statistical performance test comprises:
estimating root mean square error at different signal-to-noise ratio levels, the root mean square error being expressed as
； wherein ,/>
Indicate->
In the next Monte Carlo experiment +.>
Estimate of the angle of incidence of the individual signals; the root mean square error gradually decreases with increasing signal to noise ratio for the monte carlo number k=100.
7. A system based on a matrix-filled DOA estimation method in the case of data loss as claimed in any of claims 1-6, characterized in that the system comprises:
the data matrix reorganization module is used for constructing a reorganized data matrix by utilizing a space smoothing scheme when data are lost, and disturbing the positions of damaged elements;
the data recovery module is used for carrying out data recovery on the reconstructed data matrix by utilizing a matrix filling technology and carrying out characteristic decomposition on covariance of the reconstructed data matrix;
and the DOA direction estimation module is used for obtaining a spatial frequency spectrum based on the signal subspace and the noise subspace obtained by the feature decomposition and searching the peak of the spatial frequency spectrum to obtain the DOA direction.
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